- Email: [email protected]
Excited states of 154Gd
~ I
NuclearPhysics A l l 6 (1968) 433~451; (~) North-HollandPublishing Co., Amsterdam 3.A
I
Not to be reproduced by photoprint or microfilm without written permissionfrom the publisher
EXCITED STATES OF lS4Gd L. K. NG, K. C. MANN and T. G. WALTON Department of Physics, Universityof British Columbia, Vancouver, B.C., Canada Received 17 May 1968
Abstract: The radiations emitted in the decay of lS4Eu to lS4Gd have been examined with Ge(Li) and intermediate-image beta-ray spectrometers. The energies and intensities of the gamma rays, primary betas and conversion electrons have been measured and two new branch decays from the 1396.9 keV level in X54Gdobserved. Reduced transition probability ratios for both E0 and E2 transitions have been deduced from the data together with electric monopole strengths. The results are compared with the predictions of the asymmetric rotator model of Davydov and Chaban and with the unified model of Bohr and Mottelson. RADIOACTIVITY. 154Eu, 154Gd[from an3Eu(n, y)]; measured Er, I~, Ice, E#, 10, 7V-coin. I ~4Gd. Deduced cc, B(E2) ratios, I(E0)I(E2) ratios, monopole strengths, model parameters. Enriched target.
I
1. Introduction The two c u r r e n t theoretical a p p r o a c h e s to the description o f d e f o r m e d nuclei are the unified m o d e l o f B o h r a n d M o t t e l s o n 1) with i n t e r b a n d mixing a n d the a s y m m e t r i c r o t a t o r o f D a v y d o v a n d C h a b a n 2). The considerable successes o f b o t h m o d e l s are a b o u t equal, a n d at this stage o f our knowledge, one c a n n o t with confidence choose between them. M o r e o v e r , in recent years, evidence has a c c u m u l a t e d t h a t indicates there m a y be a f u n d a m e n t a l i n a d e q u a c y in b o t h m o d e l s in their t r e a t m e n t o f certain types o f deexcitation. This is indicated by the investigations o f nuclei lying in the transition region between the spherical a n d the d e f o r m e d shape [15ZSm, X54Gd, 156Gd etc. (refs. 3 - 5 ) ] . F o r transitions between equal spin states o f the b e t a - v i b r a t i o n a l a n d the g r o u n d - s t a t e r o t a t i o n a l bands, the r e d u c e d transition probabilities for b o t h electric m o n o p o l e a n d q u a d r u p o l e transitions are c o n s i d e r a b l y different f r o m the predicted values. The presence o f a large M1 a d m i x t u r e could explain this, b u t experiments such as g a m m a - g a m m a directional correlation studies 6) do n o t s u p p o r t this possibility. This p a p e r describes experiments p e r f o r m e d to investigate the beta decay o f l S4Eu to excited states o f 154Gd a n d their subsequent de-excitation by g a m m a ray a n d conversion electron emission. O u r m a i n concern has been to achieve the highest accuracy possible with the e q u i p m e n t we h a d available. W e have chosen to describe o u r results in terms o f the a s y m m e t r i c r o t a t o r m o d e l as d e v e l o p e d by D a v i d s o n v,8). 433
434
L.K. NG et
al.
But because either model could have been used, we have computed from our data the parameters of interest in the unified model as well.
2. Experimental details The 154Eu was obtained from the Oak Ridge National Laboratory in the form of europium oxide; it was prepared by slow neutron irradiation of europium enriched to 98.8 % in 153Eu" The oxide was then dissolved in concentrated HC1, evaporated to dryness and a distilled water solution prepared. From this solution, sources were prepared for conversion electron and primary beta analysis by drop deposition on thin vinyl resin films, which were estimated to have thicknesses less than 10 # g . cm -2. Each film was made electrically conducting by evaporating onto it a thin layer of aluminium. Sources for gamma-ray analysis were prepared by drop deposition onto thin cardboard discs, which when dry, were covered with Scotch tape. The primary beta and internal-conversion spectra were obtained using an intermediate-image beta-ray spectrometer equipped with a surface-barrier detector. The conversion peaks were scanned with the instrument set for a line width at half maximum of 0.7 % in momentum and a transmission of about 1%. The primary beta spectrum was taken with the spectrometer baffles opened to give a resolution of 2.2 % and a transmission of 6 %. The gamma-ray spectroscopy was performed with a planar Ge(Li) crystal having a volume of 5 cm 3 and a depletion depth of 7.5 mm; it was operated at liquid nitrogen temperature. The pulses were analysed in a 1024-channel pulse-height analyser. The electronic circuits employed resulted in a photopeak of 3.5 keV F W H M for the 1333 keV gamma ray of 6°Co. The system was calibrated as carefully as possible for both energy and intensity measurements. The following energy standards were used (with the adopted energy values in keV shown in parentheses): 241Am(59.57), 2°3Hg (73.0, 279.1), la3Ba (81.0, 276.0, 302.0, 355.0 and 383.0), STCo (122.0, 136.4), RdTh (238.6, 511.0, 583.0, 727.0, 860.0 and 1592.4), 22Na (511.0, 1274.6), ~34Cs (563.0, 569.0, 604.7 and 796.0), 1 aTCs (661.6), 54Mn (835.0), aSy (897.5, 1841.0) and 6°Co (1173.3, 1333.0). As expected, the detector proved to be highly linear. When energy was plotted against channel number, a straight line could be drawn such that all calibration points were within 3 keV, and all but two were within 1 keV of the line. The intensity standards were obtained from the International Atomic Energy Commission, Vienna. The sources included 241Am, 2°3Hg, 57C0, 22Na, 137Cs, 54Mn, 6°Co and s s y and covered an energy range from 60 to 1841 keV. They were all spot sources and when in use, they were placed in the same mount as that used for the 154Eu ' so that all geometries were essentially identical. The spectrum of each calibration standard was taken, and the intensity of the standard photopeaks measured. Then the ratio of the calculated relative intensity of the gamma-ray standard to the measured intensity of the corresponding photopeak was plotted as a function of
EXCITED
435
S T A T E S O F l~i4Gd
energy. This calibration curve is shown in fig. 1. The window effect of the detector and the aluminium window of the vacuum chamber become troublesome at about 80 keV. The curve is quite smooth and is just the inverse of the total efficiency curve. Each g a m m a spectrum taken was followed by 10 min runs of each of the energy calibration sources. To insure that no drift occurred in the system (amplification, threshold, bias voltages etc.), frequent monitoring was performed using a 22Na spectrum as a " p r o b e " at the beginning and at the end of each run. I f any detectable shift occurred in the two photopeaks of 22Na (511.0 and 1274.6) keV, the run was discarded.
4.4
4.0
c
~o~8s
3.6
8 3.2 c
2.a Hg 0 3
o
2.4
2.0 °~o133
"%
~ao
.,~o
~oo
.oo
,&o
,~'oo
,.~o
doo
doo
zoo~
ENERGY (keY)
Fig. 1. Intensity calibration of the Ge(Li) detector.
3. Results and analysis Typical gamma-ray spectra are shown in figs. 2 and 3, and the summaries of the energies are presented in table 1. The comparative intensity of the 152Eu contaminant was deduced from the conversion-electron spectrum shown in fig. 6, where the 121.8 keV K-conversion line of 152Sm is sufficiently separated from the 122.9 keV Kconversion line of 154Gd to make it possible to deduce their relative intensities (approximately 1 : 2 5 ) . Only the more intense components of the g a m m a rays resulting from the decay of x54Eu would be observable in our spectra, and in those cases, corrections were made where a 154Gd line was affected. There are three such cases in table 1.
436
L.K. NG et al.
In the majority of cases, the gamma rays found in this experiment can either be fitted into the accepted decay scheme as shown in fig. 4 or can otherwise be identified. The 558.0 and 892.7 keY transitions were observed by Harmatz e t al. 9) in the decay of 154Tb to 154Gd but have not previously been found in the decay of 154Eu" Other gamma rays not reported before, but which fit between accepted levels, are those of X I0" 722.9 122.9
:543.6
~Q 409.5 440.0
I I
479.5
rZsB~y
582.1
i i 55~o
692.0
79 i z5.7 ~15
.,.}.
247.6
...]
. ,.:.? , ....J "."
! 190.0
X20
i
/I. :;/ I
~o
h
100
2ao
360 CHANNEL
4bo
500
NUMBER
Fig. 2. Lower energy half of the gamma-ray spectrum of 154Gdtaken with Ge(Li) detector (6.7 cmZx7.5 mm). 401.0 and 582.1 keV energy. These de-excite the 1396.9 keV level to the 995.9 and 814.8 keV levels, respectively. In every instance illustrated in fig. 5, the discrepancy between the gamma-ray energy and the level-energy differences involved is never greater than 0.6 keV and is usually less than 0.3 keV.
EXCITED STATES OF
437
1540d
Some of the low-intensity gamma rays appearing in our spectra, which do not fit the established scheme, can be identified as belonging to the X52Eu decay family. We ascribe to the 152Sm impurity the 964.1, 1112.0, 1085.5 and 1408.2 keV gamma rays and the 343.6, 778.6 and 1299.3 keV transitions to a52Gd. The 86.9 and 105.3 keV gamma rays are most likely due to 155Eu and are formed by double neutron
x,d 1004.5
50 ,9
/ - -
\
--\ 1274.4
40
1595.9 1408.2
xlo tn
~: 3c
I
~...
