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Magnetic Moment and Hyperfine Field Studies Using
Gamma-Gamma Perturbed Angular Correlation
DHARMENDRA KUMAR GUPTA M. Sc. (Aligarb)
Thesis Submitted to the Aligarh Muslim University^
AHgarh in Partial Fulfilment For the Award ef
Ph. D. Degree in
PHYSICS
1972
T1258
' ' DEC 1373
1 1
Cert i f ied that the work presented in t h i s
t h e s i s i s the or ig inal work and has heen ca r r i ed
out by me <,
i^l/vG4t Dharmendra Kumar Gupta
Research Officer Department of Physics
A.M.Uo, Aligarh
Ill
ACOOWLEDGE^EHTS
The work presented in this thesis was carried out at
the Central Nuclear Laboratories of the Indian Institute of
Technology, Kanpur (India) under the able guidance of
Dr. G« No Rao, Assistant Professor. I am deeply indebted
to him for introducing me to this field, for taking keen
interest in my work, for his valuable guidance and for
placing all facilities at my disposalo
I wish to thank Professor J.J. Huntzicker, Dr. T.M.
Srinivasan, Dr. G.K. Mehta, Dr. S. Mukerjee and group
co-workers, Dr. B.V.N. Rao, Dr.D.N. Sanwal, Dr. K.B. Lai,
Mr. A.K. Singhvi, Mr. C. Rangacharyulu and Mr. R. Singh for
the useful discussions and assistance during the completion
of this work. I am also grateful to Messrs B.K. Jain and
G.P. Mishra for technical help throughout this v/ork. The
help in computer programming from Mr. A.K. Chopra and in
making alloys from Metallurgy Department is also gratefully
acknowledged.
I am deeply indebted to Professor Rais Ahmed whose
encouragement and guidance have throughout been a source
of inspiration to me. I take this opportunity to thank
various of my well wishers and colleagues particularly
Dr. S. Pazal Mohammed, Dr. M.L. Sehgal and Dr. K. Rama Reddy
who helped me in the preparat ion of t h i s t h e s i s . I am also
thankful to my teachers namely Professor Mohdo Zi l lu r Rahman
Khan and Prof« D.G. Sarkar for t h e i r kind help and encouragement,
I g ra te fu l ly acknowledge the f inanc ia l as,'jist.ance from
N.B.S. Washington, D.C. (USA) under PL-480 Scheme ( H B S ( G ) 1 2 7 ) .
I also thank the o f f i c i a l s of I IT, Kanpur for providing me
the r e s i d e n t i a l f a c i l i t i e s and the a u t h o r i t i e s of t h i s
Univers i ty for grant ing me leave for the period I v/as in
I . I . T „ , Kanpur.
F ina l ly , I thank to Kr N. Ahmad for exce l len t typing
of the manuscript.
(DoK. Gupta)
V
LIST OE GONTSI TTS
Page
List of Tables vii
List of Figures viii
Abstract xii
I. INTRODUCTION 1
lie NUCLEAR STRUCTURE STUDIES - EXPERIMENTAL RESULTS 5
A. Study of the Time Resolution of the Delayed Coincidence Spectrometer Using Different Nuclear Radiation Detectors 5
l- Time resolution of Ge(Li) detector ' 6
2. Time resolution of scintillation detectors 7
Bo Lifetime Measurements 8
C« The Decay Scheme of ^^Rh 27
III. MAGNETIC MOMENT MEASUREMENTS 38
Ao Magnetic Mom.ent of 206-keV State in ^ ' Re 40
1. Source preparation 40
2. Experimental set-up 40
3. Deca.y scheme and gamma-rays 41
4.. Magnetic moment measurem-ent of 206~keV
level in - - 'Re 41
B. Magnetic Moment of 68-keV state in ^Sc 43
1c Source preparation 43 2. Decay scheme and gamma-rays 43 3= Magnetic moment measurement of 68-keV
l eve l in ^^Sc 43 Co Results and Discussion 45
VI
IV. HYPERFINE PIEID MEASUREBffiNTS _ 50
A. Origin of the Hyperfine Fields, Hyperfine Field Models and Systematics of the Hyperfine Fields 50
Bo The Hyperfine Field Measurements at 'Re Nuclei in Nickel Lattice at Room Temperature 63
1. Source preparation 63
2. Experimental set-up 63
3c Experimental results and analysis of the data 64
44 Ce The Hyperfine Field at Sc Nuclei in Iron lattice at Room Temperature 65
1. Source preparat ion 65 2. Experimental arrangement 65 3c Experimental results and analysis of
the data 66
D. Results and Discussion 68
REFERENCES 77
PUBLICATIONS 83
V l l
Table
LIST OP TABLES
1 Comparison of the present l i a l f - l i i e measurements v/ith ava i lab le published valueso
2 Comparison of the experimental t r a n s i t i o n p r o b a b i l i t i e s and matrix elements ¥ith""slngle p a r t i c l e estim,ates and theore t i ca l matrix elements due to Arima et a l .
99 3 Gamma-rays observed in the decay of 16.1 d Rli
and t h e i r r e l a t i v e i n t e n s i t i e s . 4 Summary of the Ge(Li)-Ge(Li) f a s t - s low-eo inc i -
dence measurements.
5 Summary of the Nal(Tl)-NaI(Tl) sum-coincidence measurements.
5 Comparison of the present magnetic moment measurements with avai lable published va lues .
7 Comparison of the present hyperfine f i e ld
measurements with ava i lab le published va lues .
V l l l
LIST OF FIGURES
Figure
1 Slock diagram of delaj 'ed coincidence spectrometer.
2 MCA channel calibration and TPHC linearity.
22
3 Prompt time spectrum of Na t;ource wi th g a t i n g s
around 72-keV and 480-keV. A l ead loaded p l a s t i c
s c i n t i l l a t o r f o r t h e 72-keV and a Nal (Tl ) c r y s t a l
fo r t h e 480-keV are used . —
4 Li fe t ime spectrum of 68-ke? s t a t e i n Sc.
75 5 L i f e t ime spectrum of 280-keV s t a t e i n As (hollow
22 do t s ) along v/ith prompt time spectrum of Na ( s o l i d do ts ) under the same energy gate s e t t i n g s .
99 6 L i fe t ime spectrum of 89-keV s t a t e i n Ru.
170 7 Li fe t ime spectrum of 84-keV s t a t e i n Yh.
1 Pii 8 Lifetime spectrum of 206-keV state in Re.
ITL 9 L i fe t ime spectrum of 124-keV s t a t e i n CSc
131 10 Lifetime spectrum of 134-ke'V state in Cs.
11 Lifetime spectrum of 81-keV state in -' •Cs.
197 12 Lifetime spectrum of 77-keV state in Au
(hollow dots) along with prompt time spectrum
22 of Na (solid dots) under the same energy gate
settings.
IX
Figure
13 Gamma-ray s i n g l e s spectrum of Kb. i n the .-:;nergy
reg ion 0-443 keV obta ined wi th a Ge(Li) d e t e c t o r
( l i v e t i m e 60 min) .
go
14 Gamma-ray s i n g l e s spectrum of Rh i n the energy
reg ion 443-1208 ke? with a Ge(Iii) d e t e c t o r
( l i v e t i m e 600 min) .
99
15 Gamma-ray s i n g l e s spectrum of Rh in~ttre energy
r eg ion 1208-1749 keV ob ta ined wi th a Ge(Li)
d e t e c t o r ( l i v e t i m e 1200 min ) .
99 16 Gamma-ray s i n g l e s spectrum of Pli i n t h e energy
r eg ion 1749-2059 keV ob ta ined wi th a &e(Li)
d e t e c t o r ( l i v e t i m e 1800 min) .
17 Block diagram of Ge(Li)-Ge(Li) sl 'ow-fast co inc idence
spec t rome te r .
18 The spectrum of y-^^ays in the r eg ion 0-511 keV
c o i n c i d e n t with the 322-ke7 y-vs^J' r ecorded wi th
a Ge( I i ) -Ge(L i ) f a s t - s l o w assembly^
19 The spectrum of y~rajs i n the region 0-941 keV
c o i n c i d e n t with the 353-keV y-raj r ecorded wi th
a Ge(Li)-Ge(Li) f a s t - s l o w assembly. 99
20 Level scheme of Ru. Dashed l i n e s shown a r e new t r a n s i t i o n s .
X
Figure
21 Arrangement of magnet and detectors.
22 Decay scheme of " 'W (24h) -^ " ' Re.
23 Time differential perturbed angular correlation
spectra of Re in an external magnetic field
of 7 KOeo
24 R(t) vs time t plotted for the TDPAC spectra of 1 R7
Re i n an e x t e r n a l magnetic f i e l d of 7 KOe.
25 The F o u r i e r t r ans fo rms of R( t ) for Re i n an
e x t e r n a l magnetic f i e l d of 7 KOe.
26 Decay scheme of ''"' Ti i^'^^k) —?• "^"^Sc.
27 Time d i f f e r e n t i a l p e r t u r b e d angu la r c o r r e l a t i o n
spectrum of Sc i n an e x t e r n a l magnet ic f i e l d
of 7 KOe.
28 R( t ) vs time t p l o t t e d for t h e TDPAC s p e c t r a of
44 Sc in an external magnetic field of 7 KOe.
29 The Fourier transforms of R(t) for Sc in an
internal magnetic field of 7 KOe.
30 Magnetic hyperfine fields at solute nuclei in
iron matrix plotted vs the atomic number Z of
the solute atom. Open circles indicate that
the sign of the field has not been directly
measured.
X I
Figure
31 Magnetic hyperfine f i e l d s a t solute nuc le i in
cobalt matrix p lo t ted vs the atomic number Z
of the solute atom. Open c i r c l e s indicate tha t
the s ign of the f ie ld has not been d i r e c t l y
measured.
32 Magnetic hyperfine f i e lds a t solute nucle i in
nickel matrix p lo t ted vs the atomic number Z
of the solute atom. Open c i r c l e s ind ica te t h a t
the sign of the f i e ld has not been d i r e c t l y
measured.
33 Calculated po la r iza t ion P. of the S-electrons
a t the impurity s i t e as a funct ion of the
valence Z. of the impurity atom. Curve ' a '
represents the estimate of Daniel and F r i e d e l ;
Carve ' b ' represents the estimate of Campbell.
j?cr i r on P, = 1, h
34 R(t) vs time t for the TDPAC spectra of • ' HeNi
in an external polarizing magnetic field of 2 KOe.
1 on 35 'fhe Fourier transforms of R(t) for ReNi in an
external polarizing magnetic field of 2 KOe.
36 R(t) vs time t for the TDPAC spectra of ^^ScPe
in an external polarizing magnetic field of 3 KOe,
37 'Ihe Fourier traiisforms of R(t) for ScFe in an
external polarising magnetic field of 3 KOe.
Xll
MAGNETIC MOMENT AND HYPERPINE FIELD STUDIES USII G
GAMMA-GAMMiii PERTURBED ANGULAR GORPJCLATION
ABSTRACT
Using time differential pertur'bed angular correlation
technique (TDPAC), the hyperfine fields on Sc in Pe_ and on
Re in Ni_ are measured. The hyperfine field on ScFe is
reported for the first time. Using th-e-same method^ the
44 magnetic moment of the 68-keV state in Sc and of the
1 Rl 206~keV state in Re are also measured^
Detailed studies on the time resolution of Ge(Li)
detectors and scintillation detectors were carried out.
44 75 99 I'l 1'5' The nuclear lifetimes in ^^Sc, '^Se, ^Ru, " Cs, " Cs,
1 70 1 Pil 1 Q7 Yb, Re and Au are also measured using the delayed
coincidence techniques. A new value for the lifetime in
131
Cs is reported. In most of the other cases the errors
in our measurements are considerably less compared to the
earlier reported values. The nuclear lifetime measurements 151 133 197
in Cs, Cs and Au fall under the category of l-forbidden transitions. The experimental Ml, E2 transition probabilities
obtained from the present measurements in the 1-forbidden
131 133 197 transitions in Cs, Cs and Au are compared with the
predictions of Arima et al. Por the remaining cases, the
experimental values are compared with the single particle
estimates.
Xlll
The detailed decay scheme studies in the de-excitation
99 of Ru are also reported. These studies are carried out
using Ge(Li) detectors, G-e(Li) detectors in coincidence,
Nal(Tl) detectors etc. The genetic relationships are estab
lished from accurate intensity measurements and coincidence
studies. One nev/ gamma ray and four-n«4v cascade transitions
are establishedc
The existing hyperfine field models are discussed in
brief. The systematics of the variation of the dilute impu
rity hyperfine fields in the host matrices of Fe, Ni, C£ are
studied. All the reported dilute hyperfine field values are
plotted against the atomic number of the solute for each
of the Pe, Ni, £0 matrices and some new trends are pointed
out, e.g.
(i) The hyperfine field H, „ is negative in 3d, 4d and 5d
impurities in all the three hosts F_e, _G£, Ni except in the
4d series for ^^Fe, ^^ZrFe and " ZrOo.
(ii) In iron host, the field increases gradually for Ru, Rh
and Pd and the maximum value is obtained for Pd. However,
the reverse trend is clearly seen for the same impurity
metals for the other host matrices of _C£ ind Ni.
(iii) In 5d impurities, the maximum value of hyperfine
field is obtained at Ir for all the three matrices.
(iv) In the case of 5p impurities, the field starts with
a small negative value and gradually increases to a maximum
XIV
value for I and falls off to zero.
(v) In 4f series the fields are negative for low 4f values
and then it changes from negative to a large positive value
and again from positive value to a large negative value.
The hyperiine fields for ScFe_, B.eNi are compared with
the models suggested by Shirley et al.; Camphell; Balahanov
et al.; and Stearns. It is found that none of these models
can successfully explain the measuradr-f4.elds in ScPe and
ReNi. The observed field in Se?e both in magnitude and
sign may be qualitatively explained by the conduction
electron polarization (GEP) and the core polarization (GP)
models suggested by Shirley. The field on Re in Ni may be
understood if we assume that conduction electron polariza
tion and the overlap polarization (OP) are vectorially added
to give the final experimental value. The experimental
magnetic moments are compared with the prediction of the
existing nuclear models. The magnetic moment value of
206-keV level in Re is in fair agreement with the
theoretical value obtained from the modified Nilsson's
model proposed by De Boer et al. Attempts are made to
explain the experimentally measured magnetic moment for
68-keV state in Sc assuming the configurations for a
1 "^ proton and neutron groups as ( 7/0)7/0 ^^ • 7/? 7/?
respectively. But the value for magnetic, moment thus
XV
obtained is found larger by a factor->• 1.4 compared with
the experimental value. Therefore, the absence of any
definite knowledge of the configuration of 68-keV state
44 m Sc is the hind: ronce in interpreting the magnetic
moment of this state.
