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Excitation of unnatural-parity states in (α, α′) scatterings on O16, Ne20, Mg24 and Si28 at 28.5 MeV
Volume 8, number 5
PHYSICS
LETTERS
1 March 1964
L' ~ n e r g i e c o u l o m b i e n n e s' 6 e r i t a l o r s : 3 e2 Ec - 4 2~2 j (~P I [(FP + Fn)2 - (FP 2 - Fn2)(Tz(i) + Tz(J)) + (Fp - Fn) 2 "rz(i) ~'z(J)] exp ik(xi-xj)l~P) d3__kk k2 • P o u r d e s f o n c t i o n s d ' o n d e du t y p e (2), t e n a n t c o m p t e du c e n t r e de m a s s e , la d i f f 6 r e n c e e n t r e l ' 6 n e r g i e c o u l o m b i e n n e de He 3 eL de H 3 e s t : e2 F p 2 _ Fn2 AE c = - - j ' [F~(,,/3k) + ab Fn(,,/3k)] d 3 lz 27r2 k-2 A v e c un p r o t o n eL un n e u t r o n p o n c t u e l s (Fu = 0, F n = 0) on o b t i e n t AE c = 0.85 MeV, u t i i i s a n t p o u r F p un f a c t e u r g a u s s i e n a v e c a p = 0.7 fm et n ~ g l i ~ e a n t le f a c t e u r de f o r m e du n e u t r o n : ~xEc = 0.72 MeV. On p e u t donc d i r e que, c o m p t e t e n u d e s e r r e u r s e x p ~ r i m e n t a l e s eL de l ' i g n o r a n c e off l ' o n e s t de l a c o r r e c t i o n e x a c t e A a p p o r t e r au p o t e n t i e l c o u l o m b i e n du fair que l ' o n ne s a l t p a s j u s q u ' f i q u e l p o i n t l a s t r u c t u r e de c h a r g e pp d e s p r o t o n s peut ~ t r e m o d i f i ~ e p a r l e u r p r o x i m i t ~ la v a i e u r e x p ~ r i m e n t a l e de 0.76 MeV e s t c o m p a t i b l e a v e c un f a c t e u r de f o r m e de n e u t r o n n ~ g l i g e a b l e p o u r k ~< 2 f m - 1 .
R e f ere;~ces 1) L.I. S c h i f f e t a l . . Phys. Rev. Letters 11 (1963) 387. 2) H.S. Valk, Phys. Letters 7 (1963) 335.
EXCITATION
OF UNNATURAL-PARITY STATES IN (~,c~') SCATTERINGS O N 0 16 , N e 2 0 , Mg 24 AND Si 28 AT 28.5 MeV J. K O K A M E and K. F U K U N A G A
Laboratory of Nuclear Science, Institute_fo~" Chemical Research, Kyoto Univc~'sily, Kyolo, Jaban and N. INOUE and H. N A K A M U R A
Departn~ent of Physics, Faculty of Science, Kyolo University, Kyoto, Japan Received 4 February 1964
R e c e n t l y u n n a t u r a l - p a r i t y s t a t e s ( 2 - , 3 + etc) in s e v e r a l l i g h t n u c l e i s e e m to b e f a i r l y w e l l e s t a b f i s h e d 1-4). E x c i t a t i o n s of t h e s e s t a t e s of z e r o s p i n t a r g e t n u c l e i b y a l p h a p a r t i c l e s ( z e r o spin) a r e v e r y i n t e r e s t i n g , b e c a u s e t h e y c a n not be e x c i t e d in (a, a') scatterings by simple first order direct int e r a c t i o n s on a c c o u n t of the p a r i t y c o n s e r v a t i o n a s d i s c u s s e d in the r e p o r t s of E i d s o n a n d C r a m e r 5) a n d o t h e r s . On the o t h e r hand, m a n y of the i n e l a s t i c s c a t t e r i n g s of a l p h a p a r t i c l e s l e a d i n g to the u s u a l r e s i d u a l s t a t e s c a n be now u n d e r s t o o d a s e x c i t a t i o n s of o n e - o r m o r e - p h o n o n s t a t e s t h r o u g h a d i r e c t one s t e p o r m u l t i p l e e x c i t a t i o n in the e n e r g y r a n g e a b o v e a few t e n s of MeV 6 - 1 2 ) . T h u s , i n v e s t i g a t i o n s e x c i t i n g u n n a t u r a l - p a r i t y l e v e l s s e e m to b e u s e f u l in u n d e r s t a n d i n g both the r e a c t i o n m e c h a n i s m a n d t h e l e v e l s t r u c t u r e of t h e s e s t a t e s . R e l a t i v e l y few e x p e r i m e n t s 5, 12, 13) h a v e b e e n 342
p e r f o r m e d on t h i s p r o b l e m s o that m o r e e x p e r i m e n t a l i n f o r m a t i o n s e e m s to be n e c e s s a r y , e s p e c i a l l y at d i f f e r e n t i n c i d e n t e n e r g i e s . We h a v e i n v e s t i g a t e d the p r o b l e m a t E a = 28.5 MeV on 0 1 6 , Ne20, Mg24 a n d Si 28 at f o r w a r d a n g l e s s m a l l e r t h a n 90 ° l a b , in w h i c h r e g i o n the y i e l d i s m o s t i n t e r e s t i n g in c o n n e c t i o n w i t h the r e a c t i o n m e c h a nisms. A b e a m of a l p h a p a r t i c l e s a c c e l e r a t e d to a b o u t 28.5 MeV by the 105 c m c y c l o t r o n of K y o t o Univ e r s i t y w a s l e d to a s c a t t e r i n g c h a m b e r t h r o u g h a c o u p l e of q u a d r u p o l e m a g n e t s . T h e e x p e r i m e n t a l arrangement was the same as reported elsew h e r e 14). F o r a d e t e c t o r of s c a t t e r e d a l p h a p a r ticles a junction detector, RCA C-4-250-2.0, was u s e d . G a s t a r g e t s of n a t u r a l o x y g e n and n a t u r a l n e o n h a d the e f f e c t i v e t h i c k n e s s of 0.41 m g / c m 2 a n d 0.19 m g / c m 2 f o r t h e d e t e c t o r at 900 l a b r e -