20
..:.::". 1493.7
..f:
,°665
[
1299.3
I
"
. 10
1112.0
/S,.,
-~396.
i ] I
1246 2
' '-.../ i
500
600
..jI-""
146i'~~79 :"':.~,....~
i
700 CHANNEL
600 NUMBER
900
Fig. 3. Upper energy half ofthe gamma-ray spectrum oflb4Od taken with Ge(Li) detector (6.7 cm~× 7 ram). capture. The very weak peak at 1396.6 keV is probably a sum peak of the strong 122.9 and 1274.4 keV gamma rays. Its intensity is about what is expected from the efficiencies of the detector for the two contributing gamma rays. The remainder of the weak gamma rays are unassigned. It is possible, in view of the accuracy of the energy
438
L.K. NG e t
al.
m e a s u r e m e n t s , to p o s t u l a t e o t h e r levels in 1 5 , G d to a c c o m m o d a t e them. H o w e v e r , in the absence o f o t h e r s u p p o r t i n g evidence, such speculation is n o t very useful. It is quite possible t h a t there are o t h e r w e a k g a m m a - r a y lines hidden in the scatter o f e x p e r i m e n t a l points between the strong peaks. The w e a k lines listed in table 1 were limited, r a t h e r arbitrarily, to those g r o u p i n g s o f p o i n t s in which there were at least six consecutive channel counts f o r m i n g a p e a k - l i k e structure. A n a d d i t i o n a l requirem e n t was t h a t for such a p e a k , the h a l f m a x i m u m c o u n t i n g rate could be j u d g e d to lie a b o v e the c o n t i n u u m u p o n which the p e a k was situated. M a n y o f the g a m m a rays listed in table 1 have never been resolved before, the TABLE l
Energies and relative intensities of the gamma rays of 154Gd T-ray energy (keV)
Relative intensity
86.9 105.3 122.9 190.0 247.6 343.6 401.0 409.5 444.0 479.5 558.0 582.1 591.6 625.7 692.0 722.9 756.7 778.6 815.0 845.2
15.42 4-1.31 9.704-0.84 100 1.344-0.13 15.864-0.72 3.76 4-0.29 0.65 4-0.20 0.59 4-0.20 1.134-0.14 0.88 t0.25 0.874-0.16 1.73 4-0.16 10.51 4-0.54 0.81 4-0.20 3.80 4-0.29 47.30 4-2.05 10.364-0.60 2.43 4-0.40 1.31 4-0.22 1.62 4-0.35
Remark X55Gd X55Gd (corrected) a) (corrected) 15~Gd a) (corrected) ~)
lS2Gd 4)
),-ray energy (keV)
Relative intensity
872.6 892.7 903.6 964.1 995.9 1004.5 1085.5 1112.0 1127.9 1140.7 1186.3 1246.2 1274.4 1299.3 1396.6 1408.2 1460.9 1493.7 1537.7 1595.9
29.38 4-1.36 1.234-0.20 2.04-t-0.23 1.824-0.25 24.694-1.12 43.85 4- 1.92 1.67 4-0.22 2.40 4-0.24 0.804-0.25 0.61 4-0.20 0.634-0.30 2.27 4-0.21 92.004-4.13 0.21 4-0.05 0.15 4-0.04 3.29 4-0.20 0.394-0.10 1.71 4-0.11 0.13 4-0.02 4.67 4- 0.22
Remark
lszSm 15aSm xs2Sm a) a) a) X52Gd b) lb2Sm a) a) a)
a) Gamma ray is unassigned. b) Sum peak. s e p a r a t e energies having been d e d u c e d f r o m the c o r r e s p o n d i n g conversion electron peaks. E x a m p l e s are the strong 995.9-1004.5 keV a n d the m o d e r a t e l y strong 582.1591.6 keV pairs. I n o r d e r to confirm their p r o p e r p o s i t i o n s in the decay scheme, g a m m a - r a y spectra were m e a s u r e d in coincidence with the 722.9 a n d 591.6 keV g a m m a rays. F o r this experiment, the source was placed between the G e ( L i ) detector a n d a 2.5 c m x 4.0 cm NaI(T1) scintillator, the latter being in c o n t a c t with an R C A 5819 p h o t o m u l t i p l i e r . The coincidence circuit was o f the slow-fast type. The p h o t o m u l tiplier o u t p u t f r o m the a n o d e was used for one side o f the fast coincidence circuit.
t54Eu
054Gd ~-Band
~
0 keV, 2 6 . 5
i
x
y-Bond
I
%
-4 ~/÷%'o ,~.
-,,
Tf
1718.7'
2-
1396 9
2-
--rJ
O~OJ
1263.4
TT_ IIIT
1127.3
___
!
814.8
o;
680.4
it) b.
_
t'
3~
995 9
Ii
f
3705
I22.9
T
0
Fig. 4. D e c a y s c h e m e o f 154Eu --->a54Gd. T h e relative intensities o f the beta groups s h o w n here were t a k e n f r o m c o l u m n 4 o f table 3. T h e e n d - p o i n t energies were deduced f r o m energy level differences a n d the m e a s u r e d end-point energy o f 1 8 6 6 ± 12 keV f r o m fig. 8.
gate peak 722.9 keV
gate peak 591.6 keV
(o) 872.6
(b)
keV
240
995.9
IZO
keV
~004.6
keV
160
80
.,° ..
40
, .*.'o
"'.', ,'o .... ,,'o':,,', 0
16
16
i
14elelem I
4
I
°'"'t" ' " " '
76
36
56 CHANNEL
°
"..".:.,:.......~......
76 NUMBER
•
96
96
.......... .,.
• .°.
°16
'
3'6
4°f, o
'
• .i,[......."
s'e
• ..:.'.-.....:......i
16
36
56 CHANNEL
'
~,~
96
................ 76
96
NUMBER
Fig. 5. Portion o f the g a m m a - r a y s p e c t r u m o f XS4Gd in coincidence a) with the 722.9 keV g a m m a ray a n d b) with t h e 591.6 keV g a m m a ray. (The lower figures s h o w the s a m e spectra t a k e n with the gate settings m o v e d just off the selected peaks.)
440
L.K. no et al.
Pulses from the eighth dynode were fed through a white cathode follower, amplified by a fast linear amplifier, clipped to a 1 #sec pulse width and fed to an antiwalk single-channel analyser for gate selection. The fast coincidence pulses from the Ge(Li) detector side were taken directly from the low-noise preamplifier before pulse-shaping. The shaped pulses from the following time-constant box were fed to a 128-channel pulse-height analyser via a low-noise amplifier. The coincidence pulse width of the fast circuit was set at 50 nsec. The window of the single-channel analyser was set at 20 keV. Fig. 5 shows the coincident spectra with the gate set on each of the 722.9 and the 591.6 keV peaks and also with the gate set just off those peaks. The results support the positional assignments of these gamma rays in the decay scheme.
1500 247.6
K
105.3 K
sml52 l
I000
500343.6
591.6 K
K
679.4K
;/
r/I i
400
~
.OK
T22,K
1004.5
K
- -
"..,., S.9K
22.9K
500
%....
~
".,...,,,
122.9 M
.d X~
I
i
i 0,20
,ol , I , 0.30
" ",A\
"..~E)O ".°.
.... r~ 0.1"~ ) 0
300
..°..°
,
, , I , , , , I , 0.40 0.50 POTENTIOMETER
i
/'i....,.,.,
, t . . . . 0.60
"'...jt...A..
i . . . . O.TO
t 0.80
,
SETTING
Fig. 6. The conversion-electron spectrum of 154 Gd. The intermediate image spectrometer was set for a line width at half maximum of 0.7 ~ in momentum. The conversion-electron spectrum of fig. 6 was taken with the magnetic spectrometer set for a resolution of 0.7 7ooin momentum. Most of the counting time was spent on the peaks rather than on the continuum, and a summary of their identification and relative intensities is given in table 2. The corresponding data from the work of Bobykin and N o v i k 10), of Juliano and Stephens 11) and of Hamilton e t al. 12) are included for comparison. It should be noted here that although the region was very carefully scanned, we could find no evidence for two close-lying K-conversion peaks as reported by Hamilton e t aL a2). Their published curve shows two clearly separated
441
EXCITED STATES OF 154Gd
peaks of roughly equal intensity corresponding to transition energies of 678 a n d 682 keV. It appears that their i n s t r u m e n t resolution is very nearly the same as our own, in which case two such peaks will n o t be resolved b u t will appear as a single peak with a F W H M approximately 50 ~ larger t h a n that of a single peak. Fig. 7 shows this section of the conversion-electron spectrum from our data, the dashed lines shows a single peak shape superimposed. The p o i n t is i m p o r t a n t , for this is the only evidence advanced for the excitation of the 4 + b e t a - v i b r a t i o n a l level in the decay of 154Eu. TABLE2 Intensities of conversion electrons Transition energy (keV)
Shell
Present work
Bobykin and Novik 10)
86.9 86.9 105.3 105.3 122.9 122.9 122.9 247.6 247.6 247.6 591.7 679.4 692.0 692.0 722.9 722.9 756.7 872.6 872.6 995.9 1004.5 1274.4
L M K L K L M K L M K K K L K L K K L K K K
0.73 ±0.08 0.14 ~0.03 4.04 ~0.15 0.47 ±0.10 100 65.6 ±1.3 18.8 ±0.7 2.20 ±0.05 0.56 ±0.06 0.12 ±0.01 0.10 ~0.01 0.052±0.005 0.32 ~0.07 0.049±0.01 0.18 ±0.01 0.018 ~0.004 0.092±0.008 0.157±0.007 0.032 ~0.007 0.090t0.018 0.151 ±0.031 0.100±0.027
2.08 0.59 4.95 0.86 100 <208 a) 23 <10 a) 0.58 0.10 0.125±0.005 ~0.04 <0.68 a) ~0.04 <0.15 a) <0.05 a) 0.07 ±0.003 <0.31 a) <0.20 a) 0.11 ~0.003 0.190 0.074±0.003
Juliano and Stephens 11)
Hamilton et al. 12) b)
100 109 18.9 3.1 1.2
0.55
0.32
0.31 0.08 0.40
0.064±0.013 0.16 ±0.02
0.15 0.39 0.37
0.12 ±0.02 0.20 i0.02
a) Conversion peaks contain unresolved components of other transitions. b) Data have been normalized to our value of 0.32 for the intensity of the K-conversion line for the 692.0 keV transition. The p r i m a r y beta spectrum in the intervals between the conversion peaks was taken with the higher t r a n s m i s s i o n setting m e n t i o n e d earlier. The spectrum is k n o w n to be complex with a n u m b e r of first-forbidden groups. A K u r i e analysis was applied to the data in the usual m a n n e r . First, an experimental shape correction f u n c t i o n C a was calculated from the data. Then, following the proposal of K o t a n i a3) that firstforbidden spectra of this type have C a = q 2 + O . 8 0 7 p 2 + D , the value of D was determined to be 2 0 + 2 , in good agreement with the work of Langer a n d Smith 14). A least-squares fit with this f u n c t i o n gave a n e n d - p o i n t of 1 8 6 6 _ 12 keV. F o l l o w i n g
442
L.K. NG et al.
the subtraction of this group, a cluster of points showing a wide scatter appeared at energies j u s t b e y o n d the e n d - p o i n t of the next intense group. This cluster we interpreted as the high-energy end of a weaker group, the statistical scatter being what one would
692.0
K
I00
50
679.4
K
1
0.620
0,630 0.640 POTENTIOMETER SETTING.
0.6,~0
Fig. 7. The conversion-electron spectrum of 154Gdin the region of 680 keV energy. The primary beta background obtained by interpolation of the continuum under the peaks has been subtracted. The dashed line profile is the shape of the 692.0 keV K-conversionpeak, suitably scaled and centred at the setting for a 679.4 keV K-conversion peak. The arrows show the expected positions of the two close-lying K-conversion lines reported by Hamilton et al. 1~).
expect near the e n d - p o i n t of a beta group. W e fitted the cluster as best we could with C1 = q2 + 0.79 p2 + ( 0 _ 4). The procedure was repeated with appropriate subtractions down to a n d including an intense group with an e n d - p o i n t near 270 keV. F o r all groups
443
EXCITED STATES OF lS4Gd
after the second, the experimentally determined correction factor was a constant. Fig. 8 shows the plot of the Kurie analysis. The relative intensities of the separated beta groups were determined by area measurement. Table 3 shows the total formation and decay rates for all levels of ~ 54Gd deduced from the intensities of the gamma rays and the conversion electrons. (These may be found in the second and third columns of table 4). The differences between these two rates should correspond to the intensity of the beta group populating the level, and in table 3 these differences are compared with the results of the Kurie analysis. The results
30 \\ 20
\\ x "
\\ \\ \
X20 \ \ \
I0
--..
