DEFLECTION ON NON-EQUILIBRIUM LIGHT PARTICLES BY THE NUCLEAR MEAN FIELD

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DEFLECTION ON NON-EQUILIBRIUM LIGHT PARTICLES BY THE NUCLEAR MEAN FIELD

M. Tsang, W. Trautmann, R. Ronningen, G. Bertsch, Z. Chen, C. Chitwood, D. Fields, C. Gelbke, W. Lynch, T. Nayak, et al.

To cite this version:

M. Tsang, W. Trautmann, R. Ronningen, G. Bertsch, Z. Chen, et al.. DEFLECTION ON NON-

EQUILIBRIUM LIGHT PARTICLES BY THE NUCLEAR MEAN FIELD. Journal de Physique

Colloques, 1986, 47 (C4), pp.C4-91-C4-93. �10.1051/jphyscol:1986410�. �jpa-00225773�

JOURNAL DE PHYSIQUE

Colloque C4, supplbment au n o 8 , Tome 47, aoiit 1986

DEFLECTION OF NON-EQUILIBRIUM LIGHT PARTICLES BY THE NUCLEAR MEAN FIELD

M.B. TSANG, W. TRAUTMANN', R.M. RONNINGEN, G. BERTSCH, Z . CHEN, C.B. CHITWOOD, D.J. FIELDS, C.K. GELBKE, W.G. LYNCH, T. NAYAK, J. POCHODZALLA and T. SHEA

National Superconducting Cyclotron Laboratory, Michigan State university, East Lansing, MI 48824, U.S.A.

Abstract - The emission s i g n of t h e average emission a n g l e of non-equilibrium

-- l i g h t p a r t i c l e s was determined from t h e c i r c u l a r p o l a r i z a t i o n of coincident Y-rays emitted from r e s i d u a l n u c l e i i n '*N-induced r e a c t i o n s 'on

"Sm a t E/A=20 a n d 3 5 MeV. P o s i t i v e p o l a r i z a t i o n a s l a r g e a s 35% was o b s e r v e d i n d i c a t i n g t h a t l i g h t p a r t i c l e s a r e e m i t t e d p r e f e r e n t i a l l y t o n e g a t i v e a n g l e ? . The p o l a r i z a t i o n becomes more pronounced a s t h e mass and energy of the d e t e c t e d p a r t i c l e i n c r e a s e s . The observations d e m o n s t r a t e d e f l e c t i o n of l i g h t p a r t i c l e s by t h e a t t r a c t i v e n u c l e a r mean f i e l d , i n q u a l i t a t i v e agreement with numerical c a l c u l a t i o n s s o l v i n g t h e Boltzmann-Uehling-Uhlenbeck equation.

I n i n t e r m e d i a t e energy nucleus-nucleus c o l l i s i o n s , non-equilibr ium 1 i g h t p a r t i c l e s a r e o b s e r v e d t o be e m i t t e d p r e f e r e n t i a l l y i n t h e e n t r a n c e c h a n n e l s c a t t e r i n g plane , / l / i n d i c a t i n g a c o l l e c t i v e motion i n t h i s p l a n e and t r a n s v e r s e t o t h e beam a x i s . / l , 2 / M i c r o s c o p i c c a l c u l a t i o n s with t h e Boltzmann-Uehling-Uhlenbeck equation i n t e r p r e t t h i s e f f e c t i n terms of t h e d e f l e c t i o n t o negative emission a n g l e s by t h e a t t r a c t i v e n u c l e a r mean f i e l d . / 3 / Since t h e c o l l e c t i v e motion i n t h e nuclear mean f i e l d 1s damped by i n d i v i d u a l nucleon-nucleon c o l l i s i o n s , t h e r e l a t i v e importance of p o s i t i v e and n e g a t i v e e m i s s i o n a n g l e s i s s e n s i t i v e t o t h e i n t e r p l a y between mean f i e l d dynamics and two-body d i s s i p a t i o n .

