On the possibility of resonant transfer processes in nuclear reactions

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1} G. Goldring, Proc. Phys. Soc. A 67 (1954) 930. 2) N. VinL Mau and G. E. Brown, to be published.

ON

THE

POSSIBILITY IN

OF RESONANT TRANSFER NUCLEAR I~EACTIONS*

PROCESSES

G. M. T E M M E R ** bepa~~mer, t of P h y s i c s Florida State University. T a l l a h a s s e e Florida Received 19 Ft:bruary 1962

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c _dent He + b e a m of v a r i a b l e e n e r g y . ~,-=,, 1=~,,~,~,-, a g a i n s t t h e r e c i p r o c a l s q u a r e - r o o t of the b o m b a r d ing e n e r g y (in the r a n g e of 250 k e y to 2 keY), t h e n e u t r a l f r a c t i o n e x h i b i t s a s e r i e s of r e g u l a r l y s p a c e d p e a k s and v a l l e y s with e x t r e m u m v a l u e s of a b o u t 700/0 and 20010. T o w a r d t h e v e r y }ow e n e r g i e s t h e , ' w a v e l e n g t h " i n c r e a s e s s l i g h t i y and g r a d u a l l y . T h e a u t h o r s a d v a n c e d t h e ~ol:owing q u a l i t a t i v e e x p l a n a t i o n of t h i s s t r i k i n g p h e n o m e n o n : the a b s c i s s a c h o s e n above is p r o p o r t i o n a l to the collision t i m e ;

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~-~!BYSICS L E T .... T "E R'" S • ". • '" :'::i "

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1 April l~S2 . . .

