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Energy dependence of 26Mg(p,t)24Mg and 12C(p,t)10C L = 0 and L = 2 angular-distribution shapes
Volume 25B. number 5
PHYSICS
References 1. P.Stoler. M.Slagowitz, W.Makofske and T . H . K r u se. Phys. Rev. ]55 (1967) 1334. 2. P.H.Stelson and L. Grodzins, Nuclear Data, SectionA. Vol. 1 (1965) 21.
LETTERS
18 September 1967
3. G.R.Stachler, Nucl. Phys. A91 (1967) 75; T. Tamura and T. Terasawa, to be published. 4. T . T a m u r a , Rev. Mod. Phys. 37 (1965} 679.
ENERGY DEPENDENCE OF 26Mg(p,t)24Mg L = 0 AND L = 2 ANGULAR-DISTRIBUTION
AND
12C(p,t)10C SHAPES *
S. W. C O S P E R **,. H. B R U N N A D E R , J. C E R N Y and L. M c G R A T H Lawrence Radiation Laboratory and Department of Chemistry, University of California. Berkeley. CaliJbrnia. USA Received 11 August 1967
Though (p. t) angular distributions with L = 0 and 2 normally show a static behavior, their measurement on ZffMg and 12C targets for proton energies between 20 and 54 MeV shows a marked shape and magnitude deterioration at the lower energies. These results are compared to two-nucleon transfer DWBA theory. D u r i n g a r e c e n t e x p e r i m e n t [1] in w h i c h t h e l o w e s t T = 2 (15.43 M e V ; 0 +) s t a t e in 24Mg w a s p o p u l a t e d via t h e 26Mg(p, t) r e a c t i o n , it w a s n o t e d that t h e t y p i c a l L = 0 t r i t o n a n g u l a r d i s t r i b u t i o n of t h i s s t a t e [2] s h o w e d a m a r k e d m a g n i tude and s h a p e d e t e r i o r a t i o n w h e n the i n c i d e n t p r o t o n e n e r g y w a s l o w e r e d f r o m 38.7 to 32.5 MeV. T h a t both the m a g n i t u d e and s h a p e of t h i s angular distribution could undergo such a drastic c h a n g e with only a 6 MeV c h a n g e in i n c i d e n t p r o ton e n e r g y n e a r E _ ~ 35 MeV a p p e a r e d to be of i, c o n s i d e r a b l e i n t e r e s t f o r t h r e e r e a s o n s : a) M o s t o t h e r L = 0 and L = 2 (p, t) a n g u l a r d i s t r i b u t i o n s , p r i m a r i l y i n v o l v i n g r e l a t i v e l y high c . m . e n e r g y t r i t o n s , had shown a n e a r l y s t a t i c s h a p e w h i c h c h a n g e d s l o w l y with t a r g e t m a s s n u m b e r [ c . f . r e f s . 3 and 4] - a f a c t w h i c h had b e e n u s e d to a s s i g n L = 0 o r L = 2 t r a n s f e r to unknown (p, t) and (p, 3He) a n g u l a r d i s t r i b u t i o n s ; b) T h i s m a g n i t u d e and s h a p e d e t e r i o r a t i o n , if not p r e d i c t e d by c u r rent two-nucleon transfer theory, could cause u n c e r t a i n t i e s in t h e s p e c t r o s c o p i c i n f o r m a t i o n e x t r a c t e d f r o m s o m e (p, t) r e a c t i o n d a t a ; and c) Any e x p e r i m e n t s d i r e c t e d t o w a r d e s t a b l i s h i n g the l o c a t i o n [2] o r d e c a y p r o p e r t i e s [1] of * Work performed under the auspices of the U . S . A t o m ic Energy Commission. ** Present address: Physics Department, University of Southwestern Louisiana, Lafayette, Louisiana, 70501. 324
