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Deuteron vector polarization in (p, d) reactions at 185 MeV
Volume 27B, number 7
DEUTERON
PHYSICS LETTERS
VECTOR
POLARIZATION
IN
(p,d)
2 September 1968
REACTIONS
AT
185
MeV
A. INGEMARSSON, A. JOHANSSON and G. T I B E L L The Gustaf Werner Institute, University of Uppsala, Uppsala, Sweden Received 24 July 1968
The vector polarization of deuterons from (p, d) reactions, induced by 185 MeV protons in 9Be. 12C and 28Si, has been measured using a carbon polarimeter.
A ng u l ar i n t e n s i t y d i s t r i b u t i o n s in (p, d) and (d, p) r e a c t i o n s have been e x t e n s i v e l y studied for many y e a r s . It is, h o w e v e r , e s s e n t i a l both to the u n d e r s t a n d i n g of the r e a c t i o n m e c h a n i s m and to the e x t r a c t i o n of n u c l e a r s t r u c t u r e i n f o r m a t i o n that we a l s o have a thorough knowledge of all s p i n - d e p e n d e n t effects, such as the p o l a r i z a t i o n s of p r o t o n s and d e u t e r o n s and the a s y m m e t r i e s in l e f t - r i g h t s c a t t e r i n g . In m o s t of the c o m p a r a t i v e l y few m e a s u r e m e n t s of spin effects which have been m ad e, one has been c o n c e r n e d with the d e u t e r o n a s y m m e t r y in (p, d) r e a c t i o n s using p o l a r i z e d p r o t o n s or with the proton p o l a r i z a t i o n in (d, p) r e a c t i o n s using u n p o l a r i z e d d e u t e r o n s . E x p e r i m e n t s i n v o l v i n g p o l a r i z e d d e u t e r o n s have been r a r e until quite r e c e n t l y due to the lack of useful b e a m s of p o l a r i z e d d e u t e r o n s and good polarization analyzers. In this p a p e r we p r e s e n t the r e s u l t s of m e a s u r e m e n t s on the v e c t o r p o l a r i z a t i o n of d e u t e r o n s f r o m (p, d) r e a c t i o n s at 185 MeV f r o m s o m e light nuc le i. D e u t e r o n p o l a r i z a t i o n can a r i s e f r o m many d i f f e r e n t s o u r c e s . If we c o n s i d e r the (p, d) r e a c t i o n in the DWBA ( d i s t o r t e d - w a v e Born a p p r o x i m a t i o n ) m o d e l , d e u t e r o n p o l a r i z a t i o n can r e s u l t f r o m s p i n - d e p e n d e n t d i s t o r t i o n of e i t h e r or both of the incident (proton) and outgoing (deuteron) w a v e s . W h e r e a s the s p i n - d e p e n d e n t d i s t o r t i o n of the p r o t o n s is known to s o m e extent, that of the d e u t e r o n s is a l m o s t totally unknown. The d e u t e r o n p o l a r i z a t i o n can a l s o be expected to depend on the p r o t o n - n e u t r o n i n t e r a c t i o n r e sponsib l e fo r the f o r m a t i o n of the d e u t e r o n , and m o r e o v e r , the d e u t e r o n D - s t a t e can be i m p o r tant. With r e s p e c t to n u c l e a r s t r u c t u r e i n f o r m a tion it might, f o r i n s t a n c e , turn out that the j - d e pendence is much m o r e p r o n o u n c e d for p o l a r i z a tion than it is f o r i n t en s i ty d i s t r i b u t i o n s . Since t h e r e a r e no p r e d i c t i o n s for the d e u t e ron v e c t o r p o l a r i z a t i o n s f r o m (d, p) r e a c t i o n s
