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UBC Theses and Dissertations

Carbon 12C(alpha, alpha) 12C*[i.e. Carbon 12 (alpha alpha prime) carbon 12] and 10B([alpha]d)12C* reactions… Spuller, Joseph 1974

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THE 1 2C (cX, a ) 1 2 C * AND 1 0 B ( of ,d) 1 2 C * REACTIONS TO THE T=0 12.71 MEV AND T=l 15.11 MEV STATES IN 1 2 C by JOSEPH SPULLER B.S., SUNY AT STONY BROOK, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of Physics We accept t h i s thesis as conforming to the required standard The University of B r i t i s h Columbia February, 197^ In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirer n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Co lumb ia , I a g ree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s tudy . I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d tha t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i thout my w r i t t e n p e r m i s s i o n . Department o f PhyslCS The U n i v e r s i t y o f B r i t i s h Co lumbia Vancouver 8, Canada D a t e February 27, 197^ A b s t r a c t The y i e l d s of the r e a c t i o n s 1 2C(cx , C c') 1 2C* to the T=0 s t a t e at 12.71 MeV (J 1 f=l + ) and the T=l s t a t e a t 15.11 MeV (J i r=l + ) were measured by d e t e c t i n g the decay of these l e v e l s t o the ground s t a t e by gamma emmission. A 90° (lab) y i e l d curve from th r e s h o l d t o ^  = 27.0 MeV was obtained f o r each r e a c t i o n . Both s t a t e s have to be populated v i a an unnatural p a r i t y process and i n a d d i t i o n the population of the 15.11 MeV l e v e l i s i s o s p i n forbidden. Nevertheless, e x c i t a t i o n of both l e v e l s i s unambiguously detected. Although the r a t i o of the y i e l d s has a considerable energy dependence ( 1%^^SA/CX — 20$), c o n c l u s i v e evidence i s shown f o r the breaking of i s o s p i n i n l 6 0 * ( E x = 24.0 to 27.3 MeV). The 15.11 MeV y i e l d curve had considerable s t r u c t u r e , suggesting the formation of i n t e r -im * mediate s t a t e s i n x 0 . While the y i e l d of the 12.71 MeV gamma ray a l s o showed evidence of s t r u c t u r e , i t was not as . dramatic as the 15.11 MeV gamma ray. The y i e l d of the r e a c t i o n 10B(a , d y ) 1 2 C * to the 12.71 and 15.11 l e v e l s was a l s o measured. I f the outgoing p a r t i c l e i s a true deuteron and not an unbound n-p p a i r , the population of the i 5 . l l i s i s o s p i n forbidden. Contrary to the 15.11 and 12.71 y i e l d s i n 12C(a , 0C) 1 2C* f no resonant s t r u c t u r e was found l n e i t h e r the 12.71 or 15.11 y i e l d s ; i t i s suggested that the r e a c t i o n s proceed through an i s o s p i n allowed sequence. TABLE OF CONTENTS page CHAPTER I INTRODUCTION 1 A. I s o s p i n and nuclear r e a c t i o n s 1 B. The I s o s p i n of composite p a r t i c l e s 3 1. Two nucleons 3 2. The i s o s p i n of more than two nucleons 7 3. Coulomb mixing of ground s t a t e s .. 8 C. The 15.11 and 12.71 MeV l e v e l s of 1 2 C .. 11 D. Unnatural p a r i t y aspects 15 CHAPTER I I EXPERIMENTAL PROCEDURE AND RESULTS ..... 19 A. The equipment 19 B. Gamma ray l i n e shape and data a n a l y s i s . 28 CHAPTER I I I THE 1 0 B ( a ,dY ) 1 2 C REACTION kO CHAPTER IV THE 12C{&,aY ) 1 2 C REACTION 53 A. The ( cH , or) process 53 B. The 1 2 C ( Oi , cr'Xs.,, ) 1 2 C process 55 C. The 1 2 C ( a , a Y / 2 7 ) ) 1 2 C process 64 CHAPTER V CONCLUSIONS BIBLIOGRAPHY 70 i i i LIST OF TABLES page I . I s o t o p i c s p i n i m p u r i t i e s of ground s t a t e s from the s h e l l model 10 I I . Example of u n n a t u r a l - p a r i t y l e v e l s e x c i t e d i n i n e l a s t i c alpha s c a t t e r i n g 17 I I I . I d e n t i f i c a t i o n of peaks i n the spectrum of f i g u r e k 26 IV. A. P o s i t i o n of peaks seen i n the 1 2C(of ,dY)12C 15.11 Reaction B~. P o s i t i o n of peaks seen i n the 1 2 C ( cx ,ocV) 1 2C IX-f I Reaction 57 V. L e v e l s i n l 6 0 * seen by the ( 3 H e , a ) , (Y.n) (Y.p), (3He,yo), (e.eM, (<X .cx'Xj,. (d.X>). ( a . Y J , ( d . r f ' Y J , and %(d,d» ) 1%(T=1) Reactions 60 i v LIST OF FIGURES Page 1. Decay scheme of the 15.11 and 12.71 MeV l e v e l s of 1 2C 13 2. Physical layout of the Nal c r y s t a l and the surrounding shielding . 20 3. Electr o n i c c i r c u i t used to c o l l e c t the data 21 4. Example of a gamma ray spectrum f o r E^ = 22.05 MeV on 1 2C 25 5. Example of the rejected and accepted spectra f o r the 1 0B(oc , d Y) 1 2C reaction 31 6. Line shapes used i n the analysis of the spectra 32 7. Example of a computer f i t to the experimental data of the 12C(a , QCY ) 1 2 C reaction 36 8. The 9 0 ° y i e l d curve of the 12.71 and 15.11 MeV gamma rays i n the 12C(<x ,ctfy) 1 2C reaction. The ordinate includes a correction f o r the branching of the 12.71 and 15.11 MeV states to other states besides the gamma decay to the ground state. The error bars only include the f i t t i n g and s t a t i s t i c a l errors and do not include the 30$ uncertainty i n the absolute cross section 37 9. The 9 0 ° y i e l d curve of the 12.71 and 15.11 MeV gamma rays l n the 1 0B(cx ,dY) 1 2C reaction. v The ordinate i n c l u d e s a c o r r e c t i o n f o r the branching of the 12.71 and 1 5 . I I MeV s t a t e s to other l e v e l s other than the ground s t a t e . The e r r o r bars only i n c l u d e the f i t t i n g and and s t a t i s t i c a l e r r o r s and do not in c l u d e the 30 % u n c e r t a i n t y i n the absolute cross s e c t i o n The 9 0 ° y i e l d curve f o r the 10.71 MeV gamma ray i n the 12C(cx . p Y ) 1 ^ r e a c t i o n . A c o r r e c t i o n f o r the brancing r a t i o of the 10.71 s t a t e has been in c l u d e d i n the or d i n a t e . The e r r o r bars only i n c l u d e s t a t i s t i c a l and f i t t i n g u n c e r t a i n t i e s and do not incl u d e the 30% u n c e r t a i n t y i n the absolute cross s e c t i o n . L e v e l s i n 1 3 C and 1 3 N which decay to the 1 5 . I I MeV l e v e l of 1 2 C Feynman l i k e diagrams f o r the s t r i p p i n g , knock-out, heavy p a r t i c l e s t r i p p i n g and compound processes i n the r e a c t i o n A. The r a t i o of the 9 0 ° y i e l d curves f o r the p o p u l a t i o n of the i 5 . l l and 12.71 MeV s t a t e s i n 1 2 C from f i g u r e 9. B. The same as A. except that a c o r r e c t i o n f a c t o r has been f o l d e d i n to remove the e f f e c t s of p e n e t r a b i l i t i e s . A Hauser-Feshbach technique was used v i 14. The a. l 60(Y,aY ) 1 2 C , b. 1 3 C ( 3 H e,a Y< ) 1 2 C , c. ^ ( d . o c ^ y ) 1 2C, d. ^ N i p ^ Y ^ ) 1 ^ and «. 1 2C-(a »c< >y^ J /) 1 2C y i e l d curves f o r 23 ^ E_ 28 MeV 58 15. A comparison of the 1 2C(a » C< ^ 2 7 / l S ^ 1 2 c a n d  1 2 C ( a ) l 6 0 reactions. Note that the ( a . Y>) and (oCtce ' Y ) reactions are not drawn to scale . 