Volume 8, number 5
PHYSICS
s p e c t i v e l y . T a r g e t s of n a t u r a l m a g n e s i u m and natu r a l s i l i c o n w e r e 1.00 m g / c m 2 and about 3.3 m g / c m 2 in t h i c k n e s s , r e s p e c t i v e l y . The l a t t e r had r e l a t i v e l y poor u n i f o r m i t y and the absolute c r o s s s e c t i o n was c a l i b r a t e d by c o m p a r i n g the y i e l d with that of an e l a s t i c peak f r o m a t a r g e t of SiO2-foil of which the t h i c k n e s s is 3.25 m g / c m 2. F i g s . 1-4 show the obtained angular d i s t r i b u t i o n s of i n e l a s t i c a l l y s c a t t e r e d alpha p a r t i c l e s f r o m the u n n a t u r a l - p a r i t y s t a t e s of O 16, Ne 20, Mg 24 and Si 28 r e s p e c t i v e l y . (1) O 1 6 ( a , a')O 1 6 . , £ a (c.m.) = 21.8 MeV, Q = -8.88 MeV(2-). The a n g u l a r d i s t r i b u t i o n shows a v e r y c l e a r diff r a c t i o n p a t t e r n . The p e r i o d of the o s c i l l a t i o n is s o m e w h a t long in c o m p a r i s o n with that of the e l a s t i c s c a t t e r i n g . The p h a s e r e l a t i o n of both p a t t e r n s is r a t h e r in phase. The c r o s s s e c t i o n s e e m s to be r e l a t i v e l y l a r g e r than that of other t h r e e nuclei. (2) Ne20(~, ot')Ne20 *, £ot (c.m.) = 22.8 MeV, Q = -4.97 MeV(2-). M a x i m a and m i n i m a of the d i f f r a c t i o n p a t t e r n Lend to s m e a r out at a n g l e s l a r g e r than about 50 °. H o w e v e r , a definite o u t - o f - p h a s e r e l a t i o n to the e l a s t i c s c a t t e r i n g s e e m s to be exist. P o s i t i o n s of m a x i m a and m i n i m a of the p a t t e r n shift to b a c k w a r d a n g l e s a s c o m p a r e d with those of the e l a s t i c s c a t t e r -
ing.
LETTERS
1 March 1964
(3) M g 2 4 ( ~ , ~ ' ) M g 2 4 . , E ~ ( c . m . ) : 24.3 MeV, Q= -5.22 MeV(3+). In this c a s e the peak m e a s u r e d in the pulse height s p e c t r u m was c o v e r e d by an e l a s t i c and ine l a s t i c peak of c a r b o n c o n t a m i n a t i o n at angles b e tween 20 ° ~ 27.5 ° and 67.5 ° ~ 72.5 ° lab r e s p e c t i v e ly. A n g u l a r d i s t r i b u t i o n s of alpha p a r t i c l e s s c a t t e r e d f r o m c a r b o n w e r e m e a s u r e d s e p a r a t e l y at the s a m e incident e n e r g y using a s e l f - s u p p o r t i n g c a r b o n film and M y l a r t a r g e t . A f t e r e s t i m a t i n g the a m o u n t of c a r b o n in m a g n e s i u m f r o m a r e s o l v e d peak, the c o n t r i b u t i o n f r o m the c a r b o n c o n t a m i n a tion was s u b t r a c t e d f r o m the o v e r l a p p i n g peaks. A d a m p i n g in o s c i l l a t i o n in the d i f f r a c t i o n paLt e r n can be o b s e r v e d at a n g l e s of about 50 °. The p h a s e r e l a t i o n to the e l a s t i c s c a t t e r i n g is n e a r l y in phase. (4) Si28(a,oF)Si 2 8 . , E ~ ( c . m . ) = 24.8 MeV, Q = -6.27 MeV(3+). Owing to the t h i c k n e s s and r e l a t i v e l y poor unif o r m i t y of the t a r g e t , the 3 + - l e v e l w a s r e s o l v e d p o o r l y f r o m a d j a c e n t l e v e l s having r e l a t i v e l y l a r g e c r o s s s e c t i o n s . Thus the r e s u l t has m u c h u n c e r tainty in c o m p a r i s o n with above t h r e e c a s e s . Howe v e r , a d i f f r a c t i v e n a t u r e of the p a t t e r n can be s e e n and the p h a s e is f a i r l y in phase with the e l a s t i c , though the m a x i m a (minima) shift to b a c k w a r d angle.
