Concerning the magnetic properties of deformed nuclei in the region 153 ⩽ A ⩽ 187

Volume 3, number 6

PHYSICS LETTERS

Table 1 2p-1s transition energies of p-mesonic atoms. All energies are in KeV. EJHA g BRIX[ EBRIX _ E F W . EFW[

EJHA

10% change i n t. I n c r e a s e s in c and in t both lead to d e c r e a s e s in ~ E . The d e t a i l e d s e n s i t i v i t y of the e n e r g y of the 2 p - l s X - r a y to c h a n g e s i n c a n d t s e p a r a t e l y i s g i v e n i n ref. 3). The i n t r o d u c t i o n of the m o r e r e a l i s t i c c h a r g e d i s t r i b u t i o n s l e a d s to c o r r e c t i o n s which a r e of the r i g h t m a g n i t u d e f o r a l l the e l e m e n t s c o n s i d e r e d . Of c o u r s e , t h e r e will a l s o be c o n t r i b u t i o n s due to n u c l e a r p o l a r i s a t i o n and q u a d r u p o l e i n t e r a c t i o n , but t h e s e a r e of the s a m e o r d e r a s the e x p e r i m e n t a l u n c e r t a i n t i e s . We c o n c l u d e that the 2 p - l s t r a n s i t i o n e n e r g i e s in ~ - m e s o n i c a t o m s a r e c o n s i s t e n t with the c h a r g e d i s t r i b u t i o n s o b t a i n e d from electron scattering experiments.

EHH

__EF w

i

296.3_+2.0

2.0+2.0

401.1+1.8

4.5_+/.8

522.7+1.7 516+4 0.9+1.7

1.7 + 0.9 1.8 ± 1.7 t

4.2_+41 3.3

+

2.4

2.6 791.5-+.2.0 784+3 ;0.2+2.0 12.7--+3 10.8-+ 4.7 5.0 i

I I

10.3

+ -

6.4 6.8

i332.814261337:~5132"8±6982 14 ~ 19.5 +_126.139.12"0 i442.3+6.2

. _ . 16.5

7.8 _+ 14.6 + 28.8 24.2 _ 30.1

3360

-5

2516 + 50.1 - 52.0

3546

19

250: 0:

1 February 1963

We a r e g r a t e f u l to D r . T. Y. Wu for h i s helpful c o m m e n t s and to M r . E. P. Hincks f o r k i n d l y showing us their latest experimental results. Varshni thanks P r o f e s s o r J. M. R o b s o n f o r h i s kind i n t e r e s t i n the work.

References 1} P. Brix et al., Physics Letters 1 (1962) 56. 2} C. S. Johnson, E . P . Hincks and H. L. Anderson, Phys. Rev. 125 (1962) 2102: Phys. Rev., to be published. 3) K.W. Ford and J.G.Wills, Report LAMS-2387 (1960); Nuclear Phys. 35 (1962) 295. 4) R. Herman and R. Hofstadter, High-energy electron scattering tables, (Stanford University Press, Stanford, California, 1960). 5) H. Crannell et al., Phys. Rev. 121 (1961} 283. 6) G. E. Pustovalov, J. Exptl. Theoret. Physics. 36 (1959) 1806.

* Interpolated the l a s t c o l u m n of t a b l e 1 a r e the m a x i m u m v a r i a t i o n s o b t a i n a b l e by c o m b i n i n g 2% change in c with

CONCERNING THE MAGNETIC PROPERTIES OF DEFORMED NUCLEI IN THE REGION 1 5 3 ~< A --< 1 8 7 J. DE BOER California Institute of Technology, Pasadena, California and JOHN D. ROGERS ** Institute for Theoretical Physics, University of Copenhagen, Denmark Received 21 December 1962