59 v i i I. Introduction A. Isospin and nuclear reactions The study of Isospin i n nuclear reactions has provided much understanding of nuclear structure and reaction mechanisms. Isospin was f i r s t introduced In the 19 3 0 , s by Wigner and Heisenberg to simplify the analysis of the nucleon-nucleon 1 2 interactions. * In order to compare the proton-proton and proton-neutron interactions, they found i t convenient to remove the Coulomb dependence and Isolate the strong force. This was done by breaking the Hamiltonian into two parts: H t = H s + Hc» where t stands f o r t o t a l , s f o r strong and c f o r Coulomb. Since Wigner r e a l i z e d that t h i s separation resulted i n the same Hs f o r the n-n, p-n and p-p interactions, he postu-lated that the neutron and proton could be viewed as being the same p a r t i c l e but i n d i f f e r e n t charge states. The Generalized Pauli Exclusion P r i n c i p l e i s a consequence of Wigner's postulate. This p r i n c i p l e states that the wave-function of a system of nucleons must be anti-symmetric under the exchange of a l l the coordinates of a p a r t i c l e , including the isospin coordinate. Of course, mass differences and Coulomb forces prevent the rigorous a p p l i c a t i o n of t h i s p r i n c i p l e ; but these corrections can be treated as perturba-tions on the dominating strong force. 2. The v a l i d i t y of i s o s p i n r e s t s f i r m l y on the assumption of the charge independence of the nuclear f o r c e s . This hypothesis has been v e r i f i e d to a few percent i n many experiments. The use of i s o s p i n i s b r i e f l y reviewed i n the next s e c t i o n i n context w i t h the studi e d r e a c t i o n s : 10B(ct,d )12 C(12.71, 15.11) and l 2 C ( <* , oc')l 2C( 12.71. 15.11). A d e t a i l e d treatment of i s o s p i n i s a v a i l a b l e i n the book: I s o s p i n i n Nuclear Physios, e d i t e d by D. H. W i l k i n s o n 3 . For completeness, i t should be noted th a t there i s evidence f o r the breaking of i s o s p i n even w i t h i n the strong f o r c e s (See a r t i c l e by Henley i n I s o s p i n i n Nuclear P h y s i c s ) , but the e f f e c t i s small and i s manifested by a 2% d i f f e r e n c e i n the e f f e c t i v e p o t e n t i a l s governing the p-p and p-n l n t e r -k a c t i o n s . This d i f f e r e n c e i s thought t o a r i s e I n part from the mass d i f f e r e n c e of the d i f f e r e n t charge s t a t e s of the pions which i s an i n d i r e c t consequence of the Coulomb f o r c e . The p-p and n-n i n t e r a c t i o n s appear t o be equal w i t h i n present e x p e r i -mental u n c e r t a i n t i e s , although a s l i g h t d i f f e r e n c e i s expected. The e q u a l i t y of the strong p-p and n-n forces i s c a l l e d 'charge symmetry' and i s a weaker c o n s t r a i n t on the form of the n u c l e a r Hamiltonian. The small i s o s p i n mixing due to the strong f o r c e s w i l l r e s u l t i n v i o l a t i o n s of the i s o s p i n s e l e c t i o n r u l e s . Before a c o n c l u s i o n can be made on the c o n t r i b u t i o n of the strong f o r c e 3 to an observed v i o l a t i o n of i s o s p i n , i t i s necessary t o determine whether the Coulomb f o r c e can e x p l a i n the mixing. This i s o f t e n a d i f f i c u l t task. F o r t u n a t e l y , the Coulomb for c e i s w e l l known; but knowledge of n u c l e a r s t r u c t u r e i s necessary f o r a proper accounting of i t s e f f e c t . Large d i s c r e p a n c i e s between Coulomb mixing estimates and experimental r e s u l t s may be i n d i c a t i v e of the enhancement of the strong f o r c e ' s i s o s p i n breaking component or may be a r e f l e c t i o n of the l a c k of knowledge of n u c l e a r s t r u c t u r e and r e a c t i o n mechanisms. Through an i t e r a t i v e process, new i n s i g h t can be gained as theory and experimental r e s u l t s converge. The f i r s t question which should be confronted i s the i s o s p i n p u r i t y of the ground sta t e of a composite p a r t i c l e . In order to a v o i d the d i f f i c u l t i e s from the e f f e c t of the Coulomb energy of l a r g e Z n u c l e i ( Z > 1 5 ) , the d i s c u s s i o n w i l l be l i m i t e d to l i g h t n u c l e i (A,_=30). In c o n s t r u c t i n g the wavefunction of a many p a r t i c l e system, i t i s p o s s i b l e to expand the wavefunction l n terms of s t a t e s w i t h w e l l defined i s o s p i n . This i s represented by B. The i s o s p i n of composite p a r t i c l e s 1. Two nucleons T,<X 4. where T i s the i s o s p i n number and CC i s a l l the other quantum numbers used t o describe the s t a t e . I t i s not necessary t o use the i s o s p i n formalism, but i t ' s use leads to s i m p l i f i c a -t i o n and I n s i g h t i n t o the p h y s i c a l process. This can be e a s i l y i l l u s t r a t e d i n the case of two nucleons which can couple t o form e i t h e r T=0 or T=l s t a t e s . The c o n s t r u c t i o n of the two nucleon s t a t e f o l l o w s the simple s p i n algebra r u l e s . ^ We f o l l o w the phase convention of Condon and S h o r t l e y , where |rL> = |i,^)> and |p^ = The p o s s i b l e s t a t e s of the two nucleon system are: Some simple conclusions are evident from the perusal of these equations. The p-p and n-n systems are both T=l st a t e s (charge symmetry), and i t i s not p o s s i b l e to mix a T=0 component i n t o them. However the s i t u a t i o n i s d i f f e r e n t i n the n-p system which can form e i t h e r the T=0 or T=l s t a t e . I f the nuclear Hamiltonian can be d i a g o n a l l z e d i n i s o s p i n space, the n-p system w i l l be i n an eigenstate of the T 2 |N> |N) /&(|N>|P> + |P>|N>) 0/,-  p)lp> 5. operator. In t h i s s i t u a t i o n the T=0 and T=l components do not mix. I t i s represented by where i s analogous t o the J operator. I f the t o t a l Hamiltonlan of the nuclear system needs to be expressed i n terms of a T=l and T=0 p a r t , i t i s necessary t o incl u d e a wavefunction which i s mixed i n i s o s p i n . I n t h i s s i t u a t i o n , the f o l l o w i n g i n e q u a l i t y holds. The Coulomb forc e i s an example of a non-conserving i s o s p i n i n t e r a c t i o n which i s present i n n u c l e i . I t w i l l not commute w i t h the T 2 operator. P h y s i c a l l y , t h i s means that i n any r e a l nucleus the s t a t e s w i l l be mixed. This e f f e c t i s most e a s i l y seen by expanding the Coulomb i n t e r a c t i o n i n terms of three q u a n t i t i e s : C s ( i s o s c a l a r ) , C v ( i s o v e c t o r ) , and C t ( i s o t e n s o r ) J [Hi. T l ] = 0 [H 0. TS] = 0 8 -I __/__- -1 !