- Email: [email protected]
Analogue states from the (He3, d) reaction on Fe54, Ni58, 60
Volume 16, number 1
ANALOGUE
PHYSICS LETTERS
STATES
FROM
1 May 1965
THE --(He3,d) R E A C T I O N
ON F e 5 4 , N i 5 8 , 6 0 *
A. G. BLAIR and D. D. ARMSTRONG Los A lamos Scientific Laboratory, Los A lamos, New Mexico Received 26 March 1965
Recently, t h e r e h a s been i n c r e a s i n g e m p h a s i s on the q u e s t i o n of the c o r r e c t wave function for the c a p t u r e d p a r t i c l e in the d i s t o r t e d - w a v e a n a l y s i s of s t r i p p i n g r e a c t i o n s . In the p a s t , it h a s been c u s t o m a r y to u s e the wave function for a nucleon moving in a p o t e n t i a l w e l l a d j u s t e d to give a binding e n e r g y equal to the nucleon s e p a r a t i o n e n e r g y . T h i s p r o c e d u r e h a s been shown to y i e l d s a t i s f a c t o r y r e s u l t s in a r e c e n t (d, t) r e a c t i o n study by B j e r r e g a a r d et al. [1]. T h e r e i s o t h e r e x p e r i m e n t a l e v i d e n c e [2, 3], however, that in s o m e c a s e s this t r e a t m e n t m a y not be s a t i s f a c t o r y . S h e r r et al. [2], in an i n t e r p r e t a t i o n of t h e i r (p, d) r e a c t i o n data, have found i t m o r e a p p r o p r i a t e to u s e the wave function of the z e r o - o r d e r s h e l l m o d e l o r b i t a l for s t a t e s f r a g m e n t e d f r o m this o r b i t a l . A t h e o r e t i c a l view of the p r o b l e m h a s been given by A u s t e r n [4], and the p r o b l e m i s c u r r e n t l y being e x a m i n e d by o t h e r s [5]. The m a t t e r i s of s o m e i m p o r t a n c e in n u c l e a r s p e c t r o s c o p y , s i n c e the s p e c t r o s c o p i c f a c t o r e x t r a c t e d f r o m d i s t o r t e d - w a v e a n a l y s e s of s t r i p p i n g and pickup r e a c t i o n s d e p e n d s upon the choice of the wave function [6]; in the work of S h e r r et al. diff e r e n c e s of the o r d e r of 4 o r 5 w e r e s o m e t i m e s o b t a i n e d f r o m the two m e t h o d s of t r e a t m e n t . The p r e s e n t L e t t e r r e p o r t s the r e s u l t s of an e x p e r i m e n t a l (He 3, d) r e a c t i o n study on F e 45, Ni 58, and Ni 60, in which i s o b a r i c analogue s t a t e s a r e e x cited; t h e s e r e s u l t s indicate a c l e a r p r e f e r e n c e for the c u s t o m a r y method ,of a n a l y s i s o v e r the constant binding e n e r g y p r o c e d u r e . The (He 3, d) r e a c t i o n can e x c i t e s t a t e s in the f i n a l n u c l e u s with i s o b a r i c spin quantum n u m b e r s of e i t h e r T = Tz o r T = T z + 1, the l a t t e r being analogue s t a t e s . The way in which the r e a c t i o n s t r e n g t h i s s p l i t b e t w e e n t h e s e two g r o u p s of s t a t e s h a s been d i s c u s s e d by F r e n c h and M a c f a r l a n e [7]. If s p e c t r o s c o p i c i n f o r m a t i o n i s a v a i l a b l e f r o m a (d, p) r e a c t i o n study on the s a m e t a r g e t nucleus, it i s then p o s s i b l e to p r e d i c t the value of the * Work performed under the auspices of the U.S. Atomic Energy Commission.
