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Applications of plastic nuclear track detectors in heavy ion physics
0191-278X/89 $3.00 + .00 © 1989 Pergamon Press plc
Nucl. Tracks Radiat. Meas., Vol. 15, Nos. 1-4, pp. 393--402, 1988 Int. 1. Radiat. Appl. lnstrum., Part D Printed in Great Britain
APPLICATIONS OF PLASTIC N U C L E A R T R A C K DETECTORS IN H E A V Y ION PHYSICS W. HEINRICH, C. BRECHTMANN, J. DREUTE, D. WEIDMANN U n i v e r s i t y of S i e g e n, D e p a r t m e n t of Physics A d o l f - Relchwein - S t r . , 5 9 0 0 S l e g e n , West Germany
A b s t r a c t - The e x p e r i m e n t a l t e c h n i q u e of c o m p u t e r i z e d t r a c k m e a s u r e m e n t s for p l a s t i c n u c l e a r t r a c k d e t e c t o r s was used In d i f f e r e n t e x p e r i m e n t s i n v e s t i g a t i n g i n t e r a c t i o n s o f r e l a t i v i s t i c heavy ions. In this paper the method is d e s c r i b e d , r e s u l t s a r e p r e s e n t e d and discussed. To m e a s u r e c r o s s s e c t i o n s s t a c k s w e r e e x p o s e d at the BEVALAC, at Brookhaven and at CERN to d i f f e r e n t beam n u c l e i having energies f r o m O.6 G e V / n u c l e o n up to 200 GeV/nucleon. The c r o s s sections f o r one nucleon r e m o v a l a r e c o n s i d e r a b l y enhanced at high energies due to e l e c t r o m a g n e t i c d i s s o c i a t i o n . We i n v e s t i gated the e f f e c t of e l e c t r o m a g n e t i c d i s s o c i a t i o n f o r d i f f e r e n t t a r gets and p r o j e c t i l e s . For heavy p r o j e c t i l e s an e x c l u s i v e a n a l y s i s of n u c l e a r f r a g m e n t a t i o n on an e v ent by e v ent basis was p e r f o r m e d . Based on this the e f f e c t of m u l t i f r a g m e n t a t i o n can be s t u d i e d . We exposed a stack of t 0 0 CR39 f o i l s to a I G e V / n u c l e o n is 7 Au beam at the BEVALAC. Events w i t h up to 10 p r o j e c t i l e f r a g m e n t s having a charge Z~5 and coming out of the same i n t e r a c t i o n v e r t e x w e r e o b s e r v e d . To search f o r p r o j e c t i l e f r a g m e n t s w i t h f r a c t i o n a l charge in r e l a t i v i s t i c heavy ion c o l l i s i o n s , we e x p o s e d s t a c k s of 50 CR39 f o i l s behind a lead block of 15 cm depth to the u l t r a r e l a t i v i s t i c heavy Ion beams at B r o o k h a v e n and CERN. The charge r e s o l u t i o n achieved in these e x p e r i m e n t s is o = 0 . 0 2 7 e .
1. INTRODUCTION D i e l e c t r i c n u c l e a r t r a c k d e t e c t o r s have some unique c h a r a c t e r i s t i c s in c o m p a r i s o n to o t h e r d e t e c t o r s . They r e c o r d the e n e r g y loss of i o n i z i n g p a r t i c l e s w i t h en o u t s t a n d i n g p r e c i s i o n . The reason f o r this is t h a t Landau f l u c t u a t i o n s of the e n e r g y loss caused by high e n e r g y 8 - e l e c t r o n s do not c o n t r i b u t e to the t r a c k f o r m a t i o n in p l a s t i c d e t e c t o r s . Also the s p a t i a l r e s o l u t i o n of m e a s u r e d p a r t i c l e t r a j e c t o r i e s Is e x t r e m e l y good. It Is l i m i t e d only by the p r e c i s i o n of m i c r o s c o p i c t r a c k m e a s u r e m e n t s . D i s t o r t i o n s of d e t e c t o r g e o m e t r y like they are t y p i c a l f o r n u c l e a r e m u l s i o n s play a m i n o r r o l e f o r p l a s t i c d e t e c t o r s . E x p o s u r e s to a p a r t i c l e beam are r e l a t i v e l y simple f o r passive p l a s t i c n u c l e a r t r a c k d e t e c t o r s . It is not n e c e s s a r y to a s s e m b l e and t e s t a s o p h i s t i c a t e d d e t e c t o r s y s t e m , e l e c t r o n i c equipment and c o m p u t e r s y s t e m s at an a c c e l e r a t o r . The t y p i c a l beam t i m e s which a r e needed f o r the e x p e r i m e n t s d e s c r i b e d b e lo w a r e some m i n u t e s . On the o t h e r hand t h e r e a r e also w e l l known d i s a d v a n t a g e s of p l a s t i c n u c l e a r t r a c k d e t e c t o r s like f o r e x a m p l e a s e n s i t i v i t y changing f r o m batch to batch and w i t h t e m p e r a t u r e . But in a c c e l e r a t o r e x p e r i m e n t s in many cases it is p o s s i b l e to d e t e r m i n e d i r e c t l y the c a l i b r a t i o n f r o m t h e e x p e r i m e n t , so t h a t f l u c t u a t i o n s of s e n s i t i v i t y are a minor p r o b l e m . The main d i s a d v a n t a g e of n u c l e a r t r a c k d e t e c t o r s is the t r e m e n d o u s e f f o r t which is n e c e s s a r y to scan f o r t r a c k s and to m e a s u r e them. T h e r e f o r e the use of p l a s t i c d e t e c t o r s was l i m i t e d to low s t a t i s t i c s e x p e r i m e n t s . This s i t u a t i o n changed completely due to p r o c e d u r e s of a u t o m a t i c t r a c k m e a s u r e m e n t s which we developed over the last y e a r s . High p r e c i s i o n e x p e r i m e n t s w i t h high s t a t i s t i c a l s i g n i f i c a n c e w e r e p e r f o r m e d In the f i e l d of heavy Ion physics or a r e under p r o g r e s s . In this paper we w i l l d e s c r i b e methods and r e s u l t s of e x p e r i m e n t s p e r f o r m e d at t he BEVALAC and at a c c e l e r a t o r s at CERN and B r o o k h a v e n . 2. AUTOMATIC TRACK MEASUREMENTS Scanning and m e a s u r i n g of m i l l i o n s of t r a c k s is p o s s i b l e c o m p l e t e l y a u t o m a t i c a l l y w i t h image analysis s y s t e m s and c o m p u t e r i z e d m i c r o s c o p e s . A f i r s t e x p e r i m e n t making
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use of t h i s t e c h n i q u e w a s p e r f o r m e d t e n y e a r s a g o a t t h e U n i v e r s i t y o f San F r a n c i s c o using a Q u a n t l m e t s y s t e m I . M o r e s o p h i s t i c a t e d and f a s t e r t r a c k m e a s u r e m e n t s g o t p o s s i b l e s o m e y e a r s l a t e r u s i n g s y s t e m s w h i c h w e d e v e l o p e d at t h e U n i v e r s i t y o f S l e g e n 2 . N u m b e r s of 10 7 m e a s u r e d e t c h c o n e s a r e t y p i c a l f o r t h e s e e x p e r i m e n t s . We w i l l s u m m a r i z e b e l o w s o m e p r o p e r t i e s o f t h e d a t a t a k e n by a u t o m a t i c m e a s u r e m e n t s w h i c h w e r e d i s c u s s e d In m o r e d e t a i l in an e a r l i e r p a p e r ~1 For t r a c k m e a s u r e m e n t s t h e p l a s t i c d e t e c t o r f o i l s a r e m o u n t e d on a m i c r o s c o p e s t a g e w h i c h is m o v e d by m o t o r s u n d e r c o m p u t e r c o n t r o l . T h e m i c r o s c o p e is k e p t In f o c u s by t h e c o m p u t e r and t h e d e t e c t o r is s c a n n e d in a m e a n d e r p a t h . For e a c h f i e l d o f v i e w t h e p i c t u r e a n a l y s i s s y s t e m d e t e c t s a l l t r a c k s and m e a s u r e s t h e m . F o r a l l e t c h c o n e s t h e a r e a , p o s i t i o n on t h e f o i l , v a r i a n c e s and c o v a r l a n c e o f t h e a r e a and t h e v a l u e of b r i g h t ness In t h e c e n t e r of the d e t e c t e d o b j e c t a r e m e a s u r e d by t h e a u t o m a t i c s y s t e m . T h e c e n t r a l b r i g h t n e s s can be u s e d t o d i s t i n g u i s h e t c h f i g u r e s f r o m d a r k s t r u c t u r e s on t h e d e t e c t o r s u r f a c e w h i c h a r e no t r a c k s b u t w e r e d e t e c t e d and m e a s u r e d by t h e s y s t e m • F i g u r e 1 s h o w s t h e d i s t r i b u t i o n of m e a s u r e d a r e a s on o n e d e t e c t o r s u r f a c e f o r a b e a m of r e l a t i v i s t i c s u l p h u r n u c l e i and of p r o j e c t i l e f r a g m e n t s . P e a k s f o r d i f f e r e n t a r e a s of t h e p r o j e c t i l e s and I n d i v i d u a l f r a g m e n t s can be o b s e r v e d . F i g u r e 2 s h o w s a s c a t t e r p l o t o f m e a s u r e d a r e a and of b r i g h t n e s s m e a s u r e d In a m a t r i x o f 3 x 3 p l x e l s f o r t h i s s e t of d a t a . N u c l e a r t r a c k s a r e r e p r e s e n t e d by a b a n d o f d a r k o b j e c t s . B a s e d on t h e i n f o r -
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Fig• 1: D i l t r i b u t i o n of t r a c k a r e a s f o r f o r a r e l a t i v i s t i c s u l p h u r b e a m and beam fragments m a t l o n c o n t a i n e d in t h l l f i g u r e i t is p o s s i b l e t o m a k e a c u t t o t h e d a t a and to eliminate a large amount of surface s t r u c t u r e s w h i c h a r e no t r a c k s • F i g u r e 3 shows the distribution of track sizes for the lame data prllented in f i g u r e 1 after this cut. This reduction of noise f r o m t h e d a t a is e s s e n t i a l f o r l a t e r r e constructions of particle trajectories t h r o u g h a s t a c k of d e t e c t o r f o i l s • A c a l i b r a t i o n o f t h e d e t e c t o r s is p o s s i b l e b a l e d on t h e p e a k s seen in f i g u r e 3 The mean areas measured for beam part i c l e s and f r a g m e n t s d i f f e r f o r t h e s a m e c h a r g e on d i f f e r e n t f o i l s . R e a s o n s f o r t h i s a r e non c o n s t a n t s e n s i t i v i t i e s f r o m f o i l t o f o i l o r as w i l l be s h o w n b e l o w non c o n s t a n t e t c h c o n d i t i o n s . F i g u r e 4 shows for a sample of detector foils the correlation of the mean area for fragment tracks with the mean area f o r b e a m t r a c k s . B a s e d on t h i s l i n e a r c o r r e l a t i o n an I n d i v i d u a l c a l i b r a t i o n f o r f r a g m e n t t r a c k s m e a s u r e d on e a c h
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d e t e c t o r f o i l can be d e t e r m i n e d in d e p e n d e n c e on t h e m e a n a r e a o f t h e b e a m t r a c k s . F u r t h e r m o r e t h e d a t a of f i g u r e 4 can be u s e d t o c a l i b r a t e d e t e c t o r f o i l s l o c a l l y . For this purpose we determine a map of mean track size for beam particles within a grid of c o o r d i n a t e s on t h e d e t e c t o r f o i l . F i g u r e 5 s h o w s c h a r g e d i s t r i b u t i o n s f o r t h e s a m e d e t e c t o r f o i l w i t h o u t and w i t h l o c a l c a l i b r a t i o n . A l o c a l c a l i b r a t i o n o f t h e d e t e c t o r f o i l s is n e c e s s a r y due t o i n h o m o g e n i t i e e o f t h e d e t e c t o r o r t h e e t c h i n g p r o c e s s . S i m i l a r c o r r e c t i o n s a r e In s o m e c a s e s n e c e s s a r y f o r t h e t r a c k s i z e a s a f u n c t i o n o f t h e c o o r d i n a t e s o f t h e p a r t i c l e t r a c k s in t h e v i d e o p i c t u r e . If one m e a s u r e s t h e s a m e t r a c k a t d i f f e r e n t p o s i t i o n s in t h e v i d e o p i c t u r e t h e a r e a c h a n g e s w i t h t h i s p o s i t i o n . The r e a s o n f o r t h i s is • s h a d i n g o f t h e b r i g h t n e s s in t h e v i d e o p i c t u r e w h i c h is in c o n f l i c t w i t h t h e c o n s t a n t t h r e s h o l d in g r e y l e v e l o f t h e p i c t u r e a n a l y s i s s y s t e m f o r t r a c k m e a s u r e m e n t . T h i s s h a d i n g e f f e c t can be m i n i m i z e d by a s h a d i n g c o r r e c t o r e l e c t r o n i c s o f t h e c a m e r a s , b u t a s m a l l r e m a i n i n g s h a d i n g e f f e c t can c a u s e e r r o r s o f t h e m e a s u r e d t r a c k s i z e . We c o r r e c t f o r t h i s e f f e c t in a similar way like described above for the local calibration of the detector foil. 3. R E C O N S T R U C T I O N OF T R A J E C T O R I E S AND I N T E R A C T I O N S F o r a s t a c k o f p l a s t i c d e t e c t o r s e x p o s e d t o an a c c e l e r a t o r b e a m t r a j e c t o r i e s o f t h e p a r t i c l e s can be r e c o n s t r u c t e d f r o m t h e m e a s u r e d e t c h c o n e s on t h e I n d i v i d u a l f o i l s u r f a c e s . For e a c h e t c h c o n e t h e c o o r d i n a t e s on t h e d e t e c t o r f o i l , t h e c h a r g e d e r i v e d f r o m t h e t r a c k a r e a and t h e d e p t h of t h e d e t e c t o r l a y e r in t h e s t a c k a r e k n o w n . Due t o t h e m e a s u r i n g p r o c e d u r e t h i s i n f o r m a t i o n is s t o r e d in f i l e s c o n t a i n i n g a l l d a t a f o r one f o i l s u r f a c e , t h a t m e a n s a t a c o n s t a n t d e p t h In t h e s t a c k . A r e c o n s t r u c t i o n of individual p a r t i c l e t r a j e c t o r i e s t h r o u g h t h e s t a c k m e a n s t h a t a l l d a t a have t o be o r d e r e d in a
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d i f f e r e n t f o r m so t h a t t h e i n d i v i d u a l c o n e m e a s u r e m e n t s along a trajectory are available T h i s w a s a t r e m e n d o u s p r o b l e m o f a c c e s s t o l a r g e m a s s s t o r a g e d e v i c e s 3 w h e n w e did t h i s on a PDP 1 1 / 4 5 . On a tzVAX w i t h s e v e r a l m e g a b y t e s of memory which we are using n o w t h i s p r o b l e m can be s o l v e d in r e a s o n a b l e c o m p u t e r t i m e . T h e s o f t w a r e f o r t r a j e c t o r y t r a c i n g m u s t be c a p a b l e t o m a n a g e p r o b l e m s a r i s i n g f r o m t r a c k s c r o s s i n g e a c h o t h e r and f r o m i n t e r a c t i o n s o f t h e p a r t i c l e s . A c h a r g e c h a n g i n g i n t e r a c t i o n o f a p a r t i c l e is s h o w n in f i g u r e 6 . T h e c h a r g e o f t h e p a r t i c l e is m e a s u r e d a l o n g i t s p a t h m a n y t i m e s on e a c h d e t e c t o r s u r f a c e . D e p e n d i n g on the length of the reconstructed trajectory t h e m e a n c h a r g e o f t h e p a r t i c l e c a n be determined very accurately from a large number of charge measurement for individual etch cones. Starting with the detector surface following behind the interaction vertex a s m a l l e r c h a r g e o f a p r o j e c t i l e f r a g m e n t is m e a s u r e d . If w e t a k e t h e m e a s u r e m e n t o f t h i s s m a l l e r c h a r g e o v e r m o r e t h a n o n e o r t w o d e t e c t o r s u r f a c e s as a c r i t e r i o n t o d e f i n e an i n t e r a c t i o n , t h e e f f i c i e n c y f o r t h e d e t e c t i o n o f c h a r g e c h a n g i n g i n t e r a c t i o n s is a l m o s t 1. The p o s s i b i l i t y t o d e t e c t t h e s e c h a r g e c h a n g i n g i n t e r a c t i o n s is u s e d in interaction mean free path measurements a n d in t h e a n a l y s i s o f i n d i v i d u a l i n t e r a c t i o n vertices of muItifragmentation events described below. 4 . I N T E R A C T I O N M E A N FREE P A T H M E A S U R E M E N T S F o r m e a s u r e m e n t s of i n t e r a c t i o n m e a n f r e e p a t h s w e f o l l o w a l a r g e n u m b e r o f p a r ticle trajectories o f i n d i v i d u a l l e n g t h I i u n t i l an i n t e r a c t i o n is d e t e c t e d o r t h e t r a j e c t o r y l e a v e s t h e s c a n n i n g v o l u m e . T h e i n t e r a c t i o n m e a n f r e e p a t h o f t h e p a r t i c l e s c a n be d e t e r m i n e d by ),= E l i / n , w h e r e n is t h e n u m b e r o f d e t e c t e d i n t e r a c t i o n s . In t h e s e m e a surements deep stacks of a large number of detector foils are exposed to beam part i c l e s so t h a t l o n g p o t e n t i a l p a t h s a r e a v a i l a b l e f o r t h e b e a m p a r t i c l e s and a l s o f o r t h e p r o j e c t i l e f r a g m e n t s p r o d u c e d in t h e s t a c k . B a s e d on t h i s m e t h o d w e p e r f o r m e d i n t e r a c t i o n m e a n f r e e p a t h m e a s u r e m e n t s 4 in C R 3 9 a n d C R 3 9 + A g f o r p a r t i c l e s w i t h c h a r g e s 8
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.
