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The magnetic moments of three excited states in 149Pm
I I.E.3 ]
Nuclear Physics A159 (1970) 494--512; (~) North-HollandPublishint7 Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
T H E M A G N E T I C M O M E N T S O F T H R E E E X C I T E D S T A T E S I N 149Pro T. SEO and T, HAYASHI Research Reactor Institute, Kyoto University, Kumatori-cho, Osaka, Japan and A. AOKI Department of Physics, Kyoto Prefectural University, Kyoto, Japan Received 4 August 1970
Abstract: The magnetic moments of three excited states in 149Pm were determined through the measurements of g-factors of the corresponding states by the perturbed Y3' angular correlation method using a Ge(Li) detector and an NaI(TI) scintillation counter. The results obtained are # = 2.0+0.2, 2.2+0.6 and 3.6-4-0.2 n.m. for the 114, 189 and 270 keV states, respectively. The experimental values are discussed in comparison with contemporary models of the nucleus.
E
RADIOACTIVITY 149Nd [from 14aNd(n,7,)]; measured yy(O), y~,(O,t), y~,(O,H), 7'ce-delay. 149prodeduced levels, J, muitipolarities, mixing ratios, T,!,,9, #. Enriched target, Ge(Li) detector.
[
I
1. Introduction The nucleus 149pm with 88 neutrons lies in the so-called transition region where a sudden change in the nuclear shape is generally known and, therefore, considerable interest has been shown in the study of the structure of this nucleus. The first study of this nucleus was made by Rutledge et al. 1) in 1952. About ten years later, Gopinathan and Joshi 2) established a number of levels with scintillation coincidence techiniques and fl-ray measurements. Further work with the delayed coincidence technique by Currie and Dougan 3) has revealed three levels having lifetimes of several nanoseconds. A study with a Ge(Li) detector of the y-rays of this nucleus was made by Nieschmidt et al. 4), and in 1966 Helmer and Mclssac 5) measured the y-rays and fl-rays in detail and established a large number of new levels. Angular correlation measurements with NaI(TI) detectors were made by Gopinathan 6), and the spins of several levels and the multipolarities of many transitions were elucidated. In the following year, B~icklin et al. 7) published an extensive study on transitions, lifetimes and levels in this nucleus. As for the measurements of the magnetic moments of excited states, Svensson et al. 8) studied the magnetic moment of the 114 keV level and Tandon and Devare 9) also published their result on the same level. The first measurement of the 270 keV 494
149pm MAGNETIC MOMENW$
495
level was reported recently by Begzhanov et al. 10). However, there remains some doubt as to their application of the Kisslinger and Sorenson theory 11) to the experimental results. The value for the 189 keV level is to be newly Presented by the present authors. In this work a Ge(Li) detector was used for the measurements of the magnetic moments with the angular correlation technique. The use of the Ge(Li) detector made it possible to distinguish many ?-rays from others, and then to perform angular correlation measurements on several new cascades. Thus the measurements of the magnetic moments of three (the 114, 189 and 270 keV) excited states were accomplished without the ambiguity accompanied with the use of NaI(TI) detectors.
2. Source preparation Sources of 149Nd were prepared by irradiating enriched (93.3 ~ ) t4SNd in the form of Nd2 0 3 for 30 min each in a flux density of 2.34 x 1013 neutrons/era 2 • see in the pneumatic tube irradiation facility of the Kyoto University reactor. The irradiated sources for the angular correlation measurements were dissolved in dilute hydrochloric acid and the solution was then transferred to a cylindrical source container of acril resin, 2 mm in diameter and 4 mm in depth. Dry sources on aluminium coated taylor films were used for the detection of conversion electrons. The undesired impurities o f short-lived activities such as those of i s iNd were allowed to decay for about an hour before the measurements were started. The measurements for each source were stopped 6 h after the irradiation to avoid interference from 54 h 149pm.
3. Angular correlation measurements 3.1. APPARATUS Singles spectra of ?-rays were measured with an O R T E C 22 cm 3 Ge(Li) detector and coincidence spectra gated by the pulses from a 7.62 cm ~ x 7.62 cm NaI(TI) detector were also taken in some cases. Through these measurements the decay scheme of 149Nd reported by other authors s, 7) was confirmed. The decay scheme is shown in fig. 1. The angular correlations were measured with a fast-slow coincidence system having a resolving time of 2~ = 100 ns. An RCA 8054 photomultiplier mounted with the 7.62 cm ~ x 7.62 cm NaI(TI) crystal and the 22 cm 3 Ge(Li) detector were used as detectors. The measurements were made at four angles (90 °, 120°, 150 ° and 180°) by obtaining coincidence spectra of the Ge(Li) detector on each quarter division of the display of a 400-channel pulse-height analyser. A block diagram of the coincidence system is shown in fig. 2. 3.2. MEASUREMENTS AND RESULTS For the cascades involving the 114 keV ?-ray, measurements on the 541-114, 424-114 and 156-114 keV cascades were made by taking the coincidence spectra
T. SEO et al.
496
E
5/2
(keY)
7-,_ 2
-
149 r~l r,I 60 ~ " ~ 8 9
1.78 h
gg~
"'~ (7/2)-
655
Od f~ f¢l ~r
5.,'2-
~
538
(.=/2)+
388
o O ~
7/2-
°
~r
1112-
=
~
11
270 240
2.55 ns
189
3.24 ns
114
2.54 ns
7/2 +
54 h
149 ,-,, 611-'m88
Fig. 1. Level scheme of l"gPm based on Blcklin et aL 7). The half-lives of excited states are those determined in the present work.
SOURCE
~MSTOR
*
I L,NEAR AMP.I
ITiME PICK OFF I t LINEAR AMR I ITIME
PICK OFF CONTROL I
I SINGLE CHANNEL ANALYSERI ISPECTRUM STABILIZER I
DELAY AMP. J
I FAST COINCIDENCE I LINEAR
GATE I '=
1 400 ch. P.H.A. 1 IO0 ch. X 4 q
Jl
I TELETYPECONTROLLERl
I
I
1
"I GONIOMETERCONTROLLER. ~
I
Fig. 2. Block diagram of the angular correlation measurements with the Ge-NaI system.
149Pro MAGNETIC MOMENTS
497
gated by the pulses from the NaI(TI) detector for the 114 keV y-ray. The data were analysed by a least-squares fitting method. The angular correlation coefficients obtained were corrected for attenuations due to the finite size of the detectors and the time-dependent perturbation. The attenuation factors for the time-dependent perturbation are described in the next section. The same procedure and corrections were applied to all the data for the other cascades. Since the quadrupole content of the 114 keV transition was found to be.very small ( 2 . 8 -+0 t..62 X 10 -2) [ref. 7)], the P4 term was neglected when the data for the three cascades were analysed. The obtained A2 coefficients are shown in table 1. The coefficient for the 541-114 keV cascade agrees with the values of other authors 6,s,,o) within experimental errors. Our A2 coefficient for the 424-114 keV cascade is in agreement with those of other authors s,1 o) within experimental errors and also is in good agreement with the value obtained in our time-differential angular correlation measurement described in sect. 4 (see table 3). In the measurement of the 156-114 keV cascade, the Compton part of the 268 keV y-rays which entered into the 114 keV gate introduced interference from the 268-156 keV cascade. The value corrected for this effect is presented in table I. TABLE 1 Results of the angular correlation measurements Cascade (keV) 541-114 424-114 156-114 199- 74 268-156 268-270
Present results A2 0.040-60.007 --0.140-60.008 0.050-60.006 0.095-60.022 ") 0.173-60.012 --0.315-60.011
--0.089-60.022 ")
A2G2
A,G,
0.0424-0.006 --0.102-60.006 0.074-60.026
--0.009-60.010 --0.027-60.010 0.026-1-0.040
--0.227-60.008
0.013-60.013
Ref. 8)
Cascade (keV)
541-114 424-114 156-114 199- 74 268-156 268-270
A4
Ref. e)
A2
Ref. ' o) A,
A2
A4
0.027=1=0.011 --0.131 =1=0.023
0.047=t=0.009 --0.127=1=0.011
0.007+0.008 0.008=[=0.010
--0.220-60.020
--0.142=[=0.009 --0.218-60.012
0.020-/-0.011 0.012-60.012
=) See appendix 1.
Measurement of the 199-74 keV cascade was impossible without the use of an NaI-Ge system, but even with this system the measurement for this cascade was cliffcult due to admixtures of large amounts of the Compton tails of higher energy y-rays.
498
T. S£O et al.
As the spin of the intermediate state of this cascade had been determined to be ½ by B~icklin et al~ 7), the analysis was carried out without the P4 term. The result is listed in table 1. For the cascades involving the 268 keV transition, the 268-156 and 268-270 keV cascades were measured in the same runs, gated at about 268-270 keV by the pulses from the NaI(TI) detector. As the 156 keV transition is almost pure E1 [ref. v)], the data for the 268-156 keV cascade were analysed with terms up to P2. Our Az coefficient corrected for the attenuations is shown in table 1. Recently, Begzhanov et al. 1 o) measured the angular correlation coefficients for this cascade. Their coefficients are different from the present value. For the 268-270 keV cascade, the present result gives the A2 coefficient of - 0 . 3 1 5 _ 0.011 which is about 40 % as large as the values by other authors. No decisive reason has been found for this discrepancy. As shown in sect. 4, the present result of the timedifferential angular correlation measurement for this cascade gives the A2 coefficient of -0.347___ 0.024, which is in good agreement with our value described above. 3.3. SPINS A N D MULTIPOLARITIES
The spin of the ground state of 149pm was determined to be -Tzby Cabezas et al. x 2). According to the shell model, the l~roton states which are expected to occur in this mass region are gt and d{. Therefore, it is natural to assign ~ and k to the 114 keV and the ground states, respectively. In the analysis of the present data for the angular correlation measurements the spins and multipolarities as assigned by B/icklin et al. v), were referred to for decisions. Our results are generally consistent with those of B/icklin et al. 7) within experimental errors. These are listed in table 2. TABLE 2 Spins and multipolarities obtained from the analysis of the present data Energy level (keV)
Gamma ray (keV)
Measured cascade (keV)
Spin
Quadrupole content
(%)
Sign of
655
541
541-114
(-])
0.(g-0.1
(M2)
538
424 268
424-114 / 268-270 [ 268-156
]
0.1 ") 3.0-3.7
(M2) (E2)
---
388
199
199- 74
3.1-4.5
(E2)
-l-
270
270 156
268-270 268-156
~
0.3 ~) 0.07 °)
(M2) (M2)
+ q- or --
189
74
199- 74
~ a)
26 - 39 a) (E2)
+
114
541-114 ~ 424-114 156-114
~]
2.2-3.0
-I-
114
a) Ref. 7).
