Ttiu repcti « u ipom-atJ by (h Uu Uiiiid S u m i n (h« UnUid s u i n Ala mix E u n n CmnmlUlCil, QUI »n( of Ituu .mpjorftt, w «n» o( HUB cuniiuiidt tumontrjtlQii. m ihiu tmjlafit.
trail wiaiiir &• •tftaniibililf foi ifi ( U C U I K ) com-tlntfttu ui uafuirju ut u r lafurnutlun, ipput t ia , product oi sauz* i iituiuuj, oi upfiunti inn iu uu « d d n... Inftutt ptinlilr ovutS itfliU.
ION HOLECULE REACTIONS: CC3RELAII0N TIME-OF-FLIGHT IOS SPECTROSCOPY AND THE CO* - H_ SYSTEM
Contents
ABSTRACT vii
INTRODUCTION 1
CHAPTER I
Ion Beam Experimentation 4
Classical Time-of-Flight Spectroscopy 12
CHAPTER I I
Correlation Tioe-of-Flight Spectroscopy 19
TOF as a Linear System 20
Correlation Functions . . . . . . . 23
Impulse Response Determination . . . . . . . . . . . . . . . 26
Broadband Noise . . . . . . . . . . 28
K-Sequenees 31
Theory of Correlation Detection 44
Applying Correlation TOF 50
Correlation with Neutral Molecular Beams 51
Correlation with Neutron Beams (Reactor Response) 52
The Present Correlation Method for Ion Beams . . . . . . . . 56
The Data Address Method 58
Vector Space Picture 64
Stat is t ical Analysis 7 0
System Optimisation 70
Correlation Measurement Variance 7 1
Detector Paralysis . . .
Shannon's S a i l i n g Theorem
78
84
-iv-
CHAPTEB. III
Computer Organization 90
Operations Codes • • 93
The Omnibus 95
Programmed Operation 95
Data Transfers 95
The Correlation System Computer Interface 98
Overview of Interface Operation 100
I. Bin Time Clock Board i a o
1. Interface Bin Time Clock IQQ
2. Pseudorandom Binary Hoise Sequence Generator . . . . ^QB
3. Classical TOF Capability 105
4. Digital Delay Line XQ5
5. Command Word Control and IOT's ill
6. Detector Input H g
II. Data is ic.sk. Board H9
1. Data Break Hardware 119
2. Generation and Storage of the Break Memory Address . 122
3. Data Overflow 126
IH. Hardware Test Facilities and Checkout Procedures . . . . 127 t
IV. Board Interconnect Cable 129
V. D/A Converter Board 129
VI. Voltage Comparator 131
MI. Ion Beam Chopping 134
The Present Beam Chopping System 143
Computer Program Monitor (see Appendix C) 147
I. Keyboard Monitor 1*7
II. Operational Subroutines I*8
III. Data Overflow Service 155
Experimental Measurements Using the TOF Correlator 157
CHAPTER IV
Reaction of CO- with H, Isotopes 16*
Models for Ion-Molecule Reactions 16*
Experimental Description 169
Ion Source Assembly 169
Scattering Cell 171
Detector Train . . . . . 172
Experimental Procedure and Data Analysis 173
Kinematics and Incensity Distributions 1'6
States and Energetics l f il
Molecular Orbital Correlation Diagrams I 8 6
CO Results and Discussion . I 9 8
DC0 2+ . IS 8
DCO + 211
Honreactive C 0 2+ 2 2 3
C0 + 231 "
0D +t 0 +, H-O^ 2 3 6
Sumaary of Results " 9
Appendix A: The Mathematical Description of Random Processes . 2 * 2
Appendix B: Detector Coincidence Analysis « 2*6
-vi-
Appendlx C: Listing of PDF S/f Cosputer Honitor for TOF
System.- 2SZ
Bibliography for Correlation Time of Flight Spectroscopy . . . . 266
Acknowledgments 269
- v i i -
10N MOLECULE HEACTIOHS: CORRELATION TIHE-OF-FLIGHT ION SPECTEOSCOPY AND THE CO* - H- SVSTEM
Peter J . Schubart
Inorganic Hater ia l s Besearch D iv i s i on , Laurence Berkeley Laboratory, and Department of Chemistry; Univers i ty of Cal i fornia ,
Berkeley* Cal i fornia
ABSTRACT
A tiae-of-flight analysis eye tea for ocas uresis! t of velocity dis
tributions of the ionic products of gas phase ion-oolecule reactions was
developed. The sysceo enployed pseudorandoa binary noise for ion source
modulation, coupled with detector crosscorrelaticn for extraction of
velocity distribution spectra. Crosseorrelaticn was accaopllshed by
direct cKsory access storage of coded correlation information by a
PDP 8/f ainlcoHputer with subsequent application of a decoding algorithm
for transformation of accunulsted data-
Maximal length shift register sequences were utilized for ion source
Qodulation- The codulation code sequence was transduced for beaa gating
by an electrostatic deflection bees chopper. Storage of the modulation
sequence for later crosscorrelation was accomplished with a variable
length digital delay l ine. The hardware options of the cocputer corre
lation interface were controlled by a software implemented, keyboard con
trolled system monitor cocputcr progran.
The tice-of-flight systeo was applied to an existing ion beaa
apparatus for measurement of N * N_, and Kr ion velocity distributions.
Measured N, distributions agreed well with retarding potential energy
analysis neasureEents. The Kr velocity distribution clearly resolved
- v i l i -
taass peaks due to three naturally occurring isotopes.
I.- a separate series of experiments, intensity distribution naps of
the products of the CO- + H- reaction were measured over an in i t i a l CO
laboratory energy range oi" 25-250 eV. At low energies there was strong
evidence of long lived intermediate complex formation. With increasing
relative energy there occurred a transition to a direct spectator s t r i p
ping mechanism.
Intensity distributions for six ionic products were measured at
various relative energies. DCO- product distr ibutions reflected a large
amount of direct interaction formation even at low energies, although the
broad distribution at low energy suggested an intensi ty contribution from
complex formation. With increasing energy DCO. distributions continually
reflected a larger proportion of formation by direct stripping interaction
up to 10 eV relat ive energy. Above 10 eV significant intensity loss due
to pro*1-—t 'tissoelation vas noted accompanied by forward movement of the
product intensity peak, indicating product s tabi l iza t ion by forward recoi l .
The DCO product distributions displayed the symmetric behavior of
complex formation at low energy. Increasing energy led to distribution
asymmetry and forward peak movement. High energy distribution peaks and
Intensity levels were explained in terms of two stripping mechanises.
tfonreactive C07 distributions showed broad ine las t ic intensity even at
low relative energies, in contrast with C0_ scattered nonreactively by
He. This was further evidence for low energy complex formation and
showed significant translation to vibration energy transfer.
CO and 0 product distributions showed a coll is ional dissociation
mechanism. OD distributions showed forward scattering and low intensi ty.
- i ^
Ho D~0 product was noted at any energy studied.
The CO- + H. product distributions were analyzed in teres of molecu
lar orbital correlation diagrams. There was reasonable qualitative
agreement between theoretical expectations and experimental resul ts .
- 1 -
IHTRDDtlCriOH
Although the majority of cheaica l r e a c t i o n s which occur natural ly
r e s u l t from c o l l i s i o n s between neutral molecu les , for a number of years
chemists have s tud ied ion-molecule reac t ions In an e f for t to e l u c i d a t e
the bas i c dynamic mechanisms important i n a l l chemical reac t ions . With
the aid of molecular bean apparatuses, p h y s i c a l chemists have been able
co measure d i f f e r e n t i a l c r o s s - s e c t i o n s for the production of i o n i c pro
ducts in ion molecule react ions , a n a l y s i s of these i n t e n s i t y d i s t r i b u t i o n
maps have contributed ouch to the understanding of dynamic i n t e r a c t i o n s
and the e f f e c t s of p o t e n t i a l energy sur faces f o r intenaoleculax c o l l i s i o n s .
Experimental ly, product d i s t r i b u t i o n s f o r ion-molecule react ions are
most often measured wi th energy bandpatb a n a l y s i s sys teas (energy f i l t e r s ) .
However, i t i s o f t en convenient t o aeasure product v e l o c i t y d i s t r i b u t i o n s
using a t i m e - o f - f l i g h t (TOF) p r i n c i p l e . The f i r s t part of t h j t h e s i s i s
devoted t o the development of such a TOF system. This version of the
TOF method employs an ion beam coding algorithm with a companion detec tor
decoding system ( c r o s s c o r r e l a t i o n ) . Th^ system r e l i e s on the tae of a
minicomputer f o r data information s torage ; i t i s an adaptation of a
method which has been applied previously for measurement of neutron 2
reactor response funct ions .
The i n i t i a l d i scuss ion deals with the construct ion of the TOF e x p e r i
mental system for study of i cn -co l ecu le r e a c t i o n s . I t includes a pre
sentat ion of the theory behind t h i s type of experimental measurement as
wel l as l o g i c a l , e l e c t r o n i c , and computer or iented descript ions of the
actual implementation of th i s method.
- 2 -
The experimental results obtained with the computer correlation
system indicate that correlation TOF analysis has a place in che study of
ion-molecule reactions. In fact, i t i s our feeling that this type of
system wil l find bioad application in a variety of experimental discip
lines including biological science. Although the principles of the
method are well known in engineering c i r c l e s , i t i s only in the last
several years that dissemination of the necessary information to other
disciplines has begun. I t i<s entirely possible that in the future this
method may find a degree of acceptance comparable to that achieved by
Fourier transform analysis in recent years.
In contrast, the second section of the thesis (Chapter IV) presents
a series of experimental measurements made with an existing energy band
pass system. The CO, + H, chemical system was studied at a variety of
i n i t i a l C0„ energies and the product distr ibutions for six ionic products
were analyzed in terms of kinematic models (intermediate complex forma
tion vs direct interaction), thermodynamic data and molecular orbital
correlation diagrams. The experimental resul ts were found to be amenable
to such analysis and provide an example or how i t is possible to visualize
a more complicated reaction process in terms of basic electronic and
dynamical pr inciples . The resulCs also provide a further understanding
of the limits placed on the interpretation of reaction systems hy
electronic correlation diagrams.
While the two sections of the thesis are somewhat independent, each
reflects an important aspect of the process of ar.alysis of chemical
reactions. The improvisation of experimental measurement systems i s an
Integral part of the process of product analysis. There is thus an
- 3 -
underlylng u n i t y t o t he d i scuss ions p r e s e n t e d .
REFERENCES FOR THE INTRODUCTION
1 . J . L. F r a n k l i n , e d . Ion-Molecule Reac t ions Vol . I and I I , Plenum
Press 1972.
2a . F. Hoss fe ld , R. Amadori, and R. Scherm, Proceed ings of the Pane l
Conference on In s t rumen ta t ion fo r Neutron I n e l a s t i c S c a t t e r i n g
Research, IAEA, Vienna, 1970.
2b . X. E. S t e r n , A. B laqu ie re and J . V a l a t , J . Nuc lea r Energy, P a r t s
A/B, 16 , 499 ( 1 9 6 2 ) .
_4-
CHAPTER I
ION BEAM EXPERIMENTATION
Molecular and ion bean exper iments as a c l a s s employ a col l imaLed
beam of r e a c t a n t p a r t i c l e s which a r e d i r e c t e d onto a gas phase t a r g e t
s p e c i e s w i t h subsequent d e t e c t i o n of r e a c t i o n products as a func t ion of
p roduc t -mass , - s c a t t e r i n g ang le , and - v e l o c i t y . The v e l o c i t y v e c t o r of
the i n i t i a l beam p a r t i c l e s se rves to d e f i n e a zero degree s c a t t e r i n g ang le
and to s c a l e the f i n a l d i s t r i b u t i o n of p roduc t v e l o c i t i e s . Most o f t e n , a
s e r i e s of exper iments i s conducted d u r i n g which the i n i t i a l l a b o r a t o r y
energy of t he p r o j e c t i l e p a r t i c l e s i s v a r i e d , changing the amount of
r e l a t i v e t r a n s l a t i o n a l energy a v a i l a b l e t o t he r e a c t i o n p a r t n e r s . The
measured a n g u l a r - v e l o c i t y d i s t r i b u t i o n s , when viewed as a func t ion of
i n i t i a l p r o j e c t i l e energy, s e rve t o e l u c i d a t e and support some p o s s i b l e
k inema t i c mechanisms for the r e a c t i o n w h i l e exc luding o t h e r s .
S ince the ob jec t of the p r e s e n t i n v e s t i g a t i o n i s ion beam r e a c t i o n s ,
we w i l l d e a l e x p l i c i t l y wi th t h i s c a s e . As Ions a r e e l e c t r o n i c a l l y
charged, mass and energy a n a l y s i s a r e cons ide rab ly s i m p l i f i e d over the
n e u t r a l c a s e , a l though the expe r imen ta l l y a t t a i n a b l e e n e r g e t i c range i s
l i m i t e d from below by focusing and space charge c o n s i d e r a t i o n s .
For the purposes of d e s c r i b i n g a t y p i c a l ion beam exper iment , we
suppose t h a t an ion A of mass M, and l a b o r a t o r y v e l o c i t y V, i s d i r e c t e d A —A
toward a n e u t r a l t a r g e t molecule BC of mass M and thermal l a b o r a t o r y BC
v e l o c i t y V and which i s contained i n a f ixed t a r g e t s c a t t e r i n g c e l l .
*For a more complete d e s c r i p t i o n , see Chapter IV.
- 5 -
The most convenient method for analyzing such a reaction i s the construc
tion of an appropriate velocity vector diagram (Fig- 1) . In this diagram
the assumption has been made that since a typical projecti le ion velocity
1G ^ 10 s cm/sec while the target molecule has a low thermal velocity,
V. » V__, and we can approximate V_„ by C. The to ta l momentum of Hiq
system i s then M.V,, which i s of course conserved throughout the reaction.
Though experiments are carried out in a laboratory frame of reference,
theoretical analysis i s considerably simplified i f the reaction i s viewed
in a center of mass (C.H.) coordinate system. The C.H. coordinate system
is a frame of reference which moves with the velocity of the center of
mass for the system of ^a>lllding par t ic les ; an observer in this frame of
reference would say that the tota l net momentum for a l l the particles in
the system was zero. In the present case the velocity of the center of
mass i s
M A
Since the relat ive velocity of A with reBpect to BC i s fixed (equal to
divided between A and BC (Fig. 1) with
*"7" i s used here to denote laboratory velocity while "u" denotes velocities measured with respect to the velocity of the*"center of mass. k prime ( ') denotes a vector after an intermolecular collision.
A + + BC Products
*A
XBL 748-6905
Fig. 1. A velocity vector diagram for A + BC.
V , - uA - u„„ * V.. - r e l -A --BC -A
about the center of mass as a result of deflecting intermolecular inter
actions. In general, I U A I ^ I U A | due t o Inelast ic or superelastic collision.
processes. (Since only ionic products can be detected, the final vector
of BC, u! , i s of no fundamental interest . ) The vector u* wil l describe
the motion of A after the coll ision, A having been scattered through a
CH. angle X- Viewed from the laboratory frame, the scattered ion wi l l
be found at an angle 3 with a velocity V*.
Experiments in the laboratory measure ion intensi ty as a function of
V' and 9 . Trans formation of the results to a CM. picture gives a
typical scattering map (Fig. 2) which plots intensi ty contours in a
(oli X) representation. In a similar manner, reactive products ( i . e . + +
A + BC -*• AB + C) are also t33pped, the only difference being a change
in the mass which i s selected for detection by a quadrupole mass f i l t e r .
There are two al ternat ive methods of constructing the two dimen
sional (u ' , X) intensity contour map which represents re la t ive scat ter
ing probabili t ies. One method, that of energy or velocity bandpass,
consists of measurement of product ion intensi t ies a t a large number of
discrete (V*, 9) points by the use of angular and velocity (energy) f i l
t e r s . After coordinate transformation, the in tens i t ies are recorded in
-8-
0 + + D 2 — 0 D + + D(75eV) * Relative Energy = 15.0 eV j s
Q = 0.4 eV
J80"
Fig. 2. A typical product velocity distribution map. The center of the nap corresponds to the velocity of the center of mass of the system. Angles are specified in the center of nass franc of reference. Contours represent points of equal Intensity. Beam profile is full width at 20J maximum.
-9 -
a Cul» X) coordinate system and contours constructed by connecting points
of equal intensity by interpolation.
The angular f i l ter used in the bandpass method consists of a mechani
cal aperture in front of the detector restricting thv sol id angle viewed
by the detector. The complete detector assembly i s desx£**ed to rotate
through a wide range of laboratory scattering angles, viewing only an
"infinitesimal" cone of scattering at each angle.
A wide variety of energy and velocity f i l ters have been devised*
including spherical and cylindrical electrostatic energy analyzers,
tfien f i l ters , retarding potential filters* -.- (in the case of neutral
products) slotted disc velocity selectors. The advantage of the band
pass system i s that i t s measurements are made in a nondynamic Banner
Baking the» easily reproducible. Further, the system i s amenable to com
paratively straightforward data analysis. A disadvantage of the system
i s the large number of discrete measurements which are required to con
struct a scattering map.
A second method i s that of time-of-flight (TOF) analysis. While
this method also uses angular definition to restrict the solid angle of
scattering viewed by the detector, i t employs a different mode of energy
analysis. This method measures the distribution of arrival times for
pulses of ions which are admitted to the apparatus. As such, the TOF
system does not explicitly cst^loy any energy fi ltering system; rather.
ions of al l energies arc detected as a function of arrival tioc at the
detector and che Arrival d e c used to characterise the energy distribu
tion of detected ions (at a fixed scattering angle). Thus, a TOF oeasure-
ment provides a one dimensional s l ice through the scattering intensity
-10-
dlstributlon along a constant laboratory angle ray ( i . e . a s l ice taken
perpendicular to the plane of the page in Fig. 2) . In contrast with the
energy bandpass system then, a TOF system produces data as a "continuous"
one dimensional distr ibution of product intensi ty rather than as a series
of discrete points.
The TOF system employs a time domain measurement rather than one in
energy domain. Using a beam chopping device (see below), a short pulse
of projectile beam par t ic les Is emitted Into a reaction chamber. This
i n i t i a l beam pulse contains Ions with a narrow distr ibution of veloci t ies ,
f(V), characterist ic of the i n i t i a l beam composition (weighted by
H(V) "* Vf(V) by flux considerations). Soon after emission, the pulse
Ions interact with the target molecules causing chemical reactions as
well as e l a s t i c and ine las t i c processes, a l l of which a l t e r the I n i t i a l
narrow velocity dis t r ibut ion. The resulting product ions enter an in t e r
action-free dr i f t region in which products with different velocities be
come separated spa t ia l ly . A mass f i l t e r then removes a l l product ions
except those of the desired mass. Subsequently these ions of a l l
velocities are detected as a function of ar r ival time at the detector
which has been stationed at a predetermined laboratory scattering angle.
(The arrival time i s measured with respect Co the time of i n i t i a l beam
pulse emission.) Using the known path length through the apparatus, the
distribution o£ product ar r ival times i s converted to a corresponding
product ion velocity distr ibution. By measuring this distribution for a
single ion product a t several laboratory scattering angles, a complete
( u ' t x) contour map i s developed. The advantage of the TOF system is the
relatively small number of measurements necessary to determine an
in tens i ty d i s t r i b u t i o n . The disadvantage of the syetem i s that the
dynamic nature of the measurement makes the r e s u l t s suscept ib l e to s u b t l e
dynamically induced measurement errors and more complicated data reduc
t ion schemes.
The object of our current i n v e s t i g a t i o n has been the analys i s and
construction of a modified TOF system. This method, termed "correlat ion
t ime-of - f l ight" t employs an Information coding algorithym by which the
i n i t i a l ion beam i s modulated with pseudorandom binary no ise and the
v e l o c i t y d i s t r i b u t i o n l a t e r extracted by d i g i t a l cross corre la t ion .
After a b r i e f de scr ip t ion of the mechanics of c l a s s i c a l TO? spectroscopy,
we w i l l examine i n d e t a i l the theory and a p p l i c a t i o n of correlat ion TOP,
and H i l l describe a computer based implementation of such a system.
•Although the number of experimental measurements i s smal ler than that required with a bandpass system, the net number of d i s c r e t e data points (data information) required to construct a s c a t t e r i n g map i s the same for both methods.
- 1 2 -
CLASSICAL TIME OP FLIGHT SPECTROSCOPY
In order t o present a discuss ion of c o r r e l a t i o n spectroscopy, i t i s
f i r s t necessary to d i scuss the c l a s s i c a l t i n e of f l i g h t method. C l a s s i
c a l TOP spectroscopy has previously been appl ied primarily to neutral
p r o j e c t i l e systems. Beam sources are t y p i c a l l y thermal ovens, supersonic
nozz l e s , or slow neutron sources . The e l e c t r i c a l l y neutral nature of
the p r o j e c t i l e s and t h e i r r e l a t i v e l y low v e l o c i t i e s have encouraged the
use of mechanical beam choupers, such as the s l o t t e d d i s c chopper, for
admitting short pu l se s of beam p a r t i c l e s i n t o the react ion chamber.
In a t y p i c a l n e u t r a l beam experiment, ^ s l o t t e d d i s c beam chopper
cons i s t ing of a r o t a t i n g d i s c with one or s e v e r a l rad ia l s l i t s machined
an i t s periphery i s placed i n front of a been source , as the d i sc
rotates at high angular speed, each time a s l o t passes over the cross
s e c t i o n of the beam, a short pulse of beam p a r t i c l e s passes through the
aperture and i n t o the react ion charier . Often, the s l o t i s a l so used to
tr igger a photodiode which r e s e t s a time of f l i g h t clock such as a t ime-2
Co-pulse he ight converter (F ig . 3 ) .
As the bean p a r t i c l e pulse t rave l s through the apparatus, the pulse
height of the converter ramp voltage increases l i n e a r l y with time u n t i l
the arr iva l of a p a r t i c l e at the detector t r i g g e r s a s top pulse . The
time of arr iva l i s recorded by s tor ing the he ight of the t ime-to-voltage
pulse in a multichannel analyzer. Repet i t ion of t h i s process Leads to
accumulation of a d i s t r i b u t i o n of pulse he ight s in the multichannel
analyzer which represents the overal l TOF spectrum.
There are many var ia t ions of th i s method. Each employs a chopper,
time of f l i g h t c lock , p r o j e c t i l e in teract ion and p r o j e c t i l e d r i f t reg ions ,
-13-
N
« fe\2 g Jo M» IM
JO
ZS S
e
and a time of f l ight storage device.
The steady s ta te beam flux from the beam source is given by
I - / J(s)ds = yn j sf(s)ds
where X = to t a l beam flux a y = most probable velocity
(u = molecular velocity)
s = u/y = dimensionless molecular velocity
n = number density of molecules in the beam
f(s) = beam velocity distribution function
J(s) = flux of beam molecules with veloci t ies between s and s+ds.
As the beam chopper s l i t passes over the beam, an instantaneous cross
sectional area of the beam, A(t ') i s admitted through the s i l t ( t = t* =
o i s taken when the s i l t f i r s t allows beam par t ic les to pass ) . The r e
sulting signal measured at the detector Is given by (for a flux sensitive
detector)
K t ) - f J(s) £ =• &( t ' )d t ' J v f c - l : ' ^
2 where L = the f l ight path length and the factor L/Tf(t-t') is a Jacobian factor between ds and a t ' . The quantity of interest here i s the
*t « detector time variable; t ' = chopper time variable
-15-
measured velocity distribution function f(s) which i s contained in the
differential flux, J ( s ) , Since the measured detector signal Is a con
volution of the gate function and the final velocity distribution, the
measured TOF distribution mist be deconvoluted using numerical approxi-4 5
nation, moaent analysis (Laplace Transform), Fourier Transform inversion,
or integration f i t t ing methods.
The resolution of a TOF experiment i s inversely proportional to the
width of the shucter function. Ideally one wishes to use an extremely
narrow "6-function" gate signal for ^ " ^ resolution and to ^.. iaize
the problems associated with TOF deconvolution. unfortunately, detector
signal intensity i s linearly proportional to the width of the gate func
tion and the ensuing tradeoff between intensity and resolution sets a
practical maximum on the time resolution possible in any experiment.
Hagerrs and Varna have calculated that for a flight time fit and
shutter function width T, the resolution, R • —-, necessary to achieve a
TOF half width error of less than 2.5Z i s R^5. This i s readily attained
in most experimental systems by choosing a flight path long enough to
increase At sufficiently to achieve Che desired resolution.
Young has recently pointed out that the measured TOF distribution
also contains 3 convolution of a detector response function and the TOF
signal arriving at the detector. The isiportance of the detector response
depends on the relative time constants for the TGF distribution and the
detector response time. In the present system, this factor is of
negligible importance.
rOF systems have been used to study ion-molecule reactions as well q
as neutral molecule reactions. Paulson et al . have used a TOF double
system has been reported by Haier and Murad for the study of the reac
tions of N ul th N2. A TOF system using a fast cesium ion charge exchange 11 12
source has been described by Leffert. Dittner and Datz have used a TOF system for the analysis of ine las t ic and dissociative processes r e -
+ + 13
suiting from Ha and K ions colliding with H2 and D 2 . Toennies et a l .
have reported similar experiments using Li over an energy range of
6-60 eV.
Though TOF has been applied to ion-neutral systems, the method has
not come into general use. The single most important reason for this i s
the problem of chopping fast ions at a sufficiently high r a t e . Also,
bandpass analysis systems have been highly developed in the ion beam
field.
We .have seen that the classical TGF system provides a useful a l t e r
native to energy bandpass systems. In the next chapter we will present
a detailed discussion of the similar correlation time of flight system
which i s a logical refinement of the c lass ical system.
-17-
HEFEREHCES FOR CHAPTER 1
I. Estermann, "Molecular Beam Technique". Reviews of Modern
Physics. 18, 300 (1946)
J. B. Anderson, R. B. Andres, and J . B. Fenn, Advances in
Chatrrlfal P h y s i c s . J . Ross, Ed. (John Wiley & Sons, I n c . , New
York, 1966) Vol . X pp. 275-317.
4th IAEA Symposium on Neutron I n e l a s t i c S c a t t e r i n g . Volume I I
Copenhagen, 1968.
C. B. t e f f e r t , H. H. Jackson, E. W. Rothe S R. W. Fenstermaker.
Rev. S c i . Instrum. « , 917 (1972)
J. A. Alcalay and E. L. Knuth. Rev. Sci. Inscrum. 40, 438 (1969).
See Reference (3).
J. S. Rollett and L. A. Biggs. Proc. Phye. Soc. London A79, 87 (1962).
R. N. Bracewell and J. A. Roberts, Australian J. Phys. 2., 615 (1954).
A. R. Stokes, Proc. Phys.Soc.London A61, 382 (1948)
K. T. Gillen and B. H. Hahan, Journal of Chemical Physics, 56_,
2517 (1972).
J. D. Horrison, J. Cham. Phys. 39, 200 (1963).
0. P. Hagena and A. K. Varma, Rev. Sci. Instrum. 3J3, 47 (1968).
H. S. Young. Rev. Sci. Instrum. 44, 715 (1973).
-18-
9. J. F. Paulson, F. Dale and S. A- Studniarz, Int. J. Mass Spec- and
Ion Physics. 5_, 113 (1970).
10a. H. B. Maier and E. Hurad. J. Chem. Phys. 55_, 2307 (1971)
b. W. B. Haler, J. Chem. Phys. 55.2699 (1971).
11. See Reference (2).
12. P. F. Dlctner and S. Datz, J. Chem. Phys. 4£, 1969 (1968);
J. "hen. Phys. JM 4228 (1971).
13. V. Held, J. Schottler, and J. P. Toennles. Chem. Phys. Lett. 6_,
304 (1970).
- 1 9 -
CBAPTER I I
COEBELaTION TIME-OF-FLKHT SPECTBDSCOPY
Voile the c l a s s i c a l t i c*=-of - f l igh t method i s adequa te fo r experimen
t a t i o n with r e l a t i v e l y i n t e r n e ion or n e u t r a l b e a m and w i t h favorab le
s i g n a l to no i se r a t i o (S /H) , t h e system becomes l e s s a p p l i c a b l e as s i g n a l
i n t e n s i t i e s dec rease o r as r e l a t i v e background l e v e l s i n c r e a s e . These
f a l l i b i l i t i e s r e s u l t from the sma l l duty cyc le (0.5-1%) neces sa ry t o
achieve reasonable (<5Z) expe r imen ta l r e s o l u t i o n . (The duty cyc le of a
beam apparatus i s de f ined a s t h e t ime f r a c t i o n d u r i n g which t h e beam i s
e f f e c t i v e l y turned " o n . " ) A. s m a l l duty c y c l e , which reduces t h e n e t
p a r t i c l e f l ux by a f a c t o r o f 100, accompanied by an un favo rab l e S/H r a t i o
o r small s c a t t s r e d i on i n t e n s i t y n e c e s s i t a t e s very long d a t a a c q u i s i t i o n
t imes t o accumulate a s i g n a l w i t h accep tab le s t a t i s t i c a l p r o p e r t i e s .
The use of a c o r r e l a t i o n TOF system avoids t h e s e p i t f a l l s . The
c o r r e l a t i o n method p e r m i t s a du ty cyc le of a t l e a s t 5 0 2 ; t h i s , coupled
w i t h the exc lus ion of u a c o r r e l a t e d n o i s e , a l lows e x p e r i m e n t a l measurements
t o be made i n t he face of a d v e r s e S/H r a t i o s (as s m a l l a s 10 o r 10 )
o r i n the case of s m a l l s c a t t e r e d i on i n t e n s i t i e s .
I n t h i s c h a p t e r , we w i l l d i s c u s s t he theory of c o r r e l a t i o n d e t e c t i o n
i n d e t a i l . F i r s t , t he TOF system i s descr ibed i n t h e language of l i n e a r
systems a n a l y s i s . Ther^ fo l lows a d i scuss ion of random i n p u t modulation
wi th subsequent output c r o s s c o r r e l a t i o n fo r c h a r a c t e r i z i n g t h e response
funct ion for t h e TOF l i n e a r sys tem. A d e s c r i p t i o n of c o r r e l a t i o n func
t i o n s and t h e i r p r o p e r t i ^ i s g i v e n . The gene ra t i on of m-sequencea for
exper imenta l modulat ion, and the p r o p e r t i e s of such sequences a r e d i s
cussed . Next, the theory of t h e c o r r e l a t i o n method f o r beams i s de r ived
-20-
and the experimental methods for applying correlation detection axe re
viewed. A description of our current computer based correlation system
i s presented along with a summary of the s t a t i s t i c a l analysis of the
correlation method.
Time of Flight as a Linear System
In a time of fl ight experiment, a narrow, impulsive input (beam
pulse) i s applied to an experimental system. The molecular interactions
with target molecules and the spat ia l distribution of product ions are,
to f i r s t approximation, l inear processes which act on the impulsive input
to generate the measured system output (TOF function) . As such, the TOF 2 system can be analyzed as a constant parameter linear system. Any such
system i s rather completely characterized by a weighting function, h ( t ) ,
(or impulse response function) which describes the output of the system
a t a time t after application of a unit impulse a t the system's input
(Fig. 4) . In the case of the TOF system, the impulse response, h(t)»
describes the spat ia l (and hence temporal) smearing of an impulsive input
of source particles as the par t ic les undergo collisions and drif t toward
the detector.
Using the principle of superposition, for a constant parameter linear
system the output generated for any arbitrary f in i te system input i s
described by the convolution integral ,
y(t) = J h(t')x(t-t')dt' (1) o
The convolutions! lower l imit i s taken as t 1 = o rather than t b - m since
in order for physical causality to hold, h ( t ' ) = 0 for t T <o.
-21-
x(t) h(t) — - y ( t ) -Output
y'(t) x(t) h(t) — - y ( t ) -Output V
b(t)
y'(t) Input
— - y ( t ) -Output V
b(t)
detected Signal
Noise XBL748-6907
Fig. 4. The response of a einple linear stationary system.
-22-
Some further properties of h(t) have fundamental importance but arc
practically always sa t i s f ied . For a stable system h(t> i s absolutely
integrable, i . e .
/ |b(c)|dc
and for a bounded systen Input the output will also be bounded. A neces
sary and sufficient condition for system s tab i l i ty is that the transfer
function of the system defined by
H(p) - f h{ t )e~ p C dt p - a+iv
(the Laplace trans form of the response function) have no poles in the 2 RHP or on the imaginary axis . For a physical system this i s equivalent
to a f inite system frequency response (gain) at a l l frequencies.
Sines measurement of any real systea's output (including TOF) will
inelude detection of ran don noise, b ( t ) , the detector output Is
y'CO » y(c) + b ( t ) . (2)
The object of our investigation is chat, given y*(t) as a ceasured de-
tector output, we wish to recsove a l l randon noise and d. ternine the
sys ten response function, h ( t ) , which i s equivalent to the TOF spe certa
in classical TOF experioencs, the input i s characterized by widely
spaced narrowly shaped pulses which approxicate a delta function. Thus
23-
y(t) nj S U - e O h U ^ d t ' ~ b ( t ) (D o
By measuring signal and noise and noise separately, b{t) la calculated
and Subtracted:
b(tj - y'(e) - bU) (4)
and the TOP spectrum la thus determined.
Correlation Functions
As background for discussion of correlation TOF, we now review the
properties of correlation functions. A correlation Suction la a joint
moment which measure* the similarity between two waveforms (functions)
aa a function of tttalr relative displacement In tlaa with rcspcet to one
another* lhe correlation function la calculated for eeeh temporal dis
placement by integrating the product of the displaced waveforms over al l
else. For any given cine displacement, two v m f o i u which are similar
wil l have a large positive correlation, while dissimilar waveshapes will
lead to a ssall positive or negative correlation. In general, as the
displacencnt tine i s varied, both the relative similarity of the wave-
fores and their correlation function will change. The correlation
function for repetitive waveform will be repetitive.
There are cue- general types of correlation functions. An auto
correlation function of a function, x( t ) , denoted by *L_Ct), i s a ceasure
of similarity between the function x(t) and a verscn of i t s e l f displaced
by a t i o c t . Mathematically,
. * / Kir) - Hm 4 / x ( t ) x ( t £ t ) d *
N " 1 1 a J £ x(jAc)x(jic+T) (5)
H * + ° J - l
where the l a t t e r descr ip t ion i s used for a d i s c r e t e parameter function
and the former for the continuous parameter case . Examples of some
autocorrelat ion funct ions are shown in F ig . 5 . 4
Some of the propert ies of the autocorrelat ion are :
(1) R^Cr) - R ^ C - T )
(2) E^CO) ? I R « < T > | V T
(3) ~& - R ^ (T-O)
A croascorre lat ion funct ion measures the s i m i l a r i t y between two
d i f ferent waveforms. For two functions x ( t ) and y ( t ) the crosscorre la
t ion as a function of time displacement T i s
xy •p++o> » / B (T) - l i o y / x ( t )y ( t+T)dt
= llo i Y>xC}A>:) y(JAM-T) (6)
A crosscorrelation of two seemingly unrelated waveforms can be used to
*See Random Process Appendix.
X(t) R- x (r)
a. Sine wove ' X(t) - R „ ( T )
wk/v b. Square wave
nX(t)
"i n n n , 4R»(r)
A A A A A „
c. Narrow band noise X(t) ."nW
d. Broad band noise > X(t) R X X ( T )
XBL748-6920
Fig. 5. Some RxninplpR of autocorrelation functions (after Bendat'*).
-26-
determine whctlicr Chcy are related by a l i n e a r system; If they are r e
lated , the corrc lac lon w i l l allow dctera inac iaa of the t i c e delay between
the input and output of the system.
Soce proper t i e s of the crasscorre lat ion are:
(1) B ^ (-T) - B y x ( T )
(2) I V T ) | 2 s £ R x x C O ) V 0 )
(3) i R ^ W l ^ y l R ^ O ) + R y y (0)J
If for some delay T, R ( T ) = 0 , x ( t ) and y ( t ) are sa id to be un-xy
correlated (assuming the scans , u a u « 0 ) ; i f R ( t ) • 0 for a l l T,
the two funct ions are s t a t i s t i c a l l y independent*
Impulse Response Determination
Using the concept of cross corre lat ion we now derive the method of
ex tract ing the impulse response function for a l i n e a r system using
system input modulation with output c r o s s c o r r e l a t i o n .
Recal l Eq. (1)
y ( t ) - / h(u)x( t -u)du (1)
where x ( t ) i s the input , y ( t ) the output, and h(u) the impulse response
function. To e x t r a c t the function h (u ) , we confute the crasscorre lat ion
of input and output , R ( T ) by mult iplying both s l u e s of (1) by x ( t - x )
and integrat ing:
KIT) £ l im ~ [ x ( t - T ) y ( t ) d t (LHS) (7) \ f *(t o
T » lim i f x ( t -T)dt / h ( u ) x ( t - u ) d (EHS)
-27-
R * y ( T ) ° f h ( u ) d u **• ? / »(t-t)*(t-u)dt x-*«
when change in integration order is justified because of the finite
properties of the inpulse response function. Changing che variable of
integration in the latter integral
R x y ( T ) " / n ( u ) d u U m / *(t ,-Hl-T)x(t ,)dt ,
. / h(u) R<u-T)du (9)
where the limits of integration are left unchanged since the autocorrela
tion function i s relatively independent of which time interval i s used
for i t s computation. Hote the similarity between Eq. (1) , the determinis
t ic input-output relation for a Hn«»qr system, and Eq. (9), the analogous
stochastic input-output relation.
Assume for the moment that the system input, x(t) can be chosen such
that i t s autocorrelation function Is of the form, R (x) = C$(T) for some
constant, c (£(x) i s the Dirac delta function.) Then
/ h(u) 6(u-x)d R w (T) = c / h(u) 6(u-x)du - ch(x) (10)
and for this type of input modulation, the measured cross correlation
functions wil l be exactly proportional to the Impulse response function
-28-
of the linear system under examination (TOF). I t remains to determine
which type of input modulation is necessary to achieve a delta function
autocorrelation.
Broadband Hoise
As illustrated in Fig. 5 (c and d) , the width of the autocorrelation
function of a noise signal i s inversely proportional to the bandwidth of
the signal. In the limit of infinite bandwidth, the autocorrelation
function of a noise signal becomes vanishingly narrow, approximating a
delta function. Such infinite bandwidth noise i s called "white noise"
and has a power spectral density function which i s a constant over a l l
frequencies.