.
.
.
.
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A f i r s t e x p o s u r e o f a s e t o f s t a c k s c o n t a i n i n g d i f f e r e n t t a r g e t s w a s p e r f o r m e d to a 7 2 0 M e V / n u c l e o n s2 S beam a t t h e B E V A L A C . F i g u r e 7 s h o w s t h e d i s t r i b u t i o n o f a r e a s o f a u t o m a t i c a l l y m e a s u r e d t r a c k s on a f o i l s u r f a c e d o w n s t r e a m t h e t a r g e t a f t e r e t c h i n 9 t h e d e t e c t o r s in 6n NaOH a t 7 0 ° C f o r a b o u t 2 2 h . T h e p o s i t i o n o f t h e p e a k s can be i d e n t i f i e d as t h e mean a r e a s o f t r a c k s o f c h a r g e n u m b e r Z = 6 t o Z = 1 6 . The c h a r g e c a l i b r a t i o n b a s e d on t h e m e a s u r e m e n t o f a s i n g l e e t c h c o n e v a r i e s f r o m o = 0 . 1 8 e f o r Z = 6 t o o=0.27e for Z=16. By t r a c i n g t h e t r a j e c t o r i e s w i t h a p a t t e r n r e c o g n i t i o n s o f t w a r e f r o m o n e f o i l s u r f a c e to the next we get 8 charge measurements for each nuclear track. This leads to a charge r e s o l u t i o n o f o = O . 0 6 e f o r Z = 6 and o = 0 . 1 e f o r Z = 1 6 . F i g u r e 8 s h o w s t h e d i s t r i b u t i o n o f m e a s u r e d c h a r g e s e a c h c o m p u t e d as t h e m e a n o f 8 s i n g l e m e a s u r e m e n t s d o w n s t r e a m t h e t a r g e t . The aim of t h e m e a s u r e m e n t is t o g e t u n b i a s e d d i s t r i b u t i o n s o f c h a r g e s at b o t h t a r g e t s u r f a c e s . For t h i s p u r p o s e s o m e s y s t e m a t i c e f f e c t s h a v e t o be c o n s i d e r e d . I n t e r a c t i o n s in t h e d e t e c t o r f o i l s have t o be t a k e n I n t o a c c o u n t c a r e f u l l y . I t is n o t correct to build the average of the eight charge values measured for a track. These v a l u e s have t o be a n a l y z e d l i k e d e s c r i b e d a b o v e t o d e t e c t c h a r g e c h a n g i n g c o l l i s i o n s in t h e d e t e c t o r f o i l s . The I n t e r a c t i o n p o i n t s can u n a m b i g u o u s l y be d e t e r m i n e d If on b o t h s i d e s of t h e i n t e r a c t i o n at l e a s t t h r e e c h a r g e v a l u e s w e r e m e a s u r e d . T h e r e f o r e w e d e t e r m i n e t h e c h a r g e d i s t r i b u t i o n in t h e t h i r d b u t l a s t d e t e c t o r s u r f a c e . T h e d e v e l o p m e n t o f t h e c h a r g e d i s t r i b u t i o n f r o m t h i s d e t e c t o r s u r f a c e u p s t r e a m and d o w n s t r e a m t o t h e t a r g e t m u s t be c a l c u l a t e d . T h i s Is a c h i e v e d by a p r o p a g a t i o n c a l c u l a t i o n u s i n g c r o s s s e c t i o n s d e t e r m i n e d f o r t h e CR39 t a r g e t . As a r e s u l t o f t h i s p r o c e d u r e w e g e t e x t r e m e ly a c c u r a t e c h a r g e m e a s u r e m e n t s w i t h a m i n i m u m b i a s due t o i n t e r a c t i o n s in t h e d e t e c t o r . No o t h e r d e t e c t o r s y s t e m is k n o w n t h a t c o u l d c o m p e t e w i t h t h e s e e x c e l l e n t r e s u l t s achieved with plastic nuclear track detectors. S o m e p e r c e n t o f a l l t r a j e c t o r i e s a r e so c l o s e t o e a c h o t h e r t h a t t h e i r e t c h c o n e s a r e o v e r l a p p i n g . In g e n e r a l t h e t r a n s v e r s e m o m e n t a of t h e p r o d u c e d f r a g m e n t s a r e v e r y s m a l l in c o m p a r i s o n t o t h e l o n g i t u d i n a l m o m e n t a . T h e r e f o r e t h e e t c h c o n e s o f t w o o v e r l a p p i n g t r a c k s do n o t s e p a r a t e w i t h i n f o u r p l a s t i c d e t e c t o r f o i l s . In t h e s e e x p e r i m e n t s w e m a k e no use o f p i c t u r e a n a l y s i s s o f t w a r e w h i c h is c a p a b l e t o s e p a r a t e o v e r l a p p i n g t r a c k s , b u t w e use a f a s t e r and s i m p l e r m e t h o d t o o v e r c o m e t h i s p r o b l e m . By u s i n g t h e v a r i a n c e s and c o v a r l a n c e o f t h e e l l i p t i c a l o b j e c t f i t t e d by t h e a u t o m a t i c measurement to the two overlapping tracks, we get some Information about the amount o f o v e r l a p and t h e o r i e n t a t i o n o f t h e t w o t r a c k s . T h u s t h e 8 e t c h f i g u r e s a l o n g t h e t r a j e c t o r y can e a s i l y be i d e n t i f i e d as o v e r l a p p i n g . T h e d i s t r i b u t i o n o f c h a r g e s In t h e s e t o f o v e r l a p p i n g t r a c k s is c a l c u l a t e d b a s e d on t h e c h a r g e d i s t r i b u t i o n of n o n o v e r l a p p i n g t r a c k s and t h e t y p i c a l a r e a s o f t h e e t c h c o n e s f o r d i f f e r e n t f r a g m e n t s . B a s e d on t h i s i n f o r m a t i o n / h e m e a s u r e d c h a r g e d i s t r i b u t i o n s can be c o r r e c t e d t o i n c l u d e t h e o v e r l a p p i n g b e a m p a r t i c l e s and f r a g m e n t s . W i t h t h e k n o w n c h a r g e d i s t r i b u t i o n on b o t h t a r g e t s u r f a c e s t h e t o t a l c h a r g e c h a n g i n g f r a g m e n t a t i o n c r o s s s e c t i o n s and t h e e l e m e n t a l f r a g m e n t a t i o n c r o s s s e c t i o n s f o r t h e b e a m n u c l e i can be d e t e r m i n e d . T h i s is d o n e b a s e d on a p r o p a g a t i o n c a l c u l a t i o n as d e s c r i b e d in d e t a i l by B r e c h t m a n n and H e i n r l c h S . in t h i s c a l c u l a t i o n t h e f r a g m e n t a t i o n o f f r a g m e n t s has t o be c o n s i d e r e d . For t h i s p u r p o s e t h e f r a g m e n t a t i o n c r o s s s e c t i o n s o f t h e f r a g m e n t s a r e n e e d e d w h i c h in m o s t c a s e s can o n l y be e s t i m a t e d b a s e d on t h e s e m i e m p i r i c a l f o r m u l a o f S i l b e r b e r g and T s a o 10 and on t h e l a w o f f a c t o r i z a t i o n o f NT 15:1/4-AA
398
W. H E I N R I C H et al.
the cross sections 11 To m i n i m i z e s y s t e m a t i c e r r o r s due to this c o r r e c t i o n t he t a r g e t should be as thin as possible. On the o t h e r hand the s t a t i s t i c a l e r r o r of t h e r e s u l t decreases with increasing t a r g e t t h i c k n e s s . By m o d e l l i n g the f r a g m e n t a t i o n inside the t a r g e t one finds that s y s t e m a t i c e r r o r s can be n e g l e c t e d In c o m p a r i s o n to s t a t i s t i c a l e r r o r s as long as a t a r g e t w i t h a t h i c k n e s s below about 0. 2 i n t e r a c t i o n l e n g t h s of the beam p a r t i c l e s is used. Total charge changing and p a r t i a l c r o s s s e c t i o n s f o r the p r o d u c t i o n of f r a g m e n t s of charge Z : 6 and Z : 7 in c o l l i s i o n s of 16 0 beam nuclei at e n e r g i e s of 60 and 200 GeV/nucleon in t a r g e t s H, C, AI, Cu, Ag and Pb w e r e m e a s u r e d using the method described above 12 . Two d i f f e r e n t p o i n t s of I n t e r e s t w e r e I n v e s t i g a t e d : a] The cross sections f o r h y d r o g e n t a r g e t are e s s e n t i a l p a r a m e t e r s f o r the c a l c u l a tion d e s c r i b l n 9 the p r o p a g a t i o n of cosmic ray n u c l e i in the i n t e r s t e l l a r space. We c o m pared them with p r e d i c t i o n s of t h e s e m l e m p l r i c a l f o r m u l a s 10,1s and e x p e r i m e n t a l d a t a by Olson et al .14 and Webber is at BEVALAC e n e r g i e s . We o b s e r v e d t h a t t h e p a r t i a l cross sections f o r H t a r g e t a r e v a r y i n g even beyond 2 G e V / n u c l e o n . At 60 G e V / n u c l e o n they have d e c r e a s e d by 20Y,. For h i g h e r e n e r g i e s f r o m 60 to 2 0 0 G e V / n u c l e o n they are staying c o n s t a n t . The t o t a l c h a r g e changing c r o s s s e c t i o n does not d i f f e r s i g n i f i c a n t l y f r o m r e s u l t s in the 1-2 G e V / n u c l e o n r e g i o n . b) For h e a v i e r t a r g e t s e l e c t r o m a g n e t i c d i s s o c i a t i o n (ED) plays an i m p o r t a n t r o l e in the process of f r a g m e n t a t i o n . ED o c c u r s when a p r o j e c t i l e nucleus w h i c h passes along a heavy t a r g e t nucleus is e x c i t e d by its Coulomb f i e l d . In f a s t r e l a t i v e m o t i o n t h i s f i e l d is e q u i v a l e n t to a v i o l e n t e l e c t r o m a g n e t i c pulse i n c i d e n t on the p r o j e c t i l e . In a s u b sequent step the decay of t h e e x c i t e d nucleus by e m i s s i o n of one or m o r e n u c l e o n s Is possible. F r a g m e n t a t i o n c r o s s s e c t i o n s are I n c r e a s e d by t h i s p r o c e s s s in c e it o c c u r s at impact p a r a m e t e r s beyond the r a n g e of the s t r o n g n u c l e a r f o r c e . Using the W e i z s ~ c k e r W i l l i a m s method or a m o r e s o p h i s t i c a t e d q u a n t u m m e c h a n i c a l approach by B e r t u l a n i and Baur 1l the e l e c t r o m a g n e t i c pulse can be s u b s t i t u t e d by s p e c t r a of v i r t u a l photons i n c i d e n t on the 160 p r o j e c t i l e nucleus w hic h a r ~ agiv e n f o r d i f f e r e n t m u l t i p o l a r i t i e s . By f o l d i n g t h e s e s p e c t r a w i t h c r o s s s e c t i o n s o`( of 0 for the decay into a special f r a g m e n t a t i o n channel under i r r a d i a t i o n by beams of r e a l p h o tons of d i f f e r e n t e n e r g i e s the e l e c t r o m a g n e t i c c o n t r i b u t i o n o em f o r t h i s fragmen2tatlon channel in c o l l i s i o n s upon a n u c l e u s t a r g e t can be c a l c u l a t e d . Roughly it is o ern" Z T in'( w h e re Z T is the t a r g e t c h a r g e and `( is the r e l a t i v i s t i c L o r e n t z f a c t o r of t h e p r o j e c t i l e in the l a b o r a t o r y f r a m e . In our e x p e r i m e n t f r a g m e n t a t i o n by e l e c t r o m a g n e t i c and s t r o n g n u c l e a r f o r c e is not d i s t i n g u i s h a b l e so t h a t we m e a s u r e c r o s s s e c t i o n s o exp "O
e m
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Fig. 9 shows p a r t i a l f r a g m e n t a t i o n c r o s s s e c t i o n s o ( Z = 8 - - > Z = 7 ) vs. t a r g e t charge as o b t a i n e d f r o m our e x p e r i m e n t at 60 and 200 G e V / n u c l e o n . For c o m p a r i s o n we have included pure nuclear c r o s s s e c t i o n s o nuc which w e r e o b t a i n e d using t h e f a c t o r i z a t l o n r u l e 14 e x p r e s s e d as opT F = `( P F y PT- O nuc = O PT F IS the n u c l e a r f r a g m e n t a t i o n cro s s s e c t i o n f o r the p r o j e c t i l e P i n c i d e n t upon a t a r g e t T p r o d u c i n g a f r a g m e n t F. ¥ p F IS a f a c t o r which depends only upon the species of p r o j e c t i l e and f r a g m e n t , ¥ PT is a f a c t o r which depends only upon the species of p r o j e c t i l e and t a r g e t . The e l e c t r o m a g netic cross s e c t i o n o em v i s i b l e in f i g u r e 9 as the d i f f e r e n c e b e t w e e n the e x p e r i m e n t a l and pure n u c l e a r cross s e c t i o n s Is i n c r e a s i n g w i t h t a r g e t c h a r g e and p r o j e c t i l e energy. C,b~
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PLASTIC NUCLEAR TRACK DETECTORS
Fig. 10 shows t h a t also o ( Z = 8 - > Z = 6 ) is a f f e c t e d by ED. Total c h a r g e c h a n ging c r o s s s e c t i o n s o tot (•Z:¢1) w e r e m e a s u r e d and Included In f i g u r e !1 as d a t a p o i n t s . Pure nuclear t o t a l c r o s s s e c t i o n s o nuc o b t a i n e d f r o m o v e r l a p f o r m u l a s and c o r r e c t e d on AZ--O r e a c t i o n s are s i g n i f i c a n t l y s m a l l e r . For t h e f r a g m e n t a t i o n channel &Z~l p h o t o c r o s s s e c t i o n s o y f o r 16 O are k n o w n f o r photon e n e r g i e s f r o m p r o t o n e m i s s i o n t h r e s h o l d up to some GeV, t h e c u t o f f e n e r g y of the v i r t u a l photon s p e c t r a 12 F u r t h e r m o r e the d e c o m p o s i t i o n of o into m u l t i p o l a r i t l e s is not I m p o r t a n t ~'or u l t r a r e l a t i v l s t i c c o l l i s i o n s . So we c a l c u l a t e d t o t a l c h a r g e changing ED c r o s s s e c t i o n s o em f o r 60 and 200 G e V / n u c leon and added them to o nu© as s h o w n in f i g u r e 11. The r e s u l t i n g lines o nu¢ ÷ o em are c o n s i s t e n t w i t h the r e s u l t s f r o m our e x p e r i m e n t .