T =: i Tzi + 2 s t a t e s v i a (p, t) i n v e s t i g a t i o n s w o u l d r e q u i r e k n o w l e d g e of t h e c o n d i t i o n s u n d e r w h i c h the c r o s s s e c t i o n to t h e s e high i s o s p i n s t a t e s w a s a maximum. In o r d e r to obtain f u r t h e r d a t a c o n c e r n i n g t h i s p h e n o m e n o n , the e x t e r n a l p r o t o n b e a m of the B e r k e l e y 88-in. c y c l o t r o n w a s u s e d to b o m b a r d t a r g e t s of 26Mg and 12C. T h e r e s u l t i n g t r i t o n s w e r e i d e n t i f i e d by m e a n s of a AE-E d e t e c t o r t e l e s c o p e and a p o w e r - l a w t y p e p a r t i c l e i d e n t i f i e r [5]. A n g u l a r d i s t r i b u t i o n of t r i t o n s l e a v i n g 24Mg in i t s g r o u n d and f i r s t e x c i t e d (1.37 MeV, 2 +) s t a t e s (L = 0 and 2, r e s p e c t i v e l y ) w e r e o b t a i n e d at e i g h t i n c i d e n t p r o t o n e n e r g i e s b e t w e e n 20.0 and 50.0 MeV. T h e L = 0 t r i t o n a n g u l a r d i s t r i b u t i o n s r e s u l t i n g f r o m the f o r m a t i o n of the 15.43 MeV 0 +, T = 2 s t a t e in 24Mg w e r e o b t a i n e d at s i x p r o t o n e n e r g i e s b e t w e e n 32.5 and 50.0 MeV. In addition, L = 0 and 2 a n g u l a r d i s t r i b u t i o n s f r o m the 12C(p, t)10C g r o u n d and f i r s t e x c i t e d (3.55 MeV, 2 +) s t a t e s , r e s p e c t i v e l y , w e r e i n v e s t i g a t e d at s i x p r o t o n e n e r g i e s b e t w e e n 30.0 and 54.1 MeV. T h e s e L = 0 (p, t) d a t a a r e shown in fig. 1 and t h e L = 2 d a t a in fig. 2. T h e s o l i d c u r v e s in both f i g u r e s r e p r e s e n t t w o - n u c l e o n t r a n s f e r [6] DWBA f i t s to t h e d a t a [7], w h e r e e a c h fit h a s b e e n i n d i v i d u a l l y n o r m a l i z e d . R e a l and i m a g i n a r y w e l l d e p t h s w e r e a l l o w e d to v a r y s m o o t h l y with e n e r gy [8], the a c t u a l v a l u e s of the p a r a m e t e r s u s e d f o l l o w e d quite c l o s e l y t h e a p p r o x i m a t e e x p r e s s i o n s p r e s e n t e d in fig. 1. T h e t w o - n u c l e o n t r a n s -
Volume25B, number 5
PHYSICS
LETTERS
18 September 1967
Z6Mg(p,t) ~4Mg (g.s.) IzC
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Fig. 1. Some L = 0 triton angular distributions resulting from the proton b o m b a r d m e n t of 26Mg and 12C at various incident e n e r g i e s . The solid c u r v e s a r e two-nucleon t r a n s f e r DWBA fits which were generated using the p a r a m e t e r s shown in the figure plus a real and i m a g i n a r y radius p a r a m e t e r of 1.25 fm (E o and Eex c a r e the incident proton e n e r gy and the excitation of the state being fit in MeV, respectively). Each fit has be~n independently n o r m a l i z e d to the data. fer DWBA clearly reproduces the general feat u r e s of t h e o b s e r v e d s h a p e v a r i a t i o n of t h e s e (p, t) a n g u l a r d i s t r i b u t i o n s w i t h i n c i d e n t p r o t o n energy. T h e m a g n i t u d e a n d s h a p e d e t e r i o r a t i o n of t h e a n g u l a r d i s t r i b u t i o n of t h e 15.43 M e V 2 4 M g s t a t e a t low e n e r g i e s i s r e a d i l y a p p a r e n t i n fig. 1. T h e f i r s t m a x i m u m , b e y o n d z e r o d e g r e e s , of t h e characteristic L = 0 shape, clearly seen from 50.0 d o w n t o 38.7 M e V , h a s d i s a p p e a r e d a t
