7 К з / 3 / 9

7 К з / 3 / 9

K F K I 1 9 /1 9 6 9

1964 SEP 1 6

A SURVEY O F THE ANGULAR DISTRIBUTION DATA O N n-p SCATTERING BELOW 10 M eV

T. Cxibólc

HUNGARIAN ACADEMY OF SCIENCES CENTRAL RESEARCH INSTITUTE FOR PHYSICS

B U D A P E S T

P r i n t e d i n t h e C e n tr a l R e se a r c h I n s t i t u t e f o r P h y B ic s , B u d ap est K ia d ja az MTA K ö z p o n ti BizikegL K u tató i n t é z e t e , B u d ap est

K ö n y v tá r -K ia d ó i O s z t á l y . O .v .i D r. B arkas I s t v á n n é

Példányszám » 255 Munkaszám: 4665 B u d a p e st, 1969* j ú l i u s 29*

Szakm ai l e k t o r : P á l l á G a b r i e l l a . N y e lv i l e k t o r : D o lin s z k y Tamás K é s z ü lt a KFKI h á z i s o k s z o r o s i t ó j á b a n . B . v . t G yenes Imre

A SURVEY OF THE ANGULAR DISTRIBUTION DATA ON n - p SCATTERING BELOW 10 MeV

T. C zib ó k

C e n t r a l R e s e a r c h I n s t i t u t e f o r P h y s i c s , B u d a p e s t, H ungary

I n v ie w o f t h e n - p s c a t t e r i n g i n v e s t i g a t i o n s now i n p r o g r e s s I n t h i s l a b o r a t o r y th e b u lk o f th e p u b l i s h e d e x p e r i m e n t a l d a t a c o n c e r n in g th e r a n g e b elo w 10 MeV h a v e b e e n a n a l y s e d . C o n tr a r y t o th e g e n e r a l l y assu m ed i s o t r o p y o f t h e a n g u l a r d i s t r i b u t i o n s i n t h i s e n e r g y r a n g e , a n a l y s i s o f th e a v a i l a b l e s p a r s e d a t a s u g g e s t s t h e p r e s e n c e o f a more c o m p le x s t r u c t u r e i n t h e d i f f e r e n t i a l c r o B S - s e c t i o n .

I n t r o d u c t i o n

The a n g u l a r d e p e n d e n c e o f t h e d i f f e r e n t i a l c r o s s - s e c t i o n o f t h e n - p s c a t t e r i n g a t low e n e r g i e s i s a s a r u l e d e t e r m in e d f r o m a n g u l a r d i s t r i ­ b u t i o n o f t h e x 'e c o i l p r o t o n s , s i n c e t h e r e c o r d i n g o f t h e s c a t t e r e d n e u t r o n s

i n v o l v e s m ore d i f f i c u l t y . F o r d e t e c t i n g th e p r o t o n s t h e i r i o n i z i n g p o w e r i s u t i l i z e d , e i t h e r b y v i s u a l i z a t i o n o f th e i o n i z a t i o n t r a c k s o r by c o n v e r t i n g t h e i o n i z a t i o n e n e r g y i n t o e l e c t r o n i c p u l s e s . To r e a c h a g o o d r e s o l u t i o n i s p r o b l e m a t i c w i t h b o th m ethod a r o u n d t h e C.M. a n g le s 0° and 1 8 0 ° .

W o rk in g w ith t h e t r a c k v i s u a l i z a t i o n m e th o d / c l o u d c h a m b e r, n u c l e a r e m u ls io n / w h e th e r t h i n p r o t o n r a d i a t o r o r , p r e f e r a b l y , p r o t o n s d i s p é r s e d i n t h e s e n s i t i v e volum e o f t h e d e t e c t o r a r e u s e d a s t a r g e t , a l l p r o t o n s

s c a t t e r e d a f t e r c o l l i s i o n i n t o t h e t o t a l s o l i d a n g le a r e d e t e c t e d . T h e r e f o r e , t h e a n g u l a r d i s t r i b u t i o n o f th e p r o t o n s g iv e s t h e d i f f e r e n t i a l c r o s s - s e c t i o n m u l t i p l i e d b y t h e f a c t o r s i m ^ c m ' h a v e a good r e s o l u t i o n e v e n f o r a n g l e s a b o u t t h e C.M. a n g l e s г^ = 0 ° , 1 8 0 °, a c e r t a i n n u m b e r o f e v e n t s i s n e c e s s a r y , im p ly in g a r e l a t i v e l y t o o g r e a t d e a l o f e v a l u a t i o n e f f o r t . I n t h e b u l k o f m e a s u re m e n ts t h e s t a t i s t i c s I s n o t g o o d en ou g h t o r e s o l v e t h e f i r s t