We have addressed t h e s e i s s u e s experimentally by determining t h e s i g n of t h e average emission angle of non-equilibrium l i g h t p a r t i c l e s from t h e c i r c u l a r p o l a r i z a t i o n of a s s o c i a t e d Y-rays emitted by t h e r e s i d u a l nucleus f o r

induced r e a c t i o n s on 15'Sm a t E/A

20 and E/A

35 MeV. For t h e s e mass-asymmetric systems, t h e l i g h t p a r t i c l e s p e c t r a a r e dominated by non-equilibrium processes./2,4-5/

The experiment was performed a t t h e National Superconducting Cyclotron Laboratory a t Michigan S t a t e U n i v e r s i t y . A m e t a l l i c s e l f - s u p p o r t i n g '5*Sm t a r g e t of 11 mg/cm2 a r e a l d e n s i t y was bombarded with '*N i o n s of 280 and 490 MeV energy. Light p a r t i c l e s w e r e d e t e c t e d w i t h f o u r A E - E t e l e s c o p e s a r r a n g e d i n a d o u b l y s y m m e t r i c geometry/6/ a t polar angles of 0=30° and 60° and azimuthal a n g l e s of @ = O O and 1 8 0 ° w i t h r e s p e c t t o t h e beam a x i s . The c i r c u l a r p o l a r i z a t i o n of c o i n c i d e n t Y-rays was measured w i t h two forward s c a t t e r i n g polarimetera/6/ positioned a t 0=90°, @-90° and 0=90°, @=270°. The p o l a r i m e t e r s had in-beam a n a l y s i n g powers of 1.30k0.258 and 1.20+0.25%, a t t h e bombarding e n e r g i e s of E/A=20 and 35 MeV, r e s p e c t i v e l y . Only s t a t i s t i c a l e r r o r s a r e displayed i n t h e f i g u r e s .

*CSI. Postfaoh 110541, D-6100 Darmstadt. P.R.G.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986410

JOURNAL DE PHYSIQUE

The m e a s u r e d l i g h t p a r t i c l e e n e r g y s p e c t r a a n d Y-ray p o l a r i z a t i o n s a r e shown i n F i g u r e s 1 and 2. The c r o s s s e c t i o n s a r e f o r w a r d p e a k e d a n d t h e e n e r g y s p e c t r a e x h i b i t n e a r l y e x p o n e n t i a l s l o p e s i n a g r e e m e n t w i t h t h e t r e n d s e s t a b l i e h e d p r e v i o u s l y f o r n o n - e q u i l i b r i u m l i g h t p a r t i c l e e m i s s i o n . / 4 , 5 / P o s i t i v e p o l a r i z a t i o n s a r e o b s e r v e d a t b o t h e n e r g i e s a n d e m i s s i o n a n g l e s . The magnitude of t h e measured p o l a r i z a t i o n i n c r e a s e s w i t h i n c r e a s i n g e n e r g y a n d m a s s o f t h e c o i n c i d e n t l i g h t p a r t i c l e s . No s i g n i f ~ c a n t d e p e n d e n c e o n beam e n e r g y i s o b s e r v e d . For a g i v e n p a r t i c l e and e n e r g y , t h e p o l a r i z a t i o n i s s l i g h t l y l a r g e r a t 0=60° t h a n a t 0 = 3 0 ° . I n o u r s i g n c o n v e n t i o n , / 6 / p o s i t i v e c i r c u l a r Y-ray p o l a r i z a t i o n s c o r r e s p o n d t o n e g a t i v e d e f l e c t i o n a n g l e s a n d v i c e v e r s a . Our e x p e r i m e n t c l e a r l y e s t a b l i s h e s t h e p r e f e r e n t i a l e m i s s i o n o f n o n - e q u i l i b r i u m l i g h t p a r t i c l e s t o n e g a t i v e e m i s s i o n a n g l e s , c o n s i s t e n t w i t h an a t t r a c t i v e n u c l e a r mean f l e l d a n d w i t h m e a s u r e m e n t s a t lower e n e r g i e s . / 7 / The s i g n is o p p o s i t e t o what is e x p e c t e d i f o n l y shadowing by t h e r e s i d u a l n u c l e u s would a f f e c t t h e p a r t i c l e e m i s s i o n . / 2 / For l i g h t p a r t i c l e e n e r g i e s o f E/A