Ep = 32.5 M e V - t h e c r o s s s e c t i o n i n t h a t a u g u l a r r e g i o n h a v i n g d e c r e a s e d a l m o s t a f a c t o r of 8. T h e o t h e r t w o L = 0 d i s t r i b u t i o n s i n fig. 1 a l s o s h o w comparable magnitude and shape deterioration at the lower incident proton energies. The nearly s t a t i c L = 0 s h a p e r e f e r r e d to e a r l i e r i s c l e a r l y e v i d e n t i n t h e d a t a of fig. 1. T h e L = 2 a n g u l a r d i s t r i b u t i o n s s h o w n i n fig. 2 l i k e w i s e s h o w a n a l m o s t s t a t i c s h a p e f o r F ~ > 38.7 M e V , h o w e v e r , like the L = 0 shapes they tend to deteriorate at 325
Volume25B, number 5
PHYSICS LETTERS
26Mg(p,t) Z4Mg (I.57) _ , I , p i i i -7 10 2 - •
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l o w e r p r o t o n e n e r g i e s . It is i n t e r e s t i n g to note that the L = 2 t r a n s i t i o n to the 24Mg (1.37 MeV) state does not show the c r o s s - s e c t i o n r ed u ct i o n seen in the L = 2 t r a n s i t i o n to the 10C (3.35 MeV) state at the l o w e r p r o t o n e n e r g i e s . Fig. 3 p r e s e n t s a s u m m a r y of t h e s e data and t h e i r DWBA fits. In the left p o r t i o n of the f i g u r e a r e plotted the i n t e g r a t e d c r o s s s e c t i o n s v e r s u s the outgoing t r i t o n c.m. en er g y , while the right p o r t i o n of the f i g u r e shows the f i r s t m a x i m u m peak c r o s s s e c t i o n * p l o t t ed ag ai n st t r i t o n c.m. energy. The points connected with dashed l i n es r e p r e s e n t the e x p e r i m e n t a l data and the solid c u r v e s the DWBA p r e d i c t i o n s . The m o s t s t r i k i n g p r o p e r t y of the t h r e e L = 0 t r a n s i t i o n s is that they all s e e m to r e a c h a m a x i m u m i n t e g r a t e d and f i r s t m a x i m u m c r o s s sect i o n a t e t (c.m.) ~ 17 ± 2 MeV. The L = 2 t r a n s i t i o n to the 10C (3.35 MeV) state also shows this b e havior. In c o n t r a s t , both the i n t e g r a t e d and f i r s t m a x i m u m c r o s s s e c t i o n s f o r the 24Mg (1.37 MeV) state a r e st i l l r i s i n g at E t (c.m.) ~ 8 MeV. An i n t e r c o m p a r i s o n of figs. 1, 2 and 3 shows that the c h a r a c t e r i s t i c (p, t) L = 0 and 2 s h a p e s begin to d e t e r i o r a t e below E t (c.m.) ~ 10 MeV. Hence a s s i g n m e n t of L - t r a n s f e r v a l u e s to unknown (p, t) t r a n s i t i o n s by c o m p a r i n g t h e i r an g u l ar d i s t r i b u tion shapes to known t r a n s i t i o n s could p o s s i b l y be m i s l e a d i n g if the incident e n e r g y i s such that E t (c.m.) < 10 MeV. Since the DWBA a p p e a r s to r e p r o d u c e the o b s e r v e d e n e r g y dependence of t h e s e (p,t) c r o s s s e c t i o n s quite well, s p e c t r o scopic i n f o r m a t i o n e x t r a c t e d f r o m (p, t) r e a c t i o n data using the DWBA should not be affected by t h i s o b s e r v e d s t r o n g e n e r g y dependence.
8O
Fig. 2. Some L = 2 triton angular distributions from the 26Mg(p. t) and 12C(p, t) reactions at various incident proton energies. See caption of fig. 1.
326
18 September 1967
* If the angular distribution shape had deteriorated to the point that no clear first maximum was observable, the peak angle was chosen to be that last observed.