It is well known that the s t r o n g l y d e f o r m e d n u c l e i c a n be d e s c r i b e d by a w a v e - f u n c t i o n , which is the p r o d u c t of two p a r t s : the w a v e - f u n c t i o n of a s y m m e t r i c r o t o r and the w a v e - f u n c t i o n of the i n t r i n s i c s t r u c t u r e . The m a g n e t i c p r o p e r t i e s of a d e f o r m e d * This work was supported in part by the U.S. Atomic Energy Commission. ** National Science Foundation Fellow. 304

n u c l e u s can thus be e x p r e s s e d in t e r m s of two p a r a m e t e r s , g R and g K 1). Under the a s s u m p t i o n of the v a l i d i t y of this s t r o n g coupling s c h e m e , B e r n s t e i n and De B o e r 2) have d e r i v e d v a l u e s f o r g R and g K f r o m the e x p e r i m e n t a l data on m a g n e t i c dipole m o m e n t s and t r a n s i t i o n p r o b a b i l i t i e s . A c o m p a r i s o n of g K with t h e o r e t i c a l p r e d i c t i o n s of the N i l s s o n m o d e l 3) shows d e v i a t i o n s of 50 to 100%. Such d e -

Volume 3, number 6

PHYSICS LETTERS

1 February 1963

Table 1 S u m m a r y of experimental r e s u l t s and theoretical predictions for the magnetic p r o p e r t i e s of ground state rotational bands in odd-A nuclei with K ¢ ½ in the region 153 ~
2

Nucleus I°

3

4

5

6

7

8

9

/~O 11)

(gK-gR) ~

(gK-gR)~

gR

gK

theor, gK

gs,eft gs

Eu 153 ~ +1.507(3)

0.31

±0.06

12)

0.033 ±0.005 12,13) 0.475±0.008 +0.654±0.004 +0.34 0.61+0.01

Gd 155 ~ +0.242(2)

0.62

±0.09

13)

0.31 +0.04

-0.48 +0.03

-0.79 0.61+0.05

Gd 157 ~ +0.3225(10)

0.66

±0.08

13)

0.27 ±0.03

-0.54 ±0.02

-0.79 0.69+0.03

1.72

±0.30

0.35 ±0.14

+1.65 +0.14

+2.20 0.62±0.10

0.26 ±0.ii

-0.31 ±0.05

-0.59 0.52+0.07

]Tb 159 } +1.7(2)

1.67

±0.30

0.32

±0.16

14)

I

!Dy161 ~ -0.37(4) Dy 163

! ~ i+0.58(6)

+3.8(5) Er167 I{ +0.54(6)

Ho165 i½

0.27 ±0.025 +0.218+0.024 +0.58 0.38+0.04

0.68

0.44 ±0.15

+0.10

0.157 ±0.016 13)

Yb 173 ~ -0.6725(28) 0.66 Lu175 ~1~ +2.230(11)

0.0024±0.0008

±0.11

0.138 ±0.010

14,15) 0.46

±0.10

+1.27 ±0.14

+1.52 0.60±0.21

0.153±0.020 -0.244+0.018 -0.44 0.56±0.04

13)

0.28 ~-0.04 -0.49 ±0.02

16,17) 10.110 ±0.013 13)

-0.63 0.77±0.02

0.37 ±0.01

+0.714±0.005 +0.42 0.60+0.01

0.0018±0.0002 16,18) 0.0022~0.0012 13)

0.17 ±0.01

+0.16 ±0.01

-} -0.47(3)

0.221 ±0.018

17)

0.141 ±0.028

0.258±0.016 -0.184±0.035 -0.35 0.52±0.10

Ta 181 ½ +2.35(1)

0.203 ±0.010

17)

0.208 ±0.025 13)

0.319±0.008 +0.773±0.004 +0.4310.51±0.01

1.41

±0.14

0.420±0.043 +1.61 +0.002 +1.88 0.75+0.02

1.47

±0.15

0.377±0.044 +1.64 +0.02

Hf 177 ½ Hf 179

+0.61(3)

Re 185 ~ +3.1717 Re 187 ~ +3.2044

1.82

±0.43

19)

vlations have been noted p r e v i o u s l y in discussions of ground state magnetic m o m ent ' s 4 - 6). Using the latest available experimental r e s u l t s , we have recalculated the p a r a m e t e r s gK and gR for 15 deformed odd-A nuclei. We then determined an effective spin g - f a c t o r , gs,eft, so that the values of gK, obtained f r o m the f o r m u l a * g gK = gs,eft (Sz') + gl (lz') a g r e e with the experimentally derived values. The expectation values (Sz,) and (lz,) were evaluated using Nilsson , s wave functions 3 ). The r e s u l t s of such a calculation, shown in fig. 1, indicate that the experimental values can be r e p r o duced assuming an effective spin g - f a c t o r of about * See ref. 3), formula 24c.