CHAPTER I
INTRODUCTION
Since the discovery of Samoilov et al. in 1959 that
diamagnetic gold nuclei dissolved in ferromagnetic iron experience
a large magnetic hyperfine field ('•>l MOe), the range and usefulness
of application of hyperfine fields has increased considerably. The
large magnetic fields seen by the impurity nuclei can be favourably
exploited to measure the magnetic dipole moments of the short
lived nuclear excited states of the impurity nuclei. The hyperfine
field measurements are also useful as sensitive probes for the
understanding of the Core and Conduction electron wave functions.
A formal solution of the problem of the impurities in
ferromagnetic hosts is quite complex and would involve the solu
tion of a many body problem. However, the systematic variations
of the signs and magnitudes of the hyperfine fields as a function
of the electronic configurations of the impurity atoms (in
particular as a function of the atomic number Z) has provided us
the insight to understand the major mechanisms responsible for
the origin of these hyperfine fields. The large experimental
data currently available with literature enabled many workers
to suggest many models for the hyperfine fields. Because of
this reason, there has been considerable interest to measure
the magnetic hyperfine fields on magnetic and nonmagnetic
2)
impurities in ferromagnetic and paramagnetic hosts. As pointed
by Jaccarino, Walker and Wertheim (see page 51), the experimental
data with temperature variation of the hyperfine field on the
impurity can be used to detect the possibility of a localized
moment around the impurity., It has been our interest to measure
the hyperfine fields on dilute diamagnetic impurities in ferro
magnetic hosts to have a better understanding of the mechanisms
involvedo
Many experimental techniques in principle can be used for
the hyperfine field measurements. These techniques may-iroadly
be divided into two categoriess a) stable nuclei are used (nuclear
magnetic resonance (NMR), electron spin resonance, nuclear
specific heats etc.), and b) radioactive nuclei are used~(pertur-
bed angular correlation, nuclear orientation, Mossbauer effect,
nuclear magnetic resonance/nuclear orientation ( M R / N O ) ) . In
this thesis, v/e have used the time differential perturbed angular
correlation techniques (TDPAC) for the hyperfine field measurements.
Normally WIR techniques give results of highest accuracy.
However, the recent improvements in the TDPAC techniques like the
Fourier transform of the auto-correlation function has made it
competetive with NMR accuracy. In addition, the TDPAC technique
has certain advantages when compared to the NMR in terms of its
higher sensitivity and wider applicability in terms of temperature
etc. The higher sensitivity of the PAC technique will be parti
cularly helpful for the measurement of the dilute impurity
hyperfine fields because the impurity-impurity interactions
are negligible.
In the PAG technique of measuring the hyperfine fields
one observes the change in the angular correlation pattern of the
3
nuclear radiation when the intermediate state having a magnetic
dipole moment is perturbed "by the internal hyper fine fields o In
the ahsence of any external perturbations, the angular correla
tion of the y-^ays could he expressed as a sum of a series of
legendre polynomials " <, V/hen the intermediate state is perturbed
by magnetic field, classically speaking, the dipole moment
processes around the applied field with Larmor frequency. The
larmor frequency and hence the internal hyperfine field could be
obtained from the observed change in the (y-y) angular correla
tion pattern, if we know the magnetic dipole moment of the
nuclear state involved.
For the cases measured in this thesis, cubic hosts were
chosen so that the quadrupole effects are sm.all. In addition,
the impurities form solid solutions with the corresponding hosts.
All the experimental data available in the literature for the
impurity hyperfine fields have been plotted as a function of
the impurity atomic number for the host matrices of Fe_, _C£» Ni.
Similar plots for Fe host are already available in the literature
(see Chapter lY), From the studies of these systematics, we are
able to draw some nev/ trends which were not pointed out until
now such asi (i) The hyperfine field H, is negative in 3d, 4d
and 5d impurities in all the three hosts Fe, C_o, Ni except in
the 4d series for '- YFe, ' ZrFe and ZrCo. (ii) In iron host,
the field increases gradually for Ru, Rh and Pd and the maximum
value is obtained for Pd. Hov/ever, the reverse trend is clearly
seen for the same impurity metals for the other host matrices
of Oo and Ni„
The magnetic moments of some of the nuclear states are
also measured using the TDPAC technique., These values are
compared with the existing nuclear models.(see Chapter III).
99 The nuclear level structure of Ru is studied using
Ge(Li) detectors J Nal(Tl) sum-coincidence spectrometers and
G-e(Li) detectors in coincidence. These studies resulted in
99 an improved level schemxe of Ru„ The short nuclear lifetime
measurements in ^^Sc, ' Se, ^Ru, '^^^Cs, ^^^Cs, " Yh, " Re
197 and Au were also carried out. One new value for the 134--
keV state in Cs is reported. In other cases the existing
errors in the m.easurements are reduced. The experimental Ml,
E2 transition probabilities obtained from, the present measure
ments in the 1-forbidden transitions are compared with the
predictions of Arima et al. Por the remaining cases;, tke
experimental values are compared with the single particle
estimates (see Chapter II). Detailed studies on the time
resolution of Ge(Li) detectors and scintillation detectors
were carried out.
CllPTSR II
NUGLBAR STRUCTURE STUDIES - EXPERIMENTAL RESULTS
Ao STUDY OE THE TIMS RESOLUTION OF THE DELAYED COINGIDENCE
SPECTROMETER USING DIFEER3NT NUCLEAR RADIATION DETECTORS
The time resolution of the spectrometer plays an
imp'ortaiit role in the measurements of lifetime, magnetic
moment and hyperfine fields. The "block diagram of the
electronics is shown in Eig. 1. Depending upon the parti
cular case under investigation the comMnation of the
detectors among Nal(Tl), lead loaded plastic scintillator,
plastic scintillator and Ge(Li) detector is chosen. All
the scintillators used in the present experiments are
coupled with 56 AVP photomultiplier tubes. The fast pulses
from the detectors are amplified (particularly low energy
radiations) using EGi G 1 nsec DC amplifiers and then fed
into Past discriminators ORTEG model 417" The outputs are
fed into model 437A ORTEG time-to-pulse height converter
(TPHC). The TPHC is calibrated by recording prompt ^°Co
spectra and by observing the channel corresponding to the
centroid of this prompt spectrum for various values of
delay introduced in the 'stop' arm. This delay is varied
in the interested range by using the ORTEG model 425 delay
box (nsec region) or ORTEG model 42? delay amplifier (jisec
region). These delay sources are in turn calibrated with
standard techniques say for example using standard lengths
of 50i" (RG58A/U) cable which has delay of 5.06- nsec per meter.
5
o
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The introduction of delay gives rise to a shift of the
centroid of the prompt time spectrum^ It is found that a
plot of delay versus the centroid position (channel number)
was a straight line (shown in 'Fig,2) thus confirming the
linearity of the TPHC. A least squares fit to this straight
line (given in Fig. 2) gave the slope, or the calibration
of the spectrometer^ It was found that the linearity of
the system is better than O.lX-
1. Time resolution of Gre(Li) Detector
In the study of the time resolution of electronic
system, one 5.1 cm x 5.1 cm plastic scintillator coupled
with 56 AVP photomultiplier tube in start channel and a
Ge(Li) detector of 7 mm depletion depth and 6 sqcm effec
tive area in the stop channel are used. A bias voltage of
+900 V is applied to Ge(Li) detector while -2000 V to the
P..M. tube. Here in place of fast discriminators Constant
Fraction Timing Discriminators ORTEC model 453 are used in
fast channels. In the Ge(Li), using veiy narrow window,
a wide range of energy is scanned and 'corresponding time
spectra are recorded. The FWHM is found to be varying from
2.9 nsec to 3.7 nsec and slope from 0,4 nsec to 2.8 nsec in
4) the energy range from 32-keV to 1830-keV '. This response
5-7) i s compared with the exis t ing l i t e r a t u r e ' for 100-keV
to 1330-keV region and found in good agreement. This study
gives the information about the l i m i t s of the system and i t
20 30 40 Delay in nsac
50
Fxa.2 MCA CiiANNiiL C.\L iBR Al'lON AND TPHC LiNEAiilTY /"usee RliGIONJ.
u c
a
Q
I
I 4:
I
0 <
0 01
0 0
0 GO
0 CD
0 ^
0 CM
jaqujnN puuDMO
7
is helpful in selecting the cases of magnetic moment and
hyperflne fields.
2. Time resolution of the scintillation detectors
Similar studies are made using 5.1 cm x 5.1 cm
Nal(Tl) scintillators in both the channels i.e. start and
stop respectively» Best timing conditions are achieved
when -1900 V is applied to the photomultiplier tube in
start channel and -2000 V to the photomultiplier tube in
stop channel. For carrying out the measurements on the
g
44
44 g - factor of 68-keV state in Sc and hyperfine field at
So nuclei in iron lattice, the time resolution of the
electronic system gating 78-keV gamma rays in start channel
and 68-keV gamma rays in stop channel is determined. The
values obtained for the FWHM and slope of the prompt spec-
22 trum using Na radioactive source are 15.0 nsec and 2.0
nsec respectivelyo In the g-factor measurement of 206-keV
1 87 state in Re, 480-keV gamma rays are gated in start channel
and 72-keV gamma rays in stop channel. Under these energy
gate settings the FWHM and slope of the prompt spectrum are
found to be 4.8 nsec and 0.5 nsec respectively. While in
1 87
the hyperfine field measurement at Re nuclei in nickel
matrix the Nal(Tl) is replaced by a 5.1 cm x 5.1 cm lead
loaded plastic scintillator for the detection of 72-keV
gamma rays in stop channel. Under these energy gatings
the FWHM and slope of the prompt spectrum are found to be
1.3 nsec and 0.24 nsec respectively. A sample of the prompt
time spectrum is shown in Pig. 3.
B. THE LIFETIME MEASUREMENTS^"^^^
Several half-lives of the excited states in various
44 99 nuclei are measured. All the sources except Ti and Rh
in the present measurements have been purchased from the
Atomic Energy Commission, Bombay (India). The dimension
of the sources used is taken very small so as to have
better true to chance ratio. The detectors are kept at
2% geometry and the source is at the centre of the detec
tors. The final values of the lifetime reported in this
work are the statistical average of many runsc The least
squares fit of the coincidence data is done with the help
of an IBM 7044 computer.
(i) The half-life of the 68-keV state in ^^Sc : The 48.2 Y
44 activity of Ti decays through electron capture to the
excited levels in " Sc. The measurement of the half-life
is accomplished by observing the delayed coincidences
between 78- and 68-keV gamm.a rays. Since these gamma rays
cannot be resolved in Nal(Tl) detectors, the combined peak
is gated in both start and stop channels. Therefore, the
slope is obtained on both the arms of the time spectra.
The recorded time spectrum is shown in Pig. 4. The final
computed value of many runs for the half-life of the 68-keY
state is 155.5 + 2.0 nsec.
3x10'
c D O U
u c •o u c o u
10
FWHM = 1.3 nsec.
Slope /5i/2=0.2A
-
n sec. ^
10
20 Ch.No.
30 J
0 5 10 Time in n sec.(Arbitrary Zero)
F I G . 3 PROMPT TIME SPECTOUM OF ^^Na SaiRCE WITH GATINGS
ARCVND 7 2 - k e V AND URO-keV. A LEAD LOADED PI A3TIC
SCINTILLATOR FOR THE 7 2 - k e V AND A N a l ( T l ) CRYSTAL
FOR THE i^fiO-keV ARE USED.
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•Ji
> 0
1
Cl:.,
c «p
i o y
t?? - j )
% H H y ( b ,—t
•-, r " .
- I -
I I I ' ' ' L
o o en
SINHOD BDNBQIONIOD
o
Our measured half-life value agrees very well with
the earlier measurements of Bergstrom et al. ' (153+1)
12) nsec, and Ristenen et al, ' (153+2) nsec and disagrees
13)
with the measurements of Kliver et al. ' (166+5) nsec
and Bandi et al. ' (192+40) nsec. Ristenen and Sunyar
concluded from their angular correlation data that 68-keV
transition is a mixture of Ml and E2. They also confirmed
that 68-keV level has spin, parity as 1+. The measured
half-life is employed to calculate the experimental transi
tion prohabilities T (Ml)^^^ and 'T (E2) ^ from the following exp exp
relations, ^ (-)e.p - f r H ^ ^ exp - Ti (1 + a ^ -J (1 ^2)
2.
exp = T T T F T T ^ ^ (1 ^ 52) T (E2)_ = . ^ I'T' ^ X — ^ (2-1)
The values of branching ratio (R), mixing ratio (6 ) and
total internal conversion coefficient (a, ,) are taken from tot
"IP "I 7^
the existing literature ' , and thus on substituting the p
values of R, 6 and a, , in eqn. (2-1), the experimental transition probabilities obtained are,
T (E2) ^ 2,5 X 10^ soc~^ 'exp
T (Ml) - 2.0 X lo' sec"-"-^ 'exp
16) and the theoretical single particle estimates ' are
T (Ml)g . 7.7 X 10- ^ sec""
T (E2) - 4.0 X 10^ sec"- ^ ^sp
10
On comparison we find that the Ml part of the 68-keV gamma
-4 transition is retarded by a factor of .v4 x 10 and the E2
is enhanced hy a factor of--16 relative to the single parti
cle estimates. It is in agreement with the earlier measure-
12) ments ' .
(ii) The half-life of the 280-keV state in '''As : The
75 half-life of the 280-keV state in '- As is determined by
75
using a Se (120d) source. The measurement of the half-
life is accomplished by observing the delayed coincidences
between 121-keV and 280-keV gamma rays. Here a lead loaded
plastic scintillator is used in stop channel for the detec
tion of 280-keV gamma ray. Since the slope of the prompt
time spectrum under the same energy gate settings is of
the same order as the lifetime under study, the lifetime
of the excited state is determined by the centroid shift
method a,nd it is found to be Ti_ = 0.277 + 0.031 nsec. The
lifetime and prompt time spectra are given in Pig. 5.
The 280-keV transition has been identified as mixture
of electric quadrupole (E2) and magnetic-dipole (Ml) '.
The experimentally observed half-life is employed to calculate
the transition probabilities T (Ml) and T (E2) from the
eqn. (2-1),
The values of branching ratic (R) and mixing ratio p 2.5)
(6 ) are taken from the published literature ' obtained
with Coulomb excitation technique. The experimentally
in ••-•
c D o u u c C9
u C o (J
0 5 10 T ime i n n s e c (Arbitrary 2ero)
F I G . 5 LIFETIME SPECTRUM OF 2 8 0 - k o V STATE IN ^^Aa (HOLLOW 22
DOTS) A3.0NG WITH PROMPT TLME SPECTRUM OF Na {SOL.ID
DOTS) UNDER THE SAME .ENERGY GATE SETTINGS.