Volume 25B, n u m b e r 5
PHYSICS
(p,t)
Reactions
on
LETTERS
iZC
L=O
2500
18 S e p t e m b e r 1967
and
2SMg
L=O
1500
-
I
I
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I
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.
)
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,
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I
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,
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40
(MeV)
=
0
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I
20 c.m.
energy
,
I
30
i
t
40
(MeV)
F i g . 3. I n t e g r a t e d (10°-60 ° c.m.) and f i r s t m a x i m u m (past 0°) peak c r o s s s e c t i o n s plotted v e r s u s t r i t o n c . m . e n e r g y f o r s o m e L = 0 and L = 2 (p,t) t r a n s i t i o n s to s t a t e s i n 2 4 M g and 10C. T h e data points a r e connected with d a s h e d lines while the solid c u r v e s a r e DWBA p r e d i c t i o n s . All DWBA v a l u e s for a given s t a t e have the s a m e n o r m a l i z a t i o n .
References 1. R . 1 . M c G r a t h , S . W . C o s p e r and J . C e r n y , P h y s . Rev. L e t t e r s 18 (1967) 243. 2. G . T . G a r v e y , J . C e r n y and R. H. Pehl, P h y s . Rev. L e t t e r s 12 (1964) 726. 3. J . C e r n y , C. D~traz and R. H. Pehl, P h y s . Rev. 152 (1966) 950. 4. G. Bassani, N.M. Hintz and C. D. Kavaloski, Phys. Rev. 136 (1964) BI006; G. Bassani, N.M. Hintz, C.D. Kavaloski, J.R. Maxwell and G. M. Reynolds, Phys. Rev. 139 (1965) B830.
5. F . S . Goulding, D . A . Landis, J. C e r n y and R. H. Pehl, Nucl. I n s t r . and Methods 31 (1964) 1. 6. N . K . G l e n d e n n i n g , P h y s . Rev. 137 (1965) B102. 7. F o r a m o r e c o m p l e t e d i s c u s s i o n of this DWBA code, s e e D . G . F l e m i n g , J. C e r n y , C . C . M a p l e s and N.K. Glendenning, to be published. 8. F o r e x a m p l e s of optical model p a r a m e t e r v a r i a t i o n with e n e r g y , see: F . G . P e r e y , P h y s . Rev. 131 (1963) 745 ; F. Bjorldund, P r o c . I n t e r n . Conf. on N u c l e a r Optical Model, T h e F l o r i d a State U n i v e r s i t y (Rose P r i n t i n g Co., 1959) p. 1.
327
PHYSICS
References 1. P.Stoler. M.Slagowitz, W.Makofske and T . H . K r u se. Phys. Rev. ]55 (1967) 1334. 2. P.H.Stelson and L. Grodzins, Nuclear Data, SectionA. Vol. 1 (1965) 21.
LETTERS
18 September 1967
3. G.R.Stachler, Nucl. Phys. A91 (1967) 75; T. Tamura and T. Terasawa, to be published. 4. T . T a m u r a , Rev. Mod. Phys. 37 (1965} 679.