.
.
.
.
I
5OO
.
.
.
.
I
,
I000 ENERGY (keY}
1866~12
I 1500
Fig. 8. Kurie analysis of the primary beta spectrum of 154Eu. are more consistent than was expected considering the multiple subtractions performed in the latter process. Nevertheless, because of their greater accuracies, we preferred to rely on the gamma-ray and conversion-electron data in estimating the end-points and intensities of the beta groups, rather than on the results of the Kurie analysis. 4. Transition multipolarities Table 4 lists all relative conversion-electron intensities and the corresponding
444
L.K. NG e t al.
relative g a m m a - r a y intensities. The conversion-electron intensity d a t a have been n o r m a l i z e d to the g a m m a - r a y scale b y assuming t h a t the 122.9 keV t r a n s i t i o n is pure E2 with a K - c o n v e r s i o n coefficient o f 0.652 [ref. 15)]. The conversion coeffÉcients so calculated confirm the expected p r e d o m i n a n t l y E2 c h a r a c t e r o f the transitions between p o s i t i v e - p a r i t y states. W h e r e one o f the states has negative parity, the transition a p p e a r s to be E l . The exceptions to the p o s k i v e - p a r i t y rule are the 679.4 a n d 692.0 keV transitions. T h e first goes between 0 + states o f the b e t a - v i b r a t i o n a l a n d g r o u n d - s t a t e r o t a t i o n a l bands, a n d therefore it proceeds b y TABLE 3 Transition intensity balances for the energy levels of a54Gd Level energy (keV)
Output (74-conversion)
Difference (~ of total Eu decay)
1718.7
64.71 ±3.05
64.71 ±3.05 (26.3 ~ )
(29.1 ±2.5)
1396.9
94.45 ±4.51
94.45 4-4.51 (38.4 ~)
(37.8 4-3.5)
1263.4
1.84 5_0.40
1.84 4- 0.40 (0.7 ~ )
54.29 4-2.55
43.71 4-3.10 (17.8 ~ )
1127.3 995.9 814.8
Input (74-conversion)
10.58 4-0.55 47.95+2.25 3.774-0.39
680.4
55.04 ±2.70 6.51-4-0.66
7.09 4-4.95 (2.9 ~ ) 2.744-1.05 (1.1 ~)
0.90±0.18
0.90±0.18 (0.4 %)
370.5
13.754-0.95
17.664-0.79
3.91 4-1.74 (1.6 ~ )
122.9
193.374-9.13
219.604-2.00
26.23±11.13 (10.8 ~)
Beta intensity (~)
(17.0 4-3.9) (4.6 4-3.8) (0.674-0.49)
(10.8 4-0.12)
Gamma-ray intensities are normalized to 100 for the 122.9 keV transition. Conversion electron intensities are normalized to 65.2 for the 122.9 keV transition. the emission o f conversion electrons alone. The m u l t i p o l a r i t y is E0, a n d the absence o f g a m m a rays establishes the 680.4 keV level as the b e t a - v i b r a t i o n a l b a n d head. The 692.0 keV t r a n s i t i o n links the 2 + states o f the same two bands. F r o m a c o m p a r i son o f the m e a s u r e d K - c o n v e r s i o n coefficient with the theoretical value for an E2 transition, we deduce t h a t the E0 c o m p o n e n t is 5 . 0 + 0 . 9 ~ o f the total intensity. The energy o f the pure E0 transition listed in table 4 as 679.4 keV has a b o u t a 1 keV u n c e r t a i n t y since it lies in the tail o f the m u c h stronger 692.0 keV K - c o n v e r s i o n peak. The g a m m a - r a y b r a n c h f r o m the same level is the cascade ( 5 5 8 . 0 + 1 2 2 . 9 ) k e V or
43.85-5-1.92
92.00±4.13
1004.5
1274.4 0.065±0.018
0.099i0.02
0.059~z0.012
0.102~0.005 (0.0214-0.004)
0.060~z0.005
0.120±0.005 (0.012±0.003)
0.210i0.004 (0.032±0.006)
0.034£0.004
0.065-4-0.008
1.43 4-0.03 (0.37 ±0.04)
6.520 4-0.70 (42.70 ~0.90)
Conversion intensity (relative~
~0.008 ±0.004)
4-0.006 i0.009)
0.00071i0.00023
0.00225±0.00055
0.0024 ±0.0006
0.0035 ±0.0004 (0.00071i0.00017)
0.0058 -4-0.0008
0.0025 ±0.0002 (0.00025~0.00007)
0.055 ~0.005 (0.0084 ±0.0022)
0.0062 ~0.0011
0.090 (0.023
0.652 (0.427
Experimental conversion coefficient
The L-conversion coefficients, where measured, are indicated in parentheses.
24.69±1.12
47.30~z2.05
722.9
995.9
3.80~0.29
692.0
10.36±0.60
0
679.4
29.38~1.36
10.51-~0.54
591.7
872.6
15.86:~0.72
247.6
756.7
100
G amma-ray intensity (relative)
122.9
Transition energy (keV)
0.00145
0.0023
0.0023
0.00314 (0.005)
0.0043
0.0047 (0.0008)
0.00519 (0.0009)
0.0076
0.082 (0.023)
0.652 (0.430)
E2
0.0022
0.0039
0.0040
0.0054 (0.0012)
0.0077
0.0086 (0.0019)
0.00954 (0.0020)
0.0140
0.135 (0.020)
0.941 (0.135)
M1
Theoretical coefficient
TABLE 4 Experimental and theoretical 15) conversion coefficients for the gamma rays of 154Gd
0.00063
0.00097
0.00099
0.0013 (O.OO017)
0.0017
0.0018 (0.00025)
0.00201 (0.00028)
0.0028
0.0218 (0.0034)
0.142 (0.021)
E1
E1
E2
E2
E2
E2
El
E2 + E0
E0
E2
E2
E2
Assignment
.Ix
446
L.K. NG et al.
680.9 keV. Since we consider the uncertainties in the gamma-ray energy measurements to be less than 0.5 keV, we have established the 0 + beta-vibrational state at 680.4 keV.
5. Comparison with model predictions 5.1. THE E2 TRANSITION PROBABILITIES The theory of the asymmetric rotator has been described elsewhere 2, 7). Briefly, the energy eigenvalues and reduced transition probabilities are computed in terms of three parameters which are used to describe the physical properties of the nucleus. They are the quadrupole asymmetry parameter T, the nuclear "stiffness" # and the equilibrium deformation fl0. The value of fl0 for 154Gd is taken as 0.303; it was deduced from Coulomb excitation probability data a). The values of T and p are those which make the theoretically predicted energy level structure best fit the observed values. The theoretical energy values for even-parity states are given by ELN . = h~o o (v,+½)
+ ~
1+
2Z 2 . ] j ,
where eLn are the rotational energies for a rigid asymmetric top in units of h 2 / 4 B 2 f12. The three quantum numbers are the nuclear spin L, the ordering label N for spin L and the ordinal number n of the vibration band. The quantity h m o is the oscillator energy which is used as a scale adjustment factor. To obtain the values of T and ft, we made use of the five basic machine programs written by Davidson 16). The first three programs calculate the energy eigenvalues for a given pair of 7 and ft. These predicted levels are then compared with the experimental values for the same states and the r.m.s, deviation calculated. Then both ~ and # are varied within suitable ranges until they enclose the minimum r.m.s, deviation. The values we obtained with this procedure are ~ = 11.52 ° and # = 0.402 (with an r.m.s, deviation of 1.5 %). This can be compared with 11.62 ° and 0.4006 obtained by Davidson 8) for slightly different values of the energy levels. De Aisenberg and Suarez (ref. 17)) quote values of 11.5 ° and 0.8 for lSaGd. Table 5 lists the observed and predicted positive-parity levels with these parameter values. The E2 transition probabilities can now be calculated. For the asymmetric rotator, this was accomplished using the last two of Davidson's five programs 16). In the case of the unified model, it is well known that particularly in the transition region between the spherical and the deformed shape, the assumption of pure Kstates will not give either the correct energy levels or the correct transition probabilities. This assumption implies the adiabatic condition, in which the rotation and vibration excitations are completely decoupled. A relaxation of the adiabatic restriction will allow coupling between the vibration and the rotation bands. This results in a degree of mixing of the wave functions of the bands which can be described 18) by a functionf(z, Ii, It) such that the reduced probability for an interband transition
447
EXCITED STATES OF 154Gd
is given by B(E2 : I i
~
If) = Bo(E2
: Ii ~
If)f (z, Ii,
If).
Here Bo is the adiabatic probability which is proportional to the square of the appropriate Clebsch-Gordan coefficient. Tables of the form o f f ( z , Ii, If) are available
(refs. 18,19)).
TABLE 5 Energy levels o f the asymmetric r o t a t o r for 154Gd with the parameters ~ = 11.52 °,/~ = 0.402 and fl0 = 0.303
LNn
0 2 4 0 2 2 3 4
1 1 1 1 1 2 1 2
1 1 1 2 2 1 1 1
Experimental
Theoretical
Deviation
ELNn
ELNn
(%)
(keY)
(keV)
0 122.9 370.5 680.4 814.8 995.9 1127.3 1263.4
0 122.9 365.4 676.5 831.9 1052.7 1121.3 1212.0
1.4 0.5 2.1 5.4 0.5 4.2
TABLE 6 Experimental and theoretical reduced transition probability ratios (E2) Transition description
Theoretical
Energy
Asymmetric rotator
Unified model
Observed ratio
Asymmetric rotator
Unified model
625.7 872.6
221 -+ 411 221 "-+ 211
27+ "-+ 4g+ 27+ ~ 2 +
0.145i0.035 (0.12 4-0.03) a)
0.113
995.9 872.6
221 -+ 011 221 --~211
27+ ~ 0g+ 27+-+2g+
0.4344-0.040 (0.39 ±0.03) a)
0.443
0.443
1004.5 "756.7
311 ~ 211 311--~411
37+ ~ 2g+ 37+_+4g+
1.0264-0.104 (1.0 4-0.1) a)
1.004
0.976
1140.7 892.7
421 -+ 211 421 ~ 41]
47+ ~ 2g+ 47+ -+ 4~+
0.1464-0.065
0.119
0.093
444.0 692.0
212 ~ 411 212 --~ 211
2# + --~ 4g+ 2#+ _+ 2g+
2.75 4-0.63 (3.0 ± 0 . 6 ) a)
4.35
6.46
815.0 692.0
212 -+ 011 212 --~ 211
2# + ~ 0g+ 2#÷ __+ 2g+
0.1524-0.014 (0.18 4-0.04) a)
0.373
0.266
(z~ = 0.079) 0.109
(z0 = 0.064)
a) Values quoted by Liu et al. 3).