11
measured value of total internal conversion coefficient
(a, , ) by G-rigorev et al. ' is used to obtain the
experimental transition probabilities,
T (Ml) •-• 2 X 10^ sec"- ^ ' exp
T (E2) ^ 4 X 10^ sec"^ ^ 'exp '^
Theoretical single particle transition probabilities are
17) estimated from the known relations ' using statistical
factor as unity.
T (Ml) - 6.6 X 10 - sec"- ^ ^ sp
T (E2) . 4.9 X lo' sec""'-^ ' sp
On comparison one finds that E2 transitions are enhanced
by a factor--'8 and Ml transitions are retarded by a
-3 factor'-'3 x 10 as compared to the single particle estimates. Our results are in agreement with the earlier
, 18) workers '.
( i i i ) The h a l f - l i f e of the 89-keV in ^^Ru : The half-
l i f e of 89-keV" level in - - Ru i s measured by the delayed 99 coincidence method using Rh (16.1 d) source. One lead
loaded p l a s t i c s c i n t i l l a t o r (5 .1 cm x 5.1 cm) i s used in
the stop channel to accept 89-keV gamma rays and Nal(Tl)
c rys ta l of (5.1 cm x 5.1 cm) in the s t a r t channel to
accept gamma rays from 320-520 keV. The l i f e t ime spectrum
i s shown in Fig. 6. The f ina l computed value of many runs
for the h a l f - l i f e (T^) i s 20.5 + 0.1 nsec. 2 ~"
T—nr
rO CVJ
CO
m
T — I I I o O if) c
o in d CVJ
CT> CO
FT—I I U»L
• • • • • •
. • • • •
ro in ro
in
cc 0^
• •
CM
O 0 ^
O
O in
o ro
o O
o
o 1^
o in
o ro
U l U—J—I L I • ' » > • I 1 I I I ' • *' *
o 5r
o
o o
o GO
o VD
O sr
o k .
c N
>>
n • 4 -
<
u (^
r. N E
H-
r^
0 .
ic K
<t
C/5
> W !
CN
oc-& H
o
H O '-4 P4 f,0
W
r-r.
o CM
o ro Cvi
J- O
H
VO
S
s^unoo 3Duappu|03
12
The 89-keV gamma ray is a mixture of Ml and E2
19) multipolarities. Kistner ' from his Mossbauer studies
2
reported that the mixing ratio 5 =2.7+0.6. The
total internal conversion coefficient '^x.^x. of the 89-keV
transition is taken as 1.43 from the tables of Sliv and 20)
Band ' , The presently reported half-life is corrected
for internal conversion and transition probabilities T(M1)
and T (E2) are computed. It is found that the experimental
E2 transition probability T(E2) is enhanced by a factor
.•••25 and the Ml transition probability T (Ml) ie retaitVed by -5 a factor'- 8 x 10 when compared to the single particle
21) estimates. Moss and McDaniels '' from their experimental observations concluded that the lower excited states of 99 Ru are the result of a multiplet formed by a coupling of
the 2dc-/p neutron to the first 2+ state of the even core 98
of the neighbouring nucleus, Ru. However, recent work
22) of Kaindl et al. on the analysis of the quadrupole
99 polarization on isomer shift measurements in Ru using
Mossbauer technique ruled out the possibility of any such
coupling. This discrepancy can be removed with the help
of our lifetime measurements. The core-excitation model
proposed by Moss and McDaniels suggests that the B (E2)
values of such multiplets should be equal to the B (E2)
values of the even core. The B (E2) value is computed
from our presently measured and corrected value of the
lifetime of the E2-transition of the 89-keV gamma ray.
13
The experimental B (E2) value of the 2+ —^ 0 + transition
of Ru is taken from the work of Stelson et al.' . The
ratio of these two quantities ^^Ru B (E2)/^ Ru B (E2) is
found to be 1.4, which is nearly unity. This indicates
that the conclusion drawn by Moss and McDaniels that the
99 lower excited states in Ru are the result of a multiplet
98 formed by a coupling of the neighbouring nucleus, Ru
seems to be valid.
(iv) The half-life of the 84-keV state in '''''Yb : The
170 half-life of the 84-keV level in lb is determined by
170 using a Tm (130 d) source. The measurement of the
lifetime is accomplished by observing the delayed coinci
dences between 84-keV gamma rays and 886-keV p-rays. Here
tv/o plastic scintillators 5.1 cm x 5.1 cm are used in both
the channels. The plastic scintillator used in stop channel
for the detection of 84-keV gamma rays is mounted in an
aluminium can of sufficient thickness ( 400 mg/cm ) so as
to absorb p-rays. The lifetime spectiiim is shown in Fig. 7»
The final statistically computed value of many runs for the
half-life (T^) of the state is = 1.62 + 0.02 nsec.
The 84-keV transition is from 2 + to 0+ states and
24) i s a pure E2 t ransi t ion . The experimental t ransi t ion probabili ty i s calculated from our measured ha l f - l i f e value
20) using theoretical total internal conversion coefficient
«tot = •^^-
2x10"
1000
c O
u
c
^ 100 u c o u
10
• * T =1.62t0.02 ns«c
to
•I J
. • I "
Ch. No. 20 30
_ j . j _ 40 .
u 1 1 r 0 10 20 30 40 50 60 70
Time in nsec(Arbitrary-zero)
170 FIG. 7 LIFETIME SPECTRUM OF 84-keV STATE IN Yb
14
T (E2) ~ 5.6 X lo' sec"- ^ ' exp
The single particle estimate for E2 transition is-3.0 x
10^ sec"^ where E = 0.08423 MeY. Y
It can be seen from the above data that the experi
mental transition rate is faster than the single particle
estimates "by a factor' -'1S9. This much of enhancement is
commonly observed in deformed region for E2 transitions 25)
within rotational band for even-even nuclei . The theory of rotational motion can be applied in-this case also since
170 Yb lies in the strongly deformed region.
1 R7 (v) The half-life measurement of 206-keY level in Re :
1 ft7
The 24 h a c t i v i t y of W decays through the p-decay to the 1 R7
excited states in 'Re. The measurement of the half-life
is carried out by observing the delayed coincidences between
48C-keV and 72-keV gamma rays. Here two Nal(Tl) scintil
lators 5.1 cm X 5.1 cm are used in both channels. The time
spectrum obtained is given in Pig. 3. The same experiment
is also perfoOTied by keeping a lead loaded plastic scintil
lator in place of Nal(Tl) in stop channel for the detection
of 72-keV gamma rays. The final computed value of many runs
for the half-life (Ti_) of 206-keV state is 555-3 + 1.7 nsec.
The 72-keV gamma ray from the de-excitation of the
206-keY state in 'Re is known to be a pure El transition ' .
Our measured half-life value gives the experimental transition
probability,
'OJ
M ^ » ioo
r" '^3 H
• ^
i K
;p:
a •^
31
.-• ^
M
^ t X* o <;
j > H r-M
00 _^ ^ 0
H
I ^ _ . D
O n
^ i - ^
> •n 2?
o •n »<
N f ) O
x _ ^
"^J
en
en o
00 O O
o
CD O O
"«s3
(Jl
o
00
o o
_ A
o (J) o
>
o o
CD O
o o
- 1 ^
CD cn O
_ i k
00 o o
1.
~o ^ PO
o
_ >
o
o
_ 0 0
o
_ 4 ,
-o o
_»
- ro o
-it^ o
o
- 0 0
o
ro -o o
fO - rv:»
O
NJ - ^ o
Coincidence Counts
-TT-TTTJ-"(Ji
1—I—rr
1 N)
%
1
/
, 1 ,„J 'l I I I 1,
1 +
u (/I
o
1 1 1 1 1 1 1 1 J 1
•15
T (El)^^^-- 6.77 X 10^ sec"^
The value of total Internal conversion coefficient is taken
20) from the table of Sliv and Band '. The single particle
12 -1 estimate for the El transitioii is~1.7 x 10 sec . One
finds from these values, the El hindrance factor is -
4 X 10"'^. The 72-keV transition is from the band K=9/2
to the band E=5/2 with A K = 2. This transition is a K -
forbidden transition and the El-hindrance factor for such
-A -7 transitions is known to vary from 10 to 10 or even less.
Our conclusions are in agreem.ent with the results by
27) Perdrisat ^ ' . An empirical law has been proposed by
Rusinov^ ' connecting the hindrance factor to the degree
of K-forbiddeness. He gave log H = 2 ( A K - L ) , v/here H
is the observed hindrance and I the transition multipolarity,
This law is roughly compatible with K-forbidden El transi
tions measured in odd and even -A nuclei. An attempt to
evaluate the hindrance of K-forbidden El transitions has
29) also been presented by Rouchanine jad -^' , He used a method
of projecting the Nilsson eigen functions on the eigen-
states of the total angular momentum.
(vi) The nuclear life-time measurements in 1-forbidden
transitions in Cs, Cs and Au :
(a) The half-life of the 124- and 134-keV states in ^^^^^ •
1'51 The 14d activity of •" Ba decays through the electron
131 capture to the excited states in Cs. The half-life
16
of 124-keV state is determined "by observing delayed coinci
dences between 496-keir'and 124-keV gamma rays. This delgiyed
coincidence spectrum is obtained with Nal(Tl) scintillator
on the stop side (gated at 118-keV with a window of.'• '•30-keV)
and the Ge(li) detector on the start side (gated at 495-keV
with a window of 6-keV). The final computed value for the •
half-life (T^) = 3.80 + 0.01 nsec. While the lifetime of
134-keV state is determined from the delayed coincidence
spectrum obtained with the Nal(Tl) scilrfcillator on the stop
side (gated at 128-keV with a window of'--30 keV) and the
Ge(Li) detector on the start side (gated at 493-keY with
a window of 6-keV). The final computed value of the half-
life (Ti) of the 134-keV level is = 8.1 + 0.1 nsec. These
half-life values a-re obtained after the subtraction of the
slope due to electronics obtained with prompt spectra of
22
Na weak source having the same statistical accuracy and
under the same energy settings. The lifetime spectra
corresponding to 124-keV and 134-keV levels are shown in
Pigs. 9 and 10 respectively. (b) The half-life of the 81-keV state in ^^^Cs : The half-
133 life of the 81-keV state of Cs is determined by using 133 -^^Ba (7.2 I) source. The measurement of the half-life
is accomplished by observing the delayed coincidences
between 556-keV and 81-keV gamma rays» Here two 5.1 cm x
5.1 cm Nal(Tl) scintillators are used in both the channels.
io^
i2|10 § ! O i O I <^ i J= i
"O i
El 5! 10'
10 0
^ '
20 l _
-L
?2 ' ' 2 ' (V,.3/J -
V>. T, =(3.80i0.01)ns
\ " .
40 _ j
V
620
496
\(\''/2)-^-^
V5,;
•124
131 Cs
• •
•••
»• • • • • • ~
Ch. No. 60
I . 80 . t
100 120
10 15 20 25 30 35 40
Time in nsec (Arbitrary zero)
140
45
FIG. 9 LIFETIME SPECTRUM OF 124.keV STATE IN ^ ' ' ^Cs .
"1—r •'I I I I I M i l l — r
i
-t -( t - —1
4- ( p o
Is: IC
t- •• .h -H
& O
V Cj
--^
6 tl 00
II
Cv(
1 - ^
•s < ;
• » • ,y . . • • •
• • •
• •5
. • • . , : •
. . ^
• ; • •
, ^
y
• » . . • « •
V
X_J L. 1 I 1-J L _ _ L , li.. O
m O
04
T 22
o ID
O
o CM
O
2 O
o
o • o
o
o oo
. o
C9 c c a x: o
o 00
o CD
O
o
O
_o
o
N
o o ±:
"CD J 3
i n Ci» 0)
c
C9
(V) f—
O "CM
r\
H
>
A. I
o
-J
J
O
s^unoo 2DU3ppuio3
17
The same spectrum is also obtained with a Nal(Tl) crystal
for ':hc detection of 356-keV gamma rays and a lead loaded
plastic scintillator (5.1 cm x 5.1 cm) for 81-keV gamma
rays. I'he plastic scintillator is mounted in an aluminium
can of sufficient thickness (- 400 mg/cm ) so as to ahsorh
p-rays. The time spectrum is shown in Pig. 11. The final
statistically computed value of the half-life (Tj ) of the
81-keV state is 6o36 +_ 0.03 nsec.
(c) The half-life of the 77-keV state in ^^^Au ; The 65h
1Q7 activity of Hg decays through electron capture to the
197 excited states in Au. Two 5.1 cm x 5.1 cm lead loaded
plastic scintillators are used for this measurement. The
half-life measurement is done hy observing the coincidences
between 68-keY X-rays and 77-keV gamma rays. Since these
cannot be resolved in the plastic scintillators the combined
peak around 70-keV is gated in both the channels. For
obtaining the lifetime of the 77-keV state the contribution
to the slope from the electronics is subtracted with the
22
help of the prompt spectrum of Na having the same statis
tical accuracy obtained under the same energy settings. The
final computed value for the half-life (Ti) of the excited
state is 1.84 + 0.02 nsec. The lifetime spectrum alongwith
prompt spectrum is given in Fig. 12. The experimental
transition probabilities T (Ml)^„^ and T (E2)^^^ have been Gxp exp
obtained from the observed half-life (Tj ) using the values 2
>
>5'
CM
to
CO
in
c O
d +1
5 o
a o-(>4
- . 0
tn u
u
c CO O 6 +1
CD
: • ^ • '
/
CM
+ + ^ CM in to .V
. .«•
o o rr CM-
o CD
o •CO
V ' . /
/
o. 00
o CD"
O
j , . i .1,1 I M I I I L 1 1 1 ( 1 L _ _ L
o CM
„o
n:
0 CD
0 I f)
0
0 CO
0 i _
C9 N
a 1 -
xi I -
< ^ — » •
u CJ
c
£ 0 £
I—
ti)
y rn
> Of •?
CO
k y^-'
Si •A:
53i
1 Hi
co «s
sj,uno3 aDuappujoo
c D o u tJ o c
C ' o o
10~
10^ =t
10 3i B t t f
IQ
o • » o
o
o
0 o o
o '
00 o •
<? (f
o o
o <h
00° 0
"<p
o o
oo o
• •
— 00
• * *
o
ooo
t/2*
3/2^
Hg(65h)
197,
77 KeV (1.8 4 t0.02)nsL_
0
Au
o •
o
CO o
Lifetime of the 77 KeV 197
X Stole in Au = (1.84 t0.02)n sec-
-4i
Na Promt spectrum
^
• • • o o
o o
oo o
o o o
• • i
. . • •
h40 80 Ch. No.
o o o o
o oo
o o
120 160 J
T AO 10
F * l . 12
10 20 30i Time in nsec (Arbitrary zero)
50
197 LIFETIME SPliXJTRUM OF 77 -k«V STAfE IN "^'Au (HOLLOW DOTS) -22-
ALONG WITH PROMPT TIME SPECTRUM^ OF • N» (SOLID DOTS)
UNDER THK SAME ENERGY GATE SETTINGS.
n
of tt-f. +> & and R in the eqn. (2-1) while the single
particle transition prohabilities T (Ml) and T (E2)
are those which have been calculated with the help of the
17) ' 2 laiown relations ' . The values of mixing ratio (6 ) are those which have "been reported in literature as a result
50-33) of angular correlation of polarisation measurements '.