Although white noise i s unphysical ( i t would require infinite power
to generate), in practice one can approximate white noise to any desired
degree by using rinite broadband noise ("pink noise"). Pink noise, with
i t s broad bandwidth, has a relatively constant power spectral density
function within this bandwidth (Fig. 6) . The corresponding autocorrela
tion function i s f initely narrow (width a bandwidth >. To approximate
a delta function autocorrelation to any desired degree, a sufficiently
large bandwidth of random noise is chosen for system input modulation.
*The power spectral density function is the Fourier Transform of the autocorrelation function:
B»<» - 2 / ^™*-MtT * (The two functions are related much the same as position and momentum in quantum mechanics.) ^^(f) describes the frequency composition of a signal x(t) in terms of the spectral density of its mean square value, (Fig- 6).
a. White Noise
tR, xx <T>
(Dirae 8-Function)
* G „ ( f )
oo
b. Broad Band Noise (Pink Noise)
J R x x ( r ) f G . x ( f )
XBL 748-6918
Fig. 6. Autocorrelation and Power Spectral Density functions for broadband and white noise.
-30 -
For the case of TOP, we chose the bandwidth such that the width of
E (T) « width of the TOF function.
In the following section we wil l investigate the application of
random sequences for broadband source modulation.
- 3 1 -
H-SEQUEHCES
For modulat ion of our l i n e a r TOF sys tem i n p u t , we turn t o t he c l a s s
of pseudorandom l i n e a r sequences . We w i l l d i s c u s s t he gene ra t ing methods
for maximal l eng th sequences and i n v e s t i g a t e some of t h e p r o p e r t i e s of
such sequences which favor t h e i r a p p l i c a t i o n t o c o r r e l a t i o n spec t roscopy .
We a re p r i m a r i l y i n t e r e s t e d i n b ina ry n o i s e sequences because e x p e r i
mental ly t h e r e a r e only two p o s s i b l e s t a t e s ("on" and "o f f " ) of the i on
beam which i s b e i n g modulated. While t h e r e e x i s t many methods of g e n e r a t
ing t r u l y random n o i s e , ' we w i l l dea l e x c l u s i v e l y wi th pseudorandom
no i se sequences ; t h e former methods a r e more d i f f i c u l t t o c o n s t r u c t ,
allow l i t t l e leeway i n t h e a r ea of c o n t r o l and a r e n o t as r e a d i l y r e p r o
duc ib le as pseudorandom methods. For t h e s e r e a s o n s t h e use of sequences
generated by l i n e a r feedback of s h i f t r e g i s t e r s h a s found wide a p p l i c a -
.-• 8
t ion.
Of the sequences which can be generated by sh i f t register feedback,
the maximal length sequences (m-sequences) have been used exclusively.
H-sequences have well known properties, a proportionately larger band
width and more evenly distributed signal s t a t i s t i c s than those sequences
generated by "short-circuited" feedback.
An m-sequence can be generated by the use of an n-stage linear shift
register whose input i s determined ly modulo 2 summation of stage n and
an intermediate s tage(s) , k, with k<n (Fig. 7 ) . The shift register i s
run by an external clock of period 6 and frequency m = 6 . In theory,
the feedback for generation may consist of several loops or of pyramided
registers with separate loops. However, in most applications, as in
the present one, a single register with a single loop and two stage
Y 1 *- Sequence Out
1 2 3 k n-l n
k n\*—
Modulo 2 Adder
Fig. 7. Shift regis ter configuration for m-sequence generation.
X k o 0 0 I
I 0 I
XBL 748-6908
Fig. 8. Exclusive OR Truth Table.
-33 -
feedback is used. Determination, of the necessary feedback circuits will
be discussed la te r .
the two stage feedback i s accomplished by an "exclusive or" gate
which adds modulo 2. the function of an exclusive or gate i s that i t s
output will be logical "one" i f and only if the s ta tes of the two inputs
are different (one 1R a 1, one i s a 0) . Otherwise, the output i s logical
"zero." This i s the characteris t ic of modulo 2 addition ( 0 © 1 = 1 © 0 -
1; QQ^>Q = 1 © 1 = 0) (see Fig. 8) . We note that for pract ical experi
mental electronic purposes a binary sequence consists of {0, 1} while
for mathematical and computational the sequence i s considered to be com
posed of {+1, - l } . As long as the use i s consistent, there i s no contra
diction; because of the manner in which data i s transformed the experi
mental {0} has the same effect as the computational {-lK
The mechanics of the sequence generation axe simple. I n i t i a l l y , the
s ta te of the shift reg is te r i s some nonzero binary sequence, typically
100.. .0. During each external clock pulse, stages n and k of the register
are sampled, added modulo 2, and the result applied to the input of stage
1. Then a l l stages are shifted one position (to the r ight l a our culture)
and stage 1 Is occupied by the result of the modulo 2 addition. The
final result i s a sequence with one new b i t and a displaced version of
n-1 bi ts of the original sequence.
Each m-sequence has a well defined length. For an n-stage register
there are 2 possible s t a t e s . However, one of the s ta tes 0 forms a
"kernel" of the sequence; that i s , this s ta te generates only i t se l f and
i s generated cnly by i t s e l f . Thus once a non-zero sequence i s placed in
the register, i t wil l remain nonzero throughout the sequence generation.
-34-
The 2 -1 remaining s tates a l l appear once and only once during the period
of the sequence leading to a nonrepetitive sequence 2 -1 b i t s long. Thus
the period of the sequence i s T = (2 -1)6 = N6 seconds long. By choosing
the clock rate and the regis ter length correctly, any "reasonable" band
width (determined by 6) and sequence period (N) can be achieved. The
sequence i s easily generated, completely reproducible and i s well
characterized. After the complete sequence has been generated, the
i n i t i a l shift register s t a t e wi l l be repeated and the modulation will
consist of repetitions of the unit sequence.
The theory of m-sequence generation has been thoroughly explored.
M-sequences are part of a larger class known as " l inear recurring
sequences." In general, p-nary sequence (modulo p addition) generation
i s described by rings of primitive polynomials in an indeterminate, x,
over a Galois Field of sca la rs . Although this general theory has con
tributed much to the understanding of simple binary sequences, ve wil l
not discuss i t . The reader i s referred to the sources in Ref. 12.
For the binary case, consider an n stage shif t regis ter which wil l
be described by a state vector, "a = (a , a 1 ( . . . a - t a.) where {a.}, con-' n n-1 e. 1 1 * tained in the set (0, l } , are the bi ts of the reg is te r . The ordering
of state bi ts is inverted because the f i r s t b i t generated is contained
in the last shift register stage. The mode of feedback (Boolean feed
back function) i s described by a weighting sequence, ( c . , c_, . . . . c )
with {c.} e {0,1} where i f c. = 1, stage k is involved in the feedback
loop.
Given an i n i t i a l regis ter sequence the s tate of the register at
some later tine is determined by the linear recurrence relat ion,
-35-
a = c i a i^c-^a -if*")-*- + c a r 1 r-l^-' 2 r-2 v- / n r-a (11)
where (+) denotes modulo 2 addition.
The operation of generating the sequence is said to be the result
of an operator. T, which is the sua of a feedback operator, C, and a
shift operation S.
f = C + I or in matrix notation: iii . .0 "
. .0
. .0 -
- . 0
+
iii . .0 " . .0 . .0
-+
iii . .0 " . .0 . .0
-+
iii . .0 " . .0 . .0
-+ 0000.
. oooo. . . 1 . . 0 .
-. c x c 2 c 3 . .c
n J
+ 0000.
. oooo. . . 1 . . 0 .
-L c x cz c 3 V .c J
n
(12)
We represent the i n i t i a l vector a by
(13)
Then after k shift pulses the s ta te of the register i s given by:
Since the output of the f i r s t register stage i s used for experi
mental modulation, and since the sequential titae history of stage 1 is
equivalent to a s tate vector description, i t i s convenient to describe
the sequence generated in teres of the stage 1 output. This output can
-36 -
be associated vlcb a generating polynomial. G(x) by a one to one
napping defined by (assuaiog c • 1)
1 1 1 G(x)
(-!oVr) ( -Sv 1 ) ( » £ • / ) $(x) (15)
where the third equality follows fron the fact that in oodulo 2 arith
metic, addition and subtraction are equivalent. The polynomial, $(x) is
the adjoint characteristic polynomial of the generating operator. "
*(x) = det (T-x-I) * IT - x«l|
- 1 © c,x + c^x2 + . . . © c x n - 1 + £ e x 1 (16)
where I i s the identity natrix. The characteristic polynomial may also
be represented as a series in D, an algebraic operator whose effect i s to
delay by one bit the variable on which i t operates, each tice i t operates.
(D can be viewed as a sicple pepory element with a one period delay, one 14 input, and one output.)
*(x) = x(l + £ D j) j=l
Thus the generating function (Eq. (15)) is given by
(17)
G(x) = x
- ^ (18)
Equation (18) provides a prescr ipt ion for d e c e m i n i n g the output
sequence given the feedback c o e f f i c i e n t s ( c , } . The c o e f f i c i e n t s (1 or 0)
are used to wri te out e x p l i c i t l y the generating funct ion in teres of the
Delay operator. Hanual d i v i s i o n w i l l resul'. in a polynomial in powers of
D. The elements of the binary sequence vhose sequence numbers appear as
powers of D in the r e s u l t a n t polynomial w i l l be ones; those whose
sequence numbers do not appear as powers w i l l be a e r o .
For c l a r i f i c a t i o n , we w i l l use as an example the case of a four-
14
s tage s h i f t r e g i s t e r . The s h i f t r e g i s t e r conf igurat ion i s shown i n
F i g . 9 . The feedback i s from s t a g e s 3 and 4 . I f we assume an i n i t i a l
sequence of 1000, the outpuc of the f i r s t s tage ( a . ) w i l l be ( s e e F ig . 9
f o r s t a t e vectors)
100110101111000.. . (H - 2 4 - 1 - 15)
For t h i s con f igu ra t ion t h e c h a r a c t e r i s t i c polynomial i s $(X) - Ax 2*! s i n c e c , " c
2
= °» ** " CA m l - A**0 *<*> * * U © D 3 + D 4 ] . Then
G(X) - ^ x * X [ I © D 3 © D 4 © D 6 © D 8 © D 9 © D 1 0 © . . . (I © D J © D ^
So the output sequence I s
1(D°), OCD1), 0CD 2 ) , K B 3 ) , l ( D 4 ) . . . .
= 10011 . . . , the same as computed manually In Fig . 9 .
To ensure that the sequence generated by a s h i f t r e g i s t e r i s maximal,
the feedback connections must be chosen c o r r e c t l y . Fa i lure to apply a
proper feedback loop r e s u l t s i n the l o s s of s i g n i f i c a n t port ions of the
maximal sequence by "short c y c l i n g , " that i s r e s t a r t i n g the sequence
-38-
Figure 9. A 4-stage shif t register configuration
| — > " l a 2 a 3 a 4
a
3 © * 4 T I n i t i a l s ta te <* 0000;
Enter " 1 " into at
with f i r s t shift pulse
Calculated s ta te after k shift pulses
1c = 0 aj az
1 1 0 0 0
2 0 1 0 0
3 0 0 1 0
4 1 0 0 1
a 1 1 0 0
6 0 1 1 0
7 1 0 1 1
8 0 1 0 1
9 1 0 1 0
10 1 1 0 1
11 1 1 1 0
12 1 1 1 1
13 0 1 1 1
14 0 0 1 1
15 0 0 0 1
-39-
before i t has terminated. Tables of appropriate feedback connections
have beea published.
The mathematical cri terion for establishing ^yMfO sequence genera
tion is that the characteris t ic polynomial of the feedback configuration,
<Kx), must be irreducible and primitive ($(x) i s a minimum polyncmical
of the m-sequence) . A polynomial p(x) of degree n i s called irreducible
if i t i s not divisible by any polynomial of degree less than, a, provid
ing that p(x) > 0 . The polynomial p(z) of degree n i s said to be
primitive i f i t does not divide x +1 for k<2 n - l . (A primitive polynomial
i s also irreducible.) Since tables of primitive and irreducible poly
nomials are available, i t i s a simple matter to construct proper feed
back connections for any reasonable length shi f t r eg i s te r .
Properties_of_M-Sequences
As mentioned above, an m-sequence contains N=2 - 1 b i t s and during the
sequence each possible n-tuple (except 0 } appears once and only once in
the shift regis ter . An m-sequence is an example of a "random telegraph
wave" whose rate of zero crossings i s described by a Poisson distr ibu
tion (the o-sequence i s often called a Poisson Square Wave). A picture
of the m-sequence in shown in Fig. 10.
If che mean zero crossing rate for the random process i s m sec ,
the Poisson law states that the probability of k crossings occurring
during a time interval t i s given by
P(k;t) = e " m c -rr- (19)
!
"P
This distribution describes the likelihood of the shi f t register output
containing any given nunber of +L*s or - l*s during any interval .
The s ta te of the m-sequence i s +1 one half of the ting, so the duty
cycle of the sequence i s 0*5. The sequence contains subsequences (runs)
of a l l +1 or a l l -1 during which the shif t regis ter output remains un
changed. During the period of the sequent , one half of a l l runs are of
length 1 (+1, - 1 ) , one quarter are of length 2 (+1 +1, -1 -1) and 1/k
will be of length K ((+1) , (-1) ) . Furthermore, there are exactly as
many runs of +1 of length k as there are runs of —1 of length k (except
( - l ) n =(0) n which i s excluded). 19 An m-sequence i s closed under the operation of shift-and-add:
for a l l s f 0 (cud N), there exists an integer H such that if a i s
any b i t of an m-sequence,
a
r © r+s r+v (20)
The sequence ta^, } is a shifted version of the original sequence. s 20
(The set of sequences {{a }, r:l,H} forms a K-module.)
The most important property of m-sequences i s , for our application,
the autocorrelation function. Recall that we wished to find an experi
mental modulation function which had an autocorrelation function which
approximated a 5-function. A normalized representation of the autocorre
lation function for an m-sequence of length N «* 2 -1 (± 1 states) i s
shown in Fig. 11. This function consists of triangular peaks of height 1
and width 26 at T = 0 (modulo H) ?ad an intermittent background of height
+ R x x (r )
-AT =N8-
l l /N
T = 0 XBL 748-6917
Fig. 11. Normalized autocorrelation function - H - 2 n - l , aequonco period • N6.
-43 -
H . By choosing 6 small and H large, this correlation function becomes
very much like a 6-function. For our application, 5^5x10 sec, n c 20,
H=10» so the autocorrelation function wi l l consist of 1 usee wide peaks
spaced 1 sec apart with a relative background level of 10 . The shape
of the autocorrelation function was measured experimentally with an
Hewlett-Packard 3721A Correlator and was found to conform to the expected
shape. The width of the function, M. usee, should be easily adequate
for measuring Time of Flight spectra of 30 usee duration and 10 usee
tota l width.
Now that i t i s apparent that a suitable modulation sequence can be
generated for extracting the TOF impulse response function, ve proceed
to derive explici t ly how the impulse response method i s applied to TOF
spectroscopy.
THEORY OF CORRELATION DETECTION
Though ue have d i scussed the g e n e r a l t heo ry of impulse response
de terminat ion by c r o s s c o r r e l a t i o n , i t remains t o e l u c i d a t e the theory
ce s p e c i f i c a p p l i c a t i o n s . To f a c i l i t a t e an unde r s t and ing of the n a t u r e
and o r i g i n of an expe r imen ta l ly measured c o r r e l a t i o n function and i t s
components, we n e x t p r e s e n t the mathemat ica l theory of c o r r e l a t i o n d e t e c
t ion as app l i ed t o beam systems. This theory p rov ides the conceptual
b r idge between random exper imenta l modulat ion and the computation of
c o r r e l a t i o n f u n c t i o n s .
Ue f i r s t suppose t h a t the modulat ing m-sequence can be r e p r e s e n t e d
by a cont inuous func t ion s ign i fy ing a s e r i e s of s t a t i s t i c a l p u l s e s , x . ,
p laced randomly a t u n i t time i n t e r v a l s , t . :
x(t) =Ex. 6(t-t±) (21) i
The actual experimental modulation function is the convolution of this
statistical function with the experimental beam pulse shape (gate
function) , <£( t) :
fT M(t) = f x(tt)4>(t-t,)dt' = E x , *(t-t.) (22)
1
where T is the period of the m-sequence and fT i s the total measurement
interval. 21 Hossfeld has shown that the shape of the modulation pulse must be
of a certain minimum symmetry type to ensure a proper ^-function auto
correlation and to avoid "input transducer error." This symmetry
condition i s expressed (for al l t ines, T) as
S * . (T-t ) - 1 (23) i J 2
Since the binary sequence always contains one. more (+1) pulse t-ian (-1)
pulses, this condition requires that the t r a i l i ng edge of a modulation
pulse be the mirror image of the leading edge. Connonly used triangular
(trapezoidal) and rectangular pulseshapes sat isfy this condition i n
herently .
We also note that the discrete autocorrelation function for the
s t a t i s t i c a l sequence can be written in terms of the duty cycle, c, and 21
the modulation rate, m, of the sequence,
ass<k> - £ Vi-ft = m C 1 " c ) 6 k + • (24)
Now ue reca l l that the measured crosscorrelation with the linear
TOF system i s
H a y'( t )x( t-T)dt - V x , y ' ( T + t )
j= l J J (25)
where only the s t a t i s t i c a l portion of the modulation function i s ueceasary
to confute the correlation, and where
U) = J h(T o
)H(t-T ')dT' + b(t)
= J h(T £N
1=1 x±iKt -h-T') b(t) (26)
is the measured detector output at time t . In Eq. (26), h(T) is the
impulse response function (true TOF distribution), b(t) is the uncorre
c ted "constant" background signal, and we have changed the upper limit
of integration from +™ to T. since the TOF signal is of finite duration
(h(T) = 0 for al l T>Th) • Equation (22) for the modulation function has
been used to derive (26) .
Putting the expression for detector output (Eq. (26)) into the
correlation function (Eq. (25)) we get:
£N f n fH fH R ay ' ( T ) = .? X j J h ( T ' } S xi(J>(T-ti-T,+tj)dT' + V ^ C ^ ) (27)
J o -'"
T h r N r N
= f £ X
n
X / h(T')*(T-t -T'+CJdT'-H) X! X -(28)
where the averaged noise included in the correlation function will be
independent of T (uncorrelated) and so can be removed from the summation,
by rewriting the double summation as
E V j • ? ? V i 4 k - £ » « * > - S f a ( l - c ) 6 k -mc} x,j J k i k k
= m(l-c) +£mc {lit j
and by no t i ng t h a t
N £ x = m ( t h e number of pu l se s p e r p e r i o d ) j = l - •J
t h e c o r r e l a t i o n expres s ion becomes
R ^ . C T ) = fm { (1-c ) / h ( T ' ) « T - T ' ) jtt-c) / o
f N I J h ( T ' ) ^ ^ ( T - T ' + ^ d T 1 + b [ + C J h ( T ' ) ^ ^ ( T - T ' + ^ d T 1 + b j (30)
o
R e c a l l i n g t he symmetry c o n d i t i o n (23) t t he sum i n t h e second terra is
e q u a l t o u n i t y . We de f ine
H(T) = J h(T,)4>(T-T») (31)
which i s the convolut ion of t h e modulat ing p u l s e shape w i t h t h e t r u e TOF
f u n c t i o n . H ( T ) i s e x a c t l y t h e TOF d i s t r i b u t i o n which would be measured
w i t h a c l a s s i c a l TOF exper iment u s i n g a ga t e func t ion <|>(t) . Thus
/ h
R ,(T) - fm {( l -c)H(T) + c / h (T ' )dT ' + b> (32) xy j
o
The integral in the second term of Eq. (30) may also be expressed In
terms of H(x): let
/ 6 = 1 $ ( t ) d t (33)
be the t o t a l a r ea under a u n i t modulat ion p u l s e . Then
/h r h /-Ti
H(T) dx - / dx / h(x')4i (x-x*)dx f
o o o
T T = f hCT^dx' y
o
T
h(x')dx' / tfx-x^dx
6 / hCxMdT* = 6<h> (34)
(35)
R ,(x) - Era {(l-c)H(x) + § <H> + b} (36) xy u
This i s the desired resul t . The computed crosscorrelation i s proportional
to the classical TOF signal superimposed on two constant background terms.
The background due to the average TOF signal, -r- , has been called the 22 background of ignorance." I t s origin i s the association of each
detector pulse to m modulation pulses during the correlation, whereas
physically the detected ion could have come from only one of these pulses;
the detector signal i s erroneously attributed to the other m—1 modulation
pulses. However, due to the s t a t i s t i c a l properties of the modulating
signal , this error becomes evenly distributed among a l l channels of the
correlation function and assumes the identity of a constant background.
- 4 9 -
The Cera In £q. ( 1 0 ) , a b , i s due Co each true background pulse being
a t t r ibuted to m channels, the r e s u l t being a constant Increased back
ground.
The method of modulation described in the above d i s c u s s i o n was
assumed Co use a ( 1 , 0) type of corre la t ion , racher Chan a (+1 , -1 )
t y p e . Since our corre la t ion method uses the l a t e r type ( s e e be low) ,
both sources of constant background are removed and the r e s u l t of corre
l a t i o n i s d i r e c t l y proport ional Co the c l a s s i c a l TOF s i g n a l H ( T ) . . Thus
Che r e s u l t s of Che c o r r e l a t i o n experiment are equiva lent Co Chose of the
c l a s s i c a l TOF method; we now proceed t o discuss how a c o r r e l a t i o n system
may be implemented experimental ly .
- 5 0 -
APPLtlHG CORRELATION TOF
Having shown how random modulat ion of a beam sou rce might be used to
t reasure the TOF spectrum and hav ing d iscussed the g e n e r a t i o n and p r o p e r -
c i t s of the modulation s i g n a l , ve now examine the mechanics of applying
t h e c o r r e l a t i o n or thod to t i m e - o f - f l i g h t systems.
There a r e s e v e r a l d i s t i n c t methods by which c o r r e l a t i o n spect roscopy
has been appl ied to TOF, Each method has i n common t h e concepts of modu
l a t i o n , c o r r e l a t i o n , and d a t a s t o r a g e . To our knowledge, t h r e e v a r i a t i o n s
of t he c o r r e l a t i o n method have been implemented. The f i r s t , used wi th
n e u t r a l molecular beams, -ropl ies a. r e l a t i v e l y s h o r t modula t ion sequence
which I s coupled synchronously w i t h r e p e t i t i v e c yc l i ng of a mul t i channe l
a n a l y z e r for da t a s t o r a g e . Accumulated da t a i s l a t e r t r ans formed
( c o r r e l a t e d ) by c o r r e l a t i o n of t h e mul t ichannel a n a l y z e r c o n t e n t s wi th
t he r e p e t i t i v e modulation s i g n a l . The sequence of e v e n t s i s then modu
l a t i o n , da t a s t o r a g e , and c o r r e l a t i o n , a l l r e l y i n g on t h e u s e of the
s h o r t modulation sequence . (The r e q u i r e s e a t t ha t a s h o r t modulation
sequence be used i s the r e s u l t of the l imi t ed number of slots which can
be machined i n a mechanical chopper and the f i n i t e number of mul t i channe l
ana lyze r channels a v a i l a b l e . )
The second method, used i n neut ron spec t roscopy , uses a long pseudo
random s i g n a l which no t only modulates the source beam, b u t a l s o c o n t r o l s
the s t o r a g e of d a t a by g a t i n g t h e inpu t s of a s e r i e s of d a t a accumulation
s c a l e r s . This method does no t r e q u i r e any l i m i t a t i o n on the pe r iod of
t h e modulation sequence, and f i l t e r e d t rue random b i n a r y n o i s e modula
t i o n could j u s t as w e l l be employed. The sequence of e v e n t s is modula
t i o n , c o r r e l a t i o n , and d a t a s t o r a g e .
-51-
The third type of application Is the one developed in our laboratory
for use in ion beam experiments. This method, which i s actually a hybrid
of the other two, can also use long pseudorandom sequences for beam modu
lation. Data storage i s achieved by storing detector output signal in a
computer core memory by associating individual detector events with the
modulation signal responsible for their genesis. Subsequent transforma
tion of the stored data using the associated modulation signal leads to
calculation of the correlation function. The sequence of events in this
method i s modulation, data storage, and correlation; the method thus
resembles that used for neutral molecular beams, though no limits are
placed on the length of the modulation sequence and synchronized data
storage i s not required.
Correlation with general Molecular Beams
As previously described, slotted disc rotat ing choppers have been
used to modulate neutral beam systems. Correlation modulation i s achieved
by machining the chopping disc with slots placed in a pseudorandom mannez 23 so that the gate function of the chopper approximates an m-sequence.
The resolution of the chopper i s fixed by the width of the "unit beam
slot" (the circumference of the chopper i s divided in to H unit s lots which
are either open or closed) and by the angular velocity of the disc. In
practice both the number of unit slots and the number of multichannel
analyzer slots are limited to M.000 and this places a l imit on the length,
H, of the binary sequence used for modulation. (This has the effect of
limiting the background height of tne modulation sequence autocorrelation
function to 1/1000 of the peak height. See the description of the m-
sequence autocorrelation function.)
-52 -
Data storage with the s lot ted disc system Is achieved by use of a
multichannel analyzer. The analyzer and the beam chopper are synchronized
so that as the chopper runs through the pseudorandom sequence, the
analyzer i s sequentially stepped through each of i t s memory channels.
Detector events sensed at any point in the chopping sequence are always
stored In a corresponding multichannel analyzer channel associated with
that particular sequence segment. Both the chopper and the analyzer are
cycled repeatedly, always maintaining the synchronicity between the two.
linen sufficient data (empirically determined) have been collected,
the correlation function i s calculated, a single point at a time, by
multiplication of each of the analyzer channel contents by the corres
ponding value of the modulating function (±1) and summing the result
over a l l analyzer channels. Shifting the phase betweea the multichannel
analyzer channels and the modulating sequence and repeating the multi
plication and summation provides the value of the correlation function
for different delay times* The resulting plot of net correlated signal
versus phase (time) shif t betweea modulation sequence and analyzer
channels i s the desired correlation function.
Correlation with Meutron Beams
A somewhat different system has been applied in the measurement of 24 neutron beam velocity distr ibutions and the response function of
25 neutron reactors. In the former case an incident beam of polarized 24 neutrons i s chopped using a magnetic flipper chopper, while neutron
reactors are modulated by the use of electrostat ic deflection plates in
the Van de Graaf accelerator used for neutron generation. (Often
mechanical disc choppers have been used to measure the velocity
-53-
distributions for neutron beams in a system analogous to that described
for neutral molecular beams.)
Since these methods of source modulation are e lec t r i ca l rather than
mechanical! and since data i s not stored in a f in i te sized multichannel
analyzer, there i s no physical or memory res t r ic t ion on the length of
the modulation sequence. Depending on the method of data storage, true
filtered binary random noise (such as i s produced by commercial noise
generators) could be used in place of an m-sequence.
The correlation detection system employed for reactor measurements 25
i s shown in Fig. 12, This system achieves a direct correlation between
the neutron source modulation sequence and the detector output. This i s
accomplished by use of a series of scalars which are incremented by
detector events. Each scalar i s gated by one segment of the modulation
sequence; though the segment of the sequence gating each scalar changes
s ta te constantly, tha t segment has a fixed phase with respect to the
sequence segment which i s currently modulating the neutron source.
The experiment i s controlled by a suitable d ig i t a l clock of period
6. The clock runs two shif t registers; one i s hooked up as a binary
pseudorandom noise generator whose output i s an appropriately long
m-sequence; the ether i s a se r ia l in /paral le l out storage register which
stores the sequence which has been used to modulate the source. Consider
the case of an n-bi t storage register . If M(t) i s the current modulating
sequence, the nth stage of the storage, register contains the segment
H(t-n&) since i t requires a time t «• a5 for any segment to be shifted
through the storage reg i s te r . Similarly, any stage k, l£fcsn will con
tain the segment H(t-^cS). Now the paral lel output of each register
Storage Register
Correlator Scalars Gates
XBL 748-6913
Fig. 12. Crosscorrelatlon with gated scalars.
-55-
stage, k, is applied to a gate, <L , which controls the input of a scalar
(counter), S. . When a neutron is sensed by the detector, each scalar
S, whose input Is gated on by the modulation signal H(t-kfi) will be In
cremented, indicating a positive correlation between the detector output
and a +1 segment in the modulation signal at a time (t-k6) previously.
All scalars whose modulation segment was 0 rather than +1 will not be
incremented. Since the system does not include the effects of negative
correlation, the scalar 6 is used to record the total detector signal
for later computational correlation adjustment to include negative corre
lation effects. If after same period of data collection, T (kS) is the
contents of scalar S. , and T_(kS) the total number of counts ignored by
S. , then T , the contents of scalar S , is equal to
T o = T + (k6) + T_ (k5) (37)
for any k. Then the correlation function can be calculated from
H. (i-kfi) a [T+(kfi) - T_(k5)] * [2T+(kfi) - T Q ] (38)
Recalling Eq, (6)
N
K (T) - l i m £ V x ( j A t ) y (jAt+x) (6) W j - 1
we see that the measured correlation function of Eq. (38) i s given by
summing the tota l number of positive correlations (T i s the sum of a l l
cases where x(j"nt)y(.jAt+k5) • +1) and subtracting the t o t a l number of
- 5 6 -
negative correlations (T_ i s the sun of a l l cases for which
x(juT)y(jAc+kS) = - 1 ) . The result i s a net corrected value of the corre
lation function for T = k.6.
The important concept of the method i s that any point of the corre
lation function can be calculated direct ly by using the modulating seg
ment (bit) corresponding to the proper delay to gate a data storage
scalar. Any number of points of the correlation function could be calcu
lated merely by increasing the number of sea tars and gates and by i n
creasing the length of the storage reg i s te r . The modulating sequence
need not be repet i t ive since the correlation i s direct and immediate.
Resolution i s limited only by the number of scalars and the clock rate
for modulation.
The drawbacks of this system are mainly those of electronic com
plexity and expense. The experimenter oust build a complicated and
dedicated single purpose correlator whose resolution is directly pro
portional to i t s complexity. For this reason, an alternative method was
sought for use In ion beam experimentation.
The Present Correlation Method for Ion Beams
Prior to constructing a correlation system for ion beam analysis,
we reviewed a l l of the techniques which had previously been applied.
including commercially available correlators , multichannel analyzer, and
gated scaler systems. Each system was found tc have inherent disadvan
tages which made i t difficult to apply to ion beam analysis.
Commercial correlators employ analog or d ipi ta l delay lines for
signal sampling followed by sequential single point correlation calcu
lat ion. The comparatively low signal levels (slow repetition rate) of
-57-
an ion bean system make i t infeasible to use sequential single point
correlation since excessively long sampling times would be necessary.
Ion beam TOF experiments typically have a f l ight time of 10-50 \isec
and TOF distribution widths of 2-10 usee. This fac t , coupled with the
problem of synchronicity and the long access time of multi
channel analyzers (10-100 usee) made the application of a neutral beam
analysis type system impractical.
The gated scalar type of system i s direct ly applicable; however,
i t i s more expensive and difficult to construct. Additionally,
such a system i s to ta l ly dedicated and somewhat inf lexible; i t can
only be used for specif ic correlation analysis without further data
analysis.
A solution to the ion beam problem was found In the use of a mini
computer based system. Such a system i s comparatively Inexpensive
(<$6,000), requires only construction of an appropriate computer in te r
face, and allows the use of available hardware (the computer) which can
be applied to a variety of data analysis problems.
The computer used in the ays tern i s a Digital Equipment Corporation
PDF 8/f which i s a 12 b i t minicomputer with a 1.2 Usee cycle time (see
"Computer Organization" below). I t was decided that simultaneous compu
tation of 30 points of the correlation function would provide adequate
experimental resolution for viewing the TOF ion spectrum in a maimer
similar to the gated scalar technique. Since the computer has only a
single data input channel (12 data l ines ) , and since i t would require
1.2 usee to add data to each of 30 "scalar" addresses in core memory,
direct Implementation of a "scalar system" would require a 40 Usee
-58 -
downtiae for each detector event accumulated. This i s excessive con
sidering the s ignal intensi t ies (^10 /sec) typically measured with an
ion beam apparatus; a significant portion of the detector signal would
he lost, negating the duty cycle advantages of the correlation system.
The solution to th is problem l ies in the application of the "Data Address"
concept.
The Data Address Method
While the computer has only one data input channel (even though this
channel contains 12 b i t s ) , i t does have multiple inputs available in the
form of i t s 12 b i t address code. The basic concept of a "data address"
i s that the information necessary to compute a TOF correlation function
is present in the modulation sequence (which has been stored in a
storage shif t regis ter) a t the time of a detector event {as we saw in the
gated scalar system) . I t i s possible to re ta in this information while
simultaneously reducing data storage time for the computer by a factor
of 10 i f the applicable modulation sequence i s used as an address code
for the computer memory. Each code sequence i s uniquely associated with
a core memory address in the computer. Each time a particular modulation
code i s contained in the storage register at the time of a detector
event, the address corresponding to that code in incremented. As an
experiment proceeds, the core memory addresses accumulate as their con
tents a distr ibution function representing the number of times each modu
lation sequence code was contained within the storage register at the
time of a detector event. The connection between data addresses and the
calculation of the cross correlation function wi l l be described below.
-59-
Siuce we wish a 30 bi t correlation function, 30 bi ts of the current
modulation sequence must be held in a storage regis ter . For each detector
event, the 30 current bi ts are stored as three 10 b i t segments.
The 10 b i t length is suggested because of an access time-core memory
size tradeoff. This tradeoff can be visualized as follows: i t would
take 30 computer cycles of 1.2 usee or 40 jisec to store 30 independent
data b i t s , but only 30 core memory addresses to accumulate the resul t .
On the other hand, i t would only require one memory cycle to store one
data sequence 30 b i t s long by the data address method; however, to s tore
a sequence k b i t s long by the data address method requires 2 core
addresses since there are that many possible outcomes iu a k b i t sequence.
Thus, for one 30 b i t segment i t would require an astronomically large
C2 3 0
S 10 8 core addresses) core memory, the compromise point is the
use of three 10 b i t segments, requiring 5 usee storage time and 3 x 2
- 3 x 1024 addresses, both parameters tolerable for the present system.
Data transfer of a modulation code sequence i s achieved through the
use of a direct memory access mode of the computer. In this "data break"
mode (see "Computer Organization"), the computer's central processor i s
disabled and program execution is temporarily s ta l led . The actual data
transfer is controlled by the external logic of the computer interface.
To increment the contents of three separate data addresses, 3 sequential
data breaks must be used.
He note that one could store the modulation code just as easily by
using 10 b i t s of the computer data l ines . In this manner, a 30 bi t
sequence would be stored as the contents of three addresses rather than
in the address i t s e l f . For each detector event, three new addresses
-60-
would be required. However, th is method would allow only about 1000
detector events to occur before the memory overflowed. In contrast, the
data address will allow an average of 5 K 10 detector events to occur
before core memory overflow.
A block diagram of the computer system i s shown in Fig. 13. A
feedback shift register generates the beam modulating m-sequence. This
sequence is also stored sequentially in a digital delay l ine and then in
a storage shift register (DBMA) . All registers are controlled by a
variable frequency crystal generated digi tal clock. Detection of an ion
causes the sequence in the storage register to be strobed into the data
break logic, where the sequence i s used to increment three addresses by
direct memory access. By use of a Tektronix display terminal keyboard,
the functions of the Interface may be controlled by programmed commands.
Since the data address method stores correlation information in a
coded manner (the code being that the binary modulation sequence specifies
a 10 b i t portion of a 12 b i t address), a decoding transformation of
the accumulated data i s necessary to compute the desired correlation
function.
The data transformation mimics the function of the gates used in a
gated scalar system (see "Program Description") (Fig. 14). Each address
is examined separately. Since the 10 least significant b i t s of the
address contain the equivalent of the modulation sequence at the time of
detector events, each b i t , k, describes whether (for that part icular
address) the modulation segment, H{t-k6) (where 6 is the clock period),
i s positively or negatively correlated with the number of detector
events contained within the address contents. If bi t k is a " 1 " , the
iX , u , I Z77
a , - - . TOF i y Analysis
--xnr 1% Amplify and Digitize
Chopper < COAX
1 I PRNG j »•
Variable X-TAL
Clock
Variable Delay
Latches D.B.U.A.
Oata Break Logic (IOT, Priority, Control)
POP 8/F (Data Address)
Tekfrcnii Terminal
RECC Line to LBL CDC 6600
Asynchronous Units:
1. Computer 2. X-TAL Clock and Bean Modulation 3. Detector Signal
XBL748-6929
F i g . 1 3 . Correlation TOF Block Diagram.
Figure 14. Data transformation for the data
Transformation of addresses 1325a and 0723B
(10 significant b i t s to be transformed)
1325s:
file position 1 2 3 4 5 6 7 8 9 10
Data address 1 0 1 1 0 1 0 1 0 1
Contents: 34
Result:
add to signal scalar: 34 - 34 34 - 34 - 34 - 34
Add to noise scalar: - 34 - - 34 - 34 - 34 -
Hext address for example:
0723a:
Bit position 1 2 3 4 5 6 7 8 9 10
Data address 0 1 1 1 0 1 0 0 1 1
Contents: 21
Result:
Add to signal scalar: - 21 21 21 - 21 - - 21 21
Add to noise scalar: 21 - - - 21 - 21 21 - -Cumulative result:
Signal scalars 34 21 55 55 - 55 - 34 21 55
Noise scalars 21 34 - - 55 - 55 21 34
Net (^0) 13 - 55 55 - 55 - 13 - 55
-63-
contents of the address are added to signal accumulation scalar k; other
wise the contents are added to noise scalar k. This process i s carried
out for each c* the 10 b i t s of each address. There are three sets of
Bignal and noise accumulators in the computer memory, corresponding to
the three 10 b i t segments of the modulation sequence uaed as independent
data addresses. When each of the 3K possible addresses have been t rans-
formed in this manner, the resul t ing contents of each of the 30 noise
seal are i s subtracted from the contents of the companion signal scalar .
