Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1953-06

A study of the problems involved in the detection of

mu meson pairs from the MIT synchrotron.

Julian, A.

Massachusetts Institute of Technology

http://hdl.handle.net/10945/24863

library

U. S. Naval Postgraduate School

Monterey, California

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Cii^Il^H PAGE

1. IKTRODU0T2ON TO THE ?nMXU. . .,.,....<,. o ,. . 1

XX • D!k«T£CTXON XII vSnSRAjUa •a9e*«»«»oait«o«<ie»aaoa 4

III. DSTSCTOB Dmian c , . • , • . , . • . • . .

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IV, D£T^CTlOfl fiPriCIE^OY ...•c... 14

V, EXPECTED YIELDS • «..,....,.,. 28

VI, EtEOtaONICS o «

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29

VII. KKP£Bli!lEKTS Ilil THE SYHCHHOTFOS BUH 43

BISUOORAPHX 60

APi^OiDlX A - DETAILS Of DKTiiCTOB COt^STKUCTIOW. . , , .. 5X

Figure X • Detector Bodj.,... <•,..Figure 8 - Phototube Mounts... .o. o. » o

Figure 3 - Housing and Shielding.... ..«.. ..

APPSMDIX B - ORDER OF MAOBITUDE ESTIHATS CF fUtmmm or sffsotiv^ pkotohs at tks pkoto-CATHODi;, PSR MSrV L03T. 54

APFEKDIX C - APPROXIMATE OALCULATIOil FOBEFFX 01 *iINCX FACTOH i^ »oesa««ae».«a.o.»ae»9.tte ttf

A$»P15«DIX D • TABLE V-1 « Values of the eleotro-aagnetio prooese aeeon pair productionintegral froa grapiiloal integration. , oa. a. . 64

TABLS V»2 - Sleetrosaagnetio prooeeecross section for m\i aeeon pair productionas a function of quantua energy... .e. .^c.^ 65

APPSHDIX S « DlAaiUMS, aa-^FHS AJiD TABLES..

«

o., 66Figure It 2 ^ Optical ray diagraas illus*trating the reflections in the detectortt^6w9*uo ooooc9r><>ocoDooad^eeoocoeevooooo6»ee0 Ow

Graph IV-1 - Energy Distribution of mesonpairs « extrapolated froa electron pair&XIie^*S VXQS . •ao«....a.9ao«B9oaea**»*ei>»»«««« Of

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¥flr7»ph TT-l • eBM6 Bes'^onee Testing: Coincidence:'ul8e Positive Overshoot vs Mas 70

C^raoh VX-8 - 6Bii<S ??e«ponee Testln*^ Hlee Tlrae ofColnoldenee Pulse vs Blas« • • • 7D

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73

Qr^iph YI-9« - Dlsojflffilnator Motion of 8BH6 Co-incidence Counting Hate « ^u»idrature Orld Bl^^.... 7^

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CHAPTER I

INTRODUCTION TO THE P HDBLEM

Experiment Indloatee that mu-mesons are not produoed,

singly, in nuclear interactions, although pi mesons can be pro-

duced, and with relatively high orose-sectlons. The appearance

of the mu has always been traced to the deosy of a parent pi

meson. Moreover, the pi meson has been observed to interact

strongly with nucleons, while insignificant nuclear interaction

is known to occur with single mu mesons.

However, these observations do not necessarily mean

that the mu meson is completely unrelated to the quanta of the

nuclear force field. Wentzel has proposed a theory in which the

pi meson is essentially a quantum state of a mu meson pair

(muon—antlmuon). In this theory, the nuclear interaction,

and creation, of a single mu meson is expected to be very small.

However, Wenttel has suggested that a consequence of the ex-

citation of the nuclear field would be an appreciable production

of mu meson pairs (as compared, for instance, to single pi mesons)

.

It is to be observed that it should also be possible to

create mu meson pairs, with photons of adequately high energy,

by an electromagnetic process analagous to Dirao electron-pair

2 ,

production. (Such an event assumes the mu to be a Dirac parti-

cle.)

^enttel, . r.'^. "^^. '^l^ fiotr,n>

2Dirao, P. A.M., Quantum Theory .

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In orA«r th..^t an att«trpt to obsenr* th«»% proptat^t

b« a«Aningful, a otuintltAtiTe dnaXyele of the detootlon problon

was needed in view of the poBSibilily th«tt the Went&ellan orose-*

seotion mtif be Tory ssall.

This Daner pressnti: euch an anAljrsis 'A th tsphaaia on

d«t«ctor design, ^ne Vficricue iciccors «ni*eri&g inw deteotion

efficiency are explored to indicate optisua geoisetriee* and a

nev tytsft of det^otor has been eonetruetad to r«,^lift« the optiama

effioienoy ae oloeely as poneible.

Heson electronics » s.X ready on hand, have been adapted*

with 90 me fflodifie ^ition«» to this experiment. Data have be«n

talcen to establiah the functioning of the eleotronice* and to

reeoXve shielding and housing probleme.

The calculation of expected counting rates has been

carried forward in soae detail for the electrooagnetio process

as well as the '«^'ent£elian» in order to provide a goo.l ooffip&rison

of the relative weights of each at the quanta energies available

in the MIT Synchrotron beam, Approorl^te extrapolation to other

Synchrotron energy spectra An6. intensities can easily be aade.

Detection of either laode of production would be signifi- .

oant» and in partioul<%r the .>^entielian» which ssight reveal the

respective roles of the pi and su in nuclear interactions.

One previous attest has been smde to detect ou pairs—

by Mother, Nartinelli, and Jarnaie with the University of Calif-

ornia 3S2 Nev Breasstrahlung. Xheir experiment suffered fro«

very high b^okgroundSf and detector bloc^^ing, due to high electron

Suggested by Dr. A, Wattenbtrg and Dt, S.T. Feld of theHIT Synchrotron taborfitory.

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fluxeSf but they were able to assign an upper limit to the

Wentzelian production oroes-sectlon as 2 x 10^ larger than the

4expected electromagnetic cross section.

4Mather, »4artlnelll and Jarmie, HCVL 1166 W 7405-eng-48,

University of California.

,8^-^ ^O-i

4

CH.\P1Ti:R II

DETECTION IK GENERAL

The proposed experiment Involves the detection of rau

meson pairs produced by the BreaiSFtrahlung of the -^IT Synchro-

tron interacting wl th a suitable target.

With the existing electronics, detection of a single

fflu meson depends on a delayed coincidence between the meson

pulse and the decay electron pulse. Detection of a pair of

meaons will Involve some type of final coincidence between the

delayed coincidence pulses of each meson.

To measure the pair production, a certain basic ge-

ometry Is envisioned. Figure 8-1, illustrates this geometry

and the associated essential electronics in block diagram.

Desirable features for the measurement are as follows:

1. The separate meson signals must be in fast co-

incidence: a) to reduce the accidentals rate

from the high flux of electrons and other

particles at the detector positions; and

b) to improve their cognlEabllity.

2. For highest efficiency, all mesons with enough

energy to leave the target and pass into either

detector must be required to decay In the

detector. The greatest meson range must lie

within the meson detector dimensions. In

other words, the detector should be as long

as practicable.

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3. The decay eleoci-on (mean life -^2 mlcrosec) must

be obeerved in detectors physically separated

from the meson detector to preclude ambiguity in

meson and electron Tjulses in cases of very fast

decay, and to negf*te the effects of phototube

"after pulsing." It also appears desirable to

require the electron to make coincidence between

the iceson and the separated electron-detector to

keep accidentals rates down.

4. A delayed coincidence must be required between

meson-coincidence pulse (l above) ana tne electron

coincidence pulse (3 above) to verify the identity

of the particles. For single mu meson lifetime

oeasurements the delayed coincidence will use

timed gate techniques to provide decay time data.

5. A final coincidence Is required between the

Individual delayed-ooincidence meson pulses to

establish the pair count.

An analysis of the basic requirements listed above

shows that, apart from the eleotronlos of the problem, the

critical factor In determining success will be In the detector

manifold use in the experiment. Experimental difficulties

that have been encountered by previous workers (Martinelll

et al ), and the requirements Just mentioned, are, of course,

a result of the anticipated very low cross section for mu pair

production with the available quanta energy and intensities.

^Ibid .

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Tliese may, for eorphasis, be groopsd Into thres miijor o&tegories;

A, Small effective solid angles for the

detection of the Dalr process. The

detection efficiency decreases with the

product of the solid angles of each

syete^a.

B. Low efficiency of the decay electron

detectors in detecting the neson decay

in a tandem or slde-by-slde geometry with

the aeeon deteotor.

0. High fluxes of particles, other than

mu*8f producing high singles rates in

the electron and meson counters. In

Martinelli'e experiment, the electron

singles rates flooded his decay electron

circuits and contributed heavily to his

accidental rate. These rates probably

were not only large angle pair-electrons

and scattered-ln electrons from the target

«

but also photoprotonSf and pi mesons. In

any event, as he pointed out, reduction of

this cause of accidentals rate must begin

with shielding of the electron detectors.

And they must be shielded, not only from

the target, but from showers produc^ed by

the beam (or its penumbra) in the shielding

material and collimators.

. _ : ^ . , ^ ;'•''- jft: ^'i ^^.^ ^ i- ' "^^ ^ : -^

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The problems inciioated above are discussed In the

following chapters:

Chapter III Detector Design

Chapter IV Detection Efficiency

Chapter V Expected Ylclde and Counting Rates

YC'

CHi^FTSR III

DETECTOR DESIGN

Single nuclear-reaotlon-produot parti cleB generally

hare a distribution In energy and solid angle. The counting

rate from suoh a reaction is given by:

CR «^ Auj'AE-F M-/where Ato is the fractional solid angle;

^£ is the fractional gpectrum energy;

p" is the fraction counted (an efficiency factor)

For pair detection, simultaneous events in physically

separated and distinct detectors are involved. The counting

rate from a pair production reaction is then given by:

if there is no correlation in energy or angle between

the two emitted particles.'

Majcimum counting rates result from maximizing the

effective solid angle of each detector, both by decreasing

detector distance, and increasing detector area. For example,

a decrease in the effective detector- target distance from 35em

to 20om, increases the solid angle factor for this two particle

process by about 9. This particular improvement is so slgnlfi-*

cant that special efforts were made to realiae it. Further,

to obtain as lainge a value as possible for ?j (discussed later)

The factor 7t is the fraction of the total number of decayelectrons, from mesons stopred in the inner detector, which arecapable of being detected in the outer detector. See Chapter IVon Detection Sfficienoy for a discussion of >7,.

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It l8 neoeasary that the deoay eleotron deteotor have as large

a solid angle as possible.

The latter oonsideration suggegted a raodifl option of

the type of deteotor, first used at the MIT Synchrotron Lab-

oratory by J. 3. Clark, L.w^. Oaborne, and Y. Goldsohmidt-

Claremont in their meson experiments. The model is an inner-

cylindrical deteotor, with a peripherally-contiguous outer

cylinder; figure 3-1 illustrates this detector, which was

used in the first experimental runs to line up the electronics.

Such geometry is quite efficient for observing particles

(deoay electrons) in the outer detector which originate in

the center detsctor.

The axial length of this design is determined by the

upper limit of the mu energy spectrum that can be obtained v,lth

the maximum quanta energy available. This limit is reduced

by the energy needed by the companion meson to Just enter the

second detector. The first modification, figure 3-2 , shows

the increase in length to this upper limit.

The basic design is purely cylindrical. The effective

solii angle per detector, for this cylindrical geometry, can

be taken as a crude estimate to be the solid angle subtended

by the deteotor at mid-length. In other words, for a 30 cm

long cylindrical system of diameter 4", with the deteotor face

at 20 cm from the target, the effective solid angle is taken

to be that subtended at the deteotor midpoint i 36 cm from the

target. For this untapsred cylinder, however, it is impossible

to attain an effective detector distance of 20 cm because the

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Fm<S-T nOOIFICATlON

Fie J -J

NOTE HOW FFUSTRUn CONSTRUCT/ONREDUCED riejf TO n. actual .