The values of total internal conversion coefficient (a, ,) tot
32 34-) are taken either from the experimental measurements'^ ^ ^^' 20) or from the extrapolation of Sliv. and_^and's table ' ,
The value of branching ratio (R) is taken as 0.75 in the
133 33) 131 197 case ^^Cs -^ and for - Cs and Au as unity. Before
discussing the results of transition probabilities v/e will
discuss in brief the 1-forbidden Ml transitions.
35)
l-?'orbidden Ml transitions : According to strict
single particle model, the Ml transitions between states
of different angular momenta are forbidden. The calculation
of the transition probability for such 1-forbidden Ml transi
tions requires modified assum.ptions about nuclear v/ave func
tions. The radiative transition probability for a magnetic
dipole radiation '\ (Ml) may be expressed in terms of nuclear 35)
matrix element by the relation ',
r . mc
= 0.419 X lO-"- \'^ tp-Ty sec"- (2-2)
//here E is measured in MeV and I,, is the angular momentum
^ 2 of the initial state. The square of matrix element7'A is
19
"* ,'
Where V \i is the summation of the magnetic moment operators
35") of each nucleon in the nucleus. Arima et al. ' have
derived the simple expressions for the calculations of
matrix olemont of 1-forbidden Ml transitions on the basis
of configurational mixingj and are written as:
Ao For like core (L) transitions i.e. when odd particle
changes its state,
i f ^ (I.) I^ (0) -^ if (0) i f 1 (I^)
The matrix element is given hy:
™ - ^ ( I + l)($T^ +1) J ^ Lgd.^i^^i)]
X (gg - g- ) X Fj (2-4)
where (g^-gn) is 4.585 n.m. for an odd proton nucleus and
-3.826 n.m. for an odd neutron nucleus» The Fj which has
the meaning of the unfavoured factor, takes into account
of the'contribution due to all the possible models of
excitation as given below:
1. P (when I-, , Ip are two different mixing states but
having same orbital angular momenta 1-, )
, V 1(1 I.;I I /(/ E) _ n-^ i21^+l-n^) 1^ (1- +1) J s 1 2 1 1
^LI^ - ^LI^ = (21^+1) (2I2+I) "21"^: 'i y _y
^ g(-V^)i(i-Li2;iiV
(-A.E)
(2-5)
20
n-| , Hp denote the even number of particles in I-, and Ip
mixing states respectively.
The values in the curly "bracket in (2-5) must be
chosen in such a way that the even numbers of nucleons in
the orbits I-, and Ip are like or unlike nucleons with those
in the outer most orbit I.. The value of g is 0.834 for
the effect of proton excitation on the odd neutron transi
tion. The interactions between nucleons are assumed to be
attractive and the attractive force inutile triple state is
assumed to be stronger than the single state of the two
nucleons in the ratio; V = 1.5 ]v j . I is a Slater
integral for a delta function interaction:
(2-6)'
The product of the singlet strength and the integral I has
the form
?gl (I^lg; I^I^) = - C2 F (I^Ig; Iilf)/2A (2-7)
A is the mass of the nucleus and Cp is a constant taken to
be equal to 250 MeV for harmonic oscillator wave function.
P is a non-dimensional constant which does not depend on A
35) but depend's on the shape of the wave function '^.
2. J'TTJ (when the mixing s ta te I-, coincidences with I^)
^11. = ^LII = 2 1 ^ ^ ll^+l ^s^ ^4' ^i^f) (- -h ) (2-8)
21
3. ^TTTT (when the mixing state lo coincidences with I.)
(2I.-1-P) l.(l.-i-l) ^^^2 . . . / 1
(2-9) •
^Liii^ - iiii^ = (2ij_-i)"" ' XIIT|-TT * s^^^'^'^i^f^ V T E .
B* For unlike core (U) transitions i.e. when the even
particle changes its state I?"- (I ) l| (O) -^ I^ (O) I^"^ (I^)
The matrix element is given hy:
TT r Pq il/2 l. (lf+l) 1/2 U = 2i._+l)(2I -H)J ^2(l.+l^+lJ^ (Ss-Sl) U
(2-10)
The contribution due to the first mode of excitation i.e.
P .j is given hy the same formula as the corresponding F-|.-|-,
while the contrihution due to other two modes are calculated
"by the follov/ing expressions,
q - 2 2 •'"f • f"'"-'-
^uii^ = uii^ = 2TpT ' s ^^f' i f "^ipT: ^2-^^^ and
21 +1-P 1^(1 +1 ) 2
UIII^ ~ ^UIII^ ~ 21^-1 21T+I s^ ^^i' ^i^'f^
(2-12)
The above expressions hold good only for the same case when
the angular moments of the initial and final configuration
are I. = 1 . - -J- and I„ = 1^ + -h. However, for the other case
in which 1. = 1 . + •§• and I^ = l.p - •§•, we need only exchange
the role of initial and final states i.e. I^, 1^, q should
be replaced by I., 1., p and vice versa in the above formulae.
All the measured lifetimes are tabulated in Table 1
along with the recent values of half-life reported in
literature. We observe that our measured half-life values
22
fairly agree with the previous measurements except in the
case of 154-ke? level in ' Os. V/e claim our results to
be more accurate compared to the previous measure-
ments^^'^^'^^'^'^?. They ' - ^ selected the K-capture
131 X-rays of Ba in one of the channels which do not feed
151 directly the 154-keV level in Cso Hence in their
measurements they had assumed that there exist no other
lifetimes which would interfere with the lifetime measure
ments of 134-keV state Besides this,the statistical
uncertainties in their measurements seem to be largeo
Our measurement is a direct one, in which the 486-keV
y-ray in the start channel is precisely selected with
the help of a G-e(Li) detector. It directly feeds to
134-keV state and a Nal(Tl) detector is used for the
detection of 154-keY y-raj. Table 2 summarizes the
results of the measurements on the transition probabi
lities and matrix elements of 1-forbidden Ml transitions
131 l^^ 197 in - Cs, Cs and ' Au along with the theoretical
single particle transition probabilities and matrix
elements due to Arima et alo
It is evident from Table 2 that the magnetic
131 dipole transitions from the excited states of Cs,
133 197
Cs and - 'Au are in general retarded by a large factor
because of the 1-forbiddeness. The E2 transitions on the
other hand are enhanced. The enhancement may be expres
sed in terms of an increase in the effective proton charge
25
from the closed shell of protons at 50 and 80. Pechrxer
51) et al. ' from their angular correlation data predicted
151 the 124-keV transition in ^ Cs to be pure E2-transition,
The analysis of the results (Table 2) indicate
that the large retardation factor observed for the
1-forbidden Ml transitions cannot be explained by the
simple single particle picture in which the transition
takes place from one pure state to another pure state.
But the comparison of the experimental matrix elements
with those calculated from Arima's theory shows that such
a picture yield theoretical values in reasonable agree
ment with the experimental values. The configurations
which give the best agreement with the experimental
values have been considered.
24
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26
27
C. THE DECAY SCHEME OF ^^Rh^^
(i) Source preparation and cheiDical separation : The source
was obtained in solid form from the Oak Ridge National Labo
ratory (ORNL), U.S A.. According to the given specifications,
the enriched target material (99.9 ./ ) was enclosed in an
aluminium capsule and was bombarded with the proton beam of qq
the ORNL Cyclotron^ The 16.1 d - Rh activity was produced
by means of a (p,n) reaction.
Chemical separations are carried out to separate the
rhodium activity from the impurities, particularly aluminium.
The method used for it is a:s follows; The target material
is dissolved in aqua regia, then repeatedly evaporated to
dryness after adding a few drops of cone. HCl each time
and then final residue is dissolved in distilled water.
Milligram quantities of Rh in the form of chloride solotion
is added and rhodium activity is precipitated by adding
aluminium foils to the solution. The ppt. is centrifuged
and washed a fevv' times with distilled v-/ater»
All the measurements reported here are carried out
with the chemically separated source.
(ii) Single spectra, Q-amma ray energies and relative
intensities : The single spectra are recorded in different
energy regions with the help of a Ge(Li) detector of deple-
tion depth 7 mm with sensitive area 6 cm (given in Figs.
13-16). The energy resolution (FWHM) for 7 mm detector
28
was 2.8keV. The dynode pulse is amplified with the linear
amplifier ORTEC model 410. All the singles spectra are
recorded with the help of Packard 400-Channels Analyser.
Figo 13 gives the y-rajs observed in the energy range of
0-442 keV. We have found no evidence for the existence
of the 119.4-keV Y"-2?ay which was reported hy Moss and
21) McDanicls . The spectra recorded with the impurity
source showed the existence of a well defined photopeak
at 119.4 keV. This shows that the 119.4-keV y-T&j does
not "belong to the decay of Rh. Tne rest of the y-rays
in this region, hov/ever, agree well with the earlier work
21) of Moss and McDaniels . The y-raj spectrum in the energy
range 440-1200 keY is given in Fig. 14. In addition to
21)
the y- ays reported earlier ^ we have observed an addi
tional Y~ a-y at an energy of 910.8-keY. This is found to
decay with the 16.1 d half-life. The peak at 778.1-keV QQ
does not belong to the decay of 16.1 d - Rh. In Pig. 15
we have plotted the y-raj spectrum in the energy range
1200-1750-keV. Pig. 16 gives the y-Tsy spectrum in the
high-energy region (>1960-keV). The y-^ays observed by
us in the singles essentially confirm the results reported
by Moss and McDaniels except for minor variations. The - , . . . . . . . 241. 57n 203TT 22„
energy calibration is done using Am, Co, Hg, Na,
Cs, Mn, Co and Y standard sources, providing y-rays
with energies in the region 60-1850 keV. The energies of
E z "5 c c a D
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Channal Number
F i a . 16 GAMMA-RAY SINGLES SPIKIRUM Of ^%h IN THE
ENERGY REGION 17^9-2059 keV OBTAINED WITH
A G«(Li) DETECTOR (LIVETIMi iSCft) MIN) .
29
the Y-3 ays observed by us in the 16.1 d decay of - Rh
are listed .in Table 3. The energies of the y-vfi.js a.
obtained from our energy clibration are very close to
the values reported by Moss and McDaniels. Therefore,
we have adopted their energy values except in the case 99 of the 1295-keV level in Ru. The starred peaks in
99 Figs. 13-16 do not belong to the 16.1 d decay of Rh;
the origin of these lines has not been explicitly
determinedo
The full-energy peak efficiency of the detector
used for recording the singles spectra is experimentally
determined ,using standard sources giving energies in the
range of interest, at a fixed geometry. The same geometry
is maintained throughout the single's studies. The area qq
under the photo-peaks of the y- rays of - Rh are determined
after subtracting the background and are used for the
evaluation of the relative intensities. The relative
intensities obtained by us are listed in Table 3 along
21) v/ith the values reported by Moss and McDaniels ^ and
Antoneva et al. . The intensities reported by us are
relative y-ray and no attempt are made to correct data
for internal conversion.
(iii) Goincldence Spectra
(a) Ge(Li)-G-e(Ll) slow-fast coincidences : Two Ge(Li)
detectors of depletion depths 7 mm and 5 mm with sensitive
30
2 areas of 6 cm each a re used for the slow-fast coincidence
s tud ies . The energy reso lu t ion (FWHM) for the 7 mm and
5 mm de tec tors were 2.8-keV and 3.5-keV respec t ive ly
1'57 for the 662-keV y-Tajs of CSo The "block diagram of
the associated e lec t ron ics i s given in Pig. 17• l he
resolving time ( 2 T ) of the f a s t coincidence c i r c u i t used
in the Ge(Ii)-Ge(Li) fas t -s low coincidence spectrom-eter
was 40 nsec while that of the slow coincidence c i r c u i t
was 2 (isec.
The coincidence spectra are recorded with gates
accepting the peaks at energies 322„4- and 353«0-keV.
The widths of the gate settings used are m.ainly to
include the photo-peaks of the y-Tscys of interest.. The
results are summarized in Table 4. The coincidence
spectruffx obtained with the gate at 322.4-keV is shown
in Pig. 18. The peaks observed in Pig» 18 at 175.2-, 322.4-
and 353.0-keV have probably resulted from coincidence with
the compton part of the annihilation radiation present
under the gate setting of 322.4-keV. The 295.7-keV y-ray
observed in coincidence with 322.4-keV y-^ay is due to a
transition leading from the level at 618.0-keV going to
the level at 322.4-keV. The peak at 511-keV is due to
the coincidences between the 322.4-keV y-va.j and the
511-key annihilation radiation feeding the level at
322o4-keV. No evidence for the existence of the 119.4
keV y-raj reported by Moss and McDaniels is seen in Pig.18.
5 i^ l < </) X > j O -J 1 < ' O Z = o < , <
UJ
o
^^
o
y o y n H
?»: H
-• o
( Sr O
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J a
t^
CI
0*119
0-Gse • .
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31
The y-Vd,j which are observed in coincidence with
353.0-keV y-raj are shown, in Pig. 19.' The'SVidefte^'lor•-
the existence of coincidences between 553.0-keV y-xduj
and 89.4--, 175.6-, 941.5-keV y-rays is clearly seen. The
peak at 511-keV is due to the annihilation radiation. The
broad hump around 340-keV is due to the compton edge of
the 511-keV radiation.
(b) NaT(Tl)-Nal(Tl) sum-coincidence m-easurements : The
sum-coincidence spectrometer consisted of two 5.1 cm x
5.1 cm Nal(Tl) scintillators coupled to 56 AVP photo-
multipliers. The energy resolution (FWHM) for these two
detectors was 9-10% for the 662-keV y-rays of "'' ' Cs. The
linear signals from the two detectors are summed and
operated in a slow-fast coincidence modes. The resol
ving time (2T:) of the fast coincidence circuit was 30 nsec
coincidence spectra are reported by fixing the gates at
energies of 575-, 618-, 734-, 850-, 897-, 941-, 1000- and
1295-keV. The sum-coincidence experiments are carried out
for establishing the existence of the cascade transitions.
