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Electrodisintegration of the deuteron at low momentum transfer: Magnetic transitions
Volume 20, number 2
PHYSICS LETTERS
i n c r e a s e the width. The l a r g e width of the excited state in 6Be c o m p a r e d to the c o r r e s p o n d i n g state in 6He is also not s u r p r i s i n g , s i n c e the state in 6He is stable a g a i n s t decay to 5He + n and only has the open channel 4He + 2n. Qualitatively, one expects the width in 6Be to be l a r g e r than the c o r r e s p o n d i n g state in 6Li; however, the d i f f e r ence between our m e a s u r e d width of the 6Be state and the r e p o r t e d width of the 6Li state is l a r g e r than one would expect f r o m s i m p l e phase space considerations. Our r e s u l t s a r e c o n s i s t e n t with the work of Whaling [4], but i n c o n s i s t e n t with the other data on s t a t e s in 6Be ([1], [2] and [3]). Some v e r y r e c e n t work at the L a w r e n c e Radiation L a b o r a t o r y in B e r k e l e y [9] on the 6Li(3He,t) r e a c t i o n is in a g r e e m e n t with the above e x p e r i m e n t a l r e s u l t s . The a n g u l a r d i s t r i b u t i o n of n e u t r o n s leading to the ground state of 6Be a p p e a r s to be m o r e or l e s s i s o t r o p i c f r o m the 4He(3He, n) r e a c t i o n within the r a t h e r l a r g e e r r o r s in the d e t e r m i n a t i o n of the c r o s s s e c t i o n s (~ 30%). A typical value for the c r o s s s e c t i o n is 0.3 m b / s r . The i n t e n s i t y of
ELECTRODISINTEGRATION LOW MOMENTUM TRANSFER:
1February 1966
the excited state in 6Be is m u c h l a r g e r , in both r e a c t i o n s , than the ground state (see figs. 1 and 2). A m o r e c o m p l e t e account of this work, along with a study of s t a t e s in 6Li, will be published elsewhere. 1. C.J. Batty, E. Friedman, P.C. Rowe and J. B. Hunt, Physics Letters 19 (1965) 35. 2. F. Ajzenberg-Selove, C.F. Osgood and C. P. Baker, Phys.Rev. 116 (1959) 1521. 3. H.C. Bryant, J.G. Berry, E.R. Flyrm and W. T. Leland, Nuclear Phys.53 (1964} 97. 4. J.L. Honsaker and W. Whaling, Bull. Am. Phys. Soc. 9 (1964) 627. 5. A part of these results have been given previously in S.F.Eccles, J.D.Anderson, H.F.Lutz and C. Wong, Bull. Am. Phys. Soc. 11 (1965) 693. 6. J.D. Anderson, C. Wong, J. W. McClure and B.D. Walker, Phys. Rev. 136 (1964) B 118. 7. R. W. Bauer, J.D. Anderson and C. Wong, Nuclear Phys. 56 (1964) 117. 8. T. Lauritsen and F. Ajzenberg-Selove, Energy Levels of Light Nuclei VII, submitted to Nuclear Phys., Sept. 1965. 9. N. Mangelson, F. Ajzenberg-Selove and M. Reed, private communication.
OF THE DEUTERON AT MAGNETIC TRANSITIONS
*
J. GOLDEMBERG ** and C. SCHAERF ***
High-Energy Physics Laboratory, Stanford University Stanford, California Received 12 January 1966
The c r o s s s e c t i o n for e l a s t i c e l e c t r o n - d e u t e r o n s c a t t e r i n g has b e e n r e c e n t l y i n v e s t i g a t e d by v a r ious people [1, 2]. Since the d e u t e r o n has isotopic spin 0, only the i s o s c a l a r p a r t of the e l e c t r o m a g n e t i c field c o n t r i b u t e s to the e l a s t i c s c a t t e r i n g c r o s s section. F o r this r e a s o n s i n g l e - m e s o n exchange c o n t r i b u t i o n s a r e i d e n t i c a l l y zero. A d l e r and D r e l l [3] have e s t i m a t e d the i m p o r t a n c e of t h r e e pion exchanges and found them to be s m a l l and in r e a s o n a b l e a g r e e m e n t with experiments. U n f o r t u n a t e l y t h e r e i s no such s e l e c t i o n r u l e * Work supported in part by the U. S. Office of Naval Research, Contract [Nonr 225(67)]. ** Now at Universidade de S. Paulo, Caixa Postal 8105, S. Paulo, Brazil. *** Now at Laboratori Nazionali di Fraseati, Frascati, Italia.
