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CALCULATIONS OF THE CONTINUUM γ-RAY
SPECTRA IN (HI, xn) REACTIONS
Ph. Hubert, F. Leccia, R. Liotta, P. Mennrath, Mm. Villard
To cite this version:
JOURNAL DE PHYSIQUE CoZZoque CIO, supptdment a u n012, Tome 41, ddcembre 1980, page ~ 1 0 - 1 3 9
CALCULATIONS
OF
THE
CONTINUUM Y-RAY SPECTRA IN( H I t x n ) REACTIONS
Ph. Hubert, F. Leccia, R. ~ i o t t a ' , P. Mennrath and M.M. V i l l a r d .
Centre d l E t u d e s NucZdaires de Bordeaux-Gradignan, 33170 Gradignan, France.
KLsum6.- Les s p e c t r e s gamma du continuum obtenus dans l a d d s e x c i t a t i o n d e s noyaux r g s i d u e l s p r o d u i t s p a r d e s r e a c t i o n s (Ions Lourds, xn) o n t 6t&, c a l c u l 6 s pour d e s noyaux ddformds e t sphgriques de l a rdgion A %150. Un bon accord avec l e s r d s u l t a t s expLrimentaux e s t obtenu, d'une p a r t , avec un choix j u d i c i e u x de l a s t r u c t u r e de l a l i g n e y r a s t , e t , d ' a u t r e p a r t , en i n t r a d u i s a n t une compdtition MI/E2 dans l e processus d e d s s e x c i t a t i o n .
Abstract.- C a l c u l a t i o n s of t h e continuum y-ray s p e c t r a following p a r t i c l e e v a p o r a t i o n i n (HI,xn) reac- t i o n s have been performed f o r deformed and s p h e r i c a l n u c l e i w i t h A%150. Good agreement w i t h v a r i o u s experiments i s o b t a i n e d when choosing an adequate s t r u c t u r e of t h e y r a s t l i n e , and when allowing f o r an M I t o E2 competition i n t h e y d e - e x c i t a t i o n o f t h e n u c l e u s .
Recent (H1,xn) experimental d a t a have shown t h e r i c h v a r i e t y of phenomena o c c u r r i n g a t high s p i n . Thus, t h e continuum spectrum corresponding t o sphe- rical:: Er n u c l e i shows two bumps [I]
.
The low ener- gy bump corresponds t o t h e d e - e x c i t a t i o n of t h o s e n u c l e i along known d i s c r e t e l e v e l s ( f o r 1 5 4 ~ r up t o s p i n 36). The high energy bump seems t o correspond t o t h e y r a s t cascade a l o n g p a r a l l e l bands a t high s p i n ( i n 1 5 4 ~ r above s p i n 36) g e n e r a l l y a s s o c i a t e d w i t h well deformed n u c l e i . One may t h e n i n t e r p r e t et h e s e two bumps a s m a n i f e s t a t i o n of a phase t r a n s i - t i o n around s p i n 36. Up t o t h i s s p i n t h e n u c l e a r l e v e l s t r u c t u r e would b e provided by f o u r neutrons and f o u r protons moving around t h e c l o s e d s h e l l c o r e W = 8 2
,
Z = 64 ( t h e ~ iand nhl ~ ~s h e l l s allow , ~ j u s t t o b u i l t up s p i n 36 i n t h i s c a s e ) . A d d i t i o n a l u n i t s of angular momenta beyond s p i n around 36 can- n o t be provided by rearrangements of t h o s e e i g h t p a r t i c l e s w i t h i n t h e shell-model u n l e s s a major s h e l l is broken, but b e f o r e t h a t t h e c o r e i t s e l f be- comes deformed. One would t h e n expect t h a t t h e edge of t h e high energy bump w i l l move with i n c r e a s i n g p r o j e c t i l e energy, i . e . w i t h i n c r e a s i n g .pin i n t h e e n t r y s t a t e , f o l l o w i n g t h e (41-2) r o t a t i o n a l r u l e f o r t h e energy of t h e y-ray e m i t t e d a t high s p i n a l o n g t h e y r a s t l i n e [2].
