- Email: [email protected]
A search for unbound T = 12 levels in 3He
Volume 24B, number 2
PHYSICS
LETTERS
m e n t a l v a l u e s a r e only about one half t h o s e p r e d i c t e d . No r e a s o n is known f o r this d i s c r e p a n c y . T h e o b s e r v a t i o n of an L = 0 t r a n s i t i o n f o r 121Sb(t,p) c o n f i r m s that the t r a n s i t i o n is not to the g r o u n d s t a t e , s i n c e this would be ~+ to 3 + 5+ ( L = 2 ) , but to the e f i r s t e x c i t e d s t a t e [2]. The 123Sb(t,p) g r o u p c o r r e s p o n d s to the n o r m a l g r o u n d s t a t e to g r o u n d s t a t e t r a n s i t i o n s i n c e t h e s e a r e both ~+ s t a t e s . The relative total cross sections for these two Sb r e a c t i o n s , c o r r e c t e d f o r a b u n d a n c e d i f f e r e n c e s , a r e s h o w n in table 2 and a r e in r e m a r k a b l e a g r e e m e n t w i t h the p a i r i n g m o d e l p r e d i c t i o n .
at a l o w e r t r i t o n e n e r g y of 10.0 M e V is s h o w n a s a b r o k e n c u r v e in f i g . 1. T h i s study of l l 0 C d ( t , p ) d e m o n s t r a t e d that the g r o u n d s t a t e t r a n s i t i o n d o m i n a t e s the s p e c t r u m , a r e s u l t that has b e e n c o n f i r m e d u s i n g the ] ] 8Sn(t, p) r e a c t i o n [8] and s o m e (p, t) r e a c t i o n s [10]. Y o s h i d a u s i n g the p a i r i n g m o d e l [11] p r e d i c t e d t h i s g r o u n d s t a t e e n h a n c e m e n t . It is e x p e c t e d to be a g e n e r a l f e a t u r e of (t, p) r e a c t i o n s in this m a s s r e g i o n and it e x p l a i n s why only the Cd g r o u n d s t a t e t r a n s i t i o n s w e r e o b s e r v e d . S i n c e a l l t h e s e t r a n s i t i o n s h a v e L=O the odd m a s s i s o t o p e s m u s t all h a v e the s a m e g r o u n d s t a t e s p i n s and p a r i t i e s (½+). The r e l a t i v e t o t a l c r o s s s e c t i o n s crT w e r e c a l c u l a t e d f r o m the Cd a n g u l a r d i s t r i b u t i o n s and a r e shown in t a b l e 2, c o r r e c t e d f o r the d i f f e r e n c e s in a b u n d a n c e . T h e l l 0 C d ( t , p ) v a l u e has b e e n a r b i t r a r i l y n o r m a l i s e d to unity. The crT v a l u e s f o r the e v e n N n u c l e i m a y be c o m p a r e d with the v a l u e s e x p e c t e d f r o m the p a i r i n g m o d e l [l l ]
~T ~ 1~ (2J+I)Uj(A) Vj(A +2)12 , J
References 1. R. Middleton and S. Hinds, Nucl. Physics 34 (1962) 404. 2. G. Bassani, M. Conjeaud. J.Gastebois. S. Harar. J. M. Laget and J. Picard, Phys. Letters 22 (1966) 189. 3. J . H . E . Mattauch, W. Thiele and A. H. Wapstra. Nucl. Physics 67 (1965) 32. 4. M . W . B r e n n e r , Phys.Rev. 129 (1963) 765. 5. P . M . E n d t , Paris, Sperduto and Buechner. Phys. Rev. 103 (1956) 961. 6. R . L . B i s h o p , Barber, McLatchie. Macdougall, Rookhuyzen and Duckworth, Can. J. Phys. 41 (1963) 1532. 7. J.D.MacDougall, MeLatchic, Whineray and Duckworth, Z. Naturforschg. 21a (1966) 63. 8. S. Hinds, J.H. Bjerregaard, O. Hansen and O. Nathan, Phys. Letters 21 (1966) 328 and to be published, 9. J . H . B j e r r e g a a r d , O. Hansen, O. Nathan and S.Hinds. Nucl. Physics 86 (1966) 145. 10. Bassani, Hintz and Kavaloski, Phys.Rev. 139 (1965) B830. 11. S.Yoshida, Nucl. Physics 33 (1962) 685. 12. R.Arvieu, Ann. Phys. (France} 8 (1963} 407.