FOR •/>" - 'b'', FI03-2, THEPHYSICAL DISTANCE OF TIfIS

&EOn£TRy 16 Q-REATER. THAN JZFOR SAtnC CLEAHANCE RESTff/CT/OAIS,BUT WITH A HeT DECREASE IN fleff.

S£COND nODlFICATION

FI& J-'i

THE OUTER FRU3TRUM GEOMETRYALLOWS FOR CLOSER ACTUAL OlSTANCaAND INCREASE IN SHIELDING WIOTH,"W. A SlI^HT INCRFASE IN flcii

FROM ORTimUM, 3-3 , IS ACC^RTEDAS >SPAC£ AND iYEI&HT SA^ING^.

Z' ySH/£LOl1ING-WlOTtt AVAlLAeL£

FINAL MODIFICATION

Itf)

edge of the detector system vlll be In the beam. Figure 3 ~<i

demonstrates the requlrementfi for minimum beam clearances,

and the djfflculty encountered with the rectangular crose section.

Forming the inner half of the Inner detector ae a conical

frustrum of appropriate angle, effectively moves the detector

towards the target by 15 om, since the solid angle throughout

is now that subtended at the face. Figure 2K3 illustrates such

a detector with the resulting conditions irapoeed. Note that,

despite the deoreaae in the effective detector distance, the

factor ri has suffered in the critical forward section of the

grouping because of the separation of the two detectors in this

configuration.

A final modification to allow actual use of the system

at 20 cm, and to preserve the factor it neoegsitated that the

outer cylinder also be formed of conical frustums. Details of

the final design geometry are sho^n in figure 3-4 and appended

as Appendix A. The physical distance from the detector front-

face to the target center is about 20 o.u. To make r^^^ equal

^° ^actual* ^^ inner detector, in this case a oontinuouE

conical frustrum, would have had a base diameter of some 25 cm,

and a volume of some 8 liters— the outer detectors in turn would

be tremendous, an unwieldy and heavy apparatus requiring a large

number of phototubes for reasonable ohoto efficiency and an

ianiense amount of liquid. As a conpromise, the frustrum extends

to half length only, resulting in a reduction in weight and

7The scale of figure 3-31 e net the same as the scale of

figure 3-2. Dimensions b and b' , the inner detector windowdiameter, are actually equal.

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11

volume of liquid scintillator by £t.bout 45^, aad reducing th«

number of phototubes required,

We do not gain the full Increase of 9 in the solid

angle factor ^ uj , mentioned in the early paragraphs of thlg

Chapter. Instead, the actual net gain le about 6,5.

Another advantage to the outer fruetrum deeign is that

it perailte heavier shielding of the systeai against eleotro-

laa.Tentlc production at siiiall ans^es, without ir^crlficing the

^actual °^ ^^ °'" ^^^^ attained.

The sides and end window of the inner detector are

made of 20 mil brass, as Is the inner wall of the outer detector.

The fonmrd «nd plate, ^nd the outer wall of the outer detector

are made of 1/16" brase to give strength and rigidity to the

entire structure. The back plates of both detectors are made

of 3/8 inch brass. The interior of each is lined wi th 2 mil

aluminum foil as a reflector. All seams were soft soldered

at rolled Joints, except for the baoJt plate junction which was

a oosEbination butt-lap joint to the siding. The back plates

contain the liquid filling and vent holes, and the plastic

phototube mountings.

Six 581S photoinultipliers are used with each system:

two, mounted parallel with the cylinder axis, in the inner

detector; and four, mounted at 90*^ to each other on the cir-

cumferential center line of the outer detector back plate.

Attached mounts of plexiglass hold the phototube to the back

plates in such a way that the photooathode surface is at the

surface of the back plate, and is separated from the scintillator

XX

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12

liquid by 1/16 inoh of plexiglass and an optical contact of

Dow-Corning "200 fluid," a viscous silicone. Some consider-

ation was given to direct liquid contact with the phototubes,

but sealing between the glass envelope and the brass has not

been found reliable. It is for this reason that the full

plastic envelope was used. Rubber "0" ring seals maintain

the viscous oil reservoir between the tube and the plastic,

and act as a mechanical clamp to hold the phototube in position.

A small hole near the base of the flange of the plastic mount-

ing allows for venting of surplus viscous oil during tube in-

sertion. The sirapl© contact seal between the baok plate and

the plexiglass tube-mounting provides the liquid seal for the

cyolohexylbenEene containers. Figure 2. , Appendix A shows

details of the fitting and mounting.

Besides making possible the 20 cm target distance,

the frustrum construction increased the photon collection

efficiency for the liquid system because of the funneling of

successive reflections toward the large end of the cones.

Bay diagrams, flguresl and 2 , Appendix E illustrates this

effect.

An order of magnitude calculation of the number of

effective photons collected (those producing secondary elec-

trons on the photo- cat hod©) per Mev lost in the liquid indi-

cates an expected average of about 10 per Mev. A minimum

ionising electron at radial passage through the thinnest

part of the outer detector will lose about 4 Mev, to produce

an expected 40 effective (3 ev) photons in the outer detector.

SI

-;faiioa5 oi. salcr »...1J lo saaftl^i ?».fi3 lo sead eri; '\Jien sXoil iJLjifije A

"io siiiiie:-. ...: to i;v,:u..,-,Ow.o aS(iJi:;\,3 j:;^i;pi,/. ei;i3 lo"* <,o.ei«fi,vi.i'i*^

'-Ibiil i>i "•! nl yJaci ¥8.4 i*q v»i-Oja3rat;-o3^odq ©iij ao ano-xc?

»©«x)Oiq o;;^ ,v iuocia «eoI ' 'io^09?9f) isJifo »iio lo ;iiji»q

.io4ot^©b i9ijJ0 ©il3 rtl an (» R) •ti;toett« 0^ £)»^©. ..?

13

See Appendix B for this calculation.

The detectors are to be mounted at 45 to the beam

on each side, and at about 20 cm target to detector-face

dlstf-iioe. A beam oollimated to 1 inch width will be used.

An arbitrary selection of 1 1/2 inches from the beam center-

line was taken to be minimum approach distance for any housing

naaterlal. The method of housing the detectors is shown in

figure J, Appendix A.

tham

gjsiJij^^

.l;Dnj;-;*3i:^fc

.o_.3-a^

BiO$ .8^'tifi J,G

14

CHAPTER IV

DETECTION EFFICIENCY

Equation JJlL-2, amat be an&lyzed in detail, and the

correlation between tiie energy of the eaitted partiolee taken

into account.

The detection efficiency of a single detector la:

where (<$^>l^) is the factor F of equation Bl-f.

The detection efficiency for the pair of detectors is:

where the additional factors 2,g, and f, tske account of

Qthe characteristic physics of the process,

g is a factor which results from the energy correlation

between the emitted mesons for the pair process,

(l-<r) is the fraction of the meson decays which occur

during the dead time of the counting circuit after the

meson pulse. This dead-time comprises the electronic

transit tiaie, and fixed delays in the circuit. 6 is

the fraction counted of the total pairs of decays after

dead time.

dC is the factor relating to the competitive processes

of decay and nuclear absorption for negative mu mesons.

7^ is the fraction of the mesons which decay in a

6The factor 2 is a statistical one which arises in the

following way: Since either meson can be counted in either de-tector, there are two combinations that will resiJ^t in a success-ful deiection. Meson 1 in detector 1; meson 2 in detector 2; ormeson I in detector 2; meson 2 in detector 1.

VT.

Su.;'^* S-JrC aoli&Vi ,T

iieicj aalui.i'-ii'.q i^fr^aime X^t&r.

-J V u

i^

15

detector that form r detectable decay electron.

f l8 a factor that gives the true angular distribution

as oorapared to an unoorrelated spherically aymnetric

angular diet rlbi tlon.

The value of £. calculated will be a lower limit on

the detection efficiency, based on the assuirption of absolutely

no correlation between the fractional solid anglesAa/, and

Au)^,

These factors are discussed below in detail.

Factor Act?/ 'AuJa.

The solid angle product is a very critical part of

the efficiency. The basic solid angle geometry is shown In

Figure y-/.

^eff ^^ ^^® effective

detector aperture area.

^Qff is the effective

detector distance.

2.

Some representative values of (^«^ for various A^^--r6^* eff

Cofliblnations, which appear reasonable and attainable, are listed

in Table

'^'££et l/*

Table 4-1 (A uJ and (-^ ">) )

^eff/^eff Au) A"-*

80. 8/go 1.61 X 10-2 2.57 X 10-4

125.8/20 2.51 X 10-2 6.25 X 10-4

30.3/35 .536 X 10-2 .275 X 10-4

126.8/35 .821 X 10-2 .67 X 10-4

A = SO. 8 c-n is the4 inch diameter

A = 125. 8cm^ is th<

5 inch diameter

.>^iiJ

iJow&o^

V--V

,m !.£ .Ol^O^yi

.&uaedBi£j *x3i

9X1^

^HiS

I:, A,

a% .

i\^ V\

^ >:^35^

X-i-

X-^ ^PS

n-tciiooj

X- ,.

16

Note that an Increase In detector diameter by 1* In-

creases the efflclenoy o.t either value of haff by p. factor of

about ?*4. Decreasing r^^f from 35 om to 20 ora, holding A^ff

oonatant, Increases efficiency by a factor of about 9.

The path length of the decay electron beconE s too

large in general, and the factor ;^^ decreases, for a detector

diameter of aiore than about 6 1/2 Inches. Consequently this

was the maximum diameter used In the Inner detector, result-

ing In choosing an aperture diameter of 4 inchti {^Qff^BO.Q cffl )

.

The value of (Auj) for this ^eff^etf combination from Table

-^-iis 2.57 X 10"*^.

Faoteor S

The transit time of the circuit Is negligibly short

compared to the fixed delay time in the meson electronics.

The meson coincidence pulse triggers the electron-meson gate

after a 1/2 mlcrosec fixed delay. The 1/2 miorosec delay Is

used to preclude false coincidences In the gate circuit due to

slowing of one or the other pulse In the discriminators. The

fraction of all the mesona that decay In 1/2 mlcrosec Is:

(x -i) = 1 - eKpC - ^) ^ ^^^ J^~^^

hence S , the fraction of the total that are observable In

pairs, Is

Mote that an Improvement in 6 can be obtained by

decrea^ng the fixed delay in the electronics to 1/4 mlciroseo In

lieu of 1/2 miorosec. This results in an increase by a factor,

ar

S.

life ""'lit?

!!—iiii tw rTiiii imififiiiinT

csitaij no:? sol-no's: *o?^ I© arliJ sncesisii;? eairr bioaxoo noesas bsSH

«i ,8TiJ3Cr

17

.79 • 1.27,762

i&sxstz JT

fh« tx^«rl«enti of Tleiio,^ an* CoiiTersl «t al, havt

s^ovrn that the neg!^tlve mt, a«son i^ froiuently absorbed in

high Z iBRterlale lnet«ad of deo&ying. ?or the purpoaec of

this experiment, ^beorptlon of a negi&tive »u seeon will result

In « lost p«lr oountp sinoe oounting depaode on the production

and detection of the deeay eleetrons.

For our absorber (the ecintlllator liquid) the average

1 l6 about 4.

11The results of Sigurgelrason sLud Yamaisawa'—relative

numbftr of d^eay electrons per stopped «e8on-"-are statietically

about the ««»e for Be and C, both beini^ uprroxi^iately equal to

unity. For our oalculatione* the factor ^Is therefore taken

to be 1.

Fleeter >?^

The decay electrons have a distribution in energy,

ecneequently a distribution in range, «ind thus eo«e of then

will not reach the outer detector. Dae to the shape of the

detector, the fraction that r@)^ohet the outer deteotor is a

function of the position of the aeson decay.

"7^ is the fraction of decay electrons produced in one

of the inner detectors that re^ch the outer detector—and ara

^Ticho, H./.., P.H, 74, (lv^37) 1948.

"^°Convi?rsi, Fsnolni and Ploeloni, P.R. 68* 2^?,, 1946, T.B,71, 209, 1947.

^^Sigurgeirrso.'i, T. and ifasakaira, K./»,, -lev. :<©d. Phys. 81,124, 1949.