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Fig. 1. Angular distributions of scattered alpha particles leading to the ground state and the 8.88 MeV (2-) level of 016 .
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number 5
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PHYSICS
LETTERS
1 March 1964 t0~
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S u m m a r i z i n g the p r e s e n t r e s u l t s , s o m e c h a r a c t e r i s t i c s of the s c a t t e r i n g in c o m p a r i s o n w i t h t h o s e of l o w e r i n c i d e n t e n e r g i e s c a n be d e s c r i b e d a s f o l lows: (a) T h e f o r w a r d p e a k in the a n g u l a r d i s t r i b u tion i s m o r e p r o m i n e n t and the d i f f r a c t i o n i s m o r e c l e a r . (b) T h e r e a r e f a i r l y d e f i n i t e p h a s e r e l a t i o n s in the d i f f r a c t i o n p a t t e r n s b e t w e e n the u n n a t u r a l p a r i t y s t a t e and the g r o u n d s t a t e . T h e p h a s e r e l a t i o n i s f a i r l y " i n " o r " o u t " of p h a s e c o r r e s p o n d i n g to the m o m e n t u m t r a n s f e r t h r e e o r two r e s p e c t i v e l y , e x c e p t in the c a s e of 0 1 6 w h e r e the r e l a t i o n i s a l m o s t the r e v e r s e . (c) T h e e n e r g y d e p e n d e n c e of the c r o s s section shows a roughly monotonic decrease as f u n c t i o n of the i n c i d e n t e n e r g y . F i g . 5 s h o w s the i n t e g r a t e d c r o s s s e c t i o n s o v e r 15 ° to 80 ° c . m . c a l c u l a t e d on g r a p h s f o r c o n v e n i e n c e of c o m p a r i s o n . A s f o r the d a t a o b t a i n e d by o t h e r a u t h o r s , the c r o s s s e c t i o n s w e r e c a l c u l a t e d f r o m c u r v e s r e p o r t e d in t h e l i t e r a t u r e 5, 12, 13). S e v e r a l p o s s i b l e m e c h a n i s m s f o r the e x c i t a t i o n of u n n a t u r a l - p a r i t y s t a t e s a r e a l r e a d y d i s c u s s e d in t h e l i t e r a t u r e by E i d s o n a n d C r a m e r 5). T h e s e ¢.re (1) a c o m p o u n d n u c l e u s f o r m a t i o n , (2) a s p i n - o r b i t i n t e r a c t i o n , (3) a n e x change process (knock-out or heavy particle stripping), a n d (4) s u c c e s s i v e phonon p r o d u c t i o n s o r a multiple scattering process.
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Fig. 3. Angular distributions of scattered alpha p a r t i c l e s leading to the ground state and the 5.22 MeV (3+) level of Mg24.
344
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Fig. 4. Angular distributions of scattered alpha p a r t i c l e s leading to the ground state and the 6.27 MeV (3+) level of Si 28.
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Fig. 5. Integrated c r o s s sections over 15 ° to 80 ° c . m . of the yields from unnatural-parity states of O 16, Ne20, Mg24 and Si 28. Points corresponding to energies l e s s than 20 MeV (c. m.) were obtained by calculation along curves in refs. 5, 12, 13).