an d th e f i n a l a n g u l a r r a n g e o f t h e w id th At?1 = 20° o r r a t h e r 4 0 ° . W ith t h e s c i n t i l l a t i o n a n d i o n i z a t i o n / p r o p o r t i o n a l / c o u n t e r s th e s m a l l e n e r g y p a r t o f p r o t o n s , i . e . t h e a n g u l a r r a n g e a b o u t t^> _ M = 180° P , U . IVi . ,c i s n o t d e t e c t a b l e b e c a u s e o f t h e e l e c t r o n i c n p i s e . A lso a r o u n d t?> c M = 0 t h e a n g u l a r r e s o l u t i o n i s s t r o n g l y r e s t r i c t e d . N am ely, t h e a n g u l a r d i s t r i -

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b u t io n i s d e te r m in e d from th e e n e r g y d i s t r i b u t i o n by th e e q u a t io n

Ep = Eo c o s 2Op / a l l q u a n t i t i e s i n la b o r a t o r y sy ste m , &0 i s th e n e u tr o n e n e r g y b e f o r e t h e s c a t t e r i n g / . The вате e q u a tio n g iv e s th e r e l a t i o n s h i p

ft 2 A

b e tw e e n t h e a n g u la r and t h e en erg y r e s o l u t i o n a s Av> r M ** H --- • р ,и .м . ь о e i n vp f C . M.

Thus th e a n g u la r r e s o l u t i o n grows r a p i d l y w orse when 7* g o e s t o 0 ° , w hich ca n be i l l u s t r a t e d w ith t h e f o l l o w i n g rem ark. F o r Ae/E=10% th e a n g u la r r e s o l u t i o n a t г* c M = ° ° i 0 M =37° and ®ven f o r AE/E=1% th e a n g u la r r e s o l u t i o n i s n o t b e t t e r th e n ЛЛ, .. С . M. = 12°.

S u rv ey o f t h e D ata

W ith in th e ran ge c o n c e r n e d , m easurem ents w ith r e l a t i v e l y good e n e r g y r e s o l u t i o n a re p u b lis h e d o n ly f o r th e n e u t r o n e n e r g i e s 2 .5 t 5 . 2 7 and 8 . 8 MeV, r e s p e c t i v e l y . A v a ila b le d a t a are d i s c u s s e d f o r e a c h group s e p a r a t e ­ l y .

2 . 5 MeV

At t h i s e n e r g y , m easu rem en ts were c a r r i e d out w it h n e u tr o n s ob­

t a i n e d from t h e r e a c t io n D /d ,n / f o r d e u te r o n en erg y E^ = 100 - 200 keV and n eu tro n d i r e c t i o n 0n = 90 , The e a r l i e s t e x p e r im e n ts were p erfo rm ed w it h tr a c k v i s u a l i z a t i o n o f t h e r e c o i l p r o t o n s . M ention m ust be made o f th e w orks o f B onner [ 1 ] , Dee and G i lb e r t [2 ] and Lampson [33 . A ngular d i s t r i ­ b u t io n o f t h e n - p s c a t t e r i n g was fou n d i n e a c h o f t h e s e i n v e s t i g a t i o n s

a n i s o t r o p i c f o r En = 2 .5 MeV due t o th e e x c e s s o f th e s m a ll a n g le p r o to n s o v e r t h o s e o f medium a n g l e s . I n r e f . [21 t h i s d e p a r tu r e i s g iv e n a s

/10+ 10/% . I n r e f s . [21 and [3З t h e d e p a r tu r e was i n t e r p r e t e d as a c o n se q u ­ e n c e o f t h e lo n g ran g e com ponent o f t h e n u c le a r f o r c e s , w h i l e i n r e f . E li m e r e ly a s an e r r o r i n th e b ack grou n d c o r r e c t i o n . A cco rd in g t o th e f r e q u e n t l y q u o te d work o f B a r s c h a ll and Kanner [ 4 ] , one o f th e f i r s t m easurem ents w it h i o n i z a t i o n c o u n t in g , t h e d i f f e r e n t i a l c r o s s - s e c t i o n i s i s o t r o p i c . H ow ever, t h i s v e r y m easurem ent y i e l d e d also f o r t h e n-d s c a t t e r i n g an