99 99
The 16.1 d Rh decays to the excited levels in Ru
through Ec and p decay. The intense sum-coincidence
peaks at 511-keV that are obtained in the spectra are
mostly due to the coincidence*between the intense 511-
keV annihilation radiation feeding the levels and the
compton part of the following y-rays. The results are
summarized in Table 5.
o o CO
6)
E 3 2
"5 c c a x: u
g
H
H O « H o o >
CO
s i
f - <<ll
I O f o H S Qi
S H
Z H
en >H
< OS
1
V ^
s p ^
' * * < '
S • *
g w > a in S i i <m *2 ««
ii*
0* to
o
S (M
o o ^ s^unoo aDuappupo 2 c i
32
(iv) Results and discussion for establishing the decay
Bchome of ^Rh : The level scheme suggested "by Moss and
MdDaniels with some modifications which are warranted by
our experimental results is reproduced in Fig, 20. Our
investigations essentially support the decay scheme sug
gested by Moss and McDaniels except for the following
results:
(a) Our coincidence data gave no evidence for the
presence of a 119.4-keV y- ray. The fact that we
have observed an intense 119.4-keV y-Ta.j in the
singles spectrum of the chemically separated
impurity led.us to conclude that the 119.4-keV QQ
y-ray does not belong to the decay of 16.1 d Rh.
(b) The existence of a 232-keV transition from the
322- to 89-keV level was reported by Moss and
McDaniels. Though we did observe a small peak at
232-keV in the Ge(Li)-Ge(Li) slow-fast coincidence
spectrum with the gate at 89.4-keV, we cannot
explain the sum-coincidence spectra obtained with
the sum-coincidence gate at 850-ke7 unless we keep
the 232-keV transition between the 850- and 618-keV
levels,
(c) Moss and McDaniels suggested that the 264-keV tran
sition is between the 1662-and 897-keV levels. Our
sum-coincidence data warrants that it should be
vQ n o» CO O CO
04 £ ! 2 2 2 £
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in
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1662
.1532.9 1505.1
1382.9
1295.2
•IOOO,2
897 .
8SO.
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618 575
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89 .4
• ? t • • • • • * t » • • • • o
99
FIG. 20 LEVW. SCHEME OF ^^Ru . DASHED LINES SHOWN ARE THE NEW TOANSITIONS.
33
between 1381- and 618-keV levels. However, our
results do not rule out the possibility that there
could be one more 764-keV transition between 1662-
and 897-keV levels,
(d) The sum-coincidence spectrum with the gate at
1000-keV energy gave evidence for a new transition
of 911-keV energy. This transition is probably
from the 1000- to 89-keV level;;—A y-raj with
911-keV energy was also observed in the singles
spectra recorded with Ge(Li) spectrometer.
(e) The sum-coincidence spectrum recorded with the
gate setting at 1295-keV energy gave evidence for
a new transition of 295-keT energy from 1295- to
1000-keV level.
TABLE 3
Gamma-rays observed in the decay of 16.1 d
99 Rii and t h e i r r e l a t i v e i n t e n s i t i e s
34
Energy (E ) in keV ''
89.36
'119 .4
175.2
232.4
295.7
322.4
553.0
442.8
486,5
Annihi la t ion
527.7
575.2
618.0
734.2
763.9
306.6
850.3
897.2
910.8
941.5
Relative y
Moss et a l ,
76
0.13
5.8 ,
1.3
2 .1
16.5
81.3
4.3
1.5
rad ia t ion
100
0.6
10.0
0.8
1.0
3.5
0.6
1.7
-
3.8
-ray
21) •
I n t e n s i t i e s ( I )
Anton'eva e t a l . '
100 + 10
< 2
4.5 f - i . O
1.5 + 0.5
3.5 + 0.5
18 + 2
100 + 10
4.5 + 0 .5
1.5 + 0.5
100
0.8 + 0 .2
11 + 1
0.9 + 0.2
-
3.6 + 0 .5
41 1.7 + 0.2
-
3.3 + 0.5
Present
56.3
-
3.8
0.72
2.6
9 .1
78.3
5.4
0.89
100
0.47
11.9
0.61
0.88
3.5
1.1
2 .1
0.13
3.4
Table 3 (Contd.)
35
Energy (E ) in keV '
1000.2
1061.2
1089.4
1208.3
1295.2
1323.9
1382.9
1442.1
1484.3
1505.1
1532.9
1572.4
1618.0
1662.1
1749.1
1970.3
2058.6
Relative y-vaj
21) Moss et al. ^
1.7
0.4
0.8
0.4
0.9
0.4
0.4
0.2
0.4
0.2
1.4
0.58
0.6
0.15
0.15
0.4
0.08
intensities
Antoneva ei
2.0 + 0.
0.6 + 0.
41
4 0.8
1.0 ± 0.
4 0.5
%0.4
<50.4
<0.4
<0.4
1.9 + 0.
0.7 + 0.
^< 0.6
< 0.4
< 0.4
< 0.4
-
<S^ , : aT:«'
2
2
3
4
2
p-r*p op-n-f X i- \^ iD\^li.\J
2.0
0.55
1.0
0.66
0.72
0.66
0.29
0.34
0.14
0.1
1.3
1.3
0.9
0.23
0.6
0.21
0.43
21 The values reported earlier by Moss and McLaniels ' and Antoneva et al, ' are also given.
•36
TABLE 4
Summary of the Ge(Li)-Ge(Li) fast-slow
coincidence measurements
y-ray Energy E (keV) Y~ a-y i^ coincidence with E
322.4 295.7
353.0 89.4,175.2, 941.5
37
TABLE 5.
Summary of the Nal(Tl)-NaI(Tl)
sum-coincidence measurements
Sum-coincidence gate energy (keV) Cascades observed
575 5 7 5 ^ ^ 89 0
618 (a) 618 ^ 89 0
(b) 618 ^ ^ 522 ^ 0
(c) 618 i ^ 443 ^ 0
734 734 ^^^0
'850 (a) 850 - ^ ^ 618 ^ ^ 0
(b) 850 ^ 0
897 897 ^ ^ 89 0
941 941 ^ ^ ^ 175
1000 1000 ii^ 89 ^ 0
1295 (a) 1295 ^ ^ 1000 i ^ ^ 0
(b) 1383 ^ ^ 443 ^ 89
(c) 1383 ^ ^ 618 ^ 89
CHAPTER III
MAGNETIC MOMENT MEASUREMENTS
Recently the techniques of measuring magnetic dipole
moments of nuclear excited states with short lifetimes
have developed to the extent where they can provide,a
significant addition to our knowledge about the magnetic
properties of nuclei. Already the experimental work done
has proved to he of major significance in testing the
well developed theories, and one can no doubt expect
that the additional results in other areas now being
obtained will also play a significant role in under
standing other aspects of nuclear structure and nuclear
magnetism. The magnetic moment measurements are carried
out with the help of the time differential (y-y) perturbed
angular correlation technique (TDPAC). This technique
yields directly the interaction strength independent of
any knowledge of the nuclear lifetime of the excited
state. This method also gives information on the environ
mental conditions of the source, i.e. the time dependent
perturbation effects, relaxation processes, etc. The dif-
ferential method has an upper limit, it can also be used
if the resolving time of the coincidence arrangement is
considerably smaller than the lifetime of the excited
state under consideration. Since the number of oscil
lations obtained in the measurements with TDPAC technique
38
59-
is quite large, therefore, the Larmor frequency can be
determined very accurately using Fourier transformation
technique. Hence the''value of the magnetic moment obtained
with this method will be more accurate as compared to other
techniques.
The angular correlation and Mbssbauer methods of
determining electromagnetic moment of excited nuclear
states are based on the static interaction between
external field and the nuclear moments. "ffinTB, these
methods give results which are independent of any assump
tion concerning the origin of these moments and are,
therefore, classified as model-independent or spectro
scopic methods. It is possible to establish relationships
between the static electromagnetic moments and dynamical
properties of nuclear states v;ith some degree of confidence.
It is thus feasible to obtain reasonably reliable values
of the electromagnetic moments of excited states by observing
the properties of transitions between nuclear states. The
results on nuclear moments obtained in this manner are
obviously model dependent. The magnetic properties of
deformed nuclei (in this thesis we are presenting a case
of Re which belongs to the deformed region) are of
interest both liecause they represent another group of
nuclei whose structure is thought to be reasonably well
understood, and also because there is a considerable amount •
of experimental data available.
40
The measurements on lifetimes together with the
measurements on magnetic moments should he very valuable
for the understanding of the structure of the particular
nuclear excited level.
A. MAGNETIC MOMENT OF 206-lceV STATS IN " j' Re n- ' ^ :# ^
1. Source preparation : The g factor measurement of
the 206-key level is carried out with the source in the
solution form as sodium tungstate. The source is procured
from the Department of Atomic Energy, Bomhay (India).
2, Experimental set-up i A smaller, C-frame iron core
electrom.agnet, capable of producing a maximum field of
7 kOe over a 1 cm gap with a 1 cm diameter of pole piece,
is used. The stability of the magnetic field is 1 7 for
a typical run of 7 days. The field of the magnet is
measured either by a-Hall probe (Bell model 240) or by a
rotating coil gaussmeter (New Rochelle, model PM). These
instruments arc calibrated using proton resonance. Thus,
errors in fields are due principally to inhomogeneities
and drift.
There are two basic types of shielding material -
medium permeability (NETIC) material for medium attenuation
(which will withstand high magnetic fields) and high
permeability (Co-NETIC) or high attenuation shielding
material (which will saturate at lower fields). Multiple
41
layers of Co-netic and Netic material, separated by non
magnetic spacers, are used for shielding the photomulti-
plier tubes. For maximum shielding of the phot omultipliers
these layers of Co-netic and Netic material are extended
well beyond the face of the photomultiplier tubes. The
effect of the field is checked in single y-^ay spectra
and prompt time spectra as well.
In the magnetic moment measuremen±£_the two detectors
are kept at an angle of 135° to each other in a plane
perpendicular to the external polarizing field (as shown
in Fig. 21).
3. Decay scheme and gamma rays : In Fig. 22 the decay
scheme of W pertinent to our studies is given . The
(480-72) keV gamma cascade is used for the magnetic moment
1 Pii micasurement of the 72-keV state in Re.
4. Magnetic moment m^easurement of 206-keV state ; Two
5.1 cm X 5.1 cm Kal(Tl) scintillation detectors coupled
to 56 AVP photoff/dltipliers are used for the detection of
480-72 keV cascade. The fast pulses from the photom.ultiplier
tube in the stop channel are amplified using EG&LG- 1 nsec DC
amplifier. The outputs of the ORTEC fast discriminators
are fed into a model 437 ORTEC time-to-pulse height converter.
The source of appropriate strength is put in very smiall bulb
provided at one end of the pyrex glass capillary tube. This
source is placed at the centre of the pole pieces of the
J,
L,
T. in mec.
COUNTER
STOP CHANNEL
COUNTER I
START CHANNEL
MAGNET
F I G . 21 ABRANaEMl!3<JT OF MAGNET AND DETECTORS
u
C
CM
U
c in ir» tr)
tn Q.
II JN 'CM
to m to o
en en II
> ^
* o o H °o i: <r C
o •
o N . o
;
-;;
c 2 f*
(*>—• r»^^
*—N
00 > "* - 6 to ^ CM * - '
O X
ac GO
x: CO CM
M
s bi
CO
42
magnet. The experiment is carried out at 7«00 KOe and a
iDackard 400 channel analyzer is used tc record the time
spectra. The ratio,
p^ + '\ - C!(9,t,H- -) - C(6,t,H-v) /_ \ ^ "'' - c(e,t;Hi) + 0(9,t,Hi) ^5-1)
3 exp (-A t) Ag Sin (2c^t) ^^^
" 2 + exp (->.2t; t Ag ' H = 0
is obtained for each time channel.
Here G(9,t,H4/) and C(9,t,Ht) are coincidence c'ounts in
the same time channel for field down and field up respec-
tively and A - relaxation constant, u. ^ = -—.- is
the larmor frequency of a nucleus in the magnetic field
I-I. The time spectrum with field on is given in Pig. 23.
Pig. 24 shows the measured expression R as a function of
52) time t . The s i n e , cosine and a b s o l u t e t r ans fo rms ' defined by
A (c...) =. "> R( t ) Sin (27itc^t)
B (L5) - ' >R( t ) Cos (27lu:^t)
F M - WWnrWW) (3-2) a re p l o t t e d in F i g . 25 .
The va lue of the Larmor frequency i s ob ta ined from the
a b s o l u t e t ransform P(co) which i s independent of p h a s e .
The va lue of the double Larmor frequency i s = 1 2 , 1 + 0.2
MHz. The measured Larmor frequency i s r e l a t e d through
the r e l a t i o n ,
.o1
^ in-•^ 10 D O U
u c
u
#
10 b
' • • • • • • • • w t ^
' • ^ • • . . ^ . . M ^ ^ ^ • • • •^ • •MM.!^
••••*«^«> • • ^ - — - - ^ A . , ,-f-H,. ^ • M M M ^ , ,
Source
^ :
• • • •*•• • •%••( •••••^••^.••.••, •s* •%•.•«,
••^•^H.,„
10 20 AO _ L _
Ch. No. 60 80 _L ±
too J
120 J
uo _I
16Qi
100 200 300 AOO 500 600 700 800 900
Time in nscc(arbitrary zero)
FIGj. 23 TIME DIFFERENTIAL PERTURBED ANGULAR CORRELATION SPECTRA OF 187 Re IN AN EXTERNAI. MAGNETIC FIELD OF 7 KOe.
o o H ft.
i
OJ' s
o o LfX
o o St
i
^
o o CO
c - « - •
9
5 z H
•
00 >•
<
e §. 0 . CO
o <
s s
Q
O
5i
« tt O > «
« I
^ CM s:: o ?:; $^ $5 • • • o o o o o o o
+ + • o ' I I rr
T7-TT
^
• • f
o . / f t :
X
/ •• •,
•••
•• •
c S d c J o o o d d o •f + I I I i
(/ jDJ)|qjv)apni!lduLJV
CM CM
O CM
00
CD * "
;£
CM
O ' ^
CO
CO
<
N X 2 c
3
§
g 9
PC4
•P
&< o «5
2 o ^
^
e H
8 p
9 O
t -
fa o Q sJ H fo o H
<3
2 9i
CM
^
6 H E>A
R
43
^-L = - iS ^5-3)
Where (j. is the nuclear magneton and H , is the externally
applied magnetic field. After applying the diamagnetic
correction, the final measured value for g-factor is
= + 1.12 + 0„03o Since the spin of the 206-keV level
is 9/2 ^ and the value of the magnetic moment_4i_of the
state is = (+5.04 + O.I4) nm.
B. MAGNETIC MOMENT OF 68-keV STATE LN ' " Sc
1„ Source preparation : The Ti source is obtained in
solution form as chloride from Nuclear Science and Engineerirg
Corporation (NSEG), USA and is used as such for carrying out
the experiment for the magnetic moment measurement.