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We used our r e s u l t s to c a l c u l a t e t h e s m a l l and not s i g n i f i c a n t ED c o n t r i b u t i o n f o r C t a r g e t and s u b s t r a c t e d it f r o m our e x p e r i m e n t a l c r o s s s e c t i o n s . We f o u n d the r e m a i n ing p u r e n u c l e a r t o t a l end p a r t i a l c r o s s s e c t i o n s to be f u l l y c o n s i s t e n t w i t h e x p e r i m e n t a l r e s u l t s measured at BEVALAC e n e r g i e s 14,1s and c o n c l u d e t h a t t h e y a r e e n e r g y i n d e p e n d e n t above 1 G e V / n u c l e o n f o r non h y d r o g e n t a r g e t s . 6. FRAGMENTATION OF HEAVY PROJECTILES The i n v e s t i g a t i o n of n u c l e a r f r a g m e n t a t i o n f o r v e r y heavy p r o j e c t i l e s i n t o f r a g m e n t s • w i t h c h a r g e s In a w i d e range f r o m Z:~5 up to a l m o s t t h e c h a r g e of t h e p r o j e c t i l e Is of p a r t i c u l a r I n t e r e s t . V a r i o u s m e c h a n i s m s d o m i n a t e the f r a g m e n t a t i o n p r o c e s s . T a b l e 1 shows a c o m m o n l y used s u b d i v i s i o n of t h e d i f f e r e n t m e c h a n i s m s b a s e d on c h a r g e n u m ber of t h e f r a g m e n t and on t h e m u l t i p l i c i t y of f r a g m e n t s w i t h c h a r g e Z>5 p r o d u c e d in the same i n t e r a c t i o n 17. Heavy f r a g m e n t s w h i c h a r e p r o d u c e d w i t h l a r g e c r o s s s e c t i o n s o r i g i n a t e f r o m s p a l l a t i o n I n t e r a c t i o n s . In t h e s e I n t e r a c t i o n s t h e p r o j e c t i l e c o l l i d e s w i t h a t a r g e t nucleus in a p e r i p h e r a l c o l l i s i o n w i t h o n l y a s m a l l o v e r l a p . A s m a l l p a r t of the p r o j e c t i l e is a b r a d e d and a f t e r e m i t t i n g some n u c l e o n s in a f o l l o w i n g phase of a b l a t i o n one s i n g l e n u c l e a r f r a g m e n t s u r v i v e s w h i c h t y p i c a l l y has a l a r g e m a s s . The c r o s s s e c t i o n f o r t h i s p r o c e s s d e c r e a s e s w i t h i n c r e a s i n g mass d i f f e r e n c e b e t w e e n t h e p r o j e c t i l e and the f r a g m e n t . Light f r a g m e n t s h o w e v e r w i t h c h a r g e s b e l o w a b o u t Z = 2 5 a r e p r o duced again w i t h i n c r e a s i n g c r o s s s e c t i o n s . They a r e b e l i e v e d to be p r o d u c e d in s o c a l l e d m u l t l f r a g m e n t a t l o n e v e n t s In w h i c h a l a r g e r n u m b e r (N~3) of s m a l l f r a g m e n t s o r i g i n a t e s f r o m the e x c i t e d m a t t e r of a heavy p r o j e c t i l e a f t e r a n u c l e a r c o l l i s i o n . B e t w e e n t h e s e t w o domaines in the r e g i o n a r o u n d h a l f the mass of t h e p r o j e c t i l e e v e n t s w i t h t w o f r a g m e n t s a r e o b s e r v e d w h i c h o r i g i n a t e f r o m a f i s s i o n r e a c t i o n of t h e p r o j e c t i l e . The p r o cess of deep s p a l l a t i o n In w h i c h only one f r a g m e n t Is p r o d u c e d f r o m t h e p r o j e c t i l e Is e x p e c t e d to e x i s t as a l i m i t of s p a l l a t i o n t o w a r d s s m a l l e r f r a g m e n t s , but only l i t t l e is known a b o u t i t . For t h e open a r e a s of t a b l e 1 t h e p r o d u c t i o n of f r a g m e n t s is b e l i e v e d be r a t h e r u n l i k e l y but no d e t a i l s a r e k n o w n . No d e t a i l e d e x p e r i m e n t i n v e s t i g a t i n g n u c l e a r f r a g m e n t a t i o n in an e x c l u s i v e e v e n t by event a n a l y s i s w a s p e r f o r m e d u n t i l n o w . The s u b d i v i s i o n s h o w n in t a b l e 1 is b a s e d on i n c l u s i v e c r o s s s e c t i o n m e a s u r e m e n t s and on r e a s o n a b l e m o d e l s . multiplicity
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We p e r f o r m e d an e x p e r i m e n t t o i n v e s t i g a t e f r a g m e n t a t i o n o f h e a v y p r o j e c t i l e s in e x c l u s i v e l y a n a l y z e d e v e n t s . A s t a c k c o n t a i n i n g a l t e r n a t i n g 6 0 0 ~m t h i c k CR39 d e t e c t o r s and 2 0 0 (~m t h i c k Ag t a r g e t f o i l s w i t h a t o t a l d e p t h of 8 cm w a s e x p o s e d t o a 9 9 0 M e V / n u c l e o n Au beam at t h e B E V A L A C . T r a j e c t o r i e s o f p r o j e c t i l e s and f r a g m e n t s w e r e r e c o n s t r u c t e d as d e s c r i b e d a b o v e . F o r a l l i n t e r a c t i o n s of t h e g o l d t h e v e r t i c e s w e r e a n a l y z e d in d e t a i l to r e c o n s t r u c t t r a c k s o f a l l f r a g m e n t s w i t h c h a r g e s Z ~ 6 c o m i n g o u t of t h e i n t e r a c t i o n . F i g u r e 12 s h o w s as an e x a m p l e an e v e n t in w h i c h 8 f r a g m e n t s w e r e produced. Altogether 15573 vertices with different multiplicity of fragments were anal y z e d . The a n a l y s i s of t h i s e x p e r i m e n t is s t i l l u n d e r p r o g r e s s . But s o m e p r e l i m i n a r y r e s u i t s can a l r e a d y be p r e s e n t e d in t h i s p a p e r . T a b l e 2 s h o w s t h e o b s e r v e d a b u n d a n c e s o f d i f f e r e n t t y p e s of i n t e r a c t i o n s s u b d i v i d e d in t h e f o r m p r o p o s e d in t a b l e 1. The l a r g e n u m b e r of e v e n t s in t h e d i a g o n a l e m p h a s i z e s t h e i m p o r t a n c e o f s p a l l a t i o n , f i s s i o n and m u l t i f r a g m e n t a t i o n . But w i t h high probability also other events are observed. Clearly deep spallation events were found and f u r t h e r m o r e a l s o e v e n t s in w h i c h s i n g l e l i g h t f r a g m e n t s w i t h c h a r g e s Z ~ 2 5 a r e p r o d u c e d . The p r o b a b i l i t y f o r t h e s e " l i g h t s i n g l e s " is s u r p r i s i n g l y h i g h . T h e r e is a l m o s t no c o n t i n u o u s d e c r e a s e in f r a g m e n t y i e l d f r o m d e e p s p a l l a t i o n t o t h e s e e v e n t s . It is l i k e l y t h a t t h e y a r e p r o d u c e d in a d i f f e r e n t i n t e r a c t i o n m e c h a n i s m w h i c h may r e s u l t f r o m an i n t e r a c t i o n v e r y s i m i l a r t o a m u I t i f r a g m e n t a t i o n b u t in w h i c h only one l i g h t f r a g m e n t s u r v i v e s . T h i s i d e a is s u p p o r t e d by t h e l a r g e n u m b e r o f e v e n t s in w h i c h t w o l i g h t f r a g m e n t s a r e p r o d u c e d . The l a r g e n u m b e r o f e v e n t s w i t h t w o f r a g m e n t s w h e r e one f r a g m e n t is h e a v i e r t h a n Z = 5 2 can be u n d e r s t o o d as a s y m m e t r i c f i s s i o n e v e n t s o f t h e g o l d p r o j e c t i l e . E v e n t s o f t h i s t y p e w e r e o b s e r v e d b e f o r e 17'. A m o r e d e t a i l e d a n a l y s i s of t h e e v e n t s w i t h t h r e e f r a g m e n t s o f w h i c h one is h e a v i e r t h a n Z = 2 5 w i l l s h o w w h e t h e r t h e s e can be u n d e r s t o o d as a t a i l of t h e m u t i f r a g m e n t a t i o n regime, As s h o w n in o t h e r e x p e r i m e n t s ( r e f e r e n c e d in 17) t h e y i e l d o f l i g h t f r a g m e n t s p r o d u c e d in m u l t i f r a g m e n t a t i o n i n t e r a c t i o n s can be d e s c r i b e d by a p o w e r l a w of t h e f o r m o ( Z ) = oO Z - ~ . The e x p o n e n t x t a k e s v a l u e s b e t w e e n 1.5 and 3 . 5 and d e p e n d s on p r o j e c t i l e , t a r g e t and e n e r g y . A s i m i l a r p o w e r l a w f o l l o w s f r o m c a l c u l a t i o n s f o r t h e d i s t r i b u tion of droplet sizes for a liquid-gas transition at the critical point. There exist formal a n a l o g i e s b e t w e e n a van d e r W a a l s g a s and t h e e q u a t i o n of s t a t e o f n u c l e a r m a t t e r . The q u e s t i o n w h e t h e r t h e o b s e r v e d p o w e r l a w i n d i c a t e s a p h a s e t r a n s i t i o n f o r n u c l e a r m a t t e r is o p e n . We h o p e t o g e t m o r e i n f o r m a t i o n a b o u t t h i s p h e n o m e n o n b a s e d on o u r e x p e r i m e n t s . The e x p o n e n t x can be d e t e r m i n e d f o r d i f f e r e n t e n e r g i e s and t a r g e t s and a l s o f o r d i f f e r e n t m u l t i p l i c i t i e s o f t h e f r a g m e n t a t i o n e v e n t s o b s e r v e d in o u r e x p e r i m e n t . T h i s w o r k is u n d e r p r o g r e s s . 7 . SEARCH FOR F R A C T I O N A L CHARGES F r o m e x p e r i m e n t s in high e n e r g y p h y s i c s w e k n o w , t h a t n u c l e o n s a r e a s s e m b l e d f r o m e l e m e n t a r y c o n s t i t u e n t s , t h e s o c a l l e d q u a r k s . T h e s e q u a r k s c a r r y c h a r g e s of 1 / 3 e o r 2 / 3 e and a r e c h a r a c t e r i z e d by a n e w q u a n t u m n u m b e r , t h e c o l o u r . T h e y a r e b o u n d t o g e t h e r by t h e c o l o u r f o r c e w h i c h is t r a n s m i t t e d by t h e q u a n t a o f t h i s f i e l d , t h e s o c a l l e d g l u o n s . B a s e d on q u a n t u m c h r o m o d y n a m i c s , t h e t h e o r y d e s c r i b i n g t h e f o r m a t i o n of p a r t i c l e s by q u a r k s , t h e p r o d u c t i o n o f f r e e q u a r k s c o u l d be p o s s i b l e i f g l u o n s have a m a s s . But w h e n q u a r k s a r e s e p a r a t e d t h e e n e r g y w h i c h is p u t i n t o t h e g l u o n f i e l d s is u s e d f o r t h e c r e a t i o n of q u a r k - a n t i q u a r k p a i r s o u t of t h e v a c u u m w h i c h c o m b i n e w i t h t h e s e p a r a t i n g q u a r k s and f o r m p a r t i c l e s w i t h i n t e g e r c h a r g e . T h i s m a y e x p l a i n t h a t
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q u a r k s w e r e n e v e r o b s e r v e d as f r e e p a r t i c l e s In c o l l i s i o n s b e t w e e n high e n e r g e t i c particles . In h e a v y ion c o l l i s i o n s h o w e v e r t h e s i t u a t i o n m a y be q u i t e d i f f e r e n t . If one a s s u m e s t h a t q u a r k s end g l u o n s c a r r y i n g c o l o u r can m o v e I n s i d e a n u c l e o n , w h i c h is colour neutral seen from outside, a free quark could polarize a nucleon. That means t h a t n u c l e a r m a t t e r w o u l d b e h a v e c o m p a r a b l e t o a d i e l e c t r i c m e d i u m In an e l e c t r i c f i e l d . As a resuJ~t t h e c o l o u r f i e l d e n e r g y o f s e p a r a t i n g q u a r k s w o u l d be r e d u c e d in n u c l e a r m a t t e r ~ . T h e r e f o r e t h e s e p a r a t i o n o f q u a r k s c o u l d be p o s s i b l e w i t h o u t c r e a t i o n of n e u t r a l i z i n g q u a r k s . T h e s e p a r a t e d q u a r k s on t h e e t h e r hand c o u l d s t r o n g l y bind up to 20 p o l a r i z e d n u c l e o n s and f o r m a q u a r k n u c l e a r c o m p l e x o f a c h a r g e Z:~5 w h i c h is d e t e c t a b l e in p l a s t i c n u c l e a r t r a c k d e t e c t o r s , even If i t m o v e s w i t h r e l a t i v i s t i c v e l o c i t i e s . An e s t i m a t i o n p r e d i c t s a t h r e s h o l d e n e r g y o f 10 GeV a c t i n g on a n u c l e o n f o r p r o d u c t i o n of f r e e q u a r k s l l . C e n t e r o f m a s s e n e r g i e s in t h i s o r d e r o f magnitude recently got available for ultrarelatlvistic h e a v y ion b e a m s . We p e r f o r m e d e x p e r i m e n t s u s i n g t h e is O b e a m s o f 14.5 G e V / n u c l e o n a t B r o o k h a v e n and o f 2 0 0 G e V / n u c l e o n at CERN. P l a s t i c d e t e c t o r s w i t h e x t r e m e s e n s i t i v i t y w e r e n e c e s s a r y t o d e t e c t the r e l a t i v i s t i c o x y g e n a n d h e a v y p r o j e c t i l e f r a g m e n t s . We u s e d CR39 p l a s t i c of t y p e USF3S . T h e t h r e s h o l d o f t h i s d e t e c t o r m a t e r i a l is b e l o w t h e e n e r g y l o s s o f a r e l a t i v i s t i c n u c l e u s w i t h c h a r g e Z = S e . B e h i n d a 15 cm d e e p b l o c k o f l e a