(½) ")
(E2)
-
-
499
149Pro MAGNETIC MOMENTS
4. Time-differential angular correlation and lifetime measurements
It is necessary to know the attenuation factors G2 of the angular correlation functions and the lifetimes of the intermediate states whose magnetic moments are to be determined. The measurements of the attenuation factors G2 for the cascade involving the 114 and 270 keV levels were performed by the time-differential angular correlation method. The detectors consisted of two 4.45 cm ~ x 5.08 cm NaI(TI) crystals mounted on Philips XP1021 photomultipliers. They were connected to a time-analysing system consisting of an ORTEC 437 time-to-pulse-height converter and the 400-channel pulse-height analyser. As the coefficient A4 could be omitted in the case of the 424--114 keV cascade, it was sufficient to measure the correlations at the angles 90 ° and 180°. The experimental data were analysed by the following procedure. The time-differential angular correlation function is expressed as
W(O, t) = Ne-'/'(l+A2e-Z"P2(cos 0)}
for t > O,
where • and 3.2 are the lifetime and the spin relaxation constant of the intermediate state, respectively. However, because of the finite time resolution of the detecting system, the function experimentally obtained should be W'(O, t) instead of the original function W(O, t). Here, W'(O, t) is given as
W'(O, t) =
P(t-t')W(O, t')dt',
where P(t) is the normalized prompt curve function. The experimental data were taken at 90 ° and 180 °, so that W'(O, t) is expressed as
iooP(t-t')e-"/'(1-½A2e-~")dt
',
w ' 0 8 o °, t) = N fo oP(t-C)e-"/'(l+A~e-"2")dt
".
W'(90 °,
Since the functions,
t) = N
Fl(t) and Fz(t) defined as
Fl(t) - ~{2w'(90 °, t) + w ' 0 8 0 °, t)} = N F2(t) - ~{w'(18o °, 0 - w ' ( 9 o
°, t)} = SA~
P ( t - t')e-"l"dC,
Io e(t-C)e-~"2÷"~"dC,
have the similar form, they can be analysed with the same computer program for the least-squares fitting. The function P(t) was assumed to be Gaussian. The best-fit Ft(t ) and F2(t ) curves for the 424--114 keY cascades are shown in fig. 3(a) with the experimental data. The parameters A2, • and 3.2 + 1/z were determined by this proce-
T. s~o et aL
500
r.l) I-Z
0 0
U
~
IU
I~
~
~
~
rl$
Fig. 3a, b. Results of the time-differentialangular correlation measurements (a) for the 424-114 keV cascade and (b) for the 268-270 keV cascade. Detailed description for Ft(t) and F2(t) is given in the text. dure. The attenuation factor G2 was obtained by taking the ratio of slopes of the two curves Fx(t ) and Fz(t) as follows t3), 1/~
1 --
A2 + l/'c
_
_
~
G2
o
1 +A2"C
In the case of the 268-270 keV cascade, the two y-rays could not be separated, therefore the function W(O, t) changed into the form
W(O, t) =
Ne-Itl/t{l + a 2
e-~tzlP2(cos 0)},
was used for the least-squares fitting. In this formula the P4 term is omitted, because this term is small compared with the P2 term as seen in table 1. The best-fit curves thus obtained are shown in fig. 3b. It was impossible to apply the time-differential angular correlation technique for the 199-74 keV cascade involving the 189 keV state because of the difficulty in sep-
149pro MAGNETIC MOMENTS
501
10"
03 I---
z o
-40
- 3 5 - 3 0 -25 -20 -15 -I0
-5
0
5
10
15
20
25
30
35
ns
Fig. 3b
arating the 199 and 74 keV ?-rays from other ones having similar energies. Therefore, the 6/2 for this cascade was obtained from a calculation by using the attenuation factors for the aforementioned two levels on an assumption that the perturbation was mainly due to a time-dependent magnetic dipole interaction. A detailed description on this assumption is given in appendix 1. The lifetime of the 189 keV level was measured by taking a delayed coincidence curve between the 349 keV ?-rays and the Kconversion electrons emitted in the 74 keV transition. The ?-rays and the electrons were detected with the 4.45 cm ~ x 5.08 cm NaI(T1) crystal and a 3 cm ~ x 0.2 mm plastic scintillator, respectively, both coupled to Philips XP1021 photomultipliers. The measured curve is given in fig. 4.
502
T. SEO et aL i0~
I0'
(I) I--
o
4
++
,02
I0'
,I.,,,I I,,..I,.++1,,,,I,~ 0
5
I0
15
20
25
50
ns
Fig. 4. Results of the delayed coincidence measurement for the 349-74 keV cascade. Measurement w a s made by detecting the 349 keV y-rays and the 74 K conversion electrons.
The results of these measurements are summarized in table 3. 5. Measurements of the magnetic moments of the 114, 189 and 270 keV levels
The g-factors of the three excited states were measured by observing the rotations and the attenuations of the angular correlation patterns in an external magnetic field o f H = 15900 G. The perturbed angular correlation function, FF(O, B ) in the integral form is given as
3cos2(O-AO) I W(O, B) = 1 +¼A2 G2 1 + [1+(2toTG2)2]+) ' where
AO =- ½ arctg (2co~G2), co -- - glen B = #H.
B/h,
t49pm MAGNETICMOMENTS
503
TABLE 3 Results of the time-differential angular correlation and the lifetime measurements Level (keV)
Measured cascade (keV)
G2
A2
424--114
2.544-0.07 2.524-0.04 a) 2.624-0.10 b) 2.4 4-0.2 c) 2.584-0.07 d) 2.524-0.12 c) 2.424-0.09 r)
0.878 ::t:0.031
--0.1424-0.008
268--270
2.554-0.07 2.58 4-0.04 ") 2.7 4-0.2 b) 2.6 4-0.2 c) 2.644-0.07 a)
0.781 +0.018
--0.3474-0.024
349-- 74(K)
3.244-0.07 3.464-0.14 a) 3.244-0.10 a)
0.62 4-0.12 B)
114
270
189
Half-life (ns)
") Ref. a). b) Ref. t4). c) Ref. e). d) Ref. e). e) Ref. a). t) Ref. a). a) The value calculated by using the G2 values of the other two levels (see appendix 1).
In the above equations g and fl are the gyromagnetic ratio of the intermediate state and the paramagnetic correction factor, respectively. The electromagnet was specially designed for the Ge-NaI angular correlation measurements. An improvement was made to reduce the stray magnetic field by covering the coils of the magnet with thin iron plates. Thus, the light-pipe which coupled the crystal to the photomultiplier could bz saved and the deterioration of the energy resolution of the NaI(T1) detector caused by the use of the light-pipe was avoided. The detectors and the electronic circuits used are the same as those described in subsect. 3.1. The measurements on the 541-114, 424-114, 199-74, 268-156 and 268-270 keV cascades were made at four angles 90 °, 120°, 150 ° and 180 °, and for the two cases of the magnetic field up and down. A few examples of the angular correlation patterns obtained in these measurements are shown in fig. 5a-c. The results are listed in table 4. The paramagnetic correction factor was taken 13) to be fl = 1.93 at room temperature. The magnetic moments were calculated by using the spins and the g-factors of the corresponding states. The results are summarized and compared with the values by other authors in table 5. The present result for the 114 keV state is rather small compared to the values of other authors 8-1 o), although the differences are within experimental errors. The value for the 189 keV level was measured for the first time by the present authors. The experiment for this level was done through 48 runs, where one
T. SEO et aL
504
•!
H=OG
~'f
,.oo,
t.OOL ,
, H= ± 15900G
t
0.95
0.90~
0.85
[
,
90 °
,
120=
150 °
1
180"
90*
e (degrees)
120 °
150"
180"
E) (degrees)
Fig. 5a-c. Results of the angular correlation measurements with and without the magnetic field. The solid lines are obtained by least-squares fit.to both of the experimental data with a common parameter A2. The angular correlation functions W(O) and W(O, B) are normalized at the points of 90* and 90°+/10, respectively. (a) the 424-I 14 keV cascade, (b) the 199-74 keV cascade, (c) the 268-270 keV cascade.
03 .(D
=
(1) v
H= +_15900 G
v
1.05
1.05
I:00
I.OC
t 90*
I
t
120* 0
150°
I 180*
90*
(degrees)
120*
I 150*
I 180 °
(9 ( d e g r e e s ) Fig. 5b.
run took about 5 h, and about 35000 counts were taken at each angle for the two directions of the magnetic field. The magnetic moment for the 270 keV state was measured by using the 268-156 and 268-270 keV cascades. F o r the 268-270 keV
505
149pm MAGNETIC MOMENTS
(D
I00
0.90
~
=OG
ioo
0.90
~,
0.80
~0
0801
i I
0.70
I
!