/« r3lr3i~3 TL'Ti AT=o;/,2> 6 The C s p a r t of the Coulomb i n t e r a c t i o n i s u s u a l l y i n corporated i n t o the nuc l e a r Ramiltonian since i t does not mix i s o s p i n . However, the C and C^ . i n t e r a c t i o n s do not p commute w i t h the T operator and mix i s o s p i n as the above formulae i n d i c a t e . This property i s a consequence of the the Coulomb operators. The i s o t e n s o r i n t e r a c t i o n i s g e n e r a l l y assumed to be much weaker than the i s o v e c t o r component and i s o f t e n ignored. I t ' s e f f e c t has been observed only i n the AT=2 alpha decay of the T=2 s t a t e s l n l 6 0 a t 22 .7 and 24.5 MeV.8 symmetric i n the exchange of the proton and neutron s p a t i a l c o ordinates. Thus to s a t i s f y the Generalized P a u l i E x c l u s i o n p r i n c i p l e , the i s o s p i n of the deuteron needs to be T=G (anti-symmetric), and t h i s has been v e r i f i e d e x p e r i m e n t a l l y . 1 The T=l S Q s t a t e i s unbound, i n d i c a t i n g that the HQ and H^ i n t e r a c t i o n s are not i d e n t i c a l . The ground s t a t e of the deuteron would have a very small admixture of a T=l component. This would be p r i m a r i l y due to mass d i f f e r e n c e s and the magnetic i n t e r a c t i o n of the proton and neutron. Of course, the l a s t q u a n t i t y i s e s p e c i a l l y weak and i s not represented i n the above expansion of the Coulomb f o r c e . asymmetric treatment of the two d i f f e r e n t charge s t a t e s by The deuteron i s a J =1 nucleus and i s 7 . 2. The i s o s p i n of more than two nucleons For the case of more than two nucleons, i t i s necessary to adopt a c o u p l i n g scheme. I t can be shown by means of a h e u r i s t i c argument that the ground s t a t e of A nucleons w i l l form a T=|T-j| c o n f i g u r a t i o n . This i s most e a s i l y seen i n a s h e l l model context. De-Shalit and Talmi have shown that the most symmetric c o n f i g u r a t i o n i n a c l o s e d s h e l l r e s u l t s i n a T=0 i s o s p i n . ^ For a c l o s e d s h e l l nucleus, t h i s would give a T=0 assignment t o the ground s t a t e . Furthermore, they have shown that w i t h N=Z the ground s t a t e w i l l a l s o be T=0. De-Shallt and Talmi had assumed that the n u c l e a r f o r c e was charge Independent and had neglected the Coulomb f o r c e . For l a r g e Z t h e i r arguments do not hold and i t i s expected that i s o s p i n w i l l not be w e l l d e f i n e d i n t h i s r e g i o n . However, i t ' s e f f e c t s have been d r a m a t i c a l l y observed i n (p.n) r e a c t i o n s on heavy n u c l e i by the Livermore g r o u p . L a n e and Soper were the f i r s t t o e x p l a i n t h e i r r e s u l t s i n terms of i s o b a r i c analogue s t a t e s . T h i s i s a more g e n e r a l i z e d treatment of I s o s p i n operators because the e f f e c t s of the Coulomb i n t e r a c t i o n are incorporated i n t o the analogue operators. However, f o r l i g h t n u c l e i i t i s s u f f i c i e n t to consider only the i s o s p i n operators and t r e a t the Coulomb force i n an e x t e r n a l f a s h i o n . 8 Coulomb mixing of ground s t a t e s B e r t s c h and Mekjian have reviewed the v a r i o u s mechanisms r e s p o s i b l e f o r the mixing of i s o s p i n i n g r o u n d s t a t e s (low l y i n g s t a t e s ) . 3 - 2 The a n a l y s i s i s i n terms of two body Coulomb matrix elements between v a r i o u s s h e l l model s t a t e s . The i s o t e n s o r i n t e r a c t i o n i s neglected due to i t s r e l a t i v e l y small e f f e c t i n i n t r o d u c i n g I s o s p i n i m p u r i t i e s . However, Adelberger et a l . have shown that the i s o t e n s o r p a r t of the i n t e r a c t i o n can be important i n the o f f - d i a g o n a l elements of 13 the <H C^ matrix. J Since t h i s e f f e c t i s f o r s t a t e s w i t h higher e x c i t a t i o n energy, i t does not need to taken i n t o account f o r ground s t a t e s . B e r t s c h and Mekjian conclude that the three p r i n c i p l e mechanisms f o r i s o s p i n mixing l n ground s t a t e s are: The f i r s t process i s c a l l e d ' d i r e c t mixing'. I n t h i s case, two d i f f e r e n t c o n f i g u r a t i o n s are mixed without an i n t e r -mediate s t a t e being Involved. I t r e q u i r e s that two nucleons occupy simultaneously two d i f f e r e n t o r b i t s . The P a u l i E x c l u s i o n P r i n c i p l e would p r o h i b i t the two nucleons from occupying the same o r b i t a l and, thus, minimize t h e i r overlap. The matrix element f o r t h i s process i s small and of the order 1. 2. 3. two nucleons change t h e i r o r b i t one nucleon changes i t ' s o r b i t no nucleon changes i t s o r b i t 4ire' 2. 10 KeV where K i s the Fermi momentum of the nucleus and V i s the f nuclear volume. For heavy n u c l e i , t h i s process i s even less important. The second process i s c a l l e d 'monopole mixing'. A p a r t i c l e w i l l undergo a change of o r b i t a l n-^n+1, where n i s the p r i n c i p l e quantum number. For l i g h t n u c l e i , lp-*2p mixing i s small due to the large separation i n energy between these states. These one particle-one hole states are usually i d e n t i f i e d with the giant dipole resonance and are t y p i c a l l y about 25 MeV above the ground state. The t h i r d mechanism i s a purely diagonal term i n the Coulomb mixing matrix. I t i s often the most important mechanism f o r mixing i s o s p i n . I f there are two d i f f e r e n t states i n the same s h e l l configuration which have d i f f e r e n t Coulomb energies, the isovector part of the inte r a c t i o n w i l l mix t h e i r isospin. For example, the mixing of the 12.71 (T=0) 1 2 and i 5 . l l (T=l) MeV states of A C i s due to t h i s process. They both have a [(^P3/2^~^ ® ^ P l / 2 ^ ] con?iguration. MacDonald has done calculations on the isospin. mixing impurities of A LJk, 2-n n u c l e i . ' Harmonic o s c i l l a t o r wavefunctions were used to represent s h e l l model states. He assumed that the impurities i n the ground spates arose from the monopole mechanism ( n , l , j ) to ( n + l , l , j ) . . See table on page 10. f o r his r e s u l t s . 