448
L . K . NG e t
al.
In table 6, we present the results of calculations based on both models. In the case of the g a m m a band, the unified model mixing parameter z 2 was deduced for each of the four ratios shown. In the order that they are presented in table 6, the values of z 2 are 0.125___0.045, 0.082+0.008, 0.076___0.008 and 0.058+0.029. All four values agree within the error limits, and the average value is 0.086. The value of z 2 chosen to represent the band is 0.079, the average of the second and third which were measured with the greatest precision. For the beta band, the mixing parameter z o was computed from the ratio B(E2 : 2~- ~ 4+)/B(E2 : 2~- ~ 0 +) since in this way, possible M1 admixtures are avoided. The value z 0 = 0.064+0.009 was then applied to calculate the other transition intensity ratios. Table 6 demonstrates the fact that either model is adequate to predict g a m m a band to ground-state-band transition probability ratios within the limits of experimental error. But it also shows that neither model is successful in dealing with beta-band E2 transitions. The problem is associated with the 692.0 keV transition which links the first and second 2 + states. The gamma-ray intensity for this transition, assumed here to be pure E2, is too large, and this has the effect of reducing the experimentally determined transition ratios below the values predicted. It has been suggested 5) that there exists a large M 1 component, which if subtracted from the gamma-ray intensity, would bring observation into line with theory. However, the directional correlation measurements on the 692.0-122.9 keV cascade in 154Gd by Hamilton et al. 6) definitely rules out the possibility of any M1 component large enough. In fact, these authors conclude that the 692.0 keV transition is pure E2. The same problem has been encountered in 152Sm and in 155Gd [ref. 5)], where it has been estimated that the M1 component would have to be about 40 ~ . 5.2. THE E0 TRANSITIONS AND ELECTRIC MONOPOLE STRENGTHS Electric monopole transitions can take place between beta and ground-state bands if the two states involved have equal spins. The absolute E0 transition probability as defined by Church and Weneser 20) is T(E0) = O p 2 , where I2 is the electronic factor, which is available for the K-shell as a function of energy in graphical form 2 o). The quantity t2 2 is called the monopole strength. In the case of 154Gd ' there are two such transitions for which intensity measurements can be made. For the transition between the first and second 0 + states, no g a m m a rays can be emitted, and the transition proceeds entirely by electron conversion. This is confirmed by the absence of any gamma ray of energy 680.4 keV, and by the presence of the corresponding K-conversion peak (fig. 8). If we use the data given in tables 1 and 4, we can determine the absolute intensity ratio for the E0 and E2 branches from the second 0 + state.
449
EXCITED STATES OF l~"tGd
The transition between the first and second 2 + states is complicated by the presence of E2 radiation. However, as mentioned earlier, analysis of the conversion coefficients leads to a value for the intensity ratio of the E0 and E2 components in this transition. The theoretical values of both the above intensity ratios can be calculated easily from Davidson's programs s, 16) with a simple modification. In table 7, we list both the experimental ratios and the theoretical values as calculated in terms, of the asymmetric rotator. In each case, the predicted values are two to three times too large. Recently, interest has focussed on the values of the monopole strengths and how they vary from one level to another within the band 5,21,z2). F r o m the observations available, one concludes that p2 is approximately constant for all members of the beta band. The calculations of Davidson s) on/92 for symmetric nuclei (~ = 0) are in agreement with this conclusion at least for moderately "stiff" nuclei, (i.e. # < 0.3). For greater values of/~, p2 increases with the level spin. It is not expected that values of y different from zero will affect this behavior very much. Since in 154Gd ' we have a nucleus that is only moderately soft, the p2 values for the 0 + and 2 + members of the beta band should be about the same. TABLE7 Electric monopole -quadrupole transition ratios Transition
Observed
Calculated
p2
T(E0; 0/~+ ~ 0g+) T(E2; 0#+ --~ 2g+)
0.0394-0.012
0.085
0.474-4-0.23
T(E0; 2#+ -+ 2g+) T(E2; 21/+--+2g+)
0.0534-0.013
0.158
0.464-0.30 a)
a) Calculated using T(E2; 2#+ --+ 0g+). In order to calculate pZ for any E0 process, one must know the absolute value of the transition probability for its decay. This can be determined best by Coulomb excitation experiments. Yoshizawa et al. 23) have measured B ( E 2 ; 0 + ~ 2 ; ) for 154Gd and obtained the value 0.12+0.03 in units eZ(10 -48) cm 4. For the transition (2~" ~ 2+), the procedure is now straightforward. The absolute transition probability T(E2) is related to the reduced probability through the relation 24) 8 ~ ( l + 1) E~ B(E2; + T(E2; 2 ; --, 0 +) - •[(2•+ 1)!!] 2 h6C 5 2p
0~-).
Also, B(E2: 2 ; --* 0 +) = ½B(E2:0 + --+ 2 ; ) = 0.024_+0.006 e2(10 -4s) cm*. F r o m the second ratio in table 7, with the value f2 = 0.35 x 1011 sec-1, p2 can be computed. The monopole strength p2 for the ( 0 ; ---, 0 f ) transition can be deduced from the first ratio in table 7, but for this we must know B(E2: 0 ; ~ 2+). This may be computed from the Coulomb excitation data, except that in this case band mixing must be
L.K. NG et al.
450 included. Thus
B(E2: 0~- ~ 2 + ) = B ( E 2 : 0 + ~ 2~-) i + 6 z o _ 0.606+0.150. 1 - 6z o F o r this transition, ~ is 0.335 x 1011 see -1. T h e two values o f pZ are also listed in table 7. Their internal consistency ( a p a r t f r o m the uncertainties in the C o u l o m b d a t a ) does indicate t h a t within the b a n d , pZ is a constant. W e also calculated p2 using the p r o g r a m s of D a v i d s o n s,16) a n d o b t a i n e d the value 0.66. I n this connection, we wish to a d d t h a t if the E0 conversion p e a k c o r r e s p o n d i n g to the transition o f energy 679.4 keV does c o n t a i n a c o m p o n e n t due to a t r a n s i t i o n f r o m a 4 + b e t a - v i b r a t i o n a l level as claimed by H a m i l t o n et al. lz), then b o t h the transition p r o b a b i l i t y ratio a n d the value o f p2 for the 0 + levels in table 7 will be c o r r e s p o n d i n g l y reduced. 6. C o n c l u s i o n s
W e have sought in this e x p e r i m e n t to examine the decay o f l S4Eu to 154Gd in careful detail a n d to interpret the results in terms o f the two basic descriptive a p proaches. The results a p p e a r to confirm t h a t where one m o d e l is adequate, the o t h e r is also, at least in this region o f nuclear d e f o r m a t i o n . B o t h models fail to describe a d e q u a t e l y the same aspects o f nuclear behaviour, that is, the de-excitation o f specific levels o f the b e t a band. Other w o r k s have d e m o n s t r a t e d t h a t an a p p e a l to a s t r o n g M1 c o m p o n e n t is n o t confirmed. Mixing o f other b a n d s t h a n the K = 0 or 2 m a y p r o v i d e an answer, b u t if not, then the difficulty m a y be m o r e f u n d a m e n t a l and m a y even lie in the initial expression for the nuclear surface. T h e a u t h o r s wish to acknowledge their great indebtedness to Dr. G. T. E w a n for his helpful c o m m e n t s a n d suggestions a n d to Dr. J. P. D a v i d s o n for valuable assistance in interpreting the a s y m m e t r i c r o t a t o r theory. One o f us ( L . K . N ) . is i n d e b t e d to the C a n a d i a n Office o f External A i d for a fellowship held d u r i n g the course o f this work. This w o r k was s u p p o r t e d by a g r a n t - i n - a i d f r o m the N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a to K . C . M . . References
1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, No. 16 (1953) A. S. Davydov and A. A. Chaban, Nucl. Phys. 20 (1960) 499 I. Liu, O. B. Nielsen, P. Salling and O. Skilbreid, Izv. Akad. Nauk SSSR (ser. fiz.) 31 (1967) 63 L. L. Riedinger and N. R. Johnson, Phys. Rev. Lett. 19 (1967) 1247 G. T. Ewan and G. I. Andersson, Int. Conf. on Nuclear structure, Tokyo (1967) J. H. Hamilton, A. V. Ramayya, L. C. Whitlock and A. Meulenberg, Phys. Rev. Lett. 19 (1967) 1484 J. P. Davidson and M. G. Davidson, Phys. Rev. 138 (1965) B316 J. P. Davidson, Nucl. Phys. 86 (1966) 561 B. Harmatz, T. H. Handley and J. W. Mihelich, Phys. Rev. 123 (1961) 1758 B.V. Bobykin and K. M. Novik, Izv. Akad, Nauk SSSR (ser. fiz.) 21 (1957) 1556
EXCITED STATESOF l~4Gd 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)
451
J. O. Juliano and F. S. Stephens, Phys. Rev. 108 (1957) 341 J. H. Hamilton, T. Katoh, W. H. Brantley and E. F. Zganjar, Phys. Lett. 13 (1964) 43 T. Kotani and M. Ross, Phys. Rev. 113 (1959) 622 L. A. Langer and D. R. Smith, Phys. Rev. 119 (1960) 1308 L. A. Sliv and I. M. Band, Coefficients of internal conversion of gamma radiation (Academy of Sciences of the USSR, Moscow-Leningrad, 1956-1958) J. P. Davidson, USNRDL Report-TR901 (1965) E. Y. de Aisenberg and J. F. Suarez, Nucl. Phys. A97 (1967) 529 O. Nathan and S. G. Nilsson, in Alpha-, beta-, and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) P. G. Hansen, O. B. Nielsen and R. K. Sheline, Nucl. Phys. 12 (1959) 389 E. L. Church and J. Weneser, Phys. Rev. 103 (1956) 1035 O. Lbnsj~5 and G. B. Hagemann, Nucl. Phys. 88 (1966) 624 N. R. Johnson, L. L. Riedinger and J. H. Hamilton, Int. Conf. on nuclear structure, Tokyo (1967) Y. Yoshizawa, B. Elbek, B. Herskind and M. C. Olesen, Nucl. Phys. 73 (1965) 273 M. A. Preston, Physics of the nucleus (Addison-Wesley Publ. Co., Reading, Mass. 1963) chapt. 11, p. 298
NuclearPhysics A l l 6 (1968) 433~451; (~) North-HollandPublishing Co., Amsterdam 3.A
I
Not to be reproduced by photoprint or microfilm without written permissionfrom the publisher
EXCITED STATES OF lS4Gd L. K. NG, K. C. MANN and T. G. WALTON Department of Physics, Universityof British Columbia, Vancouver, B.C., Canada Received 17 May 1968
Abstract: The radiations emitted in the decay of lS4Eu to lS4Gd have been examined with Ge(Li) and intermediate-image beta-ray spectrometers. The energies and intensities of the gamma rays, primary betas and conversion electrons have been measured and two new branch decays from the 1396.9 keV level in X54Gdobserved. Reduced transition probability ratios for both E0 and E2 transitions have been deduced from the data together with electric monopole strengths. The results are compared with the predictions of the asymmetric rotator model of Davydov and Chaban and with the unified model of Bohr and Mottelson. RADIOACTIVITY. 154Eu, 154Gd[from an3Eu(n, y)]; measured Er, I~, Ice, E#, 10, 7V-coin. I ~4Gd. Deduced cc, B(E2) ratios, I(E0)I(E2) ratios, monopole strengths, model parameters. Enriched target.