s t r e n g t h C2S for e a c h analogue s t a t e e x c i t e d in the (He 3, d) r e a c t i o n . H e r e , C i s the i s o b a r i c spin C l e b s c h - G o r d a n coefficient and S i s the s p e c t r o s c o p i c f a c t o r . T h i s p r e d i c t i o n i s to be c o m p a r e d with the value of C2S o b t a i n e d f r o m d(r ~ ( 2 J f + 1) p2~ ,, d-~ = "" ( ~ - - ~ ~ " " ~'
(1)
w h e r e d a / d ~ i s the e x p e r i m e n t a l d i f f e r e n t i a l c r o s s s e c t i o n , J o and J f a r e the i n i t i a l and final s t a t e s p i n s , r e s p e c t i v e l y , a i s 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 p r e d i c t e d by the d i s t o r t e d - w a v e c a l c u l a t i o n , and N i s a n o r m a l i z i n g f a c t o r which i n c l u d e s the o v e r l a p f o r d i s s o c i a t i o n of the He 3 n u c l e u s into a d e u t e r o n plus a p r o t o n [8]. The e x p e r i m e n t a l a r r a n g e m e n t h a s been d i s c u s s e d p r e v i o u s l y [9]. The e n e r g y r e s o l u t i o n of the outgoing d e u t e r o n g r o u p s was ~ 110 keV in the c a s e of the F e 54 t a r g e t , and ~ 70 keV for the Ni 58 and Ni 60 t a r g e t s . The e x c i t a t i o n e n e r g i e s of the g r o u n d - s t a t e a n a l o g u e s a r e known f r o m the work of A n d e r s o n et al. [10]. T h e s e and o t h e r s t r o n g l y e x c i t e d analogue s t a t e s o b s e r v e d in the p r e s e n t e x p e r i m e n t and the c o r r e s p o n d i n g s t a t e s e x c i t e d s t r o n g ly in the (d, p) r e a c t i o n [11] a r e l i s t e d in table 1. Fig. 1 shows the a n g u l a r d i s t r i b u t i o n s of the a n a logue s t a t e s . The d i s t o r t e d - w a v e p r e d i c t i o n s w e r e obtained f r o m the T - S A L L Y p r o g r a m ~. The value for the c o n s t a n t N i n eq. (1) w a s d e t e r m i n e d f r o m o t h e r (He3, d) r e a c t i o n s t u d i e s in this l a b o r a t o r y on the N = 28 n u c l e i [12] and the ground s t a t e t r a n s i t i o n s to Cu 59, 61, 63, 65 [13]. A j - d e p e n d e n c e was u s e d for N, to s i m u l a t e an I. s effect f o r the w e l l depth of the c a p t u r e d p r o t o n [6, 8]. P r e v i o u s l y d e t e r m i n e d o p t i c a l - m o d e l p a r a m e t e r s w e r e u s e d [14, 15]. A r a d i a l cutoff of ~ 4.5 f m was u s e d in the c a l c u l a tion; i n t e g r a t i n g to 0 fm changed the p r e d i c t e d c r o s s s e c t i o n s by l e s s than 15%. Column 4 of table 1 is obtained i r o m the r e We are indebted to R.M.Drisko and R.H. Bassel for furnishing us with this program. 57
Volume 16, number 1
PHYSICS LETTERS
I0
6 4
~
Co$5
2--
°\
I --
5.14 MeV I -6 4
2
"" ~i;'-~,\.
cu~9
\ -
i
E 2
b "0
!