90*
120°
I
150°
I
I
180"
90*
(9 ( d e g r e e s )
i
120°
I
150°
i
I
180"
e (degrees)
Fig. 5c. TABLE 4 Results of the angular correlation measurements in the external magnetic field Level (keV)
Measured cascade (keV)
Gz coz
r ")
g-factor
114
541-114 424-114
0.37+0.03 0.39 4-0.14
3.644-0.04
0.79+0.07 0.83 4-0.30 weighted mean 0.794-0.08
189
199- 74
0.744-0.16
4.864-0.09
1.484-0.40
270
268-156 268-270
0.42 4-0.06 0.464-0.02
3.74 4-0.06
0.98 4-0.14 1.074-0.07 weighted mean 1.044-0.07
• ) The mean lives taken from the weighted mean values over all the measured values listed in table 3.
cascade, the m a g n e t i c m o m e n t was o b t a i n e d only by the m e a s u r e m e n t s of a change o f the a t t e n u a t i o n o f the a n g u l a r correlation p a t t e r n in the magnetic field because of the difficulty i n separating the two 7-rays from each other. The values o b t a i n e d for the two cascades show good a g r e e m e n t as seen i n table 4. The magnetic m o m e n t o f this state was measured by Begzhanov et al. lo), recently, using the 268-156 keV cascade. T h e i r result is c o n s i d e r a b l y different from the present value.
506
T. sEo
et al.
6. Discussion 6.1. T H E G R O U N D
AND
114 keV STATES
The intermediate coupling (I.C.) theory is most widely used and has been quite successful for describing several properties of the nuclei belonging to the so-called vibrational region. As for the magnetic moments, Choudhury and O'Dwyer 16) made the I.C. calculation for this nucleus taking into account the gt and d~ single proton states and the core states up to three phonons, and obtained the magnetic moments of 1.75 and 3.91 n.m. for the ~ and ~ states, respectively, when gs = 5.58 was used for a free proton. In a similar calculation, Heyde and Brussaard 17) got 2.79 and 2.96 n.m. for the ground and first excited states, respectively, by using gs = 2.62, the most favourable effective value in this region according to them. However, their value for the 114 keV state is, as seen in table 5, a little higher than the experimental values including the present work. Kisslinger and Sorensen it) in their calculation based on a pairing-plus-quadrupole model obtained 2.06 and 2.55 n.m. for the ~ and ~ states, respectively. For the ground state the value of Kisslinger and Sorensen is far from the experimental value z 5), but for the first excited state it agrees with the values by two authors s, 9), though it is somewhat larger than our value. TABLE 5 Magnetic m o m e n t s of the ground and three excited states in ~49Pm Level
1n
(keV)
p.p (n.m.)
tttheor(n.m.) e) KS gs= 5.58
I.C. gs = 5.58
Nilsson
gs =
gs=
2.62
state
5.58
gs =
2.62
0
t+
3.3 -t-0.5 °)
2.06 t)
1.78 *)
2.79')
[404]
1.66
2.56
114
~+
2.0 4-0.2 2.4 4-0.3 b) 2.554-0.3 c) 2.204-0.20 e)
2.55 f)
4.05 ,)
2.96 s)
[402] [413]
3.71 1.17
2.69 1.76
189
OZ+
2.2 4-0.6
0.89 h) 1.65 ~)
1.66 h) 1.25 ~)
[411] [422]
1.92 0.69
1.44 0.99
270
~--
3.6 4-0.2 2.174-0.21 e)
6.53
5.06
[523]
4.16
3.44
") Ref. *s). t) Ref. 11).
b) Ref. s). s) Ref. 17).
c) Ref. 9). d) Ref. lo). c) Values for glt = h) t + ( l ) state. ~) ~+(II) state.
Z/A.
Meanwhile, provided this nucleus has a small deformation, the ground ~+ and the first excited ~r+ states are considered to be the [404] and [402] Nilsson states, respectively. The magnetic moments calculated from the Nilsson model are also listed in table 5. For the [404] and [402] states the calculated values with Os = 2.62 show a better agreement than with gs = 5.58. For the first excited ~+ state the [413] configuration seems to be more favourable for the present work than the [402] configura-
14"9pro MAGNETIC MOMENTS
507
tion, but the strong M1 hindrance in the 114 keV transition cannot be explained by the [413] first excited and the [404] ground states. 6.2. THE 189 keV STATE No single proton state of ½+ is expected near the 189 keV, so that this state may be the phonon state built on the gt or d~ particle states. The 189 keV E2 transition to the ground state is enhanced by a factor of 2.9 compared with the single-particl~ estimate, while the E2 enhancement and the M 1 retardation in the 74 keV transition to the first excited ~+ state are 96 and 540, respectively 7). This indicates that the 189 keV state is mainly composed of one phonon and the d~ proton state. But according to our I.C. calcu.lation with the same parameters as adopted by Heyde and Brussaard 17), this ½ state should be mainly composed of one phonon coupled with the gt state and not with the d~ state. Moreover, from the same calculation the level mainly composed of one phonon and the d~ state should be located in an energy region about twice as high as the first ½+ state. The magnetic moments for both the first ½+(I) and the second ½+(II) states were also calculated by the present authors (see appendix 2), and the results are listed in table 5. As the experimental value has a large error due to an indirect estimation of the G2 value, a comparison with the I.C. values would not give any decisive information. However, the value for the ½+(I) state may be more favourable for the 189 keV level because it agrees with our experimental value. On the other hand, if this level corresponds to a single-particle state in a softly deformed potential, possible states should be the [411 ] or [422] states. As for the magnetic moment, the [411 ] state is more suitable. However, the [411] state lies below the [404] ground state for a prolate deformation. This difficulty may be removed when the 189 keV state is the hole state of the [411 ] Nilsson state. 6.3. THE 270 keV STATE According to the shell model, no ½ proton state with negative parity is found in this mass region. The E2 transition from the 270 keV 3- state to the 240 keV ~ - state is enhanced by a factor of about 137 [ref. 7)] compared with the single-particle estimate. This suggests that the 270 keV 3- state is a phonon state built on the h÷ state. The I.C. calculations involving three phonons and the h,~ state were newly performed by us (see appendix 2). The result is shown in fig. 6. As is seen in fig. 6, a 7zstate appears above the ~ - - states and the energy difference between the two states is approximately equal to the energy of one phonon, namely 220 keV. Nevertheless the observed energy difference is 30 keV and such a small value cannot be reproduced by the I.C. model with one phonon energy of 220 keV and a reasonable value of the coupling constant. Therefore, it is hard to assign the 270 keV state to this 3- state. As for the magnetic moment of this state, the present calculation gives 5.06 n.m. for gs = 2.62, which is considerably larger than the value obtained in the present experiment. Meanwhile, a possible state in the Nilsson model may be the 3-[523] state. The
$08
T. see
900
e t a~.
,49 Pr'd
80C
tl
+
7OC (7.,';2) .-:.
:5,~÷
6oE
s/2+~"
rvZ-
•7/2; ,
"
11/2 -
.5t2+ I/2 ~7/~' + -5/2 +
C9 0:: -U.I Z
40C
( i,.'2 ) ÷
3/2+ ?'PZ--s
3oc 2OC
712 I1~" S/2.1312+
.. ~r/Z + "llf~-11/2+ 3/2+ 9/2 +
I0C
5/2÷,
7/2+
....
exp.
772÷
theory
Fig. 6. Comparison of the experimental and the theoretical ievel scheme of ~'gPm. Negative parity states in the theory are those cal~tlated by the present autliors. The theoretical positive parity states are those by Heyde and Brussaard 17).
m.sgnetic moment for this state was calculated to be 3,44 n.m. for g. -- 2,62. As is seen in table 5, theagreement between the experimental and theoretical values is quite good, However, there exists some difficultT in this case, too. The ~ - [532] state which should exist below the ~ : state has not been observed and the level sequence of the - "and~ ' ~ states is reversed as compared with the one predicted by the Nilsson model for a po~five deformation. Begzlumov et a/. d e s ~ b e d in their paper i o) that their value was in good agreement with the prediction by Kisslinger and Sorensen Zl). However, the theoretical val~e ~ e y referred to was the one not for the 5" state but for the ground gt + state. '
6.,4. £~NCLUSION
• ~ s fo~.themagneticmon~ent, an agreement between ©xperiment and theory is better for the Nilsson model than for other models.iHowcver, in some cases, transition rates ~ u n o t be'expl~ned by the Nflsson model. The E2 enhancement o f 137 for the 3OkeV
149pm MAGNETIC
509
MOMENTS
transition from the 270 keV ~- state to the 240 keV -~-- state is in contradiction with the assignment of [523] and [505] to these states, and the E2 enhancement of 96 for the 74 keV transition from the 189 keV ½+ state to the 114 keV ~+ state can also not be explained by the [411] or [422] configuration for the 189 keV level and the [402] for the 114 keV level. Such strong enhancements indicate the collective character, especially a rotational one, for these excited states. Nevertheless, because of a spin relation these g2+ and ~- states cannot be regarded as rotational states built on the 114 keV ~+ and 240 keV ~ - - states respectively. On the other hand, the I.C. model may explain the above enhancements, but may not reproduce small energy differences of 30 and 74 keV between the ~r- and ~ states and the ~+ and ~+ states, respectively. If one adopts an extraordinary small phonon energy, < 100 keV, this difficulty may disappear, but such a small phonon energy is not reasonable for the vibrational states. Seaman et al. la) investigated doubly even Sm nuclei in this transition region and found the vibrational character for the Sm nuclei with up to 88 neutrons. The phonon energy of lso~_62,,~.asis about 330 keV and is not smaller than I00 keV. Meanwhile, for the nuclei with N = 88, Kumar and Baranger 19) gave from their theoretical calculations static deformations of fls = 0.184 and 0.196 for 14aNd and 150Sm ' respectively. These situations indicate a complicated character in the structure of the 149pm nucleus. In conclusion it may be said that no overall agreement between the theories and experimental results has been obtained as yet, and further studies both in experiments and theories are expected. The authors are grateful to Mr. T. Takeuchi for his help in the I.C. calculations. Thanks are also due to Mr. Y. Nakano for his cooperation in the measurements.