The " c l u s t e r " description of nuclear structure is at the highest energy (250 keV) t h t s t i m e .is-s0: found experimentally to apply to many nuclear short t h a t an e l e c t r o n f r o m the~-:neutral t a r g e t a t o m states with a considerable degree of truth. One h a s Just t i m e to t r a n s f e r to the "He+ ion and n e u t r a l typical example, which we shall use for the reize it; at 80 keY the electron h a s time to j'~-np to mainder of this discussion, is the ground ~,ate of the ion and back to the original atom; at 43 keV the IA 6 (and f i r s t few excited states), which consists electron i s able to jump over, back, and over once of t h e configuration He 4 plus deuteron to the extent m o r e , and so on:: Incidenta~y, it was observed of abOut 60~ of the Wigner limit. Li 6 has the leastthat the r e s u l t s for a scattering ansle 0f 100 a r e bound ground state of any stable nucleus and concoincident w i t h ~ 5 ° c u ~ e f o r e n e r g i e s above stitutes an excellent test body for a number of im15keY; a t the lower e n e r g i e s the peaks a r e s o m e plications of parentage ideas. We shall cover some what displaced. of these in a future publication. T h e o r e t i c a l predic~ons of such behaviorlind For our p r e s e n t purposes, consider a target of been made by Ftrsov ~, and Bates, Massey, and Li 6 = He 4 + d, with a beam of incident deuterons Stewart 3)about 1 0 y e a r s ago, leading to.an ex(or alpha p a r t i c l e s ) ; during the t i m e of passage the pression of the neutral f r a c t i o n of the f o r m possibility exists of t r a n s f e r r i n g an alpha particle sin$,(bE'~), k b e i n ~ : a : c o n s t a ~ , and E the incident (or a deuteron) f r o m the target to the projectile, e n e ~ . Z i e m b a and R u s s e k 4~ have made a theoforming Li 6. T h i s p r o c e s s is of the Q = 0 type and r e t i c a l c o m p a r i s o n of these t h e o r i e s with the exr e p r e s e n t s a contribution to elastic scattering. We p e r i m e n t a l data. with considerable success at the must now examine the characteristic differences higher energies. from the at~mic case. F i r s t of all, the potential It should be emphasised that this p r o c e s s is obbinding the body tc be t r a n s f e r r e d is no longer the served a s .a contribution to e l a s t i c scattering, since Coulomb potential (although it will still have to it is a Q = 0 p r o c e s s , in nuclear parlance; hence penetrate the Coulomb barrier). Secondly, the body the term ,,resonant" transfer. to be t r a n s f e r r e d (one or more nucleons) has a nonClearly, t w o characteristic times are of imnegligible m~ss compared to the "centers of force", portance h e r e : in contrast to t~.e electron in the atomic case. a. t~e coHfsio~ Hme, t, a l r e a d y mentioned, which Therefore, one might expect that the im ~per,dence i~ of the o r d e r of the c h a r a c t e r i s t i c dietance of ang',~e of the t r a n s f e r pattern in the arc mic c~se over which exch..r~e o c c u r s , divided by the efmay no longer exist here; in fact, one m ty have to fectl;-e velocity of the incident ion; make judicious changes of obse,vatiort tngle with b. the ~ a ~ s f e r lime, ~, t . e . , the time it takes for changing collision time, accordi':~g to a prescribed the e l e c t r o n to make a transition between its law~ in o r d e r to detect the chara<:teri~ic peak~ two equivalent sites. and va,leys in the yield of, say, ~,i6 ions relative The t i m e ~ is illustrated by the well-known to alphas at forward angles. 1.25-cm inversion line of ammonia, where it is Using a naive, one-dimensional square-well one-half the tunneling period of the nitrogen atom model for Li 6, wRh ~ deuteron bound to an alpha between two equivalent t e t r a h e d r a l sites. ';his particle with 1.47 MeV, in a square well of 10-MeV t r a n s f e r t i m e can be calculated quantum-mechadepth and 2 - f e r m i radius, and another square well nically by solving the p r o b l e m of two approaching at a distance ~ f r o m the edge of the f i r s t , one obwells, one of which contains a bound particle in its tains an energy splitting ground state. The p r e s e n c e of the other well p r o t ~ "~' 5.6 e -0"33° MeV , (1) duces a splitting of the ground state into a s y m m e tric and an (higher) antisymmetr~c state; h divided where ~ ~.s expressed in f e r m i s . by twice the energy difference is 'the t r a n s f e r t i m e Taking. as an example p = 2 f e r m i , the resonant in question. Calculations of this s o ~ , "~ased upon transfer time c for the deuteron t u r n s out to be the Born-Oppenheimer t r e a t m e n t , have been c a r 7.1 × 10 -22 second for that separation. !"he transit ried out by Bates and c o l l a b o r a t o r s 5-'~) for the time t of ~ 4-MeV alpha particle a c r o s s a Li 6 nusystem H + + H(ls), using the wave functions of [he cleus is 5 "< 10 -22 sec. We see that the two critical u~ ~... o° ,~,~ L~__~!cset; and the kinetic energy of aa z times are comparable, a~u ,,~,,~ ~,,,-~ .... . . . . . . . . ~-the H + ion as perturbation. These authors have ~f ,~bserv~ng peaks and valleys of the type discussed also considered the nonresonant transfer to ex.i~: ~. In view of the exponential nature oi :he barcited states at the other site. A most beautiful ~ ~. t r a n s m i s s i o n , the contribution to the transfer demonstration of the H + + H ( l s ) resonances has process can be assumed to come predo-~na~t!5 " ~n~ just been obtained by Lockwood and E v e r h a r t 8). ly from a s m a l l region around the "distance of In view o~ the a~ailability of precisely c o n t r o l closest approach", so that the t r a n s f e r time might lable b e a m s of e-particle~ and heavy ions, it is remain reasonably constant, and the peaks and now of interest to inquire whether a nuclear anavalleys m e r e l y measure the number of transfer logue to this atomic p r o c e s s might be observable.

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V ~

I~ m e ~ e r !

PHYSICS

LETTXRS

i n t h e t i m e ¢~ l ~ m a ~ . Of c o u r s e , picture will ~ h o ~ a m o r e c o m p l i c ~ . t e d v a r ~ a t ~ with e r r ~ , and with ar,,gle. F~ra~e ~ x ~ : ~ ! e s t o te..~ these i d e a s a r e :

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at f o r w a r d a n g l e s when b o m b a r d i n g IA ° t a r g e t s

with d e u t e r o n s and alphas f r o m our tandem a c c e l e rator, . : i a m indebted to H. R. B l i e d e n for computational a i d , a n d t o U. Fano for a u s e f u l d i s c u s s i o n .