(1)
w h e r e U- and Vj a r e the o c c u p a t i o n a m p l i t u d e s t a k e n froJm A r v i e u [12]. T a b l e 2 s h o w s that t h e r e is good a g r e e m e n t b e t w e e n the p r e s e n t r e s u l t s and t h e o r y and a l s o r e a s o n a b l e a g r e e m e n t w i t h the t h r e e (p, t) m e a s u r e m e n t s of B a s s a n i et a l . [10]. F o r the odd N i s o t o p e s the p a i r i n g p r e d i c t i o n h a s b e e n c a l c u l a t e d f r o m eq. (]7d) of r e f . 10; t h i s only d i f f e r s f r o m the e v e n N c a s e f o r the one t e r m in the s u m f o r w h i c h j i s e q u a l to the s p i n s of the s t a t e s i n v o l v e d (½). F o r odd N the e x p e r i -
A SEARCH
FOR
23 January 1967
UNBOUND
T
= ½ LEVELS
IN 3He
R. E. W A R N E R * Oberlin College, Oberlin, Ohio and J . S. V I N C E N T and E. T . B O S C H I T Z Lewis Research Center, Cleveland, Ohio Received 2 January 1967 Energy spectra of inelasticaIly scattered ~ particles from the ~ + 3He reaction were measured, yielding no groups corresponding to the unbound 3He levels reported by Kim et al.
I n t e r e s t in p o s s i b l e e x c i t e d s t a t e s of the t h r e e n u c l e o n s y s t e m h a s b e e n a r o u s e d by the e x p e r i -
m e n t of A j d a c i ~ et a l . [1], w h i c h s u g g e s t s that the * Supported by the National Science Foundation. 91
Volume 24B, n u m b e r 2
PHYSICS
f
~
12.6
40
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~-30 i
L E
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,t
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23 January 1967
T h e 42 M e V ~ p a r t i c l e b e a m f r o m t h e N A S A L e w i s c y c l o t r o n w a s s c a t t e r e d f r o m 3He g a s , and absolute cross sections thus obtained are s h o w n in fig. I . T h e s e s p e c t r a r i s e m o n o t o n i c a l l y f r o m t h e t h r e s h o l d e n e r g y f o r 3He --* p + d, a n d s h o w no s t r u c t u r e e x c e p t a s m a l l , r a t h e r b r o a d p e a k a t 17.5 ° a n d a t a b o u t 13 M e V e x c i t a t i o n ; t h i s a p p e a r s to b e r e l a t e d to t h e p l a t e a u a t 20 ° n e a r 16 M e V l a b o r a t o r y e n e r g y , a n d m a y b e a phase space effect. Deuterons can lose at most 15.6 M e V i n t h e 800 ~ Si d e t e c t o r , a n d t h e s e p a r ticles cause the sharp rise just below this energY. T h e t h r e e p r e v i o u s l y r ~ p o r t e d 3He l e v e l s [2] were at the threshold for "He ~ p + p + n and at 10.2 a n d t 2 . 6 M e V e x c i t a t i o n ; t h e 10.2 M e V l e v e l w a s e x c i t e d w i t h a c r o s s s e c t i o n of 1 o r 2 m b , t h e o t h e r s l e s s s t r o n g l y . A t 10.2 M e V we u s e d s t a n d a r d s t a t i s t i c a l p r o c e d u r e s [6] to s e a r c h f o r a G a u s s i a n p e a k of w i d t h 1.0 M e V f . w . h . m , superimposed on a smooth continuum. Upper limits of a b o u t 0.3 m b (80 p e r c e n t c o n f i d e n c e l i m i t ) a t 17.5 ° a n d 20 ° a n d 0.2 m b a t 22 ° a n d 25 ° w e r e o b tained. This experiment thus gives strong evid e n c e a g a i n s t T = ½ l e v e l s in 3He.
....
