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Proton-deuteron interactions at 77 MeV
Volume 3, number 7
PHYSICS LETTERS
PROTON-DEUTERON
15 February 1963
INTERACTIONS
AT
77 M e V
M. DAVISON, H . W . K . HOPKINS *, L. LYONS and D. F. SHAW Nuclear Physics Laboratory, Oxford Received 21 January 1963
The Oxford 12 c m d e u t e r i u m bubble c h a m b e r 1) has b e e n u s e d with the H a r w e l l c y c l o t r o n to e x a m i n e the i n t e r a c t i o n of 77 MeV p r o t o n s with d e u t e r o n s . The following a n a l y s i s is b a s e d on a p p r o x i m a t e l y 2000 of the e v e n t s which have b e e n m e a s u r e d . A t o tal c r o s s - s e c t i o n of 146 + 7 mb, and a t o t a l e l a s t i c c r o s s - s e c t i o n of 55 + 3 m b have b e e n obtained, with a cut-off applied at a n g l e s l e s s than 10o ( c e n t r e of m a s s ) to r e m o v e the f o r w a r d s c a t t e r i n g C o u l o m b peak. The d i f f e r e n t i a l c r o s s - s e c t i o n for the e l a s t i c e v e n t s , s e l e c t e d on the b a s i s of c o p l a n a r i t y , a n g l e angle, and a n g l e - e n e r g y c o r r e l a t i o n s , is shown in the f i g u r e . The shape and a b s o l u t e m a g n i t u d e a r e c o n s i s t e n t with r e s u l t s at h i g h e r and l o w e r e n e r gies 2-4). C u r v e A is an i n t e r p o l a t i o n b e t w e e n i m p u l s e a p p r o x i m a t i o n c a l c u l a t i o n s for 156, 90 and 40 MeV. The two-body s c a t t e r i n g a m p l i t u d e s were d e r i v e d f r o m the G a m m e l - T h a l e r p o t e n t i a l 5), and the M o r a v c s l k 6) wave f u n c t i o n was u s e d for the d e u t e r o n . The C o u l o m b a m p l i t u d e s have not b e e n i n cluded. The b a c k w a r d peak c a l c u l a t e d f r o m the theory of Chew and G o l d b e r g e r 7) is shown as c u r v e B. The m o m e n t u m d i s t r i b u t i o n of s p e c t a t o r p a r t i cles for i n e l a s t i c e v e n t s , in which the o t h e r two p a r t i c l e s have m o m e n t a g r e a t e r than 140 M e V / c , a g r e e s with the m o m e n t u m d i s t r i b u t i o n of the n u c l e o n s in the d e u t e r o n . With this s a m e r e s t r i c t i o n of the m o m e n t a of the o t h e r p a r t i c l e s , 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 s were found for s p e c t a t o r p r o tons of m o m e n t a 60 to 95 M e V / c and s p e c t a t o r n e u t r o n s of m o m e n t a 0 to 95 M e V / c . T h i s is in c o n t r a d i c t i o n with a f o r w a r d p e a k i n g found in i n t e r a c t i o n s at 140 MeV 8), although we do find an e x c e s s of f o r w a r d s p e c t a t o r p a r t i c l e s of h i g h e r m o m e n t u m . C h e w - L o w e x t r a p o l a t i o n s 11) for the f r e e p - p and n - p c r o s s s e c t i o n s a r e c o m p a r e d with d i r e c t l y m e a s u r e d v a l u e s 9, 10) in the table. The e x t r a p o l a t i o n s have been p e r f o r m e d for e n e r g i e s in the r a n g e 32-42 MeV ( c e n t r e of m a s s ) and v a l u e s for d i r e c t m e a s u r e m e n t s have b e e n taken at 75 MeV (lab.) Although the s t a t i s t i c a l e r r o r s a r e l a r g e , the r e s u l t s s u g g e s t that the e x t r a p o l a t i o n p r o c e d u r e may be valid in this e n e r g y r e g i o n . * Now at Brookhaven National Laboratory.
