A note on band mixing in 154Gd

1.D.2: ] 3.A

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Nuclear Physics A153 (1970) 647--651 ; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

A NOTE ON BAND MIXING IN tS4Gd G. E. KELLER t and E. F. Z G A N J A R

Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana Received 16 March 1970 Abstract: The relative intensities of the ),-rays emitted in the decay of ~54Eu were measured using

Ge(Li) detectors. The E2 components of the intensities of transitions from the K = 2 and K = 0 vibrational bands to the ground state rotational bands were used to calculate ratios of reduced E2 transition probabilities and the corresponding band-mixing parameters. The band mixing of the K = 2 and the K = 0 vibrational bands could not be described by a two-parameter analysis. E [

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RADIOACTIVITY 154Eu [from lS3Eu(n,y)lS4Eu]; measured Iy, Ey. lS4Gd deduced B(E2) ratios, mixing parameters.

1. Introduction

The nucleus 154Gd has been thoroughly investigated 1- 1t) and a level scheme containing a beta vibrational band (K = 0) as well as a gamma vibrational band (K = 2) has been established. The nucleus 154Gd lies in the region of transition from spherical to deformed nuclear shape and its study provides a critical test of the applicability of the band-mixing model 12,13) to transitional nuclei. This model has been shown to be applicable to the nuclei 166Er [ref. 14)] and 16SEr [refs. 14-~7)], which are located in the region of largest deformation. Some of the previous band-mixing results for transitional nuclei have shown that the model is applicable to 152Sm [ref. s)] and 1S4Gd [refs. 6, a)] for mixing of the gamma and ground state bands. Ng et al. 6) obtained agreement with a single-parameter mixing model, whereas Reidinger s) obtained agreement only by including an additional parameter which corrects for the mutual coupling of the beta and gamma vibrational bands. Reidinger s) did not obtain agreement with band-mixing theory for the beta band of either 152Sm or 154Gd" Other recent investigations s. 1o) have suggested that the band-mixing model is incapable of describing the band mixing in transitional nuclei. Meyer 5) reported a singleparameter analysis for 1S4Gd and Varnell et al. 1 o) reported results of a two-parameter analysis for 154Gd and 152Sm, neither of which accounted for the observed B(E2) ratios. The results of refs. s, 1o) are quoted with higher precision than those of refs. 6, s). The results presented below support the conclusion that the band mixing in 154Gd cannot be described by a two-parameter analysis. t Present address: Physics Department, West Georgia College, Carrollton Georgia, USA. 647

648

G. E. KELLER AND E. F. ZGANJAR 7 - bond

1265.65

104,7.65

1127.75 -

+

.bond

4 ,o

996.25

3+,2

~ I

~

4+,2

l

,

~

~ 2 ÷ 2

'

815.46 680.64

370.96 - -

924.05 I~lI .45 (0.16) 2i) 6~_07 .~.2~ 69: __(4

'?'."

I

0+'0

I (,o.,)I

(,,9,

I

I

(,6.4)

I 23.07 0.0

897.68 ~ 756o77 I 873.15

123.o7

(lop)

'

154 64

Gd

~

(29,)i

I

o

I

+,o

90

Fig. 1. The partial level scheme of ts4G-d showing the energies and intensities of the interband transitions.

TABLE 1 Gamma-ray energies and intensities for the transitions between the K = 0 and K = 2 vibrational bands and the ground state band Transition 11Ki--~Ir Kt

Present exp. energy intensity =) (keV)

energy (keV)

Meyer intensity b)

Varnell et aL energy ¢) intensity b) (keV)

22--->40 22-->20 22-->00 32440 32->20 42-->40 42--*20

625.27(6) 873.15(3) 996.25(3) 756.77(3) 1004.70(3) 892.68(3) 1140.64(10)

0.731(40) 29.13 (61)o) 25.46 (77) 10.41 (26)a) 43.98 (1.14) 1.19 ( 6 ) a) 0.565(40)

625.22(5) 873.19(5) 996.32(4) 756.87(5) 1004.76(4) 892.73(5) 1140.9 ( 1 )

0.777(23) 28.82 (58) 25.81 (52) 10.88 (22) 43.48 (87) 1.15 ( 3 ) 0.541(16)

625.2 873.2 996.3 756.9 1004.8 892.7 1140.9

0.796(25) 29.10 (50) 25.37 (50) 10.97 (12) 43.53 (75) 1.22 ( 2 ) 0.547(25)