Fig. i. Inelastic cross sections in mb/sr-MeV for the el + 3He reaction• Abscissae are O~ particle laboratory energies, and laboratory scattering angles are specified. For clarity the eleastic peaks at 20 °, 22 ° and 25 ° are omitted; at 17.50 ° the elastic ~ and 3He particle groups differ in energy by only 0.4 MeV and the elastic peak shown consists of these two unresolved groups.
t r i n e u t r o n i s b o u n d , a n d b y t h e u n b o u n d l e v e l s in 3He r e p o r t e d b y K i m e t a l . [2] f r o m a s t u d y of t h e p + 3He r e a c t i o n . H o w e v e r , T h o r n t o n et a l . [3] f a i l e d to f i n d t h e t r i n e u t r o n i n a m o r e s e n s i t i v e e x p e r i m e n t , a n d b o t h A n d e r s o n e t a l . [4] a n d C o o k s o n [5] h a v e f a i l e d to o b s e r v e t h e c o r r e sponding, slightly unbound, triproton. We have o b s e r v e d i n e l a s t i c ~ p a r t i c l e s f r o m t h e el + 3He r e a c t i o n , a n d w e f i n d no e v i d e n c e f o r t h e l e v e l s reported by Kim et al.
92
LETTERS
W e w i s h to t h a n k D r . W i l l i a m F . F o r d f o r a n enlightening discussion and Dr. Norton Baron for t h e u s e of h i s s o l i d s t a t e d e t e c t o r s .
References 1. V.Ajda~id, M. Cerineo, B•Laiovid, G . P a i d , I.~laus and P . T o m a ~ , P h y s . R e v . L e t t e r s 14 {1965) 444. 2, C . C . K i m , S . M . B u n c h , D . W . D e v i n s and H . H o F o r s t e r Phys. L e t t e r s 22 (1966) 314. 3. S . T . T h o r n t o n , J . K , B a i r , C . M . J o n e s a n d H . B . W i l lard, P h y s . R e v . L e t t e r s 17 (1966) 701. 4. J o D . A n d e r s e n , C.Wong, J . M . McClure and B . A . P o h l , P h y s . R e v . L e t t e r s 15 {1965) 66. 5. J . A . Cookson, Phys. L e t t e r s 22 {1966) 612. 6. Details of t h e s e calculations a r e given in a NASA Technical Note, available f r o m the authors.
PHYSICS
LETTERS
m e n t a l v a l u e s a r e only about one half t h o s e p r e d i c t e d . No r e a s o n is known f o r this d i s c r e p a n c y . T h e o b s e r v a t i o n of an L = 0 t r a n s i t i o n f o r 121Sb(t,p) c o n f i r m s that the t r a n s i t i o n is not to the g r o u n d s t a t e , s i n c e this would be ~+ to 3 + 5+ ( L = 2 ) , but to the e f i r s t e x c i t e d s t a t e [2]. The 123Sb(t,p) g r o u p c o r r e s p o n d s to the n o r m a l g r o u n d s t a t e to g r o u n d s t a t e t r a n s i t i o n s i n c e t h e s e a r e both ~+ s t a t e s . The relative total cross sections for these two Sb r e a c t i o n s , c o r r e c t e d f o r a b u n d a n c e d i f f e r e n c e s , a r e s h o w n in table 2 and a r e in r e m a r k a b l e a g r e e m e n t w i t h the p a i r i n g m o d e l p r e d i c t i o n .