d as t a r g e t a s t a c k of 50 d e t e c t o r f o i l s w i t h a t h i c k n e s s o f 600t~m e a c h w a s a s s e m b l e d t o i d e n t i f y p r o j e c t i l e s , p r o j e c t i l e f r a g m e n t s and q u a r k n u c l e a r c o m p l e x e s . A b o u t 4 0 0 0 0 e t c h c o n e s w e r e m e a s u r e d on e a c h f o i l s u r f a c e . T h e t r a c k d e n s i t y on t h e f o i l s w a s a b o u t 1 0 0 0 / c m 2 . F i g u r e 13 s h o w s a d i s t r i b u t i o n o f t h e a r e a s o f n u c l e a r t r a c k s m e a s u r e d a u t o m a t i c a l l y on a s i n g l e f o i l s u r f a c e d o w n s t r e a m t h e t a r g e t . T h e p o s i t i o n s o f t h e p e a k s in t h i s p i c t u r e can be i d e n t i f i e d as t h e m e a n a r e a s o f t r a c k s o f f r a g m e n t s w i t h c h a r g e s Z = 5 e , 6 e , T e and 8 e . B a s e d on t h e s e m e a s u r e d d i s t r i b u t i o n s an i n d i v i d u a l c a l i b r a t i o n of e a c h d e t e c t o r f o i l s u r f a c e is p o s s i b l e g i v i n g t h e r e l a t i o n b e t w e e n m e a s u r e d t r a c k a r e a and c h a r g e of t h e r e l a t i v i s t i c p a r t i c l e . The c h a r g e r e s o l u t i o n b a s e d on t h e m e a s u r e m e n t o f a s i n g l e e t c h c o n e is o=O.18e f o r c h a r g e s Z = 6 e , T e and 8 e . We g e t up t o 100 c h a r g e m e a s u r e m e n t s p e r n u c l e a r t r a c k a f t e r f o l l o w i n g t h e t r a j e c t o r i e s of t h e p a r t i c l e s f r o m one f o i l s u r f a c e t o t h e n e x t o n e . To e x c l u d e o v e r l a p p i n g e t c h c o n e s w h i c h w e r e d e t e c t e d as one s i n g l e e l o n g a t e d o b j e c t o v e r m a n y f o i l s h a v i n g an a r e a t h a t t y p i c a l l y d o e s n o t c o r r e s p o n d t o an i n t e g e r c h a r g e , o n l y o b j e c t s o f exactly circular shape were considered for the charge measurement. Also etch cones f l a w e d by s u r f a c e s t r u c t u r e s w e r e r e j e c t e d by a c u t in s x c e n t r i c i t y and n o t u s e d f o r t h e d e t e r m i n a t i o n of the m e a n c h a r g e . So t h e n u m b e r o f e t c h c o n e s u s e d t o d e t e r m i n e t h e f r a g m e n t c h a r g e is t y p i c a l l y r e d u c e d by a b o u t 2 0 ~ . For t h e c h a r g e d i s t r i b u t i o n o f r e c o n s t r u c t e d t r a c k s s h o w n in f i g u r e 14 w e g o t s t a n d a r d d e v i a t i o n s o f o = 0 . 0 2 7 e [ 2 0 0 G e V / n u c l e o n s t a c k , 100 d e t e c t o r s u r f a c e s ) . F o r t h e B r o o k h a v e n e x p o s u r e w e g o t o = 0 . 0 3 8 e ( 1 4 . 5 G a Y / n u c l e o n , 4-4 d e t e c t o r s u r f a c e s ) . In a f i r s t a t t e m p t w e l o o k e d f o r q u a r k n u c l e a r c o m p l e x e s w h i c h w e r e p r o d u c e d in t h e l e a d t a r g e t and l i v e d long e n o u g h t o p e n e t r a t e t h r o u g h t h e r e s i d u a l l e a d t a r g e t and CR39 s t a c k . T h i s w o u l d r e q u i r e a m i n i m u m d e c a y t i m e in t h e o r d e r o f ~>10-11 s and a m e a n f r e e p a t h o f ),210 c m . F o r t h e d a t a s h o w n in f i g u r e 14 c h a r g e m e a s u r e m e n t Is u n a m b i g u o u s l y p o s s i b l e w i t h r e s p e c t t o 1 / 3 e . W e f o u n d no e v e n t in any 8 o r e g i o n a r o u n d c h a r g e s o f p o s s i b l e q u a r k n u c l e a r c o m p l e x e s in t h e 2 0 0 G e V / n u c l e o n e x p e r i m e n t . In t h e I & . S G e V / n u c l e o n e x p e r i m e n t w e e x c l u d e d e v e n t s in a 40 r e g i o n . As a c o n c l u s i o n w e can g i v e u p p e r l i m i t s f o r t h e p r o b a b i l i t y p t h a t a p r o j e c t i l e f r a g m e n t o f c h a r g e Z=~Se c o m i n g o u t o f a c o l l i s i o n o f 15 O on Pb is c a r r y i n g a n o n - i n t e g e r c h a r g e . T h i s p r o b a b i l i t y is p < 2 . S x 1 0 - 4 f o r 14.5 G e V / n u c l e o n and p ~ 1 . g x | 0 - 4 f o r 2 0 0 G e V / n u c l e o n a t a c o n f i d e n c e l e v e l o f 95:~. 104
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To i n v e s t i g a t e the p o s s i b i l i t y t h a t q u a r k n u c l e i decay in s h o r t t i m e s or have e x t r e m e l y enhanced c r o s s s e c t i o n s f o r n u c l e a r c o l l i s i o n s we e x t e n d e d o u r a n a l y s i s to s h o r t t r a c k s w h i c h were v i s i b l e o v e r only 10 f o i l s u r f a c e s or m o r e w i t h o u t n u c l e a r i n t e r a c t i o n s . As c a n d i d a t e s we a n a l y z e d in d e t a i l p a r t i c l e s w i t h a c h a r g e i n s i d e a 20 r e g i o n a r o u n d any f r a c t i o n a l c h a r g e v a l u e . For t r a c k s w i t h a l e n g t h of 5 d e t e c t o r f o i l s having t y p i c a l l y 8 usable s i n g l e c h a r g e m e a s u r e m e n t s we g o t a r e s o l u t i o n of o = 0 . 0 6 4 e . T h e r e f o r e we looked f o r c a n d i d a t e s w i t h c h a r g e s of m o r e t h a n 0 . 2 0 e a p a r t f r o m i n t e g e r c h a r g e s . We found 5 c a n d i d a t e s in the t w o e x p e r i m e n t s . To t e s t w h e t h e r t h i s is a s i g n i f i c a n t hint for the e x i s t e n c e of q u a r k n u c l e a r c o m p l e x e s or w h e t h e r we can u n d e r s t a n d the d e v i a t i o n s as f l u c t u a t i o n s of our m e a s u r e d c h a r g e s we p e r f o r m e d a Monte C a r l o s i m u l a t i o n of our e x p e r i m e n t . This c a l c u l a t i o n s h o w e d t h a t the n u m b e r of c a n d i d a t e s found in the e x p e r i m e n t a r e e x p e c t e d due to f l u c t u a t i o n s based on t h e experimental charge resolution f o r these short t r a c k s . T h e r e s t i l l r e m a i n s the p o s s i b i l i t y t h a t q u a r k n u c l e a r c o m p l e x e s a r e p r o d u c e d in c o l l i s i o n s of p r o j e c t i l e s h e a v i e r t h a n oxygen w i t h a p r o b a b i l i t y l a r g e enough to d e t e c t t h e m in a type of e x p e r i m e n t l i k e t h o s e d e s c r i b e d above. For 1114 t h i s r e a s o n we p e r f o r m e d a new e x p e r i m e n t using the 200 G e V / n u c l e o n 32S beam at CERN. 1113 In t h i s e x p e r i m e n t we e x p o s e d a s t a c k of CR39 behind a Pb t a r g e t '~ of 3.5 cm t h i c k n e s s . To e n a b l e ~ 111= p r o d u c t i o n of q u a r k s in c o l l i s i o n s IL w i t h heavy t a r g e t nuclei we • s t a c k e d the 6 0 0 p m t h i c k p l a s t i c ,~ lg x f o i l s each b e t w e e n 200pm t h i c k i,::1 s i l v e r f o i l s . The analysis of t h i s C e x p e r i m e n t is under p r o g r e s s . 1 F i g u r e 15 s h o w s the c h a r g e d i s t r i b u t i o n of r e c o n s t r u c t e d t r a j e c t o r i e s p e n e t r a t i n g 30 of a l t o 18 11 12 11 14 15 16 g e t h e r 150 CR39 d e t e c t o r f o i l s . charge The c h a r g e r e s o l u t i o n is o = O . 0 5 e . No hint f o r q u a r k nuclear c o m p l e x e s was found until now. Fig. 15: C h a r g e d i s t r i b u t i o n of f r a g m e n t s f r o m 32S This w o r k has been funded by t h e G e r m a n F e d e r a l M i n i s t e r f o r R e s e a r c h and T e c h nology (BMFT). REFERENCES 1. W. H e i n r i c h , H. D r e c h s e l , R. R u d a t , E.V. B e n t o n , D. H i l d e b r a n d , Nucl. I n s t r . M a t h . 190, 369 (1981) 2 . W. T r a k o w s k i , B. S c h 6 f e r , J. D r e u t e , S. S o n n t a g C. B r e c h t m a n n , J. B e e r , H. O r e c h s e l and W. H e i n r i c h , Nucl. I n s t r . and M a t h . 2 2 5 , 9 2 ( 1 9 8 4 ) 3. H. O r e c h s e l , C. B r e c h t m a n n , J. O r e u t e , S. S o n n t a g , W . T r a k o w s k i , J. B e e r and W. H e i n r i c h , Nucl. I n s t r . M a t h . in Phys. Res. 2 2 7 , 3 4 2 ( 1 9 8 4 ) 4. H. D r e c h s e l , C. B r e c h t m a n n , W. H e i n r i c h , J. D r e u t e and E.V. B e n t o n , Phys. Rev. L e t t . 55, 1258 (1985) 5. C. B r e c h t m a n n , H. D r e c h s e l , J. B e e r and W. H e i n r i c h , N u c l e a r T r a c k s 12, 361 (1986) 6. W. Hteinrich, H. D r e c h s e l , W. T r a k o w s k i , J. B e e r , C. B r e c h t m a n n , J. D r e u t e and S. S o n n t a g , Phys. Ray. L e t t . 5 2 , 1401 ( 1 9 8 4 ) 7. H. D r e c h s e l , J. O r e u t e , C. B r e c h t m a n n ' , W. H e i n r i c h and W. T r a k o w s k i , Phys. Ray. L e t t . 54, 30 ( 1 9 8 5 ) 8. W. H e i n r i c h , H. O r e c h s e l , C. B r e c h t m a n n and J. D r e u t e , N u c l e a r T r a c k s 12, 327 ( 1 9 8 6 ) 9. C. B r e c h t m a n n and W. H e i n r i c h , Nucl. I n s t r . M a t h . in Phys. Res., B29, 675 ( 1 9 8 8 ) IO.R. S i l b e r b e r g and C.H. T s a o , A s t r o p h y s . J. S u p p l . 25, 315 (1973) 11.P.J. L i n d s t r o m , D.E. G r e i n e r , H.H H a c k m a n , B. Cork and F.S. B i e s e r , L a w r e n c e B e r k e l e y Lab. R e p o r t , L B L - 3 6 5 0 (1975) 12.C. B r e c h t m a n n and W. H e i n r i c h , s u b m i t t e d to Z e i t s c h r i f t f u r Physik 13.J.R. L e t a w , R. S i l b e r b e r g , C.H. T s a o , A s t r o p h y s . J. S u p p l . 271, 51 ( 1 9 8 3 ) 14.D.1.. O l s o n , B.L B a r m a n , D.E. G r e i n e r , H.H. H a c k m a n , P.J. L i n d s t r o m , H.J. C r a w f o r d , Phys. Ray. C 2 8 , 1602 ( 1 9 8 3 ) 15.W.R. W e b b e r , p r i v a t e c o m m u n i c a t i o n 1 6 . C . A . B e r t u l a n i and G. B a u r , Nucl. Phys. A 4 5 8 , 725 ( 1 9 8 6 ) 1 7 . J . HUfner, Phys. Rep. 125, 129 ( 1 9 8 5 ) 18. C.J. W a d d i n g t o n and P.S. F r e i e r , Phys. Ray. C 31, 8 8 8 ( 1 9 8 5 ) 1 9 . A . H o f f m a n n , C. B r e c h t m a n n , W. H e i n r i c h and E.V. B e n t o n , Phys. L e t t . B 2 0 0 , 583 (1988)
Nucl. Tracks Radiat. Meas., Vol. 15, Nos. 1-4, pp. 393--402, 1988 Int. 1. Radiat. Appl. lnstrum., Part D Printed in Great Britain
APPLICATIONS OF PLASTIC N U C L E A R T R A C K DETECTORS IN H E A V Y ION PHYSICS W. HEINRICH, C. BRECHTMANN, J. DREUTE, D. WEIDMANN U n i v e r s i t y of S i e g e n, D e p a r t m e n t of Physics A d o l f - Relchwein - S t r . , 5 9 0 0 S l e g e n , West Germany
A b s t r a c t - The e x p e r i m e n t a l t e c h n i q u e of c o m p u t e r i z e d t r a c k m e a s u r e m e n t s for p l a s t i c n u c l e a r t r a c k d e t e c t o r s was used In d i f f e r e n t e x p e r i m e n t s i n v e s t i g a t i n g i n t e r a c t i o n s o f r e l a t i v i s t i c heavy ions. In this paper the method is d e s c r i b e d , r e s u l t s a r e p r e s e n t e d and discussed. To m e a s u r e c r o s s s e c t i o n s s t a c k s w e r e e x p o s e d at the BEVALAC, at Brookhaven and at CERN to d i f f e r e n t beam n u c l e i having energies f r o m O.6 G e V / n u c l e o n up to 200 GeV/nucleon. The c r o s s sections f o r one nucleon r e m o v a l a r e c o n s i d e r a b l y enhanced at high energies due to e l e c t r o m a g n e t i c d i s s o c i a t i o n . We i n v e s t i gated the e f f e c t of e l e c t r o m a g n e t i c d i s s o c i a t i o n f o r d i f f e r e n t t a r gets and p r o j e c t i l e s . For heavy p r o j e c t i l e s an e x c l u s i v e a n a l y s i s of n u c l e a r f r a g m e n t a t i o n on an e v ent by e v ent basis was p e r f o r m e d . Based on this the e f f e c t of m u l t i f r a g m e n t a t i o n can be s t u d i e d . We exposed a stack of t 0 0 CR39 f o i l s to a I G e V / n u c l e o n is 7 Au beam at the BEVALAC. Events w i t h up to 10 p r o j e c t i l e f r a g m e n t s having a charge Z~5 and coming out of the same i n t e r a c t i o n v e r t e x w e r e o b s e r v e d . To search f o r p r o j e c t i l e f r a g m e n t s w i t h f r a c t i o n a l charge in r e l a t i v i s t i c heavy ion c o l l i s i o n s , we e x p o s e d s t a c k s of 50 CR39 f o i l s behind a lead block of 15 cm depth to the u l t r a r e l a t i v i s t i c heavy Ion beams at B r o o k h a v e n and CERN. The charge r e s o l u t i o n achieved in these e x p e r i m e n t s is o = 0 . 0 2 7 e .
