Mixing of the γ-vibrational band and the ground state rotational band of Pu238

Nuclear Physics 29 (1962) 5 1 5 - - 5 2 1 ; ~ ) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

MIXING

OF T H E v - V I B R A T I O N A L B A N D A N D T H E S T A T E R O T A T I O N A L B A N D O F P u ~* J. B O R G G R E E N ,

O. B. N I E L S E N

GROUND

and H. NORDBY

Institute/or Theoretical Physics, University of Copenhagen, Denmark R e c e i v e d 4 J u l y 1961 T h e c o n v e r s i o n fines of P u *ss following t h e / ~ - d e c a y of N p ua h a v e b e e n remea.sured. T h e b r a n c h i n g ratios for t h e 7 - r a y s d e - e x c i t i n g t h e ~ - v i b r a t i o n a l b a n d a t 1030 k e V h a v e b e e n a n a l y z e d a n d a m i x i n g p a r a m e t e r z ~ 0.025 is f o u n d . T h e d e p e n d e n c e of t h e m i x i n g o n M1 t r a n s i t i o n probabilities a n d o n t h e d e v i a t i o n s f r o m t h e I ( I + 1) l a w ior t h e r o t a t i o n a l energies is discussed.

Abstract:

1. I n t r o d u c t i o n

In a number of cases 1-4) it has been possible to explain the observed intensity ratios for the v-rays from the 7-vibrational band to the ground state rotational band in deformed even nuclei b y assuming a mixing of the two bands. The admixed amplitude is small, but it represents an electromagnetic transition probability of the same magnitude as for transitions taking place within a rotational band. Correction factors to the intensities of transitions between different members of the two bands can be expressed b y a parameter z (ref. 1)) which is essentially the E2 transition strength of the admixed component. Considerable interest is attached to a systematic determination of z, partly to confirm the above interpretation b y establishing that the same value of z explains the intensities of all observed transitions between the two bands, partly to correlate the magnitude of z with other effects of band mixing, such as the occurrence of M1 admixtures in the predominant E2 radiation, and the deviations from the I ( I + 1 ) dependence of the rotational energies. In the t - d e c a y of Np zas to Pu *3s, two levels at 1030 (refs. 5-10)) and 1071 keV with angular momenta 2+ and 3 + are strongly excited. It is established that the 7-rays to the ground state band are mainly E2, and the branching ratios point to K = 2. An interpretation as a 7-vibrational band is thus suggested. The branching ratios are, however, not measured with sufficient accuracy to yield information on band mixing. Since t - r a y sources of Np *3s are available with high quality, it was decided to perform a measurement with higher accuracy. 515

516

J. BORGGREEN et ~ .

2. E x p e r i m e n t a l Method About 5/~g of Np 23~as Np(NO3) 5 were irradiated for 3 d at a neutron flux of 1013 neutrons, cm -2. sec -1 in the DR2 reactor at Ris0. The material was dissolved in conc. HC1 and absorbed on a Dowex A--1 anion exchange column of 50/~1 free volume. It was then eluted with 6 n HC1 and concentrated on a 1 #1 column of the same type and eluted with 1 n HCI t. The activity held in a 1/A drop was placed on a ~ 40 #g/cm ~ organic film (80 %) polystyrene, 20 % VYNS) and dried under an infra lamp. This source contained 92 % of the original Np ~ activity on an area of about 1 x 3 mm ~. The conversion lines were measured in a six-gap r-ray spectrometer with a resolution of 0.27 %. Only two gaps of the spectrometer were used, and the transmission amounted to about 0.6 % of 4~. With 5/~g Np 2s~ on about 3 m m 2, the effective source thickness was large enough to influence the measurement of the low energy lines, especially the L-conversion lines of the strong 44 keV transition. The continuous/~-ray spectrum and a few of the stronger conversion lines were obtained with a moderate resolution of 0.7 %. This run was performed to normalize the intensity of the conversion lines to the total number of disintegrations represented by the continuous spectrum.