10. TABLE I . I s o t o p i c s p i n i m p u r i t i e s of ground s t a t e s from the s h e l l model a Nucleus ( E . - E ) b MeV Impurity *He 35 1 x 10"5 6 L i 33 -4 1 x 10 * 8Be 33 -4 3 x 10 ^ i o B 33 7 x 10'** 1 2 c 33 1 x 10"3 30 2 x l O " 3 l 6 o 30 4 x 10~3 3^ci 24 2 x 10~2 a. See reference (:'7i.). b. (E Q-E) i s the energy separation between the ground s t a t e and an e x c i t a t i o n of hw. As expected, MacDonald's calculations exhibit the general trend that the mixing increases as Z increases. Furthermore, MacDonald has shown that states with the same spin and parity-w i l l mix more readi l y than those of d i f f e r e n t spin and p a r i t y . This i s the case f o r the 12.71 and 15.11 MeV states i n 1 2 C which are both J11" = 1 + but of d i f f e r e n t isospin (T=0 and T=l, res p e c t i v e l y ) . C. The 15.11 and 12.71 MeV le v e l s i n 12 C The 12.71 and 15.11 MeV l e v e l s In l 2 C have been extensively studied. Since the 15.11 l e v e l i s the f i r s t T=l state i n l 2 C , i t affords an excellent opportunity to study the role that i s o s p i n plays i n nuclear reactions. Both states are =1 + states, and they form an isotopic doublet. Waddell was the f i r s t to observe the 15.11 MeV state. He populated the state i n the * 2C(p,p')* 2C* reaction. It was found that the y i e l d could be interpreted i n terms of a s i n g l e - p a r t i c l e t r a n s i t i o n which has been confirmed by 18 Hasselgren. A s p i n - f l i p mechanism was the predominate mechanism f o r populating the state. This i s i n agreement with 12 the [(IP3/2)""1 ® ( l P l / 2 ) 1 ] s h e l l model c o n f i g u r a t i o n . Waddell could not observe the s t a t e i n the (d, d*) r e a c t i o n a t E d = 85 MeV nor i n the ( a , Of) r e a c t i o n at E a ( l a b ) =48 or 1?5 MeV, and t h i s was the supporting evidence f o r the T=l assignment. Nakamura has a l s o found no y i e l d to the 15.11 19 l e v e l i n the (oC , <x') r e a c t i o n a t E^ (la b ) =28.5 MeV. However, Jacquot et a l . have i n t e r p r e t e d the r e s u l t s of t h e i r (Of , oc) experiment w i t h 90 MeV alphas as i n d i c a t i n g the e x c i t a t i o n 20 of the i 5 . l l l e v e l . I t should be noted that they d i d not see the 12.71 l e v e l and that t h e i r technique of us i n g an emulsion t o detect f i n a l s t a t e resonances i s not s e n s i t i v e t o low cross s e c t i o n s . Therefore i t i s d o u b t f u l that they saw the i 5 . l l l e v e l i n the ( p f . c r ' ) r e a c t i o n . 21 0 0 Recently, Reisman et a l . and Alburger and Wilkinson have i n v e s t i g a t e d the 12.71 and 15.11 l e v e l s and determined t h e i r branching r a t i o s f o r decay by p a r t i c l e emission and by gamma emission. See f i g u r e I . on page 13 f o r t h e i r r e s u l t s . The strong Ml gamma decay of the i 5 . l l l e v e l i s i n d i c a t i v e 23 24 25 of i t s T=l character. ' The gamma decay of the 12.71 l e v e l to the ground s t a t e i s i n h i b i t e d because *the AT=0 Ml r a d i a t i v e t r a n s i t i o n s are forbidden i n f i r s t order f o r s e l f conjugate n u c l e i . The observation of t h i s gamma decay channel i s due t o the f a c t that the a l t e r n a t i v e (X decay i s , 26 s t r o n g l y suppressed. The weak alpha decay of the 15.11 l e v e l 13. FIGURE I J it T= I /5.//MEV 1.4% ~2% 26% 2.3% 92% .12.71 15 /0.3 765 ofr 4.44 0 The decay of the 12.71 a n d . i 5 . l l MeV l e v e l s of 12c, Broad state around 10.3 MeV; both 0 + and 2 + have been assigned. This branching has never been observed; Alburger and Wilkinson estimate on t h e o r e t i c a l grounds. This value i s i n dispute, although i t i s known to be small. 14. i s i n accord w i t h the T=l assignment, but i s a l s o s t r o n g l y i n f l u e n c e d by the r e l a t i v e l y small Of width of the 12.71 MeV l e v e l . As p r e v i o u s l y mentioned, the 12.71 and 15.11 MeV l e v e l s w i l l have small i s o s p i n i m p u r i t i e s introduced by the i s o v e c t o r part of the Coulomb f i e l d . Since these two s t a t e s are the only two l e v e l s w i t h a J ^ = l + i n the same e x c i t a t i o n region, 2"^ i t i s adequate to consider that a l l the mixing w i l l occur only between themselves.12,15,27 Reisman et a l . have estimated that the i s o s p i n i m p u r i t i e s introduced by Coulomb e f f e c t s should 21 be approximately 50 keV. However, they deduce from t h e i r measurement of the alpha width of the 15.11 MeV l e v e l that the mixing i s 1.1 t o 3*5% (260 t o 440 keV). Artemov et a l . have a l s o reported a mixing l a r g e r than the 50 keV d e r i v e d from c o n s i d e r i n g the Coulomb p e r t u r b a t i o n . They give a value of 26 approximately 1% admixture of T=0 i n the 15.11 l e v e l . They a l s o based t h i s number on t h e i r experimental determination of the alpha width of the 15.11 l e v e l . A f t e r a n a l y z i n g the 12 12 C(d.d') CU5.11 MeV) r e a c t i o n , B r a l t h w a i t e et a l . have found a 1% (250 keV) admixture of T=0 i n the 15.11 l e v e l . 2 8 Although these experiments disagree w i t h each other, i t does appear that the Coulomb fo r c e s can not account f o r the e n t i r e T=0 component of the 15.11 l e v e l . B r a l t h w a i t e has suggested t h a t the discrepancy might be a r e s u l t of a charge dependent strong f o r c e . However, t h i s i s only s p e c u l a t i v e . 15. D. Unnatural parity mechanisms Since the 12.71 and i 5 . l l MeV level s i n 1 2 C both have =1+, they must be excited by an unnatural parity mechanism. In an unnatural parity process (77V (-if" ) both the i n i t i a l p a r t i c l e s and one f i n a l p a r t i c l e need to be splnless and of positiv e p a r i t y . When t h i s c r i t e r i a i s met, Edison and Cramer have shown that the unnatural p a r i t y l e v e l s can not be excited with the ordinary assumption of a single scattering with a single transfer of angular momentum.2^ This assumes a l o c a l p o t e n t i a l and a v e l o c i t y independent in t e r a c t i o n . However, there are situations i n which t h i s argument w i l l not apply. Edison and Cramer have shown that the ex c i t a t i o n of un-natural p a r i t y l e v e l s can proceed through the following: a. compound nucleus b. spin-orbit i n t e r a c t i o n c. nonsimultaneous, multiple-phonon exc i t a t i o n (or any multiple scattering process) d. d i r e c t exchange. Processes a. and c. are possible because they both form an intermediate state which can couple to the f i n a l state to conserve the t o t a l angular momentum and pa r i t y . I t should be noted that one important consequence of the l 2C(Cr , a') 12c* reaction to the 12.71 or 15 .11 MeV state proceeding through a compound nucleus i s the conservation of the o r b i t a l angular momentum (1^ = l f ) . This i s not true f o r the other three processes. 16. Processes b. and d. are examples of d i r e c t r e a c t i o n s and occur i n a time which i s comparable to the n u c l e a r t r a n s i t time. The d i r e c t exchange mechanism occurs when an incoming alpha exchanges i t ' s s p a t i a l coordinates w i t h an alpha c l u s t e r i n the t a r g e t and i s c h a r a c t e r i z e d by an enhancement of the cross s e c t i o n a t backward angles. I t has a n a t u r a l i n t e r p r e t a -t i o n i n terms of the alpha c l u s t e r model. Edison and Cramer reviewed the evidence f o r the formation of unnatural p a r i t y l e v e l s i n v a r i o u s n u c l e i w i t h the ( CX , CX) r e a c t i o n and concluded that the multiple-phonon process and the d i r e c t exchange mechanism were the c h i e f modes of excitation.'