ENERGY DEPENDENCE OF 26Mg(p,t)24Mg L = 0 AND L = 2 ANGULAR-DISTRIBUTION
AND
12C(p,t)10C SHAPES *
S. W. C O S P E R **,. H. B R U N N A D E R , J. C E R N Y and L. M c G R A T H Lawrence Radiation Laboratory and Department of Chemistry, University of California. Berkeley. CaliJbrnia. USA Received 11 August 1967
Though (p. t) angular distributions with L = 0 and 2 normally show a static behavior, their measurement on ZffMg and 12C targets for proton energies between 20 and 54 MeV shows a marked shape and magnitude deterioration at the lower energies. These results are compared to two-nucleon transfer DWBA theory. D u r i n g a r e c e n t e x p e r i m e n t [1] in w h i c h t h e l o w e s t T = 2 (15.43 M e V ; 0 +) s t a t e in 24Mg w a s p o p u l a t e d via t h e 26Mg(p, t) r e a c t i o n , it w a s n o t e d that t h e t y p i c a l L = 0 t r i t o n a n g u l a r d i s t r i b u t i o n of t h i s s t a t e [2] s h o w e d a m a r k e d m a g n i tude and s h a p e d e t e r i o r a t i o n w h e n the i n c i d e n t p r o t o n e n e r g y w a s l o w e r e d f r o m 38.7 to 32.5 MeV. T h a t both the m a g n i t u d e and s h a p e of t h i s angular distribution could undergo such a drastic c h a n g e with only a 6 MeV c h a n g e in i n c i d e n t p r o ton e n e r g y n e a r E _ ~ 35 MeV a p p e a r e d to be of i, c o n s i d e r a b l e i n t e r e s t f o r t h r e e r e a s o n s : a) M o s t o t h e r L = 0 and L = 2 (p, t) a n g u l a r d i s t r i b u t i o n s , p r i m a r i l y i n v o l v i n g r e l a t i v e l y high c . m . e n e r g y t r i t o n s , had shown a n e a r l y s t a t i c s h a p e w h i c h c h a n g e d s l o w l y with t a r g e t m a s s n u m b e r [ c . f . r e f s . 3 and 4] - a f a c t w h i c h had b e e n u s e d to a s s i g n L = 0 o r L = 2 t r a n s f e r to unknown (p, t) and (p, 3He) a n g u l a r d i s t r i b u t i o n s ; b) T h i s m a g n i t u d e and s h a p e d e t e r i o r a t i o n , if not p r e d i c t e d by c u r rent two-nucleon transfer theory, could cause u n c e r t a i n t i e s in t h e s p e c t r o s c o p i c i n f o r m a t i o n e x t r a c t e d f r o m s o m e (p, t) r e a c t i o n d a t a ; and c) Any e x p e r i m e n t s d i r e c t e d t o w a r d e s t a b l i s h i n g the l o c a t i o n [2] o r d e c a y p r o p e r t i e s [1] of * Work performed under the auspices of the U . S . A t o m ic Energy Commission. ** Present address: Physics Department, University of Southwestern Louisiana, Lafayette, Louisiana, 70501. 324
T =: i Tzi + 2 s t a t e s v i a (p, t) i n v e s t i g a t i o n s w o u l d r e q u i r e k n o w l e d g e of t h e c o n d i t i o n s u n d e r w h i c h the c r o s s s e c t i o n to t h e s e high i s o s p i n s t a t e s w a s a maximum. In o r d e r to obtain f u r t h e r d a t a c o n c e r n i n g t h i s p h e n o m e n o n , the e x t e r n a l p r o t o n b e a m of the B e r k e l e y 88-in. c y c l o t r o n w a s u s e d to b o m b a r d t a r g e t s of 26Mg and 12C. T h e r e s u l t i n g t r i t o n s w e r e i d e n t i f i e d by m e a n s of a AE-E d e t e c t o r t e l e s c o p e and a p o w e r - l a w t y p e p a r t i c l e i d e n t i f i e r [5]. A n g u l a r d i s t r i b u t i o n of t r i t o n s l e a v i n g 24Mg in i t s g r o u n d and f i r