2. Decay scheme and gamma rays : In Eig. 26 the decay
44 12) scheme of Ti pertinent to our studies is given . The (72-68)-keY gammia cascade is used to carry out the magnetic
44 m.oment experiment of 68-keV state in Sc.
3. , Magnetic moment measurement of 68-keV state : Two
5ol cm X 5.1 cm Nal(Tl) scintillators coupled to 56 AVP
photomultiplier tubes are used for the detection of (78-
68)-keV cascade. The fast pulses from the photomultipliers
are amplified using EG tG- 1 nsec DC amplifiers. The outputs
are processed through the ORTEC fast discriminators and
time-to-pulse height converter. The source of proper
strength is put in a very small bulb provided at one end
o ^
flO II t^ J=
N — '
rf"-^
^ o w ' ^ o ( O II
'-^ > i::! w o 3<^ ' I T
II ® u to _ S f c ^
fc
£
r)
sr
.8 ^.
C«J
^ o U) II £S,
u eg
c in tn M
«-C4
^ » -
13
44
of the pyrex glass capillary tute. This source is placed
at the centre of the pole pieces of the magnet. This
experiment is also carried out at 7.00 KOe, applied per
pendicular to the plcine of the detectors, and a Packard
400 charjiel analyzer is used to record the data. The
application of magnetic field produces oscillations on
the time spectrum with the sign of the moduilation depending
upon the direction of the applied field (see Fig. 27)__. With
the field up and field down the spectra have modulations
of opposite phase. The ratio,
^ ^ ^ ~ G (9,t,H,0 + C (9,t,Hf)
3A2 Sin 2«^t
where 0 (9,t,Hi) and 0 (9,t,Ht) have the usual meaning
as explained earlier since the intermediate state has a
12)
spin 1, therefore, the A^ term, is zero ' . Fig. 28 shows
the plot of the measured expression R as a function of
time t. No attenuation of R is seen upto some [isec.
Using the expressions given in relation (3-2), the Fourier
transforms of the data are plotted in Fig. 29. The Larmor
frequency is obtained from the absolute transform F (-o)
which is independent of phase (^). Thus the value of the
double Larmor frequency is = 3.65 + 0.05 MHz. Using the
relation (3-3) the value of the g-factor is calculated.
After applying diamagnetic correction the value obtained
a u
SB
o a
< H
OS p
•J - X
S
<? 0 H «
* J-
ft i
H (3
o
^
' O O o R fa
1 1 1 1 1 r
' ' I > t * I ' t t
8 S 5 9 o S 8 o o o o o o + • * ^ I I I
cr
•
o e . Ck O
Q
si
m o > w
4*
« O
00
••J '•. T — r - * T
3 CD
:'? •••••• / • - . „ ,
.1 , • • ^ ^
• • • • i
••. \ .••
J L X iK 1 L I , I
CD
ID
N CD «^
: 2
<D
CO
« • • . • ^ • • . o o o o o o o o o • • 4 • • I I I
•<r: If) o o
I I
o
(AJDijiqJV) apn^iiduiv
4>
m
9 Wl O 3; ui
a M
S h
45
f o r the g - f a c t o r i s = + 0.345 + 0 . 0 0 ? . Since the sp in IP)
of the oS-keV s t a t e to "be 1 % the magnetic moment
(J, of t he 68-keV s t a t e i s (+ 0.345 + OoOO?) nm.
C RESULTS AND DrsCUSSION
Our measured r e s u l t s a re t a b u l a t e d in Tahle 6 along
wi th the o the r a v a i l a b l e exper imenta l v a l u e s i n the l i t e r a
t u r e f o r comparison. The 206-keV exc i t ed s t a t e i n odd A
187 53)
deform.ed nucleous Re has been identified ' as a
Nilsson state- ' ' with the q_uantum numbers 9/2" (514+)
i.e. [I = I , K =-Ci.= |-, N=5, 1^2=1,A=4, and ^ =l].
Using the Differential perturbed angular correlation method Koicki et al. ' , Walter et al. ^ and Nigam and
51) Bhattacharya ^ obtained the values for g are 1.046 + 0.03,
1.11 + 0.03 and 1.04 + 0.04 respectively. Koicki et al.
made their measurement at two different fields 1720 and 5020
Oe. respectively while Walter et al. and Nigam-Bhattacharya
used external fields of 3150 and 3100 + 30 Oe. respectively.
In the present measurement, however, the external magnetic
field is 7000 + 70 Oe. Our measured g-factor is in fair
agreement with the previous measurem.onts (see Table 6).
Z • If rotational g-factor is taken as g-^ = - ^ =
0.407 and free proton spin g-factor g„ = 5.585,then using
the Nilsson's formula - a value of g = 1.32 is obtained,
which is considerably larger than the experimentally
measured g value. However, as suggested by De Boer and
46
55)
Rogers ' if the free nucleon spin g-factor is taken to
"be 0.6 g^, then a value of g = 1.08 is obtained and it
is in fair agreement with the experimentally determined
value of g. The sign of the g-factor is also determined
from the sign of the anisotropy and the sign of the first
oscillation (when the modulated time spectrum is carefully
extrapolated to zero time). From Table 6 we observe that our measured g-factor
A A
value for 68-keV s t a t e in Sc a lso agrees well with the
previously reported values for go If the l eve l s of Sc
are a l l derived from the same configuration for the
neutrons and protons , the magnetic moments of the l e v e l s
are given by:
. I-, ( 1+2) - I (I +1) V- = {-^1) (g^+gg) + (gi-g2^ 2 (I + 1)
where I is the total angular mom.entum, I-, and I^ are the
angular m.omenta and g-, and gp are the g-factors for the
proton and neutron groups respectively. If the angular
i< 4 momenta of the proton and neutron groups in '' Sc are
taken 7/2 ', the g-factors for all the energy levels
will be identical and will be given by g = -I (g-i+gp)-
Using Schmidt values for the odd neutron and odd proton,
a g-factor of + 0.55 is obtained. If the configurations
for a proton and a neutron groups are assumed to be
1 '5 " 7/2 7/2 ^^ " 7/2 7/2 respectively, a g-factor of
47
+ 0.50 is obtained. These values of g-factor do not
agree with the experimentally measured g-factor values
for various levels in So. This clearly indicates that
this simple model is not appropriate for Sc« The absence
of any definite knowledge of the configuration of 68-keV
44 state in Sc is an hindcrance in interpreting the g-factor
of this state.
It is interesting to note in Figs. 24 and 28 that f
no attenuation of the function R or of the differential
1 R7
angular correlation in a period of 0.7 (isec (in Re
measurement) and 0.4 jisec (in ' Sc measurement) is detected.
Nevertheless, for sources in liquid form, this attenuation
must always be present (even though too small to detect
during the nuclear lifetime)due to the interaction between
the nuclear quadrupole moment and the fluctuating electric
field gradients produced by neighbouring atoms. From
Figs. 24 and 28 a limit may be set for the exponential
attenuation factor or relaxation constant X > 4 x 10
sec" andX'^ 2 y: 10 sec" respectively for 'Re and be .
The Fourier transform of the R(t) function is
essentially the NMR line having a Lorentzian shape. In
Azi the case of Sc magnetic moment measurement, the
observed width (F¥HM)--9 x 10 eV is about twice the
48
natural width = 4.4 x 10 - eV. In tlie 'Re magnetic
moment measurement the observed width (PWHM)~15 x 10 _Q
eV compared to the natura,! width of ~ 1.25 x 10 eV.
The large observed width may probably be due to the
quadrupole interactions etc.
49
TABLE 6
Comparison of the p r e s e n t magnetic moment measurements
wi th a v a i l a b l e pub l i shed v a l u e s
M,^-i^ „ Level Ex te rna l f i e l d .P 4. D -P--Nucleus jc^g^) app l i ed (KOo) g - f a c t o r References
^^'^Re 206 1.72 1.046+0.03 47
5.02
3.15 1.11 + 0.03 46
3.10 + 0.03 1.04 + 0.04 51
7.00 + 0.07 +1.12 j^ 0 .03 P r e s e n t mcasure-and
p,= +5.04+0.14 nm ment
^^Sc 68 5.560 + 0.011 +0.35 + 0.02 11
2.648 + 0.005
7.550 + 0.075 +0.342 + 0.006 12
7.00 + 0.07 +0.345 + 0.007 Present
"" measure-and
^= +0.345+0.007 nm ment
CHAPTER lY
T f P E R P I J J E P I E L P MEASURE^IEKTS
A iri a ORIGIN OF THE HYPERPINE PIELDS, HYPERPINE PIELP MODELS
AM) SY5TEMTIGS OP HYPERPIHE FIELDS
Hyperfine field determinations are often used as a
tool in the study of the magnetisui and magnetic matericils.
Hyperfine fields at impurities in ferromagnets can iDe
studied with respect to (a) variation with atomic numher
A (or'Z) for different im.purities in the same host ,
(h) variation with tem.perature , and (c) changes with
the impurity content '. The first case will give infor
mation on spin polarization, transfer and overlap effects.
Prom (b) one can find out a possihle local m.ome2it behaviour,
whereas case (c) is used to study neighbour effects for
higher concentrations. Most of the experiments reported
in the literature have been carried out in iron and nickel
hosts. The interpretations of the measurements is then
relatively simple, since impurity atoms usually occupy
regular cubic sites. The general trends in the variation
of the magnetic hyperfine fields with impurity A (or Z)
are reasonably understood. The hyperfine fields are
discussed in terms of a semiempirical model by Shirley
et al. . In the Daniel-Friedel theory , we consider
the scattering of the electrons around the impurity which
50
51
results in a net spin polarization at the nucleus. This
model was further extended "by Campbell ^.
V/hen we measure the hyperfine fields on dilute
impurities we essentially sample the m.agnetization on the
impurity nuclei alone. These measurements need not strictly
confirm to the bulk magnetization measurements like suscep
tibility etc. In fact, experimental measurements on the
temperature variations of the hyperfirte fields have clearly
showed these ef f ects " '.
The hyperfine field measurements as a function of
temperature on many dilute impurity atoms showed that the
magnetization at the impurity does not follow the host /'p^
magnetization curve. As suggested by Jaccarino ct al. '
in those cases there is a possibility for a localized
moment around the impurity atom. Similar experimental
studies are made by Rosenblum et al. ' and Pramila et al. '
also confirm the above conclusions. However, the hyperfine
fields as a function of temperature are found to follow the
bulk magnetization properties of the host ' '.
Till 1967, the most precise values have, in general,
been obtained by spin-echo magnetic resonance exploited
extensively by Eontani and Itoh ', though it should be
em.phasized that these measurements are probably on solutes
in domain.walls while other methods sample the entire bulk
material. This difference may account for the discrepancies
52
in H, r. reported from different techniques. The time-
differential perturbed angular correlation (TDPAC)
technique is a powerful tool for precision hyperfine
field measurements in ferromagnetic lattices. The TDPAC
technique has two important advantages OYBV other methods
such as nuclear magnetic resonance; the measurements can
be performed (i) at lov/ impurity ccricentrations, and (ii)
over a wide temperature range.
(i) Origin of hyperfine fields on impurities in ferromagnets 44
Before we start discussion on our measurements on Sc and T on
Re, we give a discussion of the observed solute hyperfine
fields in iron, cobalt and nickel latticeSo Taken individually
the solute fields are of little importance but their variation
with host magnetization and particularly v/ith solute atomic
number can lead to an understanding of their origins. The
origin of hyperfine interactions in ferromagnets is still
not well understood. However, further theoretical work on
the manybody problem may better our understanding of these
interactions. Here we shall try to define the 'hyperfine
field' and shall elaborate the mechanisms that can give
rise to these fields in ferromagnets. These mechanisms can
then be related to the electronic configurations of solute
and the solvent atoms.
In a ferromagnet the effective field experienced by
a nucleus may be defined as,
53.
H. „„ = H, J, + H ( i n a domain w a l l ) e f f h f jj ^
or
H ^^ = H, n + H-p + H - DM ( i n a domain) e i f Txi L 0 ^ •
Here H, ^ and H represent the hyperfine f i e ld and the
applied f i e l d , DM i s the demagnetizing f i e ld and H-j- i s
the Lorentz f ie ld (4n;/3 M) plus the f i e l d a r i s ing from . . - . .-—V
dipoles in Lorentz cavity. Hi and H-j- are found, in
general parallel (or antiparallel) even in domain walls.
In order to understand that hov/ the hyperfine fields in
57)
ferromagnetic metals a r i s e from hfs ; Shirley et a l , '
defined a Hamiltonian which i s appl icable to both a
ferromagnetic host metal and so lu te ,
= ^cf "2 ^-^x ' ^ ^ ^ ' S - YiHe -"^
+ 2 p Yj v.-"^- ^'1*1 + [?^L(L+l)-lc] "S-I
~ I I [(L.S)(L-I) + (L.I)(L^)] ^ J
In using and explaining this Hamiltonian we think of a
particular solute atom characterized by the quantum
numbers L, S, and I acted upon by all the other impurity
atoms in the lattice characterized by the crystal field
interaction (V ) ,• the exchange field (H ), and the
conduction electron polarisation (K ). The XI'S term
is the electronic spin-orbit interaction and the terms 67) in curly brackets represent the magnetic hfs interaction '
54
in operator equivalent notation . The L'l term represents
the interaction of the iilectronic orhital angular momentum with
the nuclear spin, the ."kS'I term, the polarisation and the
three terms in - the interaction of the electronic spin
with the nuclear spin. Here p is the Bchr magneton, and
<'r > is evaluated for open electronic shell (if any) of
72) _
the solutec The first three terms are the largest and must
he evaluated first to give the zero order wave functions.
Except for rare earth solutes j the /\ 1 • S is smaller than
the other two parts. The fourth term descrihes condactioh-
electron polarization, H . It is approximately proportional
to the lattice magnetization.