3. E x p e r i m e n t a l Results The conversion line intensities are given in table 1. They are used for a calculation of the y-rays b y means of the theoretical conversion coefficients. The position of the transitions in the decay scheme can be studied on fig. 1. As mentioned above, the source thickness prevented an accurate measurement of the conversion lines from the 44 keV transition. The effect shows up, i.e., in an anomalously low L/M ratio of 1.5. For this reason, we have adopted the intensity of 8000 of the units in table 1 for the 44 keV transition, as indicated b y earlier measurements with thin sources 5,8,9). Even with a resolution of 1/R ~ 0.27 %, the conversion lines K102~.4 and K1029.9 are not resolved, and the relative intensities had to be found b y analyzing the composite peak. This curve analysis (fig. 2) was greatly helped b y the fact that the energy difference of the two lines is accurately known from the measurement of Albridge and Hollander. On fig. 2 is also shown the position of the two lines K989.1and K10~.8 reported b y Albridge and Hollander. They do not stand up in our curves; the upper limit we can set on the intensities are somewhat lower than the values given by these authors. Fermi analysis of the continuous r - r a y spectrum indicated that the soft component (Emax ~ 260keV) amounted to 584-4 % and the hard t A similar procedure is described in ref. ix).

MIXING OF TRig ~-VIBRATIONAL BAND

517

TABLE I T r a n s i t i o n intensities

E~, (keV)

Shell

44.1

LI+u Lm M N L,+,, Lm M N K K

I01

884.6 925.4 940.6 +943.3

9.858

/ltne X lO t

1450 1065 1750 360 188 88 I00 24 1.0 2.6

E2 E2

8.7

E0

K L M+N K

2.0 0.6 23.1 5.9 2.1 / 7.3

L

1027.4

M+N K 23.0

1029.9 1027.4 +1029.9

K

Assignment

/

15.7

L

5.6

M

1.7

~K

theo x I0s

I~,x 10 4

Itrtt~ltlon × lO t

E2

4625

E2

400

11.6 10.7

88 246

89 250 ~11

E2

9.6

2410

2440

E2

9.0

812

820

E2

9.0

1745

1765

The energies are t a k e n f r o m Albridge a n d Hollander. All intensities are based on t h e conversion lines and theoretical conversion coefficients. The u n i t s are p a r t s in 10~ of all decays.

(Emx ~ 1240 keV) to 424-4 ~/o-This result is in good agreement with the earlier measurements and also'with the intensities expected from the F-ray intensities (fig. 1). From fig. 1 it can also be concluded that the high energy//-rays mainly excite the 2+ level of the ground state rotational band, and that the branches to the 0 + and 4 + levels are weak. This decay pattern is consistent with the spin 2 assigned to Np 23s. 4. D i s c u s s i o n 4.1. D E T E R M I N A T I O N O F z

Tho contribution to the E2 transition rates due to the admixed component is expediently expressed b y z = V ~ Q00/Q2oe,with V ' ~ e being the admixed amplitude in the 2+ states t, Qo0 the mean quadrupole moment of the two bands, and Q20 the E2 transition amplitude from the K = 2 to the K = 0 band. The correction factors to the~E2 transition rates are given explicitly in refs. 1) and s). t T h e a d m i x e d a m p l i t u d e in the r o t a t i o n a l s t a t e w i t h a n g u l a r m o m e n t u m I is e ~ / ( I 2 - 1 ) I ( I + 1 ) ( I + 2) =

eV'IZ(I+1 p - - 2 1 ( 1 + 1).

618

J. BORGGREitN 8~

ai~.

Np "~ "1

t071 2 3 ÷

/

to3o l z +

..... I/ ...... to.~.4 i E2 E2 I I

/ gos7 1 g , o ,

I I l

!

E2E2E2 I I I

EO ,

250 820 8g 2240t"/65 tt

,, ,,

4200

:: I

,\ \ 1

_~._=

,o,.,I._2_

~___..___.__~.=~>ZB

__ ~

~ ~

,~,~.t._1~ ~

~ o

pu 2"

i' ,

t4~o o 4

+

44Jl 0 2 +

o o+

Fig. 1. T h e d e c a y s c h e m e N p l " --> P u 13s according to Albridge a n d Hollander. T h e intensities g i v e n as p a r t s in l 0 t a r e f r o m t h e p r e s e n t work.

•30xt03Counts

D

-

/ i

! //i\ t

-t0

-5

i

I

0

I

S

Fig. 2. Analy~s of the peak K~olT.i~-Kzosg.o. The full drawn curve is the measured line, and the d o t t e d c u r v e s r e p r e s e n t t w o lines of t h e s a m e s h a p e as t h e s t r o n g single line K0s6.s w i t h a 2.5 k e V e n e r g y difference. T h e crosses, w h i c h are f o u n d b y s u b t r a c t i n g t h e d o t t e d line Kx01t.t f r o m t h e e x p e r i m e n t a l p o i n t s , are a p p a r e n t l y well r e p r e s e n t e d b y t h e d o t t e d K100~.t. T h e two arrows indicate t h e p o s i t i o n of a line K,9.1 relative to t h e d o t t e d line s h a p e of K i , . e , a n d of K10ss.e relative to K10,. 9. T h e s t a t i s t i c a l u n c e r t a i n t y o n t h e e x p e r i m e n t a l p o i n t s is s m a l l e r t h a n 1% of t h e p e a k h e i g h t .