The result i s the TOF correlation function.
He have seen how the correlation TOF system can be applied In
several ways. In the following section we wi l l discuss a somewhat more
abstract picture of the correlation method applications.
-64-
VECTOR SPACE PICTDRE
Having exp la ined in d e t a i l t h e mechanism by which t h e c r o s s c o r r e l a -
t i o n funct ion i s c a l c u l a t e d , ve now p r e s e n t a more t h e o r e t i c a l c o n s i d e r a
t i o n of t h i s process w i t h t h e hope t h a t i t w i l l c l a r i f y how the c o r r e l a
t i o n i s accomplished. Th is d e s c r i p t i o n i s couched i n t h e language of
v e c t o r space theory .
He mentioned p r e v i o u s l y t h a t the b i t s conta ined i n random n o i s e
g e n e r a t o r s h i f t r e g i s t e r can be r ep resen ted by a s t a t e v e c t o r , a . I t i s
only n a t u r a l then t o d e f i n e a v e c t o r space , U, which i s spanned by the
c y c l i c l y genera ted s t a t e v e c t o r s . He c a l l V the state or sample s p a c e .
For a s n - s t a g e s h i f t r e g i s t e r , t h i s space i s i d e n t i c a l t o E . The p o i n t s
i n D which a r e a c c e s s i b l e t o t h e s t a t e v e c t o r form t h e v e r t i c e s of an
n—dimensional hyperspace cube . Since t he s t a t e v e c t o r i s r e p r e s e n t e d by
a b ina ry n - t u p l e , a = ( a , a _ . . . a . ) , t h e r e a r e 2 v e r t i c e s of t h i s
cube, a l l of which a r e a c c e s s i b l e except the a l l z e r o n - t u p l e . This i s
cons i s t an t w i th the number, 2 n - l , of s t a t e s which a r e gene ra ted dur ing
the modulation sequence .
We a l s o noted e a r l i e r ( s ee "M-sequences") t h a t t h e genera ted sequence
i s s a i d t o be the r e s u l t of an ope ra to r T o p e r a t i n g on an i n i t i a l s t a t e
v e c t o r . T i s the sum of a feedback o p e r a t o r , C, and a s h i f t ope ra to r ,
S . Given an i n i t i a l s t a t e v e c t o r , a , the v e c t o r space U i s genera ted 27
by T. Because of the s h i f t and add p roper ty of m-sequences , t he
ope ra to r T i s a l i n e a r o p e r a t o r , a l though t h i s i s by no means obvious .
k t h I f T a r e p r e s e n t s the k s t a t e vec to r i n the sequence a f t e r k opera t ions
by T, because of t he s h i f t and add p roper ty i t i s a l s o t r u e t h a t
-65-
aQ + T* aQ £ D, k G l , a Q C 0 (39>
where modulo 2 addition Is assumed. Thus the vector space U Is closed
under operation by T.
Because R Is complete, If we define a scalar product on U, U i s a 28 separable Hilbert space (Euclidean) . This scalar product can be
defined by the modulo 2 addition:
A
<*. y> « 2 x i y i ( 4 0 )
i - i mod 2
Thus we are dealing with a separable Hilbert space and a 1:1 linear
operator for describing the process of sequence generation.
The picture oZ operation i s thus given by specifying an in i t ia l
state vector, a . which is then repeatedly acted upon by the generating
operator, T. This operation moves the state vector about the vertices
of the hyperspace cube in a fixed cyclic manner. The a l l zero vector,
0 , i s excluded because i t i s in the kernel of the operator T. Since
each n-tuple appears only once during the sequence, the state vector
passes through each vertex once and only once during the period of the
sequence.
Because of the nice properties of the state vector space, i t i s 28 possible to define projection operators which act on the state vectors.
One Buch projection operator, G, can be used to represent the generating
polynomial, G(x), which describes the output of the f irst stage of the
shift register. The n-tuple which represents this one dimensional
-66-
projector i s simply 6 = ( 1 , 0 . . . . , 0} and we can make the association,
2 Q -1
We will now describe how the use of projection operators can be viewed
as a method of calculating the TOF correlation function.
The point of this vector space picture i s to gain a better under
standing of how the crosscorrelation function i s generated by the data
address method. In the vector space representation, the crosscorrelation
i s a measure of the correlation between the position of the s tate vector
and the occurrence of detector events. We can associate with each point
in the s ta te phase space a density in phase; th is density in phase
associates with each s t a t e vector the number of occasions on which a
detector event occurred while that s ta te vector represented the contents
of the modulation generating shift regis ter .
This representation i s especially applicable to the data address
method. In this method the addresses in the computer core memory are
used to represent the phase space points, while the contents of each
address represent the associated density in phase. In contrast with
methods such as the gated scalar scheme (see "Application of Correlation
TOF") the data address method accumulates the density in phase and la ter
computes the correlation function, as we now describe.
In the data address method, the crosscorrelation function is com
puted from untransformed raw data by the use of a binary mask, (test bit)
and a series of associated signal and background accumulators (see
"Program Description"). The process of using a masking bit for testing
-67-
the bits of each address i s equivalent to defining a series of one
dimensional projection operators vhich act sequentially on each relevant
phase space state vector. A background and signal accumulator are
associated with each projector; i f the result of the projection operation
with any projector acting on a state vector i s a non-zero vector, the
density in phase associated with the state vector i s added to the signal
accumulator ( i . e . there was a positive correlation between the position
of that state vector and the associated detector events). A zero vector
result of the same projection operation results in the associated density
in phase being added to the background accumulator {negative correlation
between the state vector and the associated detector events). The com
plete calculation of the correlation function then involves the action
of n projection operators on each of the 2 —1 Ftate vectors (assuning n
points of correlation function are being calculated).
If we define the projection operator far a delay time T as R , and
i f a i s the state vector and p(a) the associated density in phase, then
R x y ( T ) " J R x - p ( 2 ) d a ( W )
a l l space
The form of each one dimensional projection operator i s a i-tuple with
a "1" in a position determined by T and the remaining bi ts zero. For a
modulation clock period 6, i f T •= kfi, the n-tuple wi l l contain a "1" in
the k place. For a (1, 0) type of correlation (background not sub
tracted) the discrete correlation function is then
-68-
2°-l
k-1
For a (+1, -1) correlation, as is used in Che data address nethod to
account for negative correlation effects (background subtracted)
zn-i Exy ( T ) * £ { * A " ( 1" RT )2k } P (5k ) C 4 4 )
k-1
We note that the effect of the projection operation i s really equivalent
to the use of a ser ies of phase density weighted inner products.
Similarly the autocorrelation function for the modulation sequence
can be represented by an inner product sum which i s unweighted. If we
denote the n-tuple representing each projector 8.(10 by a, , then
2 n - l W ^ " < a(t) |a( t+T)> - ^ < a ( t ) | a k Xa k | a ( t+T>> (45)
k=l
where a(t) i s the true s ta te vector at time t .
This view of the calculation of the correlation function calculation
i s a convenient vehicle for displaying the conceptual difference between
the gated scalar system of correlation and the data address system.
While, as we have shown, the la t te r method accumulates the density in
phase before the sequential operation by projection operators, the
scalar system works by immediate and simultaneous projection. Each time
a detector event i s noted by the scalar system, each of the gates in the
scalar system essentially performs the projection operation on the current
-69-
state vector. All n projection operations are accomplished simultaneously
because of the extensive hardware of the system. Thus, rather than using
a single series of weighted projections, this system uses repeated un
weighted projections.
Summarizing, we see that the vector space picture of correlation
analysis provides a simple view of the operation of the data address
method. Although the formalism i s readily suggested by the framework of
the system, to our knowledge this i s the f irs t time this formalism has
been explicitly developed.
In the next section we wil l discuss the s ta t i s t i ca l analysis of the
system we have described in an effort to see h.-,v the unique method of
data address must be constructed to avoid data transduction error.
-70 -
STATISTICAL ANALYSIS
How t h a t we have erfmrfned the theory of t h e c o r r e l a t i o n method, i t
i s r e l e v a n t t o d i s c u s s the s t a t i s t i c a l e v a l u a t i o n of t he method t o see
how i t may cocpare i n accuracy wi th o t h e r s .
There a r e s e v e r a l p o i n t s of view from which the c o r r e l a t i o n system
may be ana lyzed . F i r s t , i gnor ing expe r imen ta l q u e s t i o n s , we i n q u i r e how
c lose ly t he measured e s t i m a t e of t he c o r r e l a t i o n func t ion corresponds t o
the t r u e TOP s i g n a l . Secondly, we ana lyze t h e s o u r c e s of exper imenta l
d i s t o r t i o n and compare t h e .general r e s u l t s of c o r r e l a t i o n measurement t o
those ob ta ined w i t h c l a s s i c a l TOF sys t ems , ffe t h e n proceed t o examine
the problems a s s o c i a t e d w i t h our own computer based c o r r e l a t i o n system
and d i s cus s t he g e n e r a l problem of d e t e c t o r p a r a l y s i s . F i n a l l y we view
the c o r r e l a t i o n sys tem i n l i g h t of t he Shannon sampl ing theorem i n an
e f f o r t t o e x p l a i n t h e r e l a t i v e e f f i cacy of t h e method.
System Opt imiza t ion
There has been a good dea l of d i s c u s s i o n i n t h e l i t e r a t u r e p e r t a i n -
29
ing t o t he o p t i m i z a t i o n of c o r r e l a t i o n a n a l y s i s s y s t e m s . This d i s
cuss ion c e n t e r s about de f in ing the v a r i a b l e s a v a i l a b l e w i t h i n t h e sys tem
and choosing t h e i r v a l u e s so as t o make c o r r e l a t i o n a n a l y s i s broadly
app l i cab l e i n an a c c u r a t e manner. The o p t i m i z a t i o n problem i s beyond
the scope of t h i s t h e s i s s i nce the p r i n c i p a l pa ramete r s (duty c y c l e ,
method of sequence g e n e r a t i o n , modulat ion sequence symmetry) a r e f ixed
by the expe r imen ta l e l e c t r o n i c methods which have been used i n implement
ing t he p r e s e n t c o r r e l a t i o n system.
-71 -
Correlatlon Measurement Variance
In the process of making a measurement of a correlation function,
one i s actually making an experimental estimate of the function by 25 repeated single correlat ions. Stern e t a l . have derived a detailed
s t a t i s t i ca l analysis of the correlation function "estimator" using the
fundamental lavs of conditional probability, the accumulated single
correlations and a simple assumption about the net steady s ta te part icle
flux as the modulation bandwidth i s increased to a > . They have showed
that in fact the measured estimator of the correlation function i s
equivalent to the " t rue" correlation function. Hence ve may have some
confidence that the accumulation of single correlations wi l l reveal the
true shape of a TOP dis tr ibut ion.
Given that ve are indeed measuring the shape of the TOF distribu
tion, the next question to be dealt with i s how good i s the measurement.
That i s , given that an accumulation of single correlations wi l l converge
toward the true correlation function, how fast w i l l that convergence be?
A measure of the reproducibility and (in the abeence of systematic
error) accuracy of any experimental measurement i s i t s variance. In
general, any set of measurements of a process can be represented by a mean
value and a variance. He recall that the mean of a set of measurements,
{x.} i s defined as
H T K = H m N X X = 1 ± m k f x(t)dt. (46)
*See "Random Process Appendix".
The variance describes the mean square deviation of the measurements from
the mean value:
N 1
Var(x) = a* = lim 5"2 ] E x k" P x l 2 = U m T / k( t ) -y x ] Z dt <«)
The variance of the correlation estimator has been evaluated by
various means of different authors; the most fundamental method is to work
from single correlations using simple, joint, and conditional probabili
ties to evaluate explicitly the factors of the correlation estimator
25 variance. This has been accomplished by Stern who has shown that
basically the expected relative error (dimensionless variance) is attribu
table to three sources: finite counting times, finite counting rates,
and spontaneous source fluctuations:
E r e l - y - * - - 4 + R c + R r <*8 )
** ( T o >
where R (T ) is an average value of the correlation estimator and the X? O
three terms refer to errors (variance) due to measurement time, counting
rate and source fluctuations,respectively. The last term is not applic-3 4 able in the present case; the relatively large numbers of ions (10 -10 )
released with each beam pulse make stat is t ical fluctuations L. the source
output negligible (<12). For the present system, we will evaluate the
magnitudes of the remaining terms.
The remaining terms have been shown to be represented by:
R£ = (2(H)" 1 (491
\2 <-(tf ( rT)" 1 (50)
where o = TOF bandwidth, T = tot- -.aasureosnt time, n = the modulation
index (1 in this case), and r le average counting r a t e . The factor
W i s defined by
„ _ 2m modulation bandwidth o TOF bandwidth
For the praseat system, we can evaluate the magnitude of these variance
terms using:
a = ~~ = 10" 5 s e c ' 1
10 psec
T = 30 seconds
W = 10 n = l
- 2 3 4
for the cases of r = 10 , 10 , 10 counts/sec. He then find that the
error due to counting rate is R ^ (r) = 1 0 , 1 0 , 1 0 for the
above counting ra tes , while R_ <10
Thus we conclude that for the present wideband modulation used and
the relatively intense signal expected, the experimentally generated
variances wi l l be of the order of 12 of the mean correlation estimator
value, an entirely tolerable level.
The fact that these experimental considerations do not lead to
-74 -
s i g n i f i c a n t va r iance does not imply t h a t va r iance i s a n e g l i g i b l e p r o b
lem. We have ye t to cons ider the problem of s i g n a l / n o i s e r a t i o (S/H)
and the e f f e c t s of random or c o r r e l a t e d n o i s e ; t h i s w i l l be d i s c u s s e d
n e x t .
I n a c o r r e l a t i o n measurement sys t em, the re i s no p r a c t i c a l method
of removing c o r r e l a t e d n o i s e . For i n s t a n c e , c r o s s t a l k between s o u r c e
modula t ion and s i g n a l d e t e c t i o n w i l l remain i n v i s i b l e to t he c o r r e l a t o r
and y e t could c o n t r i b u t e s i g n i f i c a n t l y t o the measured TOF d i s t r i b u t i o n ,
p o s s i b l y l e ad ing to f a l s e peaks i n t h e c o r r e l a t i o n func t ion . The e x p e r i
m e n t e r ' s only recourse i s c a r e f u l d e s i g n t o e l i m i n a t e any p o s s i b i l i t y of
c o r r e l a t e d n o i s e . One hopeful n o t e i s provided by the f a c t t h a t c o r r e
l a t e d n o i s e w i l l most probably be measured with a very s h o r t c o r r e l a t i o n
t ime ( T a; 0) s i nce e l e c t r o n i c s i g n a l s from modulation a r e t r a n s m i t t e d a t
h igh s p e e d . This bas the e f f e c t of s e p a r a t i n g any c o r r e l a t e d n o i s e peak
from t h e TOF c o r r e l a t i o n peak s i n c e ion t ime of f l i g h t i s f i n i t e . We
n o t e t h a t as y e t we have seen no ev idence of c o r r e l a t e d n o i s e i n t h e TOF
d i s t r i b u t i o n s which have been measured.
The va r i ance due to unco r r e l a t ed n o i s e has been d e a l t wi th by 22 21
Von Jan and Schena and by Hossfeld and Aoadori. They have d e r i v e d
the fo l lowing express ion fo r c o r r e l a t i o n var iance as a func t ion of delay
time ( s i n g l e poin t c o r r e l a t i o n v a r i a n c e ) :
RT+b where a » and
T R
L T (51)
-75-
R - R ( T ) ( s i n g l e p o i n t of corre lat ion function)
b - average background per channel
L • nucber of channels needed to span the measured TOF function
N •= 2 - 1 • length of the modulation sequence
f • the mnber of t i n e s the modulation sequence repeats during the
measurement
c • duty cycle • 0 .5
- i L
R • — V* R, * the average TOP s i g n a l . T«l
The f i r s t fac tor I s i d e n t i c a l t o the error which would be measured
i n a c l a s s i c a l TOF experiment with a pulse r e p e t i t i o n r a t e S~ . The
f a c t o r £B i s a measure of the t o t a l measurement time and thus f o r f ixed
s i g n a l l e v e l s , the r e l a t i v e error decreases i n an inverse manner as the
measurement time i s increased .
In order to compare the r e s u l t s for c l a s s i c a l end c o r r e l a t i o n
measurements! the " c l a s s i c a l " tern i s often divided out to g i v e a r e l a
t i v e gain factor:
2 " ^ " c l a s s i c a l . ( * • « » < * £ ( 5 2 )
t a B W 1 ccrrelacicm ^ * j | -
This gain factor expresses the gain i n accuracy which i s achieved by use
of the correlat ion method. I t i s primarily a function of the r e l a t i v e
s i z e of the correlat ion funct ion at any po int ,
R +b
-76 -
since the duty cycle, c, modulation length H, and TOF width, Lt are
relatively fixed. For a duty cycle of c • 0.5 both Von Jan and Hossfeld
have calculated that the correlation method wil l provide superior results 2
(g >1) i f o", ^ 2; this i spl les that the correlation method wi l l always
give a Bore accurate measurement of the shape of correlation peaks In the
presence of low background levels (large S/N), and wil l give higher
accuracy for the entire correlation spectrum in the presence of large
relative background levels (b>2B). Ac example of this effect is shown 22 in Fig. 15 (after Von Jan and Schero ) . In Fig. 15A a measurement is
made in the presence of a low background level. For portions of the
spectrum below a • 2 the correlation method i s less effective than the
classical method while for viewing the peak the correlation method i s
better. In Fig. 158 a measurement i s made in the presence of a high
relative background level . In this case, a l l of the spectrum l ies above
a • 2, so the correlation method i s better for the entire spectrum.
We note that a l l of the above discussion has assuaed a stationary
experimental system, this i s often not the case; expertmentally a systea
i s rarely stable in a long tern sense since bean energy fluctuates a
finite amount as does beam intensity. Also the vacuus systen nay undergo
pressure fluctuations as may the pressure of target gas contained within
a scattering celL This experimental reality provides further support for
the use of the correlation method since if in some experimental oeasure-
ment classical and correlation methods were to have identical accuracies
(gain factor equal to one), data collection by the classical method would
require a tioe interval at least 10 times as long as that required by a
correlation measurement, making the classical method tsuch core susceptible
-77-
Small Background Case
- 4
" - I
b. Large Background Case XBL748-6922
Fig. 15. Relative efficiency of the correlation taethod for small and large S/K cases.
-78-
to experimental d r i f t . This advantage, which i s e n t i r e l y due to duty
cyc le cons iderat ions , has been widely overlooked.
In summary than, the corre la t ion method i s super ior under adverse
S/N conditions and for examining correlat ion peaks. In both methods, the
examination of l e s s in tense port ions of the TOF spectrum i s accomplished
with lower e f f i c i e n c y , and t h i s face often determines the time necessary
to measure the TOF spectrum with s u f f i c i e n t accuracy; for t h i s case the
bandpass system of measurement has d e f i n i t e advantages.
Detector Paralys i s
He turn now t o the d i s c u s s i o n of measurement accuracy problems which
are part icu lar ly a s soc ia t ed wi th the present computer based system. By
f a r the most important aspect i s the problem of data transduction errors
or detector p a r a l y s i s .
TOF spectroscopy i s a dynamic method of measurement. Consequently,
i t i s suscept ib le to dynamic errors inherent i n the measurement process
which are much l e s s amenable t o analys i s and correc t ion than the errors
of a non-dynamic energy bandpass system.
The most s i g n i f i c a n t type o£ dynamic error to which a TOF system
may be subjected i s the error of data transduction. Any p a r t i c l e de tec
t i o n system has a f i n i t e bandwidth capabi l i ty ; hence each detector has
a f i n i t e period of time (deadtime) af ter i t has de tec ted a p a r t i c l e
event during which i t I s unable to r e g i s t e r the appearance of subsequent*
l y arriving p a r t i c l e s . This phenomenon, known as de tec tor p a r a l y s i s , may
have profound e f f e c t s on a dynamic peasureasnt system.
Detectors of events are generally c l a s s i f i e d as being one of two
30 types . A Type I (non-paralyzable) counter which r e g i s t e r s a p a r t i c l e
-79-
arriving at time t , wil l then lock out any further particles arriving
during a (random) period, T (the deadttme). Particles arriving in the
locking interval ( t , t+x) are not registered, nor do they affect the
counter in any way. A scinti l lat ion counter i s an example of a Type 1
Counter.
In contrast, a Type II (paralyzable) Counter does not lock out
particles which arrive during the dsadtlme associated with in i t i a l
particle detection. As each particle arrives, i t locks the counter for
a random locking tine, T , regardless of whether i t was counted or not.
For a sufficiently large particle flux, a Type II Counter can be com
pletely paralyzed, Che f irst particle being counted and a l l further
particles merely extending the dead tine. A "non-self quenching Geiger-18 duller counter with a high impedance preamplifier" i s an example of a
Type H Counter.
The computer based data acquisition method of the current correla
tion TOF system i s basically a Type I counter. Since the actual particle
detector i s much faster than the computer data storage part of the
system, the bandwidth (20GkHz) of the interface data storage system
effectively limits the bandwidth of the counting system. This bandwidth
limitation i s due to the necessity of three 1.2 usee memory access cycles
to acknowledge the arrival or a single detected ion. Since the computer
and the detector are asynchronous, a 5-7 usee deadtioe can be considered
as a reasonable worst case estimate of the limit on data storage band
width.
The question we must deal with i s whether the typical 5 usee counter
deadtime will prejudice the shape of the measured TOF distribution in
-80-
favor of faster particles which may arrive first at the detector, locking
out the slower particles which arrive later.
In general for classical TOF, the effects of Type I Counter deadtime
depend on the relative bandwidths of the detector (B ) and the dynamic
signal being measured (B___) • As we now describe, at each extreme
(B » BxoF* BTQF > : > B D e t ' * t h e raeasured T 0 F s i SPal will be measured
accurately, while the intermediate case (B- ^ B_ -) may lead to data
storage prejudice.
The case of a very fast detector (B_ > > B T Q F ) "^ C n e simplest*
In this case the dead time of the counter is negligibly small and all
relevant signal data will be stored. The opposite case ( B
T 0 F » B } is
that of random phase sampling where the detector is locked most of the
time and randomly samples the TOF signal in a "Monte Carlo" type of
detection. Note that the random phase assumption is of prime importance.
The case of detector downtime being correlated with the TOF signal may
lead to severe distortion.
The median case (B« ** B
T n P ) contains the greatest possibility of
data prejudicing. In this case, given a suitable particle flux, the TOF
signal and the detector are matched in phase in a resonant manner. The
fast particles of any beam pulse are registered and the slow particles
are locked Out. The detector becomes unlocked in time to register a fast
particle from the next TOF pulse, and the scheme is repeated. While a
distribution of arrival times will be measured, i t is conceivable that
the prejudice of the distribution may be so great as to display periodic
structure within the TOF waveform, the period being characteristic of
the detector deadtime.
-81-
Of course this discussion depends strongly on the net particle flux
and the signal repetition rate. In a classical TOF experiment, the
repetition rate i s alvays relatively slow so that given a minimum flux of
particles at the detector (say 5-10 ions/bean pulse) data transduction
would be far from perfect, favoring the high velocity portion of the
distribution.
In the case of correlation analysis, depending on the path length
of the TOF analyzer, ic may often be the case that B- *x* B___. However,
ve maintain that this method avoids prejudice because of i t s inherently
large repetition rate. The beam pulse rate on the average i s great
enough so that several or many pulses are produced within a time charac
teristic of the TOF function (Fig. 16). As these pulses travel through
the TOF system, they v i l l overlap spatially leading to a net steady state
beam flux. Since the ion flux arriving at the detector i s approximately
constant in time, the detector does not differentiate between fast and
slow ions; the distribution of ions causing detector counts v i l l be dis
tributed numerically in proportion to their velocity characterized
number density in the ion beam. Similarly, ions which are rejected due
to detect!-r downtime wil l also be rejected in proportion to the velocity
distribution ("counts neglected and not detected can be rejected"). This
i s another example of random phase sampling. "
As an Illustration, consider a measured TOF distribution of 6 usee
width at the detector generated by a mean modulation frequency of 1 mega
hertz. Since the modulation bandwidth is greater than the TOF bandwidth
(as i t must be for reasonable resolution), on the average, unit beam
pulses will overlap spatially before they approach the detector. Sow
R x y(r)
M(t)
TOF Function
, Modulation Function t —
XBL748-692I
Fig. 16. The high relative repetition rate for the correlation method.
-83 -
slnce there are runs of consecutive " l ' s " and "O's" in the modulation
sequence, there i s the possibil i ty of negligible pulse overlap if a
sufficiently long run of "O's" were present in the sequence- We recall
from the discussion of a-sequences that the probability of having n con
secutive " l ' s " or " 0 f s " i s 2 . For the 6 usee wide TOF signal, i t would
require a run of a t least 6 zeroes to eliminate beam pulse overlap; thus
runs of length k, k<6, wi l l not be subject to causing distortion. The
total probability of having a run of zeroes greater than 6 i s
5
k=i
where the factor of y i s a result of only one half of the modulation
sequence being comprised of zeroes. Thus, for th i s case, only 1.5Z of
the modulation pul&es wi l l allow the possibil i ty of TOF distort ion.
This necessity for beam pulse overlap puts another c r i t i ca l con
straint on the length of the TOF flight path. Let ' s assume that one
wishes to allow only a small fraction, £ , of the beam pulses not to
overlap. Further assume that the TOF distribution has a maiHimt velocity,
V_, minimum velocity, V., and velocity bandwidth AV = V„ - V . To
achieve overlap in a fraction of pulses 1-C we determine n from the
following inequality:
n
k=l
The width of the TOF function at a detector placed L cm away from the
source i s
T mh- L. LAV , q a l
TOF V x " V 2 V X V 2 * " '
To achieve t he n e c e s s a r y over lap t h e n ,
T T O F ^ n T H o d ^ B ^ (55)
where Tj. . and B„ . a r e t he modulat ion p e r i o d and bandwidth, r e s p e c t i v e l y .
Equat ing (2) and (3) we f ind
nVV L > M T 5 ^ C56) AV ^ d
P r a c t i c a l l y speak ing , t h i s i n e q u a l i t y w i l l p r a c t i c a l l y always be
s a t i s f i e d s i n c e choosing L s u f f i c i e n t l y l a r g e t o g ive reasonable r e s o l u
t i o n w i l l e l i m i n a t e any beam over lap problem. However, t h i s c o n s t r a i n t
warns us t h a t i f t he TOF f l i g h t pa th i s n o t s u f f i c i e n t l y g r e a t , not only
w i l l t h e r e be poor r e s o l u t i o n , bu t t h e r e may a l s o be s i g n a l d i s t o r t i o n .
We have i n c l u d e d as an appendix a more r i g o r o u s d e r i v a t i o n of the
d e t e c t o r p a r a l y s i s problem us ing a mathemat ica l d e r i v a t i o n based on the
a u t o c o r r e l a t i o n func t ion of the modulation sequence . For fu r the r d i s
cuss ion , p l e a s e s e e t h i s appendix.
Shannon's SampH"g Theorem
I n viewing t h e c o r r e l a t i o n system, i t seems somewhat l i k e an e x p e r i
menter i s " g e t t i n g something for no th ing" by u s i n g su<:h a system t o ga in
inc reased s i g n a l d e t e c t i o n c a p a b i l i t y . The answer t o t h i s a l l e g a t i o n i s 31
contained i n t h e w e l l known Shannon Sampling Theorem.
-85-
Shannon's theorem te l l s us that any in formation channel can be
characterized as having a maximal information transfer capacity, and that
any desired level of accuracy in information transfer through the channel 32 can be achieved by error correcting codes at the expense of lowering
the information transfer ra te .
The TOP system can be viewed as an information transfer channel.
The classical TOF method i s an extremely inefficient mode of data trans
fer; i t ' s somewhat reminiscent of a trans-Atlantic telephone conversation
in which each word spoken must reach the other end of the line before the
next word i s ut tered. Thus i t i s this tremendous inefficiency which nraifpg
the correlation method look efficient.
The classical method makes no expl ic i t use of any error correcting
code for information transfer. However, the use of single beam pulses
is In real i ty a very simple transmission code. The correlation method
on the other hand expl ici t ly uses an error correcting code (random modu
lation} which i s much more efficient. Whereas the classical method
simply includes signal errors (noise) with the detected signal and la ter
subtracts i t , the error correcting property of random modulation is used
explicitly to remove uncorrelated noise in the correlation method.
Although the correlation method makes much fuller use of the infor
mation capacity of the TOF channel, one can only wonder whether s t i l l
more efficient methods might be found, further enhancing experimental
accuracy and speed.
In summary, we have discussed the sources of experimental variance
and found them not overly important. The correlation and classical
methods were compared for accuracy and the former method shown to be
-86 -
superlor In many Instances. The problem of detector par 1 ysls was shown
not to apply to the correlation system providing that the system Is
designed with a sufficiently large fl ight path. Finally, we have reviewed
the information transfer aspects o£ the two systems and saw how coding
led to increased information handling capabil i ty.
-87-
REFg'.EHCES FOR CHAPTER II
1. F. Hossfeld, R. Acadori, and R. Scberm. prnrpg<Hngw nF rtig Panoi
Conference on Instrumentation for Heutron Inelastic Scattering. IAEA,
Vienna, 1970, p.126 f£.
2. P. E. Pfeiffer, Linear Systems Analysis. HcGraa Hill, 1961.
3. See L. I. Schlff. Quantum Mechanics, 3 r d Ed. McGraw Hill & Co.
1968, p.55.
4. J. S. Bendat and A. G. Piersol. Hpasurement and Analysis of Random
Data. John tfiley and Sons, Inc. Hew York, 196e.
5. X. E. Stern, A. Blaqulere, and J. Valat. J. Nuclear Energy A/B, 16_
499 (1962).
6. W. D. T. Davies. Control, June, 1966 p.302.
7. G. A. Eorn. Random Process Simulation and Hpasurement. HcGrsv
Hill, 1966.
8. See References (1) , (21) and (22) .
9. P. H. R. Scholenfield. Electronic Technology 37, 3?9 (1960).
10. T. E. Stern and B. Friedland. IRE Transactions on Information
Theory IT-5, 114 (1959).
11. See References (9) and (10).
12a. References ;i0), (13), and (17).
b. S. W. Golomb. Sequences with Randomness Properties. The Glenn L.
Martin Co. Baltimore, Hd. June, 1955.
13. H. Zlfirler. J. Soc. Indust. Appl. Math. T_, 31(1959).
14. Reference (6), p.304.
15. Heference (7), p.85.
16. Reference (13) and (17).
-88-
17. W. W. Peterson and E. J. Veldon, Jr., Error correcting Codes. H.I.T.
Press, 1972, p. 472 ff.
18. E. Parzen. Stochastic Processes, Holden Day & Co., San Francisco,
1962.
19. S. U. Golomb. Shift Register Sequences. Holden Day & Co., San
Francisco, 1967.
20. Reference (13), p. 32; reference (17), p.59.
21. F. Hossfeld and R. Amadori. On Pseudorandom and Markov Sequences
Optimising Correlation Tlae-of-Flight Spectrometry. DSAEC, JUL 684FF,
(1971) available from HTIS.
22. R. Von Jan and R. Scherm. Hud. Instrum. Heth. 80, 69 (1970).
23. V. L. Hirschy and J. F. Aldridge. Rev. Sci. Instrum. 42, 381 (1971).
24a. I. Pal, H. Kroo, P. Pellionisz, F. Slavifc a I. Vizi in 4th IAEA
Symposium on neutron Inelastic Scattering. Volume II, Copenhagen,
1968, p. 407.
b. P. Pellionisz. Hud. Instrum. Heth. 92, 125 (1971).
25. Reference (5).
26. R. E. Unrig and H. J. Ohanlan In Heutron Hoise Haves and Pulse
Propagation. USAEC, 1967.
27. References (13), (19), and (21).
28. E. PrugoveckL. Quantum Mechanics in Hilhert Space. Academic Pres3,
Res York, 1B71.
29a. K. Veise, Hud. Inscrum. Heth. 98, 119 (1972).
b. C. J. Hacleod. Int. J. Control 14 97 (1971).
c. G. Wilhelmi and F. Gompf. Hud. Instrum. Heth. 81, 36 (1970).
d. Reference (21),'
y
-89-
30. D. R. Cos. Renewal Theory. Matbaene * Co., Ltd., London. 1962, p.31. 31. C. E. Shannon and V. Heaver. Matbeeatlcal Theory of Co—iiiili.nlnn.
University of Illinois Press, Urban* 19*9. 32. Reference (17).
- 9 0 -
CHAPTER I I I ,
COMPDIER ORGANIZATION
This section i s the f irs t of several which discuss the electronic
and informational techniques which have been used to implement a computer
based TOP correlation system. Since the computer interface, the main
object of the discussion which follows, i s intimately connected with the
internal hardware structure of the computer i t se l f , we wil l f irst describe
some of the pertinent organization within the computer. This discussion
i s admittedly brief; since many of the details of the computer's operation
are beyond the scope of this thesis, the reader i s referred to the DEC
PDP8/e Small Computer Handbook.
The POP 8/f i s a 12 bi t minicomputer with a 1.2 usee cycle time.
Overall, the basic computer organization can be described as follows:
"The PDP-8/E system consists of a central processor, core memory, and input/output fac i l i t ies ; a l l of which interrelate by WMK of a **JITIMM"P bus called 'Omnibus.*
"All arithmetic, logic, and system control operations are performed by the central processor. Information storage and retrieval operations are performed by the core memory. The memory i s continuously cycling, automatically performing a read and write operation during each computer cycle. Input and output address and data buffering of the core memory are performed by registers in the central processor, and the operation of the core memory i s under control of timing signals produced by the central processor."
In essence, the central processor, via programmed control, manipu
lates the contents of the core memory in the process of performing
arithmetic and logical operations in a logically ordered temporal
-91-
Tbe computer's core memory consists of 8 K addresses (IK = 102410)
divided into two 4 K f ie lds . Each field i s labeled by a three bit
Extended Memory Address code (EMA), allowing up to 32 K of core memory to
be employed. Each core address i s capable of storing a 12 bit binary
number. Within each 4 K. f ield, memory addresses are divided into blocks
of 200B, denoted as "pages. thus addresses 0, 200. 400, etc. each de
note the start of a new cere page. All programming operations are page
relative; that i s . when an address i s named as an operand, i t i s speci
fied relative to the beginning of the page on which the computer ifi
currently operating. (For example, i f the computer i s operating on the
page starting with address 1200. the address 1302 i s specified as 102.}
This type of addressing i s a result of the 12 bi t configuration of the
computer's central processor. To specify an address In a 4 K. field
uniquely would require a 12 bi t code; page relative addressing requires
only 7 of the possible 12 bits contained as the contents of an address,
leaving 5 bits available for actual operational Instructions. It must
be remembered that there are two 12 bit numbers associated with each
address: the address code i t se l f and i t s contents.
A simplified picture of the computer operation may be described as
follows: the Central Processor (CPU) determines an operator address
whose contents wi l l determine the next operation to be carried out. The
contents of the operator address contain both the operation to be carried
out and an operand address whose contents wi l l be the subject of the
*0ctal notation wi l l be used for describing the operations of the computer.
-92-
operation. The operation i s performed on the operand contents and the
result stored either in the operand address or in a storage register
called the accumulator (AC). Next, the CPU looks in a Program Counter
(PC) register to determine the next operator address, and the prices*
then continues. A program consists of a scries of such operations
designed to achieve a mathematical calculation or logical core cecory
manipulation.
The Central Processor (CPU) of the computer consists of a tiding
sequence generator, an Instruction Register for programming operations,
paral lel adders, an Accumulator (AC) for recording the results of a r i th
metic and logical operations, and several 12 bi t registers utilized in
programming control. There are also gating networks fur taultiplexing
input to and output from the CPU and the core memory. Mosc important of
the control registers are the Central Processor Memory Address Register
(CPMA) which scores the Memory Address (MA) which i s currently being used
by the CPU as an operand address, and Che Program Counter Register which
stores the memory address from which the next instruction will he taken
ac the completion of the current programming operation. During a pro
grammed operation, the operand pare of an instruction is stored in the
CPMA, while the operational instruction is stored in the Instruction
Register.
Normally, the Program Counter limits core address manipulation to
one 4 K field of memory unt i l the EMA is explici t ly changed. In the
absence of "jump" commands, programming is sequential; the CPU accesses
the memory location contained in the Program Counter, performs the re
quired operation(s), increments the Progran Counter by one and continues
- 9 3 -
chc processing. However, manipulation of the contents of the Program
Counter allows non-sequent ia l programing using JHP (Jump) operation codes
and allows the CPU to make t r a n s i t i o n s betvecn the current core page and
any other page.
Opgrations Codes
There are 8 operations codes which ate employed in programming
sequences. Of these , f i v e arc 'memory reference i n s t r u c t i o n s " which
s tore and retr ieve data from core memory, and one i s the s o - c a l l e d "house
keeping" JHP operation which transfers program contro l t o any neaory
address uncondit ionally (not a subroutine-type t r a n s f e r ) . A l i s t of the
Heaory Reference Ins truct ions* t h e i r operat ions , and o c t a l operation
codes are given In Tabic A. The AND function i s the only l o g i c a l opera
t i o n . The TAD and DCA I n s t r u c t i o n s are used for a r l t h o e t i c manipulations,
whi le the ISZ ins truc t ion i s used for program looping . JHS transfers
contro l to a subroutine wi th an option for e x i t from the subroutine r e
turning program control t o the program locat ion request ing the sub
routine entry .
The remaining two operat ions codes are c a l l e d "augmented i n s t r u c
t i o n s . " Code 6XXn i s used for input/output transfer (IOT) between the
computer and i t s p e r i p h e r a l s , each peripheral being ass igned a s i x b i t
(2 d i g i t ) o c t a l code (XX) which i t alone recognizes . Code 7nnn i s an
operations code which a l lows manipulations of the contents of the AC and
l o g i c a l checking of the contents of the AC.