However, it was shown [3] t h a t t h i s edge does n o t move with i n c r e a s i n g e n t r y s p i n , s u g g e s t i n g t h a t t h e simple and e l e g a n t des- c r i p t i o n given above i s perhaps f a u l t y .I n a d d i t i o n t h e experimental d a t a [1,3-71 seem t o show a t low enezgy a non-negligeable d i p o l e component i n b o t h deformed and s p h e r i c a l n u c l e i . T h i s d i p o l e s t r u c t u r e appears a t about h a l f t h e energy of t h e y r a s t E2 bump. One may t h u s t h i n k
t h a t t h e s e d i p o l e components a r e mainly provided by MI t r a n s i t i o n s competing w i t h t h e y r a s t E2 t r a n s i - t i o n s a t high spin:
To complete t h i s . b r i e f review of e x p e r i m e n t a l d a t a , we must add t h a t t h e seemingly l e s s complica- ted p a r t of t h e spectrum,namely t h e high energy t a i l a s s o c i a t e d with s t a t i s t i c a l t r a n s i t i o n s , i s per s i s -
, ,
t e n t l y shown t o decay e x p o n e n t i a l l y with a c o n s t a n t temperature i n disagreement w i t h t h e o r e t i c a l calcu- l a t i o n s [8] : This t a i l i s u s u a l l y supposed t o con- s i s t mainly of
~i
t r a n s i t i o n s C6,7~],
although re- c e n t m u l t i p o l a r i t y s p e c t r a E l ] seem t o i n d i c a t e t h a t a quadrupole component i s p r e s e n t .To s t u d y t h e s e somehow c o n t r a d i c t o r y f e a t u r e s we s t a r t e d a n a l y s i n g t h e shape of t h e y l a y spectrum due only t o s t a t i s t i c a l t r a n s i t i o n s . The understan- ding of t h e s e t r a n s i t i o n s i s fundamental f i r s t l y i n o r d e r t o e l u c i d a t e t h e above mentioned disagreements a t high y-ray e n e r g i e s and secondly because t h e s e - t r a n s i t i o n s play a fundamental r o l e a t low e n e r g i e s , through t h e background s t a t i s t i c a l y-rays, i n t h e a n a l y s i s of t h e experimental s p e c t r a .
We f o l l y t h e s t a t i s t i c a l cascade u n t i l we reach t h e y r a s t l i n e u s i n g a Pbnte-Carlo method allowing a l l p o s s i b l e t r a n s i t i o n s (El and E2, s t r e ' t - ched and u n s t r e t c h e d ) t o t a k e p l a c e . The determinant q u a n t i t i e s i n t h e s e c a l c u l a t i o n s a r e t h e d e n s i t y of s t a t e s p , which u n f o r t u n a t e l y i s not well k n o m . c l o s e t o t h e y r a s t l i n e , and t h e ~ 2 . t o E l t r a n s i t i o n p r o b a b i l i t y r a t i o .
~ ~ ~ i c a l s t a t i s t i c a l s p e c t r a a r e shown i n f i g u r e s I ( a ) and l ( b ) t o g e t h e r w i t h t h e d i f f e r e n t , m u l t i p l i c i - t y and mu1 t i p o l a r i t y components. These s p e c t r a have been c a l c u l a t e d u s i n g f o r t h e y r a s t l i a e t h e r o t a t i o -
- - - - - - -
::Throughout t h i s c o n t r i b u t i o n s p h e r i c a l o r deformed n a l energy v a l u e s
( 1 )
n u c l e i mean s p h e r i c a l o r deformed n u c l e i a t low s p i n .
JOURNAL DE PHYSIQUE
F i g . I
-
S t a t i s t i c a l y-ray s p e c t r a ( f u l l l i n e ) c a l c u l a t e d f o r a nucleus w i t h A-150 and t h e p a r t i a l compo- n e n t s a s s o c i a t e d w i t h d i f f e r e n t y-ray m u l t i p l i c i t i e s ( F i g . l a , numbers) and m u l t i p o l a r i t i e s (Fig. I b ) . I'with a r i g i d body moment of i n e r t i a 3
.