MIXING OF THE F-VIBRATIONAL BAND

519

T h e b r a n c h i n g ratios o b s e r v e d in P u 2as are in table 2 c o m p a r e d with the theoretical for transitions from a pure K = 2 b a n d to a pure K = 0 band. T h e q u a n t i t y z is f o u n d from the ratio / = / ( z , It, If) b e t w e e n the e x p e r i m e n t a l a n d theoretical values. Fig. 3 shows t h a t the three e x p e r i m e n t a l ratios are consistent with z ~ 0.025. TABLE 2

Branching ratios Theoretical

Experimental B(2 --~ 0) B(2 -+ 2)

2~

B (2 -~ 4) B(2 --+ 2)

2 4 1 0 , 884.6! = 0.0634-0.006

B (3 ~ 4) B (3 -,- 2)

1745 ( 985.8/a ~

=

0.58 4-0.04

450 ( os5.st,

0.7

0.83

0.032+0.010

0.05

1.26

0.0184-0.008

0.40

1.27

0.0194-0.006

246 (1027.4~ 5 x9 - ~ . 4 /

0.51 ±0.04

=

2D

3

/ 4D

I ~ .

L'J~-

'1 ,

Z ,

OD3 0.75

,

,

CX34 0£)5

~

az - o~ ' ~ " 8Z-- Z

Fig. 3. Graphical d e t e r m i n a t i o n of z from t h e correction factor [ = / (It, I t , z). The squares represent t h e e x p e r i m e n t a l u n c e r t a i n t y . 4.2. P O S S I B L E M1 A N D E0 A D M I X T U R E S I N T H E E2 F - R A Y S

T h e a b o v e intensities were calculated from the i n t e r n a l conversion lines, and it was a s s u m e d t h a t the 7-rays were pure E2. However, M1 radiation is not excluded in the three cases corresponding to AI = 0 or l, and also an E 0 c o m p o n e n t can be present in the 2 + -+ 2+ transition. I t is seen from fig. 3 t h a t , a l t h o u g h the values for z d e t e r m i n e d from different b r a n c h i n g ratios d e v i a t e less t h a n the e x p e r i m e n t a l u n c e r t a i n t y , a possible correction to the 2 + - + 2+ t r a n s i t i o n would t e n d to i m p r o v e the agreement. Angular correlation m e a s u r e m e n t s on the 7-rays de-exciting 7-vibrational levels h a v e in e v e r y case indicated t h a t the M1 a d m i x t u r e is small. T h e a d m i x e d c o m p o n e n t s in the w a v e functions represent, however, not o n l y an E2, b u t also a n M1 t r a n s i t i o n p r o b a b i l i t y of the s t r e n g t h which characterizes transitions b e t w e e n levels in the same r o t a t i o n a l band. N a t h a n 2) has d e m o n s t r a t e d t h a t a ~ 1.2 % M1 a d m i x t u r e in the E 2 transition from the 3+ level in the 7-vibra-

59.0

J. BORGGREEN St ~ .

tional band to the 4+ level in the ground state band of Sm ls~ is consistent with a value of z ~ 0.08, as deduced from the E2 branching ratios. The M1 component is expected to be proportional to ez ~ z*Qzo/24Qoo, and the lower value of z for Pu 23s would correspond to ~ 0.1-0.2 % M1 radiation, which in spite of the larger internal conversion coefficient for M1 transitions would increase the conversion line intensities b y only 0.5---1%. There exists still, however, the possibility that M1 components of the same order can be introduced as a result of the coupling of both the K ---- 0 and the K = 2 bands to rotational bands of higher energy with K = 1. Little is known at present of a coupling between ?- and fl-vibrational bands, but these are in Pu ~s so close (fig. 1) that the possibility of mixing should be considered. The transition rate for E0 conversion electrons from a fl-band to the ground state band is of the same order as for the E2 ?-rays from a ~- or a ?-band, and a coupling would thus preferentially affect the intensity of the conversion lines for transitions between levels with the same I. A coupling would also particularly influence the intensity of the y-ray from the 2+ to the 4+ level, simply because the geometrical factor for this transition is much larger from a K = 0 t h a n from a K = 2 band. 4.3. E F F E C T O F T H E M I X I N G O N T H E R O T A T I O N A L E N E R G I E S