3 5 MeV, P i n c r e a s e s a p p r o x i m a t e l y l i n e a r l y w i t h A a s would be e x p e c t e d i n a c o a l e s c e n c e model of l i g h t p a r t i c l e p r o d u c t i o n . Y

I ' #" ~ ~ I ~ . ' II . . 8 ' ' ' ' 'I'

'% + "9m, E/A

20 MeV

ENERGY (MeV) ENERGY (MeV)

F i g . 1

C i r c u l a r Y-ray p o l a r i z a t i o n s p l o t t e d a s a f u n c t i o n o f p a r t i c l e e n e r g i e s f o r p , d , t , a n d a ( u p p e r p a r t ) f o r E/A

35 MeV. C l o s e d and open c i r c l e s c o r r e s p o n d t o m e a s u r e m e n t s i n c o i n c i d e n c e w i t h l l g h t p a r t i c l e s d e t e c t e d a t 3 0 ° a n d 6 0 ° , r e s p e c t i v e l y . The l o w e r p a r t s shows t h e i n c l u s i v e e n e r g y s p e c t r a f o r t h e c o r r e s p o n d i n g l i g h t p a r t i c l e s .

F i g . 2

C i r c u l a r Y-ray p o l a r i z a t i o n s p l o t t e d a s a f u n c t i o n o f p a r t i c l e e n e r g i e s f o r p , d , t , a n d

( u p p e r p a r t ) f o r E/A

20 MeV. C l o s e d and open c i r c l e s c o r r e s p o n d t o m e a s u r e m e n t s i n c o i n c i d e n c e w i t h l i g h t p a r t i c l e s d e t e c t e d a t 3 0 ° a n d 6 0 ° , r e s p e c t i v e l y . The l o w e r p a r t s s h o w s

t h e i n c l u s i v e e n e r g y s p e c t r a f o r t h e c o r r e s p o n d i n g l i g h t p a r t i c l e s .

We h a v e p e r f o r m e d n u m e r i c a l c a l c u l a t i o n s w i t h t h e Boltzmann-Uehling-Uhlenbeck (BUU)

e q u a t i o n / 2 , 6 / f o r 14N+'S*Sm c o l l i s i o n s a t E/A=35 MeV w i t h impact p a r a m e t e r s b e t w e e n

b=l t o 10 fm. The impact parameter a v e r a g e d a z i m u t h a l d i s t r i b u t i o n s of n u c l e o n s w i t h

e n e r g i e s l a r g e r t h a n 30 MeV, e m i t t e d a t e=30° and 6 0 ° , a r e shown i n F i g u r e 3. I n t h e

f i g u r e , p o s i t i v e a n d n e g a t i v e s c a t t e r i n g a n g l e s c o r r e s p o n d t o @=OO-go0 and @=go0-

180". r e s p e c t i v e l y . The c a l c u l a t i o n s p r e d i c t t h e p r e f e r e n t i a l e m i s s i o n o f n u c l e o n s

t o n e g a t i v e a n g l e s , i n q u a l i t a t i v e agreement w i t h t h e e x p e r i m e n t a l o b s e r v a t i o n s . To

a l l o w a more q u a n t i t a t i v e comparison w i t h t h e d a t a , we have c a l c u l a t e d t h e c i r c u l a r

p o l a r i z a t i o n , <Py>, p r e d i c t e d by t h e BUU model assuming t h a t t h e r e s i d u a l n u c l e u s d e c a y v i a s t r e t c h e d E2 t r a n s i t i o n s . The predicted p o l a r i z a t i o n s a r e 0.18f0.03 and 0 . 2 5 + 0 . 0 3 , r e s p e c t i v e l y . The v a l u e s s h o u l d be r e d u c e d by a b o u t 20% i f o n e a c c o u n t s f o r n o n - s t r e t c h e d t r a n s i t i o n s . / 6 / I n c o m p a r i s o n , t h e c a l c u l a t e d p o l a r i z a t i o n s a r e l a r g e r than t h e e x p e r i m e n t a l l y o b s e r v e d p r o t o n p o l a r i z a t i o n s o f .O7 b o t h a t 8=30° and 8x60