1. INTRODUCTION D i e l e c t r i c n u c l e a r t r a c k d e t e c t o r s have some unique c h a r a c t e r i s t i c s in c o m p a r i s o n to o t h e r d e t e c t o r s . They r e c o r d the e n e r g y loss of i o n i z i n g p a r t i c l e s w i t h en o u t s t a n d i n g p r e c i s i o n . The reason f o r this is t h a t Landau f l u c t u a t i o n s of the e n e r g y loss caused by high e n e r g y 8 - e l e c t r o n s do not c o n t r i b u t e to the t r a c k f o r m a t i o n in p l a s t i c d e t e c t o r s . Also the s p a t i a l r e s o l u t i o n of m e a s u r e d p a r t i c l e t r a j e c t o r i e s Is e x t r e m e l y good. It Is l i m i t e d only by the p r e c i s i o n of m i c r o s c o p i c t r a c k m e a s u r e m e n t s . D i s t o r t i o n s of d e t e c t o r g e o m e t r y like they are t y p i c a l f o r n u c l e a r e m u l s i o n s play a m i n o r r o l e f o r p l a s t i c d e t e c t o r s . E x p o s u r e s to a p a r t i c l e beam are r e l a t i v e l y simple f o r passive p l a s t i c n u c l e a r t r a c k d e t e c t o r s . It is not n e c e s s a r y to a s s e m b l e and t e s t a s o p h i s t i c a t e d d e t e c t o r s y s t e m , e l e c t r o n i c equipment and c o m p u t e r s y s t e m s at an a c c e l e r a t o r . The t y p i c a l beam t i m e s which a r e needed f o r the e x p e r i m e n t s d e s c r i b e d b e lo w a r e some m i n u t e s . On the o t h e r hand t h e r e a r e also w e l l known d i s a d v a n t a g e s of p l a s t i c n u c l e a r t r a c k d e t e c t o r s like f o r e x a m p l e a s e n s i t i v i t y changing f r o m batch to batch and w i t h t e m p e r a t u r e . But in a c c e l e r a t o r e x p e r i m e n t s in many cases it is p o s s i b l e to d e t e r m i n e d i r e c t l y the c a l i b r a t i o n f r o m t h e e x p e r i m e n t , so t h a t f l u c t u a t i o n s of s e n s i t i v i t y are a minor p r o b l e m . The main d i s a d v a n t a g e of n u c l e a r t r a c k d e t e c t o r s is the t r e m e n d o u s e f f o r t which is n e c e s s a r y to scan f o r t r a c k s and to m e a s u r e them. T h e r e f o r e the use of p l a s t i c d e t e c t o r s was l i m i t e d to low s t a t i s t i c s e x p e r i m e n t s . This s i t u a t i o n changed completely due to p r o c e d u r e s of a u t o m a t i c t r a c k m e a s u r e m e n t s which we developed over the last y e a r s . High p r e c i s i o n e x p e r i m e n t s w i t h high s t a t i s t i c a l s i g n i f i c a n c e w e r e p e r f o r m e d In the f i e l d of heavy Ion physics or a r e under p r o g r e s s . In this paper we w i l l d e s c r i b e methods and r e s u l t s of e x p e r i m e n t s p e r f o r m e d at t he BEVALAC and at a c c e l e r a t o r s at CERN and B r o o k h a v e n . 2. AUTOMATIC TRACK MEASUREMENTS Scanning and m e a s u r i n g of m i l l i o n s of t r a c k s is p o s s i b l e c o m p l e t e l y a u t o m a t i c a l l y w i t h image analysis s y s t e m s and c o m p u t e r i z e d m i c r o s c o p e s . A f i r s t e x p e r i m e n t making
393
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use of t h i s t e c h n i q u e w a s p e r f o r m e d t e n y e a r s a g o a t t h e U n i v e r s i t y o f San F r a n c i s c o using a Q u a n t l m e t s y s t e m I . M o r e s o p h i s t i c a t e d and f a s t e r t r a c k m e a s u r e m e n t s g o t p o s s i b l e s o m e y e a r s l a t e r u s i n g s y s t e m s w h i c h w e d e v e l o p e d at t h e U n i v e r s i t y o f S l e g e n 2 . N u m b e r s of 10 7 m e a s u r e d e t c h c o n e s a r e t y p i c a l f o r t h e s e e x p e r i m e n t s . We w i l l s u m m a r i z e b e l o w s o m e p r o p e r t i e s o f t h e d a t a t a k e n by a u t o m a t i c m e a s u r e m e n t s w h i c h w e r e d i s c u s s e d In m o r e d e t a i l in an e a r l i e r p a p e r ~1 For t r a c k m e a s u r e m e n t s t h e p l a s t i c d e t e c t o r f o i l s a r e m o u n t e d on a m i c r o s c o p e s t a g e w h i c h is m o v e d by m o t o r s u n d e r c o m p u t e r c o n t r o l . T h e m i c r o s c o p e is k e p t In f o c u s by t h e c o m p u t e r and t h e d e t e c t o r is s c a n n e d in a m e a n d e r p a t h . For e a c h f i e l d o f v i e w t h e p i c t u r e a n a l y s i s s y s t e m d e t e c t s a l l t r a c k s and m e a s u r e s t h e m . F o r a l l e t c h c o n e s t h e a r e a , p o s i t i o n on t h e f o i l , v a r i a n c e s and c o v a r l a n c e o f t h e a r e a and t h e v a l u e of b r i g h t ness In t h e c e n t e r of the d e t e c t e d o b j e c t a r e m e a s u r e d by t h e a u t o m a t i c s y s t e m . T h e c e n t r a l b r i g h t n e s s can be u s e d t o d i s t i n g u i s h e t c h f i g u r e s f r o m d a r k s t r u c t u r e s on t h e d e t e c t o r s u r f a c e w h i c h a r e no t r a c k s b u t w e r e d e t e c t e d and m e a s u r e d by t h e s y s t e m • F i g u r e 1 s h o w s t h e d i s t r i b u t i o n of m e a s u r e d a r e a s on o n e d e t e c t o r s u r f a c e f o r a b e a m of r e l a t i v i s t i c s u l p h u r n u c l e i and of p r o j e c t i l e f r a g m e n t s . P e a k s f o r d i f f e r e n t a r e a s of t h e p r o j e c t i l e s and I n d i v i d u a l f r a g m e n t s can be o b s e r v e d . F i g u r e 2 s h o w s a s c a t t e r p l o t o f m e a s u r e d a r e a and of b r i g h t n e s s m e a s u r e d In a m a t r i x o f 3 x 3 p l x e l s f o r t h i s s e t of d a t a . N u c l e a r t r a c k s a r e r e p r e s e n t e d by a b a n d o f d a r k o b j e c t s . B a s e d on t h e i n f o r -
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Fig• 1: D i l t r i b u t i o n of t r a c k a r e a s f o r f o r a r e l a t i v i s t i c s u l p h u r b e a m and beam fragments m a t l o n c o n t a i n e d in t h l l f i g u r e i t is p o s s i b l e t o m a k e a c u t t o t h e d a t a and to eliminate a large amount of surface s t r u c t u r e s w h i c h a r e no t r a c k s • F i g u r e 3 shows the distribution of track sizes for the lame data prllented in f i g u r e 1 after this cut. This reduction of noise f r o m t h e d a t a is e s s e n t i a l f o r l a t e r r e constructions of particle trajectories t h r o u g h a s t a c k of d e t e c t o r f o i l s • A c a l i b r a t i o n o f t h e d e t e c t o r s is p o s s i b l e b a l e d on t h e p e a k s seen in f i g u r e 3 The mean areas measured for beam part i c l e s and f r a g m e n t s d i f f e r f o r t h e s a m e c h a r g e on d i f f e r e n t f o i l s . R e a s o n s f o r t h i s a r e non c o n s t a n t s e n s i t i v i t i e s f r o m f o i l t o f o i l o r as w i l l be s h o w n b e l o w non c o n s t a n t e t c h c o n d i t i o n s . F i g u r e 4 shows for a sample of detector foils the correlation of the mean area for fragment tracks with the mean area f o r b e a m t r a c k s . B a s e d on t h i s l i n e a r c o r r e l a t i o n an I n d i v i d u a l c a l i b r a t i o n f o r f r a g m e n t t r a c k s m e a s u r e d on e a c h
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Fig. S: C h a r g e d i s t r i b u t i o n f o r t h e s a m e d e t e c t o r f o i l a) w i t h o u t and b) w i t h l o c a l calibration
d e t e c t o r f o i l can be d e t e r m i n e d in d e p e n d e n c e on t h e m e a n a r e a o f t h e b e a m t r a c k s . F u r t h e r m o r e t h e d a t a of f i g u r e 4 can be u s e d t o c a l i b r a t e d e t e c t o r f o i l s l o c a l l y . For this purpose we determine a map of mean track size for beam particles within a grid of c o o r d i n a t e s on t h e d e t e c t o r f o i l . F i g u r e 5 s h o w s c h a r g e d i s t r i b u t i o n s f o r t h e s a m e d e t e c t o r f o i l w i t h o u t and w i t h l o c a l c a l i b r a t i o n . A l o c a l c a l i b r a t i o n o f t h e d e t e c t o r f o i l s is n e c e s s a r y due t o i n h o m o g e n i t i e e o f t h e d e t e c t o r o r t h e e t c h i n g p r o c e s s . S i m i l a r c o r r e c t i o n s a r e In s o m e c a s e s n e c e s s a r y f o r t h e t r a c k s i z e a s a f u n c t i o n o f t h e c o o r d i n a t e s o f t h e p a r t i c l e t r a c k s in t h e v i d e o p i c t u r e . If one m e a s u r e s t h e s a m e t r a c k a t d i f f e r e n t p o s i t i o n s in t h e v i d e o p i c t u r e t h e a r e a c h a n g e s w i t h t h i s p o s i t i o n . The r e a s o n f o r t h i s is • s h a d i n g o f t h e b r i g h t n e s s in t h e v i d e o p i c t u r e w h i c h is in c o n f l i c t w i t h t h e c o n s t a n t t h r e s h o l d in g r e y l e v e l o f t h e p i c t u r e a n a l y s i s s y s t e m f o r t r a c k m e a s u r e m e n t . T h i s s h a d i n g e f f e c t can be m i n i m i z e d by a s h a d i n g c o r r e c t o r e l e c t r o n i c s o f t h e c a m e r a s , b u t a s m a l l r e m a i n i n g s h a d i n g e f f e c t can c a u s e e r r o r s o f t h e m e a s u r e d t r a c k s i z e . We c o r r e c t f o r t h i s e f f e c t in a similar way like described above for the local calibration of the detector foil. 3. R E C O N S T R U C T I O N OF T R A J E C T O R I E S AND I N T E R A C T I O N S F o r a s t a c k o f p l a s t i c d e t e c t o r s e x p o s e d t o an a c c e l e r a t o r b e a m t r a j e c t o r i e s o f t h e p a r t i c l e s can be r e c o n s t r u c t e d f r o m t h e m e a s u r e d e t c h c o n e s on t h e I n d i v i d u a l f o i l s u r f a c e s . For e a c h e t c h c o n e t h e c o o r d i n a t e s on t h e d e t e c t o r f o i l , t h e c h a r g e d e r i v e d f r o m t h e t r a c k a r e a and t h e d e p t h of t h e d e t e c t o r l a y e r in t h e s t a c k a r e k n o w n . Due t o t h e m e a s u r i n g p r o c e d u r e t h i s i n f o r m a t i o n is s t o r e d in f i l e s c o n t a i n i n g a l l d a t a f o r one f o i l s u r f a c e , t h a t m e a n s a t a c o n s t a n t d e p t h In t h e s t a c k . A r e c o n s t r u c t i o n of individual p a r t i c l e t r a j e c t o r i e s t h r o u g h t h e s t a c k m e a n s t h a t a l l d a t a have t o be o r d e r e d in a
396
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d i f f e r e n t f o r m so t h a t t h e i n d i v i d u a l c o n e m e a s u r e m e n t s along a trajectory are available T h i s w a s a t r e m e n d o u s p r o b l e m o f a c c e s s t o l a r g e m a s s s t o r a g e d e v i c e s 3 w h e n w e did t h i s on a PDP 1 1 / 4 5 . On a tzVAX w i t h s e v e r a l m e g a b y t e s of memory which we are using n o w t h i s p r o b l e m can be s o l v e d in r e a s o n a b l e c o m p u t e r t i m e . T h e s o f t w a r e f o r t r a j e c t o r y t r a c i n g m u s t be c a p a b l e t o m a n a g e p r o b l e m s a r i s i n g f r o m t r a c k s c r o s s i n g e a c h o t h e r and f r o m i n t e r a c t i o n s o f t h e p a r t i c l e s . A c h a r g e c h a n g i n g i n t e r a c t i o n o f a p a r t i c l e is s h o w n in f i g u r e 6 . T h e c h a r g e o f t h e p a r t i c l e is m e a s u r e d a l o n g i t s p a t h m a n y t i m e s on e a c h d e t e c t o r s u r f a c e . D e p e n d i n g on the length of the reconstructed trajectory t h e m e a n c h a r g e o f t h e p a r t i c l e c a n be determined very accurately from a large number of charge measurement for individual etch cones. Starting with the detector surface following behind the interaction vertex a s m a l l e r c h a r g e o f a p r o j e c t i l e f r a g m e n t is m e a s u r e d . If w e t a k e t h e m e a s u r e m e n t o f t h i s s m a l l e r c h a r g e o v e r m o r e t h a n o n e o r t w o d e t e c t o r s u r f a c e s as a c r i t e r i o n t o d e f i n e an i n t e r a c t i o n , t h e e f f i c i e n c y f o r t h e d e t e c t i o n o f c h a r g e c h a n g i n g i n t e r a c t i o n s is a l m o s t 1. The p o s s i b i l i t y t o d e t e c t t h e s e c h a r g e c h a n g i n g i n t e r a c t i o n s is u s e d in interaction mean free path measurements a n d in t h e a n a l y s i s o f i n d i v i d u a l i n t e r a c t i o n vertices of muItifragmentation events described below. 4 . I N T E R A C T I O N M E A N FREE P A T H M E A S U R E M E N T S F o r m e a s u r e m e n t s of i n t e r a c t i o n m e a n f r e e p a t h s w e f o l l o w a l a r g e n u m b e r o f p a r ticle trajectories o f i n d i v i d u a l l e n g t h I i u n t i l an i n t e r a c t i o n is d e t e c t e d o r t h e t r a j e c t o r y l e a v e s t h e s c a n n i n g v o l u m e . T h e i n t e r a c t i o n m e a n f r e e p a t h o f t h e p a r t i c l e s c a n be d e t e r m i n e d by ),= E l i / n , w h e r e n is t h e n u m b e r o f d e t e c t e d i n t e r a c t i o n s . In t h e s e m e a surements deep stacks of a large number of detector foils are exposed to beam part i c l e s so t h a t l o n g p o t e n t i a l p a t h s a r e a v a i l a b l e f o r t h e b e a m p a r t i c l e s and a l s o f o r t h e p r o j e c t i l e f r a g m e n t s p r o d u c e d in t h e s t a c k . B a s e d on t h i s m e t h o d w e p e r f o r m e d i n t e r a c t i o n m e a n f r e e p a t h m e a s u r e m e n t s 4 in C R 3 9 a n d C R 3 9 + A g f o r p a r t i c l e s w i t h c h a r g e s 8
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Fig. 6: Example of a charge changing nuclear collision. The points show values of m e a s u r e d c h a r g e s as a f u n c t i o n o f t h e f o i l n u m b e r in a C R 3 9 s t a c k . In a f i r s t nuclear collision of a relativistic Z = 1 2 n u c l e u s a f r a g m e n t w i t h c h a r g e Z = | O is produced. Later this interacts a l s o and a f r a g m e n t w i t h c h a r g e Z = 6 is p r o d u c e d .