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~L~r c a ~ s can easily be imagined, ,-.e4special~ m h ~ - e n e r g y physiazs {e. g. n + p, ^ H e + H e 4, The ~<~b~l~*,y of norn--es0nant transfer to ex.:,.*~' ~:t::~s c~.~ a l ~ be i n c l u d e d , a d a p t i n g ~he .~: >.::::,c t ~ea:a~e~ o1[ F~ies aml Dalgarno 7).

~a~e :~r~.:~p resen',~v a:ttempting to observe Li 6 ions

I) F.P. Zlemba and E.Everhart, Ph~b~_.]Rev. Letters 2 (1959) 299. 2) O.B. Ftrsov, Zhur, Eimp. I Teoret. Fig. 21 41951) 1001. 3} D.R. Bates, H.S.W. Massey and A. L. Stewart, ProC. Roy. Soe. (London~ A 21~ (1953) 437. 4) F . P . Ziemba aud A.Russek, Phys. Rev, 115 (1959) 922. 5) D.R. Bates and A. Dalgarno, Proc. Phys. Soc. (London) A 65 (1952} 919. 6) A. Dalgarno and H. N. Yadav, Pr0c. Phys. Sot.. (London) A 66 41953) 173. 7) D. 1t. Bates and A. Dalgarno, Proc. Phys. Soc. (London) A 66 (1953) 972. 8) G.J. Lockwood and E. Everhart, Phys. Rev. 125 (1962) 567.

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ANALYSIS OPTICAL

OF STRIPPING USING MODEL PARAMETERS

MEASUI~ED

S. H INDS and R. M I D D L E T O N AU~mic Weapons R e s e a r c h Establishment, Ala~rmaston, Berkshire, England ,%nd

D. J . P U L L E N Clarendon Laboratory, Oxford, England R e c e i v e d 26 F 3 b r u a r y 1962

D~.~.:~g r e c e n t y e a r s i n c r e a s i n g l y f r e q u e n t u s e ,-:;~ ~:~=,ea mz,/e of t h e D. W. B.A. ( d i s r o b e d wave gv,::~rn ~ p r o x ~ n ~ t ~ o n ) ~ e o r y of d e ~ e r o n s ~ c i p p~,r~: ;.,2, To c . a l c u l a t e a ( d , p : : - a a g a l a r d i ~ r i b , R i o n :: ~s n+.e ~ssar)" to know the o p t i c a l m o d e l p a r a m e ~:::~.- prct.::~n

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to determine these optical mo~l parameters exactly. T h e c h o i c e of a s u i t a b l e ( d , p ) - r e a c t i o n w a s i n f l u e n c e d by t h e f o l l o w i n g c o n s i d e r a t i o n s : 1) t h e t a r g e t m a s s should be s u f f i c i e n t l y h e a v y f o r t h e o p t i c a l m o d e l to be a good a p p r o x i m a t i o n and a l s o t o m i n i m i s e t h e c o ~ p o u n d m : c l e u s c o n t r i b u t i o n to t h e ( d , p ) - r e a c t i o n ; 2) t h e i n i t i a l a n d f i n a l mm~ei m u s t be s t a b l e a n d a v a i l a b l e a s s e p a r a t e d isotop~.~ a n d 3) t h e Q - v a l u e f o r t h e ( d , p ) - r e a c t i e n m u s t n~t be too l a r g e i n o r d e r that t h e p r o t o n c , c , ~ y ,~,~ . . . . . . . f o r t h e e l a s t i c s c a t t e r i n g m e a s u r e m e n t is a t t a i n a b l e on o u r T a n d e m g e n e r a t o r . T h e S e 7 6 ( d , p ) S e 77 r e a c t i o n (Q = 5.19 MeV) s a t i s t i e , 3 t h e s e conditio,~s. A s e L f - s u p p o r t i n g t a r g e t of Se 76 was b o m b a r d e d with 7.8 MeV d e u t e r o n s f r o m t h e A l d e r m a s t o n T a n d e m g e n e r a t o r and 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 g r o u n d s t a t e p r a t o n g r o u p f r o m the Se76(d, p)Se 77 r e a c t i o n w a s m e a s u r e d with o u r m u l t i - c h a n n e l m a g n e t i c s p e c t r o g r a p h 3). A s e c o n d e x p o s u r e w a s

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