Volume 8, number 5
PHYSICS
LETTERS
1 March 1964
In the p r e s e n t r e s u l t s the f i r s t p r o c e s s could be p l a i n e d a s a s t a t e of t h r e e p h o n o n s of a n g u l a r m o e x c l u d e d for m a i n r e a c t i o n m e c h a n i s m s , b e c a u s e m e n t u m two 16), s i n c e the height of e x c i t a t i o n of the a n g u l a r d i s t r i b u t i o n shows a f a i r l y d i s t i n c t difthe l e v e l s e e m s to be not so u n r e a s o n a b l e for the f r a c t i o n p a t t e r n and p r o m i n e n t f o r w a r d peak. A s for s t a t e of t h r e e p h o n o n s . E x c i t a t i o n s of the t h r e e the s e c o n d p r o c e s s , it s e e m s to be not the c a s e if phonon s t a t e w e r e r e c e n t l y t r e a t e d t h e o r e t i c a l l y by S a t h l e r ' s e s t i m a t e s for the e n e r g y d e p e n d e n c e of Q u e s n e 17) but the c r o s s s e c t i o n s of t h e s e s t a t e s t h e s e c r o s s s e c t i o n s a r e v a l i d . A c c o r d i n g to h i s by the s u c c e s s i v e m u l t i p l e phonon p r o d u c t i o n w e r e s t a t e m e n t quoted by E i d s o n and C r a m e r 5), the not c a l c u l a t e d . T h u s a s t r a i g h t f o r w a r d c o m p a r i s o n c r o s s s e c t i o n of the s p i n - o r b i t i n t e r a c t i o n m u s t i n with the t h e o r y a n d the p r e s e n t d a t a c a n n o t be c r e a s e a s the i n c i d e n t e n e r g y i n c r e a s e s . On the c o n - m a d e . t r a r y it s e e m s to d e c r e a s e e x p e r i m e n t a l l y a s shown i n fig. 5. T h e c a s e (3) c o u l d not be e x c l u d e d f r o m At p r e s e n t , no d e f i n i t e c o n c l u s i o n c a n be m a d e p r o b a b l e r e a c t i o n m e c h a n i s m s . H o w e v e r , it i s q u e s - e x c e p t that the r e a c t i o n s m o s t p r o b a b l y t a k e p l a c e t i o n a b l e that in a l l the e n e r g y r a n g e 15 ~ 25 MeV t h r o u g h the e x c h a n g e p r o c e s s a n d / o r the s u c c e s (c.m.) the e x c i t a t i o n o c c u r s t h r o u g h the e x c h a n g e s i v e m u l t i p l e p r o c e s s at an e n e r g y of a few t e n s of p r o c e s s (knock-out) only, b e c a u s e the f o r w a r d c r o s s MeV. s e c t i o n s d e c r e a s e m a r k e d l y in t h i s e n e r g y r a n g e . In t h i s c a s e the c o n s i d e r a b l e c o n t r i b u t i o n f r o m the c o m p o u n d f o r m a t i o n m a y have to be t a k e n into c o n References s i d e r a t i o n at the l o w e r e n e r g y r e g i o n . 1) T. Lauritzen and F.Ajzenberg-Selove, Nuclear Data In view of m a n y s u c c e s s e s in u n d e r s t a n d i n g Sheets: Energy Levels of Light Nuclei. May 1962. ( ~ , ~ ' ) s c a t t e r i n g s a s e x c i t a t i o n s of p h o n o n - s t a t e s in 2) P. M. Endt and C. Van der Leun, Nuclear Phys. 34 the v i b r a t i o n a l r e g i o n , the l a s t p r o c e s s (4), e s p e c i a l (1962) 1. ly the s u c c e s s i v e phonon p r o d u c t i o n s e e m s to be 3) A . E . L i t h e r l a n d et al., Phys. Rev. Letters 7 (1961) 98. w o r t h y of a t h e o r e t i c a l c a l c u l a t i o n in c o n n e c t i o n with 4) J. E. Evans et al., Phys. Rev. 131 (1963) 818. 5) W.W. Eidson and J. G. Cramer J r . , Phys. Rev. Letters a b e t t e r u n d e r s t a n d i n g of the s t r u c t u r e of the u n n a t 9 (1962) 497. u r a l - p a r i t y s t a t e . The e x c i t a t i o n of a n o n s i m u l t a n e o u s 6) H.W.Broek, Physics Letters 3 (1962) 132; Phys. Rev. double e x c i t a t i o n w a s c a l c u l a t e d by Buck 11) with a 130 (1963) 1914. DWBA m e t h o d in the c a s e of a t w o - p h o n o n s t a t e h a v 7) M. Barloutand-Crut et al., Physics Letters 6 (1963) 222. ing n a t u r a l p a r i t y (4 +) i n the N i 5 8 ( ~ , ~ ' ) r e a c t i o n at 8) J.S. Blair, Phys. Rev. 115 (1959) 982. 43 MeV. He showed that the y i e l d of this p r o c e s s is J . S . B l a i r et al., Phys. Rev. 125 (1962) 1625. r a t h e r l a r g e r than that of o n e - s t e p d i r e c t e x c i t a t i o n 9) N.Austern et al., Phys. Rev.128 (1962) 733. of the s t a t e . The s t a t e of 2- in O 16 a n d Ne 20 m a y be 10) R.H. Lemmer et al., Phys. Rev. 124 (1961) 1155. c o n s t r u c t e d a s a s t a t e of two p h o n o n s h a v i n g the a n 11) B.Buck, Phys. Rev. 127 (1962) 940. 12) J . C . C o r e l l i et al., Phys. Rev. 116 (1959) 1184. g u l a r m o m e n t u m two a n d t h r e e r e s p e c t i v e l y 15) . 