"

S'

s?"ri l'::'^t::r

X:.i-;ii. ^i}q ^ao-sdrsaie 'P

fl*'9*i

,.4.A,

18

observfible—averaged over the entire detector.

The Vftlue of 77 is caloulated in Appendix C. The

beslo oonelderatione InTOlvlng the calculation are given below.

The decay electron ipeotrum Bhow« a mopt probable energy

of about 30 Mev. Analytic forme for the spectrusi energy have12

been formal ^^ ted by Hubbard.

The number of decay electrons of energy E in dE le f(E):

f{E)dE = dE tZ£/ (W~E <-f/l4E-3W]) TY~3cc

Takingf>

here to be 25, a value nearly that recommended

by Hubbard, and oooibining the bracket, leads to:

f(E)dE = dE ia£ ^.85W«.78S) JS^-^h

The bracket may b© taken as ,8(W-E), whence,

f(E)dE - 9.6£^

(tf«E)dE 7V-Jc

^sjn/^C/i - jiia - 55 Mev, the maxlmuai kinetic

energy that the electron may carry off from the decay.

A rigorous determination of the fraction of the decay

electrons that leave the meson detector—with enough energy to

produce a pulse In the electron detector—Involves a oompll-

oated three- space-energy integration over the volurae of th«

detector and throughout the spectrum.

A reasonable approximation has been made to the evalu-

ation of >i , taking Into consideration the depth of penetration

of the meson, and tne electron spectrum. The detailed calcul-

ations (Appendix Ogive for the value:

>l = .609; yi^ .37

TSHubbard, H.W. , Thesis University of California, 10 March

1952, "Positron Spectrum from decay of mu mesons.**

ex

Mr,

o«B sfiT

-fftr?.^

^ W

s

A

•^'-' '' - jj j&jeu

".81108 Dm VS Hjijii-j,

19

Factor g l8 the fraction of the total pftlr prorluction

of aesona »coapted In the detector system, at a function of

the distribution of the available kinetic energy. The energy

distribution Is such that an unequal division of energy Is

Attoh more probable than an equal division.

If the division of kinetic energy Is such that one

neeon carries off enough energy to stop at the back wall of

one vety long detector, and decay* the other oeson nay not

get out of the target « I'he pair la not counted. For a short

detector* the high energy particle of the pair say pass through

the detector without stopping and decaying— the result Is again

a lost count.

Graph IV-1, Appendix £, energy distribution of meson

pairs, extrapolated from slAllar distributions for the electron

pair klneraatlos, has been plotted as a pleoevlse linear approx*

13laation, syiiiBetrlo about the fraction one-half.

Superimposed on these approxliaate curves are the energy

acceptance lliBlte larposed by: the target thickness to the

exiting mx; the absorber thickness; and the meson detector

front window thickness. As a not entirely arbitrary choice

of these parameters, consider a target of thickness one Inch

transverse to the beam, with 1/4 Inch of lead absorber, and a

window of .OS Inch brass. The limits of energy acceptance are

determined by! if^f - 2m/^c^ alnut the ©n«rgy loss In

lix" target ^i"Pb ->- .02" brass] ^ To -T^

ISHeltler, W . , Quantum Theory of i^adlatlon.

ITOlfQ'

? 'it '•• .-« .-''

.L^JattSCi

o

.iiirj» fU

:.-* f rsf^t-?'

iftRO ?jsd^ iionf <^i V,

?Dn V-.. ao»«fc'" " i'a -ijii^ i,\.;.xi;

$^QdB s la*"^ .fits ,lc>a Hi il^q «tii .^t.'34-i«^ «1^ \Q tfjy

::«> fiS-irt

1 - • < i 1>•

^•^3s>f«^*^

tai^n* 0i^ <;,".«•; H T.. V-« jUv' ^-J ^i>ii3v;0*5t"'

' VM

A »X-VT ^f*fi^P^

.tiolOa^. UitlASJiit^

80

For each value of k-m^x t^ -m.ax '» the aoceptance

llailts are at Tjl , Tq - T^ ; the fraction of the total area

under the distribution curve bounded by Tju and To - T^ le

the (oaxiinum fraction of the total mu pair speotrum that is

observable in the whole Bolid angle.

Note that at lower photon energies the acceptance

fraction becomes very email. The combination: oross-seotlon;

number of photons in the energy range; and acceptance fraction

In the energy range, probably tends to mate the likelihood of

an observation of a pair firona either group (those from photons

in the highest energy region, as opposed to those from photons

In an intermediate or low region) about equal, other factors

remaining unchanged.

Taking an average over the range of k, we have;

g^.75 iil-^

Factor f

To conserve momentuai and energy for pair production

from a single nuoleon, the mesons will tend to be esltted in

the forward direction. Since only the forward hemisphere is

involved, the factor X ^8 about 4, and probably greater. (See

discussion on upper limit efficiency, latter part of this section.

)

f ^ 4 2F-6The lower limit of the total detection efficiency factor

then becomes:

£ =» 2 X 2.57 X 10"* X .62 xl x .37x .75 x 4

d, » 3.53 X 10-^ UT'/

;n' ft

•o-i "if it

rioi^oifJboT

I? 'I.J.i-lu t»Oi. .... r;**! ii> iv

X:

\-3I

21

The use of this lower limit efflclenoy is a reasonable

approach to the problem of the 'Genteel product?. on, since we

haye no knowledge of the correlative effects of the assumed

Bittaosi field.

However, for the electromagnetic T^roduotion discussed

In the later parts of Chapter V following, an increase in the

•xpeoted counting rate figures may be obtained. The yield

calculations for the eleotroaiagnetio process are made assua-

ii^ a completely Inoonerent process, (linear Z dependence).

If calculation can show a 2 dependence of the type;

Z -t 2, X (Form factor), that is, with additional coherent

production over the nucleus, the expected counting rate

values will be increased. In this case there is a strong

forward correlation of the rau pairs; 1) from the theoretical

cross-section (Heitler) for Dlrao particle pair production;

and, 2) from the coiierenoe in the forward direction. Both of

these A'ill make the factor X greater than 4 for particle

detection at forward angles.

IS

eldfefloR el IV

i aOB»m

SRUOt -V®

22

CHAPTHR V

EXPECTED YIELDS

IntrodusUon i In order to oalculate t'aa counting rate to be

expected* one needs a /.nowledge of the cross section. Lacking

a knowledge of the cross section all one can do is exprees the

Counting rate as a function of the integral of the orosa eviction

over the energy range available. If a OH is observed, experi-

aents at different energies could give the energy dependence of

the cross section. In tnis {section, the general expression for

the counting rate as a function of the integral cross section is

developed.

The yield of the pair production process can be written

in differential form as:

where d Y is the yield, in meson pairs per unit target

length, per unit quantum energy interval, per

14mouse.

<y^tej is the number of quanta having energy

between E and E dE over the entire target

area, per saouse.

14The "mouse* unit is a Laboratory unit of integrated in-

tensity. The beam is monitored in an ionization chamber at thecolli .Bator face. Charge accumulated in the chamber is dischargedafter 7 x 10^ e.q. (See 3.M. Thesis H. Ratz.) Note that eventhough the collimation to one Inch absorbs some of the quantaproduced in the Synchrotron target, the rate, e*q. per nouse atthe target position will still be d , since the ionization chamberis on the target side of the wall. The collimation effect will beto increase the running time ^^ev mouse.

sajarx

9Xli?X - .nc.^J

er ^^. a.

noiJ-

-/ •!?».' ;-3PCfc

to eoii&i

10^

j»^« .i W -^ w

S ? ?»?/ ;'•' *.

'51' ?!

onti mn: Ic

XS'^&fi® Salvjsri .:$n&up t© li^dicjjfl i^n;j el {s)^\^

•cf I £lw V nol^rffiilloo ad's .IXbw ariJ lo e

.satiOffi Tisq aail;r ignJ;: . nj au4as\;c:i* ;jj

88

N le the number of target atoms per cm ,

(r(£) ^f^ ^^^ orofB ieotlon for meson pair

produotlon at energy E, per target atom.

The number of quanta per mouse in the energy Interval

E to E -H dE, d<J>

(e), is a function of the target length:

d4>(£) -- di^JS)^"^ ^-2

whence, dX = N (TiE) d<f>^fe-^'^dt K-3

where (/ / Is the yield in meson pairs per

unit quantum energy Interval In target

16length 1 j^^

ana c/y = N(^<^h {'~U-^ )^'^

dV ^ N (rd4>oLff v-s

where 1^^^ is the effective target length,

values of which^® for several elements

are tabulated in Table 5-1

Be 9,23 Al 7.01

C 8.96 Cu 2,48

^ow d <^^ ^ Targ(^t ar^^ft y^ dS ^ a! d(lnE) l/-<^' Beam area

"*"fi

15Collimatlon determines the useful target length tc be

4 Inches.

The figures in T«,ble 5-1 are oaloulated, taking/* equalto the asymptotic pair limit coefficient. '•" Qraph V-1, AppendixB, Linear absorption coefficient for the elements listed in Tablei^-1 shows that this assumption is reasonably valid at the energiesunder- consideration.

"''^rerml, E., Nuclear Phyelc s,

'kf'mti .

.- •: W-t • ^

(.a)-t)

,t(Fl l!10t

a'.

'

"^-M

<^

,

Si

^\3^o<^b-^ V\ ^ Xb

LMhMAjiMmMlLl..

I.

jjw

<;:»>"" \ 't> ":jo-

\:..

3^.8

[-• 'T T' ~ ©^

SS

u siix;;i*tt;g^D tiol;Jaa!*

*^£Ai^i{i

24

wh«re ^ - 7 X 10 equivalent quanta (e.q,) t>er mouse

In the MIT bean;

M Is the energy spectrum of the Bremsstrahlung;

C[ le the e.q. per mouse, corrected for the actual

area, and i£ equal to:

^'2 7V* = -^ X 7 X 10 e.q, per mouse

therefore I » N l^f^ ^ / ^("Ej d (£nE)

or Y = N l^j.|, a'

I

(events per mouse)^^ )/-?

The limits of integration are somewhat variable: The

upper limit is a function of the Synchrotron, with a probable

Baximum of 340 Mev, The absolute lower limit is the threshold

energy for the pair process (216 Mev). The practical lover

limit le a function of target and absorber motsrial and thick-

80ness.

The observable yield (Counting Rate) is then;

CR s€Y = €-Nl^j.^ a'

I

^^Q

The expected counting rate, in counts per mouse, is

tabulated in Table 5-2 for the four elements C, Be, Al and Cu,

as a function of the integral I. (The integral has the

2 ,

dimensions , cm .

)

18The spectrum has been theoretically predicted, and ex-

perimentally verified, as actually being about: .87 x^ .

£19

To determine the rate, "events per equivalent quanta,"divide the rate ''events oer mouse'* by f/irX "? x lo".

20'^

To reduce background, it was found necessary to put 1/4inch of lead In front of the detector—see Chapter VII.

*!' s »

\-v>•>

J^ ~ ^X:-

1 tm t f

.- io»>

8-^

« V'

'«w T*c j^ftfircr-

^^ii«i B £,

d.-A'^a

'iO-it-fl',

25

TftfrJi? ^ ^ ^W^fft^'^ qpaqUM ra^^ (oount^s per mouge)

Be - 1.783 X 10^® I Al - .66 x 10^® I

C - 1.126 X 10^® I Cu - ,718 X 10^® I

The praotioal upper limit for the length of a run was

5 21taken to be about 10 aloe. So unless the Integrated cross

section, I, Is of the order of lO"*^'^ cm , or greater, It Is

probable that no pair production will be detectable.

If a few 10 mouse runs are completed with no counting

established, It will be possible to fix the upper limit of the

Wentzelian cross section at near 10 , an improvement over

Martlnelll'e llinit by about 10^.

The expectation counting rate for electromagnetic mu

pair production can be calculated by substituting the theo-

retical cross section in the above relationships.