around 185 MeV, we have chosen to study a few light nuclei f o r which the c r o s s s e c t i o n s a r e known [1,2]. M e a s u r e m e n t s have been m a d e f o r the 12C(p, d) and 28Si(p, d) r e a c t i o n s leading to the ground s t a t e s of the final nuclei and for the 9Be(p, d) r e a c t i o n leading to the s t a t e s at 16.9 and 19.2 MeV excitation e n e r g y of 8Be. Th e main difficulty of the e x p e r i m e n t was to find a r e l i a b l e way to a n a l y z e the d e u t e r o n v e c t o r p o l a r i z a t i o n . The r e s u l t s of Baldwin et al. [3] on the e l a s t i c s c a t t e r i n g of d e u t e r o n s f r o m carbon at 125 and 156 MeV showed that the l e f t r i g h t a s y m m e t r i e s w e r e quite l a r g e f o r v e c t o r p o l a r i z e d d e u t e r o n s . T h i s i m p l i e s that the p o l a r i m e t e r used to study the proton p o l a r i z a t i o n [4] could, with s m a l l m o d i f i c a t i o n s , be u s e d to a n a l y z e a l s o the d e u t e r o n v e c t o r p o l a r i z a t i o n . T h i s method and the a s s o c i a t e d u n c e r t a i n t i e s have been d i s c u s s e d by J o h a n s s o n [5]. The d e u t e r o n s w e r e m o m e n t u m a n a l y z e d in a m a g n e t i c s p e c t r o m e t e r , and the s t a t e s of the final nuclei w e r e uniquely d e t e r m i n e d with the p o s s i b l e ex ception of s o m e m i x i n g taking p l ace in the Be cases. Since no d e u t e r o n b e a m s with n o n - z e r o p o l a r ization w e r e a v a i l a b l e the p o l a r i m e t e r could not be c a l i b r a t e d . I n s t e a d , the analyzing p o w er had to be c a l c u l a t e d f r o m the data of Baldwin et al. [3]. It m u s t f u r t h e r be a s s u m e d , e i t h e r that the t e n s o r c o m p o n e n t s of the deuteron p o l a r i z a t i o n f r o m the (p, d) r e a c t i o n s studied a r e s m a l l , or that the p o l a r i m e t e r is not s e n s i t i v e to t h e s e co m p o n en t s. The f o r m e r condition has been shown to be t r u e in DWBA f o r s p i n - i n d e p e n d e n t i n t e r a c t i o n s [6] but it cannot be expected to be g e n e r a l l y valid. The l a t t e r condition, h o w e v e r , s e e m s to be r e a s o n a b l y well j u s t i f i e d [4,5]. This m e a n s that the e x p e r i m e n t a l l y d e t e r m i n ed a s y m m e t r i e s can be used to c a l c u l a t e the d e u t e r o n v e c t o r p o l a r i z a t i o n a c c o r d i n g to the 439
Volume 27B, n u m b e r 7
PHYSICS
Table 1 Deuteron vector polarization in (p, d) r e a c t i o n s at 185 MeV. Target
O~ab
E x
(MeV)
i
12C
5
0
0.04 ± 0.03
12C
10
0
-0.03 ± 0.05
12C
15
0
0.07 =t 0.06
12C
25
0
0.11 ± 0.05
9Be
15
16.9
0.06 :e 0.08
9Be
15
19.2
0.06 + 0.09
15
0
0.12 + 0.08
28Si
LETTERS
2 September 1968
If t h e d a t a of B a l d w i n e t a l . a r e c o r r e c t , t h e u n c e r t a i n t y in t h e a b s o l u t e s c a l e of t h e p r e s e n t r e s u l t s m a y b e e s t i m a t e d to b e l e s s t h a n 25%, d u e m a i n l y to t h e p o s s i b i l i t y of d i f f e r e n t a m o u n t s of i n e l a s t i c s c a t t e r i n g . H o w e v e r , t h e a g r e e m e n t b e t w e e n r e f . 3 a n d t h e c a l c u l a t i o n s by S a w a d a i s o n l y m o d e r a t e , a n d t h e a s s u m p t i o n of n e g l i g i b l e tensor polarizations has not been thoroughly t e s t e d . I t w o u l d t h e r e f o r e b e h i g h l y d e s i r a b l e to have DWBA predictions for the deuteron polarization before these time consuming measurements are continued. T h i s w o r k w a s s u p p o r t e d by t h e S w e d i s h Atomic Research Council.