for the c o n t r i b u t i o n to the i n e l a s t i c s c a t t e r i n g c r o s s s e c t i o n and the p r o b l e m i s c o m p l i c a t e d by the final state i n t e r a c t i o n of the two nucleons. We have m e a s u r e d the s p e c t r u m of e l e c t r o n s inelastically scattered from a deuterium target at 180 ° . At this angle the t r a n s i t i o n i s m a i n l y m a g n e t i c (spin-flip) and t h e r e f o r e the dominant state of the two n u c l e o n s after the t r a n s i t i o n should be a s i n g l e t with z e r o o r b i t a l a n g u l a r m o m e n t u m (1S^). We used theUsame e x p e r i m e n t a l s e t - u p as in ref. 1 including the liquid d e u t e r i u m target. The absolute v a l u e s of the c r o s s s e c t i o n were obt a i n e d by c o m p a r i s o n with e l a s t i c e l e c t r o n p r o t o n s c a t t e r i n g . The s t a t i s t i c a l e r r o r in the n o r m a l i z a t i o n should be as s m a l l as 3%. The m e a s u r e m e n t s were p e r f o r m e d at two values of the i n c i d e n t e l e c t r o n e n e r g y : 54 and 70 MeV. 193
Volume 20, n u m b e r 2 r
M,b sr.
PHYSICS
MeV
I
I
d--~-ge
l-
Eo:70 NleV
0.02
/t ',,i t t t ,
0.01
IIll
T}I
(3.0
int.'l-'" 0
2
4
St. MeV
Eo- .54
tttt
0.02
/
, t
0.01
6
1,4eV
;
\kk
,
t \\
tit
"--.
ttt
LETTERS
1 F e b r u a r y 1966
T h i s m a d e t h e r e s u l t u n c e r t a i n i n t h e r e g i o n of high energy losses where the cross section is small. T h e r e s u l t of o u r e x p e r i m e n t i s i n d i c a t e d i n fig. 1. W e h a v e i n d i c a t e d o n l y t h e e r r o r s p r o duced by counting statistics. The solid lines ind i c a t e t h e r e s u l t of t h e t h e o r e t i c a l c a l c u l a t i o n s of J a n k u s [6] w i t h n o f i n a l s t a t e i n t e r a c t i o n . T h e b r o k e n l i n e s i n d i c a t e t h e t h e o r e t i c a l r e s u l t s of D u r a n d [7] w h i c h t a k e i n t o a c c o u n t t h e f i n a l s t a t e i n t e r a c t i o n of t h e t w o n u c l e o n s . C o n t r i b u t i o n s from meson exchange currents are not included. T h e t h e o r e t i c a l c a l c u l a t i o n s of J m a k u s , w h e r e the final state interactions in S states only were taken into account, give results not much diff e r e n t f r o m t h o s e of D u r a n d a n d a l s o m u c h l o w e r than the experimental cross sections. To the t h e o r e t i c a l c a l c u l a t i o n s we h a v e a p p l i e d r a d i a tive corrections, and the results have been folded with the experimental resolutions. Close to threshold the disagreement between theory and experiment should not be taken too seriously. T h e r e s u l t s a r e v e r y d e p e n d e n t on t h e f o l d i n g of t h e e x p e r i m e n t a l r e s o l u t i o n . W e h a v e ilo e x p l a n ation for the discrepancy at higher exitation ene r g i e s . W e t h i n k t h a t it s h o u l d b e a t t r i b u t e d to i n a d e q u a t e t r e a t m e n t of t h e f i n a l s t a t e i n t e r a c t i o n of t h e two n u c l e o n s o r t o c o n t r i b u t i o n s f r o m meson exchange currents.