22P.V.C. Hough has developed formulae based on the Bethe-

23Heltler equations for electron pair production which are rep-

resented to give better fit to experimental data than the

latter. In particular, for syametrioal division of the kinetic

energy, his equations give:

(T^p^t. s .786 (?;r^ 2

Co • .085. ,L- / ^«, \*

.y Q

At energies very slightly above threshold. Hough's

best power law approximation gives:

21This limit is set by considerations of the backgrounds

observed in the preliminary study— see Chapter VII.22

Hough, P.V.C, P.R. 73, 1 February 1948.23

Ibid .

?5^

I ^"01 X 8XV. - uo X ®^oi X dsxa- -

•1 ill , .f Ji9is "lo "bo "'^"'OX lo °ioi>iq 9ri;j ^o aJt ,1 ,nolioe*

s-i";/ Titan's' «i£: ^icf lii^'' flc.fu ox±cn:(T ""iscr Ozi ;Jsn3 sXcfacfoiq

- n .f 3

edit to ;tiiBiX leqqjj ari3 xll cj aldisaoq *jd Iiiw :ri ,x)«ftexicfii,l8e

-•rileci aff;f no £»98b<^ -sieltimiot J5>!5goXsv©i» aiiil fl^woK .O.V.H

I'-'^'Vt'^ nol:trMlX'cr:i't8, WAX 'It.. ..••-:?d

fo—^'^

£6

whioH oquAtlon la 1Z% low at it « 3» wiUi lnor««tlng •nror as

k beooffl«f ouoh greater than !•

E'xtrapclating ths equat:lone Co tha «u pair proeats by

introducing tha aaaon Maaa* givoa:

r'roB the leaas xNntio aXonoi tMa 'lypothetioal orosa

aao tion is down at onea by a factor of about 4 x 10 fron the

alsetron pair croaa saotion. Moreover, tha aquare Z dapandanoa

liBpliaa a ooharanoa whioii ie probably not valid for the maaon

production. It la probably more realistic, an^S does not change

24the order of aagnituda« to take the Z dapandence ag linear.

The expected counting rate iat

CK « £ N ^^^ CX ' I V-12

wher- T* n Cj(rd^h£j awi now be evaloated;

!• a X*(araph V-2, Appendix D) is a nusieric andC

hae the valuea tabulated in Table V-2« Appendix D» Mhorn the

integration is carried out by graphical ifiethods for varioua

ooabir itlons of the ut^rtr and lower llaita, #» practicable

24Tf,ble V-l, Appendix D, tabulates the electroaagnetlo

aroaa section (per Hough with linear Z dependence) as afunction of quantum energy.

•S)

pA " "

•-Or^

>,<^).Ex-. XA\^J\*-^) k . --„^j;p

^amiiiSiQt^ r^l

\it

27

lov«r limit, to discount energy lofs In the target and the

absorber is about 240 Mev.

For Sj^^^ - 340 Hev. i^g^g^^'^' 3-18), an! ^r^^^' 240 Kev.

^^mln* 2,25), I»' corrected for the 12^ low error inherent

in the Hough formulae, at k = 3, Is about .Od.

The constant C, here is: (See Table 6-3)

137 -^

Table 6-3 Constant C (Equation V-zV ) in oa^

Be - 4.12 X 10"^^ Al - 1.34 x lO"*^^

- 6.18 X lO"^^ Cu- 2.99 x lO"'^!

The expectation counting rate is:

CH = (€.N leffor') CI* (counts per mouse) V~/S

where the factor (CN leff^) is the coefficient

of I in Table 5- a

.

Values for this expectation counting rate are tabulated

in Table V- -^ , for these four elementa, for various liiaits of

the integral !••

.

For the particular case of Beryliua between liTiits of

340 Mev and 240 Mev, the rate is:

^'^E ^'^^ * ^^ (counts per mouse)

a rate which is of the same order of magnitude as that which

we could expect from Wentfcelian pair production with an integra-

ls'' 2ted cross section, I, of about 2.5 x 10 *" cm • For runs of

lO*' mice, both the Wentaelian rate for this cross section, and

SabtnAni Idle wol ^SX 9iii tot .6e^©©i*xoc,

"" ox X ^6.1 - XAiiiCc**.

« i •,

^?*nl 9x14

iu au

O^g

28

the electromagnetic rate are at the extreme outer limit of

our detection probability.

magna c

j

lc meson pair proauotion in counts per mouse times 10 .

Lower Limit I "-240 i^ev Lower Limit I"»260 Mev

. UpperLimit

350 Mev 340 Kev 330 Mev 350 Mev 340 Mev 330 J4ev

Be 5.35 4.46 3»68 5.11 4*23 3,44

C 5.06 4.22 3.48 4.84 3.99 3.26

Al 6.43 6.36 4.43 6,15 5.08 4.14

Cu 15,69 13.0 10»72 14.9 12.3 10.02

- .,-.

-^'

^^ .s

^

f^I,^^

SO-,0j;

of* .a

29

CHAPTER VI

ELECTRONICS

A. Tests of 6BN6 Coincldanoe - 402 Amplifier Group

The first phase of the eotual experimental Investi-

gation oomprleed an analyals of a ftBN6 faat oolnoldence olr-

oult and asBoclated distributed aapliflere, model 402. Cal-

culation showed that an iiroortant part of the solution to a

reduction In the background and accidentals rates lay in

reducing circuit resolving times to a minimum by taking ad-

vantage of fast coincidence circuits where they could be used.

The distributed ampliflerg, model 402 were slightly

redesigned in the LN3E Laboratory from the Hewli tt-Paokard

model 460A, which has the following characteristics:

MaKlmum output voltage to an open circuit—8 volts;

maximum output voltage terminated in 530 ohms—4« 75

volts; maximum gain, 20 db (10), using 6AK5 tubes

operating at g r 5000 micromhos. The essential

differences between the 402 and the H-P 460A are:

(a) voltage regulation on the 402; (Ij) addition

of screen circuit decoupling resistances on the 402;

(c) slight increase of g^ with the 402; (d) term-

ination in 200 ohmg^

Complete oircuittn' of the amplifier, including regu-

lated power supply are available as LN3E Dwg # D-382.-/\^

The 6BN6 coincidence circuit used was designed in the

IV B.

5V.i- fll bBiBntmi9^ egfeiioT Jwq^ijo aujcilXBffi

89dJU^ dMa sniBU «(0I} cff) OS ,ai£3 nuiBixAis ;8lXov

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30

LNSE Laboratory, Dwg B-1801-A > Its easentlnl feature Is the

use of the 6BN6, gated grid disorlmlnator tube. The plate

curren t-11miter grl5 charaoterlstlo curves show sharp llniitlng

action from a outoff of '^bout -3 volte for quadrature volts.

Operation as a ooinoldenoe liube rsquiree positive pulses to

both the negatively biased Halter, and quadrature grids.

Single-grid plate pulses can be formed for low values of bias*

but proper grid voltage adjuatoent with regard to expected in-

put pulse size enable its use as a oolnoidenoe oirouit with

very short resolving tliae. The time constants of the grid

stages are suoh that resolving times of the order of 10 ^ seo

are attainable. However, with associated circuitry, especially

afflplifiers, the resolving time suffers somewhat.

Rather extensive testing of the 6BN6 circuit with the

402 amplifier input was made. Use of this particular combina-

tion was predicated on the necessity for an early circuit dis-

crimination against the expected high flux of electrons, protons,

neutrons, and pi mesons into the meson detectors* And even with

a resolving time of 10 sec, a flux of 10 /sec in each detec-

tor gives an accidental meson coincidence rate of about .001

per mouse, much too high v/ithout the other restrictions placed

on the true counting rate described heretofore.

Response testing was done with artificial coincidence

pulses (sr>lit single pulses) from a lab pulser. Seriously

large secondary coincidence pulses, and coincidence over-

shoot pulses were observed for values of grid biases that

were too low. Test curves indicated that secondary and

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31

overshoot pulsea are negligible only for grid biases acre

negative than approximately minus 3 volte, on both quadrature

and 11ml ter grids. This negative 3 volts corresponds to the

beginning of the sharp rise to the limited region of operation.

On all subsequent testing, minus 3 volts was taken as the

minimum negative limit of valid data. See Oraphs VI-1,

Appendix E. The oolncldenoe pulse length and rise time

appeared to be a funotlon of both biases, but only for long

pulser input signals. No remedial measures are necessary for

the experiment wherein terphenyl-oyolohexylbeniene pulses of

Qthe order of 10- sec rise time are to be used,

(araphs VI-2, VI-3, Appendix E.

)

Similar testing, with Ha-gamma pulses, detected in

xylene, and then split for artificial coincidence, reduced to

the same qualitative behavior.

GAIN TESTING

The distributed amplifiers. Model 402, were claimed

to be capable of producing 10 volt output pulses with an over-

all maximum gain per amplifier (two stages) of 10.

Controlled gain tests showed that gain through the

amplifiers was strongly dependent on input pulse amplitude and

rise time, and that saturation output-levels were of the order

of 6-7 volts. It appears that for the H-P 460A, the published

maximum output voltage terminated is 4,76 volts, while In our

amplifier, with an output resietanoe of 270 ohms, the maximuB

output voltage (with termination into 200 ohms) is .SQCxE^y^Cmax)

,

270

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'

This It about what was found to b« t)i» ««•••

7h9 follo'^ing re«ult« vere obtained from gain teiting.

Tha flgupaa are for identical amplifier stage biases of -lo5

olts, and for input pulse heights of .3 volts. i»ote that the

gain figures for 2 amplifiers in series reflect the saturation

poutput voltage by a reduction in the overall gain, from a » to

a v&lue eonsietent with the previously determined eftaxittUA out-

put cf 6-7 voltp.

Table 6*1 shove data for three pule& uyp&si

A. Slowly rising short pulses (Ti^Z/^sj 72 ^ ^/*-^J

B. Slowly rising long pulses ( 7^ ~ z^sj 7? - 90/ejJ

C. fast rlRlng long pulses (7;^,y^j; 72^/2oy,jJ

The length of the short pulse h^ra given la the bast

length st zero voltage; the itsportant difference between the

tshort* pulses and "long* pulses here is the pulse shape near

the leaxinus height.

Table 6-1 (aain of 40S Afflollf lere)ABCSingle 3.79 d.6 18

CaJ^oaded 9.5 - 1»

It ie neoessary to specify the input pulse height

because the observed gain wat? a function of input pulse height

•^a.r-V*-., :^ ,n:;rir-'?R.i.-.'<»-

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33

as may be seen from Table 6-2 for type A pal see:

Table 6-2 (402 ^nmllfler (lain va Input)

Input Pulse Hels^ht aaln

.1 TOltS 4

.3 3.76

1.0 2.4

.05 30

.1 19

.3 9.6

1 4

The Input circuit time constant of the 402 amplifier

is approximately 2 microseconds, so that the long pulses B and

C of Table 6-1 are clipped as fairly flat, 2 aicroseoond input

pulses.

In general, for a single amplifier, gain was found to

be highest for a fast rising pulse, with a fairly flat top to

the limit of clipping time, as can be seen qualitatively from

the increase in gain from A to B to C, wherein these general

criteria are more nearly approached.

The experiment at hand will require two 402 auaplifiers

to ainplify each meson signal before the fast oolnoi lence. He-

solving time measurements were made to determine resolution of

the 402 amplifiers and the 6BN6 circuit. The determination of

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reaolTlng time of the oomplfl te olrcalt (amplifiers nnd 6BN6)

was iBade by Introducing various lengths of signal cable In ont

grid circuit or the other as a delay ni!echanl»^m. The signal

cable used Is British 200 ohm, center wire coaxial. Inasmuch

as all the av«ilable POO ohm cable was already mad* up Into

Xsads of varying length, a restriction wae placed on the amount

of delay that could be used. Datq points are separated by a

time corresT^ondlng to the oade-UT) cable lengths. The speed of

the cable Is negligibly different from the speed of light.

Resolving time data were taken for four different

source combinations,

1. Using artificial coincidence (split pulses) from a

Ra- source.

2. Using actual coincidences from cosmic rays, in two

snaall volume liquid scintillator detectors.

fif)

3. Using actual coincidences from a Co 8oui»cs.

4. Using actual coincidences In two liquid detectors

from events oroduced by a target in the synchrotron beam.