However, t h e present c a l c u l a t i o n s d o n o t i n c l u d e e m i s s i o n o f c o m p o s i t e p a r t i c l e s which have l a r g e r m e a s u r e d p o l a r i z a t i o n s . I n a c c o r d a n c e w i t h t h e coalescence p i c t u r e , one may a s s e s s t h e e f f e c t s of complex p a r t i c l e emission by e v a l u a t i n g a n " e f f e c t i v e n u c l e o n p o l a r i z a t i o n v a c c o r d i n g t o t h e d e f i n i t i o n :

"N + 'MSm

E/A

MeV * *

1

Fig. 3

Azimuthal d i s t r i b u t i o n of n u c l e o n s s c a t t e r e d t o 30?1 O 0 (closed p o i n t s ) and 60+10° ( o p e n ) p o i n t s f r o m BUU c a l c u l a t i o n s .

> 90° corresponds t o n e g a t i v e s c a t t e r i n g a n g l e s and

<

9 0 ° r e p r e s e n t s p o s i t i v e s c a t t e r i n g where A . P . ( 8 , E . ) and o ( 8 . E . ) d e n o t e angles.

m a s s . e x l ~ e r i ' l m e n t a l \ v m J e a s u r e d

p o l a r i z a t i o n and c r o s s s e c t i o n f o r p a r t i c l e i and i = p , d , t , a . For p a r t i c l e e n e r g i e s E / A Z 3 0 MeV, t h e e f f e c t i v e p o l a r i z a t i o n s a r e P ( 3 0 ° ) = 0 . 1 7 f 0 . 0 3 a n d

e [ f .

Pe f(60°)=0.12+0.03. Considering t h e e x p e r i m e n t a l uncer a l n t i e s of t h e a b s o l u t e c a 5 i b r a t i o n s of t h e a n a l y s i n g power and t h e t h e o r e t i c a l u n c e r t a i n t i e s i n a s s i g n i n g weights f o r t h e composite p a r t i c l e ? , P e f f ( 8 ) and <P (8)> a r e i n good agreement.

Y

I n order t o a s s e s s the importance of t h e nucleon-nucleon c o l l i s i o n dynamics, we have performed BUU c a l c u l a t i o n s with mean f i e l d only. For s i m p l i c i t y , c a l c u l a t i o n s were o n l y performed f o r one impact parameter, b=6.5 fm. The p o l a r i z a t i o n is l a r g e r by over a f a c t o r of t h r e e with mean f i e l d a l o n e . Thus t h e magnitude of t h e c a l c u l a t e d p o l a r i z a t i o n s r e f l e c t t h e b a l a n c e between d e f l e c t i o n by t h e mean f i e l d and randomization of the p a r t i c l e v e l o c i t i e s by nucleon-nucleon c o l l i s i o n s .

I n summary, measurements of the c i r c u l a r p o l a r i z a t i o n s of Y-rays i n coincidence with l i g h t p a r t i c l e s i n d i c a t e t h a t n o n - e q u i l i b r i u m l i g h t p a r t i c l e s a r e p r e d o m i n a n t l y emi t t e d t o n e g a t i v e e m i s s i o n a n g l e s . Negative emission angles a r e c o n s i s t e n t with 'the d e f l e c t i o n of non-equilibrium l i g h t p a r t i c l e s by an a t t r a c t i v e n u c l e a r mean f i e l d . C a l c u l a t i o n s w i t h t h e Bol t z m a n n - U e h l i n g - U h l e n b e c k e q u a t i o n p r e d i c t p r e f e r e n t i a l e m i s s i o n t o n e g a t i v e a n g l e s and s u g g e s t t h a t c o l l i s i o n s b e t w e e n i n d i v i d u a l n u c l e o n s r e d u c e t h e p o l a r i z a t i o n s s i g n i f i c a n t l y below what might be expected from mean f i e l d dynamics alone.

This work h a s been supported by t h e National Science Foundation under Grant No. PHY- 83-1 2245.

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