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A f i r s t e x p o s u r e o f a s e t o f s t a c k s c o n t a i n i n g d i f f e r e n t t a r g e t s w a s p e r f o r m e d to a 7 2 0 M e V / n u c l e o n s2 S beam a t t h e B E V A L A C . F i g u r e 7 s h o w s t h e d i s t r i b u t i o n o f a r e a s o f a u t o m a t i c a l l y m e a s u r e d t r a c k s on a f o i l s u r f a c e d o w n s t r e a m t h e t a r g e t a f t e r e t c h i n 9 t h e d e t e c t o r s in 6n NaOH a t 7 0 ° C f o r a b o u t 2 2 h . T h e p o s i t i o n o f t h e p e a k s can be i d e n t i f i e d as t h e mean a r e a s o f t r a c k s o f c h a r g e n u m b e r Z = 6 t o Z = 1 6 . The c h a r g e c a l i b r a t i o n b a s e d on t h e m e a s u r e m e n t o f a s i n g l e e t c h c o n e v a r i e s f r o m o = 0 . 1 8 e f o r Z = 6 t o o=0.27e for Z=16. By t r a c i n g t h e t r a j e c t o r i e s w i t h a p a t t e r n r e c o g n i t i o n s o f t w a r e f r o m o n e f o i l s u r f a c e to the next we get 8 charge measurements for each nuclear track. This leads to a charge r e s o l u t i o n o f o = O . 0 6 e f o r Z = 6 and o = 0 . 1 e f o r Z = 1 6 . F i g u r e 8 s h o w s t h e d i s t r i b u t i o n o f m e a s u r e d c h a r g e s e a c h c o m p u t e d as t h e m e a n o f 8 s i n g l e m e a s u r e m e n t s d o w n s t r e a m t h e t a r g e t . The aim of t h e m e a s u r e m e n t is t o g e t u n b i a s e d d i s t r i b u t i o n s o f c h a r g e s at b o t h t a r g e t s u r f a c e s . For t h i s p u r p o s e s o m e s y s t e m a t i c e f f e c t s h a v e t o be c o n s i d e r e d . I n t e r a c t i o n s in t h e d e t e c t o r f o i l s have t o be t a k e n I n t o a c c o u n t c a r e f u l l y . I t is n o t correct to build the average of the eight charge values measured for a track. These v a l u e s have t o be a n a l y z e d l i k e d e s c r i b e d a b o v e t o d e t e c t c h a r g e c h a n g i n g c o l l i s i o n s in t h e d e t e c t o r f o i l s . The I n t e r a c t i o n p o i n t s can u n a m b i g u o u s l y be d e t e r m i n e d If on b o t h s i d e s of t h e i n t e r a c t i o n at l e a s t t h r e e c h a r g e v a l u e s w e r e m e a s u r e d . T h e r e f o r e w e d e t e r m i n e t h e c h a r g e d i s t r i b u t i o n in t h e t h i r d b u t l a s t d e t e c t o r s u r f a c e . T h e d e v e l o p m e n t o f t h e c h a r g e d i s t r i b u t i o n f r o m t h i s d e t e c t o r s u r f a c e u p s t r e a m and d o w n s t r e a m t o t h e t a r g e t m u s t be c a l c u l a t e d . T h i s Is a c h i e v e d by a p r o p a g a t i o n c a l c u l a t i o n u s i n g c r o s s s e c t i o n s d e t e r m i n e d f o r t h e CR39 t a r g e t . As a r e s u l t o f t h i s p r o c e d u r e w e g e t e x t r e m e ly a c c u r a t e c h a r g e m e a s u r e m e n t s w i t h a m i n i m u m b i a s due t o i n t e r a c t i o n s in t h e d e t e c t o r . No o t h e r d e t e c t o r s y s t e m is k n o w n t h a t c o u l d c o m p e t e w i t h t h e s e e x c e l l e n t r e s u l t s achieved with plastic nuclear track detectors. S o m e p e r c e n t o f a l l t r a j e c t o r i e s a r e so c l o s e t o e a c h o t h e r t h a t t h e i r e t c h c o n e s a r e o v e r l a p p i n g . In g e n e r a l t h e t r a n s v e r s e m o m e n t a of t h e p r o d u c e d f r a g m e n t s a r e v e r y s m a l l in c o m p a r i s o n t o t h e l o n g i t u d i n a l m o m e n t a . T h e r e f o r e t h e e t c h c o n e s o f t w o o v e r l a p p i n g t r a c k s do n o t s e p a r a t e w i t h i n f o u r p l a s t i c d e t e c t o r f o i l s . In t h e s e e x p e r i m e n t s w e m a k e no use o f p i c t u r e a n a l y s i s s o f t w a r e w h i c h is c a p a b l e t o s e p a r a t e o v e r l a p p i n g t r a c k s , b u t w e use a f a s t e r and s i m p l e r m e t h o d t o o v e r c o m e t h i s p r o b l e m . By u s i n g t h e v a r i a n c e s and c o v a r l a n c e o f t h e e l l i p t i c a l o b j e c t f i t t e d by t h e a u t o m a t i c measurement to the two overlapping tracks, we get some Information about the amount o f o v e r l a p and t h e o r i e n t a t i o n o f t h e t w o t r a c k s . T h u s t h e 8 e t c h f i g u r e s a l o n g t h e t r a j e c t o r y can e a s i l y be i d e n t i f i e d as o v e r l a p p i n g . T h e d i s t r i b u t i o n o f c h a r g e s In t h e s e t o f o v e r l a p p i n g t r a c k s is c a l c u l a t e d b a s e d on t h e c h a r g e d i s t r i b u t i o n of n o n o v e r l a p p i n g t r a c k s and t h e t y p i c a l a r e a s o f t h e e t c h c o n e s f o r d i f f e r e n t f r a g m e n t s . B a s e d on t h i s i n f o r m a t i o n / h e m e a s u r e d c h a r g e d i s t r i b u t i o n s can be c o r r e c t e d t o i n c l u d e t h e o v e r l a p p i n g b e a m p a r t i c l e s and f r a g m e n t s . W i t h t h e k n o w n c h a r g e d i s t r i b u t i o n on b o t h t a r g e t s u r f a c e s t h e t o t a l c h a r g e c h a n g i n g f r a g m e n t a t i o n c r o s s s e c t i o n s and t h e e l e m e n t a l f r a g m e n t a t i o n c r o s s s e c t i o n s f o r t h e b e a m n u c l e i can be d e t e r m i n e d . T h i s is d o n e b a s e d on a p r o p a g a t i o n c a l c u l a t i o n as d e s c r i b e d in d e t a i l by B r e c h t m a n n and H e i n r l c h S . in t h i s c a l c u l a t i o n t h e f r a g m e n t a t i o n o f f r a g m e n t s has t o be c o n s i d e r e d . For t h i s p u r p o s e t h e f r a g m e n t a t i o n c r o s s s e c t i o n s o f t h e f r a g m e n t s a r e n e e d e d w h i c h in m o s t c a s e s can o n l y be e s t i m a t e d b a s e d on t h e s e m i e m p i r i c a l f o r m u l a o f S i l b e r b e r g and T s a o 10 and on t h e l a w o f f a c t o r i z a t i o n o f NT 15:1/4-AA
398
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the cross sections 11 To m i n i m i z e s y s t e m a t i c e r r o r s due to this c o r r e c t i o n t he t a r g e t should be as thin as possible. On the o t h e r hand the s t a t i s t i c a l e r r o r of t h e r e s u l t decreases with increasing t a r g e t t h i c k n e s s . By m o d e l l i n g the f r a g m e n t a t i o n inside the t a r g e t one finds that s y s t e m a t i c e r r o r s can be n e g l e c t e d In c o m p a r i s o n to s t a t i s t i c a l e r r o r s as long as a t a r g e t w i t h a t h i c k n e s s below about 0. 2 i n t e r a c t i o n l e n g t h s of the beam p a r t i c l e s is used. Total charge changing and p a r t i a l c r o s s s e c t i o n s f o r the p r o d u c t i o n of f r a g m e n t s of charge Z : 6 and Z : 7 in c o l l i s i o n s of 16 0 beam nuclei at e n e r g i e s of 60 and 200 GeV/nucleon in t a r g e t s H, C, AI, Cu, Ag and Pb w e r e m e a s u r e d using the method described above 12 . Two d i f f e r e n t p o i n t s of I n t e r e s t w e r e I n v e s t i g a t e d : a] The cross sections f o r h y d r o g e n t a r g e t are e s s e n t i a l p a r a m e t e r s f o r the c a l c u l a tion d e s c r i b l n 9 the p r o p a g a t i o n of cosmic ray n u c l e i in the i n t e r s t e l l a r space. We c o m pared them with p r e d i c t i o n s of t h e s e m l e m p l r i c a l f o r m u l a s 10,1s and e x p e r i m e n t a l d a t a by Olson et al .14 and Webber is at BEVALAC e n e r g i e s . We o b s e r v e d t h a t t h e p a r t i a l cross sections f o r H t a r g e t a r e v a r y i n g even beyond 2 G e V / n u c l e o n . At 60 G e V / n u c l e o n they have d e c r e a s e d by 20Y,. For h i g h e r e n e r g i e s f r o m 60 to 2 0 0 G e V / n u c l e o n they are staying c o n s t a n t . The t o t a l c h a r g e changing c r o s s s e c t i o n does not d i f f e r s i g n i f i c a n t l y f r o m r e s u l t s in the 1-2 G e V / n u c l e o n r e g i o n . b) For h e a v i e r t a r g e t s e l e c t r o m a g n e t i c d i s s o c i a t i o n (ED) plays an i m p o r t a n t r o l e in the process of f r a g m e n t a t i o n . ED o c c u r s when a p r o j e c t i l e nucleus w h i c h passes along a heavy t a r g e t nucleus is e x c i t e d by its Coulomb f i e l d . In f a s t r e l a t i v e m o t i o n t h i s f i e l d is e q u i v a l e n t to a v i o l e n t e l e c t r o m a g n e t i c pulse i n c i d e n t on the p r o j e c t i l e . In a s u b sequent step the decay of t h e e x c i t e d nucleus by e m i s s i o n of one or m o r e n u c l e o n s Is possible. F r a g m e n t a t i o n c r o s s s e c t i o n s are I n c r e a s e d by t h i s p r o c e s s s in c e it o c c u r s at impact p a r a m e t e r s beyond the r a n g e of the s t r o n g n u c l e a r f o r c e . Using the W e i z s ~ c k e r W i l l i a m s method or a m o r e s o p h i s t i c a t e d q u a n t u m m e c h a n i c a l approach by B e r t u l a n i and Baur 1l the e l e c t r o m a g n e t i c pulse can be s u b s t i t u t e d by s p e c t r a of v i r t u a l photons i n c i d e n t on the 160 p r o j e c t i l e nucleus w hic h a r ~ agiv e n f o r d i f f e r e n t m u l t i p o l a r i t i e s . By f o l d i n g t h e s e s p e c t r a w i t h c r o s s s e c t i o n s o`( of 0 for the decay into a special f r a g m e n t a t i o n channel under i r r a d i a t i o n by beams of r e a l p h o tons of d i f f e r e n t e n e r g i e s the e l e c t r o m a g n e t i c c o n t r i b u t i o n o em f o r t h i s fragmen2tatlon channel in c o l l i s i o n s upon a n u c l e u s t a r g e t can be c a l c u l a t e d . Roughly it is o ern" Z T in'( w h e re Z T is the t a r g e t c h a r g e and `( is the r e l a t i v i s t i c L o r e n t z f a c t o r of t h e p r o j e c t i l e in the l a b o r a t o r y f r a m e . In our e x p e r i m e n t f r a g m e n t a t i o n by e l e c t r o m a g n e t i c and s t r o n g n u c l e a r f o r c e is not d i s t i n g u i s h a b l e so t h a t we m e a s u r e c r o s s s e c t i o n s o exp "O
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Fig. 9 shows p a r t i a l f r a g m e n t a t i o n c r o s s s e c t i o n s o ( Z = 8 - - > Z = 7 ) vs. t a r g e t charge as o b t a i n e d f r o m our e x p e r i m e n t at 60 and 200 G e V / n u c l e o n . For c o m p a r i s o n we have included pure nuclear c r o s s s e c t i o n s o nuc which w e r e o b t a i n e d using t h e f a c t o r i z a t l o n r u l e 14 e x p r e s s e d as opT F = `( P F y PT- O nuc = O PT F IS the n u c l e a r f r a g m e n t a t i o n cro s s s e c t i o n f o r the p r o j e c t i l e P i n c i d e n t upon a t a r g e t T p r o d u c i n g a f r a g m e n t F. ¥ p F IS a f a c t o r which depends only upon the species of p r o j e c t i l e and f r a g m e n t , ¥ PT is a f a c t o r which depends only upon the species of p r o j e c t i l e and t a r g e t . The e l e c t r o m a g netic cross s e c t i o n o em v i s i b l e in f i g u r e 9 as the d i f f e r e n c e b e t w e e n the e x p e r i m e n t a l and pure n u c l e a r cross s e c t i o n s Is i n c r e a s i n g w i t h t a r g e t c h a r g e and p r o j e c t i l e energy. C,b~