In the PUP 8, t ee o c t a l numbers 0000-377? are p o s i t i v e whi le the
numbers 4000-7777 are n e g a t i v e . This allows twos complement addit ion
as w e l l as program looping by incrementing negative numbers (or p o s i t i v e
-94-
Table A. Memory reference lnscructions for DPD 87 f
Mnemonic Operation Op. Code (Octal)
(1) AND Logical {+) between AC and memory
Onnn
(2) TAD Two's complement addition between AC and memory
lnnn
(3) ISZ Increment memory, skip next instruction if the result is zero; for program looping
2nnn
(4) BCA Deposit AC in memory, clear AC 3nnn
(5) JHS Jump to subroutine 4nnn
(C) JHP (ho asekeeping) Unconditional jump 5nnn
-95-
numbers) unt i l a zero resul t i s obtained.
The Omnibus
The computer bus (OMNIBUS) i s available to a l l of the computer's
peripherals, as well as the CPU, and transports 96 different signals.
Some of the more pertinent bus lines are as follows: The memory address
lines (MA. 0-11) which carry the Ma being accessed currently by the CPU;
memory data lines (MD 0-11) which transfer the contents of the address
carried on the MA lines back and forth between core memory and the CPU;
data lines (DATA 0-11) which carry the contests of the AC; and the timing
pulses which are used to gate a l l operations both within the CPU and in
the computer-peripheral interfaces.
Progra™»»d Operation
He are now in a position to give a more detailed description of the
sequence of events which occurs in programmed operation. In i t ia l ly the
computer i s halted and the f i r s t address of the program i s entered on
the programmer's console. He assume that a correctly coded program has
previously been stored in the core memory start ing at th is i n i t i a l
address. When the computer Is started, the CPU examines the contents of
the program counter, which now contains the i n i t i a l address. Since the
contents of the i n i t i a l address are the f i rs t operation and operand in
the programming sequence, the CPU gates on the HA lines to access this
address (the operator) . The operations code of the operator address is
loaded into the 3 b i t Instruction Register and the operand address Is
placed In the CPHA regis ter . Using the memory data l ines to access the
contents of the operand address, the CPU carries out the specified
operation on either the operand or the accumulator contents, or both.
-96-
The results of the operation are then either stored in the AC or gated
back to the operand address via the Memory Buffer l i ne s . The Program
Counter i s then incremented and the process continues. We have assumed
here that a Memory Reference Instruction was being implemented. In Che
case of a jump or augmented instruction, the operation i s rather a manipu
lation of the Program Counter, the accumulator or a peripheral device.
Data Transfers
Besides the augmented 6XXn instruction used for communicating with
a peripheral device labeled XX, there are two additional modes of opera
tion which are used for data transfer between the computer and i t s per i
pherals: interupt transfer and direct memory access (DMA) or "data
break" modes. Both of these modes of operation rely on an interrupting
signal being generated by the peripheral i t se l f ; both modes provide for
data transfer at the request of the peripheral device.
In an interrupt transfer, the peripheral raises a "flag" (pulls down
the "interrupt l ine" on the OMNIBUS) te l l ing the CPU that i t wants access.
The raising of a flag caures the CPU to interrupt i t s normal program
routine and to jump to absolute location 0000 (within the current EMA
field)- Previously a program has been placed s ta r t ing at location zero;
this program acknowledges the interrupt, tes ts to determine which per i
pheral has made the request, and jumpB to an appropriate subroutine which
services the peripheral, using IOT'S (6XXn) to complete the data transfer.
Upon completion of the transfer, the subroutine returns program control
to the point of operation In effect prior to the interrupt . Interrupt
programming is used for servicing peripherals which do not have a
cr i t ical ly short access time.
-97-
In comparison with interrupt transfers which modify normal program
operation and require relat ively l i t t l e in the way of peripheral control
logic, the data break (DMA) transfer is a "cycle steal ing" technique
which requires a coicplicated arrangement of control logic to disable the
normal canputer functions and to make the CPU a slave of the peripheral.
With this type of transfer the normal operations of the CPU are tempo
rari ly suspended; the operational components of the CPU ( i . e . the Program
Counter, CPMA Register, Instruction Register and gating logic) are dis
abled and substituted for by a paral le l set of logic in the peripheral
device. The peripheral supplies the memory address, controls the opera
tion to be carried out by the CPU arithmetic and logical elements and
supplies i t s own data (for transfer into memory). Thus the Direct
Memory Access mode can occur at any time and can transfer large blocks of
data into or out of memory without disturbing (except temporally) the
normal programming operation. The DMA mode effects data transfer at high
speed and i s used to service peripheral (such as a high speed disc f i le)
which have a c r i t i ca l access time. I t i s this DHA mode which has been
employed in data acquisition for our correlation TOP system.
Having examined the framework of the computer's operation, we next
discuss the computer interface which allows the computer to acquire data
from an ion beam apparatus, and which forms the heart of the correlation
system.
- 9 8 -
THE CORRELATION SYSTEM COMPUTER INTERFACE
In any computer based d a t a a c q u i s i t i o n sys tem, a c e n t r a l r o l e i s
p layed by the computer i n t e r f a c e l o g i c . By i t s e l f a computer e x i s t s in
an information vacuum. The i n t e r f a c e p rov ides the l i n k between the com
p u t e r and the o u t s i d e w o r l d . The i n t e r f a c e accep t s i n fo rma t ion from
ex te rna l sources and i s r e s p o n s i b l e for t r a n s d u c t i o n of computer genera ted
commands and c a l c u l a t i o n s f o r a p p l i c a t i o n t o p e r i p h e r a l ou tpu t devices
and the exper imenta l a p p a r a t u s . T^e i n t e r f a c e i s a l s o r e s p o n s i b l e for
synchronis ing the asynchronous units involved i n t h e e x p e r i m e n t a l sys tem.
I n t he p r e s e n t computer system, the i n t e r f a c e h a s t he c e n t r a l r o l e
i n implementing t h e c o r r e l a t i o n method. I t i s t h e i n t e r f a c e which modu
l a t e s the ion beam a p p a r a t u s , and which p l ays t h e command r o l e i n s t o r i n g
c o r r e l a t i o n in format ion e x t r a c t e d from the e x p e r i m e n t a l sys tem. A gene ra l
p i c t u r e of t he c e n t r a l r o l e o f t he i n t e r f a c e i s p r e s e n t e d i n F i g . 17 .
Ove ra l l , t h e i n t e r f a c e r e s i d e s on t h r e e p r i n t e d c i r c u i t boards which
f i t d i r e c t l y i n t o t h e computer and have access t o a l l of t he computer bus
l i n e s i n c l u d i n g t iming s i g n a l s , memory address l i n e s and d a t a l i n e s . The
Bin Time C l c k Board c o n t a i n s a c r y s t a l o s c i l l a t o r and frequency d i v i d i n g
network, a pseudorandom b i n a r y sequence g e n e r a t o r (PHHG), v a r i a b l e length
s h i f t r e g i s t e r delay l i n e s , d e t e c t o r output s e n s i n g d e v i c e , and a p p r o p r i a t e
con t ro l l o g i c .
The Data Break Boprd con ta in s a l l of t he d a t a b r e a k l o g i c , a device
p r i o r i t y network, an i n p u t / o u t p u t t r a n s f e r (IOT) decoding network and a
s h i f t r e g i s t e r s t o r a g e l i n e fo r r e t a i n i n g the de layed PRHG output for
da t a c o r r e l a t i o n . A d d i t i o n a l l y t h i s board con ta in s a PEHG i-equence sample
and hold network connected i n p a r a l l e l wi th m u l t i p l e x e r s used to ga te
Data Computer System
Control >Data Display and Analysis
Modulation Interface
Correlation Experiment
Detection
XBL 748-6924
Fig. 17. The central role of Che computer correlation Interface.
-100-
the memory address lines for storing data addresses during a data break.
The Digital to Analog Conversion Board (DAC) contains two 12 bi t
d ig i ta l to analog converters used to display accumulated transformed data
graphically on an oscilloscope, as well as a separate IOT decoding net
work and control logic.
Overview of Interface Operation
A block diagram of the functions contained on the Clock and Data
Break boards is shown in Fig. 18. The time scale of interface operation
i s provided by the digital clock frequency dividing network, one of whose
outputs is chosen to f i t the required time scale of the experiment. The
clock frequency is used to run a l l the registers contained in the in ter
face including the random sequence generator (PRHG). The PRNG output is
used t.o modulate the ion beam experiment; this output i s also contained in
a variable length digital delay line and stored dynamically in the shift
regis ter storage l ine. When a detector event i s sensed, the delayed code
contained in the storage l ine i s stored in the computer core memory by
the data address method (see "Application of Correlation TOF") through
three sequential data breaks to three 1 K quadrants of the upper 4 K of
the computer's memory. The sequential storage in each of the three
quadrants is directed by the memory quadrant generator.
tn the following sections we wi l l describe in detail the design and
implementation of the electronic circuitry which comprises the interface.
I . Bin Time Clock Board
1. Interface Bin Time Clock (Figure 19)
The computer interface design using a pseudorandom experimental
modulation requires a stable, reproducible, variable rate clock signal
Experimental Modulation
X-TAL -
PRNG
E^
*N
Select
Load IOT
PDP 8/f Processor
Long Delay
MPLX = = n _ Short =
J Delay
™ • Classical * I TOF In (-
M P I - i< L , , „ . I _f\ iCIoch Out j »
MPLX
Select ' Select J r-
Hold Line
IOT Command
Words
Data Break Control
(Priority)
Data Overflow
Detector Output Detector Input Sense
Data
I i Hold Sample and
Memory Quadrant
Code
Multiplex 10 of 30
Memory Address Lines
Address
-•"To Core Memory
XBl. 748-6927 Fig. 18. Correlation Interface block diagram.
lOmHz X- la l
Pulse Shaping Network
IOmHz = O.I/i5ec SN7490|
+5 1/2 jtsec
1/2 /isec
SN7493|
+ 2 +4 +8
+ 16
•I «sec--2 /isec-
- 4 (1B6C-•8 p s e c -
SN 7490|
+ 10
5 jisec
SN7493| + 2 +4 + 8 + 16
l-IO/isec*-
SN74901
+ 10 IQOgsec |
ISN7490!
+ 2 200 usee
•20 ^sec-•40 (isec-
•80 / i sec -
Multiplex Select
— 8 0 -—too-j -200-
I of 16
Multlplexl
SN74I5I x2
Clock Out
XBL 748-6915 F ig . 19. Clackro te d i v i d i n g network,
clock p u l s e w i d t h . ) Crimen noted a re the
-103-
since i t is this clock signal which determines the absolute time scale
for the time domain measurement of the TOF dis t r ibut ion. The basic clock
rate is produced by an X-tron 10 mHz crystal osc i l la tor which is stable
to within 0.001% (10 ppm). This base rate i s divided by a digi tal
dividing network (Fig. 19) . The outputs from the dividing network are
connected to the input of a digi tal multiplexer (Texas Instruments
SN74151). Using the multiplexer, one of the available clock rates is
selected via four data select l ines, which are enabled by use of a
"command word" decoding network (see "Command Word Control and IOT's"
below) which allows programmed control of the desired clock ra te .
The clock ra te and period were measured using a calibrated Tektronix
Type 555 Dual Time Base/Dual Beam Oscilloscope and a pulse generator for
comparison. The ra te was also measured using a frequency counter; the
measured dock rate was equal to that expected) within experimental
error.
2. Pseudorandom Binary Noise Sequence Generator (PENG)
As was described in the theory of the correlation experiment, a
linear shift register with modulo-2 summing feedback i s used for generat-2
ing an m-sequence to be used in experimental modulation. The PENG used
in this case is constructed from two 10 b i t se r ia l in /para l le l out s t a t i c
shift registers (Signetics 8273) (Fig. 20) . To achieve maximal sequence
generation with a 20 b i t shif t register, feedback from stages 3 and 20 3
are employed. As previously noted, the modulo—2 feedback i s achieved
by use of an "exclusive" or gate whose truth table for the present
application i s shown in Fig. 20. The output of stage 1 of the 20 b i t
register is connected to both the input of the d ig i t a l delay line (see
HhT"^ , l n
3 Out
HhT"^ , l n 1 2 3 4 • • • 18 19 20 20 1} W y 1 2 3 4 • • • 18 19 20 1 2 4 • • • 18 19
Exclusive OR 20 Bit S/ln - P/Out Shift Register
\20 3 \ 1 0
1 0 1
0 1 0
Exclusive OR Truth Table
XBL 748-6909
Fiij. 20. PRNG configuration for maximal sequence generation: N - 20 stages.
-105-
helow) and to a coax ia l cable l i n g driver (5113) which dr ive s a coaxial
cable to the ian beam chopping c i r c u i t ( see below) .
Since the PENG s h i f t r e g i s t e r s are run by the Bin Time Clock, the
c lock frequency e s t a b l i s h e s the base frequency for the PRNG output,
thereby determining the band width of the experimental modulation.
Since the a l l - z e r o s t a t e of the s h i f t r e g i s t e r PENG excludes genera
t i o n of the desired m-sequence, the input of the PRNG (Stage 1) i s ORed
with the " I n i t i a l i z e " bus s i g n a l which i s generated each t i n e the com
puter i s turned on. A d d i t i o n a l l y , the clock in , of the PHKG i s a l so
ORed with the " I n i t i a l i z e 1 1 s i g n a l except that the a p p l i c a t i o n o f the pulse
t o the clock input i s delayed by a memos table mul t iv ibrator ("one s h o t " ) .
This c i rcu i t ry insures t h a t each t i n e the power for the i n t e r f a c e i s
turned on, a "1" w i l l be appl ied to the input of the PRHG and strobed
i n t o Stage 1 by the delayed i n i t i a l i z e pu l se ; the i n i t i a l s t a t e of the
PRHG i s always nonzero.
3 . C lass i ca l TOF Capabi l i ty
Although the normal operation of the data a c q u i s i t i o n system w i l l
be in a correlat ion node us ing PRKG output for bcaa s o d u l a t i o n , the
capabi l i ty for operation in a c l a s s i c a l TOF code has been b u i l t into the
i n t e r f a c e . This rode of operat ion allows ca l ibrat ion of the t i c e s c a l e
of the TOF spectrins and provides a Deans of corroborating the r e s u l t s of
corre la t ion TOF oeasur?*ents .
For c l a s s i c a l TOF opera t ion , an external pulse generator (Tektronix
PGS01) i s employed. The pulse width of the generator i s adjusted to g ive
a t o l e r a b l e detector output r a t e whi le maintaining the g r e a t e s t poss ib le
TOF resolut ion (pulse widths of *v2 *.!sec). The pulse r e p e t i t i o n race i s
-106-
adjusted unti l there i s no overlap of individual beam pulses at the
detector {typically 10 kHz). The pulse generator output i s connected
simultaneously to the beam chopping circuit and the input of the digi tal
delay line (via an optical coupler). The output of the PBNG is turned
off using command word I (see below) . Beam pulses then travel through the
ion path of the experimental apparatus as the corresponding digitized
generator pulses travel through the shift registers of the digi ta l delay
line and the sequence storage register (see "Data Break Board" descrip
tion below) . The mode of data storage is identical to that used in the
correlation mode of operation; using the data address method, detection
of an ion at the end of the ion drif t region causes three data breaks to
record the length of the storage registers traversed by the digitized
generator pulse responsible for admitting the ion to the beam path. The
only operational change in data acquisition comes during the process of
transforming the data stored in the core memory. Since there are only
"positive correlations" between detector events and digitized generator
pulses, i t i s unnecessary to subtract the negatively correlated trans
formed data (see "Program Description") . This positive correlation
property is the result of the non-overlaping nature of the ion (and
digital) pulse t ra in .
4. Digital Delay Line
Since the interface wi l l be used to examine the TOF spectrum of
a variety of ion reaction products and may be applied to several appara
tuses with quite different ion flight paths, the mean time of flight
expected may vary from 10 psec to over 100 ysec depending on the ion
product mass and energy and the flight path of the apparatus. I t is
-107-
thus important to have some measure of control over which particular tine
segment of the possible TOF spectrum is to be viewed by the correlator.
For long flight times one could always reduce the Bin Time Clock rate
such that no delay between beam modulation and detector signal would be
required. However, th is would entail a large loss in spectrum resolution
and the measurement of narrow TOF distributions with long fl ight times
would be fruitless (Fig. 21) . By using a delay l ine to store the experi
mental modulation sequence during a long flight time, short duration TOF
distributions with long f l ight times can be examined without a loss of
resolution.
To be of use, a delay l i ne must retain a faithful representation of
the output of the PEHG; otherwise spurious noise i s introduced into the
correlation calculation. For th is reason a shif t reg is te r delay line has
been applied in th i s case. The delay Use i s constructed in two parts
(Fig. 22). One, the "short delay" is composed of two dual 8 b i t se r ia l
in / se r i a l out s t a t i c sh i f t registers (Signetics 8277) hooked In a head
to t a l l configuration (Fig. 22). The output of each 8 b i t register i s
connected to a one of eight multiplexer ("Short Delay") whose output is
selected via three b i t s of the "Delay Command Word" (Command Word II -
see below).
The "long delay" i s constructed from a single hex-32 b i t s t a t i c
shif t register (Fairchild 3349), also hooked in a head to t a i l configura
tion (Fig. 22). The outputs are connected to a second one of eight multi
plexer ("Long Delay") whose output is selected by three separate bi ts of
the delay command word.
-108-
h(t)
0 80 100 usee
Possible "true" TOF spectrum
h(r)
3 . 23 30
T = bin No. Measured correlation function with no delay, clock period = 3 usee
h(r]
_=i~ 30
T = bin No. Measured correlation function with delay - 72 usee, clock rate = lusec
XBL748-6923
Fig. 21. Increased resolution possible using digital delay line.
-109-
TTi
o a! LJ [J =" ^
U\UI uror LJ •II
-110-
All of the delay l ine shif t registers are clocked by the output, of
the Bin Time Clock. Thus the real time delay through any series of
registers i s a direct function of the dock ra t e ; only the number of
clock pulses needed to shif t a pulse sequence through this series of
registers i s constant. To calculate the real time delay, one must
multiply the delay length by the clock period. The tota l delay i s the
sum of the long and short delays. Any delay of from zero bins (clock
pulses) to 224 bins, in steps of 8 bins, i s possible by selection of the
appropriate delay command word co<ie.
The combined use of variable clock period and delay length allows
great f lexibi l i ty in viewing the TOF correlation function. Normally, a
quick law resolution scan using a compar±t±vely large clock period and
no delay serves to determine the mean time of f l ight and i t s approximate
width. Then, by using an appropriate delay and shorter clock period, the
TOF correlation function can be expanded to f i l l the 30 channels of the
correlator in a high resolution scan (assuming a sufficiently long
flight path to establish a 30 usee wide realtime distribution) . In some
cases i t may be desirable to examine only a portion of the TOF distr ibu
tion using very high resolution. Practically, however, this would only
be applicable to high mass ion products if a reasonable length (100-200
cm) drif t path were being employed.
The delay line precision was examined as a function of delay time
and clock rate by direct cross correlation of the PENG output (delay
input) with the delay output using a Hewlett-Packard 3721A Correlator.
Since the period of the autocorrelation function of the PENG output for
20 stage feedback i s longer than any of the possible delay period, the
- I l l -
peak of the measured cross c o r r e l a t i o n function represented a d i r e c t
measure of the delay time. The measured delay was c o n s i s t e n t l y within
22 of that expected, and t y p i c a l l y was within 0.5%. A p i c t u r e of a
t y p i c a l delay cross corre la t ion measurement i s shown i n F i g . 2 3 .
5 . Command Word Control and 10T*s
The operation of the computer in ter face for data a c q u i s i t i o n
requires that the user maintain e x p l i c i t control over the hardware
generated options of the i n t e r f a c e . This control a b i l i t y i s provided by
a software mediated, hardware implemented decoding network by which the
u s e r chooses from a v a r i e t y o f modes of hardware operat ion .
As has been previously mentioned ( s ee "Computer Organizat ion") ,
computer peripherals , inc lud ing the corre lat ion i n t e r f a c e , are contro l led
from the central process ing u n i t of the computer by use of input/output
t rans fer cmmands (IOT). Each per ipheral device i s ass igned one or more
s i x b i t binary i d e n t i f i c a t i o n codes which i t alone r e c o g n i z e s . In o c t a l
n o t a t i o n , IOT commands are of the format 6XXn, where the 6 denotes that
t h i s i s an IOT command, XX i s the s i x b i t device code, and n represents
the par t i cu lar Cone of 8) command t o the peripheral d e v i c e . S ince the
recogni t ion of each device code requires an independent decoding network,
i t I s advantageous to r e s t r i c t each peripheral device to one or two
device codes. However, s i n c e there are at most 8 independent commands
(3 b i t code; 2 3 • 8) which can be executed with a s i n g l e dev ice code, in
us ing I O T ' S alone a hardware des igner i s faced with a t rade -o f f between
the needed programmable hardware f l e x i b i l i t y and the s i z e of the decoding
network needed to Implement i t .
R X ,W
XBB 748-5796
F ig . 23. C r o s s c o r r e l a t i o n measurement for expe r imen ta l m-sequence (de layed a u t o c o r r e l a t i o n ) .
-113-
This tradeoff can be avoided by the use of a "command word" s t ruc-
ture . In this method the information contained in many (up to 12 with
the present computer) b i t s can be transterred for hardware execution by
the use of a single IOT. The informational b i t s originate in the accumu
lator of the computer, having been loaded previously into the accumulator
by a program control sequence. On IOT command, the informational bi ts
which are present on the 12 data lines (on the OMSIBUS) leading from the
accumulator are strobed into a series of one bi t larches (D f l ip flop)
which are contained within the peripheral device. The latches record the
information contained in the computer code and execute the coded commands
by enabling gates controlling the hardware options or by selecting the
inputs of multiplexers. Using a command word structure as many as 96
b i t s of information for hardware control can be transferred using a
single IOT decoding network.
In the present interface, one IOT decoding system (code = 33) is
used. A summary of the IOT commands i s shown in Table I ; 3 IQT's are
used for the control of 3 command words (Cammaad Word I . Delay, Clock),
2 IOT's are used for control of the data overflow fac i l i ty , and two
othere are applied to hardware test ing procedures. Coosand Word I is a
general purpose control word which exclusively executes hardware options
by enabling AHD gates on the interface boards (Table I I ) ; these gates
are primarily used for turning on or off several logical units of the
interface hardware such as the Bin Time Clock., the Data Break fac i l i ty ,
the detector input, or the hardware test f ac i l i t i e s .
Conmand Word II (Delay) i s used to control the length of the digi ta l
delay line (Table I I I ) , while Connand Word I I I (Table IV) allows selection
-114-
TABLE I
INTERFACE BOARDS IOT INSTRUCTION SET
DEVICE CODE = 33
Co le Interface Action
6330 Not used
6331 Load command word 1 from AC
6332 Load delay (command word I I )
6333 (Software sequence e n t r y )
6334 Skip on overflow
6335 I m i t a t e d e t e c t o r p u l s e i n p u t
6336 Load b in time clock (command word I I I )
6337 Reset overflow
COHMAHD WORD I ; LOAD WITH 6 3 3 1
D a t a B i t 0 1 2 3 4 5 6 7 8 9 10 U
Gate
Data Break On
Off
1
0
Clock On
Off
1
0
Overflow On
Off
I
0
EHA Field On
Off
1 0
Classical TOF
Correlation
1 0
Detector On
Off
1 0
not used
Normal operation code: Correlation = 7500
Classical = 7700
-116-
Data Bit 0 1 2
Long Delay
0 bits 0 0 0
32 bits 0 0 1
64 bits 0 1 0
96 bits 0 1 1
128 bits 1 0 0
160 bits 1 0 1
192 bits 1 1 0
Short Delay
U bits
8 bite
16 bits
24 bits
32 bits
All zero out
All ones out
COMMAND WBD II DELAY; LOAD WITH 6332
3 4 5 6-11 not used
Code
0000
1000
2000
3000
4000
5000
6000
0 0 0 0000
0 0 I 0100
0 1 0 0200
0 1 1 0300
1 0 0 0400
1 1 0 0600
1 1 1 0700
Long delay + shore delay « long code + short code = total code =3 total delay (i.e. 64 bits + 8 bits « 2000 + 100 = Z1G0 =; 72 bits) -
- 1 1 7 -
TABIE IV
COMMAHD HQBD I I I BIH TIME QDCX; UOAD HITH 6336
(0 Data Bic
-7 not used) 8 9 10 11
Frequenej Code (101)
Bin time (usee)
2000 a Iz 0 0 0 0 0 .5
1000 1
1 0 0 0 1 1
500 2 0 0 1 0 2
250 3 0 0 1 1 4
200 4 0 1 0 0 5
125 5 0 1 0 1 8
100 6 0 1 1 0 10
50 7 0 ^ 1 1 20
25 10 1 0 0 0 40
12.5 11 1 0 0 1 60
10 12 1 0 1 0 100
5 Q 32 13 1 0 1 1 200
- U B -
of the rate for the Bin Tlae Clock. Both of these command words arc
executed by mult ip lexer s e l e c t i o n from mult ip le inputs to give a s i n g l e
desired output.
6 . Detector Input
Since a l l of the in ter face hardware employs TTL, a l l s i gna l s
cooing in to the i n t e r f a c e oust be d i g i t i z e d to the proper voltage l eve l s
before they can be u t i l i z e d . The ion detectors current ly used in our
laboratory for TOP arc of the e l ec tron c u l t i p l i c r type (Channcltron or
Bendix Magnetic Mul t ip l i er ) which, when coupled with an output pre
ampl i f ier , produce negat ive output pulses approximately one v o l t in
amplitude and SOO nanoseconds in duration. To conform with the TTt l og i c
of the i n t e r f a c e , a comparltor c i r c u i t with a v a r i a b l e discriminator
lower l e v e l and v a r i a b l e width output pulse i s used t o convert the
(0 , - 1 v o l t ) , de t ec tor output s i gna l i n t o a TTL compatible ( 0 , +4 v o l t s )
wave fore ( see below for complete coaparitor d e s c r i p c i o n ) . The coaparitor
output i s connected ay a SOU BHC coble to the input of an o p t i c a l l y
coupled TTL gate (Motorola HOC 1000 or 4825) . The o p t i c a l coupler
e l iminates the p o s s i b i l i t y of external no i se pu l se s overloadin:, the
interface TTL l o g i c causing damage to the hardware.
The output of the o p t i c a l coupler i s used to I n i t i a t e the data break
cycle of the in ter face for s tor ing corre la t ion data in the cocputer's
core memory. (A s i m i l a r o p t i c a l coupling scheme i s employed for inputt ing
pulses from the ex terna l pulse generator when the i n t e r f a c e i s operated
in a c l a s s i c a l TOP mode.)
*Transitor-Transitor Logic Defines l o g i c a l "0" as a vo l tage l e s s than -HJ.8V. and l o g i c a l "l" as a voltage greater than +2.8V.
- lW-
11. Data Break Board
1. 'nic Data Break Hardware
Within the correlation interface, the data break facil ity ful
f i l l * the Itftportont function of transferring correlation data frco the
Interface to the core aeaory of the computer, where It Is stored for
later analysis, the data break sequence is triggered Into action by the
arrival of pulses fros the 1cm detector; once this triggering has been
effected, a rapid series of hardware events takes place In an orderly
ttaaaer with each event being synchronized by the internal ctwsutcr bus
ciBing signals. As previously noted, during a data break data transfer
the functions of the central processor registers are taken over by the
external logic hardware of the interface while the C?U registers arc dis
abled. Since the description of the data break event sequence la intl*
aetely involved with the computer*a hardvart structure, we suggest that
at this point the reader should review the "Coeputer Organization" sec
tion presented earlier.
A acheaatic diagraa of the basic data break hardware i s shown In
Fig. 24. With reference to this figure, we now describe the sequence of
events which cosprlsc a data break transfer.
The data break is initiated when a Break Request latch is triggered
by an Incoalng detector pulse. At on appropriate s asp ling cine, the Hew
Break flip flop is clocked by the Internal Strobe pulse frcn the (kznlbus,
requesting a device priority check, disabling the central processor
Keoory Address register and signaling the CPU that a data break is in
progress,
-120-
r 'm^ ! Urr'i'i i ! !
1 i-CXt
\ , < L
I i-<7
i'^tf '-<•
• O r
;-i
(M Mi
6
Hi
IB
*
iiitirti f7fti<3X ifgt
Kra. T
ni!
' &
T 4L •! a
-m-
The device priority system provides a means for causing the computer
to service peripheral devices requesting a data break according to which
device has been assigned the higher priority. Such a system' is necessi
tated by the fact that often two or more devices may simultaneously
(within a single computer memory cycle of 1.2 psec) request a data break.
In such a ease, one wishes to allow data transfer from the fastest (heace
highest priority) peripheral f irs t (such as a disc). The priority network
of the correlation interface checks, by use of the data lines of the
Omnibus, whether any higher priority device Is also requesting a data
break* If so, the interface must await completion of the data transfer
from the other device before i t s own data break proceeds. As a practical
matter, there are currently no other data breaking devices presently
incorporated in the computer system and the interface wi l l be permitted
to continue i t s requested data break immediately. However, later addition
of a disc or tape f i l e to the system would require the priority system to
be installed in a l l data break devices, so i t has been included in the
present design as a matter of course. The correlation interface has been
assigned a priority of 3 (out of a possible 12; top priority i s 1).
Once the device priority has been established, the CPU Instruction
Register and the Major State Register (which controls read and write
operations) are disabled and the CPU Memory address (CPHA) loading from
the Program Counter i s inhibited. The direction of data transfer (into
the core memory in this case) i s established and the contents of the
Break Memory Address Register of the interface (denoting the core address
to be accessed during the data break - see below) are gated onto the
Memory Address line of the Omnibus (which are also connected to the CPU) .
- 1 2 2 -
Ac th i s point the contents of the object address (on the Keaory Address
l ines ) arc gated onto chc Heaory Data l i n e s , pass through the CPU p a r a l l e l
adders where the contents are incremented by one (" add-to-iaemory"), and
the resu l t returned v i a the Keaary Data and Hcoory Buffer l i n e s to the
object memory address . The net resu l t i s that the contents of the
address contained l a the Break Hfeaory Address Reg i s t er have been incre
mented by one. This completes the task of the o r i g i n a l l y requested data
break. However, in the case of the corre la t ion i n t e r f a c e , we reca l l that
s ince three separate addresses must be incremented to s t o r e the informa
t ion contained in the 30 b i t s of the Modulation sequence , two further
data breaks w i l l be immediately requested and carr ied out .
In r e a l i t y , there are many addit ional gat ing and d i r e c t i o n a l s i g n a l s
which must be generated for the success fu l completion of the data break.
However, they are not conceptually important i n understanding the method
and w i l l not be d i s c u s s e d . The reader i s again referred to the d i s c u s
s ion in the POPS Small Computer Handbook
2 . Generation and Storage of the Break Memory Address
In the descr ip t ion of the corre lat ion method ("Application of
the Correlation Method")* we noted that the c o r r e l a t i o n function i s
accumulated by incrementing three core memory addresses contained in the
delayed PENG output sequence present at the time a detec tor output pulse
arrives at the i n t e r f a c e . The conversion of the PRNG output sequence
in to usable memory addresses i s accomplished in the fo l lowing manner ( see
Fig . 2 5 ) .
The modulation sequence emerges from the d i g i t a l delay l i n e on the
Bin Time Clock Board and i s transferred v i a one l i n e of a 16 l i n e board
Bin Tims Clock Output
' ' " " D J ' T " " a g » "lOS-R. {—» 8Z73 IKIOS.R. ^ | — » | 8273 I» 10 S.R.'' | Holding Lit
Detoctor
J Computer Bus
KBL 7««-69Z8
Fl8 . 25. Generating data break memory addresses .
-124-
interconnect cable Co Che Data Break Board. The sequence i s input to a
shift register storage l ine conprised of three 10 b i t s e r i a l in/parallel
out registers (Signetics 8273) hooked in series and clocked by the Bin
Clock output (also transferred by the board interconnect cable}. The
paral lel output of the storage line is connected to the input of five
he^-latches (Texas Instruments SN74174). Using a monostable multivibrator
(TI SN74123}, each clock pulse i s delayed and then used to strobe the
contents of the storage l ine into the latches after the storage line con
tents have been shifted (sample and hold). (This strobe pulse is in
hibited by the arr ival of a detector pulse unt i l the currently stored
sequence in the latches has been used as the Break Memory Address for the
three resulting data breaks.) The storage l ine i s necessary to main tain
the continuity of the PENG output sequence while data breaks are being
completed.
With each detector output pulse, the three data breaks necessary to
record the 30 b i t s of correlation information use a 10 b i t segment of the
modulation sequence which has been stored in the sample and hold latches.
During each break, 10 b i t s of the sequence are concatenated by a data
multiplexing system with a 2 b i t "quadrant code" which supplies the two
most significant b i t s of the Break Memory Address and hence determines
which 1 K portion of the upper 4 K field of memory the least significant
10 bi ts pertain to (Fig. 26) . The quadrant code also provides the data
multiplexer data selection code necessary to choose which ten address
bi ts (of 30) will be gated onto the Memory Address l ines during each data
break. The Memory Quadrant Generator i s a 2 b i t binary counter (TI SN
7490) which is reset to the f i r s t quadrant (01) by the incoming detector
M M I I M M - » 0 0 0 0 0 0 0 0 0 0 - » I O I O I O I O I O I Storage Line
^ ^ ^ 11 i i i i I | I i 11 o6Tb~o~oooo|ooi o i o| i o i o i o| S D m p
L* ,°Jg S
H o l d
Multiple^,
Concatenate Quadrant Code
Ol . l 0,1 I
Resulting 3 BreaK Memory Addresses 01 I I I I I I I I I 1 , 1 0 0 0 0 0 0 0 0 0 0 0, I I I 0 I 0 I 0 I 0 I 0
t t t Quadrant Stored in Stored in Stored in
in Upper 4K= I000 f l - I777 8 2000 8-2777g 3000 8 -3777 8
XBL748-6912
Fig. 26. A sample of break memory address formation.
-126-
pulse and incremented (to 10 and 11} before each of the two subsequent
data breaks. Thus if the 30 b i t modulation code can be represented by
three 10 b i t numbers, Ni, Nz, Ng, the addresses which wi l l have their
contents Incremented by one during the three data breaks wi l l be OlNi,
10NZ, and IIN3.
We have now completed the connection between the delayed modulation
sequence and the storage of correlation information by the data address
method.
3. Data Overflow
As data i s accumulated through repeated data breaks, eventually
the 12 bi t capacity of the core memory addresses wi l l be exceeded causing
data overflew. The effect of an overflow i s to change the contents of a
memory data address from 7777 e to 0000B since 7777 s + 0001s = 10000e =
0000. This i s a total ly undesirable effect since overflow wi l l be corre
lated with addresses whose address b i t s are representative of sequence
segments which are highly correlated with measured detector pulses.
Preferential overflow and subsequent zeroing of some addresses will cause
distortion of the shape of the transformed TOF correlation distribution
favoring buildup of signal in those channels with smaller net signal
heights.
To avoid this overflow condition, the data break logic i s equipped
with an overflow sense l ine connected to an overflow f l ip flop. During a
data break, when the contents of a data storage address have been incre
mented, the incremented contents are gated back to the Break Memory
Address en the Memory Data l ines ; i t is at this point that a data over
flow i s sensed. When the two most significant bi ts of the Memory Data
-127-
l ines are both in a " l " s t a t e (6000a detector counts in the Break Memory
Address) during a data break., the overflow latch is sec raising a flag
which, by interrupt programming routine, causes the computer to cease
data acquisition and i n i t i a t e che data transformation routines. Since
the contents of the core memory data storage addresses never exceed 6000a
(maximum capacity is 7777a), there i s never any real data overflow which
can occur.
This concludes the description of che Daca Break Board Hardware.
I I I . Hardware Test Fac i l i t i es and Checkout Procedures
To faci l i ta te testing of the interface, several software controlled
test ing faci l i t ies were bu i l t into Che interface. We wi l l describe these
and the testing procedures br ie f ly .
Two o_ the available eight device I0T*s have been dedicated to t e s t
ing procedures. The f i rs t* IOT3, enables the user Co design a software
program for entering a given binary tes t sequence into the d ig i ta l delay
l ine and subsequently into the Break Memory Address, mimicing the function
of the random sequence generator in a known, predetermined manner. This
IOT loads the least significant b i t of the accumulator (Data 11) into the
delay line by gating Daca 11 onto the delay line input and then clocking
the delay line shift registers to enter the data b i t using the I0T3 pulse
delayed by a memos table multivibrator. One need only load the accumu
lator b i t 11 and then apply IOT3 to load each b i t of the desired testing
sequence into the delay l ine reg is te rs . By this method a known sequence
can be generated by software for use as a Break Menjory Address. To employ
this procedure, both the Bin Time Clock and the PBHG output must be de
feated using Command Ward I (Table I I ) .
-128-
Once a test sequence has been entered, the second test IOT, IOT5,
which simulates an incoming detector pulse, is used to cause one or more
data breaks to the known core memory address contained in the software
tes t sequence. Subsequent examination of the contents of th is address
reveals whether the data break system is functioning correctly.
I t should be noted that the connection between Data 11 of the
accumulator and the delay line input was removed after i n i t i a l testing
and the input employed for c lass ical TOF pulse sequence entry. (To re
establish this faci l i ty , the connections E10-7 •* E26-9 and E31-3 -*• E26-10
must be made on the Clock Board.)
Some further test procedures which have been used are as follows:
1. Clear the memory data storage block, defeat the Bin Time Clock
and use an external f i l se generator for repeated data breaks to the three
frozen Break Memory Addresses by simulating detector input. (The three
addresses can be seen on the programmer's console by single stepping the
computer operation). This process allowed estimation of the maximum
detector input rate which can be tolerated by the data break system
(about 100 kHz) and was used to check the overflow fac i l i ty . I0T5 can
also be used in place of the pulse generator for the l a t t e r t e s t .
2. Rather than using the frozen Break Memory Address in the rests
described above, by selecting the proper short delay code (Table I I I ) ,
a l l ones or a l l zeroes can be loaded into the Break Memory Address for
test ing as above.
3. To check both the function of the data break and the accuracy of
the data transformation, the PRNG is allowed to supply random Break
Memory Addresses while the unrelated asynchronous output of an external
-129-
pulse generator i s used to simulate detector output. (I0T5 can also be
used.) Since the "detector output" i s uncorrelated with the "modulation
signal" of the PRNG output, the net transformed correlation function
should be zero everywhere (except for small s t a t i s t i c a l fluctuations), as
was found to be the case.