e-~
-
~ •
Jlol 4.36
•
•
•
6.86
C U 6 =l
~ i -
,;
2'
",
MeV
Me:
•
"
6.4o .ov
"
\d';..v
CUl 0.4
0.2
•
O*
I I0"
I 20"
~
I
I 40"
8,42
80I e
MeV
I
8era Fig. 1. Angular distributions of the strongly excited analogue states observed in the present experiment. Each angular distribution is associated with the cross section scale adjacent to its forward-angle points. The curves are predictions from the distorted-wave calculation, normalized to the data in the forward angle region. 58
1May1965
s u i t s of (d, p) r e a c t i o n s t u d i e s [11] and application of the equations of F r e n c h and M a c f a r l a n e [7]. Th~ values in c o l u m n s 5 and 6 were obtained f r o m the p r e d i c t i o n s of the d i s t o r t e d - w a v e c a l c u l a t i o n and eq. (1). Column 5 shows the r e s u l t s when the proton is a s s u m e d to be captured into a well such that its binding e n e r g y is equal to its s e p a r a t i o n energy. Except for the Co55 4.71 MeV state, the low-lying analogue s t a t e s a r e unbound by a few hundred keV to a few MeV. To analyze these states, it was n e c e s s a r y to extrapolate the r e s u l t s of the d i s t o r t e d - w a v e calculation in a smooth way f r o m the r e g i o n of bound s t a t e s . The s t r e n g t h s a r e s e e n to be in good a g r e e m e n t with the p r e d i c t i o n s of column 4. (The shapes of the p r e d i c t e d d i s t r i b u t i o n s in fig. 1 a r e obtained by p e r f o r m i n g the c a l c u l a t i o n for slightly bound states.) The r e s u l t s in column 6 a r e b a s e d upon a dist o r t e d - w a v e c a l c u l a t i o n in which the proton binding e n e r g i e s a r e taken f r o m a s s u m e d u n p e r t u r b e d s h e l l - m o d e l o r b i t a l s , whose excitation e n e r g i e s a r e shown in column 7. The e s t i m a t e of these positions is b a s e d l a r g e l y upon the a n a l y s i s of the lower excited s t a t e s of these n u c l e i and the analogue nuclei. An e r r o r of a half MeV in these pos i t i o n s would change the r e s u l t s in c o l u m n 6 by a p p r o x i m a t e l y 15%. The r e s u l t s a r e s e e n to be in d i s a g r e e m e n t up to f a c t o r s of four with the p r e dictions of c o l u m n 4, the d i s a g r e e m e n t i n c r e a s i n g as the difference between the e s t i m a t e d s h e l l model position and the excitation e n e r g y i n c r e a s e s . In o r d e r to obtain the s h e l l - m o d e l positions in column 7, the (d, p) data [11] were r e a n a l y z e d , in an a p p r o x i m a t e m a n n e r , in t e r m s of a constant binding e n e r g y for s t a t e s o r i g i n a t i n g f r o m a given n e u t r o n s h e l l - m o d e l state. The r e s u l t s in column 6 should actually be c o m p a r e d not to the p r e d i c tions of column 4, but to p r e d i c t i o n s b a s e d on the r e a n a l y z e d (d, p) data. This r e a n a l y s i s , however, r e d u c e s the p r e d i c t e d v a l u e s in c o l u m n 4 and i n c r e a s e s the d i s a g r e e m e n t between these values and those in column 6. The d i s a g r e e m e n t between the p r e s e n t r e s u l t s and those of S h e r r eL al. [2] m a y be due p a r t l y to the s t r o n g a b s o r p t i o n of the H e 3 p a r t i c l e r e l a t i v e to that of the proton of the (p, d) r e a c t i o n , and also to the fact that the picked-up n e u t r o n in the l a t t e r r e a c t i o n c o m e s f r o m tightly bound s t a t e s . These f e a t u r e s would tend to make the tail of the boundp a r t i c l e wave function m o r e i m p o r t a n t in the (He 3, d) r e a c t i o n than in the (p, d) r e a c t i o n . Since the actual s e p a r a t i o n e n e r g y d e t e r m i n e s the way in which the tail of the wave function m u s t fall off, the (He 3, d) r e a c t i o n may be m o r e s e n s i t i v e to the s e p a r a t i o n e n e r g y than is the (p, d) r e a c t i o n .
Volume 16, number 1
PHYSICS
LETTERS
1 May 1965
Table 1 (1)
(2)
(3)
State excited by (d, p) reaction (MeV)
jlr
Analogue state excited by (He3, d) reaction (MeV)
Fe 55
(5)
(6)
(7)
(C2S)pr e d
(C2S) 1
(C2S)2
Estimated shell-model position (MeV)
0
~-
4.71 ~ 0.07
0.27
0.22
0.27
4.0
0.417
I-
5.14 ± 0.05
0.20
0.26
0.24
5.8
0.935
~-
5.72 ± 0.05
0.20
0.27
0.43
4.6
Ni 59
Co 55
(4)
0
~3-
3.88 + 0.05
0.17
0.18
0.37
1.5
0.340
~-
4.30 ± 0.05
0.32
0.33
0.72
2.2
0.471
I-
4.36 + 0.05
0.20
0.22
0.29
3.3
3.071
(9+)
6.86 +_ 0.10 a)
Ni 61
Cu 59
0
9-
6.40 + 0.05
0.062
0.069
5-
Cu 61
6.47 ± 0.05
0.12
0.290
t-
6.65 + 0.07 b)
2.133
~+)
8.42 +_ 0.10 a)
0.062 0.14
0.26
1.5
0.67
2.2
a) State is too far unbound to allow meaningful analysis. b) Strongly interfering state present.