For the situation in which the spin - orhit coupling
is smaller than both the crystal field and the exchange
field, we can assume that the electronic orhital angular
m.om.entum is quenched by the crystal field. For cubic lat
tices the Hamiltonian can be written as a sum of two parts,
where :,'\' -, = H ^, which determines the zero order v/ave 1 cf'
function and
Pi-^ = 2 p~Hg^ .^ - Yj H -"! - 2p Yi (^'^^ ^ "S-l
= 2 P H e x - S - Y^-tif
55
In the above equation the second term is in the form of
magnetic field interacting v/ith magnetic dipole. The
exchange term is the largest among the other terms
involved in hL. If it is considered that this is evaluated
first to give <'Sr7) , the expression for H, „ can he written
as scalar
\f = He + 2 < S^) H^
where H. = p k <r ; , the core polarization hyperfine
field arising from a single unpaired d-electrons. Accor-
69) ding "CO Shirley and tfestenbarger ' H = p >H where H
is the free atomic hyperfine field arising from atom in
ns state. This substitution is perm-issiblc because it
is expected that conduction band s-wave states resemble
the atomic functions near the nucleus. Thus the final
expression for the hyperfine field is''''',
hf ^ ns ^ S d
The first term on the right hand side is the conduction
electron polarization (CEP) contribution and the second
is the core polarization (CP) contribution, which arises
only in cases v/here there are unpaired magnetic electrons
(i.eo, open p,d shells). This equation should be valid
for all impurities in ferromagnets except for those with
incomplete f-subshells, because we assumed
56
£Q study the relative importance of the mechanisms
that produce hyperfine fields at solutes in ferromagnets,
it is useful to survey the fields reported in iron, cobalt,
79)
and nickel latcices. The earlier observation -^ that
solute fields vary smoothly with atomic nuEQber has been
very nicely confirmed for all the three host lattices. 71) A-i uptodate such compilation ' is displayed for all the
three lattices ¥e_, Co and M in Pigs. 30,31 and 32 respec
tively. In the case of iron, cobalt, and nickel the
electrons involved in this exchange interaction are the
unpaired d-electrons, A reasonably good approximation
can be made that these d-electrons are localized on
individual atoms and the spontaneous magnetisation can
be considered to arise from the summation of all the
atomic moments. It is the same d-electrons which are
also responsible for the large magnetic hyperfine fields
at the nuclei of atoms in ferromagnets. In cubic ferro-
magnets these fields arise principally from the Fermi
contact interaction of s-electrons which have been
polarized by the d-electrons. The mechanism by which
this polarization results is not quantitatively under
stood as yet, but the theoretical treatment given by
Freeman and Watson ' ' is encouraging. The exchange
interaction arises from purely electrostatic forces
as a result of the Pauli exclusion principle and is
$.8
w r
00 o o O O o
1 <J>
o o
1 to O o
^
te 8
a
8 4 ^
SJ a
S-" C/1
8-
en Q.
©^ 4^
CD. O
O O
en
•
g
m
I
o o ^^
^
6"
8-
N) XI
XI
a
1
ro«c in
3
I
o o 1_
I o o
o o • t
o o .. I
o o
0 3 * >
57
written most generally as,
;'4 =- 2 .T j . . t . •-!.
v/here J. . is the strength of the interaction and S. and
S. are electron spin operators. The summation is carried
out for all atoms i with all other atoms j ^ i. The
exchange interaction is not generally isotropic.
(ii) Hyperfine field models : The large magnetic hyper-
fine fields observed experimentally "aT the nuclei of
impurities dissolved in metallic iron, nickel and cobalt
can be explained 'tjj the following three existing models,
1. Conduction electron polarization (GEP)
2. Core polarization (CP)
3. Overlap polarization (OP)
1. Conduction electron polarization i The contribution
of the conduction electron polarisation to the hyperfine
field (Hp -rj) at the site of the nucleus is largely due to
the contact interaction of those conduction electrons that
have S-character with respect to the impurity atom. This
59) model was proposed by Daniel and Friedel \ In this
model the d moments (u, ) of the host atom.s are assumed
to act as an effective field on conduction electrons,
giving rise to a difference in energy of the conduction
electrons with spin up and spin down. Since the electrons
with spin up and spin down should fill the conduction band,
5?
therefore, a difference in their density is resulted. The
sign of the difference depends on the character of the
coupling between the 3d electrons and the conduction
electrons, which may be parallel or antiparallel.
The impurity nucleus is considered as a rectangular
potential well, having a depth Z.-Z, betv/een the impurity
atom and host atom (where Z. is the valence of the impurity
atom and Z is the valence of the host atom). The radius
of this potential well is defined as 'a' and is set by
certain assumed number of S-electrons per atom in the
conduction band. Due to their difference in energy in
conduction band both types of electrons will see a dif
ferent potential at the impurity site. This means there
will be two wave functions, "4-' 1 and H'' •• This implies a ' s s ^
difference in density of both types of S-electrons at the
s i te of the nucleus, f'Nv(0M! ^ and K^(0)'^l ^. The result ing t o . ] ' S
net conduction electron polarization will be p| (0)t . ^~
1 (0)4 !• It may be positive or negative, depending
on which effect is stronger.
Daniel and Friedel assumed the conduction band to
contain one S-electron per host atom, and calculated this
polarization at the impurity site P. as a function of the
valence (see Fig. 33, curve a). They predicted the reversal
in sign of the hyperfine field at Z.~ + 3 and concluded that
the experimental results show that the host conduction electror
-no»-
F I G . 33 CALCULATED Ptl,ARIZATTON P OF T;^':. S-LlAvCTRONS
AT THE IMI^URITY SITE AS A FUNC ril?."' OF THE /ALENCi,
Z^ OF THE IMPURITY ATOM. CURVy'a'REPRESENTS THE
ESTIMATE OF DANIEl. AND FHIED£3. } Cri';Vi.;'b'REI^RESENTS
THE ESTIMATE OF CAMPBELL. FOR IROK r . = 1^ r
59
polarization is positive.
Tliis model is later on modified by Campbell ^ when
Daniel and Priedel model could not explain certain experi
mental results of H, . (say for exam.ple Cu?e). In the
modified version of Daniel and Friedel model, Campbell
assumed that the conduction band is taken as a composite
band with 4 electrons (in S-p shell) for each direction
of spin; one of these 4 electrons is S, and there is the
same density of states curve for all electrons. The non
S--electrons can be thought of as being d-like near the
bottom of the band and p-like -elsewhere. For the details
we refer reference 60). On the basis of Campbell's model
the behaviour of the polarization at the impurity site,
P., as function of the valence is given in Pig. 33 curve b.
Finally he gave the following expression which will give
the contribution of the E. r, due to conduction electron hf
polarization,
H^gp = A (Z) P_ (0.6 - 0.4 i/[i )
A(Z) are the free atomic hyperfine fields. If we know
the host and impurity moments, v/e can calculate the
contribution from. H -pp. For iron ji, = 2.22 |ir, and for nickel
[I, = 0.606 |i where |i-n is Bohr magneton. Shirley and gq\ 57)
Westenbarger ^ and later Shirley, Rossenblum and Matthias -
also assumed this proportionality of Hp-gp with A(Z) and deduced
from the experim.ental values the empirical relation,
60
2. Pore polarization : This model is due to Freeman and
72)
Watson and they have extensively treated it hy m.eans of
Hartree-Pock calculations. Core polarization is chiefly
caused hy the exchange interaction of an unfilled d shell
with the filled S shells giving rise to a net spin density
at the nucleus. The resulting hyperfitie field (Hp-p) "being
a superposition of the contributions from all S shells. The
regular variation of H, v/ith solute atomic number in the
3d, 4d and 5d transition series is very interesting. In
Fe, £0 and Ni hosts, the fields are negative across the
three series, but they increase suddenly at the solutes
Mn, Ru and Os, and remain large for several elements before
returning to the CSP 'base line' (see Figs. 30, 31 and 32). 72) Freeman and ifetson ' have calculated hyperfine fields per
unpaired spin for 3d group, 4d group and 5d group,
H -, = -125 KOe, H,-, = -375 KOe and H^ = -1200 KOe yu. 40. 50.
respectively. They have also shov/n that within 4d elements,
the magnitude of the H, unpaired d-sp-in does not vary
considerably for different elem.ents. This was later on
confirmed by experiments. For diamagnetic atoms the contri
bution of Core polarization is relatively small.
3. Overlap polarization ; It is a nev; model proposed by
73) Stearns -. The hyperfine field contribution arising from
61
overlap polarization is due to S electron wave functions
in outer shells of the impurity atom overlapping with the
wave functions of the polarized d electrons of the host.
The magnitude of this contribution depends strongly on
the size of the impurity atom. Overlap polarization is
likely to be of considerable importance for impurities
with high valency, where the outer shell is not completely
ionized and there is a remaining density of bound outer
73) shell S-electrons at the impurity site. Stearns ' has
given this possible explanation for the m easured hyperfine
field of solute atoms in Fe.
(iii) The systematics of the hyperfine fields : The
systematics of the hyperfine fields in ferromagnetic hosts
have been studied in detail by Shirley et al. ' . Since
they published their studies on systematics, many more data
have become availableo Our aim is to review the systematics
in the light of more comprehensive data available now. Taking
the values of the hyperfine fields fromx the recently compiled
table , we have plotted the im.purity hyperfine fields in
the host matrices of Fe, C£ . and M respectively in Figs.
•50, 31 and 32. The following systematic trends are clearly
seen,
1) The magnitude of the hyperfine field is proportional to
the magnetic moment of the host matrix.
e. 2
2) The hyperfine field H is negative in 3d, 4d and 5d
impurities in all the three hosts ?e, , M . Exceptions
39 40 40 are in 4d impurities for Y, Zr in ?£ and Zr in _Co.
3) The field increases gradually with the increase in
the d-electrons and reaches a maxim.um value when the d-
shell is approximately half-full. For 3d impurities;, for
example, the field is maximum for Fe in F^, Fe in _Co, and
Mn in M .
In iron host, the field increases gradually for
Ru, Rh and Pd; the maximum value is obtained for Pd in
Fe. However, the reverse trend is clearly seen for the
same impurity m-etals in the other host matrices _Co and M .
4) In the case of 5d impurities, the maximum value of H ^
is obtained at Ir for all the three hosts.
5) For 5p impurities, the field starts with a negative
value when 5p electrons are one or two and gradually
53 reacnes a maximum positive value for I and falls off
to zero and then to a small negative value as the shell
gets fullo
6) In 4f impurities, as we increase gradually the num-her
of 4f electrons;, the field changes from, a negative value
to a largo positive value soffiewhere between Eu and G-d
and then to a large negative value. The curve is very
steep with a large slope.
63
B. THE HYPER.FIWB FIELS AT ^^^Re NUCLEI IN NICKEL LATTICE AT ROOM TEMPERATURE
1. Source Preparation : For the present measurement
pure tungsten metal (99.99^) in pov/der form is sealed in
vacuum in quartz tube and got irradiated with thermal
neutrons in the CIRUS reactor at Trombay (India). Traces
of radioactive tungsten m.etal powder are melted with pure
nickel powder (99.9%) in an argon atmosphere using an
induction furnace. The resulting shltring ball of the
alloy is hammered into a flat disc (thickness less than
0.5 mm); annealed at 850 C for 15 hrs and is gradually
cooled to room temperature,
2. Experimental Set-up : The electronic set up is the
same as described in the magnetic moment measurement
except that a Nal(Tl) scintillator is replaced by a
5.1 cm. X 5.1 cm lead loaded plastic scintillator (covered
by an aluminium cover of sufficient thickness to absorb
p-rays) in stop channel for the detection of 72-keT y-rajs.
It is done to improve the time resolution of the electronics.
The time resolution of this arrangement for the start and
stop channel energy settings respectively at 4-80- and
72-ke? is found to be 1.5 nsec (EWHM) with a slope of
0.24 nsec. An external polarizing field of 2 KOe is
applied perpendicular to the plane of the detectors and
the data are accumulated in a Packard 400 channel analyzer.
64
3. Experimenta?!. Results and Analysis of the Data : The
observed counts in the time sjjectrum ¥(H,t) in the presence
of an external magnetic field H perpendicular to the plane
of the detectors may he v/ritten for the case under study as,
W(H,t)i=: A + B e"*/^ [C Sin (4''-.5-t +0)] (4-1)
The spectra obtained with the magnetic field up (f) and
the magnetic field down (i) have modulations of opposite
phase v/hen the detectors are kept at r35 to each other.
The function R(t) is plotted in Pigo 34. The Larmor
frequency of the oscillations is extracted from the data
using the Fourier transform technique, described by Matthias
52)
and Shirley ^ (see Fig= 35). In this case also the double
Larm or frequency is obtained from the absolute transform
F(<x ) and it is = 184-0 +1.0 M z . The measured Larmor
frequency is related to effective magiietic field through
relation, cr
co^ = - -ifJkl (4-2)
The effective field PI ^ is, thus, calculated from the
experimentally measured g-factor^ The effective magnetic
field,
- eff = "^ext ^"^int ^^'5)
where H -t- is the external polarizing field. The H. ,
is calculated using the sign of the H ^^ and the known
direction of H ,. The hyperfine field
u
c
CN *- o ;=: w o o ^ o o o ^ o
• ^ ;
H rv
S5
u H X w
H
2
00
^ :
o •a;
u o
C fc, fc O
^ . ^
O « H > .'H
:w
O + I
o I
DC
+ 0.3 .--^
>»+0.2
^ 40.1
< 0.0 ^
^ -0.1
I.-0.2 E < -0.3
1 1 . . .^F(Cx))
-
.•••• # • \
• ^ •• A
• A / A ^
- V A A A /
1 1 160 180 200
GJ in MHz
220
F I G . 35 THE FOURIER TRANSFORMS OF R ( t ) FOR
''^'^ReNl IN AN EXTERNAI. POLARIZING
Mi^NETIC FIELD OF 2 KOe.
65
\ f " int - f^ Ms + 471 Ms • D (4-4)
where the second and the third terms on the right hand side
in relation (4-4) are respectively the correction terms
due to the Lorentz field and the demagnetization field.
In the present experiment H , = 2.0 KOe; A-nMs'D = 2.0 KOe
(for the source shape used) according to the tahle given
by Bozorth -. The saturation magnetization 4-%'i'ls for
nickel is 6.08 KOe. 'ihe final value of the hyperfine
field at Re nuclei in nickel matrix at 300 K (room
temp.) is
Hj f (300°K) = -107 + 3 KOe.
C. THE HYPERFIHE FIELD AT ^^Sc NUCLEI IN IRON MATRIX AT ROOM TEMPERATURE
1. Source Preparation : The liquid source, obtained from
NSEC (USA), is evaporated on a thin iron foil (99.99%pure)
which ,is later melted in Argon atmosphere inc ide an induction
furnace and slowly cooled dovm to room temperature. The
resulting shining ball is rolled into a thin foil thickness
less than 0.5 mm and is annealed at 850°C for about 24 hrs.
and then slowly cooled down to room temperature.
2. Experimental Set-up : The electronic set-up is exactly
same as it was used in the magnetic moment measurement of the
68-keV state in Sc discussed in Chapter III. Here a dif
ferent geometry of the detectors and magnet is used since
66
rough estimates showed tha,t the attenuation of the
amplitude is considerable because of the finite time
resolution of the detectors. The time resolution (PWHM)
of the system for energy gatings around 70 keV is 15 nsec.
The external polarising field is 3 We, . Nuclear data 512
Channel analyzer is used to accumulate the data.