4. The Classical TOF distribution provides an additional check, on
the operation of the data break system.
All of the above procedures were found helpful for electronic de
bugging of the correlation interface. While constant interface testing
should be unnecessary, periodic checks of the interface functions are
certainly in order.
IV. Board Interconnect Cable
Since signals are generated on each of the two main interface boards
which are required for use on the companion board, a 16 l ine interconnect
cable i s used to transfer signals between the two boards. A l i s t of
these signals is shown in Table V.
The potential user i s cautioned that both of the two main boards
must be emplaced in the computer bus and the interconnect cable must be
connected between the two i f either is to be put into the bus. Failure
to follow this rule w i l l cause destruction of core memory software and
generally will make the computer nonfunctional. I t i s also quite impor
tant to ensure the proper connection of the interconnect cable on both
ends, or damage to the interface may result .
V. D/A Converter Board
The Digital to Analog Converter Board i s used to display accumulated
transformed data. Two 12 b i t DAC'B (11 signal b i t s + sign b i t ; Hybrid
INTERCONNECT CABLE (CLOCK BOARD *» DATA BREAK BOARD)
ElO <-* C7
Pin Line
1 Clock output 9 NC
2 Delayed PENG sequence 10 NC
3 NC 11 IOT 6 [10-7]
4 NC 12 Hy device [14-3]
5 IOT 1 [10-2] 13 EHA f i e l d [E19-10]
6 IOT 2 [10-3] 14 Break on/off [E14-2] [E19-7]
7 IOT 3 [10 -4 ] 15 Overflow on/off
8 NC 16 Detector on/off [E26-3]
-131-
Syscems DAC372-11 with 0.0252 l ineari ty, 2 volt/usec slew rate, and 5 usee
maximum settling time) were chosen which were sufficiently fast and
reasonably inexpensive. One DAC i s used for converting the X-axis of the
display (TOF distribution Bin number) and the other for converting the
Y-axis (relative correlation function height). The conversion of each
axis i s accomplished by clearing the accumulator of the CPU and giving
an appropriate IOT causing the proper DAC to be loaded from the data
l i nes . The board has i t s own device codes (05, 06; see Table VI) and
IOT decoding networks. The display of data i s controlled by a software
subroutine of the main program monitor (see "Computer Program1* below)
which automatically scales the X-axis to allow 30 TOF channels to span
the entire voltage range of the X-axis DAC. The result ing analog X-T
plot of the data i s displayed on a Tektronix 545B oscilloscope.
VI. Voltage Comparator
As noted above, a voltage comparator circuit i s employed to convert
the preamplified electron multiplier detector signal into a TTL-Campatible
Have form. This c i rcui t (see Fig. 27) employs a voltage comparitor
(National Semiconductor LH306) to determine when the output voltage of
the ion detector circuit becomes more negative than a variable reference
threshold voltage which i s controlled by a potentiometer. The comparator
c i rcui t has the abil i ty to use either positive or negative going pulses
as i t s input.
When the comparator i s turned on by the magnitude of the detector
output voltage surpassing that of the reference threshold, a variable
*0riginally designed by the D.C. Berkeley Dept. of Chemistry Electronics Shop.
D/A CQHVEBIER BOARD IOT INSTRUCTION SET
DEVICE CODES = 05, 06
Code Action
6051 Clear X
6053 Clear X and load X
6054 Intensify X
6057 Clear X, load X and intensify
6061 Clear Y
6063 Clear Y and load Y
6064 Intensify Y
6067 Clear Y, load Y and intensify
HD 11 -+ load registers
HD 10 -*- enable data lines
HD 9 -*- intensify sequence
| Comporotor
*&: - A W 1 • • S
• Q - P OUTPUT
All Bmtlori l/4'W All Poll IT , 2W
1H —6\p-o-'o— LGJ—i 1/2 A On
XBL74B-69BI Fig . 27. Voltage comparator c i r c u i t for reversing detector output p o l a r i t y .
-134-
width output pulae i s generated by a monostable multivibrator (Tl SN74121) .
The width of the output pulse i s controlled by a potentiometer which
varies the RC time constant of the multivibrator. Finally, the output
pulse is driven from the comparator circuit to the computer interface on
a BUG cable by a Dual Differential Line Driver (Rational Semiconductor
DM 8830).
VII. Ian Beam Chopping
In ion beam TOF experiments, a central problem i s the construction
of an adequate beam chopping mechanism. In this section we wi l l define
the chopping problem and describe the simple electronic circuitry which
ve have applied to the correlation TOF system for beam modulation.
There are two types of problems associated with ion beam chopping:
the effects of modulation bandwidth on signal resolution and the e lec
tronic problem of implementing wide bandwidth modulation of an ion beam
using large amplitude voltages. The f i r s t problem i s more subtle and
arises from the intimate connection between modulation and detection.
The second problem i s an obvious one whose basis is technological. To
gether they require careful design of a beam chopping system to ensure
successful measurement.
In part, the difficulty in chopping an ion beam ar ises from the
large ion velocities which are typically found in ion beam experiments.
While neutral molecular beam projectiles typically have thermal velocities
of " lO1* cm/sec, slow enough to permit mechanical chopping, the pro
jec t i l es in an ion beam have velocities of the order of 10 cm/sec. This
higher velocity makes mechanical chopping of ion beams impossible. How
ever, since ions are charged par t ic les , e lectrostat ic deflection methods
-135-
are readily applicable to an ion beam system.
in an electrostat ic chopping system, one or more metal deflecting
plates (grids) are positioned paral le l to the path of the ion beam in
close proximity to i t . An electronically generated chopping signal is
used to apply voltages to the gr ids . Depending on the voltage applied
to the grids, the beam i s e i ther allowed to pass into the TOF apparatus
undeflected (beam "on") or deflected away from the apparatus so that no
ions reach the detector. Thus the problems associated with, actual beam
chopping are basically e lectronic .
Even with the fast electronic components available currently, the
problems associated with chopping an ion beam are nontr iv ia l . As has been
previously noted, a TOF experiment has i t s resolution limited by the
width and precision with which pulses of ions are admitted to the appa
ra tus . With electrostat ic chopping, the maximum chopping ra te i s deter
mined by several experimental variables: the ion mass, the deflection
required to remove ions from the beam path, the ion velocity, the r ise
time of the deflecting pulses and the width of the chopping region. All
of these variables bear on the problem of adequate deflection while ion
velocity and the width of the chopping region are responsible for signal
resolution.
The signal resolution question can be summarized in the following
way: for any TOF experiment there are two natural time periods whose
diaenslonless rat io serves to scale the experiment. These are the over
a l l time of flight and the width of the TOF distr ibution, denoted by xTOF a n d T,respectively. Of course, each of these i s a function of the
length of the flight path; however, for any given experiment the ra t io ,
-136-
a = T
w / T Topt " i l l be invariant . Typically this ra t io i s less than Q.1D,
i . e . Che width of the distr ibution i s less than 102 of the tota l flight
time. This fact by i t s e l f presents no problem. However* as we wil l
discuss below, there exis ts a fundamental limitation on the modulation
bandwidth which can be applied with a beam chopper. Since the modulation
bandwidth fixes the time resolution with which the TOP signal i s viewed,
to achieve a given resolution a severe limitation i s placed on the mini
mum flight path that must be used for experiments.
More explicitly, consider that one wishes to view a TOF distribution
with a resolution E. R I s determined by the number of discrete time
channels which span the TOF distribution as i t i s measured at the detector.
If the bandwidth of the source modulation i s such that each channel i s of
width T J , then
Recalling that x y = a r T 0 F .
n = " * » , ^ R X o l ° r T ro F = —
where again, a is the dimension less time scale which fixes the relative
width of the TOF distribution in terms of the total time of flight.
A typical limit an the modulation band width is 1 megahertz so that
the minimum T , = 1 usee. To see how this poses a restriction on the mo J
time of flight (path length), l e t ' s suppose that we desire a resolution
of 20 ( i . e . 20 points of the calculated correlation function will define
the shape of the TOF distr ibution) and that a has the value 0.05, not an
unrealist ic value. Then
-137-
. (20) (1 Usee? M A 0 ( J v n c t
i U i r 0 .05
For a typ ica l ion of mass 30 a t an energy of 5eV, the v e l o c i t y i s approxi
mately 5 x 10 5 cm/sec.
Therefore, to achieve a re so lu t ion of 20 for such an i on i n a T0F
experiment a 200 cm f l i g h t path would be required. This i s a somewhat
l arge f igure; i t becomes apparent how important the l i m i t a t i o n on modu-
l a t i n bandwidth i s .
This l imi ta t ion on bandwidth a r i s e s i n the fa l l owing manner: the
time width of an ion beam p u l s e cannot be made shor ter than the time i t
takes for an ion of nrfTHimtm v e l o c i t y ( for whatever experiment ±& at band)
t o traverse the chopping reg ion . As ions pass through the chopping
reg ion, only those d e f l e c t e d l e s s than a m n-fumm amount (d i scussed below)
w i l l pass unhindered i n t o t h e TOF analys i s system. I f the pu l se r e p e t i
t i o n rate for modulation were l arge enough so tha t s e v e r a l d e f l e c t i n g
pul ses were applied to the d e f l e c t i n g grids during the time each ion
traversed the grid reg ion, every ion would be p a r t i a l l y d e f l e c t e d as i t
passed through. (Here ve are assuming the use of c o r r e l a t i o n modulation
which cons i s t s of a rapid t r a i n of modulating p u l s e s . For c l a s s i c a l
modulation the analogous statement concerning ion transmiss ion i s that
the de f l e c t i on vol tage i s never turned off long enough t o a l low ions to
pass through the chopper.)
For correlat ion modulation, only nh t>^ ions which e n t e r the d e f l e c
t i o n region at a time when a s e r i e s of consecutive "bean on" pulses were
applied to the chopper (a run of " l ' s " in the chopping sequence) would be
- 1 3 8 -
al lowed t o pass Chrough unhindered. Depending on Che ac tua l modulation
bandwidth, a l l s ing l e "beam on" pu l se s which were contained i n runs of
one or two (or more) would be i n e f f e c t i v e for causing i o n s to enter the
TOF ana lys i s system; the ne t r e s u l t i s that no matter how large a modu
l a t i o n bandwidth was applied to the beam chopper, the e f f e c t i v e modula
t i o n bandwidth would be H a l t e d by the ion passage time Chrough the
chopper. (The problem of Ions pass ing Chrough Che beam chopper i s some
what reminiscent to the fo l lowing phys ics problem: An e lectromagnet ic
wave of a s i n g l e frequency (photon; i s propagating chrough s p a c e . Being
af a s i n g l e frequency, of course i t s pos i t ion i s completely indeterminate.
I f Che wave passes chrough an open door and you proceed t o c l o s e the door,
which s ide i s the photon on?)
A separate problem which must be overcome i n ion beam chopping i s
tha t of achieving f a s t r i se t ime chopping pulses s u f f i c i e n t to provide a
good approximation to a square wave modulation s i gna l us ing short (0 .5 cm)
chopping g r i d s . A schematic diagram def ining the system i s shown In
F i g . 28 . A pair of d e f l e c t i n g gr ids separated by a width d and of length
£ are placed in a region of t o t a l length L. A d e f l e c t i n g vo l tage of
magnitude ±V/2 i s applied to the grids to turn Che beam o f f . He assume
here that the ion beam i s of n e g l i g i b l e width, that a l l beam ions are
moving p a r a l l e l to the beam a x i s , and Chat a p o t e n t i a l of V = 0 i s
appl ied co the grids when the beam i s turned "on." The e x i t of the
chopping region i s defined by an aperture of diameter b; a co l l imated ion
beam enters Che chopping region from Che l e f t and i n the absence of de
f l e c t i n g vo l tages , passes chrough the e x i t aperture and i n t o the TOF
a n a l y s i s region. When che d e f l e c t i n g vo l tage i s appl ied , a uniform
V) E
fe lys 0>
1 - o k to
(O I
09 T
i ^ (HJ o
01 o
-140-
transverse electr ic f ield of strength V/d is present between the deflect
ing pla tes . For simplicity, we wi l l assume that the most efficient space
u t i l iza t ion (A = L) i s being employed.
The object of our investigation i s now to determine the voltage
necessary to be applied to the grids to cause sufficient ion deflection.
An ion of mass m, longitudinal velocity u and charge e entering the
chopping region will traverse that region in a time r = £/u. Using
Newtonfs laws, the to ta l deflection caused by the ion when the grids are
charged wi l l be
Ax = 1/2 aj^t2 = 1/2 e V/d (Z/u)Z
For successful deflection Ax > b/2 so the required voltage i s
V ^ ^ <u/JL)2
e 2
Mote the 2- term in the denominator. Since we wish to make the chopping
region as short as possible* i t i s easy to see how the voltage required
for deflection can increase rapidly as 2. i s diminished.
The above discussion has assumed that the deflecting voltage has
been applied before the ion enters the chopping region. For a more
general analysis we assume the modulating pulse has the r is ing shape
shown in Fig. 29. The to ta l grid voltage, V, is a l inear function of
time until i t reaches i t s "steady state" value, V :
V = ktV 0<t:£,t ; kt = 1 (linear approx.) o o o
o o ^ 1
where t . is the time the ion e i ther exits from the region or i s deflected
XBL 748-6911
Fig. 29. Voltage character of the deflection pulse.
-142-
onto the plate of the collimator. If the deflecting pulse is initiated
at t = o when the ion has already traversed a distance e into the de
flecting region there are two possible cases to consider:
{ 1 , i t s ! < t 0 : ta . !/« . Jk*,)3
u o V u /
(2) i»=a . > M : A. - 1/4 a t 2 + 1/2 a ( & ! > - t ) * u o o o \ u o /
eV where a = —j- and the results come from simply integrating F = ma. A
similar se t of equations wi l l hold for the case of an ion being present
in the chopping region when the deflecting pulse is turned off. These
expressions allow the calculation of the maximum distance, E., which the
ion can traverse before the deflecting pulse is applied and s t i l l be
deflected out of the beam path suff icient ly. In practice there wi l l
always be some ions in the chopping region which wil l not be deflected
suff icient ly. These ions wil l be negligible in number (compared to the
tota l flux in a beam pulse) provided that the deflecting voltage i s suf
ficiently large and if the risetime of the chopping pulse is small
enough.
I t has been recently pointed out that such sampling of a continuous
ion source may lead to distortions in the TOF spectrum. We have noted
some broadening of the TOF spectrum when a single deflection grid i s used.
In this case the potential along the ion path becomes nonzero when the
deflecting voltage is applied, allowing both fringing field effects and
risetime and falltime accelerating effects to affect the TOF spectrum.
The use of a symmetrical grid system removes the possibility of such
-143-
effects.
For our current TOF system, we have determined that for a 1 mega
hertz chapping ra te , a deflection voltage of ±30V wil l be sufficient to
deflect ions with a 0.5 cm grid length. The application of a 30 volt
signal at 1 megahertz leads to restr ict ions on the RC time constant for
the system. Vfe have achieved a 100 nanosecond risetime using the chopping
circuit described below by mounting the chopper as close to the chopping
grids (M. foot) as possible in order to cut down stray capacitance.
We note that there are two methods by which chopping might be im
proved. One i s to reduce the space between the chopping grids as ve i l
as the diameter of the ex i t aperture. This, however, w i l l be limited by
the increasing capacitance of the paral lel grids as they are moved
closer, and by the loss of ion flux due to the smaller aperture size.
The other means by which chopping might be improved would involve de
celeration of the ions after they have passed through the target in ter
action region of the TOF analysis system. This has the effect of in
creasing the effective f l ight time and hence the re la t ive resolution
which can be achieved with a given beam chopping modulation bandwidth.
The Present Beam Chopping System
The beam chopping system which we are currently using i s shown in
Fig. 30. The circuit i s essentially composed of two transistors which
control the grid voltages. When the transistors are turned off (beam
off) the grids float a t ±30 vol ts . When the t ransis tors are turned on,
current passes through the emitters, causing a voltage drop across the
voltage adjustment potentiometers. Thus by adjusting the potentiometers,
the grid voltages are selected to pass a "layftti"™ amount of the ion beam
. + 30V
+5V J * .
PRNG Sequence
OM 6830 Line Driver/
Receiver
Ik i i 2W
SN7545IP -+V/2 --V/2
SN7440
I H V) wv
30V
F i g . 30. Beam chopping c i r c u i t : .
XBL748-69I9
-145-
through the deflection region when the beam i s turned on.
The input of the chopping system can be chosen from two modes. In
the "adjust" mode, the input to the DM8830 l ine receiver i s held high so
that the transistors are turned on and the potentiometers can be adjusted
for maximum detector s ignal . In the "run" mode, the l ine receiver input
i s switched so that the output of the random noise generator i s applied
to the chopping c i r cu i t , turning the beam on and off randomly. The
chopper i s mounted as close to the beam apparatus as i s possible to r e
duce the capacitance of the input to the grids (<100 pf) to reduce the RC
tine constant of the grid c i rcu i t .
Because of l imitations on the interface e lect ronics , a maximum modu
lation band width of 1 mHz has been used with th i s system. For the Sen
length of the deflecting grids this i s close to the maximum chopping
rate which can be tolerated for most ions. We have determined empirically
that pulse widths of less than 1/2 Usee lead to severe attenuation of the
transmitted ion signal , so that the 1 rfig limitation i s pretty much
applicable tc each of the components within the system.
the chopping system has worked more than adequately at the lHHz
bandwidth for both classical and correlation TOP measurements. Ve note
that the chopping c i rcui t in i t s final form was designed by Hr. Paul Salz
of Lawrence Berkeley Laboratory. I t i s remarkably effective considering
i t s simplicity.
This concludes our discussion of the conceptual and electronic
methods which together comprise lite correlation TOF interfacing system.
He have shown how the use of an electronically generated modulation
system coupled with a direct memory address data storage system can be
-146-
used to extract the correlation information which describes a TOP dis
tribution.
In the following section we will describe the computer program which
controls this experimental system and which is used for data reduction.
Storage Register
Correlator Scalars Gates
XBL 748-6913
Fig. 12. Crosscorrelatlon with gated scalars.
-148-
from a peripheral device causes program control to be transferred to a
service routine appropriate to the particular device. A sample skip
chain program is shown in Fig. 31.
The keyboard monitor i s the primary control fac i l i ty for the com
puter system. This monitor i s a keyboard service routine which responds
to the ASR33 Teletype or the keyboard of a Tektronix 4010 Display Ter
minal. When an alphabetic key on either keyboard i s struck, the service
routine determines which l e t t e r was sent from the peripheral and searches
through an. alphabetically coded table of subroutine addresses. Once the
alphabetically coded address i s found, the computer jumps to the s ta r t
of the corresponding subroutine. With this method, as many as 26 inde
pendent entry points into system monitor subroutines can be accessed at
any time when the interrupt system of the computer i s enabled. To add a
new entry point for a subroutine, the user has only to place the sub
routine's starting address in the coded table position corresponding to
the (previously unused) desired code l e t t e r . The keyboard monitor re
jec t s a l l numerical and punctuation characters by typing a "?" and re
turning to a wait loop where program control normally res ides . The same
rejection procedure i s also applied to unused alphabetic codes.
1 1 . The Operational Subroutines
We will now describe the subroutines which actually control the com
puter interface and data acquisition. Each i s accessed by a separate
alphabetic code.
An important "subroutine" which i s used i s the Octal Debugging
Technique (ODT) program which i s a standard DEC program (access code = A) .
This program allows communication with and alteration of any other source
-149-
Figure 31. A skip chain
Location Command
0000
0001
0002
0003
0004
0005
0006
0007
0010
0011
Turn off interrupt
Skip if TTY flag Bet
Skip (unconditionally)
Jump to TYZ service routine
Skip i£ overflow flag set
Skip
jump to overflow service routine
Skip if printer flag set Skip
Jump to printer service routine
-ISO-
program in the lower 4 K field of memory. I t i s used in the system
monitor because i t f ac i l i t a t e s program statement modification (changing
the contents of addresses which contain other programs) . This statement
modification is used for inserting different command word options (see
"Interface Description")* for entering new subroutines and modifying them.
ODT also contains a braakpoiat faci l i ty which i s useful for debugging new
subroutines -
The "Start" subroutine (access code = S) i s used for interface
ini t ia l izat ion and to clear the date acquisition portion of the core
memory (2000a-7777e of the upper 4 K f ie ld) . This routine resets a l l
interface command words to zero and clears a l l interrupt flags. I t zeroes
the data addresses in the upper 4 K field of core memory and then sequen
t ia l ly loads each of the three command word codes in to the accumulator
and strobes them into the interface latches using the proper IOT's. The
interrupt facil i ty i s enabled, the data break system i s turned on to
in i t i a te data acquisition and program command i s then transferred to the
keyboard monitor wait loop.
The "Classical TOF" subroutine (access code = B) i s used when a
classical TOF mode of t»pe>-Stion i s desired. This routine al ters the
command word I code to enable classical TOF operation and makes a minor
change in the data transformation routine (see below) by program address
modification. I t then jumps to the "s tar t" subroutine which carries on
as before, except that a different command word I code i s loaded.
*The breakpoint faci l i ty allows the user to run a program up to any predetermined internal point (breakpoint) at which t ine program control i s returned to ODT for program analysis and modification.
-151-
The "Correlation TOF" subroutine (access code * C) i s used for corre
lation 70^ measurements. As with the classical mode* th i s routine modi
fies the Command Word I code and the data transformation subroutine and
then enters the "s tar t" procedure.
The "Data Transformation" routine (access code = U) i s exceedingly
important, as i t hal ts further data acquisition and extracts the corre
la t ion function information from the data stored in the "data addresses"
of the upper 4 K of core. Since this routine i s fundamental to the com
puter correlation method, we w i l l describe i t i s some d e t a i l .
We f i r s t recal l that the correlation information is stored within
the configuration of each address and that the contents of each address
merely denotes the number of times that address code was stored in the
Break Memory Address Hegister a t the time a detector event occurred.
What we wish to compute i s the t o t a l number of times a par t icu lar b i t
was equal to " 1 " during a detector event; this corresponds to a positive
correlation between a one being in that b i t position and a detector event
occurring. Similarly, the number of times a b i t was "0" a t the time of
a detector event provides the number of negative correlation between the
b i t position and detector events. The net value of the correlation
function associated with any b i t position i s the number of positive cor
relat ions minus the number of negative correlations.
Since the data i s stored as three 10 b i t sequence representing 30
b i t s of the correlation function, we wi l l require 30 double precision
signal {+ correlation) accumulators and 30 d?ub..e precision background
(- correlation) accumulators. Since the information was stored in 10 b i t
segments! one 1 K portion of the uppermost 3 K of the core memory i s
-152-
transformed at a time, leading to accumulation of signal and background
in 20 different signal and noise accululators at once (10 signal , 10
background).
The accumulation of signal and background i s accomplished by using a
single masking bi t ("1") in a 10 bi t binary mask in conjunction with the
logical AND function (code 0nnn) of the computer. To s t a r t the transfor
mation, the f i r s t address of the lowest 1 K section of data addresses
(2000a) i s generated. The masking b i t i s placed in the most significant
b i t position of the 10 b i t mask (corresponding to the third most s igni f i
cant b i t of the address—the f i r s t two b i t s being the quadrant code).
The address code and the mask are then AHDed together. If the third b i t
of" the address was 1, the result ing number lef t In the accumulator wil l
be nonzero; otherwise the resu l t wil l be zero. Depending an this resul t ,
the contents are added to e i ther the f i r s t signal or f i r s t background
accumulator (see Fig. 31A).
Hext, the masking b i t I s shifted right one place and the next b i t
of the address (fourth most significant) i s tested In the same manner,
the result being stored (added) to either signal or background accumu
lator number 2. The process then continues unt i l a l l 10 b i t s of interest
in the address have been tested and the contents of that address have
been added to exactly 10 signal or noise accumulators depending on the
s ta te of the bi ts of the address. Then the address i s incremented and
the process i s repeated s ta r t ing with the masking b i t in the third s ig
nificant bi t of the address. The same 20 signal and bsjcground accumu
lators are used.
-153-
Figure 31A. Masking addresses for data transformation
Example: A 4 Bit address, 0010 has contents = 0042
Address: 0010 •» 0010 •* 0010 * 0010
Mask: 0 1 0 0 0 © 0 1 0 0 00010 © 0 0 0 1
Resu l t : 0000 0000 0010 0000
I i 1 i Add 42 Co background accum, #1
Add 42 Co background accum, #2
Add 42 Co s i g n a l accum #3
Add 42 to background accum #4
Test address 0010 next.
-154-
When the f i r s t 2000a (2000-3777) addresses have been transformed, a
second group of 10 signal and 10 background accumulators are then used to
transform the second 2000s (4000-5777) addresses, and a third set i s then
used for addresses 6000-7777. The overall net resul t i s that the contents
of each of the 3 K addresses have been added to 10 signal or background
accumulators depending on the particular configuration of the bi ts of
each address.
Once the transform i s complete, the contents of each background
accumulator are subtracted from the contents of the companion signal
accumulator, and the resul t i s stored in the signal accumulator. Next a
display setup routine compresses the most significant portion of the 24
b i t signal accumulators into a 12 b i t format and stores the
result in a 36 a address display buffer. (This action scales the T «?Hp
for the display.) When th i s has been completed, the program clears the
data acquisition section of the core memory, reloads the proper command
word codes, and resumes taking data via the data break system.
The above discussion re la tes to the transformation of correlation
data. In the case of c lass ical TOF operation, only posit ive correlations
between address bi ts and detector events is possible. This is the result
of a slow repetition rate which unambiguously associates each detector
event with the modulation pulse responsible for i t s genesis. Since there
are no negative correlations, background accumulators are not used in
transforming classical TOF data; the formated signal accumulator contents
are rather displayed di rec t ly .
The "Display" subroutine (access code = D) is used to display trans
formed data on a Tektronix Type 545B oscilloscope using the D/A Board
-155-
(see "Interface Description"). The routine automatically scales the X
axis of the display so that the 36 a addresses of the display buffer will
span the entire range of the X axis D/A converter. The routine then
sequentially loads the X and Y D/A converters using the computer's accu
mulator and intensifies each display point. This process i s repetitively
cycled so that the display i s maintained even on a non-storage osci l lo
scope until the routine is interrupted by a keyboard command or a data
overflow flag. The display i s of the form of a histogram whose height i s
the value of the correlation function.
Data storage was i n i t i a l l y achieved by taking a Polaroid picture of
the displayed data. However, a l l future data storage wi l l be in the form
of punched paper tape which can be used to transmit data to a CDC 6600
computer over a telephone l ine for further data analysis.
I I I . Data Overflow Service
As we noted in the "Interface Description," the correlation in te r
face i s equipped with a data overflow facili ty which pulls down the com
puter interrupt bus line when the data addresses have been f i l led suffi
cient ly. A data overflow interrupt will be serviced by checking the
interrupt skip chain of the computer program and jumping to a data over
flow service routine.
This routine immediately turns off the data break system, turns off
the computer's interrupt fac i l i ty and jumps to the data transormation
subroutine. The use of the overflow system thus allows repeated f i l l ing
of the memory with raw data followed by automatic transformation of the
data. The only restr ict ion on the amount of data accumulated i s the
capacity of the double precision sigual accumulators which store the
-156-
accuimilated transformed data.
In summary, the system monitor pro"ides a versati le means of con
t ro l l ing tho functions of the correlation interface and of accumulating
and transforming data. In the in teres t of saving core memory for storage,
the monitor has been kept comparatively simple. However, i t wi l l be easy
to add new subroutine blocks in the future if additional programming
functions are deemed necessary.
-157 -
EXPERIMEHTAL WEASUHEMEHTS OSIHG THE TOF COEBELATOR
In order to demonstrate the appl icat ion of the TOF corre la t ion
system, we have measured the v e l o c i t y d i s t r i b u t i o n s of s e v e r a l ion beam
s p e c i e s . Although there i s no e x i s t i n g beam apparatus i n our laboratory
with a s u f f i c i e n t l y long i o n d r i f t path for TOF experiments , these low
reso lut ion measurements were made to demonstrate the operat ion of the
correlator for viewing ion velocity distributions.
The apparatus employed (which was constructed by James Fair) i s
similar to the one described in Chapter IV. An electron bombardment ion
source i s used to generate an ion beam which i s then momentum selected
with a sector electromagnet. Two beam deflection plates normally used
for beam alignment were connected to the ion beam chopper in a syanetric
(±) voltage configuration. Ion scattering takes place in a fixed
scattering cel l mounted Immediately forward of the beam chopping region.
(Bo scattering gas was employed since measurements of primary beam
velocity distributions were made.) Product ions are mass selected using
a radio frequency quadrupole mass f i l ter . In normal operation of the
apparatus in a bandpass mode, a Wien f i l ter (crossed e lectric and mag
netic fields) i s employed for velocity analysis of the mass selected
products. During TOF experiments, the Uien f i l ter was disabled so that
ions of al l velocities were transmitted to the detector, a Bendix mag
netic electron multiplier.
The apparatus, including the detector train, i s in a linear configu
ration appropriate for use in TOF measurements. The total ion flight
distance between chopping region and detector was estimated to be 40 cm.
-158-
To measure the effective path length of the apparatus (taking into
account the voltage distr ibution along the f l ight path due to focusing
elements), a 10 eV beam of N was observed by both classical and correla
tion TOF methods. The measurement confirmed the approximate figure of
AO cm for effective f l ight path and both TOP methods measured similar
flight times (30 ysec) and TOF distribution widths (2 usee). Since the
mass of N is comparatively small, no analysis of the beam velocity d i s
tribution was possible (short flight path + fast ion -+ low resolution) .
To study the velocity distribution of a primary ion beam, an H2 beam
approximately 12 eV in energy was employed. Correlation TOF spectra
were measured and compared with the velocity distr ibution measured by an
accurate retarding potent ial analysis. Measurement of an entire N,
spectrum required only 20 seconds. When the correlation spectra were
scaled to account for beam intensity fluctuations, the points of each
neasured spectrum were consistently reproducible within a 10% range,
although most spectrum points fe l l within a 5% range of the mean intensity
measured for each TOF channel.
The shape of the TOF spectrum was quite similar to that measured by
retarding potential analysis (Fig. 32) . For purposes of comparison, the
velocity distribution measured with the retarding potential were con
verted to a TOF spectrum by consideration of the potential distribution
along the ion f l ight path and integration of the to ta l time of flight
(Fig. 32a). The TOF measurement had a FWHM width of 2.5 psec while the
retarding potential measurement corresponded to a FWHM of 1.6 usee. The
low resolution of the TOF spectrum (T_-_/T , , _, <= A) and the flat-v TOF modulation ness of the correlation peak suggest that the additicnal width of the
Ol£_L 44 45 46 47 48 49 SO
Flight Time (usee) XBL 749-7310
Fig. 32. H„ velocity distributions measured by retarding potential analysis (A) and TOF correlation (lu sec channel width) (B).
-160-
TOF measurement can be at tr ibuted to counting of ions a t the peak of the
velocity distribution by more than one TOP channel (the peak velocity
l i e s between two channels so that each accounts for half of the peak
in tensi ty) . This results in an apparent flattening (and increased FHHM
dimension) of the velocity dis t r ibut ion.
To overcome the resolution problem associated with short ion drif t
path, a measurement of the TOF spectrum of Kr was made. Krypton gas
contains several naturally occurring isotopes: Kr 8 2 (112), Kr B l t (572),
and Kr B S (17Z). Hhile formation and momentum analysis of a Rr besm wil l
cause distortion of these re la t ive isatopic abundances from those of
natural krypton, i t was expected that due to the large mass of Rr
(t*84 amu) compared to the isotopic mass differences (2 ami) some of each
isotope would be transmitted by both the momentum analyzer and quadrupole
mass f i l t e r . Measurement of the Rr velocity distr ibution should thus
reveal three mass peaks in the form of one major peak bracketed by two
s a t e l l i t e s .
As with H-, several spectra of a 10 eV Rr beam were measured and
the results averaged (again the spectrum shape was consistent) . A com
plete spectrum required 20-30 seconds to acctmn ""ate. The resul ts are
shown in Fig. 33. There i s clear resolution of the three mass peaks
(beam intensity was maximized at a QPHS sett ing of 84) . The intensi t ies
of the peaks are approximately equal to the expected isotopic abundance,
although the mass 86 peak was both somewhat smaller than expected and
positioned closer to the mass 84 peak than expected.
Hhile i t i s not passible to make any definitive statement about the
efficacy of the computer correlation system on the basis of these resul ts ,
6S*
o o
ro
3
Kr + Relative Intensity
T r T 1 1 1-
-162-
they do demonstrate that the correlation method can be applied to an ion
beam system. In large par t , the need for an adequate f l ight path
(>100 cm) to increase resolution places a severe constraint on measure
ments uhich can be made with the apparatus in i t s present form. In the
near future, the flight path of the apparatus wi l l be enlarged with a
d r i f t tube and AC quadrupole lens system. After this modification, i t
wi l l be feasible to study the TOF spectra of ionic products of ion-
molecule reactions in greater de ta i l and provide a clearer indication
of the capabilities of the correlation system.
-163-
REPEBEHCES FOB CHAPTER III
1. Small Computer Handbook. Digital Equipment Corporation. Haynard,
Mass. 1972.
2. H. Davles. Control. June 1986, p. 302.
3. G. A. Korn. Bandog Process Simulation and Measurement, HeGraw Hill,
1966.
4. E. Soucek. Minicomputers In Data Processing and Simulation. Wiley
Intersdence, Hew York, 1972
5. H. A. DiValentin and J. E. Dove. Int. J. Haas Spec. Ion Physics 11,
359 (1973).
6. Programming Languages, Vol. II. Digital Equipment Corporation.
Haynard, Mass., 1972.
-56*-
REACTTON OF CO* WITH H- ISOTOPES
The second s e c t i o n of t h i s t h e s i s dea l s w i t h expe r imen ta l e l u c i d a
t i o n of the r e a c t i o n s of CO- i o n s wi th t he i so toye ; ; of H_, p r i m a r i l y D„.
This system wi th f ive atoms and 17 va lence e l e c t r o n s i s somewhat more
complicated than t h o s e p r e v i o u s l y s t u d i e d ; hence i t p r o v i d e s i n s i g h t
i n t o how mult iatom complexes might be v i s u a l i z e d and how molecular
o r b i t a l c o r r e l a t i o n diagrams can be app l i ed t o p r e d i c t i n g t h e shape of
m u l t i c e n t e r p o t e n t i a l s u r f a c e s and t h e i r e f f e c t on t h e format ion of
r e a c t i o n p r o d u c t s . A f t e r p r e s e n t i n g i n more d e t a i l t h e mo t iva t i on fo r
t h i s work, we w i l l d i s c u s s t h e system i n d e t a i l and o u t l i n e t he e x p e r i
mental appara tus which was used t o a c q u i r e d a t a . We then p r e s e n t t he
exper imenta l r e s u l t s and a d i s c u s s i o n of t h e p e r t i n e n t c o r r e l a t i o n d i a
grams along wi th an i n t e r p r e t a t i o n of the r e s u l t s from b o t h k inemat ic
and p o t e n t i a l su r f ace p a i n t s of v iew.
Hodels for Ion-Molecule Reac t ions
For purposes of d i s c u s s i o n , we w i l l assume t h a t t he hydrogen i s o t o p e ,
D„, has been used for s t u d y of t he r e a c t i o n s of CO.. ( In f a c t , D_ was
employed i n most e x p e r i m e n t s . ) Our s tudy of C0„ +D„ h a s been aimed a t
unders tanding t h e e lementary dynamics of the r e a c t i o n through t h e eva lua
t i o n of exper imenta l ly determined product v e l o c i t y v e c t o r d i s t r i b u t i o n s .
Chemical r e a c t i o n s have ge ne ra l l y been c l a s s i f i e d as be longing t o
one of the two broad c a t e g o r i e s : those p roceed ing through the formation
of a l ong- l ived i n t e r m e d i a t e c o l l i s i o n complex and t h o s e proceeding v i a
a s h o r t l i v e d d i r e c t i n t e r a c t i o n mechanism. The t ime s c a l e of the r e a c
t i o n i s provided by the p e r i o d , x , r e q u i r e d fo r a complete r o t a t i o n of
-165-
the collision intermediate formed as the reactant molecules approach each
other closely (with a distance comparable to that of a chemical bond).
If the time of this close interaction i s less than T, the reaction i s
said to occur by a direct mechanism, while i f this interaction time i s
greater than T the collision i s said to proceed through intermediate
complex formation. Whether a reaction i s direct or proceeds through a
complex i s determined by the potential energy surface representing the
total electronic energy of the react ants as they -interact and form
products, and by the in i t ia l relative translational energy of the system.
Host ion-molecule reactions previously studied have been found to
evolve by a direct mechanism. The simplest and ac31 often applied model
of direct interactions i s that of spectator stripping. For the reaction
A + BC •*• AB + C, the spectator stripping model assumes that A interacts
with B, while C remains unaffected (a spectator). The model assumes that
that as A approaches BC, the BC bond i s dissolved so that when A hits B,
C has no momentum imparted to i t . By the conservation of momentum, the
velocity of AB formed by spectator stripping i s
where M. and H„ are the masses of A and B and V. i s the i n i t i a l velocity
of A. Products formed by spectator stripping are most often forward
scattered (relative to the center of mass) anJ appear at a 0° scattering
angle relative to the direction of V.. This follows again from the con
servation of momentum; since no transverse momentum is imparted to C, the
same must hold for AB.
In the spectator s tr ipping model the internal energy of the AB
product 1B the relative energy of A with respect to B (E ) less the exo-
thermicity of the reaction:
AEW
and
" . - T - i - M r t - L
V " W'OM ~ I n i t i a l reduced mass of A an :
E_ = i n i t i a l laboratory energy of A.