. They noted that the two processes seemed to i n t e r f e r e w i t h each other. See t a b l e I I . on page 1?. f o r t h e i r r e s u l t s . Tamura has suggested that the multiple-phonon process would be p a r t i c u l a r l y e f f e c t i v e i n c o u p l i n g r o t a t i o n a l s t a t e s and v i b r a t i o n a l s t a t e s to form l o w - l y i n g unnatural p a r i t y states.-' This i m p l i e s that the 12.71 or 15.11 MeV 12 s t a t e s In C could be formed by a coupling to the f i r s t v i b r a t i o n a l s t a t e i n 1 2 C ( E x = 4.44 MeV; = 2 + ) . The c o u p l i n g t o the 15.11 MeV s t a t e would have to be e s p e c i a l l y weak since the strong i n t e r a c t i o n would only be e f f e c t i v e i n c o u p l i n g the small T=0 component i n the 15.11 l e v e l . The e x c i t a t i o n of the 12,71 MeV s t a t e would not be i n h i b i t e d by i t s T=0 i s o s p i n . Nakamura has i n v e s t i g a t e d the unnatural p a r i t y s t a t e s i n 1 2 C (12.71 MeV), 1°B (8.6 MeV), 2 4Mg (10.4 MeV), and 2 8 S i ( 8 . 9 MeV) 17. Table I I . Examples of u n n a t u r a l - p a r i t y l e v e l s e x c i t e d i n i n e l a s t i c alpha s c a t t e r i n g ^ Target L e v e l (MeV) E (cm.) (MeV) ( dVdtt average (mb/sr) l 6 o 8,88 2" 14.7 2.5 2 0Ne 4.97 2" 15.0 2.0 2^Mg 5.22 3 + 19.3 0.7 2 8 S 1 6.27 3 + 19-7 0.4 2 V 5-22 3 + 36.9 0.2 12 c 12.71 1 + 21.4 0.1 b« a. Table i s from reference (29). b. We estimate t h i s from reference (19). 18. with the (Of, Of) reaction. ^  His res u l t s are i n contradiction to Edison and Cramer's conclusions. He has found that the spin-orbit i n t e r a c t i o n w i l l explain his data. It i s apparent that the modes of ex c i t a t i o n of unnatural pa r i t y states i n d i f f e r e n t nuclei and d i f f e r e n t levels i n the same nucleus are not a l l the same. This i s an i n d i c a t i o n : that the "second order " process of unnatural parity mechanisms are competing with each other, and the data need: to be explained i n terms of the nuclear structures which are involved and the dynamics of the reactions. 19 I I . Experimental procedure and r e s u l t s A. Equipment The U n i v e r s i t y of Washington's FN tandem provided ^ H e + + w i t h energies between 18.0 and 27.0 MeV. The beam was w e l l c o l l i m a t e d and had an energy r e s o l u t i o n of a few keV. The current was kept i n the range of 100 to 500 nano-amps. The beam was focussed onto s e l f - s u p p o r t i n g t a r g e t s i n a 4 i n c h s c a t t e r i n g chamber. Less than 2% of the beam h i t the c o l l i m a t o r which was l o c a t e d about one meter upstream from the t a r g e t . A f t e r passing through the t a r g e t , the beam was c o l l e c t e d i n a Faraday cup i n s i d e a concrete w a l l about 10 meters downstream from the t a r g e t . The gamma rays were detected w i t h the U n i v e r s i t y of B r i t i s h Columbia's 1 0 M x 10" N a l ( T l ) c r y s t a l . The p h y s i c a l arrangement of the c r y s t a l and the s h i e l d i n g i s shown i n f i g u r e I I . on page 20. The p l a s t i c s c i n t i l l a t o r surrounding the c r y s t a l was operated i n a n t i - c o i n c i d e n c e to provide an e f f i c i e n t means to r e j e c t cosmic r a y s . I t a l s o served to Improve the l i n e shape of a monoenergetlc gamma ray. (This point i s discussed i n chapter I I . B.) This i s a standard technique to improve the response of a Nal c r y s t a l . Since the f.w.h.m. of the 15.11 and 12.71 MeV gamma rays were 4.2 and 4.5$, r e s p e c t i v e l y , under the experimental c o n d i t i o n s , the gamma rays were e a s i l y r e s o l v e d . Figure I I I . on page 21 i s the schematic of the e l e c t r o n i c s used i n t h i s experiment. 21. n LU LLJ 1 < Q_ CL :> < < 2 D LO 3 CO CO QL 22. The data were coll e c t e d In a PHA and written onto magnetic tape f o r analysis at U.B.C. Preliminary analysis of the data was done on a SDS computer while the experiment was i n progress. This procedure proved very useful since i t provided the experimenter with preliminary versions of the y i e l d curves. Hence, i t was possible to reinvestigate ce r t a i n parts of the y i e l d curve Immediately and v e r i f y structure. There were two sources of background: 1. cosmic rays and 2. neutron contamination. As seen i n figure I I . on page 20, the p l a s t i c counter and the Nal c r y s t a l were surrounded by 4 W of lead. This reduced the room background which would have otherwise impinged on the c r y s t a l . The back end of the c r y s t a l did not have lead shielding of a p l a s t i c counter to shie l d i t from the background. The neutron contamination was p a r t i c u l a r l y worrisome because i t i s d i f f i c u l t to shie l d against them. The neutron sources were i d e n t i f i e d as being the beam scraping along the beam pipe or h i t t i n g the collimator and the (Or,n) reaction i n the target. The former was a r e l a t i v e l y small source because the beam was well collimated before entering the experimental area. In addition there was concrete shielding to reduce any neutron flux from the machine area. In order to reduce the neutrons from the (o< tn) reaction i n the target, i t was necessary to place p a r a f f i n i n front of the c r y s t a l . We also had L l 2 c 0 j mixed with p a r a f f i n surrounding the c r y s t a l . However, i t i s not 23 possible to get r i d of a l l these neutrons. Those neutrons that entered the c r y s t a l would cause the reaction. Unfortunately, the Q value f o r t h i s reaction i s 6.825 MeV, and t h i s r e s u l t s i n a broad background i n the energy range under investigation. The front piece of lead had a variable collimation c a p a b i l i t y . We used a tapered section of lead with a front diameter of 3 M a n d a back diameter of 4.2". Inside the collimator there was a mixture of p a r a f f i n and LigCO^. Since l i t h i u m i s a good neutron absorber, i t reduced the neutron flux i n the center region of the c r y s t a l . A test was made to see i f a neutron associated background was seriously contaminating the spectrav, This was done by comparing spectra, with the lithium plug i n place with a spectrum without' the lithium plug. The difference was small. There was a gain s t a b i l i z i n g unit attached to the power supply of the photo cathodetitubes on the Nal c r y s t a l . Previous experience had shown that the gain of the photo tubes was a function of the counting rates. The changes i n the dynode currents proved to be related to changes i n the counting rate. In order to compensate f o r gain s h i f t s , the high voltage applied to the photo tubes was adjusted to s t a b i l i z e the peak po s i t i o n of the 4.44 MeV gamma ray which comes from the f i r s t excited state of * 2C. Even with the s t a b i l i z i n g unit attached, there was a 1% s h i f t i n the gain. However, a