0.0 -2
0
2 4 EXITATION ENERGY 1,4eV
6
Fig. 1. E n e r g y s p e c t r u m of e l e c t r o n s s c a t t e r e d i n e l a s tically on d e u t e r i u m at 0 = 180 o. The solid lines indicate the t h e o r e t i c a l r e s u l t with no final state i n t e r a c tion. The b r o k e n lines indicate the r e s u l t s of the theor e t i c a l calculations of Durand when the final s t a t e int e r a c t i o n is taken into account. The excitation energT~ is defined as minus the difference between the energy of the s c a t t e r e d e l e c t r o n and the energy of the s c a t t e r e d e l e c t r o n at the e l e c t r o d i s i n t e g r a t i o n t h r e s h o l d .
It is a pleasure to thank Prof. C. Barber for his continuous encouragement and support. We are very grateful to B. Bosco, B. Grossetete, P. Lehmmm and P. Quarati for many useful discussions. We wish to thank Prof. Blanc-Lapierre for his hospitality at the Laboratoire de l'Accelerateur Lin6are (Orsay) where the data have been analysed and most of the theoretical calculations performed.
References The same cross section has been measured previously at Stanford [4, 5] for an incident electron energy of 41.5 MeV. The first of these two experiments does not seem in disagreement with ours. However the use of a solid CD 2 target and the complications arising from the subtraction of the carbon radiative tail made Rs result somewhat ambiguous. In the second of these experiments a very long gas deuterium target was used. The empty target background was large.
194
1. J. Goldemberg and C. Schaerf, Phys. Rev. L e t t e r s 12 (1964) 298. 2. D.Drickey, D. F r ~ r e j a c q u e and D. B e n a k s a s , Phys. Rev. L e t t e r s 13 {1964) 353. 3. R . J . Adler and S. D. D rell, Phys. Rev. L e t t e r s 13 (1964) 349. 4. G.A. P e t e r s o n and W. C. B a r b e r , Phys. Rev. 128 (1962} 812. 5. W. C, B a r b e r , J . G o l d e m b e r g , G.A. P e t e r s o n and Y. Torizuka, Nuclear P h y s . 4 1 {1963} 1586. 6. V . Z . J a n k u s , Phys. Rev. 102 (1956) 1586. 7. L. Durand, Phys. Rev. 123 {1961) 1393.
PHYSICS LETTERS
i n c r e a s e the width. The l a r g e width of the excited state in 6Be c o m p a r e d to the c o r r e s p o n d i n g state in 6He is also not s u r p r i s i n g , s i n c e the state in 6He is stable a g a i n s t decay to 5He + n and only has the open channel 4He + 2n. Qualitatively, one expects the width in 6Be to be l a r g e r than the c o r r e s p o n d i n g state in 6Li; however, the d i f f e r ence between our m e a s u r e d width of the 6Be state and the r e p o r t e d width of the 6Li state is l a r g e r than one would expect f r o m s i m p l e phase space considerations. Our r e s u l t s a r e c o n s i s t e n t with the work of Whaling [4], but i n c o n s i s t e n t with the other data on s t a t e s in 6Be ([1], [2] and [3]). Some v e r y r e c e n t work at the L a w r e n c e Radiation L a b o r a t o r y in B e r k e l e y [9] on the 6Li(3He,t) r e a c t i o n is in a g r e e m e n t with the above e x p e r i m e n t a l r e s u l t s . The a n g u l a r d i s t r i b u t i o n of n e u t r o n s leading to the ground state of 6Be a p p e a r s to be m o r e or l e s s i s o t r o p i c f r o m the 4He(3He, n) r e a c t i o n within the r a t h e r l a r g e e r r o r s in the d e t e r m i n a t i o n of the c r o s s s e c t i o n s (~ 30%). A typical value for the c r o s s s e c t i o n is 0.3 m b / s r . The i n t e n s i t y of
ELECTRODISINTEGRATION LOW MOMENTUM TRANSFER:
1February 1966
the excited state in 6Be is m u c h l a r g e r , in both r e a c t i o n s , than the ground state (see figs. 1 and 2). A m o r e c o m p l e t e account of this work, along with a study of s t a t e s in 6Li, will be published elsewhere. 1. C.J. Batty, E. Friedman, P.C. Rowe and J. B. Hunt, Physics Letters 19 (1965) 35. 2. F. Ajzenberg-Selove, C.F. Osgood and C. P. Baker, Phys.Rev. 116 (1959) 1521. 3. H.C. Bryant, J.G. Berry, E.R. Flyrm and W. T. Leland, Nuclear Phys.53 (1964} 97. 4. J.L. Honsaker and W. Whaling, Bull. Am. Phys. Soc. 9 (1964) 627. 5. A part of these results have been given previously in S.F.Eccles, J.D.Anderson, H.F.Lutz and C. Wong, Bull. Am. Phys. Soc. 11 (1965) 693. 6. J.D. Anderson, C. Wong, J. W. McClure and B.D. Walker, Phys. Rev. 136 (1964) B 118. 7. R. W. Bauer, J.D. Anderson and C. Wong, Nuclear Phys. 56 (1964) 117. 8. T. Lauritsen and F. Ajzenberg-Selove, Energy Levels of Light Nuclei VII, submitted to Nuclear Phys., Sept. 1965. 9. N. Mangelson, F. Ajzenberg-Selove and M. Reed, private communication.