Appendix 1 The time dependent attenuation factor Gk(t) is given as
Gk = exp (--2k t),
(A.1)
where 2~ is the relaxation constant, which has different forms in accordance with the types of perturbations. In the case of a perturbation due to an electric quadrupole interaction, the relaxation constant takes the form
3 ~
k(k+l)[4I(I+l)-k(k+l)-l]
2kE -- 80 h 2 (eQ)2V~*
12(21-1) 2
(A.2) '
where Q and I are the quadrupole moment and the spin of the intermediate state, respectively. Other parameters, independent of the properties of the excited states, are described in ref. 13). In the case of a magnetic dipole interaction ;tkM is given as
2~ = ½z~o~2k(k+ 1)S(S+ 1),
(A.3)
510
T. SEO et aL
where the parameter dependent on the intermediate state is only ogs, whose value is proportional to the gyromagnetic ratio g of the state. Thus, leaving only the parameters Q, g and L one obtains the 2~ and 12M as 2~ = AEQ 2 !41(1+ 1 ) - 7 } 12(21-1) 2 ,Z~ = A"O 2.
(A.4) (A.5)
The time-integrated attenuation coefficient, G2 is given by using the total relaxation constant,
t2 = ~.~ + 3-~
(A.6)
as
1
G2 - - - ,
(A.7)
1+12"C
where z is the lifetime of the intermediate state. By putting the experimental values of -i, g, G 2 and z for the 114 and the 270 keV states into the above formulae, the following linear equations were obtained: 28.0 Q~14Ae+63.0 A u = 3.82,
(A.8)
12.7 Q~vo AE + 108 A M = 7.50,
(A.9)
where 1114 = ~:,/27o = ~, g l , 4 = 0.79, gZTO = 1.04, G2,,,4 = 0.88, G2.270 = 0.78, q , 4 = 3.64(ns) and zz7o = 3.74(ns) were used. It has been reported 20) by one of the present authors that the magnetic dipole interaction is predominant in the case of rare earth elements. If this is the case for the Pm element, too, the two A M values obtained from the above two equations with neglect of the A ~ terms must agree with each other. The obtained values are A M = 0.061+0.018 and 0.070_+0.008 for the 114 and 270 keV states, respectively, and are in agreement with each other within the experimental errors. A weighted mean of the two values gives A M = 0.067+0.008. By using this value, together with the measured mean-life and precession angle for the 189 keV state, the G2 value for this state was obtained as G2 = 0.62-+0.12. As to the G4 for the 270 keV state, G4 = 0.52-1-0.03 was obtained by using the measured Gz and the relation M M 10 (A.10) 14/2z 3
Appendix 2 In the intermediate coupling calculation the Hamiltonian can be written as H = Hs+Hp+Hint,
where Hs is the Hamiltonian for the vibrations of the core, Hp that for the odd nu-
149Pro MAGNETIC MOMENTS
511
cleon and Hin t that due to the coupling. The Hamiltonians Hs and Hint are written explicitly as
(nla2~12+Cl~2.12),
n~ = ½~ Hint
----
- -
k ~ ~2~ Y2~(O, q~).
The basic functions chosen are the eigenvectors of the Hamiltonian for the uncoupled system
[j, NR, I M ) = ~ (jRmm'IjRIM)Ijm)INRm'), sin' where (Us + np)lj, NR, I M ) = (E(j) + Nho~)lj, NR, IM). Here, j is the angular momentum of the odd nucleon with the z-component m, N is the number of phonons and R is their angular momentum with the z-component m'. The total angular momentum of the nucleus and its z-component are I = j + R and M = m+m', respectively. The non-diagonal matrix elements of H i n t a r e dependent on the coupling parameter,
= kx/5/2rchogC. The eigenvectors of the coupled system are obtained by diagonalizing the matrix of H i n t and can be expanded with the coefficients A(jNRIIE) as [E; I M ) = ~.. A(jNRIIE)Ij, NR, IM).
jNR
The corresponding expression for the magnetic dipole moment is
~l(E'~ I) = "N __ -I-'~i
×
~ ~ A(jNRIIE)A(j'N'R'IIE) jNR j'N'R"
jj'
JR(R+ 1)(2R + 1)W(RRII ; l j)
+ g,( _)R-,+~+ j+ ~'- ,CSNN' fi~R'6,,. X/(2j + 1)(2j'+ 1)x/l(/+ 1)(21 + 1) × W(jj'I1; 1R)W(lljj'; 1½)+ g~( __)Z+½+R-,cSNN"~Rg' 6,r x x/~x/(2j + 1)(2j'+ 1)Wfjj'II; 1R)Wfjj'½½; ll)}, where gR, gi and gs refer respectively to the g-factor of the core, orbital and intrinsic spin of the particle. The parameters used here are the same as the ones by Heyde and Brussaard; ~ = 4.0, ho~ = 220 keV and E ( d ~ ) - E ( ~ ) = 108 keV. For the odd parity state the energy of the h÷ single-particle state E(h~) was adjusted to give the best fit with observed ~ - - state, but the expansion coefficients were quite independent of this value. The expansion coefficients obtained are shown in table A. 1.
T. 5EO et al.
512
TABLE A. 1 Expansion coefficients corresponding to state IE(koV); I~) of t'gPm
1270; ~- ~ ]IjNR) A(jNRIIE) h~O0 0.00000 h-~12 0.73366 hJ~20 0.00000 h-~22 --0.55179 h~24 --0.27204 h Jtt30 0.00000 h~32 0.11907 h-~I-33 --0.23652 h-~34 0.10488 h-~36 0.04631
1189; ~ + (I))
]IjNR~ A(jNRIIE) g,]O0
0.00000
g~12 0.74239 g~20 0.00000 g~22 --0.56974 g~24 --0.14517 g~30 0.00000 g~32 0.12637 g½33 --0.17466 g½34 0.07495 g7~36 0.00000 dtO0 0.00000
d~12
0.14993
d~20 0.00000 dt22 --0.13221 dt24 --0.06789 d~30 0.00000 dQ32 0.03335 d~33 --0.06032 dt34 0.04209 dt36 0.00000
I189; t + (II)
IIjNR) A(jNRIIE) g]O0
0.00000
g]12 --0.07457 g[20 0.00000 g~-22 0.02148 g]24 0.47901 g.~30 0.00000 g[32 --0.00198 g7~33 0.I 7055 g~34 --0.22214 g,]-36 0.00000 cliO0 0.00000
d~12
0.64592
d~20 0.00000 dt22 --0.39837 d~24 --0.21452 dt30 0.00000 d~-32 0.07919 di33 --0.22595 dj34 0.08265 d~36 0.00000
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)
W. C. Rutledge, J. M. Cork and S. B. Burson, Phys. Rev. 86 (1952) 775 K. P. Gopinathan and IvL C. Joshi, Phys. Rev. 134 (1964) B297 W. M. Currie and P. W. Dougan, Nucl. Phys. 61 (1965) 561 E. B. Nieschmidt, V. R. Potnis, L. D. Ellsworth and C. E. Mandeville, Nucl. Phys. 72 (1965) 236 R. G. Helmer and L. D. McIssac, Phys. Rev. 143 (1966) 923 K. P. Gopinathan, Phys. Rev. 141 (1966) 1185 A. Backlin, S. (3. Malmskog and H. Solhed, Ark. Fys. 34 (1967) 495 A. (3. Svensson, L. BostrGm and M. C. Joshi, Nucl. Phys. 89 (1966) 348 P. N. Tandon and H. G. Devare, Ind. L Pure Appl. Phys. 7 (1969) 1 R. B. Begzhanov, Dzh. Gaffarov and K. T. Salikbaev, JETP Lett. (Soy. Phys.) 9 (1969) 246 L. S. Kisslinger and R. A. Sorensen, Key. Mod. Phys. 35 (1963) 853 A. Y. Cabezas, I. Lindgren and R. Marrus, Phys. Rev. 122 (1961) 1796 Perturbed angular correlations, ed. E. Karlsson, E. Matthias and K. Siegbahn (North-Holland, Amsterdam, 1964) D. B. Fossan, L. F. Chase, Jr. and K. L. Coop, Phys. Rev. 140 (1965) R. W. Grant and D. A. Shirley, Phys. Rev. 130 (1963) If00 Bl D. C. Choudhury and T. F. O'Dwyer, Nucl. Phys. A93 (1967) 300 K. Heyde and P. J. Brussaard, Nucl. Phys. A104 (1967) 81 G. G. Seaman, J. S. Greenberg, D. A. Bromley and F. K. McGowan, Phys. Rev. 149 (1966) 925 K. Kumar and M. Baranger, Nucl. Phys. A l l 0 (1968) 529 Y. Kawase and T. Hayashi, Ann. Repts. of Res. Reactor Inst. Kyoto Univ. 2 (1969) 1
Nuclear Physics A159 (1970) 494--512; (~) North-HollandPublishint7 Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
T H E M A G N E T I C M O M E N T S O F T H R E E E X C I T E D S T A T E S I N 149Pro T. SEO and T, HAYASHI Research Reactor Institute, Kyoto University, Kumatori-cho, Osaka, Japan and A. AOKI Department of Physics, Kyoto Prefectural University, Kyoto, Japan Received 4 August 1970
Abstract: The magnetic moments of three excited states in 149Pm were determined through the measurements of g-factors of the corresponding states by the perturbed Y3' angular correlation method using a Ge(Li) detector and an NaI(TI) scintillation counter. The results obtained are # = 2.0+0.2, 2.2+0.6 and 3.6-4-0.2 n.m. for the 114, 189 and 270 keV states, respectively. The experimental values are discussed in comparison with contemporary models of the nucleus.