I
1. Introduction The two c u r r e n t theoretical a p p r o a c h e s to the description o f d e f o r m e d nuclei are the unified m o d e l o f B o h r a n d M o t t e l s o n 1) with i n t e r b a n d mixing a n d the a s y m m e t r i c r o t a t o r o f D a v y d o v a n d C h a b a n 2). The considerable successes o f b o t h m o d e l s are a b o u t equal, a n d at this stage o f our knowledge, one c a n n o t with confidence choose between them. M o r e o v e r , in recent years, evidence has a c c u m u l a t e d t h a t indicates there m a y be a f u n d a m e n t a l i n a d e q u a c y in b o t h m o d e l s in their t r e a t m e n t o f certain types o f deexcitation. This is indicated by the investigations o f nuclei lying in the transition region between the spherical a n d the d e f o r m e d shape [15ZSm, X54Gd, 156Gd etc. (refs. 3 - 5 ) ] . F o r transitions between equal spin states o f the b e t a - v i b r a t i o n a l a n d the g r o u n d - s t a t e r o t a t i o n a l bands, the r e d u c e d transition probabilities for b o t h electric m o n o p o l e a n d q u a d r u p o l e transitions are c o n s i d e r a b l y different f r o m the predicted values. The presence o f a large M1 a d m i x t u r e could explain this, b u t experiments such as g a m m a - g a m m a directional correlation studies 6) do n o t s u p p o r t this possibility. This p a p e r describes experiments p e r f o r m e d to investigate the beta decay o f l S4Eu to excited states o f 154Gd a n d their subsequent de-excitation by g a m m a ray a n d conversion electron emission. O u r m a i n concern has been to achieve the highest accuracy possible with the e q u i p m e n t we h a d available. W e have chosen to describe o u r results in terms o f the a s y m m e t r i c r o t a t o r m o d e l as d e v e l o p e d by D a v i d s o n v,8). 433
434
L.K. NG et
al.
But because either model could have been used, we have computed from our data the parameters of interest in the unified model as well.
2. Experimental details The 154Eu was obtained from the Oak Ridge National Laboratory in the form of europium oxide; it was prepared by slow neutron irradiation of europium enriched to 98.8 % in 153Eu" The oxide was then dissolved in concentrated HC1, evaporated to dryness and a distilled water solution prepared. From this solution, sources were prepared for conversion electron and primary beta analysis by drop deposition on thin vinyl resin films, which were estimated to have thicknesses less than 10 # g . cm -2. Each film was made electrically conducting by evaporating onto it a thin layer of aluminium. Sources for gamma-ray analysis were prepared by drop deposition onto thin cardboard discs, which when dry, were covered with Scotch tape. The primary beta and internal-conversion spectra were obtained using an intermediate-image beta-ray spectrometer equipped with a surface-barrier detector. The conversion peaks were scanned with the instrument set for a line width at half maximum of 0.7 % in momentum and a transmission of about 1%. The primary beta spectrum was taken with the spectrometer baffles opened to give a resolution of 2.2 % and a transmission of 6 %. The gamma-ray spectroscopy was performed with a planar Ge(Li) crystal having a volume of 5 cm 3 and a depletion depth of 7.5 mm; it was operated at liquid nitrogen temperature. The pulses were analysed in a 1024-channel pulse-height analyser. The electronic circuits employed resulted in a photopeak of 3.5 keV F W H M for the 1333 keV gamma ray of 6°Co. The system was calibrated as carefully as possible for both energy and intensity measurements. The following energy standards were used (with the adopted energy values in keV shown in parentheses): 241Am(59.57), 2°3Hg (73.0, 279.1), la3Ba (81.0, 276.0, 302.0, 355.0 and 383.0), STCo (122.0, 136.4), RdTh (238.6, 511.0, 583.0, 727.0, 860.0 and 1592.4), 22Na (511.0, 1274.6), ~34Cs (563.0, 569.0, 604.7 and 796.0), 1 aTCs (661.6), 54Mn (835.0), aSy (897.5, 1841.0) and 6°Co (1173.3, 1333.0). As expected, the detector proved to be highly linear. When energy was plotted against channel number, a straight line could be drawn such that all calibration points were within 3 keV, and all but two were within 1 keV of the line. The intensity standards were obtained from the International Atomic Energy Commission, Vienna. The sources included 241Am, 2°3Hg, 57C0, 22Na, 137Cs, 54Mn, 6°Co and s s y and covered an energy range from 60 to 1841 keV. They were all spot sources and when in use, they were placed in the same mount as that used for the 154Eu ' so that all geometries were essentially identical. The spectrum of each calibration standard was taken, and the intensity of the standard photopeaks measured. Then the ratio of the calculated relative intensity of the gamma-ray standard to the measured intensity of the corresponding photopeak was plotted as a function of
EXCITED
435
S T A T E S O F l~i4Gd
energy. This calibration curve is shown in fig. 1. The window effect of the detector and the aluminium window of the vacuum chamber become troublesome at about 80 keV. The curve is quite smooth and is just the inverse of the total efficiency curve. Each g a m m a spectrum taken was followed by 10 min runs of each of the energy calibration sources. To insure that no drift occurred in the system (amplification, threshold, bias voltages etc.), frequent monitoring was performed using a 22Na spectrum as a " p r o b e " at the beginning and at the end of each run. I f any detectable shift occurred in the two photopeaks of 22Na (511.0 and 1274.6) keV, the run was discarded.
4.4
4.0
c
~o~8s
3.6
8 3.2 c
2.a Hg 0 3
o
2.4
2.0 °~o133
"%
~ao
.,~o
~oo
.oo
,&o
,~'oo
,.~o
doo
doo
zoo~
ENERGY (keY)
Fig. 1. Intensity calibration of the Ge(Li) detector.
3. Results and analysis Typical gamma-ray spectra are shown in figs. 2 and 3, and the summaries of the energies are presented in table 1. The comparative intensity of the 152Eu contaminant was deduced from the conversion-electron spectrum shown in fig. 6, where the 121.8 keV K-conversion line of 152Sm is sufficiently separated from the 122.9 keV Kconversion line of 154Gd to make it possible to deduce their relative intensities (approximately 1 : 2 5 ) . Only the more intense components of the g a m m a rays resulting from the decay of x54Eu would be observable in our spectra, and in those cases, corrections were made where a 154Gd line was affected. There are three such cases in table 1.
436
L.K. NG et al.
In the majority of cases, the gamma rays found in this experiment can either be fitted into the accepted decay scheme as shown in fig. 4 or can otherwise be identified. The 558.0 and 892.7 keY transitions were observed by Harmatz e t al. 9) in the decay of 154Tb to 154Gd but have not previously been found in the decay of 154Eu" Other gamma rays not reported before, but which fit between accepted levels, are those of X I0" 722.9 122.9
:543.6
~Q 409.5 440.0
I I
479.5
rZsB~y
582.1
i i 55~o
692.0
79 i z5.7 ~15
.,.}.
247.6
...]
. ,.:.? , ....J "."
! 190.0
X20
i
/I. :;/ I
~o
h
100
2ao
360 CHANNEL
4bo
500
NUMBER
Fig. 2. Lower energy half of the gamma-ray spectrum of 154Gdtaken with Ge(Li) detector (6.7 cmZx7.5 mm). 401.0 and 582.1 keV energy. These de-excite the 1396.9 keV level to the 995.9 and 814.8 keV levels, respectively. In every instance illustrated in fig. 5, the discrepancy between the gamma-ray energy and the level-energy differences involved is never greater than 0.6 keV and is usually less than 0.3 keV.
EXCITED STATES OF
437
1540d
Some of the low-intensity gamma rays appearing in our spectra, which do not fit the established scheme, can be identified as belonging to the X52Eu decay family. We ascribe to the 152Sm impurity the 964.1, 1112.0, 1085.5 and 1408.2 keV gamma rays and the 343.6, 778.6 and 1299.3 keV transitions to a52Gd. The 86.9 and 105.3 keV gamma rays are most likely due to 155Eu and are formed by double neutron
x,d 1004.5
50 ,9
/ - -
\
--\ 1274.4
40
1595.9 1408.2
xlo tn
~: 3c
I
~...