s t e x c i t e d (1.37 MeV, 2 +) s t a t e s (L = 0 and 2, r e s p e c t i v e l y ) w e r e o b t a i n e d at e i g h t i n c i d e n t p r o t o n e n e r g i e s b e t w e e n 20.0 and 50.0 MeV. T h e L = 0 t r i t o n a n g u l a r d i s t r i b u t i o n s r e s u l t i n g f r o m the f o r m a t i o n of the 15.43 MeV 0 +, T = 2 s t a t e in 24Mg w e r e o b t a i n e d at s i x p r o t o n e n e r g i e s b e t w e e n 32.5 and 50.0 MeV. In addition, L = 0 and 2 a n g u l a r d i s t r i b u t i o n s f r o m the 12C(p, t)10C g r o u n d and f i r s t e x c i t e d (3.55 MeV, 2 +) s t a t e s , r e s p e c t i v e l y , w e r e i n v e s t i g a t e d at s i x p r o t o n e n e r g i e s b e t w e e n 30.0 and 54.1 MeV. T h e s e L = 0 (p, t) d a t a a r e shown in fig. 1 and t h e L = 2 d a t a in fig. 2. T h e s o l i d c u r v e s in both f i g u r e s r e p r e s e n t t w o - n u c l e o n t r a n s f e r [6] DWBA f i t s to t h e d a t a [7], w h e r e e a c h fit h a s b e e n i n d i v i d u a l l y n o r m a l i z e d . R e a l and i m a g i n a r y w e l l d e p t h s w e r e a l l o w e d to v a r y s m o o t h l y with e n e r gy [8], the a c t u a l v a l u e s of the p a r a m e t e r s u s e d f o l l o w e d quite c l o s e l y t h e a p p r o x i m a t e e x p r e s s i o n s p r e s e n t e d in fig. 1. T h e t w o - n u c l e o n t r a n s -
Volume25B, number 5
PHYSICS
LETTERS
18 September 1967
Z6Mg(p,t) ~4Mg (g.s.) IzC
103
o.r
E0 (M~V)
,o' \ t
50.0
1o 2
~-25°
io ~
~46.0
io z
1 o.i
[
~
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"'
3o
io 3
I0 z
io 2
,o2
I0 3
Io 3
ol
102
io 2
0
~.<. i ,o. ~\1 ,o
"
20
Io
..
40
o
60
80 0 20 8c.m. (deg)
"Z
20
40
60
80
i0 ~
50.0
i
I°Z
40
60
80
I00
204o'ed'8o
l°'o
ZeMg (p,t) ZgMg (15.43;T=2) •
t
1V
io ~
IOlo
,o,.,v,
\---54"1 /
,o% '°1 \ ~
io 2
(p,t) IOC(gs.)
'
'.
'
PA-gAMETERS FOR DWBA FITS
3817 '
REAL AND I~AG. IqUCT~.US DIFFUSENESS (f)
REAL AND Ib~G. (SURFACE A3SORBTION) WELL DEP~I~HS (MeV)
26Mg
0.50
V
24Mg
0.60
v ~18z.5 - o.~ ( ~ - Eeoc)
~ 7~.0 - 0-5 E P W s ~ i0.0 + 0.2 Ep
WS ~ 29.6 + O.Z (Ep - Eexc) lZ C
0.~.0
v
~ 85=o- 0.5 E
P
wB ~ 19.o + 0.2 Ep i01
iO i lO C
0,60
V
~180.0 - O.5 Ep + 0.6 Eex c
Ws ~ 27.0 + 0.2 Ep - 0.3 Eex c
'°'o zo
'°°6 2 o ' 4 o - 6 o 8o ec.m. (deg)
Fig. 1. Some L = 0 triton angular distributions resulting from the proton b o m b a r d m e n t of 26Mg and 12C at various incident e n e r g i e s . The solid c u r v e s a r e two-nucleon t r a n s f e r DWBA fits which were generated using the p a r a m e t e r s shown in the figure plus a real and i m a g i n a r y radius p a r a m e t e r of 1.25 fm (E o and Eex c a r e the incident proton e n e r gy and the excitation of the state being fit in MeV, respectively). Each fit has be~n independently n o r m a l i z e d to the data. fer DWBA clearly reproduces the general feat u r e s of t h e o b s e r v e d s h a p e v a r i a t i o n of t h e s e (p, t) a n g u l a r d i s t r i b u t i o n s w i t h i n c i d e n t p r o t o n energy. T h e m a g n i t u d e a n d s h a p e d e t e r i o r a t i o n of t h e a n g u l a r d i s t r i b u t i o n of t h e 15.43 M e V 2 4 M g s t a t e a t low e n e r g i e s i s r e a d i l y a p p a r e n t i n fig. 1. T h e f i r s t m a x i m u m , b e y o n d z e r o d e g r e e s , of t h e characteristic L = 0 shape, clearly seen from 50.0 d o w n t o 38.7 M e V , h a s d i s a p p e a r e d a t