In each case, the 6BN6 grid biases were set low

enough so that single pulses of the expected normal slie were

inadequate to trigger the coincidence circuit. The observa-

tions, of course, were inaccurate to the extent that the biases

used allowed high-pulse height single- events to trigger. Howt

ever, for tne lengths of detectors used (small volume), and the

bias Bettings, a very small fraction of the total count at any

delay was due to single pulse coincidences*

^r.

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For each run, the ooincldenoe counting rate war plotted

as a function of delay on each grid.

An average of four runs using the Ra source Indicated

a cl result resolving tl'ne of the order of 8-3 x 10"® eeo.

Graph VI-5, Appendix E Is a plot of the nver^ge, nornallsed

counting rate vs delay for the four runs. CllT)r^lng the In-

-9put pulses to the 6BM6 grids to 2 x 10 sec, took the re-

solving tliie dovn by a f/^otor of 2-3, as was expected.

An average of 2 runs using cosmic ray coincidences,

again gave effectively the same resolving time. Peaking of

the resolution curve over the resolving time, with a much

cleaner cutoff, reflects the fact that most of the cosmic

coincidences counted were high pulse height events, for wnioh

the 6BN6 biases were set appropriately asore negative to pre-

clude single pulse triggering. The peaking of the curve then

qualitatively demonstrates that the individual pulses art

thin, and well seoarated at peak over the coinoidenoc count-

ing interval. (Jraph VI-6, Apoendix S, Is a plot of the 2 run

average, normalized, counting rate vs delay.

One run was made using actual Co^^ coincidenoea, ^iioh

—

s

corroborated the previous results of about 3 x 10 sec.

Several runs were made using real coincidences from

events produced In a target in the Synchrotron beam, Ho

atterapt was made to identify the coincidence particles, nor

was differential energy di scrl mlnation attempted. The results

indicated a resolving time of about 3 x 10 ° sec* As was

expected, the observed resolving time decreased markedly as

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6BM6 biases were made inore negative. In effect, by the

ohanue in biases* ve selected out of the apeotrun of pulse

heights, the higher pulse heights for which the results of

the measurement are explained as for the oosfflio ray curve

peaking. Graphs 71-8 are the plot of these data.

In the fflu pair experiment the pulses into each grid

oirouit will be random in pulse height » and single grid dis-

\ 25crimination will be of no use. It is proposed then, to

use the 6BN6 ae a crude discriminator by keeping both grids

at the same value of bias. Table 6-3 shows representative

values of discriminator voltage versus equal grid-bias

settings*

26Practicability of the use of the 6BN6 as a dual dis-

criminator is questionable in view of the number of para-meters Involved. The grids are not symmetric with respectto their behavior at Identical grid voltages, because thelimiter grid is so much closer to the cathode than is thequadrature grid. Plateau-break curves were plotted forvarious input pulse heights as a function of the two vari-ables; quadrature grid voltage and limiter grid voltage;(Graphs VI-9, Appendix E.) For a fixed value of limitergrid voltage (-3 )# the plateau-break curves show a veryclean cut-off of counting rate as quadrature grid bias isincreased. To use the circuit as a discriminator, it isaeceesary to run at input voltages lower than about 5 volts,l.e», in the region where a small change In input voltagerequires a large change in discrlminafcor voltage. For in-stance, at a quadrature bias of -4.5 volts, a change of biasof 1/2 volt disorifninates between pulses differing by only1/4 of a volt, At pulse inputs above 5 volts, however, dii-crimination becomes very poor.

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For «qual bias (}«tt:ngf> tM^e voltage at th« input

tltot It dlsorl oinated against. Data is for a reduction in

counting rats by/l-i,y

«Sx3 1*2 6x6

4x4 1.9 7x7 10

5x5 S.4

Tbie table shove di9cri;2i}. nation for input pulsesof equal height. For the random pulses we shallbe using in the experiaient» then, these valueswill be only approxiaate.

Some tentat^tve energy disorimin^tlon testet were aadt60

with a Co if^BOurce (1.16, 1.32 Her) - producing real co-

incidences in test scintillation detectors. Cut-off was

very broad and poorly defined in this test.

h survey of the tests of the 408 aapllfier—6BN6 co-

incidence circuit indicates that, for purposes of this ex-

perinent, certain basic criteria should be met:

1. Operate the 6Bi^5 at biases between -3 volts and -6 volts

to ainlaite spurious effects due to seeondftry pulses and over-

shoots and to seep the tube in an operating condition (i.e.,

Where the average pulse height expected can e^a&e coincidence).

2. Operate the 402 aaipllfiers at high i^in (each et'^ge at -1.5

volts bias). The voltage from the output-dynode is of the order

4 !-•:'

-Of-

-at*

(i"0

V -, X

no!:-nan t..,..

r58

of .1 to ,3 volts, for whioh we oan expect 4 stage gain up to

the saturation leTcl of the amplifiers. The number of ob-

servable noise pulses fron the tube (5819) is InoreaseA there-

by, but because of the fast resolving time of the circuit, no

significant increase In normal aocidentsls* rates results.

3. Use the 6BN6 as a crude discriminator only, because of

the random pulse heights which It will have to accept. Test-

ing will be done in the beam for the correct biases to cut

out much of the backiground of events that lose less than 2 Mev.

4, Operate the rig at the peak, of the coincidence resolution

curve by using the appropriate cable lengths.

B. Final Electronics System

A block diagram of the electronics circuitry and

components for the final experiment is shown in Figure 6-3.

Dependent on the factors discussed in Chapters III,

IV, and V, and within the limitations thereby Imposed, a mu

pair entering the meson (inner) detectors (Mj and M--.) pro-

duce a coincidence pulse in the 6BN6 circuit.

The meson-coincidence pulse (Mj-Mjj coincidence) is

presented, through a discriminator-amplifier, and a Model 501

amplifier, to the timing circuit as the timing initiator.

The timing sequence begins with a fixed 1/2 or 1/4 mioro-

lecond delay, followed by the 6 microsecond electron gate

pulses, a separate gate for each detector system I and II.

The decay of each meson tiroduces an electron coincidence

pulse in detectors (E-M)j and (E-M)jj. The t£-M) electron-

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39

oolaclriftoce if requirad ta recSuot Hi9 f?Burloae .j^tP-ofllnoldencet

wnicn «ouid <\rl8e frois stray eiootrona or ^^tioLcni .;* - B

dtt«otor» for instanoa. eiote, ttuit allhcugh th« tima to deoay

of tnoh BQU is nelthsr pr*4llot>»bl0# nor thm taae for tAc* J2«mber8

of A o&ir» onljr a aaall fraotloni, ^>y ^ ^^ ' ^o uncollaoted in

fita ItBitt <^^. (aoUlfiad bjr «!&« faefc da^^y l'*totor» eiiAptar

XV). i:»o, aaaanslfAllr ali th« decay aleotroii« <%ra '*oaugJ»t' in

tha 6 mlaroaaoond gata.

Tba (£••<() alaotron-oolnoii«noa palaa (h«raaftar U^a

"alc»ctron ' pulae« Eror^^)i« preaantad to Us^ 5 tiiioi*aa«eond

gata of each nyftan* ioroducln«? the alngXa **pair»«Xactr::ii co»

ineidanca pulsa ihar*aiter oaXied tiae '^laeaon'' pulaa, i»ij or M__).

Ti&o iseaoR pulsaa^ M^ and M^^, from ayeteioa i and II ara

required te be In o«tneidanee in s alov olreuit < ?*aaclylng tiaa

d mier-ofeconde) to foriB %ll# flnrA teuntad pair pulaa.

30alara ar« uaVd to datii^r^aina tha ain^Xae ratea of

deteotora Mj, Wj-, I^, B^^; the '^alectron" alngXas rataa,

(S>-«)y (S-Mjjj^J5i0fi the ^maaon" alnglaa rataa Koaonj and

Meaonjj, m tha 6 sdcroaacond gate olrcuit of eaoh ayataa,

and the finaX aaaon-^pair rata* 'Heaonj * Maaon^v.^

Tne emphaaia tiiroughout has been to reduoe the ohenea

ratea to a sinlflKim.

.'Ithough the very eXow flnai colncllenc© circuit has

i| resolving ti-Be of d oiiorossoonda, th@ aingXee rates **Hj90iu*' •* -,13

and "MeeontT* ^i3ll b« ao elow (XO"*** counts per mouee) even if

|he 8BJI6 ^-i-^ - Hjj ooincidenca vera not requiredt that it la

a»onfl»t»lofTir»9-«.t'*'v »;i^J? ;fes4T *.i; ^ffc-^i i> .? v^rtn*', f''

rttd mcas mr^ fol #«• - .n .*>rd-'?olfc«tn- ^«f!.t

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40

believed the aenon-pAir rate will be pure.

the output oonneotione of the photoraultl pliers of

eaeh deteotor are oonneeted In perallel! two tube oosiinon

for the meeon (inner) deteetore* and four tube oodMon for

the electron (outer) deteetcre. The parallel oonneotlon

does not inoreese the single tube output time constant by

suoh, and oaufiee a decrease in pulse height which is accept-

able. Two output pulses are taken froA the duo! a negative

signal froa the last dynode to a common lead into a cathode

follower stage as ons input to the electron coincidence cir-

cuit (Electronjx) J a positive signal fro^a the next to last

dynode to a cosison lead as one input to the 6BKd meson co*

incidence olreuit (M^-Mj^). In the quartet a ccm^n neg*

ative pulse froai the last dynode is taken into a cathode

follower stage as the second input to the electron coincidence

circuit (ii^lectron). The cathode follower circuits for both

duo/quartet are identical and are natohed to 100 chn cable

at the output (Figure 6-4). "

;ast»'

26„wr. Osborne advised that, in order to reduce parasitic

oscillations in the cathode followers, speoinl wiring of the6J4 socket be aiade: the extra grid pina, 5 and 6, were clippedHhort and an electrostatic shielding bar of copper was connectedfrom pin 4 (ground filaaent) across the center pin, and tochaesie ground, sep&riiting the plate, pin 7, from the grid,pin 1. In addition a 25 ohn resistor wae snubbed to the gridpin, fro^ which resistor the ncrraal grid connections were oiade.

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•yntem re^^rward 8*, with a d«t»ohabl® Qev«r for th« end, thromgh

wmeh el«otrloal ccnneotlone and AdJaBti&entii are mad^. The

phototube mount, and partlo Jl^rly the *0* ring eeal, provldee

•eehanioal support for the tubei aagnetio shield and tube

base extending b^o'^ from the deteotor end plates. The o&thode

follower elroulte are counted on the Ineide of the shield wall.

All poirsr and signal oonneetions are throt^h light-tight

fittings on the outside of the shield cyolindricml wall.

iti^T^ it wae neoeesiiry to run signal leads froa individual

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42

tub$B to ooomon junctions insid« the stiltld, ooaxlal o«bl«

was used to lc««p the inor««tee in os^paoitanee to a miniauio.

The shield was held «t the Gordmtn ^rcand potential of all the

phototubes. Tube r^igfi voli»u^:- v,a- Mutit^lned on Uie sKagnetlo

shield. Two high voltage power supplies are uaed for eaeh

detector: one supplying voltage to the duo» the other to the

quartet. Potentloatf ters are ased to adjust individual cuoe

high voltage frott the supply value in order to adjust for tube

differances. The potentioffi3t«trs» and voltseter jaoka* are

also raounted on the shield at the po«rer and signal oonneotion

point.

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. il S ¥*!

CHAPtSR VII

A t«t Of awAsuroaonts v«r« mR&n in tHe 320 'iev

br«o«»trahluiig beam of the OynohrotPon in order to:

1} ^TalufUe &nd test tne existing aeeon eleocronlos.