13} L. Seidlitz et al., Phys. Rev. 110 (1958) 682. T h e r e f o r e , it s e e m s to be i n t e r e s t i n g w h e t h e r the 14) K . K i m u r a e t a l . , J.Phys.Soc. Japan 17 (1962) 9. p h a s e r e l a t i o n a n d c r o s s s e c t i o n s of the p r e s e n t 15) P.O. Lipas and J . P . Davidson, Nuclear Phys. 26 c a s e s c o u l d be s a t i s f a c t o r i l y e x p l a i n e d by the s i m i l a r (1961) 8O. e x t e n d e d c a l c u l a t i o n a s p e r f o r m e d by Buck. 16) J.M.Arafijo, Nuclear reactions (North-Holland Publishing Co., Amsterdam, 1962) Vol. II, p. 195. As for the 3 + s t a t e of Mg 24 a n d Si 28, one p o s s i 17) C. Quesne, Nuclear Phys.46 (1963) 145. b i l i t y a m o n g o t h e r s i s that the s t a t e m a y be ex-
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L' ~ n e r g i e c o u l o m b i e n n e s' 6 e r i t a l o r s : 3 e2 Ec - 4 2~2 j (~P I [(FP + Fn)2 - (FP 2 - Fn2)(Tz(i) + Tz(J)) + (Fp - Fn) 2 "rz(i) ~'z(J)] exp ik(xi-xj)l~P) d3__kk k2 • P o u r d e s f o n c t i o n s d ' o n d e du t y p e (2), t e n a n t c o m p t e du c e n t r e de m a s s e , la d i f f 6 r e n c e e n t r e l ' 6 n e r g i e c o u l o m b i e n n e de He 3 eL de H 3 e s t : e2 F p 2 _ Fn2 AE c = - - j ' [F~(,,/3k) + ab Fn(,,/3k)] d 3 lz 27r2 k-2 A v e c un p r o t o n eL un n e u t r o n p o n c t u e l s (Fu = 0, F n = 0) on o b t i e n t AE c = 0.85 MeV, u t i i i s a n t p o u r F p un f a c t e u r g a u s s i e n a v e c a p = 0.7 fm et n ~ g l i ~ e a n t le f a c t e u r de f o r m e du n e u t r o n : ~xEc = 0.72 MeV. On p e u t donc d i r e que, c o m p t e t e n u d e s e r r e u r s e x p ~ r i m e n t a l e s eL de l ' i g n o r a n c e off l ' o n e s t de l a c o r r e c t i o n e x a c t e A a p p o r t e r au p o t e n t i e l c o u l o m b i e n du fair que l ' o n ne s a l t p a s j u s q u ' f i q u e l p o i n t l a s t r u c t u r e de c h a r g e pp d e s p r o t o n s peut ~ t r e m o d i f i ~ e p a r l e u r p r o x i m i t ~ la v a i e u r e x p ~ r i m e n t a l e de 0.76 MeV e s t c o m p a t i b l e a v e c un f a c t e u r de f o r m e de n e u t r o n n ~ g l i g e a b l e p o u r k ~< 2 f m - 1 .
R e f ere;~ces 1) L.I. S c h i f f e t a l . . Phys. Rev. Letters 11 (1963) 387. 2) H.S. Valk, Phys. Letters 7 (1963) 335.
EXCITATION
OF UNNATURAL-PARITY STATES IN (~,c~') SCATTERINGS O N 0 16 , N e 2 0 , Mg 24 AND Si 28 AT 28.5 MeV J. K O K A M E and K. F U K U N A G A
Laboratory of Nuclear Science, Institute_fo~" Chemical Research, Kyoto Univc~'sily, Kyolo, Jaban and N. INOUE and H. N A K A M U R A
Departn~ent of Physics, Faculty of Science, Kyolo University, Kyoto, Japan Received 4 February 1964
R e c e n t l y u n n a t u r a l - p a r i t y s t a t e s ( 2 - , 3 + etc) in s e v e r a l l i g h t n u c l e i s e e m to b e f a i r l y w e l l e s t a b f i s h e d 1-4). E x c i t a t i o n s of t h e s e s t a t e s of z e r o s p i n t a r g e t n u c l e i b y a l p h a p a r t i c l e s ( z e r o spin) a r e v e r y i n t e r e s t i n g , b e c a u s e t h e y c a n not be e x c i t e d in (a, a') scatterings by simple first order direct int e r a c t i o n s on a c c o u n t of the p a r i t y c o n s e r v a t i o n a s d i s c u s s e d in the r e p o r t s of E i d s o n a n d C r a m e r 5) a n d o t h e r s . On the o t h e r hand, m a n y of the i n e l a s t i c s c a t t e r i n g s of a l p h a p a r t i c l e s l e a d i n g to the u s u a l r e s i d u a l s t a t e s c a n be now u n d e r s t o o d a s e x c i t a t i o n s of o n e - o r m o r e - p h o n o n s t a t e s t h r o u g h a d i r e c t one s t e p o r m u l t i p l e e x c i t a t i o n in the e n e r g y r a n g e a b o v e a few t e n s of MeV 6 - 1 2 ) . T h u s , i n v e s t i g a t i o n s e x c i t i n g u n n a t u r a l - p a r i t y l e v e l s s e e m to b e u s e f u l in u n d e r s t a n d i n g both the r e a c t i o n m e c h a n i s m a n d t h e l e v e l s t r u c t u r e of t h e s e s t a t e s . R e l a t i v e l y few e x p e r i m e n t s 5, 12, 13) h a v e b e e n 342