OF THE DEUTERON AT MAGNETIC TRANSITIONS
*
J. GOLDEMBERG ** and C. SCHAERF ***
High-Energy Physics Laboratory, Stanford University Stanford, California Received 12 January 1966
The c r o s s s e c t i o n for e l a s t i c e l e c t r o n - d e u t e r o n s c a t t e r i n g has b e e n r e c e n t l y i n v e s t i g a t e d by v a r ious people [1, 2]. Since the d e u t e r o n has isotopic spin 0, only the i s o s c a l a r p a r t of the e l e c t r o m a g n e t i c field c o n t r i b u t e s to the e l a s t i c s c a t t e r i n g c r o s s section. F o r this r e a s o n s i n g l e - m e s o n exchange c o n t r i b u t i o n s a r e i d e n t i c a l l y zero. A d l e r and D r e l l [3] have e s t i m a t e d the i m p o r t a n c e of t h r e e pion exchanges and found them to be s m a l l and in r e a s o n a b l e a g r e e m e n t with experiments. U n f o r t u n a t e l y t h e r e i s no such s e l e c t i o n r u l e * Work supported in part by the U. S. Office of Naval Research, Contract [Nonr 225(67)]. ** Now at Universidade de S. Paulo, Caixa Postal 8105, S. Paulo, Brazil. *** Now at Laboratori Nazionali di Fraseati, Frascati, Italia.
for the c o n t r i b u t i o n to the i n e l a s t i c s c a t t e r i n g c r o s s s e c t i o n and the p r o b l e m i s c o m p l i c a t e d by the final state i n t e r a c t i o n of the two nucleons. We have m e a s u r e d the s p e c t r u m of e l e c t r o n s inelastically scattered from a deuterium target at 180 ° . At this angle the t r a n s i t i o n i s m a i n l y m a g n e t i c (spin-flip) and t h e r e f o r e the dominant state of the two n u c l e o n s after the t r a n s i t i o n should be a s i n g l e t with z e r o o r b i t a l a n g u l a r m o m e n t u m (1S^). We used theUsame e x p e r i m e n t a l s e t - u p as in ref. 1 including the liquid d e u t e r i u m target. The absolute v a l u e s of the c r o s s s e c t i o n were obt a i n e d by c o m p a r i s o n with e l a s t i c e l e c t r o n p r o t o n s c a t t e r i n g . The s t a t i s t i c a l e r r o r in the n o r m a l i z a t i o n should be as s m a l l as 3%. The m e a s u r e m e n t s were p e r f o r m e d at two values of the i n c i d e n t e l e c t r o n e n e r g y : 54 and 70 MeV. 193
Volume 20, n u m b e r 2 r
M,b sr.