2) Xeet the ohf»r*iOt^rl»tio» of the 6Bli6 ooinoldence

eircult«

3) Study the problettt of oellia^^tlag the beaa.

j^ !4) Determine the shielding requlreaenta.

s- 5) ditiXmizf'- the baokground, said asoertaiu that h^ ^n

r try

l|Rokgrouii4 vas being overlooked.j ^

Q

. 6) Det^^^riBine the feasible upper linlt of the length

ff rtpl to ••tl « low^r limit Oft the pair p»>^Otlon erost*^£

eeotion, ^o

In the fir£t experlaent* vith the geometry shown :b^0?

figure 7-1, the flr$t two cf the above Items were studied* J

7he 63^6 circuit was used for ooinoldence between tvo

deteotor$» In llne» & t^o Inoh eyo^oh8xylben£ene-b819 deteotor,

«nd the original Clarit deteoter - In two inoh xylene*1F21 <o

'^detector. This coincidence pulae was takeu through « die-: o

crl vlna tor- affipll fieri ^ model bCl ^jsplifler, ana into the^ ^-.-_J

tiding circuit to oof&^enoo the tlsiihg sequence, tleotroh

puleee* formed by an inslde-outeide coincidence in the Clark

detector, were presented to the tiaiing gates via disorl rdna tor-

aiBrlifier, and saodel 601 amplifier. In this partioular Dhase

lAlIt

tao*?© &oU

ni is>^

rtQ^&9^%i>

,i k^m:

1

— ——

1

J: 0:1

5^ ic

^ H. ^ 1

1 uT

1

1

' .

ZZ.^

KJ

r ~\ ^ V)

s

1

1

1

—

>

9K. 1

5—

»

1

1

1

vl)

1

-ot 1 ?

S 1

^1

>.1

1

Q '

JH •4 «0

<j ' ^ (U^!>

lU 1 ^J

^lro Q —

>

5 '

^ 1

§ s5'

v 1 1

b 1

A.

[1

VO V^ ^

T *

r^ ?:^ ^^V\"VV.V «^ \ \$ »-

>i v.\ * Q \ * \ * \ ' \ > \ \ \ \ ^ "*

>2-^

^t\\.'w\-co 5 :5

>..

Kic = "Jr

o•c O K kl

^o r"^ ^ ^S^ Q vb

o

I

k

T

<k^

^^K o

PV) ><«0 Hi

the eleotronioe vere used as dstlgned* i.e. ^Itri Uie tlinlng

««qu«no« Blgnftl beg'nnln;g after a fixod delay of 1/2 odoroaecond,

' 9»rle» of four coritlguous 1 1/2 sloroeeoond gatt pul«0« and

a 6 odoroaeooQd aocldontt' Is' gat«» follovod &h« 1 1/2 micro-*

•«oond delny. £«eh g&te colnoidenoe circuit drove a toalar.

The averj^ge of 8 runs mt 106® 1« shown in (Jraph VII-l,

the dsaay tine eharj^cteristlc of photoffl«8ona produced In CHg,

The 6BN6 v^e found to psrfora as antloipatod from the atudl«ft

with ooflfBlc ray« and other t9ats (q.v. Chapter VI), The

pulsa* froa the &BM were quite readily adapted to trigger-

ing the meson electronics. Cheeks were aui.de en the poctsibility

that the 6BM was failing to register all true coincidences.

The investigation showed that negligible loeeee* if any, were

©courring in the 6BII6 electronics.

As a second experiment a series of geometries similar

to th^t shown in Figure 7-S were employed to study iteais 3

and 4 of ta© list ac>ove. The detectors were placed at various

dietsnoes frois the target; runs were aiade with and without

target; vs^rious arrangeaent® of oollimatlon were earplcyed;

Varying assounts of shielding were placed around th^ detectors.

The result* of these gtudlets led %g the design geoisetry

shown in Figure 3» Appendix A, Sxtreae colli motion was found

desirable. The scattering of electrons in the beaai is a

source of many singles counts In the detectors, and it aay

be desirable to try to ©lean up the b»raa sea^netic^tlly. The

isost serious deaginds on shielding exist on the side of the

>^

0X1009 •o^oiifc 9M It' t^Xeis i>«xli

•f[. fir «._.

,ar

•Vrf,'><

;99«l

99 X« not«» »cld

; ? i" f("*V a eft.? fivfTSTri

nl iaaX«iiuooo

?iiiX »«* lo V . ..*i

.-. .:.-^, .-.*<<n 1 « 9 n*«; o *. .-

i© to

^^« ls-i»»f'

n wjf /TA^ftfJT **.H? f

9a t4 Ow 'xX99i> 9tf

Id rte 9uoXi9t ;}

N

i^

It!It

O 5-

Ciu -'3HdCf

45

housing facing the target.

In a third aeries of meaeuregaente , Items 5 and 3 of the

Above llet were studied v^ith the geometry shown in Figure 7-2.

The Clark detector was u^ed for system I, tne cyclohexylbeniene-

filled detector, alone, for system II. The electronics remained

the same as for the phase I and II runs: i.e. a oolnoidenoe

was required in the 6BN6 circuit between the "cyolo'* detector

and the inner Clark detector as before.

It was found that unless at least 1/4 inch of lead

was placed in front of the detectors, tne soft radiation

created in the trirget (or scattered by the target) aiade the

singles counting rates too high.

Using 3 inches of lead in front of the detectors es-

tablished that neutrons were an insignificant background. All

studies led to the conclusion that electrons, positrons, and

T rays were the greatest source of background counts at 45°.

There were no indications of unanticipated backgrounds.

From Figure 7-2, it can be seen that the detection

efficiency for au pairs was extremely low. because of the

short length of each msson detector (8 inches), we were

restricted to those pairs that shared the available energy

equally, plus or minus a few Mev, The fraction of the total

pairs rejected is therefore very considerable, at least ,9

for the 320 -^ev photons, and more for the lower energy events.

Also ths effective solid angle factor is very small.

Taking 12 inches and 14 inches as the effective

lojoeaex. '0101^^^ iiiefe^ai;;-^ J^wo'iio CMS &fiij i^i i)«iiijp9i- baw.

.siotfed ^£ •10^??'^ 5© 5 litfilO leant ^rt;f fins

-88 ft'to^oe:r®b ».djr 'to ^acnl al bB&l to is.'ioni 5 gnXeU

46

di«teetor dlttnnoefit and noting Ihmt tht ClarK d«t«otor w»f

oolllfflcteA to threft lnch«», the ey^iohvxylbtneent v1ftt«etor

to four laehts, th« fiotor* of tqu-^tlon IV~lb, for the

dttftotlon •fflol«noy becoo^ ^tvrroxl^ftttljr:

6c s (3.92xl0''^)(6axl0'"^)(»62)(l)(.03)(.05)(4)(2)

<o thAt utit approxiisate effielaaoy for th98« runs w&ii:

The runs vi%n this ispadt s«paratod g«09«tr:!r, iltnough

27«nd« under alvsrae conditions, antiibllahed soao intends ting

faett:

1. The ^ colncldenoa rate (6SK6 oolncldenee between

the aeson detectom on either side of the targif»t) vas estab*

llehed a<« co5K>Of©d of on©-third r«al eYenta, and t^ro-tr^lrde

aoctdentalR. This wa« det®rt^lned by delaying one of the

puleea eufflolently to throw It out of tho resolving tlae

bracket of the other pulse bjr factors of 4 to 4.5,

?-• The eleotron-colnoidence rate (inslde-outelde

colnoldenoee In the ClmHn detector) wan ccwprleed of two-

thirds to three-fourthe real event e, independent of what

shielding ve did* and at thie large target distance.

11For a particular run of about 10 * quanta—2500

•rats "--with a thin (two Inch long) Be target, and 1/4 inch

2?'

The *»et-up* vas made dovnstrea^ fro«5 another expert. aientwhich v?af? being conducted concurrently with this one.

( s) i ^S

§r :«©« U»i'3-

;bj cat

use-^9^ e'

r..-r ^ tc r 1: rd •e'^o'

1 «§*n:^Ti» r,rf>-*

;t^«»*'

47

l«ad abacrber, the following r^JGUIfcw -r^ere obtained:

i'legon-pair aecidentalR rat«7?. » . .0004 per "ratx" «

.CK>0f?74 per {BOU90 (or 4 x lo"^^ per e.q.)

i^»©8on-pair r«te, 3 see gat* OOOS per •^rsitt"

i'iefion-pair rat«, 4,6 8«o gate. ...0C04 j>tr 'rstr*

• ar9 in a posit] on to s^t an upper limit on %h9

iontzelian prooods fro® the abovi» run, ^or tn® calculation

»

vd asguoie ¥9 wQUld have been &ble to identify a real r^te

-»4that was equ^il to the nccidental rate, 2.74 x 10 per mouse.

ror the two Inoh B© target* tb« effective target length

(equations V-4 ancl V«>6) is 4.7? o.i!« and the e.q. per 3>cu6e»

corrected for actual target ?5reii, i» equal tc cc^ of ^^^uation

V«S, 4.46 X 10 e.q. per mouse.

Ihe expected yield (equation V»7) is:

y s .16 X 10*® X 1.S3 X 10^^ X 4. 46 x lo'^ x 4,77 I

t = .437 x 10^^ I

or 8.74 X 10** « .4^7 X 10^* I

and I * .627 x 10"^

Mih&TQ I = I GX^)d((jt^)A 1

Aseuaing <r constant, X - ^ ^/^/^ , henoe,

I = .4<r= 3.27 X 10"*^

or (7" ^ 1.57 X 10""^^ crn^

which i<? .^bout 8.6 X 10 ti«e« the eiectroaJagnetic proeeae

croew !«eetion, essential ly the s/^rae lii&it e«t>*bli«hed by

'^it is felt that when tKJ mu-aeeen delayed coincidences arecut Into coincidence, the nbove &cci,dentail» ccuntin? r-ste snoulddeere^se by at leaet '« f^ictor of 10-''-. If thl ? oon§srv.'ilive esti-flsate ie correct, one vculd get 1 event^ln about 10^ »iee. Inieis the b'i.sir f&r the eetiaa'ite made in ChSipter V of tae nuaber of«ioe per run.

rf5

£i 0$

TV f

^^SYxiV^T"^ V

--0J

—¥ «i

n^o

48

Martlnelli.^^

Aa ie remarked In Chapter V, the electromagnetic

procesy, or tne '"entaelian proceaa wita an integrated cross

section of 10 ^^ om , have a marginal detection probability

witti the MIT macnlne. It is interesting to note that if a

factor of only IC could be gained oy a ooaibination of increase

in beaiC intensity and Bremmstrahlung energy, observation co'jld

probably deciJe vrhether the process is occurring or not. As

a matter of fact, the detection efficiency may be increased

almost this much over the minimum figure used for the yield

calculations, from the Z dependence, and A u; oorreliition

effect B mentioned in Chapter IV. If tnie be so, experimental

runs in the MIT beam should be able to establish the pixjoess,

if it does occur.

If counting rates are obtained near the predicted

values for the electromagnetic process, some method of sep-

arating tne relative contribution of the electromagnetic and

Went£ellan modes to tne rate will have to be established. It

is possible that such a determination will have to await the

building oi machines of much hdgher eriergles and intensities.

The author is very deeply indebted to Dr. Wattenbarg

and i)r. Feld for their active guidance, unceasing interest,

and generous assist^ince in ti is work. Dr. L. S. Osborne,

whose meson electronics were used in the preliminary experiments.

29Ibid.

-

1

Xi

E '* (i

Sai?.91f;

~;?cr! o'd ^anl::!

i.jBaia;:.

'i f: Si'.

a as «a OJ ®fjEifl iiiw ^jiiTL srs

.?aii;

DSI n x^ J. -- 1; i2 w

g^-fei

t»Jfli;

!«;}.

49

was unfAillngXy generous with hi« Us* mad h«lp« ^r. vc^^r^tn

Pupl of the HI? naohiiid 3hop ttklllfully oonttrueted th<i deteot*

or*.

Many thftaka ar« al|p dae others of th« Synchrotron

Laboratory in partieular: A. Cdlan» P. 3tein« ?. SIoehlYor*

D. C^agllardlj J. iitot@ngr«n» and (»• ^ugh for Uieir tlasly and

fluoclnot aeaidtanoe.

*-$'.

hr

!i4 Ic:

, ff.'ta

;U8

Mtmxmm?m

tmki

50

BIBLIOORAI'HX

B«ll, Hinokt,: PH., 84, 1243 (X95I).