As E_ i s increased, U,_ increases unt i l eventually the internal energy of
AB exceeds i t s dissociation energy. At this point AB formed by spectator
stripping i s no longer s tab le , and any product intensity peak due to a
s t r i c t spectator interaction i s expected to disappear. In fact, the d i s
appearance of product fo ; aed by spectator stripping i s often reflected
by apparent movement of peak intensity forward to a velocity greater than
Xss-The intermediate complex model assumes the existence of a strong
chemical attraction between the reactant molecules which binds them
together into a transitory unit of unspecified geometry which lives for
several rotational periods. During this time the complex rota tes ,
finally dissociating into products which are symmetrically distributed
in angle (the angular distribution of products i s uncorrelated with the
i n i t i a l relat ive velocity vector) . This random dissociation leads to
the measurement of product intensi ty distributions which are symmetric
about the ±90° axis in the center of mass coordinate system.
As a rule, complex formation occurs uhen the Internal energy of the
may allow the possibility of complex formation, at high re la t ive energies
temporary disposition of large amounts of (ABC) internal energy may
preclude complex formation. I t should also be noted that though a
potent ial energy well for complex formation may exis t , there are cases
where th i s surface i s inaccessible to the reactants leading to reaction 2 by a direct interaction mechanism or no reaction at a l l .
The formation of a long lived complex suggests that I t should be
possible to predict the relat ive frequency of formation for competing
product channels using unlmolecular decomposition (REKH) theory or a 4
s t a t i s t i c a l phase space model*
For the CO? - D_ system there exists the possibility of forming a
bound intermediate, D_C0_. t h i s species i s the molecular ion of formic
acid and i s known from photoionization measurements to be bound by
approximately 1.75 eV. Especially at low relative energies, one might
expect that there i s a sizeable probability of forming D~C0_ during
CO. - D„ collisions, and that such intermediate formation wi l l be r e
flected in the distribution of product intensi t ies as a function of
barycentric velocity and scattering angle.
The conceivable products of the C02 + D_ reaction are numerous and
include CO* BCO*, DC0+, 0D+, D 2 0 + , D£, 0 + , C0+ and d j . As such we have
-168-
been interested not only in the distributions of products as a function
of i n i t i a l translational energy, but also in the re la t ive cross sections
for formation of each product. In measuring product intensi ty distribu
tions there are several questions which we have sought to answer:
(1) At low relat ive energies does intermediate complex formation
occur? If so, at what re la t ive energies does the complex persist?
(2) How important i s the large number of internal degrees of free
dom in the CO. - D„ system? Does this fact influence the amount of trans
la t ional •*• vibrational energy transfer or complex formation?
(3) If complex formation, occurs are re la t ive product intensi t ies
explainable in terms of RfiKU or phase space theories?
(4) If reaction proceeds by direct interaction, i s a spectator
stripping model applicable?
(5) Are the a t t rac t ive forces associated with a potent ia l energy
well displayed in product intensi ty distributions; i f not, i s i t passible
to explain the result-, by use of molecular orbital and s ta te correlation
diagrams? (See below.)
We have found that the C0? - D_ system appears to interact by way
of complex formation at low re la t ive energies (<1.5 eV) and that the
reaction mechanism gradually becomes more direct at higher energies.
After describing the apparatus used for experimental measurement, ire will
discuss the thermodynamics of the CO- + H- eystem, the pertinent correla
tion diagrams, before detai l ing the experimental results which support
the above mechanistic description.
-169-
Egperimantal
The experimental apparatus used to study the C0„ + D2 system has
been applied to the study of a large number of ion molecule reactions
and has been described in de ta i l previously. I t basically consists of
three independent regions: an ion sour: f.cr preparing a narrow beam of
incident icns of known mass and enerf -. c-cs-ctexi ce l l where the
incident ions undergo intenr leculai i l l s cms, and a product analysis
region where ionic products are counted as a function of the i r mass,
f inal energy and laboratory scat ter ing angle.
The apparatus i t se l f i s composed of two connecting vacuum chambers:
a small source chamber pumped by a single 6" o i l diffusion pump* and a
much larger (^4 ft ) reaction chamber containing the scat ter ing region
and the i n i t i a l stages of the detector t ra in , pumped by two 6" o i l diffu
sion pumps. Each diffusion pump i s mounted on a liquid nitrogen cooled
baffle to reduce o i l backs creaming and increase effective pumping speed.
The main chamber typically has a pressure of 3 x 10 Torr (in the
absence of scattering gas) .
Ion Source Assembly
For the current experiments, a Broida type microwave discharge
source was used. This source consists of a 1 cm diameter quartz tube
mounted on one side of the source chamber surrounded by a microwave
cavity. Microwave radiation supplied by a 3GHz conmserical diathermy
source maintains c steady discharge through a desired source gas once
the discharge has been in i t ia ted by a spark from a tes la co l l . - The dis
charge i s confined to a 2 cm length by a piece of platinum mesh placed
within the discharge tube.
For producing CO, ions a mixture of CO. and helium i s used. While
the actual pressure within the discharge tube is uncertain, i t i s approxi
mately 50u. The rat io of CO„/He in the discharge, as measured by an
ionization gauge i s 30/1; however, the relative efficiency for ionization
of these gases suggests that the actual rat io i s closer to 2 / 1 . From
this discharge mixture not only CO. ions, but also CO , 0 , and C ions
may be extracted. In most cases, larger fluxes of ions can be achieved
i f the CO. gas pressure in the tube i s kept just above the minimum
pressure necessary to maintain the discharge.
As has been noted previously, a primary advantage of the microwave
discharge source over electron bombardment sources i s the relat ively low
electron temperature of the discharge. While electrons in a bombardment
Bource typically have energies of 50-100 eV, the electron temperature in
the microwave discharge i s of the order of 5 eV. The r^Jult of the low
electron temperature i s that CO. ions wil l be formed almost exclusively
in the ground ionic s tate (AE = 13.78 eV) rather than in excited 2-n , Z Z + or 2 Z + states (AE ^ 17.3 eV) . u g
Once a steady discharge i s achieved, ions are extracted from the
discharge region by a 700 volt extraction potential . They then pass
through a series of e lect ros ta t ic focusing lenses and into the entrance
of a magnetic mass spectrometer. As the ions enter the spectrometer,
the beam passes through an e lec t ros ta t i c quadrupole lens which converts
the beam from one of circular cross section to one of rectangular cross
section and focuses the beam on the entrance to the analyzer; after
momentum analysis, a second quadrupole forms the ions again into a beam
of circular cross section. This maneuver increases the effectiveness of
-171-
the momentum analyzer by causing a l l ions in the beam to traverse the
analyzer in a single horizontal plane. The quadrupole lenses also aid
in focusing and shaping the ion beam before i t enters the scattering
region. The momentum analyzer i t se l f i s a 66* sector electromagnet. By
varying the energy at which ions traverse the analyzer and the strength
of the naguetic field (by adjustment of the current through the magnet)
any of the ions produced by the source discharge nay be selected for
use.
The momentum analyzer has a resolution of 2X of the energy at which
the ions are analyzed. This fact coupled with the natural isotopic
abundances relevant to CO* (C 1 3 - 1.112; 0 " - 0.0371; 0 i a - 0.20Z)
supports the experimental observation that l , 5 C0 2 and V*C0. from the ion
source do not play a significant role In interfering with Intensity dis
tribution measurements. Any such interference would be removed by
measurement of relative background levels.
Scattering Cell
As the beam of the momentum selected ions exits from the momentum
analyzer, i t i s again re focused by electrostatic lenses onto the fixed
entrance to the target gas scattering cel l . This target ce l l basically
consists of two tightly fitted concentric cylinders, capped at both ends.
The interior cylinder i s fixed in position relative to the ion source
train and contains a 2 mm x 2 cm square entrance aperture for tue cel l .
The outer cylinder i s fixed to a rota table lid mounted on top of the Daln
vacuum chamber. The complete detection train, as well as the scattering
cel l exit rotate with the movable l id , allowing analysis of ionic pro
ducts at a wide range of laboratory scattering angles. The exit s l i t of
-172-
the collision cel l i s a Z ma diameter round hole.
The path length through the scattering ce l l i s 3.8 ma. Target gas -3 pressures of approximately 10 Torr are maintained within the scattering
cel l and lead to bean attenuations of 15-202 during passage of the beam
through the cel l . This ensures that only single scattering events are
responsible for the final distribution of reaction products. The scatter
ing cell pressure is measured with a capacitance bridge manometer (HKS
Baratron) whose advantage over an ion gauge i s that i t i s insensitive to
the ionization efficiency of the gas which i s being monitored.
For the reactions of CO-, He, H-, HO, and D» gases were used in the
scattering cel l . The small size of the ce l l apertures allowed the use of
iotracell pressures 1000 times greater than the background chancer
pressure; a 10" Torr ce l l pressure typically caused a two-fold increase
In chamber pressure, an entirely tolerable figure. Since only relative
cross sections for reactions were measured, no effort to calibrate the
absolute pressure within the collision cel l was required.
Detector Train
As mentioned above, the entire detector train i s mounted on the
20 irch diameter rota table l id (which i s counted on a differentially
pumped double tec-ring seal) . Product loos emerging from the collision
cel l enter a 90° spherical electrostatic energy analyzer which passes
ions of the desired final energy into the vertical plane of the detector
train. The energy analyzer has an angular resolution of 2.3° full width
and energy resolution of 32 5WHH. The transmitted ions are focused by
a series of electrostatic lenses onto the entrance of a quadrupole nass
f i l ter and then into the ion detector.
-173-
The detector itaelf consists of a polished aluminum plate which i s
maintained at a potential of -25 kilovolts. As the highly accelerated
product ions strike the plate, they cause ejection of secondary electrons
which are then accelerated by a +28 kilovolt potential and impinge on a
lltbium-drif ted silicon semiconductor wafer which transduces the pulses
of secondary electrons into electrical pulses which are amplified by an
FET preamp and linear amplifier and counted with a Hamner HS-11 10 He
scalar. Using a Teletype Scanner, the resulting scalar counts are typed
out on ASR33 teletype along with the counting time and col l is ion ce l l
pressure for later analysis.
Experimental Procedure and Data Analysis
In undertaking an experiment an this apparatus, the f i r s t order i s
to achieve a steady gaseous discharge. The appropriate momentum analysis
energy i s chosen so as to guide extracted ions to a beam flag positioned
at Che scattering cel l . The ion current at the beam flag (10 - 10~
A) i s monitored using a Keitheiy electrometer. The gas pressure, quad-
rupole lens voltages and microwave power are used in a concerted manner
to achipve a steady discharge which yields ma***"" ion beam intensity.
At this point the bean flag i s rotated out of the beam path and the beam
current monitored using a Oary 31 electrometer connected to one of the
lens elements of the detector train. This allows monitoring and
optimization of the angular and energy widths of the beam. When this
final beam i s determined to be stable, i t i s characterized as to energy
and angular distribution. Liquid nitrogen i s then added to a reservoir
which cools the eeuiconductor detector, and after a 20 alnute cooling
period, the detector i s turned on.
- 1 7 4 -
Measurements of product i n t e n s i t y are comoLonly Bade according to
one of two schemes: the d e t e c t o r i s pos i t ioned a t a constant laboratory
angle and the energy of the product energy analyzer i s scanned, or the
product energy i s l e f t f i z s d and the laboratory angular d i s t r i b u t i o n i s
scanned. The former method i s termed as a "scan" w h i l e the l a t t e r i s
referred to as a "cut". Typica l ly one scan i s taken a t the i n t i a l labora
tory angle corresponding t o the inc ident ion beam ( c e n t e r l i n e ) to give an
idea as to the extent of the energy d i s t r ibut ion and subsequently betveen
10 and 20 cuts i n angle are taken t o span that energy d i s t r i b u t i o n .
Using the t e l e type , the i n t e n s i t y at each energy-angle po int i s recorded
u n t i l a complete map of the product i n t e n s i t y d i s t r i b u t i o n i s accumulated
c o n s i s t i n g of between 200-300 i n t e n s i t y measurements. This process takes
from 3-6 hours and requires frequent monitoring of the primary beam i n
t e n s i t y and energy-angular p o s i t i o n . Changes i n these parameters are
automatical ly taken i n t o account by l i n e a r i n t e r p o l a t i o n during data
a n a l y s i s . We note that though the time required for each i n t e n s i t y
measurement i s a funct ion of r e l a t i v e product i n t e n s i t y , each measurement
i s t yp ica l ly made over a 15-20 second in terva l to average out any i n
stantaneous beam f l u c t u a t i o n s .
The information pr inted on the te le type i s transferred to computer
data cards which arc then analyzed on the LBL CDC S600 computer.
At e*»ch energy-angle p o i n t for which product i n t e n s i t y i s measured,
the s i gna l and background counts are normalized us ing the i n t e n s i t y
conversion | = 10 7 (S-B)
T i o P g ( 6 ) E ^ / 2
-175-
where
S * signal counts
B • background
X - counting time in seconds —12 i tt peak incident beam intensity (in units of 10 A)
P = scattering gas pressure (In units of 10 Torr)
g(6) = detector angular viewing factor through the scattering cel l
(a function of scattering angle)
E- = electrostatic energy analyzer Betting 3/2
The E factor normalizes the measured intensity to the detector volume
in velocity space.
Calculated intensities are plotted by a Calcomp plotter as a function
of barycentric velocity and scattering angle. Using the plotted intensity
points, contours of equal intensity are drawn onto the array ana the
result i s an intensity contour map of the final product distribution.
One sucl. map i s required for each individual product of the reaction at
each i n i t i a l relative energy for the react an to. Comparison of the maps
for any product as a function of i n i t i a l relative energy yields informa
tion as to the mechenism(s) important for the reaction.
The resolution of each experii^ent i s a function of the angular and
energy distribution of the incident beam, as well as the thermal motion
of the gaseous target molecules. This coupled with incident beam inten
sity fluctuations makes the resultant intensity maps something less than
a high resolution picture, yet there i s a surprising amount of infatua
tion which can be inferred solely from the general shape of the distribu
tions. Put another way, the detail of the information provided i s at
-176 -
l e a s t as g r e a t as our knowledge of t he a p p r o p r i a t e p o t e n t i a l energy
s u r f a c e s (of ten much g r e a t e r ) s o t h a t t h e t e s t s which might be a p p l i e d
t o t ' -• exper imenta l da t a a r e p r e t t y much p o s s i b l e w i t h c u r r e n t v e l o c i t y
and angu la r r e s o l u t i o n .
Kinemat ics and I n t e n s i t y D i s t r i b u t i o n s
Though we b r i e f l y a l l u d e d t o t h e i n t e r p r e t a t i o n of t . o t t e r i n g d i a
grams i n Chapter I ( see P i g . 1 ) , t h e r e a r e a broad range of s c a t t e r i n g
p r o c e s s e s ubich may be i n t e r p r e t e d wi th the a id of v e l o c i t y v e c t o r d i a
grams. Figure 1 d e a l t w i t h t h e g e n e r a l case of an i on A which i s i n
c i d e n t on a n e u t r a l molecule , BC, whose thermal v e l o c i t y was cons idered
n e g l i g i b l e . The r e s u l t s of such a c o l l i s i o n can be c l a s s i f i e d i n t o
s e v e r a l broad c a t e g o r i e s :
(1) E l a s t i c s c a t t e r i n g : A + + BC •* A + + BC
(2) I n e l a s t i c s c a t t e r i n g : A + + BC + A + * +• BC
•* A + + BC*
+ A + + B+C
(3) React ive s c a t t e r i n g : A + BC * AB + C
+ AC* + B
•* AB + C +
•* A + BC + e t c .
The v e l o c i t y v e c t o r diagrams p e r t i n e n t t o each of t h e s e c l a s s e s a r e
shown i n F i g . 34.
I n an e l a s t i c s c a t t e r i n g e v e n t , no chemical r e a c t i o n o c c u r s , and
t r a n s l a t i o n a l energy r e p r e s e n t i n g r e l a t i v e motion of t he p a r t i c l e s i s
s t r i c t l y conserved ( i . e . remains w i t h i n t h e t r a n s l a t i o n a l mode) . Only
t he ang le of motion r e l a t i v e t o t h e i n i t i a l v e l o c i t y v e c t o r i s changed,
-177 -
a. Elastic collision1 A + + BC —»- A + + BC
b. Inelastic collision1 A + + B C — - A + + B C *
c. Reactive collision: A + + BC —»- A B + + C (exothermic)
XBL 749-7312
Fig. 3«. Velocity rector diagrams for elastic, Inelastic and reactive collision processes.
-178-
the amount of change depending on the strength of the e l a s t i c interaction
and the impact parameter (aiming error) of the col l i s ion. This type of
collision i s often represented as the type occurring between colliding
b i l l i a rd ba l l s .
For a l l three classes of collisions, i t i s possible to define a
quantity, Q, which denotes the amount of re la t ive t ranslat ional energy
which i s converted from trans lational to internal modes during the
collision process. If E . denotes the i n i t i a l re la t ive trans la ticraal
energy (E = •=• ug 2 ; u = i n i t i a l reduced mass, g = i n i t i a l relat ive
t 12
"rel " 1 » 1
products (E . = •=- \i g ) we define
If Q i s negative, t h i s implies that some I n i t i a l re la t ive trans l a
tional energy has been converted to electronic, vibrat ional , or rotational
internal modes of the products. If QX>, i n i t i a l in ternal energy has been
converted Into the trans la t ional energy code (superelastic col l is ion) . i
Since the e las t ic coll is ion process by detinit ion assumes E « *
E . , elast lcally scattered projectiles wil l be found at the Q = 0 locus
of points (Fig. 34a) which forms a circle about the center of mass in
the appropriate velocity vector diagram. This c i rc le represents a l l
points at which a projec t i le , A , say be found after simple rotation of
the relative velocity vectors about the center of mass following an
e las t ic collision.
-179-
By conservation of to ta l energy, a l l relat ive trans la t ional energy
lost during a collision must be found in internal nodes (electronic, i
vibrat ional , rotational or heat of formation). If U. and U, represent,
respectivelyi the energy contained in internal modes before and after a
col l is ion, then
-« - " in t " " in t
and the e las t ic case (Q » 0) i s consistent with a zero net change in
internal product energy.
For the Inelastic class of coll isions, Q<0 and
since trans la tional energy i s converted into internal modes. This case i s
represented in Fig. 34b, For th i s type of collision there i s again no
chemical transfer, only a rearrangement of the available trans la t ional
energy among translational and internal modes.
The reactive case (Fig. 34c) i s a further extension of these con
cepts. The only additional complications arise because the reaction may
f a i l to be thermoneutral, and because the product masses differ from
those of the react ants (u f1 u ) . In this case the change in energy of
formation (exo- or endo-thsrmicity) must be taken into account in
balancing the distribution of energy before and after the reaction.
Conservation of energy i s then represented by
-180-
if AE i s defined as negative for exothermic reactions following the
normal convention.
For a reactive process, i t i s apparent that if D = U. that
Q = - AE . Thus, even if the in te rna l modes of the products remain in
the i r i n i t i a l energy s tates (though of course different modes are avail
able before and after the col l is ion since chemical transfer has occurred)
there must be a net conversion of energy into (from) bond energy from
(into) translation in the case of an endoergic (esoergic) reaction. This
i s represented by the Q = - AE° c i rc le in Fig. 32c.
Thus we can begin to see how a particular coll ision may be visualized.
The vector scattering diagram for reactants ( i n i t i a l vectors) and products
( f inal vectors) i s constructed. At any point an the diagram, Q may be
calculated knowing E . = •=- pg z , E t = y u g z . Using a known value of
AE , i t i s then possible to compute the amount of internal energy con
verted into internal modes. This quantity provides information as to the
chemical state of undetected products (whether they are dirsociated) and
provides some clues as to the nature of the reaction mechanism (see
below). In real i ty , for a multiatcm system such as CO- + D_ there are
many fewer Inferences which can be made concerning energy disposal in 9
internal modes as compared with systems of two or three atoms. nevertheless, such analysis dees yield some UTTy*1"" on which products can be
-181-
formad at any init ial relative energy and maintains same usefulness in a
more complicated system.
States and Energetics
Before discussing the distributions of reaction products, i t is
°2-H2 appropriate to present the energetics of the CCL-H- system. We begin
Heutral C0„ has been thoroughly studied previously. I ts ground
electronic state is lZ and has the molecular orbital population shown
in Table 7. CO- is linear and has an equilibrium interouclear distance
r = 1.16A. Formation, of ground state CO, (2K„) occurs when one of the
nonfaending IT electrons is removed. The ITT orbitals essentially repre
sent the lone pair oxygen electrons; the nonbonding character of the
Iff orbitals is supported by the fact that the rotational constants for
CO, (^A) and CO- (*£ ) are almost equal, both species being linear.
Formation of C0o (2II ) requires 13.78 eV. 2 g
The excited states of Col" are also listed in Table 7. The 2 H u
results from removal of an electron from the bonding Iff orbital of CO,
and requires 17.32 eV. While the ZH state is also linear* both excited
£ states are known to be bent.
The vibrational frequencies for CO,, (*E ) and C0„ (2H ) have been
12 —1* determined from photcelectron spectroscopy (PES) to be (In cm )
co* co 2
V 1250 1388 (symmetric s t r e t c h )
\> 2 530 66? (bend)
\>_ 1469 2349 (asymmetric stretch)
TABLE 7. Electronic States of CO, and CO,
Species State Orbital Configuration r (A) Geometry
"8
2 U h ( l og lou2og 30g 2<iu Aog 30u) lira lirg
U 3 ltfu lug
11TU lTTg
1.16
1.17 linear 13.78
17.32
2- + IB.OB
2r + Eg 19.4
•Relative to C02 ( 1Eg +)
and the Franck-Condon factors for transitions CO- (000) •*• CO. (2II ) have
(0,0,0) (.82)
(1,0,0) (-15)
(2,0,0) (-02)
(0,0,0)
Thus, one expects that In the case of ver t ical ionization, predominantly
present in the microwave discharge source may indeed lead to adiabatic
rather than vert ical t rans i t ions , and neutral CO» may be vibrationally
excited within the discharge. However, since the equilibrium geometries
of CO- and CO, are quite similar , one expects that similar F.C. factors
wixl pertain to ionization of vibrationally excited C02 and that C0„
produced in the discharge wi l l approximately reflect the vibrational
energy distribution of neutral C0_. Moran and Friedman have discussed
the problem of vibrational excitation and determined that an upper limit
of 1 eV for the internal durat ional energy of CO- is l ike ly .
As has been reported previously, the electron temperature of the
CO- discharge i s approximately 5 eV. This makes i t unlikely that the
excited states of C0„ are produced in any quantity. Moran and Friedman + ? +
have reported that CO, ( I I ) (the excited state of CO- most likely to be
produced) decays to CO_ (X ZH ) in 10 seconds. The resul t i s that we
may assume with some certainty that the CO- ions undergoing reaction are
almost exc7usively in the ground 2II s ta te .
The thermodynamics of the CO- - H? system are presented in Table 8.
The heats of reaction have been derived using predominantly the heats of
formation tabulated in Ref. 5. Formation of H_CO_ is 2.5 eV exothermic.
The value for formation of H + HCO„ is derived using the measured proton
affinity of C0„. ' A value for the proton affinity of 5.1 eV (used in
subsequent calculations) reported in Ref. 15 represents the average value
of those reported. The resulting value for the well depth with respect
to dissociation of H2C02 to HCO- or UGO Is approximately 1.7 eV.
Although not a l l of the processes l isted in Table 8 are expected to
occur in H- + CO, coll is ions t the exhaustive l i s t ing is helpful for
evaluating the energecic l imitations placed on the formatioa of the actual + + + + + +
reaction products (CO-, HCO_, HCO , OH , CO , 0 ) . As the experimental resul ts are evaluated below, frequent reference to Table 8 wi l l be made.
3
TABLE 8
Primary Reactioas tlit^a (eV)
C 0 2 + B 2 + B 2 C 0 2
H + UCO, + i
BCO + OH
- 2 . 5 6
+
B 2 C 0 2
H + UCO, + i
BCO + OH - .75
- .77
+ HCO + OB + +3.7 + BCO+ + 0 + H + 4 . 4
-* CO+ + H 2 0
CO + U 2 0 +
CO+ + H 2 + 0
CO+ + OB + B
+0.7
+1.58
+5.79
+5 .9
- > •
0 + + H 2C0 0 + H 2 CO +
0 + + H + CO
+5 .33 +2 .58 +5 .4
- 2B + C0 2 +4 .5 - * •
H 2 + C 0 2 +1.66
Secondary Reac t ions 4H? 9 a (eV)
HCO* + B + CO* H + + C0 2
HCO+ + 0
+5.25 +5 .13 +4 .4
+ HCO + 0 + +9.4
•* CO+ + OH +6.6 + CO + OH+ 5.7
HCO+ -* CO+ + H 6.65
co+ C + + 0 8 ^ - • C + 0 + 3.35
- 1 8 6 -
MOLECULAR ORBITAL COREELAIION DIAGRAMS
While i t i s known from the thermodynamics of the CO?-H„ sys tem t h a t
t he e x i s t e n c e of a bound i n t e r m e d i a t e (H_CO_) i s p o s s i b l e , i t i s by no
means c e r t a i n ChaC Che p o t e n t i a l s u r f a c e which o r i g i n a t e s from t h e grcund
e l e c t r o n i c s t a t e s of the r e a c t a n t s l e a d s t o Che formation of t h e ground
s t a t e i n t e r m e d i a t e . For a number of ion-molecule r e a c t i o n s p r e v i o u s l y
s t u d i e d , a q u a l i t a t i v e d e s c r i p t i o n of t h e r e a l p o t e n t i a l s u r f a c e s f o r Che
r e a c t i o n has been achieved by the u s e of molecular o r b i t a l and e l e c t r o n i c 2 +
s t a t e c o r r e l a t i o n diagrams. For t he CO^-H- system, we have c o n s t r u c t e d
such d iagrams , which w i l l now be d e s c r i b e d .
For any chemical r e a c t i o n t h e dynamics of the c o l l i d i n g r e a c t a n t s
a r e determined fay the e l e c t r o n i c p o t e n t i a l energy s u r f a c e of t h e r e a c t i o n
( w i t h i n t h e framework of the Born-Oppenheimer approximation) . However,
f o r z l l b u t the s imples t r e a c t i o n s , t h e p o t e n t i a l energy s u r f a c e s a r e n o t
known i n d e t a i l ; c a l c u l a t i o n of t h e s e s u r f a c e s i s most o f t en an expens ive
and compl icated p r o p o s i t i o n , e s p e c i a l l y fo r t he mul t id imens iona l s u r f a c e s
a p p r o p r i a t e to r e a c t i o n s i n v o l v i n g many atomic c e n t e r s .
Without knowing the d e t a i l s of t h e p o t e n t i a l s u r f a c e , i t i s s t i l l
p o s s i b l e t o v i s u a l i z e the q u a l i t a t i v e f e a t u r e s of Che s u r f a c e f o r a
r e a c t i o n us ing molecular o r b i t a l (M.O.) c o r r e l a t i o n d iagrams. As a
chemical r e a c t i o n p r o g r e s s e s , t he molecu la r o r b i t a l s of the r e a c t a n t s
evo lve i n t o those of an i n t e r m e d i a t e c o l l i s i o n complex and f i n a l l y i n t o
Chose of the r eac t ion p r o d u c t s . By fol lowing the evo lu t i on of t h e s e
o r b i t a l s , i t i s pos s ib l e to a s c e r t a i n t he o v e r a l l e l e c t r o n i c energy
th roughout the r e a c t i o n In o r d e r t o d e c i d e wheCher format ion of a long
l i v e d c o l l i s i o n in t e rmed ia t e i s p o s s i b l e .
•187-
To c o n s t r u c t an M.O. c o r r e l a t i o n diagram, one f i r s t assumes a
"dynamica l ly reasonab le" c o l l i s i o n geometry wi th one o r more symmetry
e lements* The o r b i t a l s of the r e a c t a n t s , i n t e r m e d i a t e , and p r o d u c t s a r e
then i d e n t i f i e d anC resolved i n t he p o i n t group corresponding t o t h e
symmetry e lements fo r the assumed geometry . Espec i a l l y i n a low symmetry
i n t e r m e d i a t e c a s e , such as H 2C0_, t he n o d a l s t r u c t u r e of the v a r i o u s
H.O.*s p r o v i d e s usefu l c lues t o t h e e v o l u t i o n of each o r b i t a l as t h e 20 r e a c t i o n p r o g r e s s e s . The o r b i t a l energy of each o r b i t a l I s e s t i m a t e d
us ing SCF c a l c u l a t i o n s , e l e c t r o n a f f i n i t i e s , appearance p o t e n t i a l s and
p h o t o e l e c t r o n and u l t r a v i o l e t s p e c t r o s c o p y . Af te r each o r b i t a l f o r
r e a c t a n t s , i n t e r m e d i a t e and p roduc t s h a s been i d e n t i f i e d and p l a c e d
acco rd ing t o energy , o r b i t a l s of t h e same symmetry spec i e s a r e connected
( o r b i t a l c o r r e l a t i o n ) . The mixing of o r b i t a l s of t he same s p e c i e s by
nonsymmetrlc n u c l e a r motions and s p i n - o r b i t i n t e r a c t i o n s i s cons ide red
and p o t e n t i a l l y avoided c ross ings of s u r f a c e s a r e i d e n t i f i e d .
When t h e M.O. c o r r e l a t i o n has been completed, by p l a c i n g t h e e l e c
t r o n s of t h e r e a c t a n t s i n t he o r b i t a l s , t h e i d e n t i f i c a t i o n of e l e c t r o n i c
s t a t e s f o r each of t he spec i e s found d u r i n g the evo lu t i on of t he r e a c t i o n
i s made. By c o r r e l a t i n g the e l e c t r o n i c s t a t e s of l i k e symmetry f o r
r e a c t a n t s , i n t e r m e d i a t e and p r o d u c t s , a s t a t e c o r r e l a t i o n diagram i s con
s t r u c t e d which i s a rough approximation t o the p o t e n t i a l s u r f a c e s
a p p r o p r i a t e t o the r e a c t i o n .
In g e n e r a l .'here i s more than one c o l l i s i o n geometry a p p r o p r i a t e t o
the r e a c t i o n (o r s e v e r a l narrowly c o n s t r a i n e d ranges of c o l l i s i o n g e o
m e t r i e s ) o r more than one p o s s i b l e s e t of p r o d u c t s . For each p o s s i b l e
geometry range or s e t of p r o d u c t s , a s e p a r a t e s e t of c o r r e l a t i o n s i s
r e q u i r e d .
For Che CCL-H,, system the I n t e r m e d i a t e * H^CO,, con be forced in one
of two b a s i c ways (F ig . 35) . P a r a l l e l approach by iU and CO- l e a d s t o
t h e C symmetry in t e rmed ia t e f a v o r i n g the formation of HCO^ o r HCO
( F i g . 3 5 a ) , whi le pe rpend icu la r approach of H, toward CO™ leads t o on
i n t e r m e d i a t e of C 2 „ symmetry ( F i g . 3 5 b ) . Figure l e shows a t h i r d p o s s i b l e
mode of approach, but t h i s geometry does not lead t o formation of a s t a b l e
H 2 C0 2 mo lecu la r c o n f i g u r a t i o n . These geometr ies of course r e p r e s e n t
i d e a l i z a t i o n s ; any r e l a t i v e geometry of approach i s p o s s i b l e , bu t t he se
examples p rov ide a f i r s t approximat ion u s e f u l for c o n s t r u c t i n g c o r r e l a
t i o n d iagrams . Once the diagram h a s been c o n s t r u c t e d . I t i s p o s s i b l e to
c o n s i d e r the e f f e c t s of geometr ic p e r t u r b a t i o n on the s t a b i l i t y of the
complex.
We begin wi th lUCOj format ion a s a C symmetry i n t e r m e d i a t e . The
m o l e c u l a r o r b i t a l c o r r e l a t i o n diagram f o r t h i s case i s shown i n F i g . 36.
The D . p o i n t group of CO- and H 2 i s used t o c l a s s i f y the r e a c t o n t
m o l e c u l a r o r b i t a l s , while the o r b i t a l s for the HCO, product a r c c l a s s i
f i e d accord ing to C ? v symmetry. The impor tan t elements of the o r b i t a l *
c o r r e l a t i o n are the combination of t he H~ o and o o r b i t a l s t aken In 2 g u *
banding-an t ibonding combinations w i t h the in -p lane TT and IT o r b i t a l s of 20 CO. ( F i g . 37) in a manner s i m i l a r t o the pro to type H_ + e t h y l e n e c a s e .
I n each case the in-phase combinat ion l e ads to the low energy bonding
o r b i t a l whi le the ou t -of -phase combination leads to the h igh energy a n t i -
bonding o r b i t a l conta in ing an a d d i t i o n a l node. The c o r r e l a t i o n which
-189-
(a) 1 D+ AE=-2.5eV, H _jk AE = -H.75eV> „_ J ^ „ I H-rJ * H 0
AE-+ l .8eV + Parallel Inter- »- H—C=0 nuclear Axis +
Apprcaeh
+ " V + " \ + H 0 = C = 0 —* - ^ 3 - C = 0 — * • 0 + C=0 I
Perpendicular Bisector (Energy of Intermediate Unknown)
Approach
(c) 9 0 J> H - H C+ — • • H — H - C K + — ^ H + H - C ! + | + - ^ H - . H - C ^
^ 0
XBL 749-7314
Fig . 35. Col l ir ion geonetr ies for the H2-CO_ Interoedia te complex,
a) Cs synactry intermediate; b) C,y sycnetry intermediate ;
c) a perpendicular approach leading to d i r e c t I n t e r a c t i o n .
aa|<r;(CO)
2T, UsC) 3a'(UCI 2a,(liC]
ld„llsOI 2o'(UOI IbjIliO] lirQ(lsO) } lo'llsO) la, 1 ISO)
4 t d ails in plane)
(C s)
-cf +
( C 2 v )
XBL 749-7256
Fig. 36. Molecular orb i ta l correlation diagram for fomation of HCOj4" from C02+H2» p a « l l e l internucleat axis approach.
Basis Orbitals
H2:© 0 © 0
g u
C0 2: 0 O GX0 GX0
0X0 ex© 0*3
Bonding Combinations u
© 0 i G © 0 i G
©£> C g + V 6 0 ' '
© 0 ^ 3
a*+»*(7a') Antibonding Combinations
cr g-^(l lo')
©iG^O ©IS©)
0©~ <-tr*(!2a')
] <BL 749-7227
Fig. 37. Bonding and antibonding combinations of H, and CO, orbitals to form H2C02+ molecular orbitals (labeled in parentheses).
-192-
of H,Cot, a (H_) with the l l a 1 , 7T (CO.) with 7a' and a (H-) with the
12a' orbi ta l of the intermediate. This correlation leads to an avoided
crossing of the 11a* and 7a 1 o rb i ta l s as the intermediate i s formed. The
mixing of these orbitals can be visualized as due to formation geometry
less than parallel , or as due to the asymmetrizing presence of the non-
part icipating oxygen atom. In the l a t t e r case, one can see that the node
between the 0 atom and the closest H atom (Fig. 37) contains geometric
components both parallel and perpendicular to the CO- intemuclear axis
which perturb an otherwise symmetric (approximately C„„) s i tua t ion , mix
ing the 7a 1 and l l a 1 orbitals and leading to an avoided crossing. The
exact point of the avoided crossing and the height of any resul t ing
potent ia l energy ban ie r in the entrance channel are open to speculation.
The significant point i s that there theoretically exists a route by which
reactants in the ground s ta te may adiabatically evolve to the ground
s t a t e of the intermediate, suggesting that the potential well for forma
tion of an intermediate complex may be accessible.
The formation of HCO, proceeds via the ground s ta te intermediate in
a simple way when the 0 (H_) electrons evolve through the 7a* s ta te of
H-CO-. The final assignment of an electron to the ls(H) orbi ta l occurs
through the transfer of a nonbonding 10a* electron which may involve a
second avoided crossing (Fig. 36} .
The M.O. correlation diagram for formation of HCO + OH i s shown in
Fig. 38. The formation of ground electronic state products from the
ground s ta te intermediate i s readily apparent. In this case, the forma
tion of HCO over OH (see below) is explainable both on the basis of
thermodynamics (HC0+ + OH l ies some U eV below HCO + 0B +; see Table 8)
- 1 9 3 -
-10-
-12-
- 1 6 -
- 1 8 -
g -20-
»(0HH2iO) /
2o g(lsC) 3o'lllC) irtCOUfsCI l<r„ (IsO) Zn'(lsO) alOHKIsO) Ia„(ls0) la'(lsO) trlCOKHO)
i: o. (t aiis in plane) fcrt [HCO+OHJ
(Co. )
XBL749-7Z33
F i g . 38. Molecular orb lce l c o r r e l a t i o n diagram for formatim of HCff1- + OH from C0,+H 3.
and an the basis of the molecular o rb i ta l correlation. The al ternate set
of products, HCO + OH , are adiabatlcally inaccessible! and the t o t a l
energy of the f i l led molecular orbi ta ls in the HCO + OH case i s well
separated in energy from that of HCO -4- OH.
The formation of C_ H_C02 by a perpendicular approach of H- and
CO, leads to the M.O. correlation diagram shown in Fig. 39. The i n - and
out-of-phase combination of the terminal 2S oxygen orbital and the H-O
orbi ta l lead respectively to -.,e bonding 2a, and antibonding 4a.. orbi ta ls
of H„0 (since the symmetry of the intermediate and the IL,0 product are
ident ical , identification of the intermediate orbitals has been dispensed
with) . In a similar manner, combination of the in-plane TT^CO,) and
a (H_) orbi ta ls leads to the formation of a lb 2-2b„ bonding-antibending
pa i r . Combination of the CO- a and a bonding orbitals forms the
bonding and nonbonding orbitals of CO (combination leads to the local iza
tion of the orbi ta ls ) .
Start ing with the ground s ta te react ants, one finds again that the
<J(H_) electrons in i t i a l ly correlate to a high energy orbi tal (4a.) . A
crossing of the Aa_ orbital surface by that of the 3a, orbi tal again pro
vides a path to ground state products. However, in this case i t i s likely
that the energies of the adiabatic surfaces (noncrossing path) are closely
a i
regions of space. The experimental observation that no H20 i s formed in
the reaction (see below) may provide support for the conclusion that the
close orb i ta l spacing at the avoided crossing allows the react ants to
follow a non-adiabacic path in a large fraction of C0~ + H« collisions
occurring in a nearly perpendicular geometry.