+0.41 0.40±0.03

+1.88 0.78+0.02

60% of that for a f r e e particle for both neutrons and protons. An explanation of this effect in t e r m s of a polar±sat±on of the unsaturated spins in the 14 l i i l f 4 1

+iiiii

1111[i

Jl,lllllllll

o ODD • ODD

1.0

flll,

PROTON NUCLEI NEUTRON NUCLEI-

0.8 gs e*~ 0,6 gs

o2+I

I

0.4

~

°

' I

o

0.2 ,,,I+,111++

150

, , tttlJla+,Li,,

T60 ATOMIC

170 NUMBER

,,lln=,l+,,+

teO

'190

Fig. i . Attenuation factor, gs e f f / g s , of the f r e e nucleon s p m magnetic m o m e n t for 15 odd-A nuclei.

305

Volume 3, number 6

P H YS I C S L E T T E R S

d e f o r m e d c o r e h a s b e e n s u g g e s t e d by M o t t e l s o n 7) and N i l s s o n a n d P r i o r 8). T a b l e 1 s h o w s the r e l e v a n t e x p e r i m e n t a l d a t a a n d the d e r i v e d v a l u e s of g K a n d g R f o r each n u c l e u s s t u d i e d , a s w e l l a s the t h e o r e t i c a l v a l u e s of the parameter gK calculated from Nilsson's wave-funct i o n s . T h e v a l u e s of ( g K - g R ) l 2 a n d (gK-gR)22 i n c o l u m n s 4 and 5 r e s p e c t i v e l y a r e t h o s e d e r i v e d f r o m the m e a s u r e d M1 t r a n s i t i o n p r o b a b i l i t y b e tween the f i r s t e x c i t e d s t a t e of the r o t a t i o n a l b a n d a n d the g r o u n d s t a t e , and the s e c o n d e x c i t e d s t a t e a n d the f i r s t , r e s p e c t i v e l y . T h e i r e q u a l i t y i s a t e s t of the s t r o n g c o u p l i n g a s s u m p t i o n . An a v e r a g e v a l u e w a s u s e d i n the c a l c u l a t i o n s . The v a l u e of ~ R c a n b e c o m p a r e d to the one c a l c u l a t e d i n ref° 9), u s i n g a p a i r i n g - c o r r e l a t i o n m o d e l . It i s f u r t h e r p o s s i b l e to c o r r e c t the d e r i v e d v a l u e s of g K to a c c o u n t f o r s m a l l effects of the C o r i o l i s i n t e r a c t i o n 8). T h i s c o r r e c t i o n would c h a n g e the v a l u e s of gs, eff/gs b y a b o u t 10% in m o s t c a s e s 10).

References 1) Alder et al., Revs. Modern Phys. 28 (1956) 432. 2) E . M . B e r n s t e i n and J.De Boer, Nuclear Phys. 18 (1960) 40. 3) S.G. Nilsson, Mat. Fys. Medd. Dan. Vid. Seldk. 29 no. 16 (1955). 4) B.R. Mottelson and Sven G6sta Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 1 no. 8 (1959).