E
RADIOACTIVITY 149Nd [from 14aNd(n,7,)]; measured yy(O), y~,(O,t), y~,(O,H), 7'ce-delay. 149prodeduced levels, J, muitipolarities, mixing ratios, T,!,,9, #. Enriched target, Ge(Li) detector.
[
I
1. Introduction The nucleus 149pm with 88 neutrons lies in the so-called transition region where a sudden change in the nuclear shape is generally known and, therefore, considerable interest has been shown in the study of the structure of this nucleus. The first study of this nucleus was made by Rutledge et al. 1) in 1952. About ten years later, Gopinathan and Joshi 2) established a number of levels with scintillation coincidence techiniques and fl-ray measurements. Further work with the delayed coincidence technique by Currie and Dougan 3) has revealed three levels having lifetimes of several nanoseconds. A study with a Ge(Li) detector of the y-rays of this nucleus was made by Nieschmidt et al. 4), and in 1966 Helmer and Mclssac 5) measured the y-rays and fl-rays in detail and established a large number of new levels. Angular correlation measurements with NaI(TI) detectors were made by Gopinathan 6), and the spins of several levels and the multipolarities of many transitions were elucidated. In the following year, B~icklin et al. 7) published an extensive study on transitions, lifetimes and levels in this nucleus. As for the measurements of the magnetic moments of excited states, Svensson et al. 8) studied the magnetic moment of the 114 keV level and Tandon and Devare 9) also published their result on the same level. The first measurement of the 270 keV 494
149pm MAGNETIC MOMENW$
495
level was reported recently by Begzhanov et al. 10). However, there remains some doubt as to their application of the Kisslinger and Sorenson theory 11) to the experimental results. The value for the 189 keV level is to be newly Presented by the present authors. In this work a Ge(Li) detector was used for the measurements of the magnetic moments with the angular correlation technique. The use of the Ge(Li) detector made it possible to distinguish many ?-rays from others, and then to perform angular correlation measurements on several new cascades. Thus the measurements of the magnetic moments of three (the 114, 189 and 270 keV) excited states were accomplished without the ambiguity accompanied with the use of NaI(TI) detectors.
2. Source preparation Sources of 149Nd were prepared by irradiating enriched (93.3 ~ ) t4SNd in the form of Nd2 0 3 for 30 min each in a flux density of 2.34 x 1013 neutrons/era 2 • see in the pneumatic tube irradiation facility of the Kyoto University reactor. The irradiated sources for the angular correlation measurements were dissolved in dilute hydrochloric acid and the solution was then transferred to a cylindrical source container of acril resin, 2 mm in diameter and 4 mm in depth. Dry sources on aluminium coated taylor films were used for the detection of conversion electrons. The undesired impurities o f short-lived activities such as those of i s iNd were allowed to decay for about an hour before the measurements were started. The measurements for each source were stopped 6 h after the irradiation to avoid interference from 54 h 149pm.
3. Angular correlation measurements 3.1. APPARATUS Singles spectra of ?-rays were measured with an O R T E C 22 cm 3 Ge(Li) detector and coincidence spectra gated by the pulses from a 7.62 cm ~ x 7.62 cm NaI(TI) detector were also taken in some cases. Through these measurements the decay scheme of 149Nd reported by other authors s, 7) was confirmed. The decay scheme is shown in fig. 1. The angular correlations were measured with a fast-slow coincidence system having a resolving time of 2~ = 100 ns. An RCA 8054 photomultiplier mounted with the 7.62 cm ~ x 7.62 cm NaI(TI) crystal and the 22 cm 3 Ge(Li) detector were used as detectors. The measurements were made at four angles (90 °, 120°, 150 ° and 180°) by obtaining coincidence spectra of the Ge(Li) detector on each quarter division of the display of a 400-channel pulse-height analyser. A block diagram of the coincidence system is shown in fig. 2. 3.2. MEASUREMENTS AND RESULTS For the cascades involving the 114 keV ?-ray, measurements on the 541-114, 424-114 and 156-114 keV cascades were made by taking the coincidence spectra
T. SEO et al.
496
E
5/2
(keY)
7-,_ 2
-
149 r~l r,I 60 ~ " ~ 8 9
1.78 h
gg~
"'~ (7/2)-
655
Od f~ f¢l ~r
5.,'2-
~
538
(.=/2)+
388
o O ~
7/2-
°
~r
1112-
=
~
11
270 240
2.55 ns
189
3.24 ns
114
2.54 ns
7/2 +
54 h
149 ,-,, 611-'m88
Fig. 1. Level scheme of l"gPm based on Blcklin et aL 7). The half-lives of excited states are those determined in the present work.
SOURCE
~MSTOR
*
I L,NEAR AMP.I
ITiME PICK OFF I t LINEAR AMR I ITIME
PICK OFF CONTROL I
I SINGLE CHANNEL ANALYSERI ISPECTRUM STABILIZER I
DELAY AMP. J
I FAST COINCIDENCE I LINEAR
GATE I '=
1 400 ch. P.H.A. 1 IO0 ch. X 4 q
Jl
I TELETYPECONTROLLERl
I
I
1
"I GONIOMETERCONTROLLER. ~
I
Fig. 2. Block diagram of the angular correlation measurements with the Ge-NaI system.
149Pro MAGNETIC MOMENTS
497
gated by the pulses from the NaI(TI) detector for the 114 keV y-ray. The data were analysed by a least-squares fitting method. The angular correlation coefficients obtained were corrected for attenuations due to the finite size of the detectors and the time-dependent perturbation. The attenuation factors for the time-dependent perturbation are described in the next section. The same procedure and corrections were applied to all the data for the other cascades. Since the quadrupole content of the 114 keV transition was found to be.very small ( 2 . 8 -+0 t..62 X 10 -2) [ref. 7)], the P4 term was neglected when the data for the three cascades were analysed. The obtained A2 coefficients are shown in table 1. The coefficient for the 541-114 keV cascade agrees with the values of other authors 6,s,,o) within experimental errors. Our A2 coefficient for the 424-114 keV cascade is in agreement with those of other authors s,1 o) within experimental errors and also is in good agreement with the value obtained in our time-differential angular correlation measurement described in sect. 4 (see table 3). In the measurement of the 156-114 keV cascade, the Compton part of the 268 keV y-rays which entered into the 114 keV gate introduced interference from the 268-156 keV cascade. The value corrected for this effect is presented in table I. TABLE 1 Results of the angular correlation measurements Cascade (keV) 541-114 424-114 156-114 199- 74 268-156 268-270
Present results A2 0.040-60.007 --0.140-60.008 0.050-60.006 0.095-60.022 ") 0.173-60.012 --0.315-60.011
--0.089-60.022 ")
A2G2
A,G,
0.0424-0.006 --0.102-60.006 0.074-60.026
--0.009-60.010 --0.027-60.010 0.026-1-0.040
--0.227-60.008
0.013-60.013
Ref. 8)
Cascade (keV)
541-114 424-114 156-114 199- 74 268-156 268-270
A4
Ref. e)
A2
Ref. ' o) A,
A2
A4
0.027=1=0.011 --0.131 =1=0.023
0.047=t=0.009 --0.127=1=0.011
0.007+0.008 0.008=[=0.010
--0.220-60.020
--0.142=[=0.009 --0.218-60.012
0.020-/-0.011 0.012-60.012
=) See appendix 1.
Measurement of the 199-74 keV cascade was impossible without the use of an NaI-Ge system, but even with this system the measurement for this cascade was cliffcult due to admixtures of large amounts of the Compton tails of higher energy y-rays.
498
T. S£O et al.
As the spin of the intermediate state of this cascade had been determined to be ½ by B~icklin et al~ 7), the analysis was carried out without the P4 term. The result is listed in table 1. For the cascades involving the 268 keV transition, the 268-156 and 268-270 keV cascades were measured in the same runs, gated at about 268-270 keV by the pulses from the NaI(TI) detector. As the 156 keV transition is almost pure E1 [ref. v)], the data for the 268-156 keV cascade were analysed with terms up to P2. Our Az coefficient corrected for the attenuations is shown in table 1. Recently, Begzhanov et al. 1 o) measured the angular correlation coefficients for this cascade. Their coefficients are different from the present value. For the 268-270 keV cascade, the present result gives the A2 coefficient of - 0 . 3 1 5 _ 0.011 which is about 40 % as large as the values by other authors. No decisive reason has been found for this discrepancy. As shown in sect. 4, the present result of the timedifferential angular correlation measurement for this cascade gives the A2 coefficient of -0.347___ 0.024, which is in good agreement with our value described above. 3.3. SPINS A N D MULTIPOLARITIES
The spin of the ground state of 149pm was determined to be -Tzby Cabezas et al. x 2). According to the shell model, the l~roton states which are expected to occur in this mass region are gt and d{. Therefore, it is natural to assign ~ and k to the 114 keV and the ground states, respectively. In the analysis of the present data for the angular correlation measurements the spins and multipolarities as assigned by B/icklin et al. v), were referred to for decisions. Our results are generally consistent with those of B/icklin et al. 7) within experimental errors. These are listed in table 2. TABLE 2 Spins and multipolarities obtained from the analysis of the present data Energy level (keV)
Gamma ray (keV)
Measured cascade (keV)
Spin
Quadrupole content
(%)
Sign of
655
541
541-114
(-])
0.(g-0.1
(M2)
538
424 268
424-114 / 268-270 [ 268-156
]
0.1 ") 3.0-3.7
(M2) (E2)
---
388
199
199- 74
3.1-4.5
(E2)
-l-
270
270 156
268-270 268-156
~
0.3 ~) 0.07 °)
(M2) (M2)
+ q- or --
189
74
199- 74
~ a)
26 - 39 a) (E2)
+
114
541-114 ~ 424-114 156-114
~]
2.2-3.0
-I-
114
a) Ref. 7).