'gg (ISO)
( C 2 v )
4o*lHaO)
2bf IrigO)
27r«|CO)
6<r»(C0)
I +O=C=0 , . . , . ~>3-C=0 ">> + CO |_H J («ins in plane) [ _ H ^ J V^ J
<C2„ a C m v )
XBL 719-7234
Fig. 39. Molecular orbi tal correlation diagran for formation, of HiO++CO from C0 2
++B 2-
He note parenthetically that a crossing of the 3a. and 4a. orbitals
is likely to occur a t a high energy. This i s suggested by the fact that
the molecule OCF is bent (OCF can be correlated with OCOH which should
have a geometry similar to OCOH„). This suggests tha_ sn H-OCO inter
mediate would also be bent in a low energy configuration. I t may be that
formation of H70 requires achievement of a lower energy bent inter
mediate. Formation of such an intermediate would require some destruc
tion of the C0? IT bonding system, entailing a significant energy of
activation.
Throughout our discussion of correlation diagrams we have dealt only
with the orbi ta l correlations, neglecting the s ta te diagrams which actually
describe the electronic potential energy surfaces. This omission i s
motivated by the fact that the orbital energies of the intermediates are
very poorly characterized. Additionally, especially in the case of the
C intermediate geometry, the low symmetry of the intermediate leads to
labeling of the electronic states as being of only two types (A , A. ) .
Thus in any s t a t e correlation diagram there wi l l be a very large number i
of closely spaced states of the same symmetry (especially in the A
case), and i t is impossible to draw any meaningful conclusion. This i s a
problem that wil l persis t throughout the further study of reactions in
volving many atoms and low symmetry intermediate geometries.
In summary, we have seen how the molecular orbital correlation dia
grams for the CG„ + H_ system describe a possible low energy path to
product formation. The importance of lowered symmetry in the reaction
intermediate may determine whether mixing of orbitals of like symmetry
leads to avoided crossings with a significant enei^y gap allowing the
-197-
fortnation of a ground state intermediate. In the following section the
experimental measurements of product in tens i t ies are presented. la view
of the preceding discussion I t iB possible to rationalize the appearance + + + +
of HCO. and HCO as major products while l i t t l e or no H„0 or OH are found.
2 The exper imenta l ly determined p roduc t v e l o c i t y d i s t r i b u t i o n s f o r the
" 2 ^ H 2
l o n g - l i v e d in t e rmed ia t e complex and a d i r e c t i n t e r a c t i o n mechanism a r e
d i s p l a y e d . At a l l the i n i t i a l r e l a t i v e ene rg i e s s t u d i e d , t h e r e was
ev idence of s t r o n g chemical coup l ing between the r e a c t a n t s p e c i e s . Con-
s i s t a u t wi th the moderate depth of t he e l e c t r o n i c p o t e n t i a l w e l l , low
energy r e s u l t s d isp lay the symmetric behavior a s s o c i a t e d wi th complex
format ion whi le h igher energy d i s t r i b u t i o n s suppor t a s p e c t a t o r s t r i p p i n g
mechanism. In te rmedia te complex format ion and l i f e t i m e appea r t o be
governed by the e f f ec t i venes s w i t h which i n i t i a l r e l a t i v e t r a n s l a t i o n a l
energy i s disposed among the a c t i v e v i b r a t i o n a l modes of t h e i n c i p i e n t
complex.
DCO*
Prev ious s t u d i e s of CO- have p rov ided a l i m i t e d amount of i n fo rma
t i o n about t h i s product , which i s t h e major r e a c t i v e c h a n n e l . Ding has
p u b l i s h e d a b r i e f d e s c r i p t i o n of t h e zero degree energy d i s t r i b u t i o n of
DCO- a s a funct ion of i n i t i a l r e l a t i v e energy . He found t h a t a t ve ry low
r e l a t i v e energy (E .-=r 0 .5 eV) t h e r e i s some sugges t ion t h a t complex
format ion may occur, whi le a t low and in t e rmed ia t e r e l a t i v e e n e r g i e s
* ( 1 - 8 eV) , v e l o c i t y d i s t r i b u t i o n s r e f l e c t a s p e c t a t o r s t r i p p i n g mechanism.
However, t h e exper imental e r r o r r e p o r t e d for the low energy r e s u l t s make
i t u n c l e a r whether t h e r e i s indeed complex formation o c c u r r i n g .
*There i s some ambiguity i n t h e s e r e s u l t s s i n c e t he r e p o r t e d energy s c a l e s ( l a b o r a t o r y and r e l a t i v e ) a r e i n c o n s i s t e n t l y l a b e l e d .
Smith and Futrell have reported the results of ion cyclotron
for H atom transfer at low trans la t ional energies (<10 eV) . These authors
report a value of k = 4x10 ° cm3/molecule-second for the HCO- formation
rate constant; this value was found to be independent of incident ion
k inet ic energy for E < 6 eV. The fact that this rate constant i s approxi
mately one-fourth of the typical value (k = 15-20 x 10 1 0 cm3/molecule-19
second) expected from Langevin polarization theory raises a question
about the nature of the potential surface for the reactants a t impact
parameters somewhat smaller than the c r i t i c a l impact parameter for
Langevin col l is ions. While this might be viewed as evidence supporting
a moderately sized barrier to complex formation in the entrance channel
of the potent ial surface* such a proposition would be entirely specula
t ive .
The examination of HCO_ and DC0? product velocity distributions in
our laboratory i s complicated by problems of mass analysis. There are
several d is t inc t aspects of this problem. The incident CO- Ion beam con-
13 +
tains approximately 1% C 0„ (mass 45) which i s transmitted by the momen
tum analyzer of the ion source t ra in , though this was not found to pro
vide significant interference. A more significant problem encountered
was transmission of nonreactively scattered CO- (mass 44) by the quad-
rupole mass f i l t e r . Although each measurement of product intensi ty
includes a background measurement which removes mass 44 whose source i s
primary beam transmission, background measurements are incapable of cor
recting intensi t ies for nonreactively scattered CO- which i s transmitted
at a QPHS set t ing of mass 45 or 46. Since there is a relatively large
amount of inelastic nonreactively scattered C02 at a l l in i t ia l relative
energies studied, and since resolution of mass 45 from mass 44 i s very
limited with the apparatus used in these studies, DCO_ was chosen for
study at most relative energies. HCO_ was studied only at low relative
energies since use of an H~ target rather than D_ decreases the i n i t i a l
relative trans la tional energy of the reactants by a factor of one-half.
Figure 40 displays the HCO, product velocity distribution measured
in our laboratory for E . = 1.5 eV, the lowest relative energy studied.
The distribution appears quite symmetric. However, in view of the
relatively large in i t ia l beam velocity distribution (20X Beam Profi le) ,
one cannot state categorically that there i s no asymmetric component to
the map. In this figure, as well as subsequent ones, the velocity ex
pected for a spectator stripping (SS) model i s marked with an X. This
low energy result unquestionably contains a large symmetric component
suggestive of complex formation. The intensity of the product distribu
tion (I units) i s quite large and in fact i s somewhat larger than the
intensity of nonreactively scattered CO, at the same relative energy
(see below). This suggests that a large fraction of ion-molecule c o l l i
sions in this system are influenced by the chenical forces represented
by a potential energy well.
The DCO- distribution :
this taap also shows a sizeable sycoetrlc ccsponent, i t s basic nature is
asymmetric. The peak intensity fa l l s very near to the velocity expected
from a spectator stripping coll ision.
In order to establish unequivocally the stripping nature of the
product distribution at this low translations! energy, a similar nap of
-201-
the n C0 2 resulting from collisions with HD was constructed (Fig. 42) 4
Again, the velocity distribution i s quite broad with a product intensity
peak at the spectator stripping velocity. For each of these cases the
Q value of the spectator velocity i s given by the negative of the relative
energy between CO. and the 0 atom. Since the D atom comprises a larger
fraction of the total target mass in the HD case, Q appears closer to
the center of mass in the HD map, although Q i s approximately equal in
both cases.
The comparison of these two distributions provides firm evidence for
a direct interaction mechanism at relative energies as lev as 1.5-2 eV.
However, the broad extent of the product distribution suggests the con
tinued influence of a long lived complex. One possible explanation of
these results i s chat snail impact parameter collisions lead to coopleac
formation while more grazing collisions could lead to DCO_ formation by
a stripping mechanism.
Figures 43 and 44 are DC02 intensity amps (from D,) for relative
energies of 2.9 eV and 5 eV respectively. As the relative energy i s in
creased the distributions became increasingly asymmetric and more highly
peaked about the stripping velocity. This i s in keeping with the asstiap-
tioa that as relative translations! energy i s increased much above the
well depth. It becomes more difficult to fom a long lived eosplex and
the direct interact lea predominates.
As ocntioned above, the internal energy associated with formation of
DCOj by a stripping ocdianism Is a function of the relative clergy of D
and CO. since the spectator D acoa i s incapable of rcaoving this relative
energy. As troftslatinnal energy is increased, eventually this internal
energy wi l l exceed the dissociation energy for DCO-. The thermodynamics
for this process are:
CO* + D2 (0 eV) - DCO* + D (- .7 eV) •*• D + D+ + C02 (+ 4.4 eV)
2 Kcal/mole) in energy above the initial react ants.
The DCO_ product will be unstable if Q ^ - AE° or
If E denotes the energy of CO. relative to the D atom,
"D^CO.
co2
"^LAB
0 _ U L U U i b LUCU HUCU Ci_ *" =—
and the spectator stripping peak i s expected to be greatly attenuated
(and show forward movement due to loss of more highly excited product)
for i n i t i a l C02 energies greater than 100 eV.
Product intensity distributions for DC0_ were examined at laboratory
energies of 100 and 125 eV. At 100 eV (8.3 eV relative energy - Fig. 45)
the stripping peak persisted, but showed a l i t t l e forward movement. At
125 eV the peak intensity had moved farther forward and intensi ty of the
DCOo product dropped by a factor of 10. This is consistent with loss of
-203-
DCO, formed by a s t r i c t spectator str ipping mechanism and s tabi l izat ion
of the detected product by forward r eco i l . This i s consistent with the
results of Ding.
At i n i t i a l laboratory energy of 150 eV no significant amount of
DC0- was detected. At this and higher energies, product s tabi l iza t ion by
forward recoil becomes improbable and formation of products in competing
reactive channels is l ikely.
COf + H 2 —•- HCOj + H (35 eV) Relative Energy = 1.5 eV
560 tn/sec
XBL 748-7117
Fig. 40. HCO iocensicy distribution tor l .S eV relative energy <H2 target).
COg + D 2 — DCOj + D (25 eV) Relative Energy = 2.03 eV
I +90°
180°
560 m/sec
Q = 0eV
) 0°
\ !0% Beam "rofile
XBL 749-7206
Fig. 41. DCO- Intensity distribution for 2 eV relative energy (D_ target). X marks spectator stripping velocity.
COf + HD —-DCOf + H (22.7 eV) Relative Energy = 1.51 eV
480 m/sec
Q'l.OeV
01.
\ 20% Beam Profile
XBL 749-7210
Fig. 42. DCO- intensity distr ibution from HD at 1.5 eV re la t ive energy. X marks spectator stripping velocity.
C 0 | + D 2 —*~ DCOg + D (35 eV) Relative Energy = 2.9 eV f+go"
180°
560 m/sec
\ 0 ° .
X5L 748-7119
Fig. 43. DCO_ intensity distr ibution from D, at 2.9 eV re la t ive energy.
-208-
CO| + D 2 — - DCO| + D (60 eV) 981
Relotive Energy = 5.0 eV
T+90 Relotive Energy = 5.0 eV
T+90
Q = OeV S\^/!~^*~-Q = -2.5 eV / [ / / S ^ ,
>s/5* y^x ^JOOI^A
1 ( / l O K 20K
ISO" I If ( 1 [ f n n '"—-N
>—J/u 20% *-*y#y Profit*
| |
\
[ f n n '"—-N
>—J/u 20% *-*y#y Profit*
1 BOO m/sec ' 1-90°
XBL 749-7207
Fig. 44. DC02 intensity distr ibution from D- at 5 eV relat ive energy. Spectator stripping peak i s becoming more pronounced.
-209-
C 0 | + D 2 — > DCOg + D (100 eV)
Relative Energy = 8.3 eV
Q = -3.2 eV,
180°
1200 m/sec
+ 90"
jo*y^\
XBL 749-7238
Fig. 45. DC0 2 ' intensity distribution from D at 0.3 eV relative energy.
- 2 1 0 -
C 0 | + D 2 — » • DCOg + D (125 eV)
Relative Energy = 10.4eV
Q= -2.5 eV.
180°
1200 m/sec
-90°
X6L749-7237
Fig. 46. DCQ,+ Intensity distribution from D, at 10.4 eV relative eaergy. Intensity peak has moved forward of the spectator stripping velocity showing forward recoil product s tab i l ization.
DCO* (HCO+)
The DCO product forms a second Important reactive channel In the + + •*•
C 02~ a2 s v s t e m - Wai l e DC° Intensities are typically lower than DCO'
intensities by a factor of 50, there is a sizeable amount of this product
produced in the reaction.
The DCO product distributions provide further evidence for low
energy complex formation giving way to a direct mechanism at higher
energies. The reaction forming DCO + OD is 0,7 eV exothermic, very close
to the value far formation of DCO..
Figures 47-51 show HCO and DCO product intensity maps over a range
of Initial relative energies. The HCO distribution in Fig. 47 is very
close to being symmetric while Fig. 48 showing the analogous DCO distri
bution shows somewhat greater forward emphasis. In both cases cbe dis
tribution is peaked at the center of mass. As the relative energy in
creases to 8.3 eV (Fig. 49) this asymmetry becomes more marked and a for
ward peak is present. The distribution for E . = 10.4 eV (Fig. 50) is
quite similar. The position of the peak moves steadily forward with
Increasing energy until the distribution lies entirely in the forward
direction (Fig. 51).
The movement of the product distribution with increasing energy is
most clearly viewed by examination of the zero degree scattering (center
lines) with a normalized velocity scale as shown in Fig. 52. At low
energies the distribution is quite symmetric about the center of mass
and steadily progresses toward forward scattering as the initial energy
is increased. This is further evidence of complex formation at low
e n e r g i e s w i t h a more d i r e c t i n t e r a c t i o n a t h i g h e r e n e r g i e s .
To i n v e s t i g a t e whether t h e r e i s any i s o t o p e e f f e c t wi th r e g a r d t o
HCO and DCO format ion, both HCO and DCO product i n t e n s i t i e s a t low
r e l a t i v e e n e r g i e s were measured u s i n g HD as a t a r g e t . The r e s u l t s , shown
i n F i g . 5 3 , show t h a t i n both v e l o c i t y d i s t r i b u t i o n and i n t e n s i t y t h e r e
i s no d i s c e r n i b l e i so tope e f f e c t .
To v e r i f y presence of a symmetric d i s t r i b u t i o n peaked a t t h e c e n t e r
of mass a t low e n e r g i e s , HCO c e n t e r l i n e d i s t r i b u t i o n s from H_ were
measured ( F i g . 5 4 ) . These zero deg ree s c a t t e r i n g p r o f i l e s g e n e r a l l y d i s
p l a y t h e symmetric behavior expec ted from l o n g l i v e d complex f o r m a t i o n .
The e x a c t mechanism of format ion of t h e DCO product has no t y e t
been c l e a r l y def ined . Using the v e l o c i t y and i n t e n s i t y d i s t r i b u t i o n s
f o r SCO ( F i g . 52) i t i s p o s s i b l e t o make some i n f e r e n c e s . At low energy
mass v e l o c i t y . The i n t e n s i t y and p o s i t i o n of t he peak a long wi th t h e low
i n t e r n a l energy a s soc ia t ed wi th complex formation suppor t t he c o n t e n t i o n
t h a t a t low r e l a t i v e energy, DCO i s formed d i r e c t l y from decay of t h e
D2CO+
At somewhat h ighe r ene rg i e s t he peak i n t e n s i t y i n c r e a s e s and moves
forward . I n t h i s i n t e rmed ia t e energy regime (E . = 4-8 eV) , t h e DCO
p roduc t appears near a v e l o c i t y c o n s i s t e n t wi th a "double s t r i p p i n g "
mechanism (V (CO ) in F i g . 52) . The p i c t u r e of the i n t e r a c t i o n i s of
CO i n t e r a c t i n g s o l e l y wi th a s i n g l e D atom whi le 0 i n t e r a c t s w i t h t h e
o t h e r D atom. While such a p rocess r e q u i r e s a r a t h e r s e v e r e l y c o n s t r a i n e d
range of c o l l i s i o n geomet r ies , i t i s n o t e n t i r e l y u n l i k e l y t h a t such an
i n t e r a c t i o n may occur .
As initial relative energy is further increased, the intensity peak
for DCO moves further forward until (E ~ 10 eV) it appears near the
Fig. 52) . In this case one imagines that DCO, is formed by a direct
interaction and later decays to form DCO + 0 (AE° = 4.5 eV) or CO- + H
(AE° -5.2 eV). Since the relative energy (10 eV) lies above that at
which DCO- formed by a strict stripping mechanism remains stable and
rationalize the production of DCO from stripped DCO..
As relative energy is increased further, there is a dramatic drop
in DCO peak intensity at high relative energy, DCO formed both by a
double stripping mechanism and by decay of DCO„ is expected to be un
stable. For the double stripping case, the energy of the CO moiety is
28/44 of the CO^ energy and relative to the D atom.
- E a = Q = - 28/44 x 2/30 E , ^ = .0424 E ^ .
At Ey A R = 150 eV DCO formed by double stripping will be found at
Q - - 6.4 eV. If we add to this one-half the exoergicity of the reaction
(CO + D -*• DCO + + 0D AE° = .7 eV) then the internal energy of DCO is
D = - Q - &E° ss6.7 eV. o This i s equal to the dissociation energy of DCO (6.7 eV) and one expects
that DCO formed by a double stripping mechanism will disappear for
" 2 '
cion of DCO* (E a = - Q = 2/46 E ^ ) i s equal to 6.5 eV at E y j l B = 150 eV.
However, the formation of DCO + 0 from DC0_ requires 4.5 eV energy.
Since this endothermicity must be subtracted from the final internal
energy of DCO v at ISO eV In the laboratory,
U • - q - fiE° a 2 cV. o This internal energy is less than the dissociation energy of DCO by a
considerable aeounc, Ve thus expect that at 150 eV DCO forced by double
stripping wi l l be unstable vhile DCO foracd f rem decay of DCO, will
retain undlssociatcd (dissociation in the latter case occurs for E,._ > LAS
250 eV). The drop In peak intensity of DCO for E^j. > ISO eV thus pro
vides evidence for formation of a significant osount of DCO by a double
stripping mechanism at intermediate energies. It appears that at high
energies this component of the DCO Intensity distribution disappears
with the remaining DCO being that formed by deeny of DCO,. Zt i s un
clear whether the forward movement cf the DCO peak intensity tovard V
for DCO, i s actually due to DCOj stripping followed by DCC formation, or
i f the peak movement i s due to a forward recoil effect. The above d i s
cussion tends to support the latter hypothesis.
In any case, DCO formation appears to be the result of several
types of interaction mechanisms within the energy range studies. It i s
possible that several mechanisms cay work simultaneously at any given
energy. The transition between oechanises of DCO formation Is likely
a gradual one.
-215-
I COj + H 2 — - HCO* + OH (100 eV) Relative Energy = 4.37 eV
IBO*
1200 m/Me
0--0.77
XBL 749-7205
Fig. 47. BCD Intensity ducributlan froi a , *t 4.4 eV relative energy.
COg + D 2 - — DCO + + OD (52 eV) 9SZ
Relative Energy = 4.36 eV T+90"
S jS" ^-—2K -~,
/ - °K
. /° = ~3
« 1 8 0 " 1 1 1 ( > X • M 1 °°r I ) \J JJJ V S ^-20%
Beam Profile
' IOOOm/sec ' 1-90°
XBL 749-7ZC6
Fig . 48 . DCO i n t e n s i t y d i s t r i b u t i o n from D, at 4 .4 eV r e l a t i v e energy.
C0£ + D 2 — DC0+ + OD (100 eV) 104
Relative Energy = 8.3 eV * T+90*
•0 ^^ ,Q«-6 .0»V
Q = -8.0«V j//^*****^' " S^vX. \ Z \ ^ ^ v^*^eo
• ^ ^ \ \ \
^ey [ 1 i f M f §^])J^ >yyUJ I
1 1 *"~~ 0^
1 I600m/»e ' I-90*
XBL 7 4 9 - 7 2 0 4
Fig . 49 . DCO i n t e n s i t y d i s t r i b u t i o n from D, at 8 .3 eV r e l a t i v e energy; X marks spectator s t r i p p i n g v e l o c i t y of DCCf** (double s t r i p p i n g ) .
COg + D 2 —» OCO* + OD (125 eV)
Relative Energy -10.4 eV j+90'
Q=-IOeV.
1400 m/sec
20% Beam Profile
x = Vce for DCOg formation
XBL 749-7231
Fig. SO. DCO Intensity distribution from D- at 10.4 eV relative energy; X marks spectator stripping velocity of DCO2 *
- 2 1 9 -
COg + D 2 - • DCO+ + OD (200 eV) • ISO
Relative Energy = 16.67 eV . +90°
Q=-l5.5eV / 30 / \
1 / > V * > \ \ / SO /
^-Ar-100 \ \
x 180° j ' ) r 1 / s v / / A
' ) r 1 / s v / / A
1
7^20% ' Beam
Profile
1400 m/sec -90°
XBL 749-7203
F i g . 5 1 . DCO I n t e n s i t y d i s t r i b u t i o n from D, a t 16.7 eV r e l a t i v e ene rgy .
0-L 1200--
0 i 12.000--
~ 7000-
-220-
COf+ D2-»DCO*+O0
' n l * 4 - 3 6 1 '
V B S VCU \ \ . V B E * y
0 C 0 + Product Velocity * XBL749-7229
Fig. 52. DCO centerline distr ibutions from D_ as a function from long lived complex to direct interaction mechanisms.
- 2 2 1 -
C 0 | + HD — * HCO +, DCO
i 1,000- -
E r e l -- 2.22 eV Product Velocity —
XBL749-7228
Fig . 53 . HCO and DCO centar l ine d i s t r i b u t i o n s from HD shaving no s i g n i f i c a n t i sotope e f f e c t a t law r e l a t i v e energy.
COt + H, Hccr + OH 2000--
HC0+ Product Velocity BEAM
XBL749-7230
Fig. 54. HCO cencerline distributions from H_ at low i n i t i a l re la t ive energy.
i n i t i a l re la t ive energies there Is a large amount of inelas t lcal ly
scattered CO.. The distributions suggest that scattering occurs by
simultaneous direct interaction and long lived complex mechanisms.
A product map of C0_ from D„ i s shown in Fig. 55 for E , = 1.86 eV.
There i s a large component of e las t i c scattering which follows the Q = 0
c i rc le , yet in the forward hemisphere there i s a significant amount of
ine las t ic i ty displayed, even at this low relative energy. For comparison,
Fig. 56 shows the analogous experiment with Be target gas. While there
i s again a large elast ic component to the map, near the center of mass
the intensity drops, suggesting a much less inelast ic type of interact ion.
Comparison of these two distributions leads to the conclusion that even
though much nonreactive scattering occurs by a direct mechanism, the
formation of a long lived complex in collisions of CO., With D_ i s likely
responsible for the highly inelast ic CO, intensity.
The CO- distribution from D2 at E , = 3.0 eV i s shown in Fig. 57.
The relat ive inelasticity has increased and now contributes to the for
mation of a ridge projecting back toward the center of mass. The
existence of such high inelast ici ty at this relative energy i s s ign i f i -
+ 21 more ine las t ic than the Ar -D_ resul ts at a similar energy. This
-224-
suggests e i ther that complex formation is occurring or that the large
number of additional vibrational degrees of freedom in the C0_ case are
inportant.
Figures 58-60 are maps of CO from D_ at relat ive energies of 5,
8.3, and 10.4 eV respectively. They continue to display large ine las t ic
components although the overall intensity of the maps drops off as
ccllisions occur with greater relative energy. This intensity change
is couciscant with an expected drop in to ta l cross section for C0--D
collisions as the relative energy is increased.
-225-
COj+D 2 — C0| • D2 (22.7 eV)
Relative Energy = 1.88 eV [+90°
.180°
Q-OeM
680 m/sec
80% Beam Profile
X8L 748-7118
Fig. 55. Sonreactive CO.1- intensity distribution from D, at 1.9 eV relative energy showing broad inelasticity at the center of mass velocity.
- 2 2 6 -
COg + He — - C0| + He (22.7 eV)
Relative Energy = 1.89 eV f +90°
^180"
680 m/sec
20% Beam Profile
-90°
XBLMB-7IIG
Fig. 56. Nonreactive CO„ intensi ty distribution from He at 1.9 eV relat ive energy. There i s a significant lack of intensi ty due to inelastic collisions near the center of mass veloci ty.
COg + D2 — COj + 0 2 (36 eV} Relative Energy = 3.0eV 1+90°
.180°
800 m/sec
0 = OeV
20% Beam Profile
*&. 746-71 15
Tig. 57. Honreactive C0 2 intensity distribution from D at 3 eV relative energy.
-228-
C 0 | + D 2 —•*• COg + D 2 (60 eV) Relative Energy = 5 eV »
[+90°
0 = OeV Q=-2.8eV
J80"
^20% Beam Profile
1200 m/see
XBL 749-7209
F ig . 5 8 . Honreactive CO- i n t e n s i t y d i s t r ibut ion from D_ at 5 eV r e l a t i v e energy.
COj + D 2 — - CO2 + D 2
COOeV)
Relative Energy = 8.4 eV +90'
180°
2000m/sec
-90°
20% Beam Profile
XBL 749-7202
Fig. 59. Nonreactive CO- intensity distribution from D_ at 8.4 eV relative energy.
C0£+ D 2 -*• C 0 | + D 2 (150 eV)
Relative Energy = 12.3 eV
Q = OeV
180°
1600 m/sec
0% Beam Profile
XBL 749-7235
Fig. 60. Nonreactive C0 2
+ intensity distribution from D at 12.3 eV re la t ive energy.
-231-
The CO product i s a third reactive channel which was studied at
several energies. At i n i t i a l energies below 100 eV, no significant •f
amount of CO was detected. For energies above this level, in general
the CO distr ibutions are very Bimilar to products of coll lslonally
induced dissociation which have been measured in other ion-molecule 22 +
systems. The CO product lies forward of the center of mass and has
a broad angular distribution. The overall intensity remains approxi
mately constant as a function of relative energy.
One question which arises is whether the formation of CO occurs
by an impulsive dissociation, or whether the chemical interaction between
CO. and D_ plays n role In the dissociation. The distribution of CO
formed in collisions with He (Fig. 61) are quite similar to those from
D 2 (Fig. 62-64). This suggests that in both cases the dissociation
occurs by an impulsive collision in which the chemical nature of the
product plays a very small role. The large Q figures for the CO dis
tribution peaks (Figures 62-64) make it highly unlikely that any H~0
target is formed. It is more probable that (H_ + 0), (H + OH) or
(H + H + 0) are formed, with each neutral product leaving the scene of
the collision taking with it a sizeable amount of translational energy,
consistent with the large -Q valueB of the CO distribution. Another
possible source of CO intensity might be dissociation of highly excited
HC0 + formed by a stripping mechanism for Q s s > B ^ ^ H o w e v e r > ± t u
impossible to confirm this mechanism for CO production.
C0|+ He-*- CO++0 + He A (125 eV) J+90'
Relative Energy - 10.4 eV
0=-9.5eV
Q=-l0.3eV.
180'
1200 m/sec
XBL749-7232
Fig. 61. CO Intensity distribution from He at 10.4 eV relative energy.
-233-
C0| + D 2 —*• C0 + + (D20) (150 eV)
Relative Energy = 12.5 eV +90°
998
Q=-IOeV-Q = -l2eV.
.180°
2200 m/sec
20% Beam Profile
XBL 749-7200
Fig . 6'2. CO i n t e n s i t y d i s t r ibut ion from D, at 12.5 eV r e l a t i v e energy.
-234-
COg + 0 2 — CO++ (D20)(200 eV) Relative Energy = 16.7 eV +90°
Q=-15eVv
Q=-9eVv
180s
2600 m/sec
100
- £ •
20% Beam Profile
Fig. 63. CO intensity distribution from D- at 16.7 eV relat ive energy.
C 0 | + 0 2 — ^ C 0 + + ( D 2 0 ) (250 eV) 1156
Relative Energy = 20.8 eV 1 T+90°
s^~ ^ J > C \ Q = -\4eV^yS A l O t J N A
Q = -l9eV^/^ Jl p° \ \ \ \ 2 0 0 V l \ . 250O w
IW \\\V a , 1 8 0 " f 1 l\ ,¥i\ H 1
• l l 11 1
0 ° f c
^ 2 0 %
1 1 !
Beam Profile
' 2600 m/sec ' 1-90°
Fig. 64. CO intensity distribution from D, at 20.8 eV relative energy.
-236-
0D+, 0 + , and H 0 +
Both OH and 0 were noted as minor products of C0„ + H, col l i s ions .
H_0 was not detected at any of the re la t ive energies studied, which i s
consistent with a possible energy barr ier in the entrance channel sug
gested by the H O correlation diagram. + Figure 65 shows the distribution of OD from D» at a relat ive energy
of 16.7 eV and Fig. 66 the distribution for 0 from D-. Neither product
was detected for E < 100 eV. Because of the very low intensity associated
with each of these reaction products, they were not investigated to any
extent. I t i s assumed that 0 i s the product of collisional dissociation
while OH may be formed either direct ly from the H CO. intermediate or
from dissociation of highly excited HC0~ or HCO . In any case, neither
of these products has contributed to our understanding of the overall
reaction system.
I t should be noted, however, that OD i s clearly not the product of
formed by independent collisions of CO and 0 (in the form of CO-) with
separate D atoms. This possibility i s ruled out by the position of the
OD distribution- In the event of a double stripping mode of OD forma-16 , t ion, one would expect an intensity peak at V = — V where V i s the
velocity of the incident C0„. This velocity l ies behind the center of
mass where there is in fact negligible intensi ty. + 4- *
By similar reasoning the formation of 0 from excited (D„0 ) may
be ruled out since such a mechanism in which an 0 ion is stripped from
C02 as i t passes by would also lead to 0 backscattering.
COg + D 2 - * O D + + DCO (200 eV) Relative Energy = 16.7 eV .
1153
1000 m/SBC
XBL7"lfl-7ll3 F l j . 65. OD i n t e n s i t y d i s t r i b u t i o n trom D, at 16.7 eV r e l a t i v e
energy.
COg + 0 2 — " 0 + + (D2CO) (100 eV) Relotive Energy = 8.3 eV
Q=-8.0eV,
.180°
1200 m/sec •90
XBL 749-7201
Fig. 66. 0 intensity distribution from D2 at 8.3 eV relative energy.
239-
Summary of Results
As we have emphasized previously, the C0_ - H_ system can he charac
terized as a reaction evolving through both a long lived complex and a
direct spectator stripping mechanism. The DCO- product i s predominantly
the resul t of the stripping process although complex formation apparently
plays a role for E < 2 eV. The HCO product Is formed by a complex at
low energies* and i t s forjiation at higher energies can be rationalized
using two competing stripping processes. The CO? which is nonreactively
scattered shows- large inelastici ty due to vibrational mode exci ta t ion.
CO and 0 appear to be formed by col l is ional dissociation while no
H?0 was found at any relative energy. All of these results can be
rationalized in terms of the pertinent molecular orbital correlation
diagrams.
-240-
REPFRRNCES FOR CHAPTER IV
la. H. H. Chiang, E. A. Glslason, B. H. Mahan, C. W. Tsao and A. S.
Werner. J. Phys. Chem. 75, 1426, (1971).
b. Ibid., J. Chem. Phys. 52 , 6150, (1970).
c. K. T. Glllen, B. 11. Mahan and J. S. Winn. J. Chem. Phys. 58,
5373 (1973).
d. Ibid., J. Chem. Phys. 59, 6380, (1973).
B. H. Mahan and T. M. Sloane J. Chem. Phys. 59 5661 (1973).
2. B. H. Mahan. J. Chem. Phys. 55 1436 (1971).
3. R. A. Marcus. J. Chem. Phys. 42, 2658, (1965) and references
therein.
4. J. C. Light. J. Chem. Phys. 40, 3221, (1964).
5. J. L. Franklin, et al. Ionization Potentials, Appearance Potentials
and Heats of Formation of Gaseous Positive Ions. NSRDS - NBS 26_
(1969).
6. W. R. Gentry, E. A. Gislason, B. H. Mahan, and C. W. Tsao. J.
Chem. Phys. 49, 3058 (1968).
7. F. C. Fehsenfeld, K. M. Evanson, and H. P. Broida. Rev. Sci.
Instrmn. 36, 294 (1965).
8. Ref. la.
9. Refs. 1c and Id.
10a. R. S. Hulliken. J. Chem. Phys. 3_, 720 (1935).
b. J. F. Mulligan. J. Chem. Phys. 19, 347 (1951).
c. Y. Tanaka, A. S. Jursa, F. J. LeBlanc. J. Chem. Phys. 32., 1199 (1960).
d. S. Mrozowski. Phys. Rev. 61, 730 (1941).
e. ibid., Phys. Rev. 62, 270 (1942).
-241-
G. Herzberg. Molecular Spectra and Molecular Structure. Vol. Ill
Van Nostrand Beinhold Co., New York, 1966.
0. W. Turner, C. Baker, A. D. Baker and C. R. Brundle. Molecular
Fhotoelectron Spectroscopy. Wlley-Interscience, New York, 1970.
1. F. Moran and L. Friedman. J. Chan. Phys. 42., 2391 (1965).
C. S. Matthews and P. Wat neck. J. Chen. IhyB. 51, 854 (1969).
B. II. Mittmann.H. P. Weise & A. Hlngleln. Z. fur Naturforsch.
26A, 1282 (1971).
A. Roche, H. Sutton, D. K. Bobme, H. I. Schlff. J. Chem. Phys. 55
54B0 (1971).
J. A. Burt, J. L. Dunn, H. J. HcEwan, H. H. Sutton, A. E. Roche and
H. I. Schlff. J. Chem. Fhya. 52, 6062 (1970).
A. Ding. 2. fur Saturforsch, 24A, 856 (1969).
D. L. Smith and J. H. Futrell. Int. J. Haas Spectrom. Ion Fhys. 10.,
405 (1972).
G. Gioumousis and D. P. Stevenson. J. Chen. Fbys. 29, 294 (1957).
H. B. Woodward and B. Hoffman. The Conservation of Orbital Symetry.
Academic Press, 1970.
T. F. George and B. 3. Suplinskas. J. Chen. Fhys. 54_, 1037 (1971).
M. H. Cheng, H. Chiang, E. A. Glslason, B. H. Haban, C. H. Tsao and
A. S. Herner. J. Chen. Phys. 52, 5518 (1S70).
-242-
APPENDIX A
THE MATHEMATICAL DESCRIPTION OF RANDOM PROCESSES
In s u p p o r t of the d i scuss ion of pseudorandom modulation p r e s e n t e d
i n Chapter I I , ue have c o l l e c t e d a b r i e f i n t r o d u c t i o n / r e v i e w of t he
d e s c r i p t i o n of random p r o c e s s e s . This d i s c u s s i o n i s by no means c y c l o
p e d i c , b u t i s aimed a t def in ing the terms used t o d e s c r i b e random
p r o c e s s e s .
A random p r o c e s s desc r ibes a system whose ou tpu t i s no t d e t e r m i n i s
t i c ; g iven a sample record ( t ime h i s t o r y ) of t h e r e s u l t s of a random
phenomenon, i t i s only p o s s i b l e to make p rob ab l i s t i c s t a t ement s conce rn
i n g t h e n a t u r e of f u t u r e sample r e c o r d s . The c o l l e c t i o n of a l l p o s s i b l e
sample r e c o r d s from a random phenomenon i s c a l l e d a s t o c h a s t i c p r o c e s s
(random p r o c e s s ) . Thus, i n s t o c h a s t i c t heo ry no d i s t i n c t i o n i s drawn
between t h e phenomenon re spons ib le fo r sample r eco rd genera t ion and the
c o l l e c t i o n of a l l such r eco rds ; t he phenomenon and i t s r e s u l t s a r e from
a s t a t i s t i c a l p o i n t of view i d e n t i c a l .
The e v e n t s of a s t o c h a s t i c p rocess a r e d e s c r i b e d by a random
v a r i a b l e , X, and the process i t s e l f i s denoted by { X ( t ) , t £ T } where
{T} i s an i n d e x s e t desc r ib ing the time v a r i a b l e , { T } can be e i t h e r a
d i s c r e t e o r cont inuous s e t , de sc r ib ing r e s p e c t i v e l y d i s c r e t e o r c o n
t inuous pa ramete r p r o c e s s e s .
The space of a l l p o s s i b l e outcomes of t h e p rocess i s c a l l e d t he
sample s p a c e , S:
X ( t ) C S , t C T
-243-
The c o l l e c t i o n of a l l s e t s of even ts ( p a r t i a l sample records) i s
denoted by F , the family of e v e n t s . For many p h y s i c a l p rocesses t he 1 2
sample space i s R and the family of even t s i s B , t he Bore l s e t s .
The random v a r i a b l e X i s r e a l , f i n i t e va lued and de f ined on a l l of S .
A c o l l e c t i o n of sample records of a s t o c h a s t i c p rocess i s an
ensemble. In g e n e r a l , ensemble averages of p r o c e s s p r o p e r t i e s ( s imple
and j o i n t moments) a r e no t n e c e s s a r i l y e q u a l t o t h e corresponding t ime
averaged p r o p e r t i e s .
The o u t p u t of a s t o c h a s t i c process can b e d e s c r i b e d by a p r o b a b i l i t y
l a v ( d i s t r i b u t i o n f u n c t i o n ) . This c h a r a c t e r i z a t i o n may be p resen ted i n
one of s e v e r a l ways (ensemble ave rages ) :
(1) By t h e p r o b a b i l i t y dens i ty func t i on .
x,<X(t ) < t + Ax P. (x - ) = l i m — * x- e s
1 AK*O &X A
which describes the probability that the stochastic output in a small
range surrounding the value K-C s -
(2) By the moments of the distribution, including the mean value
and autocorrelation function:
H
-244-
These are,respectively!the f i r s t simple and jo in t moments. Complete
characterization of a stochastic process requires specification of higher
moments as well.