References 1. J . H . B j e r r e g a a x d , H.R.Blieden, O.Hanscn, G. Sidenius and G.R.Satohler, Phys.Rev. 136 (1964) B1348. 2. R . S h e r r , E . R e s t and B.Bayman, B u l l . A m . P h y s . Soc. 9 (1964) 458; R. Sherr, E. Rest and M. E. Rickey, Phys. Rev. Letters 12 (1964) 420. 3. J . L . Y n t e m a , Phys.Rev. 131 (1963) 811. 4. N.Austern, Phys. Rev.136 (1964) B1743. 5. G.R.Satohler (private communication). 6. L . L . L e e J r . , J . P . S c h i f f e r , B.Zeidman, G.R. Satchler, R . M . Drisko and R.H. Bessel, Phys. Rev. 136 (1964) B971. 7. J . B . French and M.H.Macfarlane, Nuclear Phys. 26 (1961) 168.
8. J . L . Yntema and G. R. Satchler, Phys. Rev. 134 (1964) B976. 9. A . G . B l a i r , Physics Letters 9 (1964) 37. 10. J . D . Anderson, C. Wong and J. W. McClure, Phys. Rev.129 (1963) 2718. 11. R.H. F u l m e r , A . L . McCarthy, B. L. Cohen and R. Middleton, Phys. Rev. 133 (1964) B955; R. H. Fulmer and A. L. McCarthy, Phys. Rev. 131 (1963) 2133. 12. D.D. Armstrong, Ph. D. thesis, University of New Mexico, 1965 (unpublished). 13. A.G. Blair, to be published. 14. C . M . P e r e y and F . G . P e r e y , Phys. Rev.132 (1963) 755. 15. R.H. Bassel, private communication.
59
ANALOGUE
PHYSICS LETTERS
STATES
FROM
1 May 1965
THE --(He3,d) R E A C T I O N
ON F e 5 4 , N i 5 8 , 6 0 *
A. G. BLAIR and D. D. ARMSTRONG Los A lamos Scientific Laboratory, Los A lamos, New Mexico Received 26 March 1965
Recently, t h e r e h a s been i n c r e a s i n g e m p h a s i s on the q u e s t i o n of the c o r r e c t wave function for the c a p t u r e d p a r t i c l e in the d i s t o r t e d - w a v e a n a l y s i s of s t r i p p i n g r e a c t i o n s . In the p a s t , it h a s been c u s t o m a r y to u s e the wave function for a nucleon moving in a p o t e n t i a l w e l l a d j u s t e d to give a binding e n e r g y equal to the nucleon s e p a r a t i o n e n e r g y . T h i s p r o c e d u r e h a s been shown to y i e l d s a t i s f a c t o r y r e s u l t s in a r e c e n t (d, t) r e a c t i o n study by B j e r r e g a a r d et al. [1]. T h e r e i s o t h e r e x p e r i m e n t a l e v i d e n c e [2, 3], however, that in s o m e c a s e s this t r e a t m e n t m a y not be s a t i s f a c t o r y . S h e r r et al. [2], in an i n t e r p r e t a t i o n of t h e i r (p, d) r e a c t i o n data, have found i t m o r e a p p r o p r i a t e to u s e the wave function of the z e r o - o r d e r s h e l l m o d e l o r b i t a l for s t a t e s f r a g m e n t e d f r o m this o r b i t a l . A t h e o r e t i c a l view of the p r o b l e m h a s been given by A u s t e r n [4], and the p r o b l e m i s c u r r e n t l y being e x a m i n e d by o t h e r s [5]. The m a t t e r i s of s o m e i m p o r t a n c e in n u c l e a r s p e c t r o s c o p y , s i n c e the s p e c t r o s c o p i c f a c t o r e x t r a c t e d f r o m d i s t o r t e d - w a v e a n a l y s e s of s t r i p p i n g and pickup r e a c t i o n s d e p e n d s upon the choice of the wave function [6]; in the work of S h e r r et al. diff e r e n c e s of the o r d e r of 4 o r 5 w e r e s o m e t i m e s o b t a i n e d f r o m the two m e t h o d s of t r e a t m e n t . The p r e s e n t L e t t e r r e p o r t s the r e s u l t s of an e x p e r i m e n t a l (He 3, d) r e a c t i o n study on F e 45, Ni 58, and Ni 60, in which i s o b a r i c analogue s t a t e s a r e e x cited; t h e s e r e s u l t s indicate a c l e a r p r e f e r e n c e for the c u s t o m a r y method ,of a n a l y s i s o v e r the constant binding e n e r g y p r o c e d u r e . The (He 3, d) r e a c t i o n can e x c i t e s t a t e s in the f i n a l n u c l e u s with i s o b a r i c spin quantum n u m b e r s of e i t h e r T = Tz o r T = T z + 1, the l a t t e r being analogue s t a t e s . The way in which the r e a c t i o n s t r e n g t h i s s p l i t b e t w e e n t h e s e two g r o u p s of s t a t e s h a s been d i s c u s s e d by F r e n c h and M a c f a r l a n e [7]. If s p e c t r o s c o p i c i n f o r m a t i o n i s a v a i l a b l e f r o m a (d, p) r e a c t i o n study on the s a m e t a r g e t nucleus, it i s then p o s s i b l e to p r e d i c t the value of the * Work performed under the auspices of the U.S. Atomic Energy Commission.
s t r e n g t h C2S for e a c h analogue s t a t e e x c i t e d in the (He 3, d) r e a c t i o n . H e r e , C i s the i s o b a r i c spin C l e b s c h - G o r d a n coefficient and S i s the s p e c t r o s c o p i c f a c t o r . T h i s p r e d i c t i o n i s to be c o m p a r e d with the value of C2S o b t a i n e d f r o m d(r ~ ( 2 J f + 1) p2~ ,, d-~ = "" ( ~ - - ~ ~ " " ~'
(1)
w h e r e d a / d ~ i s the e x p e r i m e n t a l d i f f e r e n t i a l c r o s s s e c t i o n , J o and J f a r e the i n i t i a l and final s t a t e s p i n s , r e s p e c t i v e l y , a i s 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 p r e d i c t e d by the d i s t o r t e d - w a v e c a l c u l a t i o n , and N i s a n o r m a l i z i n g f a c t o r which i n c l u d e s the o v e r l a p f o r d i s s o c i a t i o n of the He 3 n u c l e u s into a d e u t e r o n plus a p r o t o n [8]. The e x p e r i m e n t a l a r r a n g e m e n t h a s been d i s c u s s e d p r e v i o u s l y [9]. The e n e r g y r e s o l u t i o n of the outgoing d e u t e r o n g r o u p s was ~ 110 keV in the c a s e of the F e 54 t a r g e t , and ~ 70 keV for the Ni 58 and Ni 60 t a r g e t s . The e x c i t a t i o n e n e r g i e s of the g r o u n d - s t a t e a n a l o g u e s a r e known f r o m the work of A n d e r s o n et al. [10]. T h e s e and o t h e r s t r o n g l y e x c i t e d analogue s t a t e s o b s e r v e d in the p r e s e n t e x p e r i m e n t and the c o r r e s p o n d i n g s t a t e s e x c i t e d s t r o n g ly in the (d, p) r e a c t i o n [11] a r e l i s t e d in table 1. Fig. 1 shows the a n g u l a r d i s t r i b u t i o n s of the a n a logue s t a t e s . The d i s t o r t e d - w a v e p r e d i c t i o n s w e r e obtained f r o m the T - S A L L Y p r o g r a m ~. The value for the c o n s t a n t N i n eq. (1) w a s d e t e r m i n e d f r o m o t h e r (He3, d) r e a c t i o n s t u d i e s in this l a b o r a t o r y on the N = 28 n u c l e i [12] and the ground s t a t e t r a n s i t i o n s to Cu 59, 61, 63, 65 [13]. A j - d e p e n d e n c e was u s e d for N, to s i m u l a t e an I. s effect f o r the w e l l depth of the c a p t u r e d p r o t o n [6, 8]. P r e v i o u s l y d e t e r m i n e d o p t i c a l - m o d e l p a r a m e t e r s w e r e u s e d [14, 15]. A r a d i a l cutoff of ~ 4.5 f m was u s e d in the c a l c u l a tion; i n t e g r a t i n g to 0 fm changed the p r e d i c t e d c r o s s s e c t i o n s by l e s s than 15%. Column 4 of table 1 is obtained i r o m the r e We are indebted to R.M.Drisko and R.H. Bassel for furnishing us with this program. 57
Volume 16, number 1
PHYSICS LETTERS
I0
6 4
~
Co$5
2--
°\
I --
5.14 MeV I -6 4
2
"" ~i;'-~,\.