(½) ")
(E2)
-
-
499
149Pro MAGNETIC MOMENTS
4. Time-differential angular correlation and lifetime measurements
It is necessary to know the attenuation factors G2 of the angular correlation functions and the lifetimes of the intermediate states whose magnetic moments are to be determined. The measurements of the attenuation factors G2 for the cascade involving the 114 and 270 keV levels were performed by the time-differential angular correlation method. The detectors consisted of two 4.45 cm ~ x 5.08 cm NaI(TI) crystals mounted on Philips XP1021 photomultipliers. They were connected to a time-analysing system consisting of an ORTEC 437 time-to-pulse-height converter and the 400-channel pulse-height analyser. As the coefficient A4 could be omitted in the case of the 424--114 keV cascade, it was sufficient to measure the correlations at the angles 90 ° and 180°. The experimental data were analysed by the following procedure. The time-differential angular correlation function is expressed as
W(O, t) = Ne-'/'(l+A2e-Z"P2(cos 0)}
for t > O,
where • and 3.2 are the lifetime and the spin relaxation constant of the intermediate state, respectively. However, because of the finite time resolution of the detecting system, the function experimentally obtained should be W'(O, t) instead of the original function W(O, t). Here, W'(O, t) is given as
W'(O, t) =
P(t-t')W(O, t')dt',
where P(t) is the normalized prompt curve function. The experimental data were taken at 90 ° and 180 °, so that W'(O, t) is expressed as
iooP(t-t')e-"/'(1-½A2e-~")dt
',
w ' 0 8 o °, t) = N fo oP(t-C)e-"/'(l+A~e-"2")dt
".
W'(90 °,
Since the functions,
t) = N
Fl(t) and Fz(t) defined as
Fl(t) - ~{2w'(90 °, t) + w ' 0 8 0 °, t)} = N F2(t) - ~{w'(18o °, 0 - w ' ( 9 o
°, t)} = SA~
P ( t - t')e-"l"dC,
Io e(t-C)e-~"2÷"~"dC,
have the similar form, they can be analysed with the same computer program for the least-squares fitting. The function P(t) was assumed to be Gaussian. The best-fit Ft(t ) and F2(t ) curves for the 424--114 keY cascades are shown in fig. 3(a) with the experimental data. The parameters A2, • and 3.2 + 1/z were determined by this proce-
T. s~o et aL
500
r.l) I-Z
0 0
U
~
IU
I~
~
~
~
rl$
Fig. 3a, b. Results of the time-differentialangular correlation measurements (a) for the 424-114 keV cascade and (b) for the 268-270 keV cascade. Detailed description for Ft(t) and F2(t) is given in the text. dure. The attenuation factor G2 was obtained by taking the ratio of slopes of the two curves Fx(t ) and Fz(t) as follows t3), 1/~
1 --
A2 + l/'c
_
_
~
G2
o
1 +A2"C
In the case of the 268-270 keV cascade, the two y-rays could not be separated, therefore the function W(O, t) changed into the form
W(O, t) =
Ne-Itl/t{l + a 2
e-~tzlP2(cos 0)},
was used for the least-squares fitting. In this formula the P4 term is omitted, because this term is small compared with the P2 term as seen in table 1. The best-fit curves thus obtained are shown in fig. 3b. It was impossible to apply the time-differential angular correlation technique for the 199-74 keV cascade involving the 189 keV state because of the difficulty in sep-
149pro MAGNETIC MOMENTS
501
10"
03 I---
z o
-40
- 3 5 - 3 0 -25 -20 -15 -I0
-5
0
5
10
15
20
25
30
35
ns
Fig. 3b
arating the 199 and 74 keV ?-rays from other ones having similar energies. Therefore, the 6/2 for this cascade was obtained from a calculation by using the attenuation factors for the aforementioned two levels on an assumption that the perturbation was mainly due to a time-dependent magnetic dipole interaction. A detailed description on this assumption is given in appendix 1. The lifetime of the 189 keV level was measured by taking a delayed coincidence curve between the 349 keV ?-rays and the Kconversion electrons emitted in the 74 keV transition. The ?-rays and the electrons were detected with the 4.45 cm ~ x 5.08 cm NaI(T1) crystal and a 3 cm ~ x 0.2 mm plastic scintillator, respectively, both coupled to Philips XP1021 photomultipliers. The measured curve is given in fig. 4.
502
T. SEO et aL i0~
I0'
(I) I--
o
4
++
,02
I0'
,I.,,,I I,,..I,.++1,,,,I,~ 0
5
I0
15
20
25
50
ns
Fig. 4. Results of the delayed coincidence measurement for the 349-74 keV cascade. Measurement w a s made by detecting the 349 keV y-rays and the 74 K conversion electrons.
The results of these measurements are summarized in table 3. 5. Measurements of the magnetic moments of the 114, 189 and 270 keV levels
The g-factors of the three excited states were measured by observing the rotations and the attenuations of the angular correlation patterns in an external magnetic field o f H = 15900 G. The perturbed angular correlation function, FF(O, B ) in the integral form is given as
3cos2(O-AO) I W(O, B) = 1 +¼A2 G2 1 + [1+(2toTG2)2]+) ' where
AO =- ½ arctg (2co~G2), co -- - glen B = #H.
B/h,
t49pm MAGNETICMOMENTS
503
TABLE 3 Results of the time-differential angular correlation and the lifetime measurements Level (keV)
Measured cascade (keV)
G2
A2
424--114
2.544-0.07 2.524-0.04 a) 2.624-0.10 b) 2.4 4-0.2 c) 2.584-0.07 d) 2.524-0.12 c) 2.424-0.09 r)
0.878 ::t:0.031
--0.1424-0.008
268--270
2.554-0.07 2.58 4-0.04 ") 2.7 4-0.2 b) 2.6 4-0.2 c) 2.644-0.07 a)
0.781 +0.018
--0.3474-0.024
349-- 74(K)
3.244-0.07 3.464-0.14 a) 3.244-0.10 a)
0.62 4-0.12 B)
114
270
189
Half-life (ns)
") Ref. a). b) Ref. t4). c) Ref. e). d) Ref. e). e) Ref. a). t) Ref. a). a) The value calculated by using the G2 values of the other two levels (see appendix 1).
In the above equations g and fl are the gyromagnetic ratio of the intermediate state and the paramagnetic correction factor, respectively. The electromagnet was specially designed for the Ge-NaI angular correlation measurements. An improvement was made to reduce the stray magnetic field by covering the coils of the magnet with thin iron plates. Thus, the light-pipe which coupled the crystal to the photomultiplier could bz saved and the deterioration of the energy resolution of the NaI(T1) detector caused by the use of the light-pipe was avoided. The detectors and the electronic circuits used are the same as those described in subsect. 3.1. The measurements on the 541-114, 424-114, 199-74, 268-156 and 268-270 keV cascades were made at four angles 90 °, 120°, 150 ° and 180 °, and for the two cases of the magnetic field up and down. A few examples of the angular correlation patterns obtained in these measurements are shown in fig. 5a-c. The results are listed in table 4. The paramagnetic correction factor was taken 13) to be fl = 1.93 at room temperature. The magnetic moments were calculated by using the spins and the g-factors of the corresponding states. The results are summarized and compared with the values by other authors in table 5. The present result for the 114 keV state is rather small compared to the values of other authors 8-1 o), although the differences are within experimental errors. The value for the 189 keV level was measured for the first time by the present authors. The experiment for this level was done through 48 runs, where one
T. SEO et aL
504
•!
H=OG
~'f
,.oo,
t.OOL ,
, H= ± 15900G
t
0.95
0.90~
0.85
[
,
90 °
,
120=
150 °
1
180"
90*
e (degrees)
120 °
150"
180"
E) (degrees)
Fig. 5a-c. Results of the angular correlation measurements with and without the magnetic field. The solid lines are obtained by least-squares fit.to both of the experimental data with a common parameter A2. The angular correlation functions W(O) and W(O, B) are normalized at the points of 90* and 90°+/10, respectively. (a) the 424-I 14 keV cascade, (b) the 199-74 keV cascade, (c) the 268-270 keV cascade.
03 .(D
=
(1) v
H= +_15900 G
v
1.05
1.05
I:00
I.OC
t 90*
I
t
120* 0
150°
I 180*
90*
(degrees)
120*
I 150*
I 180 °
(9 ( d e g r e e s ) Fig. 5b.
run took about 5 h, and about 35000 counts were taken at each angle for the two directions of the magnetic field. The magnetic moment for the 270 keV state was measured by using the 268-156 and 268-270 keV cascades. F o r the 268-270 keV
505
149pm MAGNETIC MOMENTS
(D
I00
0.90
~
=OG
ioo
0.90
~,
0.80
~0
0801
i I
0.70
I
!