p e r f o r m e d on t h i s p r o b l e m s o that m o r e e x p e r i m e n t a l i n f o r m a t i o n s e e m s to be n e c e s s a r y , e s p e c i a l l y at d i f f e r e n t i n c i d e n t e n e r g i e s . We h a v e i n v e s t i g a t e d the p r o b l e m a t E a = 28.5 MeV on 0 1 6 , Ne20, Mg24 a n d Si 28 at f o r w a r d a n g l e s s m a l l e r t h a n 90 ° l a b , in w h i c h r e g i o n the y i e l d i s m o s t i n t e r e s t i n g in c o n n e c t i o n w i t h the r e a c t i o n m e c h a nisms. A b e a m of a l p h a p a r t i c l e s a c c e l e r a t e d to a b o u t 28.5 MeV by the 105 c m c y c l o t r o n of K y o t o Univ e r s i t y w a s l e d to a s c a t t e r i n g c h a m b e r t h r o u g h a c o u p l e of q u a d r u p o l e m a g n e t s . T h e e x p e r i m e n t a l arrangement was the same as reported elsew h e r e 14). F o r a d e t e c t o r of s c a t t e r e d a l p h a p a r ticles a junction detector, RCA C-4-250-2.0, was u s e d . G a s t a r g e t s of n a t u r a l o x y g e n and n a t u r a l n e o n h a d the e f f e c t i v e t h i c k n e s s of 0.41 m g / c m 2 a n d 0.19 m g / c m 2 f o r t h e d e t e c t o r at 900 l a b r e -
Volume 8, number 5
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s p e c t i v e l y . T a r g e t s of n a t u r a l m a g n e s i u m and natu r a l s i l i c o n w e r e 1.00 m g / c m 2 and about 3.3 m g / c m 2 in t h i c k n e s s , r e s p e c t i v e l y . The l a t t e r had r e l a t i v e l y poor u n i f o r m i t y and the absolute c r o s s s e c t i o n was c a l i b r a t e d by c o m p a r i n g the y i e l d with that of an e l a s t i c peak f r o m a t a r g e t of SiO2-foil of which the t h i c k n e s s is 3.25 m g / c m 2. F i g s . 1-4 show the obtained angular d i s t r i b u t i o n s of i n e l a s t i c a l l y s c a t t e r e d alpha p a r t i c l e s f r o m the u n n a t u r a l - p a r i t y s t a t e s of O 16, Ne 20, Mg 24 and Si 28 r e s p e c t i v e l y . (1) O 1 6 ( a , a')O 1 6 . , £ a (c.m.) = 21.8 MeV, Q = -8.88 MeV(2-). The a n g u l a r d i s t r i b u t i o n shows a v e r y c l e a r diff r a c t i o n p a t t e r n . The p e r i o d of the o s c i l l a t i o n is s o m e w h a t long in c o m p a r i s o n with that of the e l a s t i c s c a t t e r i n g . The p h a s e r e l a t i o n of both p a t t e r n s is r a t h e r in phase. The c r o s s s e c t i o n s e e m s to be r e l a t i v e l y l a r g e r than that of other t h r e e nuclei. (2) Ne20(~, ot')Ne20 *, £ot (c.m.) = 22.8 MeV, Q = -4.97 MeV(2-). M a x i m a and m i n i m a of the d i f f r a c t i o n p a t t e r n Lend to s m e a r out at a n g l e s l a r g e r than about 50 °. H o w e v e r , a definite o u t - o f - p h a s e r e l a t i o n to the e l a s t i c s c a t t e r i n g s e e m s to be exist. P o s i t i o n s of m a x i m a and m i n i m a of the p a t t e r n shift to b a c k w a r d a n g l e s a s c o m p a r e d with those of the e l a s t i c s c a t t e r -
ing.
LETTERS
1 March 1964
(3) M g 2 4 ( ~ , ~ ' ) M g 2 4 . , E ~ ( c . m . ) : 24.3 MeV, Q= -5.22 MeV(3+). In this c a s e the peak m e a s u r e d in the pulse height s p e c t r u m was c o v e r e d by an e l a s t i c and ine l a s t i c peak of c a r b o n c o n t a m i n a t i o n at angles b e tween 20 ° ~ 27.5 ° and 67.5 ° ~ 72.5 ° lab r e s p e c t i v e ly. A n g u l a r d i s t r i b u t i o n s of alpha p a r t i c l e s s c a t t e r e d f r o m c a r b o n w e r e m e a s u r e d s e p a r a t e l y at the s a m e incident e n e r g y using a s e l f - s u p p o r t i n g c a r b o n film and M y l a r t a r g e t . A f t e r e s t i m a t i n g the a m o u n t of c a r b o n in m a g n e s i u m f r o m a r e s o l v e d peak, the c o n t r i b u t i o n f r o m the c a r b o n c o n t a m i n a tion was s u b t r a c t e d f r o m the o v e r l a p p i n g peaks. A d a m p i n g in o s c i l l a t i o n in the d i f f r a c t i o n paLt e r n can be o b s e r v e d at a n g l e s of about 50 °. The p h a s e r e l a t i o n to the e l a s t i c s c a t t e r i n g is n e a r l y in phase. (4) Si28(a,oF)Si 2 8 . , E ~ ( c . m . ) = 24.8 MeV, Q = -6.27 MeV(3+). Owing to the t h i c k n e s s and r e l a t i v e l y poor unif o r m i t y of the t a r g e t , the 3 + - l e v e l w a s r e s o l v e d p o o r l y f r o m a d j a c e n t l e v e l s having r e l a t i v e l y l a r g e c r o s s s e c t i o n s . Thus the r e s u l t has m u c h u n c e r tainty in c o m p a r i s o n with above t h r e e c a s e s . Howe v e r , a d i f f r a c t i v e n a t u r e of the p a t t e r n can be s e e n and the p h a s e is f a i r l y in phase with the e l a s t i c , though the m a x i m a (minima) shift to b a c k w a r d angle.