cu~9
\ -
i
E 2
b "0
!
e-~
-
~ •
Jlol 4.36
•
•
•
6.86
C U 6 =l
~ i -
,;
2'
",
MeV
Me:
•
"
6.4o .ov
"
\d';..v
CUl 0.4
0.2
•
O*
I I0"
I 20"
~
I
I 40"
8,42
80I e
MeV
I
8era Fig. 1. Angular distributions of the strongly excited analogue states observed in the present experiment. Each angular distribution is associated with the cross section scale adjacent to its forward-angle points. The curves are predictions from the distorted-wave calculation, normalized to the data in the forward angle region. 58
1May1965
s u i t s of (d, p) r e a c t i o n s t u d i e s [11] and application of the equations of F r e n c h and M a c f a r l a n e [7]. Th~ values in c o l u m n s 5 and 6 were obtained f r o m the p r e d i c t i o n s of the d i s t o r t e d - w a v e c a l c u l a t i o n and eq. (1). Column 5 shows the r e s u l t s when the proton is a s s u m e d to be captured into a well such that its binding e n e r g y is equal to its s e p a r a t i o n energy. Except for the Co55 4.71 MeV state, the low-lying analogue s t a t e s a r e unbound by a few hundred keV to a few MeV. To analyze these states, it was n e c e s s a r y to extrapolate the r e s u l t s of the d i s t o r t e d - w a v e calculation in a smooth way f r o m the r e g i o n of bound s t a t e s . The s t r e n g t h s a r e s e e n to be in good a g r e e m e n t with the p r e d i c t i o n s of column 4. (The shapes of the p r e d i c t e d d i s t r i b u t i o n s in fig. 1 a r e obtained by p e r f o r m i n g the c a l c u l a t i o n for slightly bound states.) The r e s u l t s in column 6 a r e b a s e d upon a dist o r t e d - w a v e c a l c u l a t i o n in which the proton binding e n e r g i e s a r e taken f r o m a s s u m e d u n p e r t u r b e d s h e l l - m o d e l o r b i t a l s , whose excitation e n e r g i e s a r e shown in column 7. The e s t i m a t e of these positions is b a s e d l a r g e l y upon the a n a l y s i s of the lower excited s t a t e s of these n u c l e i and the analogue nuclei. An e r r o r of a half MeV in these pos i t i o n s would change the r e s u l t s in c o l u m n 6 by a p p r o x i m a t e l y 15%. The r e s u l t s a r e s e e n to be in d i s a g r e e m e n t up to f a c t o r s of four with the p r e dictions of c o l u m n 4, the d i s a g r e e m e n t i n c r e a s i n g as the difference between the e s t i m a t e d s h e l l model position and the excitation e n e r g y i n c r e a s e s . In o r d e r to obtain the s h e l l - m o d e l positions in column 7, the (d, p) data [11] were r e a n a l y z e d , in an a p p r o x i m a t e m a n n e r , in t e r m s of a constant binding e n e r g y for s t a t e s o r i g i n a t i n g f r o m a given n e u t r o n s h e l l - m o d e l state. The r e s u l t s in column 6 should actually be c o m p a r e d not to the p r e d i c tions of column 4, but to p r e d i c t i o n s b a s e d on the r e a n a l y z e d (d, p) data. This r e a n a l y s i s , however, r e d u c e s the p r e d i c t e d v a l u e s in c o l u m n 4 and i n c r e a s e s the d i s a g r e e m e n t between these values and those in column 6. The d i s a g r e e m e n t between the p r e s e n t r e s u l t s and those of S h e r r eL al. [2] m a y be due p a r t l y to the s t r o n g a b s o r p t i o n of the H e 3 p a r t i c l e r e l a t i v e to that of the proton of the (p, d) r e a c t i o n , and also to the fact that the picked-up n e u t r o n in the l a t t e r r e a c t i o n c o m e s f r o m tightly bound s t a t e s . These f e a t u r e s would tend to make the tail of the boundp a r t i c l e wave function m o r e i m p o r t a n t in the (He 3, d) r e a c t i o n than in the (p, d) r e a c t i o n . Since the actual s e p a r a t i o n e n e r g y d e t e r m i n e s the way in which the tail of the wave function m u s t fall off, the (He 3, d) r e a c t i o n may be m o r e s e n s i t i v e to the s e p a r a t i o n e n e r g y than is the (p, d) r e a c t i o n .