(3) By spectral density functions which are the Fourier transforms
of simple and jo in t moments ( i . e . the power spectral density function).
in general, each of these measures varies with time. If this i s the
case, the process i s said to be nonstationary. If u and R are time
invariant the process is said to be weakly stationary, while if a l l higher
moments are also time invariant the process (and hence the distribution 3
function) are said to be strongly stat ionary. From a practical standpoint, proof of weak stationarity i s often used to justify an assumption of strong s ta t ionar i ty .
For a stationary (meaning strongly stationary henceforth) stochastic
process, i f the corresponding time averaged properties of the mean and
autocorrelation,
U (k) = lim f X. ( t)dt o
T R** C T ; k ) ° iZ T / \ M V t + T ) d
are equal to the corresponding ensemble averaged (over index k) proper
t i e s , the process i s said to be ergodic. This i s an important requirement
for characterizing the properties of a stochastic process since i t i s
rarely pract ical to compute ensemble averaged properties. Ergodicity i s
difficult to prove. However, if a process i s self-stationary, i . e .
-245-
properties computed over short time intervals are relatively invariant
with respect to interval choice, then an assumption of stationarily and 3
ergodicity i s j u s t i f i ed .
An equivalent way of specifying the probability density function for
a process i s to use i t s probability law (or cumulative probability den
si ty function):
P £ Uj> = Prob [X(t)-=xL]
X l P(x )dx .
Two stochastic processes are said to be identical ly distributed i f they
have the same probability lav.
The importance of the above mentioned terminology i s this : random
processes (such as m-sequences or detector outputs) are generally assumed
to be stationary and ergodic. As s t a t i s t i c a l methods are applied to more
complicated physical systems, the systems designer must remain acutely
aware of the assumptions of stationarity and ergodicity as ve i l as the
often made assumption of system l ineari ty. Thus an understanding of the
description of random processes becomes more important as more sophist i
cated analytical systems of measurement (such as impulse response deter
mination) are employed. During our i n i t i a l evaluation of the correlation
TOP system we found the above concepts important and hence their pre
sentation here.
• /
APPENDIX B
DETECTOR COIHCIDENCE ANALYSIS
I n p r e s e n t i n g t he s t a t i s t i c a l a n a l y s i s of the c o r r e l a t i o n method i n
Chapter I I , a d i s c u s s i o n of the problem of d e t e c t o r p a r a l y s i s r e q u i r e d
the e s t i m a t i o n of the p r o b a b i l i t y t h a t two i o n s a r e de t ec t ed d u r i n g a
s h o r t i n t e r v a l . We p resen t here a d e r i v a t i o n of t h i s p r o b a b i l i t y under
t he assumption of a Gaussian TOP d i s t r i b u t i o n .
We r e c a l l t h a t t he output of t h e TOF sys tem, y ( i r ) i s g iven by t he
convolu t ion of t he TOF response f u n c t i o n , h ( t ) and the inpu t modu la t ion ,
g ( t - T ) :
y(T) = h*g = / h ( t ) g ( t - x ) d t (B - l )
The p r o b a b i l i t y of co inc iden t d e t e c t i o n of t»o p a r t i c l e s du r ing any t ime
i n t e r v a l T i s desc r ibed by the a u t o c o r r e l a t i o n func t ion , R ( T ) , of t h e
system o u t p u t :
By us ing Eq. (B- l ) iu (B-2) ,
T
VT> = i f J d T ' f h ( t , ) Sft'-T')"' M(Og(t-i'«)dt - I i -a
" 5 f / h ^ ' > d t ' / MOdt / g(t ' -T , )g(c-T'+ )dr '
KyyCt) = J h C t ^ d t ' J h ( t ) d t E ( t - t ' + T ) (B-3)
where t he t h i r d e q u a l i t y follows from changing t h e v a r i a b l e of I n t e g r a '
t i o n ( T ' - ^ " * ^ ) and t h e d e f i n i t i o n of t h e a u t o c o r r e l a t i o n funct ion f o r
the i npu t m o d u l a t i o n
T
R ( t - t ' + T ) = J= I g ( - T " ) g ( t - t ' + T - T " ) d T " (B-4) (t-f+T) S ^ f
Ste rn and coworkers have eva lua ted t h i s a u t o c o r r e l a t i o n func t ion a s :
K <-0 - e " 2 o | T ' (B-5)
where m i s t he ave rage zero c ross ing r a t e of t h e modulation f u n c t i o n .
Using t h i s e x p r e s s i o n and an assumption of a Gaussian response func t ion
(not an unreasonab le approximation) t
h(t) = A e - ^ S A 2 < B - 6 >
we can e v a l u a t e t he ou tpu t a u t o c o r r e l a t i o n func t ion a s :
; f . - C t - y 2 / . 2
d t , f e - ( t - t o ) 2 / a 2
e-2m|t-f-B (T) + A 2 f - - ( ' - O / a - • f . - ( " J / a _ - 2 m | t - t ' + t ] d t (B-7)
*T. E. S t e m , A. B laqu ie re and J . Va la t , J . Huc lea r Energy A/B 16_ 499 (1962) .
In a t y p i c a l TOF c o r r e l a t i o n experiment t h e wid th of the TOF func t ion i s
gene ra l l y much g r e a t e r than the width of a u n i t modulation pu l se
( t y p i c a l l y by a f a c t o r of 10-25 for a r e a s o n a b l e l eng th f l i g h t pa th ) :
>»k Using t h i s assumpt ion, we approximate t h e o v e r l a p i n t e g r a l
/h ( t ) e - H ^ I (B-8)
by h ( t ' - T ) * l /m . This approximation fo l lows from the f a c t t h a t t h e
smoothly v a r y i n g response func t ion , h ( t ) , w i l l have an approximately con
s t a n t v a l u e , h ( t f - T ) over the t ime i n t e r v a l where t he modulat ion a u t o
c o r r e l a t i o n func t ion i s nonzero; t h e a u t o c o r r e l a t i o n funct ion i s a p p r o x i
mated a s a r e c t a n g l e of h e i g h t 1 and wid th 1/m ( F i g . B - l ) .
Thus
^l. f e - ( f - t 0 ) 2 / a 2
e - ( t ' -T-t o ) 2 /a 2
ID J
m J a 2 (2y 2 -2yT+T 2 ) fly (y = t '-t o)
s A ^ e - T 2 / 2 a 2 f e - 2 / a Z ( y - 1 / 2 ) 2
m J dy
h(t) = Ae- ( , - , ° , 2 / ° 2
-2m|t-t '+ T |
X8L 749-7313
Fig. B-1. Estimating the overlap Integral of the TOF distribution function, h(t) t and the modulation autocorrelation function, R (t) .
R (x) ^ *i e-^2/2a2 ^[^7 - , , - - (B-9)
which i s the desired result for the output autocorrelation. As expected,
this expression is proportional to the square of the scattered s ignal , A,
and depends exponentially on the coincidence interval, T.
Using the values,
E^CT) - 10 J e " W J U " « (B-10)
Evaluating the probability of 2 detector events occurring in 5 usee (the
approximate detector deadtime), we note that the exponent in Eq. (B-10)
will be small (^.05) so that the exponential factor is = equal to 1.
To measure the tota l probability we integrate Eq. (B-10) ,
5 usee 5 2 "* ^ s e c
P - 1 0 3 / e - (T/10- ysec) d T = ; 1 0 3 j dx 0 0
Thus the probability of coincident detection occurring within a 5 usee
interval i s 0.5%. This shows that , given a sufficiently long f l ight path
-251-
and broad modulation bandwidth, deadtime losses of detector signal should
not pose a significant problem in TOP impulse response measurements by
the correlation method.
-252-
APPENDIX C
/ * » » i'OF CORRELATION PROGRAM MONITOR / EDITOR LISTING COMPILED BY / MACHO-B COMPILER
CAF=600 7
00000 0000 0000 00001 3040 DCA SAVEAC 00002 7004 RAL 00003 S005 JMP .1-2 00004 0000 0000 / SAVE FOR ODT LINK 00005 3041 DCA SAVEL 00006 5577 JMP I C400
00020 00021 00022 00023 00024 00025
00026 00027 00030 00031 00033 00033 00034 00035 00036 00037 00040 00041 00042 00043 00044 00045 00046 00047
7300 1041 7010 1040 6001 5400
7000 5026 1000 1074 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
CLA CLL /RECOVER VALUES BEFORE INTERRUPT TAD SAVEL /AND PROCEED FROM THERE RAR TAD SAVEAC ION JMP 1 0
WAIT,
BIN1A. NBJNIA. THIRD* NBINNO. BINNO. COUNT. INDEX. ADDR. SAVEACj SAVEL. SCANNO. SEGNO. INSTR. HOLDL. HOLDS. CUHADD.
NOP JMP .-1 1000 1074 0 0000 0000 0000 0000 0000 0000 0000 0 0 0 0 0 0
/ ADDRESS OF BIN1 / ADDRESS OF NB1N1
- 2 5 3 -
00101 0001 0001 ooioa 0000 0000 00103 0006 0006
/ CLOCK CODE HERE / DELAY CODE HERE / I PLACES ROTATE FOR DISPLAY / SETUP C*300) HERE
00200 6007 START1. CAF 00201 7300 CLA CLL 00202 4777 JMS D02ER0 00203 3000 3000 / CLEAR DISE 00204 3035 3035 00205 4.777 JMS DO ZERO 00206 1000 1000 / CLEAR ACCl 00207 1167 1167 00210 6337 6337 / CLEAR 01/Ei 00211 4776 JMS TYFX 00212 0233 MESS1 00213 4775 JMS ZDATA 00214 7300 CLft CLL 00215 1101 TAD 101 / SET CLOCK 00216 6336 6336 00217 7300 CLA CLL 00220 1102 TAD 102 / SET DELAY 00221 6332 6332 U0222 7300 CLA CLL 0OE23 1270 TAD A / LOAD CUI 00224 6331 6331 00235 4774 JMS WAITER 00226 7300 CLA CLL 00227 1271 TAD B 00230 6331 6331 00231 6001 ION 00232 5026 JMP WAIT 00233 4007 HESS1* TEXT * G 00234 1737 0-00235 4000 •
00270 00271
3500 7500
A, 8,
3500 7500
/Cfcl CODE / CWI CODE . . . T U R N ON DATA BREAK
l | > j O U U U U s | U u ( > l U U O U ^ U l b U > I U U t > ) C ] O U > j U U ( i . ' U U > ' O U U U O » ' U u u O u U 3 t / t f c - - j co* -oooo>ooo» is -0 ' - uiow«- , »-OLntnOi -» -o*^ ( 1 nc j 1 fc '0^ -JC* )C j« - tJ to to* -OOf f»
i O 3 Ifl W W li 'Z Ti N N N
g n c H I K P I l is igBSHsEiNgggSPsgggggegNSIg
3 0 " •"* I
• T3 TO K 1 m m m m 1 o <n - S H 3 10 H
X6i » » » » » - B O E O S S
- ! H i-i H - ) H W [O *- •- CO
p i j H o n SSM — PI c CO H H Z t l
-255-
00356 3000 BUFF* 3000 00357 0077 X2, 0077 00360 0000 DEP. 0000 00361 0000 GET, 0000 00362 0000 SETX. 0000 00363 0000 RATI. 0000 00364 0000 RAT2, 0000 00365 0000 ROT1. 0000 00366 OL'OO ROT2. 0000 00367 CO 14 TBELV. 0014 00370 0000 TEMPI. 0000 00371 7700 XI. 7700 00372 7742 KX. 7742 00373 4000 NEG. 4000
/ THE DAISY CHAIN INTERRUPT PROCESSOR
00374 0513 00375 2400 00376 1200 00377 2407
00400 6031 00401 7410 00402 521S 00403 6334 00404 7410 00405 5325 00406 5207 00407 6041 00410 5213 00411 6042 00412 5020 00413 7300 00414 5024 00415 6036 00416 6046 00417 6041 00420 S217 00421 6042 00422 1377 00423 7510 00424 5242 00425 3240 00426 1240 00427 1376 00430 7700
KSF / KEYBOARD FLAG? SKP / NO JHP KEYFLG / YESi SERVICE IT 6334 / GO TO OVERFLOW SERVICE ROUTINE SKP JHP 525 JHP UNDEF / UNDEFINED FLAB TSP / CHECK PRINTER FLAG JHP .+3 6042 „r / TCF JHP BACK CLA CLL JHP 24
ACCEPT INPUT CHARACTER AND ECHO
/ TRIM CHAR.
KRB TLS TSF JMP .-1 TCF TAD (-301 SPA JHP QM / NOT A VALID CHARACTER DCA OFFSET TAD OFFSET TAD C-32 / VALID CHARACTER? SMA CLA
-256-
00431 5343 JMP QM / NOT VALID 00438 1260 TAD SLIST 00433 1840 TAD OFFSET / CALCULATE ACTION LIST 00434 3841 DCA 1MSTRR POINTER 00435 1841 TAD 1NSTRR 00436 3S41 DCA INSTHR 00437 5641 JAV I INSTHR 00440 0000 OFFSEI. OUOO 00441 0000 INSIKK. OHOU 0044* 7 j<Ju n-;« CLA CLL 004414 ''• '/ '(D JHS TYPA 00444 0446 MQM 0G445 5020 JMP BACK 00446 4077 M9M. TEXT " ? 00447 3740 *-00450 0000 •
*460
00460 0461 SLIST. 0461 / ADDRESS OF FIRST POINTER 00461 7000 7000 / ODT 00468 8600 8600 / CLASSICAL TOF 00463 8680 8680 / CORRELATION TOF 00464 8760 8760 / DISPLAY 00465 0448 QM / E 00466 0448 QM / F 00467 0448 QM / G 00470 0448 QM / H 00471 0448 QM / I 00478 0448 QM / J 00473 0448 QM / K 00474 0448 QM / L 00475 0448 QM / a 00476 0448 QM / N 00477 0448 QM / 0 00500 0448 QM • P 00501 0448 QM / Q 00S08 0442 QM R 00503 0200 START 1 / S 00504 0448 QM / T 00505 0688 SCAN / U 00506 0448 QM / V 00507 0448 QM / la 00510 0448 QM / X 00511 0442 QM / Y 00518 0448 QM / Z
-257-
/ WAITS FOR PHNG CODE TO MOVE / THROUGH THE DELAY LIME
00S13 OOOO WAITER. OOOO 00514 7300 CLA CLL 0051S 3321 OCA TOAD 00516 2321 I S i TOAD 00517 5316 JMP . - 1 00 520 5713 JHP I WAITER 00521 OOOO TOAD, 0000
/ OVERFLOW SERVICE ROUTINE
00525 6002 10F 0 0 5 2 6 7300 CLA CLL 0 0 5 2 7 1335 TAD 0 0 5 3 0 6331 6331 00531 6 3 3 7 6337 00 532 7300 CLA CLL 0 0 5 3 3 5 7 3 4 •MP I 00534 063ft iCAM 0U535 2400 EAJ &4UO
O0S75 1200 00576 7746 00577 7477
*60C 00600 OOOO NTOTAL/ OOOO 00601 7300 CLA CLL 00602 1031 TAD NBIN1A 00603 1035 TAD COUNT 00604 1432 TAD I THIRD 00605 3033 DCA NBINNO 00606 1037 TAD ADDR 00607 6211 6211 00610 3100 DCA 100 00611 1500 TAD I 100 00612 6201 6201 00613 1433 TAD I NBINNO 00614 3433 DCA I NBINNO 00615 2 0 3 3 ISZ NBINNO 00616 7004 RAL 00617 1433 TAD I NBINNO 00620 3433 DCA I NBINNO 00621 5600 JMP I NTOTAL
-258-
00622 7300 SCAN, CLA CLL 00623 1777 TAD EX 00624 6331 6331 00625 7300 CLA CLL 00626 1267 TAD F 00627 3032 DCA THIRD •0630 1256 TAD CUD 00631 3257 DCA DUM 00632 1265 TAD K4 00633 3263 DCA INDX 00634 3255 NEXTK. DCA TEMP 00635 1264 TAD K3 00636 3266 DCA TIMES 00637 1657 TAD 1 DUM 00640 3255 DCA TEMP 00641 1255 GENERj TAD TEMP 00642 4273 JUS TEST 00643 2255 ISZ TEMP 00644 2266 ISZ TIMES 00645 5241 JMP GENER 00646 7000 NOP 00647 2032 ISZ THIRD 00650 2257 1SZ DUM 00651 2263 ISZ INDX 00652 5234 JMP NEXTK 00653 4776 JMS SIGNAL 00654 5775 JMP SETUP 00655 0000 TEMP. 0000 00656 0660 DUD. L01K 00657 •000 DUB. 0000 00660 2000 L01EC 2000 00661 4000 MID1K. 4000 00662 6000 HIIK, 6000 00663 0000 INDX. •000 00664 6000 K3. 6000 00665 7775 K4. -3 00666 0000 TIMES. 0000 00667 0670 F. AO 00670 0000 AO. 0 00671 0024 Al. 24 00672 OOSO A2> 50
00673 0000 TEST. 0000 00674 3037 DCA ADDK 00675 1320 TAD BITSTR 00676 3321 DCA BIT 00677 3035 DCA COUNT 00 700 1317 TAD Kl 00701 3036 DCA INDEX
/ TRANSFORMATION ROUTINE
-259-00702 1037 00703 0321 00704 7740 0070S 4774 00706 4200 00707 2035 00710 2035 00711 1321 00712 7010 00713 3321 00714 2036 00715 5302 00716 5673
00717 7766 Kl» 00720 1000 BITSTR, 00721 0000 BIT.
TAD ADDR AND BIT SZA CLA CLL JHS TOTAL JMS NTOTAL 1S2. COUNT ISZ COUNT TAD BIT HAH DCA BIT ISZ INDEX JMP TEST1 JMP I TEST
7766 1000 0000
00774 2200 00775 0300 00776 2223 00777 0535
*I000 01000 0000 BINlj 0 /DP AC 01001 0000 0 01002 0000 0 01003 0000 0
/BJN3. T0..BIN30. AND NBIN1 TO NBIN30 FOLLOb
01200 0000 TYPX, 0 01201 7300 CLA CLL 01202 1600 TAD I TYPX 01203 3214 DCA TYPNT 01204 2200 ISZ. TYPX
01205 1614 TYPXlj TAD I TYPNT 01206 7002 7002 01207 4215 JMS TYPY 01210 1614 TAD I npNi 01211 2214 ISZ TYPNT 01212 4215 JMS TYPY 01213 5205 JMP TYPXl 01214 0000 TYPNT*
01215 0000 TYPY, a 01216 02 34 AND IK77 01217 7450 SNA 01220 5600 JMP I IfpX 01221 1235 TAD l'hM37 01222 7440 SUA 01223 522 7 JMP TYPY1 01224 1236 TAD TK2 1 5 01225 4242 JMS TLSX 01226 1237 TAD TK.012: 01227 7510 1YPY1. SPA 01230 1240 TAD TK100 01231 1241 TAD TK237 01232 4242 d«S TLSX 01233 S615 J.'P I TYPY 01234 00 77 TK77> 7 7 01235 7741 TKM37* -37 01236 0215 TK21 5» 215 01237 7653 Th«125» -125 01240 0100 TKIOO, 100 01241 0 2 3 7 TK237. 237
01242 0000 TLSX. 0 01243 6046 TLS 01244 6041 TSF 01245 5244 JBP 01246 6042 TCF 01247 7200 CLA 01250 5642 JMP I TLSX
/ D/A DISPLAY CCNTHOLJ X AXIS AUTOMATICALLY SCALED DYL=6063 D A L = 6 0 5 3 D1X=6054
*1600
01600 7300 DISPLA. CLA CLL 01601 3266 DCA N 01602 1264 TAD STAHT2 01603 7041 CIA 01604 1265 TAD ST0F2 01605 32 72 DCA DIFF 01606 12 72 TAD DIFF 01607 7004 KAL
- 2 6 1 -
0 1 6 1 0 7 4 3 0 S&L 0 1 6 1 1 5 2 1 4 JMP . • 3 0 1 6 1 3 2 2 6 6 ISZ N 0 1 6 1 3 5 S 0 7 JMP . - 4 0 1 6 1 4 7 2 0 0 CLA 0 1 6 1 5 1 2 6 4 STAR. TAD STAhT2 0 1 6 1 6 3 2 6 7 DCA XN 0 1 6 1 7 7 2 0 0 HET. CLA 0 1 6 3 0 1 6 6 7 TAD 1 XN 0 1 6 2 1 6 0 6 3 DYL / C 6 0 6 3 ) LOAD 0 1 6 2 2 7 2 0 0 CLA 0 1 6 2 3 1 2 6 4 TAD STABT2 0 1 6 2 4 7 0 4 1 CIA 0 1 6 2 5 1 2 6 7 TAD XN 0 1 6 2 6 3 2 7 0 DCA XAXFS 0 1 6 2 7 7 1 0 0 CLL 0 1 6 3 0 1 2 6 6 TAD N 0 1 6 3 1 7 0 4 0 Crtfl 0 1 6 3 2 3 2 7 1 DCA NN 0 1 6 3 3 1 2 7 0 TAD XAXFS 0 1 6 3 4 2 2 7 1 S K I P . ISZ NN 0 1 6 3 5 5 2 6 1 JHP ROT 0 1 6 3 6 6 0 5 3 DKL / C6053J LOAD 0 1 6 3 7 6 0 5 4 DIX / « 6 0 5 4 > INTEi 0 1 6 4 0 5 2 4 2 JHP . + 2 0 1 6 4 1 7 7 6 0 7 7 6 0 0 1 6 4 2 7 2 0 0 CLA 0 1 6 4 3 1 2 4 1 TAD . - 2 0 1 6 4 4 3 2 5 1 DCA . + 5 0 1 6 4 5 2 2 5 1 ISZ . + 4 0 1 6 4 6 5 2 4 5 JMP • - 1 0 1 6 4 7 7 2 0 0 CLA 0 1 6 5 0 5 2 5 2 JMP . + 2 0 1 6 5 1 0 0 0 0 0 0 0 0 / INDEX 0 1 6 5 2 1 2 6 S TAD sToPa 0 1 6 5 3 7 0 4 1 CIA 0 1 6 5 4 1 2 6 7 TAD XN 0 1 6 5 5 2 2 6 7 ISZ XN 0 1 6 5 6 7 4 4 0 -S2A 0 1 6 5 7 5 2 1 7 JMP HET 0 1 6 6 0 5 2 1 5 JHP STAB 0 1 6 6 1 7 1 0 0 HOT. CLL 0 1 6 6 2 7 0 0 4 RAL 0 1 6 6 3 5 3 3 4 JHP SKIP 0 1 6 6 4 3 0 0 0 START2. 3 0 0 0 0 1 6 6 5 3 0 3 5 S T 0 P 2 . 3 0 3 5 0 1 6 6 6 0 0 0 0 N. 0 0 0 0 0 1 6 6 7 0 0 0 0 XN. 0 0 0 0 0 1 6 7 0 0 0 0 0 XAXFS. 0 0 0 0 0 1 6 7 1 0 0 0 0 NN. 0 0 0 0 0 1 6 7 2 0 0 0 0 D I F F . 0 0 0 0
» AXIS b'lTH CONTENTS OF XN
-262r
*2200
02200 0000 TOTAL. 0000 02201 7300 CLA CLL 02202 2200 152 TOTAL 02203 1030 TAD BINIA 02204 103S TAD COUNT 02205 1432 IAD I THIKD 02206 3034 OCA BINND 02207 1037 TAD ADDS 02210 6211 6211 02211 3100 DCA 100 02212 1500 TAD I ioo 02213 6201 6201 02214 1434 TAD I BINNO 022 IS 3434 DCA I BINNO 02216 2034 ISZ BINNO 02217 7004 HAL 02220 1434 iALi I ut *ii: • • ; ^ : ' l 3434 n:n 1 lilW 02222 56U0 JIW 1 TOTAL
02223 0000 SIGNAL, 0000 02224 7300 CLA CLL 02225 1377 TAD C-36 02226 3036 DCA INDEX 02227 1030 TAD BIN1A 02230 3034 DCA BINNO 02231 1031 TAD NB1N1A 02232 3033 DCA NBINSO 02233 1433 DSUB, TAD I NBINNO 02234 7041 CIA 02235 1434 TAD I BINNO 02236 3434 DCA I BIMNO 02237 7004 HAL 02240 3257 DCA KEEH 02241 2033 ISZ NB1NN0 02242 2034 ISZ IJINNO 02243 1433 TAD I MBINNO J2244 7040 CriA 02245 1434 TAD 1 BINNO 02246 1257 TAD KEE.° 02247 3434 1JCA I BINNO 02250 7100 CLL 02251 3257 DCA KEEH 02252 2033 152 NBINNO 02253 2034 ISZ BINNO 02254 2036 ISZ INDEX 02255 5233 JMP DSOB 02256 5623 JflP 1 5IGNAL 02257 0000 KEEP, 0000
-263-
02377 7742
02400 0000 ZDATA. 0000 02401 6211 6211 02402 420 7 JriS DOZERO 02403 2000 2000 02404 7777 7777 02405 6S01 6201 02406 5600 JMP I ZDATA
02407 0000 DOZERO. 0000 02410 7300 CLA CLL 02411 6214 6214 /RDF 02412 3242 DCA DATAF 02413 6201 6201 02414 1607 TAD I DOZERO 02415 3237 DCA FIRST 02416 2207 ISZ DOZEttO 02417 1607 TAD 1 DO ZERO 02420 32*0 DCA LAST 02421 1240 TAD LAST 02422 7040 CMA 02423 1237 TAD FIRST 02424 3241 UCA l.MDEAZ 02425 1242 I4L' JJH if-.e 0242 6 7640 St.1 (;Lft -Mlf.i'i 6211 6211 •".'•!£ 30 36:17 DCA I FIRST 02431 2237 ISZ FIRST 02432 7000 SO? 02433 2241 ISZ INDEXZ 02434 5230 JMP .-4 02435 2207 ISZ DOZERO 02436 5607 iMP I DOZERO 02437 0000 FIRST. 0000 02440 0000 LAST. 0000 02441 0000 INDEX2. 0000 02442 0000 DATAF. 0000
/ CLASSICAL TOF MODE
0 2 6 0 0 7 3 0 0 CLA CLL 0 8 6 0 1 1 2 1 0 TAD XK1 0 2 COS 3 6 1 1 DCA I X A l 0 2 6 0 3 1 2 1 2 TAD XK2 0 2 6 0 4 3 6 1 3 DCA I XA2 0 2 6 0 S 1 2 1 2 TAD XK2 0 2 6 0 6 3 6 1 4 DCA I XA3 0 2 6 0 7 5 7 7 7 JMP S T A R T 1 0 2 6 1 0 7 7 0 0 X K 1 , 7 7 0 0 0 2 6 1 1 0 2 7 1 XA1> 0 2 7 1 0 2 6 1 2 7 0 0 0 XK2> 7 0 0 0 0 2 6 1 3 0 6 5 3 XA2j T E H P - 2 0 2 6 1 4 0 7 0 6 XA3» T E S T 1 + 4
/ CORRELATION TOF MODE
0 2 6 2 0 7 3 0 0 CLA C L L 0 2 6 2 1 1 2 3 0 TAD YK1 0 2 6 2 2 3 6 3 1 DCA I YA1 0 2 6 2 3 1 2 3 2 TAD YK2 0 2 6 2 4 3 6 3 3 DCA I YA2 0 2 6 2 5 1 2 3 4 TAD YK3 0 2 6 2 6 3 6 3 5 DCA I YA3 0 2 6 2 7 5 7 7 7 JMP S T A R T 1 0 2 6 3 0 7 5 0 0 Y K l j 7 5 0 0 0 2 6 3 1 0 2 7 1 YA1» 2 7 1 0 2 6 3 2 4 7 7 6 YK2> 4 7 7 6 0 2 6 3 3 0 6 5 3 Y A 2 j T E M P - 2 0 2 6 3 4 4 2 0 0 Y K 3 , 4 2 0 0 0 2 6 3 5 0 7 0 6 YA3»
• 2 7 0 0
T E S T 1 + 4
/ C L E A R
0 3 7 0 0 4 7 7 6 JMS DOZERO 0 2 7 0 1 1 0 7 4 1 0 7 4 0 2 7 0 2 I 1 6 7 1 1 6 7 0 2 7 0 3 5 7 0 4 JMP I • + 1 0 2 7 0 4 0 2 1 2 0 2 1 2
/ ION BEFORE DISPLAY
0 2 7 6 0 6001 ION 02761 5762 JMP 0 2 7 6 2 1600 1600 0<=776 240 7 0 2 7 7 7 0200 00177 0400
- 2 6 5 -
Vartable Address Assignments
A 0 2 7 0 LAST 2 4 4 0 T K 2 3 7 1 2 4 1 ADDS 0 0 3 7 L 0 1 K 0 6 6 0 T K 7 7 1 2 3 4 A 0 0 6 7 0 MESS1 0 2 3 3 T L S X 1 2 4 2 A l 0 6 7 1 MID1K 0 6 6 1 TOAD 0 5 2 1 A 8 0 6 7 2 M M 0 4 4 6 TOTAL 2 2 0 0 B 0 2 7 1 A' 1 6 6 6 T » E L l / 0 3 6 7 BACK 0 0 2 0 sinm 0 0 3 3 T VPNT 1 2 1 4 B1MNO 0 0 3 4 ••:• >U1A 0 0 3 1 TYPX 1 2 0 0 B I N 1 1 0 0 0 - . S ? o: -. TYPX1 1 2 0 5 B I N 1 A 0 0 3 0 rtEXTK 0 6 3 4 TYPY 1 2 1 5 B I T 0 - 9 1 MM 1 6 7 1 nv i i 1 2 2 7 B I T S T H 0 7 2 0 !) TOTAL 0 6 0 0 UNDEF 0 4 0 7 B U F F 0 3 5 6 O F F S E T 0 4 4 0 » A I T 0 0 2 6 COUWT 0 0 3 5 tiM 0 4 4 2 w A I T E R 0 5 1 3 CURADD 0 0 4 7 R A T I 0 3 6 3 AAXFS 1 6 7 0 DATAF 2 4 4 2 R A T 2 0 3 6 4 XA1 2 6 1 1 DEP 0 3 6 0 HET 1 6 1 7 AA<s 2 6 1 3 D 1 F F 1 6 7 2 ROT 1 6 6 1 XA3 2 6 1 4 D I S P L A 1 6 0 0 R 0 T 1 0 3 6 5 XK1 2 6 1 0 D I X 6 0 5 4 R 0 T 2 0 3 6 6 XK2 2 6 1 2 DOZEHO 2 4 0 7 SAUEAC 0 0 4 0 X.M 1 6 6 7 0 S U B 2 2 3 3 SAVEL 0 0 4 1 X I 0 3 7 1 DUD 0 6 5 6 5AX 0 3 1 7 X 2 0 3 5 7 DUM 0 6 5 7 SCAM 0 6 2 2 YAl 2 6 3 1 DXL 6 0 5 3 SCANNO 0 0 4 2 YA2 8 6 3 3 O I L 6 0 6 3 SEGNO 0 0 4 3 YA3 8 6 3 5 E X 0 5 3 5 S E T U P 0 3 0 0 VK1 8 6 3 0 F 0 6 6 7 SETX 0 3 6 2 YK2 3 6 3 2 F I R S T 2 4 3 7 S I G N A L 2 2 2 3 YK3 2 6 3 4 BENEK 0 6 4 1 S K I t ' 1 6 3 4 ZDATA 2 4 0 0 S E T 0 3 6 1 S L I S T 0 4 6 0 ZErtO 0 3 4 5 H I 1 K 0 6 6 2 S f A r i 1 6 1 5 HOLDL 0 0 4 5 i T A R T l 0 2 0 0 HOLDS 0 0 4 6 S I A R T 2 1 6 6 4 INDEX 0 0 3 6 STOPH 1 6 6 5 INDEXZ . 2 4 4 1 TEMP 0 6 5 5 IMDX 0 6 6 3 I S i t f l 0 3 7 0 IMSTft 0 0 4 4 T E S T 0 6 7 3 1NS1KE ! 0 4 4 1 TESri 0 7 0 2 K E E P 2 2 5 7 T H I R D 0 0 3 2 KEYFLG 0 4 1 5 T I K E S 0 6 6 6 KX 0 3 7 2 TKM125 i 1 2 3 7 K l 0 7 1 7 T K M 7 1 2 3 5 K 3 0 6 6 4 T K 1 0 0 1 2 4 0 K 4 0 6 6 5 T K 2 1 5 1 2 3 6
-266-
BIBLIOGRAPHY: TOF CORRELATION SPECTROSCOPY
I_. Theory of Correlation Detection
1. T. E. Stern, A. Blaquiere, and J. Valat. J. Nuclear Energy A/B 16,
499 (1962).
2. F. Hossfeld, R. Amadori and R. Scherm. IAEA, Proceedings of the Panel,
Conference on Instrumentation for Neutron Inelastic Scattering Research,
Vienna, 1970, p. 117.
3. W. Reichardt, F. Gompf, K. U. Beckurts, W. Glaser, G. Ehret and G.
Wilhelmi, Ibid., p.147.
4. R. VonJan and R. Scherm. Nuc. Instr. Hath. 80, 69 (1970).
5. C. Visser, J. Wolleswinkel and J. Los. J. Phys. E 3, 483 (1970).
6. F. Hossfeld and R. Amadori. On Pseudorandom and Markov Sequences
0ptini*2inR Correlation TOF Spectrometry. AEC-JUL-684 FF.
(Very complete list of references—avail, "jle from NTIS.)
7. J. F. Colwell et al.. Nucl. Instr. Meth. 76_, 135 (1969); Nucl. Instr.
Meth. 77, 29 (1970).
8. D. L. Price and K. Skold, Nucl. Instr. Heth. 82, 208 (1970).
9. P. Pellionisz, Nucl. Instr. Meth. 92, 125 (1971).
10. K. Weise, Nucl. Instr. Meth. 9S_, 119 (1972).
11. J. Pearce, Nucl. Instr. Meth. 103, 435 (1972).
12. C. J. Macleod, Int. J. Control 14_, 97 (1971).
-267-
II. Correlation and Random Processes
1. Hewlett Packard Journal, Nov. 1969. (Good Introduction.)
2. J. S. Bendat and A. G. Piersol. Measurement and Analysis of Random
Data. Wiley and Sons, 1966.
3. G. A. Korn. Random Process Simulation and HeaBurements. McGraw-
Hill, 1966.
4. Y. W. Lee Statistical Theory of Communication. Uiley, 1960.
(Very good.)
5. E. Parzen. Stochastic Processes. Holden Day, 1962.
6. P. Kindlemann and E. B. Hooper, Rev. Sci. Instrum. 39, 864 (1968).
7. R. Asch and H. C. Ford, Jr. Rev. Scl. lustrum. 44. 506 (1973).
III. Random Sequences and Generation
1. W. Davies, Control. June 1966, p. 302.
2. F. Bossfeld, S. Amadorl, op. dt. AEC-JDL-684-FF.
3. T. E. Stern and B. Frledland. IRE Trans. Info. Theory IT-S 114 (1959).
4. E. Denert et al.. Hud. Instr. Heth. 91, 327 (1971).
5. G. Wilhelmi and F. Gompf, Hucl. Instr. Heth. 81, 36 (1970).
6. J. Bavel, J. Pays. E 6, 495 (1973).
7. A. C. Davies IEEE Trans. Comput. C20, 270 (1971).
8. H. Zierler. J. Soc. Indust. Appl. Math. .7, 31 (1951).
-268-
Experigental Application of correlation Detection. (See also sany
papers in Section 1.)
Heucron Hoise. WaveB. and Pulse Propagation. U5AEC 1967:
R. Uhrig, H. Ohanian; p. 31S
P. Mayer, E. Garells: p. 333
H. Hara, N. Suda: p. 247
Fourth IAEA Symposium on Heutron Inelastic Scattering. Vol. II,
Copenhagen 1968.
L. Pal et al.: p. 407
F. Gompf et al.: p. 417
V. Hirschy and J. Aldrldge, Rev. Sci. Instr. 42., 381 (1971).
Y. Hurata and A. tzuai, tfucl. Instr. Heth. 87, 261 (1970).
J. Gordon et al., Phys. Lett. 26A, 122 (1968).
K. Skold, Nuc. Instru. Heth. 63, 347 (1968).
K. Skold, Ibid. 63, 114 (1968).
A. Virjo, Ibid. 63, 351 (1968).
F. Bezel and P. Pelltools:. Ibid. 99, 613 (1972).
-269-
ACKNOVLEDGHEHTS
There have been many people who have contributed to the work
described within this thesis. It is a pleasure to acknowledge their
contributions.
It has been a priveledge to work with Professor Bruce Mahan. His
thorough scientific knowledge, independent thought, and resourcefulness
were a constant source of support. While fostering independence in the
work of his associates, he was a leader in che true sense, providing
invaluable advice and caking an active part in the formulation of both
theoretical and experimental ideas.
Thanks to Dr. Keith Gillen and Dr. John Winn for their experimental
Insights and frequent discussions. To Jin Fair, thanks for assistance
in measuring cine of flight distributions with his hard von beam
apparatus. To Ralph Terkovitz, thanks for assistance in implementation
of minicomputer programs.
Thanks to the folks in the Electronics Shops for invaluable dis
cussion and electronic construction. Hast prominent were Tan Merrick,
Steve Smirega and Phil Eggara.
Thanks to Shirley Ashley for her superior organizational abilities
in preparing the thesis and to Kelly Bamllovic for an excellent typing
job. Thanks also to Hancy Monroe for her unexcelled figure design and
execution.
Special thanks to Professor Howard Shugart for his careful reading
and comments an the thesis, and to all those in the Departcent of
Chemistry and the Inorganic Materials Hesearch Division who
-270-
provided so much support.
This thesis is dedicated to my wife, Patte, whose continual
support and encouragement were so vital in oft-occurring times of
adversity when the easy answer was "throw in the towel".
We gratefully acknowledge the financial support of the U. S.
Atomic Energy Commission (through LBL) under whose sponsorship this
work was undertaken, and support from a national Science Foundation
Tralneeehip.
This thesis is dedicated with the hope that science may continue to find a place for generalises within its ever expanding and more specialized framework.