Volume 35B, number 1 P H Y S I C S L E T T E R S 26 April 1971

X - R A Y I S O T O P E S H I F T S A N D N U C L E A R R A D I I I N

P. L. L E E and F. B O E H M California Institute of Technology, Pasadena, California, USA

Received 17 March 1971

S m *

The isotope shifts have been measu red for the KOt I X rays of six Sm isotopes. F rom the obse rva - t ions the following var ia t ions of the mean square nuclear charge radi i , 0(r2>, are obtained in units fm 2, 147-148Sm: 0.171J=0.010, 148-149Sm: 0.080±0.008; 148-I50Sm: 0.303±0.010; 150-152Sm: 0.411 ± 0.012, 152-154Sm: 0.221 ± 0.013. A compar ison with optical measu remen t s is presented .

We r e p o r t h e r e on the r e s u l t s of i s o t o p e s h i f t m e a s u r e m e n t s on s a m a r i u m i s o t o p e s . T h e s m a l l e n e r g y s h i f t s of t he K a 1 X r a y s w e r e m e a s u r e d w i t h the C a l t e c h 2 m c r y s t a l s p e c t r o m e t e r . F o r a d e s c r i p t i o n of t he t e c h n i q u e a n d the p r o c e d u r e we r e f e r to r e f s . [1] a n d [2].

T h e S m i s o t o p e s a m p l e s in f o r m of S m 2 0 3 w e r e o b t a i n e d on l oan f r o m the Oak R idge N a - t i o n a l L a b o r a t o r y . To v e r i f y the c h e m i c a l and c r y s t a l l o g r a p h i c p u r i t y h igh r e s o l u t i o n X - r a y p o w d e r p i c t u r e s w e r e t a k e n of a l l the s a m p l e s w i th a G u i n i e r c a m e r a . E a c h i s o t o p e s a m p l e w a s p r e p a r e d by m i x i n g 1.6 g of S m 2 0 3 w i th the s a m e a m o u n t of T e f l o n p o w d e r and t h e n p r e s s e d to a d i s c of 3.8 c m d i a m e t e r . F o u r s e r i e s of e x p e r i m e n t s w e r e p e r f o r m e d , e a c h i n v o l v i n g the s e q u e n t i a l m e a s u r e m e n t s of f o u r i s o t o p e s m o u n t e d on the s a m p l e w h e e l 90 ° a p a r t , v iz . t he i s o t o p e s ( 1 4 7 , 1 4 8 , 1 4 9 , 1 5 0 ) in the f i r s t s e r i e s , ( 1 4 9 , 1 5 0 , 1 5 2 , 1 5 4 ) in the s e c o n d s e r i e s , (147, 1 4 8 , 1 4 9 ) in the t h i r d s e r i e s , and f i n a l l y (148 ,154 ) in the f o u r t h s e r i e s . A s d e s c r i b e d in r e f . [1] the d a t a w e r e a n a l y s e d w i th a f i v e - p a - r a m e t e r G a u s s ± a n l e a s t - s q u a r e s f i t .

A p r e v i o u s r e s u l t on 1 4 8 - 1 5 4 S m [2] t o g e t h e r w i th the p r e s e n t m e a s u r e m e n t s o v e r d e t e r m i n e the f i v e i n d e p e n d e n t s h i f t s f o r the s i x i s o t o p e s . T h e f i n a l d a t a o b t a i n e d f r o m a l e a s t - s q u a r e s f i t of a l l t he o b s e r v e d i n d i v i d u a l s h i f t s i s p r e - s e n t e d in t a b l e 1. T h e X 2 f o r t h i s f i t w i th f ive d e g r e e s of f r e e d o m i s 0.92. T h e d a t a in t a b l e 1 w a s c o r r e c t e d f o r i s o t o p i c a b u n d a n c e ( r a n g i n g f r o m 97.46% to 99.97%) a n d m a s s s h i f t s [2]).

T h e C o u l o m b e n e r g y s h i f t s 6 E a r e r e l a t e d to

This work was pe r fo rmed under the auspices of the US Atomic Energy Commiss ion . P r e p a r e d under Contract AT(04-3)-63 for the San F ranc i s co Oper - ations Office, US Atomic Energy Commiss ion .

Table 1 Isotope shifts in meV for Sin. The values are obtained

f rom a l e a s t - s q u a r e s fit of all the data.

A ~ A ' 148 149 150 152 154

147 50 +3 73 ±3

148 23 ± 2

149

150

152

138 ±3 256 ± 4 322 ± 4

88 ± 3 a 208 ± 4 272 ±3

65 ± 3 184 ± 4 249 ±3

120 ± 4 a 184 ±3

6 4 ± 4

In comparison Sumbaev et al. [6] reported 102 ± 15 meV for 148-150Sm and 110 ± 16 meV for 150-152Sm"

Table 2 Observed 5(r 2) values in fm 2 and cor responding values based on the uniform charge model without and with

deformat ion effect.