Volume 16, number 1
PHYSICS
LETTERS
1 May 1965
Table 1 (1)
(2)
(3)
State excited by (d, p) reaction (MeV)
jlr
Analogue state excited by (He3, d) reaction (MeV)
Fe 55
(5)
(6)
(7)
(C2S)pr e d
(C2S) 1
(C2S)2
Estimated shell-model position (MeV)
0
~-
4.71 ~ 0.07
0.27
0.22
0.27
4.0
0.417
I-
5.14 ± 0.05
0.20
0.26
0.24
5.8
0.935
~-
5.72 ± 0.05
0.20
0.27
0.43
4.6
Ni 59
Co 55
(4)
0
~3-
3.88 + 0.05
0.17
0.18
0.37
1.5
0.340
~-
4.30 ± 0.05
0.32
0.33
0.72
2.2
0.471
I-
4.36 + 0.05
0.20
0.22
0.29
3.3
3.071
(9+)
6.86 +_ 0.10 a)
Ni 61
Cu 59
0
9-
6.40 + 0.05
0.062
0.069
5-
Cu 61
6.47 ± 0.05
0.12
0.290
t-
6.65 + 0.07 b)
2.133
~+)
8.42 +_ 0.10 a)
0.062 0.14
0.26
1.5
0.67
2.2
a) State is too far unbound to allow meaningful analysis. b) Strongly interfering state present.
References 1. J . H . B j e r r e g a a x d , H.R.Blieden, O.Hanscn, G. Sidenius and G.R.Satohler, Phys.Rev. 136 (1964) B1348. 2. R . S h e r r , E . R e s t and B.Bayman, B u l l . A m . P h y s . Soc. 9 (1964) 458; R. Sherr, E. Rest and M. E. Rickey, Phys. Rev. Letters 12 (1964) 420. 3. J . L . Y n t e m a , Phys.Rev. 131 (1963) 811. 4. N.Austern, Phys. Rev.136 (1964) B1743. 5. G.R.Satohler (private communication). 6. L . L . L e e J r . , J . P . S c h i f f e r , B.Zeidman, G.R. Satchler, R . M . Drisko and R.H. Bessel, Phys. Rev. 136 (1964) B971. 7. J . B . French and M.H.Macfarlane, Nuclear Phys. 26 (1961) 168.
8. J . L . Yntema and G. R. Satchler, Phys. Rev. 134 (1964) B976. 9. A . G . B l a i r , Physics Letters 9 (1964) 37. 10. J . D . Anderson, C. Wong and J. W. McClure, Phys. Rev.129 (1963) 2718. 11. R.H. F u l m e r , A . L . McCarthy, B. L. Cohen and R. Middleton, Phys. Rev. 133 (1964) B955; R. H. Fulmer and A. L. McCarthy, Phys. Rev. 131 (1963) 2133. 12. D.D. Armstrong, Ph. D. thesis, University of New Mexico, 1965 (unpublished). 13. A.G. Blair, to be published. 14. C . M . P e r e y and F . G . P e r e y , Phys. Rev.132 (1963) 755. 15. R.H. Bassel, private communication.
59