90*
120°
I
150°
I
I
180"
90*
(9 ( d e g r e e s )
i
120°
I
150°
i
I
180"
e (degrees)
Fig. 5c. TABLE 4 Results of the angular correlation measurements in the external magnetic field Level (keV)
Measured cascade (keV)
Gz coz
r ")
g-factor
114
541-114 424-114
0.37+0.03 0.39 4-0.14
3.644-0.04
0.79+0.07 0.83 4-0.30 weighted mean 0.794-0.08
189
199- 74
0.744-0.16
4.864-0.09
1.484-0.40
270
268-156 268-270
0.42 4-0.06 0.464-0.02
3.74 4-0.06
0.98 4-0.14 1.074-0.07 weighted mean 1.044-0.07
• ) The mean lives taken from the weighted mean values over all the measured values listed in table 3.
cascade, the m a g n e t i c m o m e n t was o b t a i n e d only by the m e a s u r e m e n t s of a change o f the a t t e n u a t i o n o f the a n g u l a r correlation p a t t e r n in the magnetic field because of the difficulty i n separating the two 7-rays from each other. The values o b t a i n e d for the two cascades show good a g r e e m e n t as seen i n table 4. The magnetic m o m e n t o f this state was measured by Begzhanov et al. lo), recently, using the 268-156 keV cascade. T h e i r result is c o n s i d e r a b l y different from the present value.
506
T. sEo
et al.
6. Discussion 6.1. T H E G R O U N D
AND
114 keV STATES
The intermediate coupling (I.C.) theory is most widely used and has been quite successful for describing several properties of the nuclei belonging to the so-called vibrational region. As for the magnetic moments, Choudhury and O'Dwyer 16) made the I.C. calculation for this nucleus taking into account the gt and d~ single proton states and the core states up to three phonons, and obtained the magnetic moments of 1.75 and 3.91 n.m. for the ~ and ~ states, respectively, when gs = 5.58 was used for a free proton. In a similar calculation, Heyde and Brussaard 17) got 2.79 and 2.96 n.m. for the ground and first excited states, respectively, by using gs = 2.62, the most favourable effective value in this region according to them. However, their value for the 114 keV state is, as seen in table 5, a little higher than the experimental values including the present work. Kisslinger and Sorensen it) in their calculation based on a pairing-plus-quadrupole model obtained 2.06 and 2.55 n.m. for the ~ and ~ states, respectively. For the ground state the value of Kisslinger and Sorensen is far from the experimental value z 5), but for the first excited state it agrees with the values by two authors s, 9), though it is somewhat larger than our value. TABLE 5 Magnetic m o m e n t s of the ground and three excited states in ~49Pm Level
1n
(keV)
p.p (n.m.)
tttheor(n.m.) e) KS gs= 5.58
I.C. gs = 5.58
Nilsson
gs =
gs=
2.62
state
5.58
gs =
2.62
0
t+
3.3 -t-0.5 °)
2.06 t)
1.78 *)
2.79')
[404]
1.66
2.56
114
~+
2.0 4-0.2 2.4 4-0.3 b) 2.554-0.3 c) 2.204-0.20 e)
2.55 f)
4.05 ,)
2.96 s)
[402] [413]
3.71 1.17
2.69 1.76
189
OZ+
2.2 4-0.6
0.89 h) 1.65 ~)
1.66 h) 1.25 ~)
[411] [422]
1.92 0.69
1.44 0.99
270
~--
3.6 4-0.2 2.174-0.21 e)
6.53
5.06
[523]
4.16
3.44
") Ref. *s). t) Ref. 11).
b) Ref. s). s) Ref. 17).
c) Ref. 9). d) Ref. lo). c) Values for glt = h) t + ( l ) state. ~) ~+(II) state.
Z/A.
Meanwhile, provided this nucleus has a small deformation, the ground ~+ and the first excited ~r+ states are considered to be the [404] and [402] Nilsson states, respectively. The magnetic moments calculated from the Nilsson model are also listed in table 5. For the [404] and [402] states the calculated values with Os = 2.62 show a better agreement than with gs = 5.58. For the first excited ~+ state the [413] configuration seems to be more favourable for the present work than the [402] configura-
14"9pro MAGNETIC MOMENTS
507
tion, but the strong M1 hindrance in the 114 keV transition cannot be explained by the [413] first excited and the [404] ground states. 6.2. THE 189 keV STATE No single proton state of ½+ is expected near the 189 keV, so that this state may be the phonon state built on the gt or d~ particle states. The 189 keV E2 transition to the ground state is enhanced by a factor of 2.9 compared with the single-particl~ estimate, while the E2 enhancement and the M 1 retardation in the 74 keV transition to the first excited ~+ state are 96 and 540, respectively 7). This indicates that the 189 keV state is mainly composed of one phonon and the d~ proton state. But according to our I.C. calcu.lation with the same parameters as adopted by Heyde and Brussaard 17), this ½ state should be mainly composed of one phonon coupled with the gt state and not with the d~ state. Moreover, from the same calculation the level mainly composed of one phonon and the d~ state should be located in an energy region about twice as high as the first ½+ state. The magnetic moments for both the first ½+(I) and the second ½+(II) states were also calculated by the present authors (see appendix 2), and the results are listed in table 5. As the experimental value has a large error due to an indirect estimation of the G2 value, a comparison with the I.C. values would not give any decisive information. However, the value for the ½+(I) state may be more favourable for the 189 keV level because it agrees with our experimental value. On the other hand, if this level corresponds to a single-particle state in a softly deformed potential, possible states should be the [411 ] or [422] states. As for the magnetic moment, the [411 ] state is more suitable. However, the [411] state lies below the [404] ground state for a prolate deformation. This difficulty may be removed when the 189 keV state is the hole state of the [411 ] Nilsson state. 6.3. THE 270 keV STATE According to the shell model, no ½ proton state with negative parity is found in this mass region. The E2 transition from the 270 keV 3- state to the 240 keV ~ - state is enhanced by a factor of about 137 [ref. 7)] compared with the single-particle estimate. This suggests that the 270 keV 3- state is a phonon state built on the h÷ state. The I.C. calculations involving three phonons and the h,~ state were newly performed by us (see appendix 2). The result is shown in fig. 6. As is seen in fig. 6, a 7zstate appears above the ~ - - states and the energy difference between the two states is approximately equal to the energy of one phonon, namely 220 keV. Nevertheless the observed energy difference is 30 keV and such a small value cannot be reproduced by the I.C. model with one phonon energy of 220 keV and a reasonable value of the coupling constant. Therefore, it is hard to assign the 270 keV state to this 3- state. As for the magnetic moment of this state, the present calculation gives 5.06 n.m. for gs = 2.62, which is considerably larger than the value obtained in the present experiment. Meanwhile, a possible state in the Nilsson model may be the 3-[523] state. The
$08
T. see
900
e t a~.
,49 Pr'd
80C
tl
+
7OC (7.,';2) .-:.
:5,~÷
6oE
s/2+~"
rvZ-
•7/2; ,
"
11/2 -
.5t2+ I/2 ~7/~' + -5/2 +
C9 0:: -U.I Z
40C
( i,.'2 ) ÷
3/2+ ?'PZ--s
3oc 2OC
712 I1~" S/2.1312+
.. ~r/Z + "llf~-11/2+ 3/2+ 9/2 +
I0C
5/2÷,
7/2+
....
exp.
772÷
theory
Fig. 6. Comparison of the experimental and the theoretical ievel scheme of ~'gPm. Negative parity states in the theory are those cal~tlated by the present autliors. The theoretical positive parity states are those by Heyde and Brussaard 17).
m.sgnetic moment for this state was calculated to be 3,44 n.m. for g. -- 2,62. As is seen in table 5, theagreement between the experimental and theoretical values is quite good, However, there exists some difficultT in this case, too. The ~ - [532] state which should exist below the ~ : state has not been observed and the level sequence of the - "and~ ' ~ states is reversed as compared with the one predicted by the Nilsson model for a po~five deformation. Begzlumov et a/. d e s ~ b e d in their paper i o) that their value was in good agreement with the prediction by Kisslinger and Sorensen Zl). However, the theoretical val~e ~ e y referred to was the one not for the 5" state but for the ground gt + state. '
6.,4. £~NCLUSION
• ~ s fo~.themagneticmon~ent, an agreement between ©xperiment and theory is better for the Nilsson model than for other models.iHowcver, in some cases, transition rates ~ u n o t be'expl~ned by the Nflsson model. The E2 enhancement o f 137 for the 3OkeV
149pm MAGNETIC
509
MOMENTS
transition from the 270 keV ~- state to the 240 keV -~-- state is in contradiction with the assignment of [523] and [505] to these states, and the E2 enhancement of 96 for the 74 keV transition from the 189 keV ½+ state to the 114 keV ~+ state can also not be explained by the [411] or [422] configuration for the 189 keV level and the [402] for the 114 keV level. Such strong enhancements indicate the collective character, especially a rotational one, for these excited states. Nevertheless, because of a spin relation these g2+ and ~- states cannot be regarded as rotational states built on the 114 keV ~+ and 240 keV ~ - - states respectively. On the other hand, the I.C. model may explain the above enhancements, but may not reproduce small energy differences of 30 and 74 keV between the ~r- and ~ states and the ~+ and ~+ states, respectively. If one adopts an extraordinary small phonon energy, < 100 keV, this difficulty may disappear, but such a small phonon energy is not reasonable for the vibrational states. Seaman et al. la) investigated doubly even Sm nuclei in this transition region and found the vibrational character for the Sm nuclei with up to 88 neutrons. The phonon energy of lso~_62,,~.asis about 330 keV and is not smaller than I00 keV. Meanwhile, for the nuclei with N = 88, Kumar and Baranger 19) gave from their theoretical calculations static deformations of fls = 0.184 and 0.196 for 14aNd and 150Sm ' respectively. These situations indicate a complicated character in the structure of the 149pm nucleus. In conclusion it may be said that no overall agreement between the theories and experimental results has been obtained as yet, and further studies both in experiments and theories are expected. The authors are grateful to Mr. T. Takeuchi for his help in the I.C. calculations. Thanks are also due to Mr. Y. Nakano for his cooperation in the measurements.