i s o t r o p i c d i f f e r e n c i a l c r o s s - s e c t i o n and we l e a r n t from a number o f l a t e r e x p e r im e n ts / e . g . r e f s . 153» [ 6 3 / a s w e l l a s from w e ll e s t a b l i s h e d t h e o r e t ­ i c a l c o n s i d e r a t i o n s / s e e r e f . 1 7 3 / t h a t th e d i s t r i b u t i o n i s , a c t u a l l y , by f a r n o t i s o t r o p i c . I t i s t h i s why p r e s e n t a u th o r q u e s t io n s t h e r e l i a b i l i t y o f r e f . [ 4 3 . A l a t e r r e p e t i t i o n o f t h e ex p e r im e n t by Coon and B a r s c h a ll [5З e x h i b i t e d a d e f i n i t e e x c e s s o f th e fo rw a rd s c a t t e r e d p r o t o n s w ith a r e l a t i v e l y good s t a t i s t i c s . A ls o , t h e d e v i a t i o n .from i s o t r o p y seems t o in v o lv e a f i n e s t r u c t u r e , t o o / F i g . l / , F i n a l l y , we r e f e r t o t h e m easurem ent o f C ap leh orn and Rundle [63 w it h a c lo u d cham ber. T h e ir d a t a , grupped i n t 10 r a n g e s o f

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a n g l e , show a n i s o t r o p i c a n g u l a r d i s t r i b u t i o n w i t h an e r r o r o f + 10% / s e e F i g .2/ .

л/ЛЕ

800 300 200 100

0,5 60°

E(p)/M eV CrnTn)

F i g . 1

N 160

120 - r ’ A V n * .... + ■

HO w

^Cm (n)

T— I ^{t I T I}

20° 80° 60° 80° 100° 120° K0° 160° 180°

F i g . 2

5 .2 7 MeY

A t t h i s e n e r g y o n ly a s i n g l e e x p e r i m e n t i s known [ 8 1 , [9] .

Hamouda an d M o n tf to llin c a r r i e d o u t t h e i r m e a su re m e n t i n tw o r u n s . At t h e p e r p e n d i c u l a r p o s i t i o n o f a f l a t W ils o n -c h a m b e r th e y m e a s u re d t h e p r o t o n s s c a t t e r e d b a c k w a rd i n C.M. s y s te m , w h ile t h e f o r w a r d s c a t t e r e d p r o t o n s w ere m e a su re d a t a le n g th w a y s p o s i t ! ö n . The w h o le m e a su re m e n t g a v e a n i s o t r o p i c a n g u l a r d i s t r i b u t i o n w ith good e n o u g h s t a t i s t i c s o v e r t h e w hole a n g u l a r r a n g e th o u g h t h e f i r s t an d f i n a l p a r t b e i n g u n r e s o l v e d / F i g . 3 / .

4

N 2 0 0^-

<00 -

—I---1--- 1 30° б0° 90°

~\---1--- 120° 150°

F i g . 3

8 . 8 МеУ

I n th e work Champion and P o w e ll , n e u tr o n s were o b t a in e d from B ^ / d , n / r e a c t i o n and th e r e c o i l p r o t o n s were r e c o r d e d by e m u ls io n t e c h ­ n iq u e s [1 0 1 . P r o to n s from th e s c a t t e r i n g o f t h e 8 . 8 MeV n e u tr o n group w ere s e l e c t e d and a n a ly s e d . A veraged o v e r l a r g e r a n g u la r r a n g e s , an e x c e s s o f ab ou t 20 p . c . was fou n d i n th e d i f f e r e n t i a l c r o s s - s e c t i o n a t s m a ll p r o to n a n g le s a s com pared t o th e medium a n g u la r r a n g e . What w as, h o w e v e r , c o m p le t e ly new , an o s c i l l a t i o n o f t h e p e r io d o f 2 4 ° i n c.M . a n g le s w as t o be e x t r a c t ­ ed f o r th e a n g u la r d ep en d en ce o f d i f f e r e n t i a l c r o s s - s e c t i o n . The s t a t i s t i c a l e r r o r p e r m its a sm ooth f i t , b u t t h e r e i s a good i n d i c a t i o n f o r p e r i o d i c i t y .