The energies in a rotational band are expressed by h~ E = ~ - j I ( I + 1) - j - B I ' ( I + 1)3+ . . . . The rotational parameters J and B are affected by interactions between bands. The contribution to the I2(I+1)* term due to the coupling of the ?-vibrational band to the ground state band is

A E = P ( I + 1)~e~(E~--Eo2), E02 and E** being the energies of the two 2+ levels. Since the deviations from the I ( I + 1 ) dependence in the ground state rotational band is believed to be due partly to a rotational-vibrational interaction, it is interesting to compare this energy shift with the term BI2(I+I) 2, e.g. to compare B with ~ (E~2__ Eo2) = e2. 986 keV. From the energies 44.1 and 145.8 keV for the 2+ and 4+ states, B is calculated to be 4.2 eV. The quantity~ can be estimated from

V

B(E2, O0 --~ 02)

oo

22)

MIXING OF THE •~VIBRATIONAL BAND

521

where B(E2, 00 -~ 02) and B(E2, 00 -~ 22) are the E2 transition probabilities connecting the ground state and the two 2+ levels. The transition probability B (E2, 00 -~ 02) is well established throughout the regions of deformed nuclei from lifetime measurements as well as from Coulomb excitation. In Pu ~s, the lifetime has been measured by Bell et al. to (1.83± 0.15) ×10 -l° sec, corresponding to B(E2) ~ (11.9+1.0)e2× 10-4s cm -~. The probability B (E2, 00 -~ 22) has been found by Coulomb excitation for a considerable number of deformed nuclei 1~-15). The values obtained v a r y from 40.09-0.24) e~× 10-48 cm -4 corresponding to 3-8 single-particle units, but the experimental uncertainty still amounts to ~ 20 ~ . Th ~39 and U ~38 are the only nuclei close to Pu ~8, in which the 7-vibrational band has been excited, the B(E2) values 15) being 0.134-0.04 and 0.088±0.030. If we assume 0.10 for Pu 238, we obtain AE -

-

1 2 ( / + 1 ) ~-

~ 0.2eV

for

z ~ 0.025.

The coupling to the 7-vibrational band apparently only accounts for a small part of the B term (4.2 eV). This is in accord with the result of a systematic analysis of a larger number of deformed even nuclei is). We are indebted to Professor Niels Bohr for the excellent working conditions at this Institute, and to Professors Aage Bohr and Ben R. Mottelson for stimulating advice. References

I) 2) 3) 4) 5) 6) 7) 8) 9) 10) II) 12) 13) 14) 15) 16)

P. Gregers Hansen, O. B. ~ielsen and R. K. Sheline, Nuclear Physics 12 (1959) 389 O. Nathan, Nuclear Physics 19 (1960) 148 E. Arbman, S. Bjornholm and O. B. Nielsen, Nuclear Physics 21 (1960) 406 G. T. Ewan, R. L. Graham and J. S. Geiger, Nuclear Physics 22 (1961) 610 M. S. Freedman, A. H. Jaffey and F. Wagner, Phys. Rev. 79 (1950) 410 H. Sl~tis, J. O. Rasmussen and H. Atterling Phys. Rev. 93 (1954) 646 J. O. Rasmussen, H. S1t~tis and T. O. Passell, Phys. Rev. 99 (1955) 42 J. O. Rasmussen, F. S. Stephens, O. Strominger and B. Astrom, Phys. Rev. 99 (1955) 4"I S. A. B a r a n o v and K. N. Shlyagin, J. Nucl. E. 3 (1956) 132 R. G. Albridge and J. M. Hollander, Nuclear Physics 21 (1960) 438 USAEC Collected Radio-chemical Procedures, Sept. 10, 1954, Los Alamos Scientific Lab. D. G. Alkhazov, A. P. Grinberg, G. M. Gusinski, K. I. Erokhina and I. Kh. Lemberg, J E T P (Soviet Physics) 8 (1959) 926 O. N a t h a n and V. I. Popov, Nuclear Physics 21 {1960) 631 F. K. McGowan and P. II. Stelson, Phys. Rev. 122 (1961) 1274 R. M. Diamond, B. Elbek, G. Igo and F. S. Stephens, private communication O. B. Nielsen, Proc. Rutherford Jubilee Intern. Conf., Manchester, 1961