Appendix 1 The time dependent attenuation factor Gk(t) is given as
Gk = exp (--2k t),
(A.1)
where 2~ is the relaxation constant, which has different forms in accordance with the types of perturbations. In the case of a perturbation due to an electric quadrupole interaction, the relaxation constant takes the form
3 ~
k(k+l)[4I(I+l)-k(k+l)-l]
2kE -- 80 h 2 (eQ)2V~*
12(21-1) 2
(A.2) '
where Q and I are the quadrupole moment and the spin of the intermediate state, respectively. Other parameters, independent of the properties of the excited states, are described in ref. 13). In the case of a magnetic dipole interaction ;tkM is given as
2~ = ½z~o~2k(k+ 1)S(S+ 1),
(A.3)
510
T. SEO et aL
where the parameter dependent on the intermediate state is only ogs, whose value is proportional to the gyromagnetic ratio g of the state. Thus, leaving only the parameters Q, g and L one obtains the 2~ and 12M as 2~ = AEQ 2 !41(1+ 1 ) - 7 } 12(21-1) 2 ,Z~ = A"O 2.
(A.4) (A.5)
The time-integrated attenuation coefficient, G2 is given by using the total relaxation constant,
t2 = ~.~ + 3-~
(A.6)
as
1
G2 - - - ,
(A.7)
1+12"C
where z is the lifetime of the intermediate state. By putting the experimental values of -i, g, G 2 and z for the 114 and the 270 keV states into the above formulae, the following linear equations were obtained: 28.0 Q~14Ae+63.0 A u = 3.82,
(A.8)
12.7 Q~vo AE + 108 A M = 7.50,
(A.9)
where 1114 = ~:,/27o = ~, g l , 4 = 0.79, gZTO = 1.04, G2,,,4 = 0.88, G2.270 = 0.78, q , 4 = 3.64(ns) and zz7o = 3.74(ns) were used. It has been reported 20) by one of the present authors that the magnetic dipole interaction is predominant in the case of rare earth elements. If this is the case for the Pm element, too, the two A M values obtained from the above two equations with neglect of the A ~ terms must agree with each other. The obtained values are A M = 0.061+0.018 and 0.070_+0.008 for the 114 and 270 keV states, respectively, and are in agreement with each other within the experimental errors. A weighted mean of the two values gives A M = 0.067+0.008. By using this value, together with the measured mean-life and precession angle for the 189 keV state, the G2 value for this state was obtained as G2 = 0.62-+0.12. As to the G4 for the 270 keV state, G4 = 0.52-1-0.03 was obtained by using the measured Gz and the relation M M 10 (A.10) 14/2z 3
Appendix 2 In the intermediate coupling calculation the Hamiltonian can be written as H = Hs+Hp+Hint,
where Hs is the Hamiltonian for the vibrations of the core, Hp that for the odd nu-
149Pro MAGNETIC MOMENTS
511
cleon and Hin t that due to the coupling. The Hamiltonians Hs and Hint are written explicitly as
(nla2~12+Cl~2.12),
n~ = ½~ Hint
----
- -
k ~ ~2~ Y2~(O, q~).
The basic functions chosen are the eigenvectors of the Hamiltonian for the uncoupled system
[j, NR, I M ) = ~ (jRmm'IjRIM)Ijm)INRm'), sin' where (Us + np)lj, NR, I M ) = (E(j) + Nho~)lj, NR, IM). Here, j is the angular momentum of the odd nucleon with the z-component m, N is the number of phonons and R is their angular momentum with the z-component m'. The total angular momentum of the nucleus and its z-component are I = j + R and M = m+m', respectively. The non-diagonal matrix elements of H i n t a r e dependent on the coupling parameter,
= kx/5/2rchogC. The eigenvectors of the coupled system are obtained by diagonalizing the matrix of H i n t and can be expanded with the coefficients A(jNRIIE) as [E; I M ) = ~.. A(jNRIIE)Ij, NR, IM).
jNR
The corresponding expression for the magnetic dipole moment is
~l(E'~ I) = "N __ -I-'~i
×
~ ~ A(jNRIIE)A(j'N'R'IIE) jNR j'N'R"
jj'
JR(R+ 1)(2R + 1)W(RRII ; l j)
+ g,( _)R-,+~+ j+ ~'- ,CSNN' fi~R'6,,. X/(2j + 1)(2j'+ 1)x/l(/+ 1)(21 + 1) × W(jj'I1; 1R)W(lljj'; 1½)+ g~( __)Z+½+R-,cSNN"~Rg' 6,r x x/~x/(2j + 1)(2j'+ 1)Wfjj'II; 1R)Wfjj'½½; ll)}, where gR, gi and gs refer respectively to the g-factor of the core, orbital and intrinsic spin of the particle. The parameters used here are the same as the ones by Heyde and Brussaard; ~ = 4.0, ho~ = 220 keV and E ( d ~ ) - E ( ~ ) = 108 keV. For the odd parity state the energy of the h÷ single-particle state E(h~) was adjusted to give the best fit with observed ~ - - state, but the expansion coefficients were quite independent of this value. The expansion coefficients obtained are shown in table A. 1.
T. 5EO et al.
512
TABLE A. 1 Expansion coefficients corresponding to state IE(koV); I~) of t'gPm
1270; ~- ~ ]IjNR) A(jNRIIE) h~O0 0.00000 h-~12 0.73366 hJ~20 0.00000 h-~22 --0.55179 h~24 --0.27204 h Jtt30 0.00000 h~32 0.11907 h-~I-33 --0.23652 h-~34 0.10488 h-~36 0.04631
1189; ~ + (I))
]IjNR~ A(jNRIIE) g,]O0
0.00000
g~12 0.74239 g~20 0.00000 g~22 --0.56974 g~24 --0.14517 g~30 0.00000 g~32 0.12637 g½33 --0.17466 g½34 0.07495 g7~36 0.00000 dtO0 0.00000
d~12
0.14993
d~20 0.00000 dt22 --0.13221 dt24 --0.06789 d~30 0.00000 dQ32 0.03335 d~33 --0.06032 dt34 0.04209 dt36 0.00000
I189; t + (II)
IIjNR) A(jNRIIE) g]O0
0.00000
g]12 --0.07457 g[20 0.00000 g~-22 0.02148 g]24 0.47901 g.~30 0.00000 g[32 --0.00198 g7~33 0.I 7055 g~34 --0.22214 g,]-36 0.00000 cliO0 0.00000
d~12
0.64592
d~20 0.00000 dt22 --0.39837 d~24 --0.21452 dt30 0.00000 d~-32 0.07919 di33 --0.22595 dj34 0.08265 d~36 0.00000
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)
W. C. Rutledge, J. M. Cork and S. B. Burson, Phys. Rev. 86 (1952) 775 K. P. Gopinathan and IvL C. Joshi, Phys. Rev. 134 (1964) B297 W. M. Currie and P. W. Dougan, Nucl. Phys. 61 (1965) 561 E. B. Nieschmidt, V. R. Potnis, L. D. Ellsworth and C. E. Mandeville, Nucl. Phys. 72 (1965) 236 R. G. Helmer and L. D. McIssac, Phys. Rev. 143 (1966) 923 K. P. Gopinathan, Phys. Rev. 141 (1966) 1185 A. Backlin, S. (3. Malmskog and H. Solhed, Ark. Fys. 34 (1967) 495 A. (3. Svensson, L. BostrGm and M. C. Joshi, Nucl. Phys. 89 (1966) 348 P. N. Tandon and H. G. Devare, Ind. L Pure Appl. Phys. 7 (1969) 1 R. B. Begzhanov, Dzh. Gaffarov and K. T. Salikbaev, JETP Lett. (Soy. Phys.) 9 (1969) 246 L. S. Kisslinger and R. A. Sorensen, Key. Mod. Phys. 35 (1963) 853 A. Y. Cabezas, I. Lindgren and R. Marrus, Phys. Rev. 122 (1961) 1796 Perturbed angular correlations, ed. E. Karlsson, E. Matthias and K. Siegbahn (North-Holland, Amsterdam, 1964) D. B. Fossan, L. F. Chase, Jr. and K. L. Coop, Phys. Rev. 140 (1965) R. W. Grant and D. A. Shirley, Phys. Rev. 130 (1963) If00 Bl D. C. Choudhury and T. F. O'Dwyer, Nucl. Phys. A93 (1967) 300 K. Heyde and P. J. Brussaard, Nucl. Phys. A104 (1967) 81 G. G. Seaman, J. S. Greenberg, D. A. Bromley and F. K. McGowan, Phys. Rev. 149 (1966) 925 K. Kumar and M. Baranger, Nucl. Phys. A l l 0 (1968) 529 Y. Kawase and T. Hayashi, Ann. Repts. of Res. Reactor Inst. Kyoto Univ. 2 (1969) 1