20
..:.::". 1493.7
..f:
,°665
[
1299.3
I
"
. 10
1112.0
/S,.,
-~396.
i ] I
1246 2
' '-.../ i
500
600
..jI-""
146i'~~79 :"':.~,....~
i
700 CHANNEL
600 NUMBER
900
Fig. 3. Upper energy half ofthe gamma-ray spectrum oflb4Od taken with Ge(Li) detector (6.7 cm~× 7 ram). capture. The very weak peak at 1396.6 keV is probably a sum peak of the strong 122.9 and 1274.4 keV gamma rays. Its intensity is about what is expected from the efficiencies of the detector for the two contributing gamma rays. The remainder of the weak gamma rays are unassigned. It is possible, in view of the accuracy of the energy
438
L.K. NG e t
al.
m e a s u r e m e n t s , to p o s t u l a t e o t h e r levels in 1 5 , G d to a c c o m m o d a t e them. H o w e v e r , in the absence o f o t h e r s u p p o r t i n g evidence, such speculation is n o t very useful. It is quite possible t h a t there are o t h e r w e a k g a m m a - r a y lines hidden in the scatter o f e x p e r i m e n t a l points between the strong peaks. The w e a k lines listed in table 1 were limited, r a t h e r arbitrarily, to those g r o u p i n g s o f p o i n t s in which there were at least six consecutive channel counts f o r m i n g a p e a k - l i k e structure. A n a d d i t i o n a l requirem e n t was t h a t for such a p e a k , the h a l f m a x i m u m c o u n t i n g rate could be j u d g e d to lie a b o v e the c o n t i n u u m u p o n which the p e a k was situated. M a n y o f the g a m m a rays listed in table 1 have never been resolved before, the TABLE l
Energies and relative intensities of the gamma rays of 154Gd T-ray energy (keV)
Relative intensity
86.9 105.3 122.9 190.0 247.6 343.6 401.0 409.5 444.0 479.5 558.0 582.1 591.6 625.7 692.0 722.9 756.7 778.6 815.0 845.2
15.42 4-1.31 9.704-0.84 100 1.344-0.13 15.864-0.72 3.76 4-0.29 0.65 4-0.20 0.59 4-0.20 1.134-0.14 0.88 t0.25 0.874-0.16 1.73 4-0.16 10.51 4-0.54 0.81 4-0.20 3.80 4-0.29 47.30 4-2.05 10.364-0.60 2.43 4-0.40 1.31 4-0.22 1.62 4-0.35
Remark X55Gd X55Gd (corrected) a) (corrected) 15~Gd a) (corrected) ~)
lS2Gd 4)
),-ray energy (keV)
Relative intensity
872.6 892.7 903.6 964.1 995.9 1004.5 1085.5 1112.0 1127.9 1140.7 1186.3 1246.2 1274.4 1299.3 1396.6 1408.2 1460.9 1493.7 1537.7 1595.9
29.38 4-1.36 1.234-0.20 2.04-t-0.23 1.824-0.25 24.694-1.12 43.85 4- 1.92 1.67 4-0.22 2.40 4-0.24 0.804-0.25 0.61 4-0.20 0.634-0.30 2.27 4-0.21 92.004-4.13 0.21 4-0.05 0.15 4-0.04 3.29 4-0.20 0.394-0.10 1.71 4-0.11 0.13 4-0.02 4.67 4- 0.22
Remark
lszSm 15aSm xs2Sm a) a) a) X52Gd b) lb2Sm a) a) a)
a) Gamma ray is unassigned. b) Sum peak. s e p a r a t e energies having been d e d u c e d f r o m the c o r r e s p o n d i n g conversion electron peaks. E x a m p l e s are the strong 995.9-1004.5 keV a n d the m o d e r a t e l y strong 582.1591.6 keV pairs. I n o r d e r to confirm their p r o p e r p o s i t i o n s in the decay scheme, g a m m a - r a y spectra were m e a s u r e d in coincidence with the 722.9 a n d 591.6 keV g a m m a rays. F o r this experiment, the source was placed between the G e ( L i ) detector a n d a 2.5 c m x 4.0 cm NaI(T1) scintillator, the latter being in c o n t a c t with an R C A 5819 p h o t o m u l t i p l i e r . The coincidence circuit was o f the slow-fast type. The p h o t o m u l tiplier o u t p u t f r o m the a n o d e was used for one side o f the fast coincidence circuit.
t54Eu
054Gd ~-Band
~
0 keV, 2 6 . 5
i
x
y-Bond
I
%
-4 ~/÷%'o ,~.
-,,
Tf
1718.7'
2-
1396 9
2-
--rJ
O~OJ
1263.4
TT_ IIIT
1127.3
___
!
814.8
o;
680.4
it) b.
_
t'
3~
995 9
Ii
f
3705
I22.9
T
0
Fig. 4. D e c a y s c h e m e o f 154Eu --->a54Gd. T h e relative intensities o f the beta groups s h o w n here were t a k e n f r o m c o l u m n 4 o f table 3. T h e e n d - p o i n t energies were deduced f r o m energy level differences a n d the m e a s u r e d end-point energy o f 1 8 6 6 ± 12 keV f r o m fig. 8.
gate peak 722.9 keV
gate peak 591.6 keV
(o) 872.6
(b)
keV
240
995.9
IZO
keV
~004.6
keV
160
80
.,° ..
40
, .*.'o
"'.', ,'o .... ,,'o':,,', 0
16
16
i
14elelem I
4
I
°'"'t" ' " " '
76
36
56 CHANNEL
°
"..".:.,:.......~......
76 NUMBER
•
96
96
.......... .,.
• .°.
°16
'
3'6
4°f, o
'
• .i,[......."
s'e
• ..:.'.-.....:......i
16
36
56 CHANNEL
'
~,~
96
................ 76
96
NUMBER
Fig. 5. Portion o f the g a m m a - r a y s p e c t r u m o f XS4Gd in coincidence a) with the 722.9 keV g a m m a ray a n d b) with t h e 591.6 keV g a m m a ray. (The lower figures s h o w the s a m e spectra t a k e n with the gate settings m o v e d just off the selected peaks.)
440
L.K. no et al.
Pulses from the eighth dynode were fed through a white cathode follower, amplified by a fast linear amplifier, clipped to a 1 #sec pulse width and fed to an antiwalk single-channel analyser for gate selection. The fast coincidence pulses from the Ge(Li) detector side were taken directly from the low-noise preamplifier before pulse-shaping. The shaped pulses from the following time-constant box were fed to a 128-channel pulse-height analyser via a low-noise amplifier. The coincidence pulse width of the fast circuit was set at 50 nsec. The window of the single-channel analyser was set at 20 keV. Fig. 5 shows the coincident spectra with the gate set on each of the 722.9 and the 591.6 keV peaks and also with the gate set just off those peaks. The results support the positional assignments of these gamma rays in the decay scheme.
1500 247.6
K
105.3 K
sml52 l
I000
500343.6
591.6 K
K
679.4K
;/
r/I i
400
~
.OK
T22,K
1004.5
K
- -
"..,., S.9K
22.9K
500
%....
~
".,...,,,
122.9 M
.d X~
I
i
i 0,20
,ol , I , 0.30
" ",A\
"..~E)O ".°.
.... r~ 0.1"~ ) 0
300
..°..°
,
, , I , , , , I , 0.40 0.50 POTENTIOMETER
i
/'i....,.,.,
, t . . . . 0.60
"'...jt...A..
i . . . . O.TO
t 0.80
,
SETTING
Fig. 6. The conversion-electron spectrum of 154 Gd. The intermediate image spectrometer was set for a line width at half maximum of 0.7 ~ in momentum. The conversion-electron spectrum of fig. 6 was taken with the magnetic spectrometer set for a resolution of 0.7 7ooin momentum. Most of the counting time was spent on the peaks rather than on the continuum, and a summary of their identification and relative intensities is given in table 2. The corresponding data from the work of Bobykin and N o v i k 10), of Juliano and Stephens 11) and of Hamilton e t al. 12) are included for comparison. It should be noted here that although the region was very carefully scanned, we could find no evidence for two close-lying K-conversion peaks as reported by Hamilton e t aL a2). Their published curve shows two clearly separated
441
EXCITED STATES OF 154Gd
peaks of roughly equal intensity corresponding to transition energies of 678 a n d 682 keV. It appears that their i n s t r u m e n t resolution is very nearly the same as our own, in which case two such peaks will n o t be resolved b u t will appear as a single peak with a F W H M approximately 50 ~ larger t h a n that of a single peak. Fig. 7 shows this section of the conversion-electron spectrum from our data, the dashed lines shows a single peak shape superimposed. The p o i n t is i m p o r t a n t , for this is the only evidence advanced for the excitation of the 4 + b e t a - v i b r a t i o n a l level in the decay of 154Eu. TABLE2 Intensities of conversion electrons Transition energy (keV)
Shell
Present work
Bobykin and Novik 10)
86.9 86.9 105.3 105.3 122.9 122.9 122.9 247.6 247.6 247.6 591.7 679.4 692.0 692.0 722.9 722.9 756.7 872.6 872.6 995.9 1004.5 1274.4
L M K L K L M K L M K K K L K L K K L K K K
0.73 ±0.08 0.14 ~0.03 4.04 ~0.15 0.47 ±0.10 100 65.6 ±1.3 18.8 ±0.7 2.20 ±0.05 0.56 ±0.06 0.12 ±0.01 0.10 ~0.01 0.052±0.005 0.32 ~0.07 0.049±0.01 0.18 ±0.01 0.018 ~0.004 0.092±0.008 0.157±0.007 0.032 ~0.007 0.090t0.018 0.151 ±0.031 0.100±0.027
2.08 0.59 4.95 0.86 100 <208 a) 23 <10 a) 0.58 0.10 0.125±0.005 ~0.04 <0.68 a) ~0.04 <0.15 a) <0.05 a) 0.07 ±0.003 <0.31 a) <0.20 a) 0.11 ~0.003 0.190 0.074±0.003
Juliano and Stephens 11)
Hamilton et al. 12) b)
100 109 18.9 3.1 1.2
0.55
0.32
0.31 0.08 0.40
0.064±0.013 0.16 ±0.02
0.15 0.39 0.37
0.12 ±0.02 0.20 i0.02
a) Conversion peaks contain unresolved components of other transitions. b) Data have been normalized to our value of 0.32 for the intensity of the K-conversion line for the 692.0 keV transition. The p r i m a r y beta spectrum in the intervals between the conversion peaks was taken with the higher t r a n s m i s s i o n setting m e n t i o n e d earlier. The spectrum is k n o w n to be complex with a n u m b e r of first-forbidden groups. A K u r i e analysis was applied to the data in the usual m a n n e r . First, an experimental shape correction f u n c t i o n C a was calculated from the data. Then, following the proposal of K o t a n i a3) that firstforbidden spectra of this type have C a = q 2 + O . 8 0 7 p 2 + D , the value of D was determined to be 2 0 + 2 , in good agreement with the work of Langer a n d Smith 14). A least-squares fit with this f u n c t i o n gave a n e n d - p o i n t of 1 8 6 6 _ 12 keV. F o l l o w i n g
442
L.K. NG et al.
the subtraction of this group, a cluster of points showing a wide scatter appeared at energies j u s t b e y o n d the e n d - p o i n t of the next intense group. This cluster we interpreted as the high-energy end of a weaker group, the statistical scatter being what one would
692.0
K
I00
50
679.4
K
1
0.620
0,630 0.640 POTENTIOMETER SETTING.
0.6,~0
Fig. 7. The conversion-electron spectrum of 154Gdin the region of 680 keV energy. The primary beta background obtained by interpolation of the continuum under the peaks has been subtracted. The dashed line profile is the shape of the 692.0 keV K-conversionpeak, suitably scaled and centred at the setting for a 679.4 keV K-conversion peak. The arrows show the expected positions of the two close-lying K-conversion lines reported by Hamilton et al. 1~).
expect near the e n d - p o i n t of a beta group. W e fitted the cluster as best we could with C1 = q2 + 0.79 p2 + ( 0 _ 4). The procedure was repeated with appropriate subtractions down to a n d including an intense group with an e n d - p o i n t near 270 keV. F o r all groups
443
EXCITED STATES OF lS4Gd
after the second, the experimentally determined correction factor was a constant. Fig. 8 shows the plot of the Kurie analysis. The relative intensities of the separated beta groups were determined by area measurement. Table 3 shows the total formation and decay rates for all levels of ~ 54Gd deduced from the intensities of the gamma rays and the conversion electrons. (These may be found in the second and third columns of table 4). The differences between these two rates should correspond to the intensity of the beta group populating the level, and in table 3 these differences are compared with the results of the Kurie analysis. The results
30 \\ 20
\\ x "
\\ \\ \
X20 \ \ \
I0
--..