ON

THE

992

keV

1 February 1963

5) J . O . R a s m u s s e n and L.W. Chiao, Proc. of the Int. Conf. on Nuclear Structure, Kingston, Canada, (University of Toronto P r e s s , 1960). 6) S.A.Williams, Phys. Rev. 125 (1962) 340. 7) B.R. Mottelson, Selected topics in the theory of collective phenomena in nuclei (int. School of Physics, Varenna, 1960; Nordita Publ. no. 78). 8) S.G. Nilsson and O. Priot, Mat. Fys. Medd. Dan. Vid. Selsk. 32, no. 16 (1960). 9) Yu. T. Grin' and I. M. Pavlichenkov, Soviet Phys. JETP 14 (1962) 679. 10) S.G. Nilsson, private communication. 11) Taken from I. Lindgen, to be published in a new edition of "Beta and Gamma Ray Spectroscopy" edited by K. Siegbahn. 12) M. Birk et al., Proc. of the Gatlinburg Conference, Oct. 1961, p. 70. 13) G. Goldring, H.M. Loebestein and R. Barloutaud, to be published in Phys. Rev. 14) E.E. Berlovich, M.P. Bonitz and M. K. Nikitin, Soviet Physics JETP 13 (1961) 525. 15) J.W. Milhelich, B. Harmatz and T. H. Handley, Phys. Rev. 108 (1957) 989. B.Harmatz, T . H . H a n d l e y a n d J.W. Michelich, Phys. Rev. 114 (1959) 1082. V.A.Romanov, M.G.Iedko and V.V.Tuchkevich, soviet Physics JETP 11 (1960) 733. 16) J. Lindskog, T. Sundstrom, and P. Sparrman, Proc. of the Gatlinburg Conference, Oct. 1961, p. 84. 17) A.E.Blaugrunf, Y.Dar and G.Goldring, Phys. Rev. 120 (1960) 1328. 18) M.Birk et al., Phys. Rev. 126 (1962) 726. U.Hauser, Nuclear Phys. 35 (1962) 342. 19) G. Goldring and A. E. Blaugrund, private communication

A127(p,7)Si

28 RESONANCE

L. SIMONS, K. - E . NYSTEN, M. KOSKELIN, O. SILTANEN, E. SPRING a n d G. W E N D T University of Helsinki Received 21 December 1962

Si 28 l e v e l s c h e m e a n d ~ - r a y t r a n s i t i o n s have b e e n the o b j e c t of i n t e n s i v e s t u d i e s . T h i s i s e s p e c i a l l y t r u e of the A127(p,~)Si 28 r e s o n a n c e s f o r Ep <1 MeV a n d the l e v e l s w h i c h a r e p o p u l a t e d by t h e s e . E s p e c i a l l y the 992 keV r e s o n a n c e h a s b e e n i n v e s t i g a t e d m a n y t i m e s 1-4). Though t h i s r e s o n a n c e i s v e r y s t r o n g , the r e s u l t s a r e i n s o m e c a s e s c o n t r a d i c t o r y and t h e r e a r e s t i l l s o m e t h i n g s which a r e n o t c l e a r . P a r t l y t h i s i s due to the f a c t that the r e s onance level has not been observed through ~ r e a c t i o n s with Mg 24. We have t h e r e f o r e i n v e s t i g a t e d the y - r a y s and the s p i n of t h i s s t a t e . G a m m a - r a y and c o i n c i d e n c e s p e c t r a o r i g i n a t i n ~ f r o m the 992 keV r e s o n a n c e in A127(p,~)Si 28 have

306

b e e n m e a s u r e d . P r o t o n s w e r e a c c e l e r a t e d i n the H e l s i n k i Van de G r a a f f - a c c e l e r a t o r a n d t h e i r e n e r gy w a s d e t e r m i n e d t h r o u g h 90 ° m a g n e t i c a n a l y s i s . T a r g e t s w e r e p r e p a r e d by e v a p o r a t i n g a l u m i n i u m onto a 0.2 m m t h i c k t a n t a l u m b a c k i n g . Two NaI(T1) c r y s t a l s , 5" i n d i a m e t e r by 4" thick, c o u p l e d to Du Mont 6363 p h o t o m u l t i p l i e r s w e r e u s e d to d e t e c t ~-rays. I n the m e a s u r e m e n t s of s i n g l e s s p e c t r a the d e t e c t o r w a s m o u n t e d at a n a n g l e of 125 ° to the b e a m direction. The coincidence s p e c tr a were m e a s u r e d with the one c r y s t a l a t 125o a n d the o t h e r at 90o to the b e a m . The s p e c t r a w e r e r e c o r d e d on a N u c l e a r D a t a 512 c h a n n e l p u l s e h e i g h t a n a l y s e r and w e r e