l l the l i n e s 24. which were analyzed had known energies, and the small gain s h i f t did not pose any problems. In order to ca l i b r a t e the energy scale of the PHA a spectrum was recorded with the lower discriminator set at 12 approximately 4.0 MeV. We used the G' target to obtain t h i s spectrum. Figure IV. on page 25. shows the r e s u l t s . I t was v e r i f i e d that the system was l i n e a r to within the experimental uncertainties (FZX%) • The spectrum i n figure IV. i s exemplary of the main d i f f i -c u lty i n performing t h i s experiment. The cross sections of interest were very low compared to the more p r o l i f i c ( oc ,nY) and ( or , p T ) reactions. (See table I I I . on page 26. for the i d e n t i f i c a t i o n of the peaks i n figure IV.) To minimize the dead-time from these prolific events, the lower l e v e l discriminator was set at approximately 9.0 MeV. It should be noted that there were no discernible peaks i n the spectra! from pile-up. However, the resolution of the 15.11 and 12.71 MeV gamma rays could have been effected. F'c~-? Four targets were used i n the course of t h i s experiment: 500 //g/cm2 of 12CI, 200 fig/cm 2 of 1 2C, 250 /<g/cm2 of 1 0B, and 750 /(g/cm2 of 1 1 B . Since no c a l i b r a t i o n of target thickness was done, these values have a nominal uncertainty of 20$. The carbon targets were enriched with the 1 2C isotope, and the ^ 5 . F I G U R E 4, i o f ? f I 2 2 !£ \ m •A* G A M M A R A Y S P E C T R U M E A = 2 2 . 0 5 M E V Q = 1 0 0 MC TARGET*. ' 2 C [sooH^/CT^) ' S P • • E F G H 4 ' 0 5 5 i6 7 ^ 8~b" 9 ^ POO C H A N N E L 26. Table I I I . L e v e l Gamma Energy E x c i t e d State (MeV) (MeV) A 5 .25 i . l 1 5 0 (5.24 or 5.18) 15N (5 .30 or 5.27) B 6 .25 - .1 1 5 N (6 .32) C 6.80 ±.1 1 5 0 (6 .79) D 7 .25 i . l 15N (7.30) E 8 .25 ±..1 ( 8 . 3 D 1^0 (8.28) P 9 . 1 5 - .1 1^N (9 .15) G 9 . 7 5 ±.1 1 5 N (9 .76) H 10 . 6 i . l (10 . 7 ) i d e n t i f i c a t i o n of peaks i n the spectrum of f i g u r e IV. 27 1 0 B target was 96$ 1 0 B and h% ^ B . Most of the data f o r the 1 2C ( a ' , CK. ) 0 1 2C reaction were collected with the 500 /<g/cm2 target. In general 600 fiC of alphas provided s u f f i c i e n t s t a t i s -t i c s . A t y p i c a l alpha (~22 MeV) would lose 130 keV i n traversing the target. Therefore, 150 keV steps were used i n obtaining the y i e l d curves. When i t was necessary to look at the y i e l d s with f i n e r resolution, the 200 yUg/cm2 1 2 C target was used. This v e r i f i e d certain structure which would have otherwise been ambiguous. The H B target was used to check f o r possible contamination from the 1 : LB(Of , 3 H ) 1 2 C reaction. This was p a r t i c u l a r l y worrisome because of the isospin allowed population of the i 5 . l l MeV state i n 12C. In regards to th i s problem, the low Q value i s for t u i t o u s . The Q value i s -3.85 MeV for the i 2 C ground state, and so i t would reqire incident alphas of 25.85 MeV to populate the 15.11 MeV state. The y i e l d would also be strongly i n h i b i t e d f o r alphas only a few MeV above threshold because of pe n e t r a b i l i t y effects i n the e x i t channel. The threshold f o r populating the 12.71 MeV l e v e l i n i 2 C i s lower (E^ = 22.58 MeV) and i t might present a problem f o r alphas with energies greater than 25 MeV. The spectra from the H B target v e r i f i e d that the 15.11 MeV gamma ray was not detectable and that the correction f o r population of the 12.71 MeV l e v e l was small. 28. B. Gamma ray l i n e shape and data analysis The 1 0 H x 10" Nal(Tl) c r y s t a l of U.B.C. has been described before a n ^ i t i s not necessary to explain i t s response i n d e t a i l . This section w i l l b r i e f l y discuss the empirically determined l i n e shape and the method we used to determine the cross sections. Since the c r y s t a l has a large thickness, we estimated that $8% of the incident gamma rays (^15 MeV) w i l l have some int e r a c t i o n with the c r y s t a l . These interactions can be conveniently divided into two separate categories: 1. a l l the incident energy deposited i n the c r y s t a l and 2. a f r a c t i o n of the incident energy escapes. In the l a t t e r case there i s some pr o b a b i l i t y the escaping radiation w i l l r e s u l t i n a pulse i n the p l a s t i c annulus. Depending on the setting of the discriminator l e v e l s , t h i s could re s u l t i n the r e j e c t i o n of these kinds of events. In general the re j e c t i o n of events which only deposit part of t h e i r energy i n the c r y s t a l serves to Improve the resolution. This i s quite useful f o r separating gamma rays of d i f f e r e n t energies. The h% resolution that was obtained f o r t h i s experiment was more than s u f f i c i e n t to separate the 12.71 and 15.11 MeV gamma rays. To determine the absolute cross section, a measure of the e f f i c i e n c y of the r e j e c t i o n 29. system was necessary. This was done by routing the rejected events to a separate ADC. Figure V. on page 31 shows a sample spectrum with i t s rejected counterpart. The rejected spectrum shows a peaking about .5 MeV below the peak of the 15.11 MeV l i n e which corresponds to the escape of one a n n i h i l a t i o n quantum (0.511 MeV) from the c r y s t a l . I t i s evident from figure V. that events with some loss of energy (electrons or gamma rays ) were not being f u l l y rejected. This resulted i n a poorer FWHM than i f the r e j e c t i o n was working more e f f i c i e n t l y . The geometry of the c r y s t a l dictates that the collimation of the gamma rays should be done along i t ' s a x i s . Consider a high energy gamma ray (15 MeV) that enters the c r y s t a l . Its. dominant mode of in t e r a c t i o n i s the creation of a r e l a t i v i s t i c e + - e r p a i r moving i n the forward d i r e c t i o n . Since there would be c y l i n d r i c a l symmetry of the emitted e +-e" pairs, i t i s advantageous to collimate the entering gamma ray along the :i~ central a x i s . This geometry would contain most of the shower. The events caused by the (n,y) reaction i n the c r y s t a l could occur anywhere l n the c r y s t a l . I f they occurred near the physical boundaries of the c r y s t a l , there would be a larg e r p r o b a b i l i t y f o r the radiat i o n and i t s shower to escape. This would be manifested by a higher r e j e c t i o n r a t i o f o r the neutron capture gamma rays. 30 Once the electron and positron are created they undergo energy loss by two p r i n c i p l e means: electronic c o l l i s i o n s and radiative losses. For electrons of approximately 10 MeV the r a t i o of these two modes are equal ( See Jackson,31 15.46). In a radiative loss the electron produces a secondary gamma ray, and, of course, these gamma rays have energies which are less than the primary r a d i a t i o n . The process continues u