equation
(R -L)/(R +L) = iA where R and L are the polarimeter counts on the right and left sides, respectively, and A is the analyzing power, obtained by averaging 2i of the Baldwin data in the appropriate manner. T h e f o r m a l i s m due to L a k i n [7] h a s b e e n u s e d . T h e r e s u l t s a r e g i v e n in t a b l e 1. In v i e w of t h e v e r y l a r g e p o l a r i z a t i o n s o b t a i n e d in e l a s t i c s c a t t e r i n g of d e u t e r o n s a s w e l l as nucleons it is somewhat surprising that all vector polarizations measured are consistent with zero. There is only a slight tendency tow a r d s p o s i t i v e v a l u e s of i < T l l } . A c t u a l l y , t h e s i g n c a n n o t b e d e t e r m i n e d f r o m t h e r e s u l t s of B a l d w i n et a l . [3]. H o w e v e r , if we f o l l o w t h e B a s e l c o n v e n t i o n [8], t h e c a l c u l a t i o n s of S a w a d a [9] s u p p o r t t h e c h o i c e of s i g n m a d e i n t h e t a b l e .
440
RefeYence8 1. P.Radvanyi, H.Genin and C . D e t r a z , Phys. Rev. 125 (1962) 295; D. B a c h e l i e r et at., P r o e . Conf. on Direct i n t e r actions, Padua, 1962 (Gordon and Breach, New York 1963) p. 1141. 2. O. Sundberg and J. K~tllne, The Gustaf W e r n e r Institute, Uppsala, GWI-PH 7/68, unpublished. 3. J . B a l d w i n et al., Phys. Rev. 103 (1956) 1502. 4, A. Johansson et al., The Gustaf W e r n e r Institute, Uppsala, GWI-PH 2/67, unpublished. 5. A. Johansson, The Gustaf W e r n e r Institute, Uppsala, GWI-PH 2/68, unpublished. 6. L . J . B . G o l d f a r b and R . C . J o h n s o n , Nucl. Phys. 18 (1960) 355. 7. W. Lakin, Phys. Rev. 98 (1955) 139. 8. Proc. Intern. Symp. on Polarization phenomena of nucleons (Birkh~iuser Verlag, Basel, 1961) p. 436. 9. T. Sawada, Nucl. Phys. 74 (1965) 289.
DEUTERON
PHYSICS LETTERS
VECTOR
POLARIZATION
IN
(p,d)
2 September 1968
REACTIONS
AT
185
MeV
A. INGEMARSSON, A. JOHANSSON and G. T I B E L L The Gustaf Werner Institute, University of Uppsala, Uppsala, Sweden Received 24 July 1968
The vector polarization of deuterons from (p, d) reactions, induced by 185 MeV protons in 9Be. 12C and 28Si, has been measured using a carbon polarimeter.