358
ItJ I I O*
I
I 60"
,
i I~°
OCM Fig. 1. The p-d elastic differential c r o s s section in m i l l i barns per steradian as a function of the proton centre of mass scattering angle. Curve A is an impulse approximation calculation and curve B is derived from the pick-up theory of Chew and Goldberger.
app ~np
Extrapolated 33 + 19 m b 130 + 42 mb
Direct Measurement 35 + 1 m b 109 + 3 m b
A m o r e d e t a i l e d a c c o u n t of the e x p e r i m e n t will be p u b l i s h e d l a t e r . The a u t h o r s much a p p r e c i a t e the e n c o u r a g e m e n t and advice they have r e c e i v e d f r o m P r o f e s s o r D. H. W i l k i n s o n throughout the c o u r s e of the e x p e r i m e n t . Two of us ( H . W . K . H . and L. L. ) a r e i n d e b t e d to D. S. I . R . for financia~ s u p p 0 r t . 1) H.W.K. Hopkins et al., Nuclear Instr. Meth. 12 (1961) 323. 2) V.J.Ashby, U . C . R . L . - 2 0 9 1 , see ref. 4). 3) J. M. Teem, unpublished report 1954, see ref. 4). 4) H. Postma and R . W i l s o n , Phys. Rev. 121 (1961) 1229. 5) A.K. Kerman, H. McManus and R.M.Thaler, Ann. Phys. 8 (1959) 551. 6) M.J. Moravcsik, Nuclear Phys. 7 (1958) 113. 7) G.F.Chew and M.L.Golberger, Phys. Rev. 77 (1950) 470. 8) M.J. Esten et a l . , Nuclear forces and the few nucleon problem (Pergamon Press, 1960) p. 277. 9) R. Wilson, loc cit. p. 60. 10) L.H.Johnston, loc cit. p. 68. 11) G.F.Chew and F . E . L o w , Phys. Rev. 113 (1959) 1640.
PHYSICS LETTERS
PROTON-DEUTERON
15 February 1963
INTERACTIONS
AT
77 M e V
M. DAVISON, H . W . K . HOPKINS *, L. LYONS and D. F. SHAW Nuclear Physics Laboratory, Oxford Received 21 January 1963
The Oxford 12 c m d e u t e r i u m bubble c h a m b e r 1) has b e e n u s e d with the H a r w e l l c y c l o t r o n to e x a m i n e the i n t e r a c t i o n of 77 MeV p r o t o n s with d e u t e r o n s . The following a n a l y s i s is b a s e d on a p p r o x i m a t e l y 2000 of the e v e n t s which have b e e n m e a s u r e d . A t o tal c r o s s - s e c t i o n of 146 + 7 mb, and a t o t a l e l a s t i c c r o s s - s e c t i o n of 55 + 3 m b have b e e n obtained, with a cut-off applied at a n g l e s l e s s than 10o ( c e n t r e of m a s s ) to r e m o v e the f o r w a r d s c a t t e r i n g C o u l o m b peak. The d i f f e r e n t i a l c r o s s - s e c t i o n for the e l a s t i c e v e n t s , s e l e c t e d on the b a s i s of c o p l a n a r i t y , a n g l e angle, and a n g l e - e n e r g y c o r r e l a t i o n s , is shown in the f i g u r e . The shape and a b s o l u t e m a g n i t u d e a r e c o n s i s t e n t with r e s u l t s at h i g h e r and l o w e r e n e r gies 2-4). C u r v e A is an i n t e r p o l a t i o n b e t w e e n i m p u l s e a p p r o x i m a t i o n c a l c u l a t i o n s for 156, 90 and 40 MeV. The two-body s c a t t e r i n g a m p l i t u d e s were d e r i v e d f r o m the G a m m e l - T h a l e r p o t e n t i a l 5), and the M o r a v c s l k 6) wave f u n c t i o n was u s e d for the d e u t e r o n . The C o u l o m b a m p l i t u d e s have not b e e n i n cluded. The