.
.
.
.
I
5OO
.
.
.
.
I
,
I000 ENERGY (keY}
1866~12
I 1500
Fig. 8. Kurie analysis of the primary beta spectrum of 154Eu. are more consistent than was expected considering the multiple subtractions performed in the latter process. Nevertheless, because of their greater accuracies, we preferred to rely on the gamma-ray and conversion-electron data in estimating the end-points and intensities of the beta groups, rather than on the results of the Kurie analysis. 4. Transition multipolarities Table 4 lists all relative conversion-electron intensities and the corresponding
444
L.K. NG e t al.
relative g a m m a - r a y intensities. The conversion-electron intensity d a t a have been n o r m a l i z e d to the g a m m a - r a y scale b y assuming t h a t the 122.9 keV t r a n s i t i o n is pure E2 with a K - c o n v e r s i o n coefficient o f 0.652 [ref. 15)]. The conversion coeffÉcients so calculated confirm the expected p r e d o m i n a n t l y E2 c h a r a c t e r o f the transitions between p o s i t i v e - p a r i t y states. W h e r e one o f the states has negative parity, the transition a p p e a r s to be E l . The exceptions to the p o s k i v e - p a r i t y rule are the 679.4 a n d 692.0 keV transitions. T h e first goes between 0 + states o f the b e t a - v i b r a t i o n a l a n d g r o u n d - s t a t e r o t a t i o n a l bands, a n d therefore it proceeds b y TABLE 3 Transition intensity balances for the energy levels of a54Gd Level energy (keV)
Output (74-conversion)
Difference (~ of total Eu decay)
1718.7
64.71 ±3.05
64.71 ±3.05 (26.3 ~ )
(29.1 ±2.5)
1396.9
94.45 ±4.51
94.45 4-4.51 (38.4 ~)
(37.8 4-3.5)
1263.4
1.84 5_0.40
1.84 4- 0.40 (0.7 ~ )
54.29 4-2.55
43.71 4-3.10 (17.8 ~ )
1127.3 995.9 814.8
Input (74-conversion)
10.58 4-0.55 47.95+2.25 3.774-0.39
680.4
55.04 ±2.70 6.51-4-0.66
7.09 4-4.95 (2.9 ~ ) 2.744-1.05 (1.1 ~)
0.90±0.18
0.90±0.18 (0.4 %)
370.5
13.754-0.95
17.664-0.79
3.91 4-1.74 (1.6 ~ )
122.9
193.374-9.13
219.604-2.00
26.23±11.13 (10.8 ~)
Beta intensity (~)
(17.0 4-3.9) (4.6 4-3.8) (0.674-0.49)
(10.8 4-0.12)
Gamma-ray intensities are normalized to 100 for the 122.9 keV transition. Conversion electron intensities are normalized to 65.2 for the 122.9 keV transition. the emission o f conversion electrons alone. The m u l t i p o l a r i t y is E0, a n d the absence o f g a m m a rays establishes the 680.4 keV level as the b e t a - v i b r a t i o n a l b a n d head. The 692.0 keV t r a n s i t i o n links the 2 + states o f the same two bands. F r o m a c o m p a r i son o f the m e a s u r e d K - c o n v e r s i o n coefficient with the theoretical value for an E2 transition, we deduce t h a t the E0 c o m p o n e n t is 5 . 0 + 0 . 9 ~ o f the total intensity. The energy o f the pure E0 transition listed in table 4 as 679.4 keV has a b o u t a 1 keV u n c e r t a i n t y since it lies in the tail o f the m u c h stronger 692.0 keV K - c o n v e r s i o n peak. The g a m m a - r a y b r a n c h f r o m the same level is the cascade ( 5 5 8 . 0 + 1 2 2 . 9 ) k e V or
43.85-5-1.92
92.00±4.13
1004.5
1274.4 0.065±0.018
0.099i0.02
0.059~z0.012
0.102~0.005 (0.0214-0.004)
0.060~z0.005
0.120±0.005 (0.012±0.003)
0.210i0.004 (0.032±0.006)
0.034£0.004
0.065-4-0.008
1.43 4-0.03 (0.37 ±0.04)
6.520 4-0.70 (42.70 ~0.90)
Conversion intensity (relative~
~0.008 ±0.004)
4-0.006 i0.009)
0.00071i0.00023
0.00225±0.00055
0.0024 ±0.0006
0.0035 ±0.0004 (0.00071i0.00017)
0.0058 -4-0.0008
0.0025 ±0.0002 (0.00025~0.00007)
0.055 ~0.005 (0.0084 ±0.0022)
0.0062 ~0.0011
0.090 (0.023
0.652 (0.427
Experimental conversion coefficient
The L-conversion coefficients, where measured, are indicated in parentheses.
24.69±1.12
47.30~z2.05
722.9
995.9
3.80~0.29
692.0
10.36±0.60
0
679.4
29.38~1.36
10.51-~0.54
591.7
872.6
15.86:~0.72
247.6
756.7
100
G amma-ray intensity (relative)
122.9
Transition energy (keV)
0.00145
0.0023
0.0023
0.00314 (0.005)
0.0043
0.0047 (0.0008)
0.00519 (0.0009)
0.0076
0.082 (0.023)
0.652 (0.430)
E2
0.0022
0.0039
0.0040
0.0054 (0.0012)
0.0077
0.0086 (0.0019)
0.00954 (0.0020)
0.0140
0.135 (0.020)
0.941 (0.135)
M1
Theoretical coefficient
TABLE 4 Experimental and theoretical 15) conversion coefficients for the gamma rays of 154Gd
0.00063
0.00097
0.00099
0.0013 (O.OO017)
0.0017
0.0018 (0.00025)
0.00201 (0.00028)
0.0028
0.0218 (0.0034)
0.142 (0.021)
E1
E1
E2
E2
E2
E2
El
E2 + E0
E0
E2
E2
E2
Assignment
.Ix
446
L.K. NG et al.
680.9 keV. Since we consider the uncertainties in the gamma-ray energy measurements to be less than 0.5 keV, we have established the 0 + beta-vibrational state at 680.4 keV.
5. Comparison with model predictions 5.1. THE E2 TRANSITION PROBABILITIES The theory of the asymmetric rotator has been described elsewhere 2, 7). Briefly, the energy eigenvalues and reduced transition probabilities are computed in terms of three parameters which are used to describe the physical properties of the nucleus. They are the quadrupole asymmetry parameter T, the nuclear "stiffness" # and the equilibrium deformation fl0. The value of fl0 for 154Gd is taken as 0.303; it was deduced from Coulomb excitation probability data a). The values of T and p are those which make the theoretically predicted energy level structure best fit the observed values. The theoretical energy values for even-parity states are given by ELN . = h~o o (v,+½)
+ ~
1+
2Z 2 . ] j ,
where eLn are the rotational energies for a rigid asymmetric top in units of h 2 / 4 B 2 f12. The three quantum numbers are the nuclear spin L, the ordering label N for spin L and the ordinal number n of the vibration band. The quantity h m o is the oscillator energy which is used as a scale adjustment factor. To obtain the values of T and ft, we made use of the five basic machine programs written by Davidson 16). The first three programs calculate the energy eigenvalues for a given pair of 7 and ft. These predicted levels are then compared with the experimental values for the same states and the r.m.s, deviation calculated. Then both ~ and # are varied within suitable ranges until they enclose the minimum r.m.s, deviation. The values we obtained with this procedure are ~ = 11.52 ° and # = 0.402 (with an r.m.s, deviation of 1.5 %). This can be compared with 11.62 ° and 0.4006 obtained by Davidson 8) for slightly different values of the energy levels. De Aisenberg and Suarez (ref. 17)) quote values of 11.5 ° and 0.8 for lSaGd. Table 5 lists the observed and predicted positive-parity levels with these parameter values. The E2 transition probabilities can now be calculated. For the asymmetric rotator, this was accomplished using the last two of Davidson's five programs 16). In the case of the unified model, it is well known that particularly in the transition region between the spherical and the deformed shape, the assumption of pure Kstates will not give either the correct energy levels or the correct transition probabilities. This assumption implies the adiabatic condition, in which the rotation and vibration excitations are completely decoupled. A relaxation of the adiabatic restriction will allow coupling between the vibration and the rotation bands. This results in a degree of mixing of the wave functions of the bands which can be described 18) by a functionf(z, Ii, It) such that the reduced probability for an interband transition
447
EXCITED STATES OF 154Gd
is given by B(E2 : I i
~
If) = Bo(E2
: Ii ~
If)f (z, Ii,
If).
Here Bo is the adiabatic probability which is proportional to the square of the appropriate Clebsch-Gordan coefficient. Tables of the form o f f ( z , Ii, If) are available
(refs. 18,19)).
TABLE 5 Energy levels o f the asymmetric r o t a t o r for 154Gd with the parameters ~ = 11.52 °,/~ = 0.402 and fl0 = 0.303
LNn
0 2 4 0 2 2 3 4
1 1 1 1 1 2 1 2
1 1 1 2 2 1 1 1
Experimental
Theoretical
Deviation
ELNn
ELNn
(%)
(keY)
(keV)
0 122.9 370.5 680.4 814.8 995.9 1127.3 1263.4
0 122.9 365.4 676.5 831.9 1052.7 1121.3 1212.0
1.4 0.5 2.1 5.4 0.5 4.2
TABLE 6 Experimental and theoretical reduced transition probability ratios (E2) Transition description
Theoretical
Energy
Asymmetric rotator
Unified model
Observed ratio
Asymmetric rotator
Unified model
625.7 872.6
221 -+ 411 221 "-+ 211
27+ "-+ 4g+ 27+ ~ 2 +
0.145i0.035 (0.12 4-0.03) a)
0.113
995.9 872.6
221 -+ 011 221 --~211
27+ ~ 0g+ 27+-+2g+
0.4344-0.040 (0.39 ±0.03) a)
0.443
0.443
1004.5 "756.7
311 ~ 211 311--~411
37+ ~ 2g+ 37+_+4g+
1.0264-0.104 (1.0 4-0.1) a)
1.004
0.976
1140.7 892.7
421 -+ 211 421 ~ 41]
47+ ~ 2g+ 47+ -+ 4~+
0.1464-0.065
0.119
0.093
444.0 692.0
212 ~ 411 212 --~ 211
2# + --~ 4g+ 2#+ _+ 2g+
2.75 4-0.63 (3.0 ± 0 . 6 ) a)
4.35
6.46
815.0 692.0
212 -+ 011 212 --~ 211
2# + ~ 0g+ 2#÷ __+ 2g+
0.1524-0.014 (0.18 4-0.04) a)
0.373
0.266
(z~ = 0.079) 0.109
(z0 = 0.064)
a) Values quoted by Liu et al. 3).