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We used our r e s u l t s to c a l c u l a t e t h e s m a l l and not s i g n i f i c a n t ED c o n t r i b u t i o n f o r C t a r g e t and s u b s t r a c t e d it f r o m our e x p e r i m e n t a l c r o s s s e c t i o n s . We f o u n d the r e m a i n ing p u r e n u c l e a r t o t a l end p a r t i a l c r o s s s e c t i o n s to be f u l l y c o n s i s t e n t w i t h e x p e r i m e n t a l r e s u l t s measured at BEVALAC e n e r g i e s 14,1s and c o n c l u d e t h a t t h e y a r e e n e r g y i n d e p e n d e n t above 1 G e V / n u c l e o n f o r non h y d r o g e n t a r g e t s . 6. FRAGMENTATION OF HEAVY PROJECTILES The i n v e s t i g a t i o n of n u c l e a r f r a g m e n t a t i o n f o r v e r y heavy p r o j e c t i l e s i n t o f r a g m e n t s • w i t h c h a r g e s In a w i d e range f r o m Z:~5 up to a l m o s t t h e c h a r g e of t h e p r o j e c t i l e Is of p a r t i c u l a r I n t e r e s t . V a r i o u s m e c h a n i s m s d o m i n a t e the f r a g m e n t a t i o n p r o c e s s . T a b l e 1 shows a c o m m o n l y used s u b d i v i s i o n of t h e d i f f e r e n t m e c h a n i s m s b a s e d on c h a r g e n u m ber of t h e f r a g m e n t and on t h e m u l t i p l i c i t y of f r a g m e n t s w i t h c h a r g e Z>5 p r o d u c e d in the same i n t e r a c t i o n 17. Heavy f r a g m e n t s w h i c h a r e p r o d u c e d w i t h l a r g e c r o s s s e c t i o n s o r i g i n a t e f r o m s p a l l a t i o n I n t e r a c t i o n s . In t h e s e I n t e r a c t i o n s t h e p r o j e c t i l e c o l l i d e s w i t h a t a r g e t nucleus in a p e r i p h e r a l c o l l i s i o n w i t h o n l y a s m a l l o v e r l a p . A s m a l l p a r t of the p r o j e c t i l e is a b r a d e d and a f t e r e m i t t i n g some n u c l e o n s in a f o l l o w i n g phase of a b l a t i o n one s i n g l e n u c l e a r f r a g m e n t s u r v i v e s w h i c h t y p i c a l l y has a l a r g e m a s s . The c r o s s s e c t i o n f o r t h i s p r o c e s s d e c r e a s e s w i t h i n c r e a s i n g mass d i f f e r e n c e b e t w e e n t h e p r o j e c t i l e and the f r a g m e n t . Light f r a g m e n t s h o w e v e r w i t h c h a r g e s b e l o w a b o u t Z = 2 5 a r e p r o duced again w i t h i n c r e a s i n g c r o s s s e c t i o n s . They a r e b e l i e v e d to be p r o d u c e d in s o c a l l e d m u l t l f r a g m e n t a t l o n e v e n t s In w h i c h a l a r g e r n u m b e r (N~3) of s m a l l f r a g m e n t s o r i g i n a t e s f r o m the e x c i t e d m a t t e r of a heavy p r o j e c t i l e a f t e r a n u c l e a r c o l l i s i o n . B e t w e e n t h e s e t w o domaines in the r e g i o n a r o u n d h a l f the mass of t h e p r o j e c t i l e e v e n t s w i t h t w o f r a g m e n t s a r e o b s e r v e d w h i c h o r i g i n a t e f r o m a f i s s i o n r e a c t i o n of t h e p r o j e c t i l e . The p r o cess of deep s p a l l a t i o n In w h i c h only one f r a g m e n t Is p r o d u c e d f r o m t h e p r o j e c t i l e Is e x p e c t e d to e x i s t as a l i m i t of s p a l l a t i o n t o w a r d s s m a l l e r f r a g m e n t s , but only l i t t l e is known a b o u t i t . For t h e open a r e a s of t a b l e 1 t h e p r o d u c t i o n of f r a g m e n t s is b e l i e v e d be r a t h e r u n l i k e l y but no d e t a i l s a r e k n o w n . No d e t a i l e d e x p e r i m e n t i n v e s t i g a t i n g n u c l e a r f r a g m e n t a t i o n in an e x c l u s i v e e v e n t by event a n a l y s i s w a s p e r f o r m e d u n t i l n o w . The s u b d i v i s i o n s h o w n in t a b l e 1 is b a s e d on i n c l u s i v e c r o s s s e c t i o n m e a s u r e m e n t s and on r e a s o n a b l e m o d e l s . multiplicity
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We p e r f o r m e d an e x p e r i m e n t t o i n v e s t i g a t e f r a g m e n t a t i o n o f h e a v y p r o j e c t i l e s in e x c l u s i v e l y a n a l y z e d e v e n t s . A s t a c k c o n t a i n i n g a l t e r n a t i n g 6 0 0 ~m t h i c k CR39 d e t e c t o r s and 2 0 0 (~m t h i c k Ag t a r g e t f o i l s w i t h a t o t a l d e p t h of 8 cm w a s e x p o s e d t o a 9 9 0 M e V / n u c l e o n Au beam at t h e B E V A L A C . T r a j e c t o r i e s o f p r o j e c t i l e s and f r a g m e n t s w e r e r e c o n s t r u c t e d as d e s c r i b e d a b o v e . F o r a l l i n t e r a c t i o n s of t h e g o l d t h e v e r t i c e s w e r e a n a l y z e d in d e t a i l to r e c o n s t r u c t t r a c k s o f a l l f r a g m e n t s w i t h c h a r g e s Z ~ 6 c o m i n g o u t of t h e i n t e r a c t i o n . F i g u r e 12 s h o w s as an e x a m p l e an e v e n t in w h i c h 8 f r a g m e n t s w e r e produced. Altogether 15573 vertices with different multiplicity of fragments were anal y z e d . The a n a l y s i s of t h i s e x p e r i m e n t is s t i l l u n d e r p r o g r e s s . But s o m e p r e l i m i n a r y r e s u i t s can a l r e a d y be p r e s e n t e d in t h i s p a p e r . T a b l e 2 s h o w s t h e o b s e r v e d a b u n d a n c e s o f d i f f e r e n t t y p e s of i n t e r a c t i o n s s u b d i v i d e d in t h e f o r m p r o p o s e d in t a b l e 1. The l a r g e n u m b e r of e v e n t s in t h e d i a g o n a l e m p h a s i z e s t h e i m p o r t a n c e o f s p a l l a t i o n , f i s s i o n and m u l t i f r a g m e n t a t i o n . But w i t h high probability also other events are observed. Clearly deep spallation events were found and f u r t h e r m o r e a l s o e v e n t s in w h i c h s i n g l e l i g h t f r a g m e n t s w i t h c h a r g e s Z ~ 2 5 a r e p r o d u c e d . The p r o b a b i l i t y f o r t h e s e " l i g h t s i n g l e s " is s u r p r i s i n g l y h i g h . T h e r e is a l m o s t no c o n t i n u o u s d e c r e a s e in f r a g m e n t y i e l d f r o m d e e p s p a l l a t i o n t o t h e s e e v e n t s . It is l i k e l y t h a t t h e y a r e p r o d u c e d in a d i f f e r e n t i n t e r a c t i o n m e c h a n i s m w h i c h may r e s u l t f r o m an i n t e r a c t i o n v e r y s i m i l a r t o a m u I t i f r a g m e n t a t i o n b u t in w h i c h only one l i g h t f r a g m e n t s u r v i v e s . T h i s i d e a is s u p p o r t e d by t h e l a r g e n u m b e r o f e v e n t s in w h i c h t w o l i g h t f r a g m e n t s a r e p r o d u c e d . The l a r g e n u m b e r o f e v e n t s w i t h t w o f r a g m e n t s w h e r e one f r a g m e n t is h e a v i e r t h a n Z = 5 2 can be u n d e r s t o o d as a s y m m e t r i c f i s s i o n e v e n t s o f t h e g o l d p r o j e c t i l e . E v e n t s o f t h i s t y p e w e r e o b s e r v e d b e f o r e 17'. A m o r e d e t a i l e d a n a l y s i s of t h e e v e n t s w i t h t h r e e f r a g m e n t s o f w h i c h one is h e a v i e r t h a n Z = 2 5 w i l l s h o w w h e t h e r t h e s e can be u n d e r s t o o d as a t a i l of t h e m u t i f r a g m e n t a t i o n regime, As s h o w n in o t h e r e x p e r i m e n t s ( r e f e r e n c e d in 17) t h e y i e l d o f l i g h t f r a g m e n t s p r o d u c e d in m u l t i f r a g m e n t a t i o n i n t e r a c t i o n s can be d e s c r i b e d by a p o w e r l a w of t h e f o r m o ( Z ) = oO Z - ~ . The e x p o n e n t x t a k e s v a l u e s b e t w e e n 1.5 and 3 . 5 and d e p e n d s on p r o j e c t i l e , t a r g e t and e n e r g y . A s i m i l a r p o w e r l a w f o l l o w s f r o m c a l c u l a t i o n s f o r t h e d i s t r i b u tion of droplet sizes for a liquid-gas transition at the critical point. There exist formal a n a l o g i e s b e t w e e n a van d e r W a a l s g a s and t h e e q u a t i o n of s t a t e o f n u c l e a r m a t t e r . The q u e s t i o n w h e t h e r t h e o b s e r v e d p o w e r l a w i n d i c a t e s a p h a s e t r a n s i t i o n f o r n u c l e a r m a t t e r is o p e n . We h o p e t o g e t m o r e i n f o r m a t i o n a b o u t t h i s p h e n o m e n o n b a s e d on o u r e x p e r i m e n t s . The e x p o n e n t x can be d e t e r m i n e d f o r d i f f e r e n t e n e r g i e s and t a r g e t s and a l s o f o r d i f f e r e n t m u l t i p l i c i t i e s o f t h e f r a g m e n t a t i o n e v e n t s o b s e r v e d in o u r e x p e r i m e n t . T h i s w o r k is u n d e r p r o g r e s s . 7 . SEARCH FOR F R A C T I O N A L CHARGES F r o m e x p e r i m e n t s in high e n e r g y p h y s i c s w e k n o w , t h a t n u c l e o n s a r e a s s e m b l e d f r o m e l e m e n t a r y c o n s t i t u e n t s , t h e s o c a l l e d q u a r k s . T h e s e q u a r k s c a r r y c h a r g e s of 1 / 3 e o r 2 / 3 e and a r e c h a r a c t e r i z e d by a n e w q u a n t u m n u m b e r , t h e c o l o u r . T h e y a r e b o u n d t o g e t h e r by t h e c o l o u r f o r c e w h i c h is t r a n s m i t t e d by t h e q u a n t a o f t h i s f i e l d , t h e s o c a l l e d g l u o n s . B a s e d on q u a n t u m c h r o m o d y n a m i c s , t h e t h e o r y d e s c r i b i n g t h e f o r m a t i o n of p a r t i c l e s by q u a r k s , t h e p r o d u c t i o n o f f r e e q u a r k s c o u l d be p o s s i b l e i f g l u o n s have a m a s s . But w h e n q u a r k s a r e s e p a r a t e d t h e e n e r g y w h i c h is p u t i n t o t h e g l u o n f i e l d s is u s e d f o r t h e c r e a t i o n of q u a r k - a n t i q u a r k p a i r s o u t of t h e v a c u u m w h i c h c o m b i n e w i t h t h e s e p a r a t i n g q u a r k s and f o r m p a r t i c l e s w i t h i n t e g e r c h a r g e . T h i s m a y e x p l a i n t h a t