b a c k w a r d peak c a l c u l a t e d f r o m the theory of Chew and G o l d b e r g e r 7) is shown as c u r v e B. The m o m e n t u m d i s t r i b u t i o n of s p e c t a t o r p a r t i cles for i n e l a s t i c e v e n t s , in which the o t h e r two p a r t i c l e s have m o m e n t a g r e a t e r than 140 M e V / c , a g r e e s with the m o m e n t u m d i s t r i b u t i o n of the n u c l e o n s in the d e u t e r o n . With this s a m e r e s t r i c t i o n of the m o m e n t a of the o t h e r p a r t i c l e s , 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 s were found for s p e c t a t o r p r o tons of m o m e n t a 60 to 95 M e V / c and s p e c t a t o r n e u t r o n s of m o m e n t a 0 to 95 M e V / c . T h i s is in c o n t r a d i c t i o n with a f o r w a r d p e a k i n g found in i n t e r a c t i o n s at 140 MeV 8), although we do find an e x c e s s of f o r w a r d s p e c t a t o r p a r t i c l e s of h i g h e r m o m e n t u m . C h e w - L o w e x t r a p o l a t i o n s 11) for the f r e e p - p and n - p c r o s s s e c t i o n s a r e c o m p a r e d with d i r e c t l y m e a s u r e d v a l u e s 9, 10) in the table. The e x t r a p o l a t i o n s have been p e r f o r m e d for e n e r g i e s in the r a n g e 32-42 MeV ( c e n t r e of m a s s ) and v a l u e s for d i r e c t m e a s u r e m e n t s have b e e n taken at 75 MeV (lab.) Although the s t a t i s t i c a l e r r o r s a r e l a r g e , the r e s u l t s s u g g e s t that the e x t r a p o l a t i o n p r o c e d u r e may be valid in this e n e r g y r e g i o n . * Now at Brookhaven National Laboratory.
358
ItJ I I O*
I
I 60"
,
i I~°
OCM Fig. 1. The p-d elastic differential c r o s s section in m i l l i barns per steradian as a function of the proton centre of mass scattering angle. Curve A is an impulse approximation calculation and curve B is derived from the pick-up theory of Chew and Goldberger.
app ~np
Extrapolated 33 + 19 m b 130 + 42 mb
Direct Measurement 35 + 1 m b 109 + 3 m b
A m o r e d e t a i l e d a c c o u n t of the e x p e r i m e n t will be p u b l i s h e d l a t e r . The a u t h o r s much a p p r e c i a t e the e n c o u r a g e m e n t and advice they have r e c e i v e d f r o m P r o f e s s o r D. H. W i l k i n s o n throughout the c o u r s e of the e x p e r i m e n t . Two of us ( H . W . K . H . and L. L. ) a r e i n d e b t e d to D. S. I . R . for financia~ s u p p 0 r t . 1) H.W.K. Hopkins et al., Nuclear Instr. Meth. 12 (1961) 323. 2) V.J.Ashby, U . C . R . L . - 2 0 9 1 , see ref. 4). 3) J. M. Teem, unpublished report 1954, see ref. 4). 4) H. Postma and R . W i l s o n , Phys. Rev. 121 (1961) 1229. 5) A.K. Kerman, H. McManus and R.M.Thaler, Ann. Phys. 8 (1959) 551. 6) M.J. Moravcsik, Nuclear Phys. 7 (1958) 113. 7) G.F.Chew and M.L.Golberger, Phys. Rev. 77 (1950) 470. 8) M.J. Esten et a l . , Nuclear forces and the few nucleon problem (Pergamon Press, 1960) p. 277. 9) R. Wilson, loc cit. p. 60. 10) L.H.Johnston, loc cit. p. 68. 11) G.F.Chew and F . E . L o w , Phys. Rev. 113 (1959) 1640.