Conversl, pHnolni. and Piooioni; PR. 68, 832 (1946); PH. 71,209 (1947).

Fermi, S,, Nu^el^ir rhralQ^ : Kot«8 ooarpll^d by Ortar, ^otenfeld,and Sohulter.

Olngrloh, H.3., H«ir. Mod. Phy«, 16, 19 (1943).

Hough, P.y.C, PR. 73, 1 F«bruary 1948.

Hubbard, H,^., Thegls, ''aiverslty of California, 10 .<&r©h 1958,"Positron apootrua from daoay of »u aesone.**

Maraiiak, R.E., f^ffiflR PfrTfflftt^

i«ath«r, M^rtinelli, and Jarnie, DCFtt- 1166 W 7406-eng-48,Unlveralty of Ci^lifomia.

fauli, v., Woiesikopf, Vol*., Helir. Fliys. Aota. , 7,7,709 (1934).

Peterson, Gilbert, ^Mte, PB. 8I9 1011 (1961).

Kosfli, IsJereson, PR. 63, 417 (1942).

Salts, i«'.ueller, PH. 73, 606 (1950).

Slgttz^eirreon, T, Yafflakawa, K«A«, Hov. ^d. Pliys., 21, 124,1949.

Thorndike, A.M., MsismA - a nmmnr^ of earoerimental facta.

Tioho, H.K., PH. 74, 1337 (1948).

'rfentxel, H.K., PB. 79, 710 (1950).

oa

Xh

- . .&. « •'^ t*t©X-

»98ex fltni-- •-.^, iAlirr- «l>rt«d'd»H

t©IX»i#H «ali»e

.(@»9X) ^eCI ^^'f'^ «oct»if

APPSMDIX

51

DKTAILS or DETS:CTO'< CCKSTHUCTICN

The sealing gaskets werft h??nd out from a l^^boratory

plarr^lc, tJa« iiftae of whloh reaastined tmknovrn ^fter exii^uetlve

inquiry. The aij«terlal Is a pliant sJasot, l/S inch thiCA,

with the interesting *nd useful properties of insolubility

in cyclohexylben»ene# but ytery good solubility in water.

The gaskets were hand out because of the diffioalty

of Jigging for a lathe operation, and trouble with "ohatter-

iag* tools, which produced ragged* and off-eiie pieces.

ductility of the plastic is f«irly good, bat it

possesses a very low oorapressibillty, so that the 1/16 incfa

throw for sealing pressure was more than adequate. (The

gasket grooves were milled to 1/16 inch in the back plates.)

AL0MIJIUM HEFLKCTCR LIKIKa?

The interior bodies of both inner and outer detectors

were fully lined with Z lall Aluaiinuai foil. The fell was

bonded to the braes with ARALDITE Compound, ilo. XV, a resin

aanufaotured by the CIBA Co. of New Yorit City.

The detectors were made up in preliminary forai in

four s^otionsJ

i iece 1. Outer wall and target end piece of outer

detifotor.

x«

^fi'^l ^i.m

-^aix S\i :

'**!'?!*

•lid ''i« »a&i^^»o

.32?c.? i^ ' 3 . o'l i,'™';«;v,vv

4ii Jtw ">d

J0®e fuot

.'105 r

52

>!•«« 8. Xnn«r wall and back plat* of outtr d«t90tor.

Pleoe 3. Ciyiinorlo&l walls and target window of Inner

dttdotcro

?iee« 4. Bfteii plate of inner detector.

The four pieces were coopletely eeaned %nd soldered

at their reepectiv*^ Joints Sis for finished junotlons. A

study of the deaoription of the fcur pieoee will saov; that

all interior surfuoee %re aaeessible for ^^pplying the re-

flector, further f each piece was strengthened by the joints*

60 that the heat necessary to cure the aAj^LDITE did not warp

thcfli.

Prior to alutalnlEing* the pertinent surfaces were

washed down with HI)tO» in solution, followed by water rinses

and washing with alcohol to clean and decrease the surface

for the rceln.

The pieces were heated to 135 C in a temperature

regul'^ted oven, then the ARALDITK, in stick fom, was applied

by rubbing off a thin melt on the hot ssetal surface. The

Aluncdnuffl wae placed on the setal-Belt surface and lia:htly

rolled with a cylindrical glass tube to reatove creases and

bubbles as isuoh as possible. The resin bonds were then oured

for 1^ hours at 126*^ 0,

Chemical solubility of the AiULDITE in oyolohexyl-

bensene is not known* but several eaasples were tested for

apparent solubility by iasersion in the scintillator liquid.

The cured Ar^ALDITE exhibited no effects whatsoever.

16

.lo^^Sf^itdt^

br

"'; .\,- i.< '•>\ nm ^.fnlt^i B

-»"

i%^fi

>"^i.'- V > ;• 'v i :« ;

•e

e

:a ,a:

^ir. a at! £3 Sill »2-:'tsn t^i;

^ss'-^dl

^'liJJ'^to^^:^? 5i nl

b-:

.JX> h-'i. t.- -i^. - ,i

••*t!^ ®V

"JS? li

liSiAtiw J

0a

while the raw p««ln «hovid a tendency toward ilight '^wetting*

aftar 6 daya lanierelon. Jiadlar "wetting* ooourred In water,

^o evidence of solubility wne seen. After 3 weefce of Imxieraion,

the cured ARALDITK appeared untouched by the liquid, which

showed no discoloration or other physical signs of solution.

Th« liquid WAfl obtained oomrserclally froa the MONSAKTC

CRSMICAL CC'J'IPAIiY Factory In St. Louis, but it was not Jknown

whether in pure form or not.

Purification was aoco6»pli shed by successive filter*-

atlong through S5 inches of Activ^sted rWuialna (ALOOA), Kesh

SS*46» And 5 inches of glass wool.

;«.:4«»9V K -r-iS'l C-!^ '*^ SDr??:'

860^1

iKT

iIk i)#jf

ohoUj

K

Q

OJ

^ «

64

CRDSR or MAOKlTUDa SSTIKATE OF THI IRWBER OF SmOTIVS PHOTOKSAT THE PHOW-CAtHODE, PSR ^V tOST

this oaleulafclon is carried out for th« outsr detector

of «sQii tyst^n (the electron d«teotor} whioh has a total photo-

o&thoda surfaoe of four 5819 tubes (6 squ«r« Inohss). The

vails of the dateetor are linad with reflecting foil,

Ct^nsidar fi,gttra S*l, a aaotlon in a olane eont&iniag

the axis cf sym^etrf of th« deteotor ayatajfi. Photona produoad

at F hitve & raadoa distribution in diraotion. Beo^uea of the

toroidal gaoaetry of the

actual dataotor» the oal^

oulation is pz*obmbly not

completely acourate* but

since ttoat of the peripneralF/^ e-/

reflections will be at large

angleflf it is felt that the reeults will be highly indioatitre.

Let U8 agieuate that the photons esltted in solil angles

A and 3 above, are in the ^cc^ trance oonSf and that they cos-

priae &bout 1/3 of the total solid angle*

Then, taking the reflection ooefficient for the alufsinua

reflector as .8,*^ the fraction of the photons collected after

30^k)8t hi^ndbooks give for the refleetirity about .9. «*'•

take .8 to account for ths creases und fclds in the reflectorwhich produce non-predictable reflection directions.

h.n

t k

tm\71.

%<o ? AK 10 m

to$ee$9b isfifuo ^eii tot Jiio tv . ml «oi5»XwoX«o »

•dt to ofiiiBOi^ .iSOi^o»^iJ mi$:^ to t*x3t»«»l Xsl'^-'j^f^s

»I&0 oiia ,t<fo#ootf»^ Ii»«^Jaj&

lMi9ikiH9q^ ^si$ lo t#0€i 9»aiB

•B*I«I JA otf XXiM «GoX;lo®Il9i

,0Ti;lfi8lJfcai tXiJ"sXfi ^'f^''''"-'' «^?~^-^>'

-BOO ^ftidi i&ft;? .5fi© ,o«oo 00. • on? «1

VE\ ^v\

;awal»wXe oiW tot *fio loi . itoiJ«i^X1tS's

*t99ts J&o^o&XIoo0&

#iit tc fioXt®»*it 9&i ^^,i, »i

OW ,i ^^ tv.fJn'^n.<?it «id-? 'tat ®vJt|^ ii3l€*fM!fftnari iso.v

55

relioctloiJi, !, for core E: 1/6 [ .8 ji^( .8)'^j|"M .8) j|.f 1AAAvhere a is the total area of ths fcur ^hctooathxiiee «r.4 A

Is the area of the back w&lls into wnio:i cne pao to tubes are

Inset.

The faotor(.8)'* Is the diminution of Intenelty of tha

photon group for n retifeo^icna. (the energy Ioea« for 5 eT

photona» is due tc absorption at reflection only.)

The fr&otlon colleotad froa oone A ig;

1/6 [ - X A -• (.8)^A + i-^J^A*-*--'---'!AAAThe total fraction ooXlected fro» oone A eM B iai

f=i/. 22 ^-^^"1=^/^1(76;^If

a « ^^X TT offl » the area of 4 photocathodee

A jt73t(9.4 -8,4 ) oa?, the area of the baek

faee* for a toroidal oyellndar of 3 inoh

radial thlolcnesa.

i ^mJe^4^ '--83^ * ll • -^5

r s 5/6 A « 6/6(.085) » .0709A

^G¥ let us reduce this by a factor cf 2 to take aaoount

of the olrcusferentlal reflection poeslbllitleB, euoh that:

2

Wa take the •clntill«>tor converetion efflclenoj^.ae about

8. .S

f>' .-^-s^r-iVr ..««'* ttK.f'YiM. li.*i*^P r=.r;r..t -''f:,?

>1 n:i ?,'i. ; I

.;!

•; ? **(?? j-tiii-i^it

aX ««

••be

/<

3!eit M

—A ^ ^

<ao

.jltl X*30tf •£i'X

u\i r 1

'.io -^ XV ^-

'silt-i ^'-w:T^

,j y^ ,H, n^

©0^<'i. * {;^i^Q.)ll\^ '^ ^

^<f silil'J

?«*( !A/-T •^..S fUfi •

iuofiA /% aoi O 1C' i »w

sa

• 005, for oonvtrting entr^j to light; an'i th« phctoe^thod*

efflclenoy as About 1/10, for tHe frACtlon of Inoldent

plietoni tiiAt produce 9«eondAry electron* at the $athc<l«.

Now, per Mer of eaergy lost, the expeoted auaber of

3 eT qucinta produced with ocnveraicn effioleney of .005 let

^ * 10^ 3C .005 . 1667

the nua4>er collected in the grot« cathode area ^9r

Key le then:

K « f • X <pm ,0865 jr 1667 • go

Whence, applying the photo-oatnode efflolenoy of

1/10 gives, for the nuaber of eccondariee produced pbt MeT

lost:

Ji^ « 60 X 1/10 • 6±8 per Mev.

fevJ

- M-jc,v

"raai *6 4iM ¥

tec Jtti^ii-' el'?'"

^\

.v«.-^. -s®::! ^dbd » OX\i X OS « ^^^

A?PftOXl-iATK OWLCULATlQii FOR ^mvlKHOt FACTOR7J

Con8ld«r an Inflnltely-long oyollndrloal raeson dstoot-

or, 9urround«<l by a hollow toroidal oyllndior for elsotron do-

^e<ltion.

52i^o ttStuoo Hubbard's si^eotruai.

Th« erit«ria for exit of the deoay slaotron will be

elffiply cne deo&y energy and Uie r«IatlYe position in the do*

teocor At deoay.

The Approximate oaloulation is made for the speoial

eeee of oenter line deeay, for a detaotor of arerage radiut,

2»b inohes. tins density of the oyolohexylbenKene is t^ken as

•8 gai8 per em t l«ec the arersge ra;3ial thielcnees denoted

below by ''a** ie 2.6 x 8.54 x .8 « 6.8 gme.