The r e s u l t i s shown i n F i g . 4 a s n o r m a liz e d t o an i s o t r o p i c a n g u la r d i s t r i b u t i o n o f same in t e g r a t e d c r o s s - s e c t i o n . I n t h i s c o n n e c t io n one may r e f e r t o th e m easurem ent o f Coon and B a r s c h a ll a t 2 . 5 MeV [5] , w it h in w h ich a s im il a r p a t t e r n t o t h a t o f F i g . 4 was fou n d w it h o u t b e in g , h o w ev er, su ch a pronounced one a s t h a t .

/VOty NoOV

16 12

08 08

200 80° 600 80°

;P \ 6 \

' \I \ / \ О % o 'P O ?

о

''о4 --- / ---O'0 ',4- -O.o' 0-0

C.m(p)

F i g . 4

- 5 -

P r i o r t o I968 no o t h e r m easurem ents were a v a i l a b l e on t h e s u b j e c t .

D is c u s s i o n

T h e o r e t ic a l p r e d i c t i o n f o r t h e upper l i m i t o f a p o s s i b l e c o n t r ib u ­ t i o n from p a r t i a l w aves w it h £ > о t o t h e in t e g r a t e d c r o s s - s e c t i o n o f t h e n-p s c a t t e r i n g below 10 MeV i s ab ou t 1 %o t i l ] . 8uch an estim a*- t i o n s u g g e s t t h a t when d i s c u s s i n g th e n -p s c a t t e r i n g w it h in t h i s e n erg y ran ge c o n s id e r a t i o n s can b e c o n f in e d t o s - w a v e s . I n o th e r w ord s, th e d i f f e r e n t i a l c r o s s - s e c t i o n a t a g iv e n e n e r g y s h o u ld b e in d e p e n d e n t o f th e s c a t t e r i n g a n g le . M easurem ents i n th e n e u tr o n e n e r g y ran g e 1 0 -9 0 MeV c o n fir m t h i s p r e d i c t i o n s i n c e a n g u la r d i s t r i b u t i o n s become more and more I s o t r o p i c when n e u tr o n en erg y i s d e c r e a s e d [1 2 1. N e v e r t h e l e s s , b a se d on t h e low e n e r g y d a t a , we i n s i s t on s t a t i n g t h a t a n g u la r d i s t r i b u t i o n s b elo w 10 MeV do n o t e x h i b i t th e p r e d ic t e d s im p le p i c t u r e . A c t u a l l y , a n is o t r o p y was fo u n d ev en b elo w 10 MeV t o be im p o r t a n t . Only a s i n g l e m easurem ent a t .3.27 MeV

[8] , [9I r e s u l t e d , w it h in e x p e r im e n t a l e r r o r , i n an i s o t r o p i c a n g u la r d i s t r i b u t i o n . At 2 . 5 and 8 . 8 MeV a lm o st ea ch o f t h e m easurem ents showed a n is o t r o p y . What i s m ore, a t 8 . 8 MeV an ev en more com p lex s t r u c t u r e seem s t o be p r e s e n t i n t h e d i s t r i b u t i o n .

R e fe r e n c e s

[11 T.W. B onner, P h y s.R e v . ^ 2 , 685 / 1 9 3 7 /

[21 P .I » Dee and C.W. G i lb e r t ,P r o c .R o y .S o c . A 163. 2 6 5 / 1 9 3 7 / [3] C.W. Lampson, P h y s.R e v . j ? l, 1021 / 1 9 3 7 /

[9 ] H.H. B a r s c h a ll and M.H. K anner, P h y s .R e v . Jp8, 590 / 1 9 W t 5 l J .H . Coon and H.H. B a r s c h a l l , P h y s .R e v . £ 0 , 592 /19'+6 /

[6 ] W.F. C aplehorn and (J.P. R u n d le, P r o c .P h y s .S o c . A 64, 5^6 / 1 9 5 1 /

[ ' ( 1 H .S . M assey and R .A . Buckingham , P h y s .R e v . ' ] \ , 558 /1 9 4 -7 / [8 ] G. de M on tm ollin and J . Hamouda, H e lv .P h y s . A cta 2 4 , 217 / 1 9 5 1 / [9] J# Hamouda and G .de M o n tm o llin , P h y s .R e v . 8 ^ , 1277 / 1 9 5 1 / [1 0 ] F .C , Champion and C .F . P o w e ll, P r o c .R o y .S o c . A 183« 64 /1 9 4 4 / i l l ] H ,P . N o y es, P h y s.R e v . l i O , 2025 / 1 9 6 3 /

[1 2 ] W.N. H e ss , R ev.M od .P h ys. ^ 0 , 368 / 1 9 5 8 /