Isotope Exper iment Uniform model

pair 6<r 2) 5(r2)sp h 8(r2)de f

Sm 147-148 0.171 ± 0.010 0.109 0.252 Sm 148-149 0.080 ± 0.008 0.109 -0.253 Sm 148-150 0.303 ± 0.010 0.220 0.117 Sm 150-152 0.411 ± 0.012 0.222 0.614 Sm 152-154 0.221 i 0.013 0.226 0.349

the v a r i a t i o n s of t h e e v e n n u c l e a r c h a r g e m o - m e n t s 5(r 2n ) by [2, 3]

5E : ~ Cn6(r 2n) ~ C 1 0(r 2) n

w h e r e by w r i t i n g the l a s t a p p r o x i m a t e e q u a l i t y one a d m i t s an e r r o r of a b o u t 5% f o r Z = 62. U s - ing the C 1 c o e f f i c i e n t s o b t a i n e d f r o m an a t o m i c s e l f - c o n s i s t e n t f i e l d c a l c u l a t i o n s [3], one f i n d s

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Volume 35B, number 1 P H Y S I C S L E T T E R S 26 April 1971

Table 3 Optical mass shifts M i nnd e lec t ronic factor C± for

different optical t rans i t ions repor ted in ref. [4] as de- r ived f rom a compar ison of optica[ 3rid X- ray isotope

shifts .

Optical line Opt. r~ass shift Elec t ronic fac tor in Sm M z x 10 -5 C~

(~) (mK x nucleon) (mK/fm2)

4910 0.04 ~- 0.03 -9.2 i 0.9 5088 -0.14 ~= 0.61 -174 ± 17 5175 2.1 ± 0.8 240 ±24 5252 2.4 ±1 .0 281 ±27 5271 1.7 • 0.6 162 ±15

t he n u c l e a r c h a r g e m o m e n t v a r i a t i o n s 6<r 2} l i s t e d in t a b l e 2.

I t i s i n t e r e s t i n g to c o m p a r e t he o p t i c a l i s o - tope s h i f t s [4] w i th the p r e s e n t v a l u e s . In b o t h e x p e r i m e n t s the s a m e m o m e n t of the c h a r g e d i s t r i b u t i o n i s s a m p l e d . F o r Sm t h i s m o m e n t , ( rk ) , i s found [5] to b e g i v e n by the v a l u e k = 1.93. F ig . 1 s h o w s the o p t i c a l s h i f t s d i s p l a y e d v e r s u s the X - r a y s h i f t s . A s d i s c u s s e d in r e f . [1] t h i s c o m p a r i s o n a l l o w s us to d e t e r m i n e the u n - known 9 P t i c a l m a s s s h i f t s M / and e l e c t r o n i c f a c - t o r s C~. T a b l e 3 l i s t s t h e s e o p t i c a l q u a n t i t i e s a s o b t a i n e d f r o m f i t t i n g o p t i c a l and X- l : ay da t a .

W i t h t h e s e p a r a m e t e r s lVfl and C~, good a g r e e m e n t c a n b e n o t e d b e t w e e n f i ve o p t i c a l l i n e s and the X - r a y l i ne f o r f i ve i s o t o p e p a i r s w i th the p o s s i b l e e x c e p t i o n of two p a i r s i n v o l v - ing the odd A i s o t o p e s ( s ee f ig. 1 f o r two o p t i c a l l i n e s ) .

R e f e r e n c e s [1] S .K .Bha t t ache r j ee , F .Boehm a n d P . L . L e e , Phys .

Rev. 188 (1969) 1919. [2] R . B . C h e s l e r and F .Boehm, Phys. Rev. 166 (1968)

1206.

% co I -

z

Z

<~

-<

x I-- b-

I (/)

g {..- 13_ 0

ISOTOPE SHIFTS IN Srn

0•' 150-152

8

148-15

6 -- 1 5 2 - 1 5 4 / 147-148

2

0

-2

-4

-8-- -6-- ~

I { } I I I { " ~ 0 2 4 6 8 I0 12 14

X-RAY SHIFT x AA}"(A'-A)IN UNITS I0 5 rneV

Fig. 1. A compar ison of isotope shifts of an X- ray and two optical l ines in Sin. The s t ra ight l ines r e p r e s e n t l e a s t - s q u a r e s fi ts to the c}ata; they allow to de te rmine the optical mass shifts M l and the e lec t ronic fac tors

cb

[3] E .Se l t ze r , Phys. Rev. 188 (1969) 1916. [4] J. E. Hansen, A. Steudel and H.Wal ther , Z. Physik

203 (1967) 296. [5] F. Boehm, Proc . Second P rob lem Symposium on

Nuclear physics ; Novosibirsk (1970); K. W. Ford, to be published.

[6] O . I .Sumbaev et al., Yadern. Fiz . 5 (1967) 544; Soviet J . Nucl. Phys. 5 (1967) 387.

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