n t i l a l l the radiatio n i s captured i n the c r y s t a l or u n t i l i t escapes from the c r y s t a l . The t a i l region of the l i n e shape r e f l e c t s a l l the various manners i n which d i f f e r e n t amounts of energy are deposited i n the c r y s t a l . The r a t i o of the t a i l region of the accepted events to the rejected events was found to be roughly equal. This Indicated that the p l a s t i c annulus was approximately 40$ ef f e c t i v e i n reje c t i n g events which did not deposit a l l t h e i r energy i n the c r y s t a l . I t was estimated that 30 - 3 % of the gamma rays Incident on the c r y s t a l was i n the rejected spectrum. This value was obtained by comparing the reject spectrum with the accept spectrum. In order to derive a l i n e shape an empirical determination was made. Since the ^ ^B{ c< tdK)^C reaction had less back-ground than the 1 2C( of , o r / Y ) r e a c t i o n , the former was used to derive the l i n e shapes. The re s u l t i n g l i n e shape was used to f i t both spectrauv ( the (or ,orY) and (a reactions) C O U N T S l o o d bod FIGURE 5. S P E C T R U M OF ' ° B ( a , d 7) 't E ^ = 26.70 MEV a = 4 0 0 ^ C -m R E J E C T S P E C T R U M . o o o A C C E P T S P E C T R U M o o .15.1 I MEV 60d 4 0 d 2 0 d o o X °0 Oo 0* o o o o ° +-f^_ Oo " M E V ++++++++ .<> * 0 0 ° o o o * o Lo* 0 + + ++ X o OOo rio i ^ o T3o CHANNEL i5o So '00 32. COUNTS FIGURE 6 : STANDARD LINES 700Q] NORMALIZED TO 100,000 COUNTS 600Q] 500d AOOQ 300d Ol ° o o o 200Q| 12.71 MEV „ . 15 11,MEV. 7 RAY 7 RAY o o • © • o o m ioo ilo i3c i3o" CHANNEL 3 3 . because the electronics and geometry were the same f o r both reactions. Therefore, the eff e c t of a d i f f e r e n t counting rate on the l i n e shapes was not Included i n the a n a l y s i s . The boron spectra between E ^ 26.0 to 27.0 MeV were summed to reduce s t a t i s t i c a l uncertainties. This energy region was used because of the r e l a t i v e l y high y i e l d of the 15.11 MeV gamma ray. However, i t was s t i l l necessary to subtract a background from the summed spectrum, and th i s added uncertainty to the true l i n e shape. The t a l l region was assumed to be approximated by a straight l i n e extrapolated to a value which was 1/2 the lowest energy point determined empirically. The 12.71 MeV gamma ray l i n e shape was determined by a sim i l a r technique. However, i t was necessary to use spectra which did not have any contribution from the 15.11 MeV gamma ray. I t was not possible to determine the 12.71 MeV l i n e as well as the 15.11 MeV l i n e due to s t a t i s t i c a l problems and background. Figure VI. on page 32 shows the l i n e shapes used i n the analysis of the spectra. They are normalized to an area of 100,000 counts. For c a l c u l a t i n g the error i n the absolute cross sections, the uncertainty i n estimating the l i n e shape contributed about 16$. Most of t h i s error i s i n the uncertainty i n the extrapolation of the t a i l region. The t o t a l error i n determing the absolute cross section was calculated to be ± 30^. A l l 34. errors were added incoherently ( i n quadrature), and most of the uncertainty Is i n the l i n e shape and target thickness. The spectra were analyzed by a least squares technique. A computer program was. developed by Dr. M Has ino f f at the University of B r i t i s h Columbia but was modified by the author. A l l the f i n a l analysis was done on U.B.C.'s IBM 360. The program had two parameters to describe each l i n e shape: 1. peak channel and 2. amplitude. Since we were f i t t i n g gamma rays which had the same energy as the empirically determined f i t t i n g functions, there was no uncertainty i n the energy dependence of the l i n e shapes. The carbon data were analyzed by two methods. F i r s t , both the 12.71 and 15.H MeV gamma rays were f i t t e d simultaneously. This procedure i s necessary i n obtaining the amplitude of the 12.71 MeV gamma ray l i n e because i t rested on the t a i l of the 15.II MeV gamma ray. A sample f i t i s shown i n figure VII on page 36. In the second method t h e i 5.ll MeV gamma ray l i n e was determined by only f i t t i n g the region which was above any contribution from the 12.71 MeV l i n e . This improved the estimation of the parameter which described the amplitude. Figure VIII on page 37 shows the y i e l d curve f o r the 1%C( oc »0cY) reaction. The error bars are a measure of both the s t a t i s t i c a l uncertainties and the uncertainties l n the f i t t i n g parameters. 35 The boron y i e l d curves were arrived at by f i t t i n g the 12.71 and i 5 . l l gamma rays simultaneously. This method was quite accurate since there was less background i n these spectra. See figure IX on page 38 f o r the r e s u l t s . Since we were able to measure the 10.71 MeV gamma ray from the 12c( a.pjr)1^ reaction, we also analyzed the spectra «to obtain the y i e l d curve f o r t h i s reaction. See figure X. on page 39 f o r the re s u l t s . The abscissae of the y i e l d curves are cali b r a t e d to include the corrections f o r e f f i c i e n c i e s and branching r a t i o s . The 12.71 MeV l e v e l was assumed to have a branching r a t i o of 2.5% by gamma decay to the ground state, and the 15.11 MeV l e v e l was assumed to have a branching r a t i o of 92.0$ f o r gamma decay 22 to the ground state. In order to improve the f i t s , a background function was used. This reduced the chi-squares of the f i t s and gave a better estimate of the amplitude parameters. We used a t h i r d degree polynomial to approximate the background . Careful attention was directed to the p o s s i b i l i t y of the polynomial having unwarranted minima and maxima i n the f i t t e d region, but a l l the f i t t e d spectra had a monotonically decreasing background. COUNTS 60 Oi + 12.71-5004 + + 400-4 + + + t + . 3004 200-J EXAMPLE OF FIT TARGET: iaC Q: 800 l±C = 25.20 MEV • J SPECTRUM + FIT + + + + + t ft* + + + • + + 15.11 + + o c m BACKGROUND + lOOi + + • 0-10 120 CHANNEL 130 140 37. F I G U R E ;8. - N* 25 26 , 2 7 2fl 29 30 MEV T l r 1 T ' T I i i I 1 — FIGURE 9. lubS l0B[a,d7fQ 5 0 O [ _ ? 12,71 MEV / RAY 4 15.11 MEV J RAY (x 20] * * T 4 40O 3 0 0 2 0 0 T • * 4 4 + lg T ^ I ^ i ^ i 2'6 MEV (LAB) 39. FIGURE 10. 0 2^ 26 , 2 7 MEV 1604 20H . T 80H / 4 40H • " 2 ^ 2? 2P5 26 27MEV E J L A B ) 40. I I I . The 1 0 B ( a , d y ) 1 2 C Reactions The y i e l d curves f o r the ^ °B(a , d Y ) 1 2 C reactions have been shown i n figure IX. on page 38. They reveal that the yi e l d s f o r populating the 12.71 and 15.II MeV states i n 1 2 C are r e l a t i v e l y smooth functions of energy, and there i s no evidence f o r strong resonances i n N. Both reactions show the e f f e c t s of pe n e t r a b i l i t y near threshold i n the exit channel. The dramatic increase i n the y i e l d f o r the 15.11 MeV gamma ray occurs above threshold ( E a (lab) = 22.4 MeV) for the isospin allowed (flc tPnY... ) reaction. The ( CX ,pn) reaction can proceed i n two d i f f e r e n t manners: 1. the three body f i n a l state consisting of 1 2 C ( 1 5 . 