at a l o w e r t r i t o n e n e r g y of 10.0 M e V is s h o w n a s a b r o k e n c u r v e in f i g . 1. T h i s study of l l 0 C d ( t , p ) d e m o n s t r a t e d that the g r o u n d s t a t e t r a n s i t i o n d o m i n a t e s the s p e c t r u m , a r e s u l t that has b e e n c o n f i r m e d u s i n g the ] ] 8Sn(t, p) r e a c t i o n [8] and s o m e (p, t) r e a c t i o n s [10]. Y o s h i d a u s i n g the p a i r i n g m o d e l [11] p r e d i c t e d t h i s g r o u n d s t a t e e n h a n c e m e n t . It is e x p e c t e d to be a g e n e r a l f e a t u r e of (t, p) r e a c t i o n s in this m a s s r e g i o n and it e x p l a i n s why only the Cd g r o u n d s t a t e t r a n s i t i o n s w e r e o b s e r v e d . S i n c e a l l t h e s e t r a n s i t i o n s h a v e L=O the odd m a s s i s o t o p e s m u s t all h a v e the s a m e g r o u n d s t a t e s p i n s and p a r i t i e s (½+). The r e l a t i v e t o t a l c r o s s s e c t i o n s crT w e r e c a l c u l a t e d f r o m the Cd a n g u l a r d i s t r i b u t i o n s and a r e shown in t a b l e 2, c o r r e c t e d f o r the d i f f e r e n c e s in a b u n d a n c e . T h e l l 0 C d ( t , p ) v a l u e has b e e n a r b i t r a r i l y n o r m a l i s e d to unity. The crT v a l u e s f o r the e v e n N n u c l e i m a y be c o m p a r e d with the v a l u e s e x p e c t e d f r o m the p a i r i n g m o d e l [l l ]
~T ~ 1~ (2J+I)Uj(A) Vj(A +2)12 , J
References 1. R. Middleton and S. Hinds, Nucl. Physics 34 (1962) 404. 2. G. Bassani, M. Conjeaud. J.Gastebois. S. Harar. J. M. Laget and J. Picard, Phys. Letters 22 (1966) 189. 3. J . H . E . Mattauch, W. Thiele and A. H. Wapstra. Nucl. Physics 67 (1965) 32. 4. M . W . B r e n n e r , Phys.Rev. 129 (1963) 765. 5. P . M . E n d t , Paris, Sperduto and Buechner. Phys. Rev. 103 (1956) 961. 6. R . L . B i s h o p , Barber, McLatchie. Macdougall, Rookhuyzen and Duckworth, Can. J. Phys. 41 (1963) 1532. 7. J.D.MacDougall, MeLatchic, Whineray and Duckworth, Z. Naturforschg. 21a (1966) 63. 8. S. Hinds, J.H. Bjerregaard, O. Hansen and O. Nathan, Phys. Letters 21 (1966) 328 and to be published, 9. J . H . B j e r r e g a a r d , O. Hansen, O. Nathan and S.Hinds. Nucl. Physics 86 (1966) 145. 10. Bassani, Hintz and Kavaloski, Phys.Rev. 139 (1965) B830. 11. S.Yoshida, Nucl. Physics 33 (1962) 685. 12. R.Arvieu, Ann. Phys. (France} 8 (1963} 407.
(1)
w h e r e U- and Vj a r e the o c c u p a t i o n a m p l i t u d e s t a k e n froJm A r v i e u [12]. T a b l e 2 s h o w s that t h e r e is good a g r e e m e n t b e t w e e n the p r e s e n t r e s u l t s and t h e o r y and a l s o r e a s o n a b l e a g r e e m e n t w i t h the t h r e e (p, t) m e a s u r e m e n t s of B a s s a n i et a l . [10]. F o r the odd N i s o t o p e s the p a i r i n g p r e d i c t i o n h a s b e e n c a l c u l a t e d f r o m eq. (]7d) of r e f . 10; t h i s only d i f f e r s f r o m the e v e n N c a s e f o r the one t e r m in the s u m f o r w h i c h j i s e q u a l to the s p i n s of the s t a t e s i n v o l v e d (½). F o r odd N the e x p e r i -
A SEARCH
FOR
23 January 1967
UNBOUND
T
= ½ LEVELS
IN 3He
R. E. W A R N E R * Oberlin College, Oberlin, Ohio and J . S. V I N C E N T and E. T . B O S C H I T Z Lewis Research Center, Cleveland, Ohio Received 2 January 1967 Energy spectra of inelasticaIly scattered ~ particles from the ~ + 3He reaction were measured, yielding no groups corresponding to the unbound 3He levels reported by Kim et al.
I n t e r e s t in p o s s i b l e e x c i t e d s t a t e s of the t h r e e n u c l e o n s y s t e m h a s b e e n a r o u s e d by the e x p e r i -
m e n t of A j d a c i ~ et a l . [1], w h i c h s u g g e s t s that the * Supported by the National Science Foundation. 91
Volume 24B, n u m b e r 2
PHYSICS
f
~
12.6
40
t
~-30 i
L E
2 0 ° ~12.6
,t
I
t
|12.6
~
I
!.!
10.2
,,, %/10.2 ~t~ , 10.2 ", ~',i ""'-
25 °
T ".- •
t~
'*
~ (,
) Dp~ *
.... pp~
Y i
PPN
,I
. '4,,t!, ~'I • .PD*~ *VPD~,~
115
-
20
,
25 E~ - ivleV
. . . . . .
~
30
PD . . . . . . .
I
35
,
~,:'"",.