Ep = 32.5 M e V - t h e c r o s s s e c t i o n i n t h a t a u g u l a r r e g i o n h a v i n g d e c r e a s e d a l m o s t a f a c t o r of 8. T h e o t h e r t w o L = 0 d i s t r i b u t i o n s i n fig. 1 a l s o s h o w comparable magnitude and shape deterioration at the lower incident proton energies. The nearly s t a t i c L = 0 s h a p e r e f e r r e d to e a r l i e r i s c l e a r l y e v i d e n t i n t h e d a t a of fig. 1. T h e L = 2 a n g u l a r d i s t r i b u t i o n s s h o w n i n fig. 2 l i k e w i s e s h o w a n a l m o s t s t a t i c s h a p e f o r F ~ > 38.7 M e V , h o w e v e r , like the L = 0 shapes they tend to deteriorate at 325
Volume25B, number 5
PHYSICS LETTERS
26Mg(p,t) Z4Mg (I.57) _ , I , p i i i -7 10 2 - •
102
02
I 02
~
0
I
02 ~io'~
-25.0
I02
i ,,
20.0
~
A 0
1
, I-
0
20
40
60
80
12C (p, t)
i0,I
0
Ep(MeV) ,
,
20
40
~
E
60
J_
80
I°C ( 3 . 3 5 )
1 0 3 ~
102~
~_,
~ i o3t
~
TE'p(~leV ~-
k 35.0
102
102'
103` I02 0
•
,/
/46.0
IOI~L
~ ~ L Z 20
40
r J~
60
80
~ c.ril.
p ~~ , ,
0 20 (deg)
40
6O
,
l o w e r p r o t o n e n e r g i e s . It is i n t e r e s t i n g to note that the L = 2 t r a n s i t i o n to the 24Mg (1.37 MeV) state does not show the c r o s s - s e c t i o n r ed u ct i o n seen in the L = 2 t r a n s i t i o n to the 10C (3.35 MeV) state at the l o w e r p r o t o n e n e r g i e s . Fig. 3 p r e s e n t s a s u m m a r y of t h e s e data and t h e i r DWBA fits. In the left p o r t i o n of the f i g u r e a r e plotted the i n t e g r a t e d c r o s s s e c t i o n s v e r s u s the outgoing t r i t o n c.m. en er g y , while the right p o r t i o n of the f i g u r e shows the f i r s t m a x i m u m peak c r o s s s e c t i o n * p l o t t ed ag ai n st t r i t o n c.m. energy. The points connected with dashed l i n es r e p r e s e n t the e x p e r i m e n t a l data and the solid c u r v e s the DWBA p r e d i c t i o n s . The m o s t s t r i k i n g p r o p e r t y of the t h r e e L = 0 t r a n s i t i o n s is that they all s e e m to r e a c h a m a x i m u m i n t e g r a t e d and f i r s t m a x i m u m c r o s s sect i o n a t e t (c.m.) ~ 17 ± 2 MeV. The L = 2 t r a n s i t i o n to the 10C (3.35 MeV) state also shows this b e havior. In c o n t r a s t , both the i n t e g r a t e d and f i r s t m a x i m u m c r o s s s e c t i o n s f o r the 24Mg (1.37 MeV) state a r e st i l l r i s i n g at E t (c.m.) ~ 8 MeV. An i n t e r c o m p a r i s o n of figs. 1, 2 and 3 shows that the c h a r a c t e r i s t i c (p, t) L = 0 and 2 s h a p e s begin to d e t e r i o r a t e below E t (c.m.) ~ 10 MeV. Hence a s s i g n m e n t of L - t r a n s f e r v a l u e s to unknown (p, t) t r a n s i t i o n s by c o m p a r i n g t h e i r an g u l ar d i s t r i b u tion shapes to known t r a n s i t i o n s could p o s s i b l y be m i s l e a d i n g if the incident e n e r g y i s such that E t (c.m.) < 10 MeV. Since the DWBA a p p e a r s to r e p r o d u c e the o b s e r v e d e n e r g y dependence of t h e s e (p,t) c r o s s s e c t i o n s quite well, s p e c t r o scopic i n f o r m a t i o n e x t r a c t e d f r o m (p, t) r e a c t i o n data using the DWBA should not be affected by t h i s o b s e r v e d s t r o n g e n e r g y dependence.