We t h u s l e n t t o t h e u s e of s e v e r a l i d e n t i c a l p a r a l l e l found t h a t t h e s t a t i s c a l spectrum does not reproduce bands and t h u s , does not exclude t h e p o s s i b l e e x i s - a t high e n e r g i e s t h e experimental c o n s t a n t tempera- t e n c e of t h o s e c o l l e c t i v e p a r a l l e l bands. The spec- t u r e t a i l , i n accordance with o t h e r s c a l c u l a t i o n s t r a shown i n f i g u r e 2 have been c a l c u l a t e d u s i n g aC83
,
b e s i d e s t h e maximum of t h e spectrum i s a t c o n s t a n t r i g i d body moment of i n e r t i a . A s expected about 2 MeV. This p o s i t i o n can b e lowered i f e i t h e r t h e p o s i t i o n s of t h e edge of t h e bump and of t h e t h e E l s t r e n g t h ( F i g . I b ) o r t h e mean s t a t i s t i c a l maximum m u l t i p l i c i t y change r a t h e r much w i t h t h e en- m u l t i p l i c i t y ( F i g . 1 a ) a r e i n c r e a s e d . t r y s t a t e mean a n g u l a r momentum a s indeed i s foundI
e x p e r i m e n t a l l y i n deformed n u c l e i [2].
I - . . * ~ ' * ' * . ' 4
3
I n o r d e r t o put t o g e t h e r t h e a p p a r e n t l y c o n t r a - d i c t o r y f e a t u r e s observed i n s p h e r i c a l n u c l e i of having a high energy ( c o l l e c t i v e ? ) continuum bump which does n o t m v e with i n c e a s i n g e n t r y s t a t e angu- l a r momentum a s mentioned above, we assumed t h a t a s e r i e of band c r o s s i n g s o c c u r s along t h e y r a s t l i n e beyond s p i n 40 a s shown on t h e backbending p l o t i n t h e i n s e r t of f i g u r e 3 . With such an y r a s t l i n e we could well e x p l a i n ( g i g . 3) t h e experimental spec- t r a o b t a i n e d by Aguer e t a l . C37 u s i n g t h e sum- spectrometer technique and t h e m u l t i p l i c i t y spectrum
...'"....
... _..__
....*
".,, ,S.----
- -
-----...
o b t a i n e d by Deleplanque e t a l . [ I ] u s i n g t h e multi- p l i c i t y f i l t e r t e c h n i q u e . l s F ' 23
4 5 I n t h e y-ray s p e c t r a of f i g u r e 3 t h e higherE&
( McV)eneGgy bump i s due t o t h e E2 t r a n s i t i o n s from t h e F i g . 2
-
Calculated y-ray and mltiplicity s p e c t r a high s p i n s t a t e s ( I 40). However t h e low energy f o r a deformed nucleus and d i f f e r e n t mean a n g u l a r bump i s a s u p e r p o s i t i o n of t h r e e components t h e M1 mmenta i n t h e e n t r y s t a t e . The y r a s t l i n e c o r r e s -ponds t o a r i g i d body moment of inertia. and E 2 t r a n s i t i o n s from lower s p i n s t a t e s (I < 40)
and t h e M1 t r a n s i t i o n s from high s p i n s t a t e s . I n both c a s e s t h e M1 t r a n s i t i o n e n e r e i e s a r e t a k e n t o A somehow unexpected r e s u l t of t h i s c a l c u l a -
t i o n i s t h a t t h e amount of u n s t r e t c h e d d i p o l e com- ponent i s roughly 30 % of t h e t o t a l s t a t i s t i c a l t r a n s i t i o n s f o r a r i g i d body moment of i n e r t i a and t h e r a t i o of s t r e t c h e d t o u n s t r e t c h e d t r a n s i t i o n s
i s dependent on t h e s l o p e of t h e y r a s t l i n e .
A s a second s t e p we allow t h e system t o decay f o l l o w i n g o n l y the y r a s t l i n e a f t e r t h e s t a t i s t i c a l cascade. It is important t o n o t e t h a t i n t h i s c a l - c u l a t i o n , t h e u s e of o n l y t h e y r a s t l i n e i s equiva-
b e h a l f t h e corresponding' E 2 t r a n s i t i o q , e n q r g i e s ,, ,
t h i s c o n d i t i o n b e i n g n e c e s s a r y i n o r d e r t o reprodu- ce t h e two bumps i n t h e m u l t i p l i c i t y spectrum
[IJ
.