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343
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PHYSICS
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1 March 1964 t0~
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S u m m a r i z i n g the p r e s e n t r e s u l t s , s o m e c h a r a c t e r i s t i c s of the s c a t t e r i n g in c o m p a r i s o n w i t h t h o s e of l o w e r i n c i d e n t e n e r g i e s c a n be d e s c r i b e d a s f o l lows: (a) T h e f o r w a r d p e a k in the a n g u l a r d i s t r i b u tion i s m o r e p r o m i n e n t and the d i f f r a c t i o n i s m o r e c l e a r . (b) T h e r e a r e f a i r l y d e f i n i t e p h a s e r e l a t i o n s in the d i f f r a c t i o n p a t t e r n s b e t w e e n the u n n a t u r a l p a r i t y s t a t e and the g r o u n d s t a t e . T h e p h a s e r e l a t i o n i s f a i r l y " i n " o r " o u t " of p h a s e c o r r e s p o n d i n g to the m o m e n t u m t r a n s f e r t h r e e o r two r e s p e c t i v e l y , e x c e p t in the c a s e of 0 1 6 w h e r e the r e l a t i o n i s a l m o s t the r e v e r s e . (c) T h e e n e r g y d e p e n d e n c e of the c r o s s section shows a roughly monotonic decrease as f u n c t i o n of the i n c i d e n t e n e r g y . F i g . 5 s h o w s the i n t e g r a t e d c r o s s s e c t i o n s o v e r 15 ° to 80 ° c . m . c a l c u l a t e d on g r a p h s f o r c o n v e n i e n c e of c o m p a r i s o n . A s f o r the d a t a o b t a i n e d by o t h e r a u t h o r s , the c r o s s s e c t i o n s w e r e c a l c u l a t e d f r o m c u r v e s r e p o r t e d in t h e l i t e r a t u r e 5, 12, 13). S e v e r a l p o s s i b l e m e c h a n i s m s f o r the e x c i t a t i o n of u n n a t u r a l - p a r i t y s t a t e s a r e a l r e a d y d i s c u s s e d in t h e l i t e r a t u r e by E i d s o n a n d C r a m e r 5). T h e s e ¢.re (1) a c o m p o u n d n u c l e u s f o r m a t i o n , (2) a s p i n - o r b i t i n t e r a c t i o n , (3) a n e x change process (knock-out or heavy particle stripping), a n d (4) s u c c e s s i v e phonon p r o d u c t i o n s o r a multiple scattering process.
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Fig. 3. Angular distributions of scattered alpha p a r t i c l e s leading to the ground state and the 5.22 MeV (3+) level of Mg24.
344
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Fig. 4. Angular distributions of scattered alpha p a r t i c l e s leading to the ground state and the 6.27 MeV (3+) level of Si 28.
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1 March 1964
In the p r e s e n t r e s u l t s the f i r s t p r o c e s s could be p l a i n e d a s a s t a t e of t h r e e p h o n o n s of a n g u l a r m o e x c l u d e d for m a i n r e a c t i o n m e c h a n i s m s , b e c a u s e m e n t u m two 16), s i n c e the height of e x c i t a t i o n of the a n g u l a r d i s t r i b u t i o n shows a f a i r l y d i s t i n c t difthe l e v e l s e e m s to be not so u n r e a s o n a b l e for the f r a c t i o n p a t t e r n and p r o m i n e n t f o r w a r d peak. A s for s t a t e of t h r e e p h o n o n s . E x c i t a t i o n s of the t h r e e the s e c o n d p r o c e s s , it s e e m s to be not the c a s e if phonon s t a t e w e r e r e c e n t l y t r e a t e d t h e o r e t i c a l l y by S a t h l e r ' s e s t i m a t e s for the e n e r g y d e p e n d e n c e of Q u e s n e 17) but the c r o s s s e c t i o n s of t h e s e s t a t e s t h e s e c r o s s s e c t i o n s a r e v a l i d . A c c o r d i n g to h i s by the s u c c e s s i v e m u l t i p l e phonon p r o d u c t i o n w e r e s t a t e m e n t quoted by E i d s o n and C r a m e r 5), the not c a l c u l a t e d . T h u s a s t r a i g h t f o r w a r d c o m p a r i s o n c r o s s s e c t i o n of the s p i n - o r b i t i n t e r a c t i o n m u s t i n with the