23 January 1967
T h e 42 M e V ~ p a r t i c l e b e a m f r o m t h e N A S A L e w i s c y c l o t r o n w a s s c a t t e r e d f r o m 3He g a s , and absolute cross sections thus obtained are s h o w n in fig. I . T h e s e s p e c t r a r i s e m o n o t o n i c a l l y f r o m t h e t h r e s h o l d e n e r g y f o r 3He --* p + d, a n d s h o w no s t r u c t u r e e x c e p t a s m a l l , r a t h e r b r o a d p e a k a t 17.5 ° a n d a t a b o u t 13 M e V e x c i t a t i o n ; t h i s a p p e a r s to b e r e l a t e d to t h e p l a t e a u a t 20 ° n e a r 16 M e V l a b o r a t o r y e n e r g y , a n d m a y b e a phase space effect. Deuterons can lose at most 15.6 M e V i n t h e 800 ~ Si d e t e c t o r , a n d t h e s e p a r ticles cause the sharp rise just below this energY. T h e t h r e e p r e v i o u s l y r ~ p o r t e d 3He l e v e l s [2] were at the threshold for "He ~ p + p + n and at 10.2 a n d t 2 . 6 M e V e x c i t a t i o n ; t h e 10.2 M e V l e v e l w a s e x c i t e d w i t h a c r o s s s e c t i o n of 1 o r 2 m b , t h e o t h e r s l e s s s t r o n g l y . A t 10.2 M e V we u s e d s t a n d a r d s t a t i s t i c a l p r o c e d u r e s [6] to s e a r c h f o r a G a u s s i a n p e a k of w i d t h 1.0 M e V f . w . h . m , superimposed on a smooth continuum. Upper limits of a b o u t 0.3 m b (80 p e r c e n t c o n f i d e n c e l i m i t ) a t 17.5 ° a n d 20 ° a n d 0.2 m b a t 22 ° a n d 25 ° w e r e o b tained. This experiment thus gives strong evid e n c e a g a i n s t T = ½ l e v e l s in 3He.
....
Fig. i. Inelastic cross sections in mb/sr-MeV for the el + 3He reaction• Abscissae are O~ particle laboratory energies, and laboratory scattering angles are specified. For clarity the eleastic peaks at 20 °, 22 ° and 25 ° are omitted; at 17.50 ° the elastic ~ and 3He particle groups differ in energy by only 0.4 MeV and the elastic peak shown consists of these two unresolved groups.
t r i n e u t r o n i s b o u n d , a n d b y t h e u n b o u n d l e v e l s in 3He r e p o r t e d b y K i m e t a l . [2] f r o m a s t u d y of t h e p + 3He r e a c t i o n . H o w e v e r , T h o r n t o n et a l . [3] f a i l e d to f i n d t h e t r i n e u t r o n i n a m o r e s e n s i t i v e e x p e r i m e n t , a n d b o t h A n d e r s o n e t a l . [4] a n d C o o k s o n [5] h a v e f a i l e d to o b s e r v e t h e c o r r e sponding, slightly unbound, triproton. We have o b s e r v e d i n e l a s t i c ~ p a r t i c l e s f r o m t h e el + 3He r e a c t i o n , a n d w e f i n d no e v i d e n c e f o r t h e l e v e l s reported by Kim et al.
92
LETTERS
W e w i s h to t h a n k D r . W i l l i a m F . F o r d f o r a n enlightening discussion and Dr. Norton Baron for t h e u s e of h i s s o l i d s t a t e d e t e c t o r s .
References 1. V.Ajda~id, M. Cerineo, B•Laiovid, G . P a i d , I.~laus and P . T o m a ~ , P h y s . R e v . L e t t e r s 14 {1965) 444. 2, C . C . K i m , S . M . B u n c h , D . W . D e v i n s and H . H o F o r s t e r Phys. L e t t e r s 22 (1966) 314. 3. S . T . T h o r n t o n , J . K , B a i r , C . M . J o n e s a n d H . B . W i l lard, P h y s . R e v . L e t t e r s 17 (1966) 701. 4. J o D . A n d e r s e n , C.Wong, J . M . McClure and B . A . P o h l , P h y s . R e v . L e t t e r s 15 {1965) 66. 5. J . A . Cookson, Phys. L e t t e r s 22 {1966) 612. 6. Details of t h e s e calculations a r e given in a NASA Technical Note, available f r o m the authors.