A ng u l ar i n t e n s i t y d i s t r i b u t i o n s in (p, d) and (d, p) r e a c t i o n s have been e x t e n s i v e l y studied for many y e a r s . It is, h o w e v e r , e s s e n t i a l both to the u n d e r s t a n d i n g of the r e a c t i o n m e c h a n i s m and to the e x t r a c t i o n of n u c l e a r s t r u c t u r e i n f o r m a t i o n that we a l s o have a thorough knowledge of all s p i n - d e p e n d e n t effects, such as the p o l a r i z a t i o n s of p r o t o n s and d e u t e r o n s and the a s y m m e t r i e s in l e f t - r i g h t s c a t t e r i n g . In m o s t of the c o m p a r a t i v e l y few m e a s u r e m e n t s of spin effects which have been m ad e, one has been c o n c e r n e d with the d e u t e r o n a s y m m e t r y in (p, d) r e a c t i o n s using p o l a r i z e d p r o t o n s or with the proton p o l a r i z a t i o n in (d, p) r e a c t i o n s using u n p o l a r i z e d d e u t e r o n s . E x p e r i m e n t s i n v o l v i n g p o l a r i z e d d e u t e r o n s have been r a r e until quite r e c e n t l y due to the lack of useful b e a m s of p o l a r i z e d d e u t e r o n s and good polarization analyzers. In this p a p e r we p r e s e n t the r e s u l t s of m e a s u r e m e n t s on the v e c t o r p o l a r i z a t i o n of d e u t e r o n s f r o m (p, d) r e a c t i o n s at 185 MeV f r o m s o m e light nuc le i. D e u t e r o n p o l a r i z a t i o n can a r i s e f r o m many d i f f e r e n t s o u r c e s . If we c o n s i d e r the (p, d) r e a c t i o n in the DWBA ( d i s t o r t e d - w a v e Born a p p r o x i m a t i o n ) m o d e l , d e u t e r o n p o l a r i z a t i o n can r e s u l t f r o m s p i n - d e p e n d e n t d i s t o r t i o n of e i t h e r or both of the incident (proton) and outgoing (deuteron) w a v e s . W h e r e a s the s p i n - d e p e n d e n t d i s t o r t i o n of the p r o t o n s is known to s o m e extent, that of the d e u t e r o n s is a l m o s t totally unknown. The d e u t e r o n p o l a r i z a t i o n can a l s o be expected to depend on the p r o t o n - n e u t r o n i n t e r a c t i o n r e sponsib l e fo r the f o r m a t i o n of the d e u t e r o n , and m o r e o v e r , the d e u t e r o n D - s t a t e can be i m p o r tant. With r e s p e c t to n u c l e a r s t r u c t u r e i n f o r m a tion it might, f o r i n s t a n c e , turn out that the j - d e pendence is much m o r e p r o n o u n c e d for p o l a r i z a tion than it is f o r i n t en s i ty d i s t r i b u t i o n s . Since t h e r e a r e no p r e d i c t i o n s for the d e u t e ron v e c t o r p o l a r i z a t i o n s f r o m (d, p) r e a c t i o n s
around 185 MeV, we have chosen to study a few light nuclei f o r which the c r o s s s e c t i o n s a r e known [1,2]. M e a s u r e m e n t s have been m a d e f o r the 12C(p, d) and 28Si(p, d) r e a c t i o n s leading to the ground s t a t e s of the final nuclei and for the 9Be(p, d) r e a c t i o n leading to the s t a t e s at 16.9 and 19.2 MeV excitation e n e r g y of 8Be. Th e main difficulty of the e x p e r i m e n t was to find a r e l i a b l e way to a n a l y z e the d e u t e r o n v e c t o r p o l a r i z a t i o n . The r e s u l t s of Baldwin et al. [3] on the e l a s t i c s c a t t e r i n g of d e u t e r o n s f r o m carbon at 125 and 156 MeV showed that the l e f t r i g h t a s y m m e t r i e s w e r e quite l a r g e f o r v e c t o r p o l a r i z e d d e u t e r o n s . T h i s i m p l i e s that the p o l a r i m e t e r used to study the proton p o l a r i z a t i o n [4] could, with s m a l l m o d i f i c a t i o n s , be u s e d to a n a l y z e a l s o the d e u t e r o n v e c t o r p o l a r i z a t i o n . T h i s method and the a s s o c i a t e d u n c e r t a i n t i e s have been d i s c u s s e d by J o h a n s s o n [5]. The d e u t e r o n s w e r e m o m e n t u m a n a l y z e d in a m a g n e t i c s p e c t r o m e t e r , and the s t a t e s of the final nuclei w e r e uniquely d e t e r m i n e d with the p o s s i b l e ex ception of s o m e m i x i n g taking p l ace in the Be cases. Since no d e u t e r o n b e a m s with n o n - z e r o p o l a r ization w e r e a v a i l a b l e the p o l a r i m e t e r could not be c a l i b r a t e d . I n s t e a d , the analyzing p o w er had to be c a l c u l a t e d f r o m the data of Baldwin et al. [3]. It m u s t f u r t h e r be a s s u m e d , e i t h e r that the t e n s o r c o m p o n e n t s of the deuteron p o l a r i z a t i o n f r o m the (p, d) r e a c t i o n s studied a r e s m a l l , or that the p o l a r i m e t e r is not s e n s i t i v e to t h e s e co m p o n en t s. The f o r m e r condition has been shown to be t r u e in DWBA f o r s p i n - i n d e p e n d e n t i n t e r a c t i o n s [6] but it cannot be expected to be g e n e r a l l y valid. The l a t t e r condition, h o w e v e r , s e e m s to be r e a s o n a b l y well j u s t i f i e d [4,5]. This m e a n s that the e x p e r i m e n t a l l y d e t e r m i n ed a s y m m e t r i e s can be used to c a l c u l a t e the d e u t e r o n v e c t o r p o l a r i z a t i o n a c c o r d i n g to the 439
Volume 27B, n u m b e r 7
PHYSICS
Table 1 Deuteron vector polarization in (p, d) r e a c t i o n s at 185 MeV. Target
O~ab
E x
(MeV)
i
12C
5
0
0.04 ± 0.03
12C
10
0
-0.03 ± 0.05
12C
15
0
0.07 =t 0.06
12C
25
0
0.11 ± 0.05
9Be
15
16.9
0.06 :e 0.08
9Be
15
19.2
0.06 + 0.09
15
0
0.12 + 0.08
28Si
LETTERS
2 September 1968
If t h e d a t a of B a l d w i n e t a l . a r e c o r r e c t , t h e u n c e r t a i n t y in t h e a b s o l u t e s c a l e of t h e p r e s e n t r e s u l t s m a y b e e s t i m a t e d to b e l e s s t h a n 25%, d u e m a i n l y to t h e p o s s i b i l i t y of d i f f e r e n t a m o u n t s of i n e l a s t i c s c a t t e r i n g . H o w e v e r , t h e a g r e e m e n t b e t w e e n r e f . 3 a n d t h e c a l c u l a t i o n s by S a w a d a i s o n l y m o d e r a t e , a n d t h e a s s u m p t i o n of n e g l i g i b l e tensor polarizations has not been thoroughly t e s t e d . I t w o u l d t h e r e f o r e b e h i g h l y d e s i r a b l e to have DWBA predictions for the deuteron polarization before these time consuming measurements are continued. T h i s w o r k w a s s u p p o r t e d by t h e S w e d i s h Atomic Research Council.
equation
(R -L)/(R +L) = i
440
RefeYence8 1. P.Radvanyi, H.Genin and C . D e t r a z , Phys. Rev. 125 (1962) 295; D. B a c h e l i e r et at., P r o e . Conf. on Direct i n t e r actions, Padua, 1962 (Gordon and Breach, New York 1963) p. 1141. 2. O. Sundberg and J. K~tllne, The Gustaf W e r n e r Institute, Uppsala, GWI-PH 7/68, unpublished. 3. J . B a l d w i n et al., Phys. Rev. 103 (1956) 1502. 4, A. Johansson et al., The Gustaf W e r n e r Institute, Uppsala, GWI-PH 2/67, unpublished. 5. A. Johansson, The Gustaf W e r n e r Institute, Uppsala, GWI-PH 2/68, unpublished. 6. L . J . B . G o l d f a r b and R . C . J o h n s o n , Nucl. Phys. 18 (1960) 355. 7. W. Lakin, Phys. Rev. 98 (1955) 139. 8. Proc. Intern. Symp. on Polarization phenomena of nucleons (Birkh~iuser Verlag, Basel, 1961) p. 436. 9. T. Sawada, Nucl. Phys. 74 (1965) 289.