I n deformed n u c l e i t h e c o l l e c t i v e in-band E2
t r a n s i t i o n s a r e much f a s t e r t h a n t h e corresponding band c r o s s i n g M1 and E2 t r a n s i t i o n s and t h i s l e a d s t o t h e o b s e r v a t i o n of one y r a s t bump whose behaviour
i n deformed n u c l e i would be p o s s i b l e only i f unrea- sonable l a r g e g-values were assumed [g]
.
We a c t u a l l yF i g . 3
-
C a l c u l a t e d y-ray and m u l t i p l i c i t y s p e c t r a f o r t h e s p h e r i c a l nucleus I54Er and d i f f e r e n t mean angular mmenta i n t h e e n t r y s t a t e . The y r a s t l i n e has been e x t r a c t e d from t h e backbending p l o t shown i n t h e i n s e r t .I n t h i s c a s e t h e E2 band c r o s s i n g t r a n s i t i o n s a r e hindered by a f a c t o r of about ] / I w h i l e t h e corresponding M1 t r a n s i t i o n s a r e enhanced by a f a c - t o r I [8,93
.
To t a k e i n t o account t h i s f e a t u r e we included i n our c a l c u l a t i o n a s t r e n g t h r a t i o E2/V1 depending upon t h e a n g u l a r momenta. With t h i s con- d i t i o n t h e c a l c u l a t e d m u l t i p l i c i t y spectrum( F i g . 3) e x i b i t s t h e two bumps found e x p e r i m e n t a l l y . However, f o r low v a l u e s of t h e mean a n g u l a r momen- tum a t h i r d bump appears which is connected t o t h e low s p i n s t a t e s . I t i s worthwhile t o p o i n t o u t t h a t t h e backbending p l o t of f i g u r e 3 r e f l e c t s t h e expe- r i m e n t a l l e v e l s i t u a t i o n i n 3 5 4 ~ r up t o s p i n 36. Beyond t h i s s p i n v a l u e one cannot exclude t h a t o t h e r p o s s i b l e s t r u c t u r e s of t h e y r a s t l i n e w i l l s t i l l reproduce t h e experimental s i t u a t i o n .
found t h a t t h e p-values quoted i n Ref. 9 a r e too l a r - ge by a f a c t o r of e i g h t . However a l l t h e s p e c t r a and t h e corresponding c o n c l u s i o n i n Ref. 9 a r e c o r r e c t except with g-values ei.ght times s m a l l e r .
F i g . 4
- y-ray s p e c t r a of t h e c o l l e c t i v e H1 and
Ml+E2 t r a n s i t i o n s i n a deformed nucleus 1 5 8 ~ r calcu- l a t e d i n tFe wobbling model ( E - f a c t o r = 0 . 3,
6=0.25, y=-10").c10-
142 JOURNAL DE PHYSIQUEC a l c u l a t i o n s f o r a s p h e r i c a l n u c l e u s have not y e t been done i n t h i s model however we e x p e c t a s t r o n g d e c r e a s e of t h e c o l l e c t i v e E2 t r a n s i t i o n s l e a d i n g t o a s t r o n g M1 component i n t h e c o l l e c t i v e s p e c t r u m a s o b s e r v e d w i t h t h e lfonte-Carlo c a l c u l a - t i o n s .
We have shown t h a t Monte-Carlo c a l c u l a t i o n s , u s i n g o n l y t h e y r a s t l i n e and no o t h e r c o l l e c t i v e bands c a n r e p r o d u c e t h e e x p e r i m e n t a l r e s u l t s f o r deformed and s p h e r i c a l n u c l e i . It a p p e a r s t h a t t h e M1 t r a n s i t i o n s may p l a y a n i n p o r t a n t r o l e i n t h e d e - e x c i t a t i o n of a r e s i d u a l n u c l e u s a f t e r (H1,xn) r e a c t i o n s . The e x i s t e n c e of t h e s e M1 t r a n s i t i o n s seems t o b e e x p l a i n e d w i t h i n t h e wobbling model b u t f u r t h e r c a l c u l a t i o n s a r e needed f o r s p h e r i c a l n u c l e i .
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