20-+40 20-->20 20---~00 40--->40 40-->20

444.44(13) 692.40(3) 815.45(4) 676.29(12) 924.58(30)

1.42 (10) 4.09 ( 8 ) 1.21 ( 5 ) 0.311(86) 0.155(48)

444.40(5) 692.41(5) 815.55(5) 676.59(5) 924.49(5)

1.26 ( 4 ) 4.25 ( 8 ) 1.17 ( 4 ) 0.351(11) 0.148(6)

444.4 692.4 815.6 676.6 924.5

1.42 ( 2 ) 4.38 (10) 1.19 ( 5 ) 0.373(25) 0.149(25)

a) The normalization is relative to 100 units for the 123 keV transition. b) The renormalization of the values reported by Meyer s) and Varnell et al. to) is to the sum of the intensities of the 756, 873, 996 and 1004 keV transitions. °) The uncertainties are 0.1 keV. a) If these values are corrected for the M1 intensity reported by Hamilton et a1.19), the E2 intensity is: /(756) = 10.10(26); 1(873) = 28.84(61); •(892) = 1.13(6).

154Gd BAND MIXING

649

2. Experimental procedure The 154Eu activity was produced

b y t h e r m a l n e u t r o n i r r a d i a t i o n o f 153Eu. T h e

presence of 152Eu and 155Eu activities in the source did not present any interference as far as the results to be reported are concerned. The y-ray spectra were taken with TABLE 2 ExPerimental B(E2) ratios and mixing parameters G a m m a band (K = 2) li Ki --> If Kr Ii Kl ~ If, Kt

22 22 22 22 22 22 32 32 42 42

E ( h --~ If) E ( I i -~ lf, )

--+ 00 ~ 20 --->20 --->40 --->00 --->40 ~ 20 --> 40 --> 20 --~ 40

996 873 873 625 996 625 1004 756 1140 892

B(E2) ratio experimental ") adiabatic 0.456(17)

0.698

2"2 X 10 3

gp,y × 10 3

73.1(66)

-- 1.2(47)

7.43 (44)

19.9

111. (10)

14.9(35)

3.39 (21)

13.9

92.9(52)

29.7(75)

1.056(39)

2.50

71.5(35) b)

0.147(13)

0.340

54.3(51)

6.6(20)

Zo × 10z no fl-7 mixing

fl-7 mixing c)

Beta band (K = 0) 20 ~ 00 20 --> 20 20 --->20 20 --> 40 20 --> 00 20 --->40 40 --->20 40 --->40

815 692 692 444 815 444 924 676

0.131(6)

0.698

94.6(17)

88.4(17)

0,314(23)

0.557

23.7(35)

26.5(36)

0.041(3)

0.389

64.0(24)

61.7(24)

0.104(43)

1.10

49.4(47)

42.2(52)

a) All gamma intensities corrected for M1 admixture. ¢) Adopted as the z2 value characteristic of the band and used to calculate the zpy values. b) Calculated using ~#r = 2.16 × 10 -3. This value was computed using z p , / = 12.5 x 10 -3 and the Coulomb excitation data of Yoshizawa et aL 23).

2 a n d 10 c m 3 G e ( L i ) d e t e c t o r s a n d a 4 0 9 6 - c h a n n e l a n a l y s e r . T h e n o n - l i n e a r i t y a n d d e t e c t o r efficiency c a l i b r a t i o n s h a v e b e e n d e s c r i b e d e l s e w h e r e 17). A n a l y s i s o f t h e s p e c t r a w a s a c c o m p l i s h e d u s i n g a c o m p u t e r r o u t i n e 18).