8O
Fig. 2. Some L = 2 triton angular distributions from the 26Mg(p. t) and 12C(p, t) reactions at various incident proton energies. See caption of fig. 1.
326
18 September 1967
* If the angular distribution shape had deteriorated to the point that no clear first maximum was observable, the peak angle was chosen to be that last observed.
Volume 25B, n u m b e r 5
PHYSICS
(p,t)
Reactions
on
LETTERS
iZC
L=O
2500
18 S e p t e m b e r 1967
and
2SMg
L=O
1500
-
I
I
'
'
I
'
i
'
i
I 0 0 0 _ I°C(g.s.)
'°C(g.s.)
,25o 500 c o
0 -
b
-
Z4Mg
I
'
I
o
,
(g.s)
I000
-
-
24 Mg (
g
.
s
.
)
~
1250
.~
i
~,
o
I
500 0
'
,
24"Mg (15.43)
~ 6
I
0o
I0
i
30
20
40
o cD
t
~
50
~
o
'
20
30
,
I0
0
40
u
L=2
,ooo t
I I°C
(3.35)
500 -
E
500
E ._ x
250
o
~D
~
I
o
I o
a
,
125
o
_o
I
24 Mg(15.43)
L--2 [
'
I
I
I
~
1
I
I
=
E 0
'
500
I
t
I
'
I
o
' t2
Z 4 M g ( I . ~ __
0
,
I
I
I0 Triton
J~
20 c.m.
energy
,
250 o
I
:50
,
24Mg(I.37)
40
(MeV)
=
0
I0 Triton
I
20 c.m.
energy
,
I
30
i
t
40
(MeV)
F i g . 3. I n t e g r a t e d (10°-60 ° c.m.) and f i r s t m a x i m u m (past 0°) peak c r o s s s e c t i o n s plotted v e r s u s t r i t o n c . m . e n e r g y f o r s o m e L = 0 and L = 2 (p,t) t r a n s i t i o n s to s t a t e s i n 2 4 M g and 10C. T h e data points a r e connected with d a s h e d lines while the solid c u r v e s a r e DWBA p r e d i c t i o n s . All DWBA v a l u e s for a given s t a t e have the s a m e n o r m a l i z a t i o n .
References 1. R . 1 . M c G r a t h , S . W . C o s p e r and J . C e r n y , P h y s . Rev. L e t t e r s 18 (1967) 243. 2. G . T . G a r v e y , J . C e r n y and R. H. Pehl, P h y s . Rev. L e t t e r s 12 (1964) 726. 3. J . C e r n y , C. D~traz and R. H. Pehl, P h y s . Rev. 152 (1966) 950. 4. G. Bassani, N.M. Hintz and C. D. Kavaloski, Phys. Rev. 136 (1964) BI006; G. Bassani, N.M. Hintz, C.D. Kavaloski, J.R. Maxwell and G. M. Reynolds, Phys. Rev. 139 (1965) B830.
5. F . S . Goulding, D . A . Landis, J. C e r n y and R. H. Pehl, Nucl. I n s t r . and Methods 31 (1964) 1. 6. N . K . G l e n d e n n i n g , P h y s . Rev. 137 (1965) B102. 7. F o r a m o r e c o m p l e t e d i s c u s s i o n of this DWBA code, s e e D . G . F l e m i n g , J. C e r n y , C . C . M a p l e s and N.K. Glendenning, to be published. 8. F o r e x a m p l e s of optical model p a r a m e t e r v a r i a t i o n with e n e r g y , see: F . G . P e r e y , P h y s . Rev. 131 (1963) 745 ; F. Bjorldund, P r o c . I n t e r n . Conf. on N u c l e a r Optical Model, T h e F l o r i d a State U n i v e r s i t y (Rose P r i n t i n g Co., 1959) p. 1.
327