PHYSICS
MeV
I
I
d--~-ge
l-
Eo:70 NleV
0.02
/t ',,i t t t ,
0.01
IIll
T}I
(3.0
int.'l-'" 0
2
4
St. MeV
Eo- .54
tttt
0.02
/
, t
0.01
6
1,4eV
;
\kk
,
t \\
tit
"--.
ttt
LETTERS
1 F e b r u a r y 1966
T h i s m a d e t h e r e s u l t u n c e r t a i n i n t h e r e g i o n of high energy losses where the cross section is small. T h e r e s u l t of o u r e x p e r i m e n t i s i n d i c a t e d i n fig. 1. W e h a v e i n d i c a t e d o n l y t h e e r r o r s p r o duced by counting statistics. The solid lines ind i c a t e t h e r e s u l t of t h e t h e o r e t i c a l c a l c u l a t i o n s of J a n k u s [6] w i t h n o f i n a l s t a t e i n t e r a c t i o n . T h e b r o k e n l i n e s i n d i c a t e t h e t h e o r e t i c a l r e s u l t s of D u r a n d [7] w h i c h t a k e i n t o a c c o u n t t h e f i n a l s t a t e i n t e r a c t i o n of t h e t w o n u c l e o n s . C o n t r i b u t i o n s from meson exchange currents are not included. T h e t h e o r e t i c a l c a l c u l a t i o n s of J m a k u s , w h e r e the final state interactions in S states only were taken into account, give results not much diff e r e n t f r o m t h o s e of D u r a n d a n d a l s o m u c h l o w e r than the experimental cross sections. To the t h e o r e t i c a l c a l c u l a t i o n s we h a v e a p p l i e d r a d i a tive corrections, and the results have been folded with the experimental resolutions. Close to threshold the disagreement between theory and experiment should not be taken too seriously. T h e r e s u l t s a r e v e r y d e p e n d e n t on t h e f o l d i n g of t h e e x p e r i m e n t a l r e s o l u t i o n . W e h a v e ilo e x p l a n ation for the discrepancy at higher exitation ene r g i e s . W e t h i n k t h a t it s h o u l d b e a t t r i b u t e d to i n a d e q u a t e t r e a t m e n t of t h e f i n a l s t a t e i n t e r a c t i o n of t h e two n u c l e o n s o r t o c o n t r i b u t i o n s f r o m meson exchange currents.
0.0 -2
0
2 4 EXITATION ENERGY 1,4eV
6
Fig. 1. E n e r g y s p e c t r u m of e l e c t r o n s s c a t t e r e d i n e l a s tically on d e u t e r i u m at 0 = 180 o. The solid lines indicate the t h e o r e t i c a l r e s u l t with no final state i n t e r a c tion. The b r o k e n lines indicate the r e s u l t s of the theor e t i c a l calculations of Durand when the final s t a t e int e r a c t i o n is taken into account. The excitation energT~ is defined as minus the difference between the energy of the s c a t t e r e d e l e c t r o n and the energy of the s c a t t e r e d e l e c t r o n at the e l e c t r o d i s i n t e g r a t i o n t h r e s h o l d .
It is a pleasure to thank Prof. C. Barber for his continuous encouragement and support. We are very grateful to B. Bosco, B. Grossetete, P. Lehmmm and P. Quarati for many useful discussions. We wish to thank Prof. Blanc-Lapierre for his hospitality at the Laboratoire de l'Accelerateur Lin6are (Orsay) where the data have been analysed and most of the theoretical calculations performed.
References The same cross section has been measured previously at Stanford [4, 5] for an incident electron energy of 41.5 MeV. The first of these two experiments does not seem in disagreement with ours. However the use of a solid CD 2 target and the complications arising from the subtraction of the carbon radiative tail made Rs result somewhat ambiguous. In the second of these experiments a very long gas deuterium target was used. The empty target background was large.
194
1. J. Goldemberg and C. Schaerf, Phys. Rev. L e t t e r s 12 (1964) 298. 2. D.Drickey, D. F r ~ r e j a c q u e and D. B e n a k s a s , Phys. Rev. L e t t e r s 13 {1964) 353. 3. R . J . Adler and S. D. D rell, Phys. Rev. L e t t e r s 13 (1964) 349. 4. G.A. P e t e r s o n and W. C. B a r b e r , Phys. Rev. 128 (1962} 812. 5. W. C, B a r b e r , J . G o l d e m b e r g , G.A. P e t e r s o n and Y. Torizuka, Nuclear P h y s . 4 1 {1963} 1586. 6. V . Z . J a n k u s , Phys. Rev. 102 (1956) 1586. 7. L. Durand, Phys. Rev. 123 {1961) 1393.