448
L . K . NG e t
al.
In table 6, we present the results of calculations based on both models. In the case of the g a m m a band, the unified model mixing parameter z 2 was deduced for each of the four ratios shown. In the order that they are presented in table 6, the values of z 2 are 0.125___0.045, 0.082+0.008, 0.076___0.008 and 0.058+0.029. All four values agree within the error limits, and the average value is 0.086. The value of z 2 chosen to represent the band is 0.079, the average of the second and third which were measured with the greatest precision. For the beta band, the mixing parameter z o was computed from the ratio B(E2 : 2~- ~ 4+)/B(E2 : 2~- ~ 0 +) since in this way, possible M1 admixtures are avoided. The value z 0 = 0.064+0.009 was then applied to calculate the other transition intensity ratios. Table 6 demonstrates the fact that either model is adequate to predict g a m m a band to ground-state-band transition probability ratios within the limits of experimental error. But it also shows that neither model is successful in dealing with beta-band E2 transitions. The problem is associated with the 692.0 keV transition which links the first and second 2 + states. The gamma-ray intensity for this transition, assumed here to be pure E2, is too large, and this has the effect of reducing the experimentally determined transition ratios below the values predicted. It has been suggested 5) that there exists a large M 1 component, which if subtracted from the gamma-ray intensity, would bring observation into line with theory. However, the directional correlation measurements on the 692.0-122.9 keV cascade in 154Gd by Hamilton et al. 6) definitely rules out the possibility of any M1 component large enough. In fact, these authors conclude that the 692.0 keV transition is pure E2. The same problem has been encountered in 152Sm and in 155Gd [ref. 5)], where it has been estimated that the M1 component would have to be about 40 ~ . 5.2. THE E0 TRANSITIONS AND ELECTRIC MONOPOLE STRENGTHS Electric monopole transitions can take place between beta and ground-state bands if the two states involved have equal spins. The absolute E0 transition probability as defined by Church and Weneser 20) is T(E0) = O p 2 , where I2 is the electronic factor, which is available for the K-shell as a function of energy in graphical form 2 o). The quantity t2 2 is called the monopole strength. In the case of 154Gd ' there are two such transitions for which intensity measurements can be made. For the transition between the first and second 0 + states, no g a m m a rays can be emitted, and the transition proceeds entirely by electron conversion. This is confirmed by the absence of any gamma ray of energy 680.4 keV, and by the presence of the corresponding K-conversion peak (fig. 8). If we use the data given in tables 1 and 4, we can determine the absolute intensity ratio for the E0 and E2 branches from the second 0 + state.
449
EXCITED STATES OF l~"tGd
The transition between the first and second 2 + states is complicated by the presence of E2 radiation. However, as mentioned earlier, analysis of the conversion coefficients leads to a value for the intensity ratio of the E0 and E2 components in this transition. The theoretical values of both the above intensity ratios can be calculated easily from Davidson's programs s, 16) with a simple modification. In table 7, we list both the experimental ratios and the theoretical values as calculated in terms, of the asymmetric rotator. In each case, the predicted values are two to three times too large. Recently, interest has focussed on the values of the monopole strengths and how they vary from one level to another within the band 5,21,z2). F r o m the observations available, one concludes that p2 is approximately constant for all members of the beta band. The calculations of Davidson s) on/92 for symmetric nuclei (~ = 0) are in agreement with this conclusion at least for moderately "stiff" nuclei, (i.e. # < 0.3). For greater values of/~, p2 increases with the level spin. It is not expected that values of y different from zero will affect this behavior very much. Since in 154Gd ' we have a nucleus that is only moderately soft, the p2 values for the 0 + and 2 + members of the beta band should be about the same. TABLE7 Electric monopole -quadrupole transition ratios Transition
Observed
Calculated
p2
T(E0; 0/~+ ~ 0g+) T(E2; 0#+ --~ 2g+)
0.0394-0.012
0.085
0.474-4-0.23
T(E0; 2#+ -+ 2g+) T(E2; 21/+--+2g+)
0.0534-0.013
0.158
0.464-0.30 a)
a) Calculated using T(E2; 2#+ --+ 0g+). In order to calculate pZ for any E0 process, one must know the absolute value of the transition probability for its decay. This can be determined best by Coulomb excitation experiments. Yoshizawa et al. 23) have measured B ( E 2 ; 0 + ~ 2 ; ) for 154Gd and obtained the value 0.12+0.03 in units eZ(10 -48) cm 4. For the transition (2~" ~ 2+), the procedure is now straightforward. The absolute transition probability T(E2) is related to the reduced probability through the relation 24) 8 ~ ( l + 1) E~ B(E2; + T(E2; 2 ; --, 0 +) - •[(2•+ 1)!!] 2 h6C 5 2p
0~-).
Also, B(E2: 2 ; --* 0 +) = ½B(E2:0 + --+ 2 ; ) = 0.024_+0.006 e2(10 -4s) cm*. F r o m the second ratio in table 7, with the value f2 = 0.35 x 1011 sec-1, p2 can be computed. The monopole strength p2 for the ( 0 ; ---, 0 f ) transition can be deduced from the first ratio in table 7, but for this we must know B(E2: 0 ; ~ 2+). This may be computed from the Coulomb excitation data, except that in this case band mixing must be
L.K. NG et al.
450 included. Thus
B(E2: 0~- ~ 2 + ) = B ( E 2 : 0 + ~ 2~-) i + 6 z o _ 0.606+0.150. 1 - 6z o F o r this transition, ~ is 0.335 x 1011 see -1. T h e two values o f pZ are also listed in table 7. Their internal consistency ( a p a r t f r o m the uncertainties in the C o u l o m b d a t a ) does indicate t h a t within the b a n d , pZ is a constant. W e also calculated p2 using the p r o g r a m s of D a v i d s o n s,16) a n d o b t a i n e d the value 0.66. I n this connection, we wish to a d d t h a t if the E0 conversion p e a k c o r r e s p o n d i n g to the transition o f energy 679.4 keV does c o n t a i n a c o m p o n e n t due to a t r a n s i t i o n f r o m a 4 + b e t a - v i b r a t i o n a l level as claimed by H a m i l t o n et al. lz), then b o t h the transition p r o b a b i l i t y ratio a n d the value o f p2 for the 0 + levels in table 7 will be c o r r e s p o n d i n g l y reduced. 6. C o n c l u s i o n s
W e have sought in this e x p e r i m e n t to examine the decay o f l S4Eu to 154Gd in careful detail a n d to interpret the results in terms o f the two basic descriptive a p proaches. The results a p p e a r to confirm t h a t where one m o d e l is adequate, the o t h e r is also, at least in this region o f nuclear d e f o r m a t i o n . B o t h models fail to describe a d e q u a t e l y the same aspects o f nuclear behaviour, that is, the de-excitation o f specific levels o f the b e t a band. Other w o r k s have d e m o n s t r a t e d t h a t an a p p e a l to a s t r o n g M1 c o m p o n e n t is n o t confirmed. Mixing o f other b a n d s t h a n the K = 0 or 2 m a y p r o v i d e an answer, b u t if not, then the difficulty m a y be m o r e f u n d a m e n t a l and m a y even lie in the initial expression for the nuclear surface. T h e a u t h o r s wish to acknowledge their great indebtedness to Dr. G. T. E w a n for his helpful c o m m e n t s a n d suggestions a n d to Dr. J. P. D a v i d s o n for valuable assistance in interpreting the a s y m m e t r i c r o t a t o r theory. One o f us ( L . K . N ) . is i n d e b t e d to the C a n a d i a n Office o f External A i d for a fellowship held d u r i n g the course o f this work. This w o r k was s u p p o r t e d by a g r a n t - i n - a i d f r o m the N a t i o n a l R e s e a r c h C o u n c i l o f C a n a d a to K . C . M . . References
1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 27, No. 16 (1953) A. S. Davydov and A. A. Chaban, Nucl. Phys. 20 (1960) 499 I. Liu, O. B. Nielsen, P. Salling and O. Skilbreid, Izv. Akad. Nauk SSSR (ser. fiz.) 31 (1967) 63 L. L. Riedinger and N. R. Johnson, Phys. Rev. Lett. 19 (1967) 1247 G. T. Ewan and G. I. Andersson, Int. Conf. on Nuclear structure, Tokyo (1967) J. H. Hamilton, A. V. Ramayya, L. C. Whitlock and A. Meulenberg, Phys. Rev. Lett. 19 (1967) 1484 J. P. Davidson and M. G. Davidson, Phys. Rev. 138 (1965) B316 J. P. Davidson, Nucl. Phys. 86 (1966) 561 B. Harmatz, T. H. Handley and J. W. Mihelich, Phys. Rev. 123 (1961) 1758 B.V. Bobykin and K. M. Novik, Izv. Akad, Nauk SSSR (ser. fiz.) 21 (1957) 1556
EXCITED STATESOF l~4Gd 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)
451
J. O. Juliano and F. S. Stephens, Phys. Rev. 108 (1957) 341 J. H. Hamilton, T. Katoh, W. H. Brantley and E. F. Zganjar, Phys. Lett. 13 (1964) 43 T. Kotani and M. Ross, Phys. Rev. 113 (1959) 622 L. A. Langer and D. R. Smith, Phys. Rev. 119 (1960) 1308 L. A. Sliv and I. M. Band, Coefficients of internal conversion of gamma radiation (Academy of Sciences of the USSR, Moscow-Leningrad, 1956-1958) J. P. Davidson, USNRDL Report-TR901 (1965) E. Y. de Aisenberg and J. F. Suarez, Nucl. Phys. A97 (1967) 529 O. Nathan and S. G. Nilsson, in Alpha-, beta-, and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) P. G. Hansen, O. B. Nielsen and R. K. Sheline, Nucl. Phys. 12 (1959) 389 E. L. Church and J. Weneser, Phys. Rev. 103 (1956) 1035 O. Lbnsj~5 and G. B. Hagemann, Nucl. Phys. 88 (1966) 624 N. R. Johnson, L. L. Riedinger and J. H. Hamilton, Int. Conf. on nuclear structure, Tokyo (1967) Y. Yoshizawa, B. Elbek, B. Herskind and M. C. Olesen, Nucl. Phys. 73 (1965) 273 M. A. Preston, Physics of the nucleus (Addison-Wesley Publ. Co., Reading, Mass. 1963) chapt. 11, p. 298