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q u a r k s w e r e n e v e r o b s e r v e d as f r e e p a r t i c l e s In c o l l i s i o n s b e t w e e n high e n e r g e t i c particles . In h e a v y ion c o l l i s i o n s h o w e v e r t h e s i t u a t i o n m a y be q u i t e d i f f e r e n t . If one a s s u m e s t h a t q u a r k s end g l u o n s c a r r y i n g c o l o u r can m o v e I n s i d e a n u c l e o n , w h i c h is colour neutral seen from outside, a free quark could polarize a nucleon. That means t h a t n u c l e a r m a t t e r w o u l d b e h a v e c o m p a r a b l e t o a d i e l e c t r i c m e d i u m In an e l e c t r i c f i e l d . As a resuJ~t t h e c o l o u r f i e l d e n e r g y o f s e p a r a t i n g q u a r k s w o u l d be r e d u c e d in n u c l e a r m a t t e r ~ . T h e r e f o r e t h e s e p a r a t i o n o f q u a r k s c o u l d be p o s s i b l e w i t h o u t c r e a t i o n of n e u t r a l i z i n g q u a r k s . T h e s e p a r a t e d q u a r k s on t h e e t h e r hand c o u l d s t r o n g l y bind up to 20 p o l a r i z e d n u c l e o n s and f o r m a q u a r k n u c l e a r c o m p l e x o f a c h a r g e Z:~5 w h i c h is d e t e c t a b l e in p l a s t i c n u c l e a r t r a c k d e t e c t o r s , even If i t m o v e s w i t h r e l a t i v i s t i c v e l o c i t i e s . An e s t i m a t i o n p r e d i c t s a t h r e s h o l d e n e r g y o f 10 GeV a c t i n g on a n u c l e o n f o r p r o d u c t i o n of f r e e q u a r k s l l . C e n t e r o f m a s s e n e r g i e s in t h i s o r d e r o f magnitude recently got available for ultrarelatlvistic h e a v y ion b e a m s . We p e r f o r m e d e x p e r i m e n t s u s i n g t h e is O b e a m s o f 14.5 G e V / n u c l e o n a t B r o o k h a v e n and o f 2 0 0 G e V / n u c l e o n at CERN. P l a s t i c d e t e c t o r s w i t h e x t r e m e s e n s i t i v i t y w e r e n e c e s s a r y t o d e t e c t the r e l a t i v i s t i c o x y g e n a n d h e a v y p r o j e c t i l e f r a g m e n t s . We u s e d CR39 p l a s t i c of t y p e USF3S . T h e t h r e s h o l d o f t h i s d e t e c t o r m a t e r i a l is b e l o w t h e e n e r g y l o s s o f a r e l a t i v i s t i c n u c l e u s w i t h c h a r g e Z = S e . B e h i n d a 15 cm d e e p b l o c k o f l e a d as t a r g e t a s t a c k of 50 d e t e c t o r f o i l s w i t h a t h i c k n e s s o f 600t~m e a c h w a s a s s e m b l e d t o i d e n t i f y p r o j e c t i l e s , p r o j e c t i l e f r a g m e n t s and q u a r k n u c l e a r c o m p l e x e s . A b o u t 4 0 0 0 0 e t c h c o n e s w e r e m e a s u r e d on e a c h f o i l s u r f a c e . T h e t r a c k d e n s i t y on t h e f o i l s w a s a b o u t 1 0 0 0 / c m 2 . F i g u r e 13 s h o w s a d i s t r i b u t i o n o f t h e a r e a s o f n u c l e a r t r a c k s m e a s u r e d a u t o m a t i c a l l y on a s i n g l e f o i l s u r f a c e d o w n s t r e a m t h e t a r g e t . T h e p o s i t i o n s o f t h e p e a k s in t h i s p i c t u r e can be i d e n t i f i e d as t h e m e a n a r e a s o f t r a c k s o f f r a g m e n t s w i t h c h a r g e s Z = 5 e , 6 e , T e and 8 e . B a s e d on t h e s e m e a s u r e d d i s t r i b u t i o n s an i n d i v i d u a l c a l i b r a t i o n of e a c h d e t e c t o r f o i l s u r f a c e is p o s s i b l e g i v i n g t h e r e l a t i o n b e t w e e n m e a s u r e d t r a c k a r e a and c h a r g e of t h e r e l a t i v i s t i c p a r t i c l e . The c h a r g e r e s o l u t i o n b a s e d on t h e m e a s u r e m e n t o f a s i n g l e e t c h c o n e is o=O.18e f o r c h a r g e s Z = 6 e , T e and 8 e . We g e t up t o 100 c h a r g e m e a s u r e m e n t s p e r n u c l e a r t r a c k a f t e r f o l l o w i n g t h e t r a j e c t o r i e s of t h e p a r t i c l e s f r o m one f o i l s u r f a c e t o t h e n e x t o n e . To e x c l u d e o v e r l a p p i n g e t c h c o n e s w h i c h w e r e d e t e c t e d as one s i n g l e e l o n g a t e d o b j e c t o v e r m a n y f o i l s h a v i n g an a r e a t h a t t y p i c a l l y d o e s n o t c o r r e s p o n d t o an i n t e g e r c h a r g e , o n l y o b j e c t s o f exactly circular shape were considered for the charge measurement. Also etch cones f l a w e d by s u r f a c e s t r u c t u r e s w e r e r e j e c t e d by a c u t in s x c e n t r i c i t y and n o t u s e d f o r t h e d e t e r m i n a t i o n of the m e a n c h a r g e . So t h e n u m b e r o f e t c h c o n e s u s e d t o d e t e r m i n e t h e f r a g m e n t c h a r g e is t y p i c a l l y r e d u c e d by a b o u t 2 0 ~ . For t h e c h a r g e d i s t r i b u t i o n o f r e c o n s t r u c t e d t r a c k s s h o w n in f i g u r e 14 w e g o t s t a n d a r d d e v i a t i o n s o f o = 0 . 0 2 7 e [ 2 0 0 G e V / n u c l e o n s t a c k , 100 d e t e c t o r s u r f a c e s ) . F o r t h e B r o o k h a v e n e x p o s u r e w e g o t o = 0 . 0 3 8 e ( 1 4 . 5 G a Y / n u c l e o n , 4-4 d e t e c t o r s u r f a c e s ) . In a f i r s t a t t e m p t w e l o o k e d f o r q u a r k n u c l e a r c o m p l e x e s w h i c h w e r e p r o d u c e d in t h e l e a d t a r g e t and l i v e d long e n o u g h t o p e n e t r a t e t h r o u g h t h e r e s i d u a l l e a d t a r g e t and CR39 s t a c k . T h i s w o u l d r e q u i r e a m i n i m u m d e c a y t i m e in t h e o r d e r o f ~>10-11 s and a m e a n f r e e p a t h o f ),210 c m . F o r t h e d a t a s h o w n in f i g u r e 14 c h a r g e m e a s u r e m e n t Is u n a m b i g u o u s l y p o s s i b l e w i t h r e s p e c t t o 1 / 3 e . W e f o u n d no e v e n t in any 8 o r e g i o n a r o u n d c h a r g e s o f p o s s i b l e q u a r k n u c l e a r c o m p l e x e s in t h e 2 0 0 G e V / n u c l e o n e x p e r i m e n t . In t h e I & . S G e V / n u c l e o n e x p e r i m e n t w e e x c l u d e d e v e n t s in a 40 r e g i o n . As a c o n c l u s i o n w e can g i v e u p p e r l i m i t s f o r t h e p r o b a b i l i t y p t h a t a p r o j e c t i l e f r a g m e n t o f c h a r g e Z=~Se c o m i n g o u t o f a c o l l i s i o n o f 15 O on Pb is c a r r y i n g a n o n - i n t e g e r c h a r g e . T h i s p r o b a b i l i t y is p < 2 . S x 1 0 - 4 f o r 14.5 G e V / n u c l e o n and p ~ 1 . g x | 0 - 4 f o r 2 0 0 G e V / n u c l e o n a t a c o n f i d e n c e l e v e l o f 95:~. 104
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To i n v e s t i g a t e the p o s s i b i l i t y t h a t q u a r k n u c l e i decay in s h o r t t i m e s or have e x t r e m e l y enhanced c r o s s s e c t i o n s f o r n u c l e a r c o l l i s i o n s we e x t e n d e d o u r a n a l y s i s to s h o r t t r a c k s w h i c h were v i s i b l e o v e r only 10 f o i l s u r f a c e s or m o r e w i t h o u t n u c l e a r i n t e r a c t i o n s . As c a n d i d a t e s we a n a l y z e d in d e t a i l p a r t i c l e s w i t h a c h a r g e i n s i d e a 20 r e g i o n a r o u n d any f r a c t i o n a l c h a r g e v a l u e . For t r a c k s w i t h a l e n g t h of 5 d e t e c t o r f o i l s having t y p i c a l l y 8 usable s i n g l e c h a r g e m e a s u r e m e n t s we g o t a r e s o l u t i o n of o = 0 . 0 6 4 e . T h e r e f o r e we looked f o r c a n d i d a t e s w i t h c h a r g e s of m o r e t h a n 0 . 2 0 e a p a r t f r o m i n t e g e r c h a r g e s . We found 5 c a n d i d a t e s in the t w o e x p e r i m e n t s . To t e s t w h e t h e r t h i s is a s i g n i f i c a n t hint for the e x i s t e n c e of q u a r k n u c l e a r c o m p l e x e s or w h e t h e r we can u n d e r s t a n d the d e v i a t i o n s as f l u c t u a t i o n s of our m e a s u r e d c h a r g e s we p e r f o r m e d a Monte C a r l o s i m u l a t i o n of our e x p e r i m e n t . This c a l c u l a t i o n s h o w e d t h a t the n u m b e r of c a n d i d a t e s found in the e x p e r i m e n t a r e e x p e c t e d due to f l u c t u a t i o n s based on t h e experimental charge resolution f o r these short t r a c k s . T h e r e s t i l l r e m a i n s the p o s s i b i l i t y t h a t q u a r k n u c l e a r c o m p l e x e s a r e p r o d u c e d in c o l l i s i o n s of p r o j e c t i l e s h e a v i e r t h a n oxygen w i t h a p r o b a b i l i t y l a r g e enough to d e t e c t t h e m in a type of e x p e r i m e n t l i k e t h o s e d e s c r i b e d above. For 1114 t h i s r e a s o n we p e r f o r m e d a new e x p e r i m e n t using the 200 G e V / n u c l e o n 32S beam at CERN. 1113 In t h i s e x p e r i m e n t we e x p o s e d a s t a c k of CR39 behind a Pb t a r g e t '~ of 3.5 cm t h i c k n e s s . To e n a b l e ~ 111= p r o d u c t i o n of q u a r k s in c o l l i s i o n s IL w i t h heavy t a r g e t nuclei we • s t a c k e d the 6 0 0 p m t h i c k p l a s t i c ,~ lg x f o i l s each b e t w e e n 200pm t h i c k i,::1 s i l v e r f o i l s . The analysis of t h i s C e x p e r i m e n t is under p r o g r e s s . 1 F i g u r e 15 s h o w s the c h a r g e d i s t r i b u t i o n of r e c o n s t r u c t e d t r a j e c t o r i e s p e n e t r a t i n g 30 of a l t o 18 11 12 11 14 15 16 g e t h e r 150 CR39 d e t e c t o r f o i l s . charge The c h a r g e r e s o l u t i o n is o = O . 0 5 e . No hint f o r q u a r k nuclear c o m p l e x e s was found until now. Fig. 15: C h a r g e d i s t r i b u t i o n of f r a g m e n t s f r o m 32S This w o r k has been funded by t h e G e r m a n F e d e r a l M i n i s t e r f o r R e s e a r c h and T e c h nology (BMFT). REFERENCES 1. W. H e i n r i c h , H. D r e c h s e l , R. R u d a t , E.V. B e n t o n , D. H i l d e b r a n d , Nucl. I n s t r . M a t h . 190, 369 (1981) 2 . W. T r a k o w s k i , B. S c h 6 f e r , J. D r e u t e , S. S o n n t a g C. B r e c h t m a n n , J. B e e r , H. O r e c h s e l and W. H e i n r i c h , Nucl. I n s t r . and M a t h . 2 2 5 , 9 2 ( 1 9 8 4 ) 3. H. O r e c h s e l , C. B r e c h t m a n n , J. O r e u t e , S. S o n n t a g , W . T r a k o w s k i , J. B e e r and W. H e i n r i c h , Nucl. I n s t r . M a t h . in Phys. Res. 2 2 7 , 3 4 2 ( 1 9 8 4 ) 4. H. D r e c h s e l , C. B r e c h t m a n n , W. H e i n r i c h , J. D r e u t e and E.V. B e n t o n , Phys. Rev. L e t t . 55, 1258 (1985) 5. C. B r e c h t m a n n , H. D r e c h s e l , J. B e e r and W. H e i n r i c h , N u c l e a r T r a c k s 12, 361 (1986) 6. W. Hteinrich, H. D r e c h s e l , W. T r a k o w s k i , J. B e e r , C. B r e c h t m a n n , J. D r e u t e and S. S o n n t a g , Phys. Ray. L e t t . 5 2 , 1401 ( 1 9 8 4 ) 7. H. D r e c h s e l , J. O r e u t e , C. B r e c h t m a n n ' , W. H e i n r i c h and W. T r a k o w s k i , Phys. Ray. L e t t . 54, 30 ( 1 9 8 5 ) 8. W. H e i n r i c h , H. O r e c h s e l , C. B r e c h t m a n n and J. D r e u t e , N u c l e a r T r a c k s 12, 327 ( 1 9 8 6 ) 9. C. B r e c h t m a n n and W. H e i n r i c h , Nucl. I n s t r . M a t h . in Phys. Res., B29, 675 ( 1 9 8 8 ) IO.R. S i l b e r b e r g and C.H. T s a o , A s t r o p h y s . J. S u p p l . 25, 315 (1973) 11.P.J. L i n d s t r o m , D.E. G r e i n e r , H.H H a c k m a n , B. Cork and F.S. B i e s e r , L a w r e n c e B e r k e l e y Lab. R e p o r t , L B L - 3 6 5 0 (1975) 12.C. B r e c h t m a n n and W. H e i n r i c h , s u b m i t t e d to Z e i t s c h r i f t f u r Physik 13.J.R. L e t a w , R. S i l b e r b e r g , C.H. T s a o , A s t r o p h y s . J. S u p p l . 271, 51 ( 1 9 8 3 ) 14.D.1.. O l s o n , B.L B a r m a n , D.E. G r e i n e r , H.H. H a c k m a n , P.J. L i n d s t r o m , H.J. C r a w f o r d , Phys. Ray. C 2 8 , 1602 ( 1 9 8 3 ) 15.W.R. W e b b e r , p r i v a t e c o m m u n i c a t i o n 1 6 . C . A . B e r t u l a n i and G. B a u r , Nucl. Phys. A 4 5 8 , 725 ( 1 9 8 6 ) 1 7 . J . HUfner, Phys. Rep. 125, 129 ( 1 9 8 5 ) 18. C.J. W a d d i n g t o n and P.S. F r e i e r , Phys. Ray. C 31, 8 8 8 ( 1 9 8 5 ) 1 9 . A . H o f f m a n n , C. B r e c h t m a n n , W. H e i n r i c h and E.V. B e n t o n , Phys. L e t t . B 2 0 0 , 583 (1988)