650

G . E. K E L L E R A N D E. F. Z G A N J A R

3. Results

A partial level scheme containing only the beta vibrational, gamma vibrational, and ground state rotational bands in 154Gd is presented in fig. 1. The y-rays energies and relative intensities of the interband transitions are presented in table I. The energies and intensities reported by Meyer 5) and Varnell et al. 1o) are included for comparison. As can be seen, there is good mutual agreement. The energies and intensities of this investigation were used to calculate the ratios of reduced E2 transition probabilities and the corresponding mixing parameters presented in table 2. In the calculation of the B(E2) ratios for levels in the gamma band, the total 7-ray intensities were corrected for the M1 admixtures reported by Hamilton et al. 19). The y-rays depopulating the beta bands do not involve appreciable M1 admixtures according to Hamilton et aL 20). The adiabatic B(E2) ratios in table 2 were calculated from the squares of appropriate Clebsch-Gordon coefficients, taken from the tabulation of Yamazaki 21). The Zo and z2 values were calculated in a singleparameter analysis. The zar parameters in column 6 were calculated using the z2 value (71.5 x 10 -3) obtained for the 3 + level, which should be a characteristic value for the band since reduced transition probabilities from odd spin levels are unaffected by the mixing of the beta and gamma bands. The correction factors, which modify the adiabatic ratios to achieve agreement with experimental ratios, were taken from Lipas 12) with the exception that z o is defined in the manner of Marshalek 22) and Gunther and Parsignault 14). In this case, the z o value will be one-half the value of Lipas. The z o values are calculated for the case of fl-~ mixing by taking the average (12.5 x 10 -3) of the zar values in column 6 (upper portion) and using the Coulomb excitation results of Yoshizawa et al. 23) to obtain the parameter (pr (2.16 x 10-3). The quoted errors in the mixing parameters are the average deviations due to the uncertainties in the B(E2) ratios. From table 2 it is apparent that the B(E2) ratios for both beta and gamma vibrational bands cannot be described by a two-parameter band-mixing analysis. For the gamma band, no two zpr values overlap. Thus, the two-parameter analysis does not fit the experimental ratios. To achieve agreement between theory and experiment, one must use a value of z2 = 0.086, which yields the following za~ x 103 values (presented in the same order as those of table 2): 9.3+4.8, 9.4__3.6, 9.6+7.5 and 12.2__2.0. The weighted average of the re sulting za r values are 11.2 _ 1.6. However, to have z2 = 0.086 for the 3 + level, the required B(E2) ratio would have to be 0.91 or about 14 ~ lower than the observed value, far outside the experimental uncertainty. The band-mixing analysis for the beta bands does not describe the experimental B(E2) ratios. The single-parameter analysis yields a divergent set of Zo values, no two of which overlap. There is no obvious improvement when the Zo values are corrected to account for mixing of the beta and gamma bands. To account for the secondorder effect of fl-? band mixing in the z o computations, the arithmetic average of the z~ values in column 6 of table 2 was used to compute (p~. This approach is probably

154Gd BAND MIXING

651

meaningless in view o f the divergence o f the calculated z~r values. T h e a r i t h m e t i c average was used only as a best estimate. I t was impossible to o b t a i n a satisfactory t w o - p a r a m e t e r d e s c r i p t i o n b y a r b i t r a r i l y a d j u s t i n g the value o f ~ar. W i t h a value ~ar = 0.017, which is a factor o f 8 over the e s t i m a t e d value, the c o r r e c t e d Zo values for the 2 ÷ level converged to an average value o f 0 . 0 4 5 8 _ 0.0014 while the z o for the 4 ÷ level diverged to the value - 0 . 0 0 7 + 0 . 0 0 9 . Tables o f a d d i t i o n a l 3,-ray d a t a a n d a further discussion o f the decay o f 154Eu can be f o u n d in ref. 24).

4. Discussion The results o f this investigation d e m o n s t r a t e t h a t the b a n d - m i x i n g m o d e l x2,13) is i n c a p a b l e o f describing the e x p e r i m e n t a l l y o b s e r v e d B ( E 2 ) ratios ~br levels in the b e t a a n d g a m m a v i b r a t i o n a l b a n d s o f the t r a n s i t i o n a l nucleus 154Gd. T h e failure o f the m o d e l is n o t due to M1 a d m i x t u r e s in the i n t e r b a n d transitions, as corrections for k n o w n M1 c o m p o n e n t s were m a d e . T h e first-order mixing p a r a m e t e r s which were o b t a i n e d are o f the o r d e r o f 0.1, which is a b o u t a factor 2.5 larger t h a n the mixing p a r a m eters for the m o r e highly d e f o r m e d nuclei 16 6Er a n d 16SEr ' the B ( E 2 ) ratios o f which are satisfactorily described b y the b a n d - m i x i n g theory. T w o features are a p p a r e n t . First, the m a g n i t u d e o f the b a n d m i x i n g m a y be sufficiently large that the p e r t u r b a t i o n a p p r o a c h used in the b a n d - m i x i n g m o d e l is n o t a p p r o p r i a t e , as suggested by Varnell et al. lo). Second, the b a n d - m i x i n g m o d e l m a y n o t be as a p p l i c a b l e to t r a n s i t i o n a l nuclei as to m o r e highly d e f o r m e d nuclei. W e w o u l d like to t h a n k M a r k W a l t o n for his assistance with the c o m p u t e r p r o g r a m s .

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) I1) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)

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