5. Experimental Results and Analysis of the Data : The
time depeiident angular correlation perturbed by the
external magnetic field in S-direction iflay be written as ',
-- _ - 1 -iN'.v.t W (k^, k^. t,H) = :> .V (1) A^ (2) ~j-3- e
rj J k
^ 4^(9^.0j) rl i6^, 0^ (4-5)
This may be simplified to the following form for k<s 2
W (t,H) = 1 + A22 ?2 ^^°^ ®i^ ^9 ^^°^ e2) + 3A22 Sin 0-
X Sin 02 X Cos 0-, • Cos 02 Cos2(>-4t + '^•^-^'i)
+ I A22 Sin^ 0-j_ X Sin^ ©g Cos 2(t t+j -jZf )
(4-6)
where 0-, , 0^, f>^ and jZp are the polar and azimuthal angles
of the two y-^ays respectively. In normal geometry
9 = 0 = 1 but in the present hyperfine field (H- )
measurements 0-1=7 and 0p = 7 — (°^ "j) ^'^^ "^^^ expression
for ¥(H,t) is,
¥(H,t) = I+I/I6A22 ± 3/4 A22 Cos..:5-jt + 3/16 A22 Cos 2<- t
(4-7)
67
v/liere V«'()i,t) is phase shifted hy 180° for the two values
of 9po In the geometry suggested "by Raghavan and Raghavan
the magne-cic field is in the plane of the detectors at 45
to the first detector, while the second detector is placed
successively at 180° and 90° to the first. The normalized
sum and difference in the coinciderce counting rates at
these two angles give the ratio,
R(t) = o^Ml^ll - N (90^)] (4.8) [N(180°) + N (900)]
3/2 A22 Cos -.jj t
1+1/16 A22 + 3/16 A22 Cos 2-j.t
The modulation frequency in this geometry is simply Larmor
frequencyCcV compared to 2 ' in the conventional geometry.
The function R(t) vs time is plotted in Fig. 36. Using
the Fourier transform technique the larmor frequency (ui )
obtained from the ahsolute transform ?(••") ( see Fig. 37) is
= 34.0 + 0.3 MHz. With the help of experimentally knovm
g-factor the value of H r,_p is calculated. The H. , is eiI inx
calculated using the sign of the H^r. and the known
direction of H , ,. The sign of the internal field is
measured by us for the first time. It is obtained from
the known anisotropy of the unperturbed angular correla
tion and the phase of the sign wave (when the modulated
time spectrum is carefully extrapolated to zero time).
Using the relation (4-4) the value of H, „ is obtained
O:
CO t^ ^ G r^ ^ CO Q O O . O o O
o o o ^ o o o + • + i l l
U
c
E
o|
H.
N;
O
<!
P
ft
H
H
m to >
K H
&4
CO in MHz
FIG. 37 THJB FOURIER TRANSFORMS OF R ( t ) FOR Uk
ScFe IN AN EXTERNAL POLARIZING MAGNETIC F U L D OF 3 KOe.
o c
D O
o r
r c H H
<
H O
o
3
H o
ft a
a
3 P: ^
>
I H O
m
H O
z
^
r
2
a:
c H
O 2
M
?
S 1-
N or;
c
9 M
M Z
>
H
o a N) o o o o o o J — I 1 I I
after appropriate corrections for the lorentz field and
.the demagnetization field. In the present experiment
on ^^Sc Pe H , = 3»00 KOe, An xMs-E = 4.18 (the value — ext 74) of D is obtained from the table of Bozoroth . . The
saturation magnetization Y " MS for iron is 6.97 KOe,,
44 The final value of the hyperfine field at So nuclei
in iron lattice at 300° K is H ^ (300°K) = -94+3 KOe.
D. RESULTS AND DISCUSSION '"-
Our measured values of H, r. at room temperature are
tabulated in Table 7 along with the other available experi
mental values in literature. Table 7 also gives a view of
H, in ReRi and ScPe systems using various techniques. Our
75)
value is in excellent agreement with Raghavan's ' who has
quoted a value = -105 + 3 KOe. Hov/ever, they used a dif-
ferent geometry ^ of detectors and magnet because the time
resolution of their spectrometer was comparable xvith the
expected time period of the oscillations. 77) Kontani and Itoh ' using spin-echo technique obtained
' int "" ~^^° i ^ ^^^ ^* 4.2°K for the internal field on Re in
Ni matrix. If we presume that the impurity magnetization
follows the Brioullioun function obeyed by the host matrix,
the value of the hyperfine field at room temperature is
expected to be^-5 /^less. Our value is-^10 Ailarger than
the value "reported by Kontani„ It may be probably because
our impurity concentration is low thus reducing the impurity-
69
impurity interactions which would result in a larger field.
The other possible explanation is that the impurity does
not follov/ the host magnetization curve with the possibility
of a localized moment at the impurity.
78) Kogan et ale from their nuclear orientation
experiments have determined the hyperfine field H, on Sc
in Te. Measured to an order of magnitude, they reported a
value of 100 EOe. The nuclear magnetic_resonance studies
of Koi '' gave them a value of 58 KOe. The values reported
by them vary by a factor of 2, Moreover, the M R studies
often contain impurity-impurity interactions because of the
poor sensitivity of the technique. Therefore, we have
measured the hyperfine field using TDPAC technique and it
is = -94 ± 3 KOe. In this technique, the concentration
of the impurity atoms is so small that the impurity-impurity
interactions are completely negligible. 'Eone has measured
the oign of the hyperfine field so far. The determination
of the sign of the hyperfine field on Sc in Pe_ is important
for the studies of the systematics. The -ve sign determined
by us agree with the prediction from the systematics of the
hyperfine fields.
Even though the detailed mechanisms'responsible for
the observed large hyperfine fields on the impurity nuclei
in ferromagnetic hosts are not well understood, the studies
of the systematics of the observed fields show a definite
70
trend as a function of the impurity atomic number. If we
expect a smooth variation of the hyperfine field values
around the So and Re impurities in F£ and Ni respectively,
71) the expected values from the systematics ' (see Pigs. 30-32) are;
\ f "^^ ^ * impurity) |_e = -90 KOe
Fxj ^ Re (5d impurity) Ni = -120 KOe.
which are consistent with our experimental values.
It is often found that the hyperfine fields on
dilute diamagnetic impurity atoms are proportional to the
host magnetic moment. Benski et al."' reported H,
ScNi = 25.9 + 0.3 KOe. Our m-easured value H, ScFe is =
-94 + 3» These values are proportional to the respective
host magnetic moments (ji„. = 0.606 |j.-p, |i-p = 2.22 |J-n).
77)
In the case Rhenium., Kontani et al. " reported
^\f ^eli = -100; % f "eCo = 442; H .. RePe = -760KOe. Our
measurement for Y^^^r. ReNi is in agreement with that of
Konta.ni et al. However, the observed fields are not
proportional to the host magnetic moments (|j . = 0.606 u-g,
[ip = 1.72 iJ,-o, |i-c,,, = 2.22 |i-n). This may .he due to the
formation of localised moments as pointed out in the
earlier part of the discussion, A formal Hamiltonian of the impurity atom is quite
57) complicated and may be written ' ,
71
[:} L(1+1) - k.]?-t - ||[(L"S)(I»I) + (L^I)("I'^)]
the symbols are explained in reference 57,1 The present
measurements on the impurity hyperfine fields were carried
out in cubic matrices and the impurity concentration is
negligibly small and, therefore, the electronic spin
dipole contribution is zero. For the impurities of our
interest ioe., Sc and Re in the ferromagnetic hosts of
Fe and Ni respectively, the orbital contribution to the
impurity hyperfine fields is also small. The main
contribution to the impurity hyperfine fields in ferro-
magnets come from
a) Conduction electron polarization (CEP)
b) Core polarization (CP)
c) Overlap polarization (OP).
The conduction electron polarization arises largely
from the polarization at the nucleut- from the conduction
electrons having an S-character. From the fact that the
conduction band S-electron states are similar to atomic
states near the solute nucleus, it was shown by Shirley,
57) Rosenblum and Matthias ' that,
^CEP " P ns
v/here H i s the f ree atomic hyper f ine f i e l d and p i s t he ns ''•^ ^
72
polarization at the solute, Prom the experimental data
it was derived * ^
H-, r. = 0.027 lxip H for dilute impurities in Pe_
= 0.030 UM H for dilute impurities in Co ^Co ns ^ —
= 0.024 UTIT- H for dilute impurities in Ni ^Wi ns ^ —
so that the predicted values are
\f ScFe = -47 KOe
\f ^eii = -155 KOe
The free atomic hyperfine fields were obtained from
Campbell '.
However, for the transition element impurities,
K . = pH + 2 (S > H. hf •' ns ^ z' d
where Hn is the Core polarisation hyperfine field arising
from, one unpaired d-electron. The calculations of Preeman no or) \
and Watson ' ' showed that
for 3d elements H, x>-.- - 125 KOe per unpaired spin
for 4d elements H, ^ - 375 KOe per unpaired spin
for 5d elements H, - -1200 KOe per unpaired spin
They have also showi that within the 4d elements, the
magnitude of the H, , does not vai-y considerably for dif
ferent elements. This result was later confirmed by the
experimental results. For diamagnetic atoms, the contri
bution from the core polarization is small. Since the
73
core polarisation of the d-electrons is always negative,
the sign of the field on Sc iii Ie_ can he explained using
this modelo However, since the magnitude of the d-electron
spin moment on the solute is - 0.3 jig„ The ohse:?ved field
of -107 KOe for Re in lli cannot be explained using this
model.
The observed small field in magnitude compared to
the predicted value from the systema.tics of the core polari
zation model on ReM may be due to a finite positive field
73) arising from the overlap polarization ' of the host 3d
electrons and the impurity valence electronsc This effect
is expected to be larger in heavier solutes like Re.
In the model due to Campbell ^ the contribution
from conduction electron polarization could be calculated
using the formula
H -gp = A(Z) V^ (0.6 + 0.4 fi/ji )
A(Z) are the free atomic hyperfinc fields and are tabulated
ho)
by Campbell; the host polarization i' =-0.12 S-electrons. y
If we know the host and impurity moments viz., (i. and }i, ,
we can calculate the contribution from Hp-pp.
Balabanov and Delyagin ^ have obtained a very good
fit of the experimental hyperfine fields to an empirical
equation
E/[i = Z^*^ [-2.48 + 0.113 (x)- 9)^]
74
v/here i> i s the number of e lectrons outside the closed'
s h e l l , Z i s the numher of closed she l l e lec t rons and i s 0
equal to 18, 36, 68 for IV, Y and VI group elements» The
values predicted by this model for hyperfine fields of
our interest are H,^ ScPe . + 152 KOe and H, ReM^-304
KOe» In the case ofSc in Pe the predicted value is •-
+152 KOe compared to the experimental value of -94 KOe.
For Re in M the prediction of the sign—of the hyperfine
field is correct but the magnitude is three times the
experimental value. This model is quite empirical with
the result that no plausible explanation for the observed
large deviations may be offered.
It looks that none of the existing models can
correctly explain the observed fields in ScPe and ReNi.
The observed field on ScFe both in magnitude and sign
may be qualitatively explained by the conduction electron
polarization and the core polarization model suggested
by Shirley et al. The field on Re in Ni may be understood
if v/e assume that the conduction electron polarization
and the overlap polarisation are vectorially added to
give the final experimental value. ^
The observed width (P¥HM) for ^^ScPeA-29 x 10~^ eV _q
compared to the natural width of 4.4 x 10 eV is considerably
large. This, discrepancy is attributed to some finite proba
bility where the Sc atom is not substitutional ^ ith iron
75
matrix. Since the spin of the intermediate state 68-keV
in Sc is 1, the quadrupole interactions are zero.'
Similarly, the observed v/idth (PWHM) for 'ReNl _q
'•../80 X 10 eV" compared to the natural width of 1.25 x
- 9 / \ •
10 eV is also considerably large. This may he, (i) Re
atom is not substitutional to the nickel matrix and (ii)
since the spin of the intermediate state 206-keV in "I on
Re is 5/2, hence there may be quadrupole interactions.
+ CD
0) u ?
03 CD
S CQ
H ;:i CD H •H a
o W Hi pq <a! EH
0 Pi •H ^H ^ 0 ft t> ^
4^ PJ 0 0! (D i4 ft
0)
+ CH
o P! o ra •H fH
ft o o
'xi Q) ^ m •H H rQ p! ft
Q) H ^ C
H •H
> OS
•H ^
CQ 0) O Pi CD PI CD
' ^ CD
CD
o< •H
O CD
H ID
• H
CD Pi •H
^ CD ft >5
M
EH
- P CQ O
W
o
-p
PJ 0
H
76
i n o
o < PH O
c~-! > •
w CO
1 0
CQ 03 0
0 CQ 0 PI
O <J PH
n
a
CO c-
i-q PM s
C7 c~-
p: S ^
H CO
Hi P^ "^
Q) U
CQ 03 0 S
+3
-a f R 0 0 S KJ 0 P
PH
O < i !
PM O
K>
+ 1 Ln O H 1
CM
+ 1 LA O H
1
tS~\
+ 1 [ > O H 1
O r
+ 1 O O H
CO in o
o H
tA
+ -* cn
1
« ft S 0
K> m r\i
0 W
« Hi
O o to
o Hi
r--00 H
o 1 CO
H
'vD <-
LPi
•^ VD < •
o o
•H S
•H S
•H S
0 PH
0 PH
0 PH
CD PH
•^
0 pi
0 p:;
0 p:i
o in
o CO
o CO
o CO
77
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PUBLICATIONS
1 "2 "2 "1 Q'7 1 PV
lo Nuclesir L i fe t ime Measurements i n Cs, Au and Re;
D.K. Gupta and G.N. Rao, I I T / K Technical Report 5 / 7 1 ,
March 1971. QQ
2. Nuclear Level S tud ies of Ru; D.K. Gupta et a l . ,
Nuc l . Phys, A180 (1972) 311 . 3 . Nuclear L i fe t ime Measurements of Some Exc i t ed S t a t e s
i n ^hs, 151^3, 133^3, 170.^^^ 187p^^ ^ ^ , 19JZ^„
L,K. Gupta and G.N. Rao, Nucl. Phys„ A182 (1972) 669
Lifetime and Magnetic Moment of 68-keV State in Sc;
D.K. Gupta et al., Proc. Nucl. Phys. and Sol. St.
Phys. Symp., BARC, Bombay (India) U B (1972) 349.
Timing Properties of Ge(Li) Detector (ORTEC Model
8100 - 65 SNo. 67-D); A.K, Singhvi, D.K. Gupta and
G.N. Rao, Proc. Nucl. Phys. and Sol. St, Phys. Symp.
BARC, Bombay (India) liB (1972) 555.
Hyperfine Pield Measurements on Sc in Pe and Re in
Ni; D.K. Gupta et al., IIT/K Technical Report No.
20/72, August 1972, (Under process of Publication
in Phys. Rev. B).