t h e o r y a n d the p r e s e n t d a t a c a n n o t be c r e a s e a s the i n c i d e n t e n e r g y i n c r e a s e s . On the c o n - m a d e . t r a r y it s e e m s to d e c r e a s e e x p e r i m e n t a l l y a s shown i n fig. 5. T h e c a s e (3) c o u l d not be e x c l u d e d f r o m At p r e s e n t , no d e f i n i t e c o n c l u s i o n c a n be m a d e p r o b a b l e r e a c t i o n m e c h a n i s m s . H o w e v e r , it i s q u e s - e x c e p t that the r e a c t i o n s m o s t p r o b a b l y t a k e p l a c e t i o n a b l e that in a l l the e n e r g y r a n g e 15 ~ 25 MeV t h r o u g h the e x c h a n g e p r o c e s s a n d / o r the s u c c e s (c.m.) the e x c i t a t i o n o c c u r s t h r o u g h the e x c h a n g e s i v e m u l t i p l e p r o c e s s at an e n e r g y of a few t e n s of p r o c e s s (knock-out) only, b e c a u s e the f o r w a r d c r o s s MeV. s e c t i o n s d e c r e a s e m a r k e d l y in t h i s e n e r g y r a n g e . In t h i s c a s e the c o n s i d e r a b l e c o n t r i b u t i o n f r o m the c o m p o u n d f o r m a t i o n m a y have to be t a k e n into c o n References s i d e r a t i o n at the l o w e r e n e r g y r e g i o n . 1) T. Lauritzen and F.Ajzenberg-Selove, Nuclear Data In view of m a n y s u c c e s s e s in u n d e r s t a n d i n g Sheets: Energy Levels of Light Nuclei. May 1962. ( ~ , ~ ' ) s c a t t e r i n g s a s e x c i t a t i o n s of p h o n o n - s t a t e s in 2) P. M. Endt and C. Van der Leun, Nuclear Phys. 34 the v i b r a t i o n a l r e g i o n , the l a s t p r o c e s s (4), e s p e c i a l (1962) 1. ly the s u c c e s s i v e phonon p r o d u c t i o n s e e m s to be 3) A . E . L i t h e r l a n d et al., Phys. Rev. Letters 7 (1961) 98. w o r t h y of a t h e o r e t i c a l c a l c u l a t i o n in c o n n e c t i o n with 4) J. E. Evans et al., Phys. Rev. 131 (1963) 818. 5) W.W. Eidson and J. G. Cramer J r . , Phys. Rev. Letters a b e t t e r u n d e r s t a n d i n g of the s t r u c t u r e of the u n n a t 9 (1962) 497. u r a l - p a r i t y s t a t e . The e x c i t a t i o n of a n o n s i m u l t a n e o u s 6) H.W.Broek, Physics Letters 3 (1962) 132; Phys. Rev. double e x c i t a t i o n w a s c a l c u l a t e d by Buck 11) with a 130 (1963) 1914. DWBA m e t h o d in the c a s e of a t w o - p h o n o n s t a t e h a v 7) M. Barloutand-Crut et al., Physics Letters 6 (1963) 222. ing n a t u r a l p a r i t y (4 +) i n the N i 5 8 ( ~ , ~ ' ) r e a c t i o n at 8) J.S. Blair, Phys. Rev. 115 (1959) 982. 43 MeV. He showed that the y i e l d of this p r o c e s s is J . S . B l a i r et al., Phys. Rev. 125 (1962) 1625. r a t h e r l a r g e r than that of o n e - s t e p d i r e c t e x c i t a t i o n 9) N.Austern et al., Phys. Rev.128 (1962) 733. of the s t a t e . The s t a t e of 2- in O 16 a n d Ne 20 m a y be 10) R.H. Lemmer et al., Phys. Rev. 124 (1961) 1155. c o n s t r u c t e d a s a s t a t e of two p h o n o n s h a v i n g the a n 11) B.Buck, Phys. Rev. 127 (1962) 940. 12) J . C . C o r e l l i et al., Phys. Rev. 116 (1959) 1184. g u l a r m o m e n t u m two a n d t h r e e r e s p e c t i v e l y 15) . 13} L. Seidlitz et al., Phys. Rev. 110 (1958) 682. T h e r e f o r e , it s e e m s to be i n t e r e s t i n g w h e t h e r the 14) K . K i m u r a e t a l . , J.Phys.Soc. Japan 17 (1962) 9. p h a s e r e l a t i o n a n d c r o s s s e c t i o n s of the p r e s e n t 15) P.O. Lipas and J . P . Davidson, Nuclear Phys. 26 c a s e s c o u l d be s a t i s f a c t o r i l y e x p l a i n e d by the s i m i l a r (1961) 8O. e x t e n d e d c a l c u l a t i o n a s p e r f o r m e d by Buck. 16) J.M.Arafijo, Nuclear reactions (North-Holland Publishing Co., Amsterdam, 1962) Vol. II, p. 195. As for the 3 + s t a t e of Mg 24 a n d Si 28, one p o s s i 17) C. Quesne, Nuclear Phys.46 (1963) 145. b i l i t y a m o n g o t h e r s i s that the s t a t e m a y be ex-
345