The electron apeetrujn for the decay is talten from

Hubbard:

j (E)di: » d£ i^ [(V-E) t 2/9 (3 CdF:-3W>] C-1

where P it •,.« paraaeter deteraiined by the

amounts of the various interactions

causing am meson decay.* Hubbard's

31h correction must be sade to the calculation vith the

infinite cylinder for th§? loss of decay electrons in the solidangle subtended by the front face—wherein there Is no outerdetector Yoluse. We will take ,8 of the result as an estimatefor this end effect.

,7 ft 'Ta*fv-!S,t

•lit ttf tmlsn^S9!b t«*l li ^

»rii».--

XS

t

results show good agroomint witn thsory for s •<••

Wo ttkk9 ^ here to be « ,25^ and ooablne the braoket to:

or (•83V-.70£) 9r .8 ( M-iC)

or f{E)dE . dK 9.6/W* E^ (*-S) C-2

where W « j^ . 55 jj«v.

The nuBber in energy lnterT«X dS «t 1 is f (£). Tho

eeloulatlon assuAea emis^eion from the decay Dcsltlon In a

randcii direotion.

The direction of emission for a given energj detemines

how far the electron will travel before stopping. Aaaualng

t^Ai ta% ffllnimunn lonisatlon loss of 2 Mev per ga. ooours

throughout the transit, the direotion of <>fflls8ion relative

to the 8xi8 uniquely deteroiines whether or not the decay

eleotron can exit the eenter detector. Consider Figure <^-L.

T !• tSMt dis^otion of esdssion.

a is the average radial thlckneet

in gas.

PfG C-/

Then the electron loesisi

g»(r) s 2 X r Mev in exiting (r in gas) 0-3

BO

loi 5*

2-0

^j-ii

trt? .('^^t si I 3*5

i (Sir? .?"•?«* t*^^ v^T^^fi ,;--vK f^ "

'

f? n ^j

': tiitf '^BtH «»dl SV

;

"^ *f '"*^'i

.AC

»$«niQl£U Iai£(^*x •:

\-D i>\'^

e«o (taa fill *x) »rtJf5lx« fil «« -I x S « (i)*s-

59

Allowing 4 lev sxcesfc i »r loc*? In a icuble Mi> lek-

n^stf an lonlsdtion in the outer detectorj a detectable eleo-

tron aittst hare energj:

gCr) « (2 X r -#-4) 4«v

or g(e) =. g a -^. 4) M«T C-400 9

L.tu./d/'r /r^yc/^

iilMir* U !• the "uteful" energy of the «peotrua

for <1fftectlon of the deeajr electron, /%b a

fanctlon of the lower Halt g(^).

The fraction of the tpeotrura energy avallabl© a^ "uee-

ful* energy is:

§ - /ilV Xf(S)<IE « A a sinar^^tW^S)di 0-6

The integral /^ I^<^-l£)dE • /e£w - jfj

or. U « /I ^^^^^J/yi^3^ " iyy^JJ C.7

or, U « 1 ^ yC ^^>'»«^^//^3^ '^^^/ G-8r^^/ J/>,©c/©

vhare the upper llaiit of th© volum* Integration cf the

|!d

•0

^-r^

mini:

«-D

$•0

8-0

tkJ-L'

. ^al

V

T ^ .,.Jc. - (e;.

iv.'^r'

^^^^^^IX^^l^16^^

:.« ^ 'TTBIfin-?* 'f L'l

J3> - ^ ^

tdj !• ,. ...^..,..,„ * j»t.aai«* - '^ fiefivf

60

fitt««r«tor ift token as (E> » tht limiting

•ttfXft of e»' sfIan, for which «n eleotron

with thw T^':;xAiBSjn i8p.©e trans energy oouXd

e»jCAp«, l.«.J g(C2) ) • ^ ^111 •*"^ Sft »*•

eoe ^ rs ga/51 » ,227

@ ^ 77® C-9

liow ^^^) ~ oes^e coi'-G c^s<9 C-10

and ^(&J =c^^;7^ c^I^ ^cc.4-^ c.0^^ C-Xl

whercuooR eosiblnlnf the brao-iet, eln^^Jl^ "iy^^J

C-12

^ v^The Integral fjJlA^ -^ ^^^ ^ C-13

So the Integrals reduce to: rrr-^ S jec c^

+(v - ^V -I ^--9 V/6-i;; '^^-'^ Y« -^j-c.^-0/ C.X4

•eo &> = f'9 8«o (2> =-/f3 aeo (^ - 8S'

see ~ / eeo ^O =- f seo -^cD -/

which leads to the following v^lue for equation C-143

So that, g « 1 - .136 • .864 C-lg

An setlmsLte aeet now be ts&de of the vay in whloh this

0&

8)

XI -0 ^t*>^ <^xo^ ^^i,o:i kFioi>

51-0

ii^-i.

?>f*c

61

flfure l8 tldereaeed by reason :f &cn-e«nt9rliiie deoay. Suppose

th^t the deoiky «leotron w«re diono- energy tic, tmvXng Ja«t enough

energy to produoe a pulse In tha outer detfrctor, if It tunB

decayed on the oenterline and been emitted normal to the de*

teotor axis. A ounre like figure 0-2 would represent the

fr^otlon of these noraal-lnclcenee^ laono-enffrgetio electrons

that proiuoe a pulae, aa a funqticn of the radial dletanee

33 '-•r»rv^ course the deoay eleo-frocn the oenter line at desay.

trona do not all coiee off n.rm&lly, nor frosj ©enter line.

For i oyolohejcylbenaene-fiilad cylinder of 3 inches rediua^

A relativlatio electron will loee on the order of 12 Mev exist-

ing noraelly treta. the centerlino. Integration of equation

C->2 shows that lees then l^ of the total number of deoay

eleetrons hja.ve leee i4.n<itio ent^Tgy thim 12 «4ev.

3^^o.ci

33The quail t'-^tlve shepe cf thJ. "? ourire may bf> seen by

ooneidering the problea of two die&^s of equal b^p^b^ "^hosecenters move, froa conjunotlon, to a d.l8tr«jioe equal tc theradius, the area cosaicn to the two disXe expressed as afraction of the aref* of one, eorveBp&ndB to &ur fraatlon thatproduce a pulse.

"tft

i»

^ ^- J^

ee

S'or norniftl ineldtnof d»««y, an tXeotron t*ith gr«Ater

tfcan about 24 »*T vlll be «^blo to <ixlt th«t innar dat^ctor froa

«ny point In ! t. In ether words, if all aleotrons h^vlnff*

gra»t9r tnan 24 Ma^r kinetic «n^Wf3r are noraally Inoi'iant, tnay

will leara the dateotor; adding 4 Mev for penetration of the

double wall, and energy lea« In the outer detftetor, •nor«al"

electrons having ^^r0atar than 28 Mev will a^yi be counted.

The fraction of the deoay eleetronf* havlnif greater than 28

Kev ia .673.

The frsotlOR of electrone haTing leea than 16 Mev la

about .09 (16 ^0W l« t;hi? eneriBjy neoeasary to Juet exit nonaal-

ly frofls the os*nter line with 4 Mev e:xoeea).

The energy ep*?©tr»i!« ttien oontaine tbre** regions of

interest for these acranl Inoidence deeaya?

1. Kinetic energy leae than 18 Mev.

2. fctnetle energy between 16 iev and 38 Mct,

3. Kinetic enerfy greater than 28 ?<•.

In group 1, many decay eleotrone will not be enemetio

enough to be counted. Let us take that 1/4 of all the ncroal

decaya in group 1 are emergeticnlly countable.

the fraction of decay elao&rona in group 2 that will

b$ counted is certainly gre^iter th&n .& (aee Figure C*2)

»

and ia weighted toward a higher fraction, becnuae of the

greater llkelihced for higher energies than low, in this

rang*?. Let us t*ike that *?tout .9 ia the fraction •olleoted froa

this group.

'r n r'-'A

'Iltff

' I 'S »'

isib lS«t4a 1^- noil

, (j^«(f5

i.ki. ilii?*X»i'

^(^«.K

, V^(-; 1!^.

d

].-

i-t^ *«f ^cflt X .C/*f

a^

11 }* •tsi'l^ S cr^^o'^f?^

'nsrt»/tiB Q**'in.*I

- * -^ 3

-m«ll

^•XB

feij (1,^ !^!,:U' -iifS^

&1 i&jlll

63

In Grroup Z, oollectlon of the- totAl group is ln(tle««t«d»

. le^st for nopffipil Inoltenoe deory,

Th© ooffibln»d collection fra<Stion Ibr noraal Inoi deno*

decay ie th«ii about .36 for the totrtl »p^oti»»ia.

Let tif arply thl e ftetor to lottend tht evaluation of

Sf/Tj. to A fair ap..;xxiia«.tlon for tbe wholo ^olufo©.

The factor jf then baooiBesJ

ft « .864 X .88 X .8 • .e09

«&d 71^M .£^7 C-16

-.\jZ;

r^

T6. * 51

APPSINDIX D

64

r- ^"-^'1^)'^

'iwx mln my ^?!dc!• las I?•

S60

c:40

^«>,ow^^v

340

3&0

540

330

200

280

280

260

260

260

340

840

£40

3.27 2.62

3.13 2.62

5.09 2.6P-

Z.Zf a. 45

5.18 2.45

3.0$.

£.45

3.2? S.24

3.18 2.24

2.09 2.84

.0574 .0663

.0467 .0626

.0571 .0416

.0682 .0696

.0614 .0576

.0418 .0469

.Od5 .0788

.0642 .0607

.0447 .0601

The last eoluffin 1.13 x

correction to I* for tJh© Hcugh

taken aa am aveiiage oorrsotlon

integrations.

1'* rsflacta til© 18> plus

cross section st £s3, and ifi

for %h0 range of a in the

^e

<^j-^i**.^

^- Y O- ;' '

kV^O.,

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,.''3, ^'i^l'Oa

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iii>i >ii<WM'><Mw»»-<wfe''-a*wwi*«ftg.*iw«»ii<awtWB^w«i#>*ii»WNWww»g»w^ luwweiw imnii

wi tap. .Csd ?.: «^:J ^^1 *I C.1 doWo^-itoo

65

Crost section for the •leotromjugnetio production

of isu nesor. pairs fros Hoagh's forattl^Cf imts »xtr&pol»t«d

to ttiis t^roottts fros! $leotronio oiftSf). <£ dependsnoo taken to

"bo linear a« & low<?r llwlt, 1.©., OQtml^tfi ineohertsnoe

assumed. iOrose w^ctlon tl^ee 10^^ om^.)

Einc riry ofthe quantum ^^ ''**''^ *^'*<^ ^^ *^^ *^*^ ^^ ^•^ '^^^ •^•^III 11 ^ iji 111 II III >i in i w— ii^iir - I tinmnmtmmm)mtmmmmmmmimt^mmm^ifmm0mmmmmmimi)immmKm^t^^ m 1 1

.iiupm^in^N——

—

KMjifc

Be 7.24 6.i55/6.S 4.97 1.83 .687

C 10.S8 9.49/9,3 a, 17 2.44 1.03

Al n.B S0,55/n 17.7 6.27 ^.23

Ctt 6E.5 46.S/44.9 39oe 10.9 4.97

Tfcf valueg under the slant sign for 340 i'^ev «*re lihe

eroei eecticne as v^t^ Bethe-Heitler laess extr^pslst^d* ^d. th

line$i>r Z dependence.

aa

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a«,o.-:

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coiNciocNce: oeoni^Tpy o^rccTon^ count/i/o- f^CALCOiNCIOENCa^ FPon /? CAf^OON TA/^^£T //\t THCyTyNCHf\QTPON 3£An.

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J JUL BINDERY

ies& Julian 20654J9 A study of the problems in.

volved in the detection of ma.meson pairs <>-»ju the MIT syn-chrotron. ^^ BINDERY

I

SOLO LETTERIIMlAMD

20654involvec.

Thesis JulianJ9 A study of the -oroblems

in the detection of mu meson pairsfron the MIT synchrotron.

Liniary

U. S. Naval Postgraduate SchoolMonterey, California n

Ihesjg

A study of the problems involved in the

3 2768 002 11469 6DUDLEY KNOX LIBRARY

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