1 1 MeV; T=l) and the pn system i n i t s singlet configuration (T=l), and 2. the emmission of one nucleon to a well defined A=13 (T=l/2) state which decays by the emmission of one nucleon to form 1 2 C ( 1 5 . 1 1 MeV; T=l). There are a few known l e v e l s i n and which could act as intermediate states f o r populating the 15.11 MeV l e v e l 12 32 i n C. Measday et a l . have found l e v e l s i n 1 3 N using the ( P t P ' c C i ; ) reaction and Kuan et a l . ^  have found l e v e l s i n both 1 3 C and 1 3 N which populate the 1 5 . H MeV l e v e l i n 1 2 C . See figure XI. on page 4 l f o r a summary of these l e v e l s . It should be noted that there i s no si m i l a r increase i n the y i e l d of the 12.71 MeV gamma ray. This i s not surprising because the (0t,d)( ) i s isospin allowed, and the ad d i t i o n a l degree of freedom v i a the ( CX »P n^j z # 7y ) process would only weakly a f f e c t the observed y i e l d . 41 Figure i i . 22.41 24.5 MeV 15.11 0.00 V 23.8 21.81 21.28 20.52 23.2 22.7 20.87 19.77 1? 13 L e v e l s i n VC and which decay to the 15.11 MeV l e v e l i n 12C. a. These l e v e l s are taken from Measday et a l . 3 The others are from reference (33). They are most l i k e l y T=l/2. 4 2 . Since we detected only the decay of the residual 1 2 G ( E X = 12.71 and i 5 . l l MeV) nucleus, we can not make any d e f i n i t i v e conclusions regarding the angular d i s t r i b u t i o n of the 1 °B( OC , d ) 1 2C* reaction. Hence, i t i s hazardous to guess the reaction mechanism responsible f o r the observed y i e l d . Nevertheless, i t i s in s t r u c t i v e to examine the possible reaction mechanisms. Indeed, i t i s l i k e l y that no single mechanism was responsible f o r the entire y i e l d , and i t i s probable that various mechanisms competed with each other. Some possible mechanisms are: The Feynman diagrams f o r these processes are shown i n figure X. on page 4 3 . The f i r s t three mechanisms are di r e c t and would conserve is o s p i n . Any v i o l a t i o n of isospin would be ind i c a t i v e of isospin Impurities i n either the incoming channel ( i . e . the alpha ground state and 1 0 B ground state) or the outgoing 1 ? channel ( i . e . the 15.11 MeV l e v e l of. C and the deuteron ground st a t e ) . We ignore the very small impurities introduced by the Coulomb forces i n the entrance or exit channel. 1. 2. 3. 4. two nucleon transfer heavy p a r t i c l e s t r i p p i n g knock out compound nucleus COMPOUND 44. The f i r s t two processes are s i m i l a r because they both describe the transfer of nucleons. In the two nucleon transfer process the incoming alpha loses a deuteron which i s sub-sequently absorbed by the *-®B nucleus to form 1 2 c * . i f the deuteron i s transferred i n i t s singlet configuration (T=l), the population of the 15.11 MeV l e v e l (T=l) would be isospin allowed. Of course, the emmitted deuteron would also have to be l n the singlet state to conserve the isospin of the system. In order to v e r i f y the occurence of t h i s process i t would be necessary to observe the proton and neutron d i s t r i b u t i o n and determine i f they had a f i n a l state i n t e r a c t i o n which indicated the presence of the T=l singlet state. As previously mentioned, our data are not capable of either disproving or proving processes of t h i s kind. The heavy p a r t i c l e s t r i p p i n g mechanism describes the transfer of a ®Be c l u s t e r (j"^ =0 +; T=0) from the *°B target to the incoming alpha and the subsequent formation of ^-2C*. The outgoing deuteron i s from the stripped 1 0B; Again, i t might be argued that the deuteron could be i n i t s s inglet state and, correspondingly, the population of the 12 T=l states i n C would be isospin allowed. It should be noted that Ascuitto and Glendenning have shown that i t i s possible f o r st r i p p i n g reactions to proceed v i a a two step process.3^ This implies that the 1 0 B nucleus can be in an excited state before the transfer of the deuteron 1 ? or that the xe"C system i s excited a f t e r the transfer. It i s 45. possible f o r t h i s two step process to be more important than a simple single transfer (This phenomenon has been observed i n two step c o l l e c t i v e e x c i t a t i o n processes.). However, i t w i l l s t i l l conserve isospin unless i t i s a Coulomb ex c i t a t i o n . A detailed c a l c u l a t i o n on the parentage of the nuclear states involved i n the process i s necessary before a d e f i n i t i v e statement can be made on the contribution from t h i s mechanism. Noble has discussed a semi-direct mechanism to explain isospin mixing i n the (d,CX) reaction and concluded that i t i s possible f o r isospin mixing to arise from the po l a r i z a t i o n process would be characterized by a strong forward peaking of the deuteron. Weller has found that t h i s mechanism can explain his data on the 1 2 C ( d , a ) 1 0 B ( j ' ( T =0 +; T=l) reaction i f the assumption i s made that the process has an intermediate of the deuteron i n the f i e l d of the nuclear core.35 The state with a d e f i n i t e spin and p a r i t y . 36 He conjectures: oc + ( pw[T=j ;r,.o +J -f % ) fi # 8 The L i and Be configuration would be coupled together to form an intermediate state. 46. Besides d i r e c t reactions i t i s possible that the ( CX ,d) reaction proceeds through a compound nucleus i n Isospin may be conserved depending on the l e v e l densities and widths of the states i n the compound system. Wilkinson 3 ? and ILane and Thomas 38 have reviewed the necessary conditions f o r conservation of isospin, and we b r i e f l y summarize t h e i r observations. The d i s t r i b u t i o n of compound states can be conveniently divided into three regions: 1- n; < DT 2- r, ~ D, where i s the average width of the states with the same and Dj i s the average separation of these states. I t i s assumed that only states with the same spin and parity w i l l be e f f e c t i v e i n mixing isospin. For low energies (1^ .4. D3) the l e v e l s are well separated and ^Hc) « Dj ( (H c) i s the average Coulomb energy between these s t a t e s . ) . Isospin would only be weakly mixed, and the ( (X ,d) reaction would have a small AT = 1 component. 47. At higher e x c i t a t i o n energies (HJ- ~ Dj ) the l e v e l widths and densities become nearly equal i n magnitude, and isospin isospin number. However, isospin w i l l s t i l l have an e f f e c t on the exit channel i f the state decays before s i g n i f i c a n t mixing takes place. Consequently, there w i l l be an e f f e c t i v e conservation of the i s o s p i n quantum number, and any v i o l a t i o n of isospin i s attributed to the incoming and (or) outgoing channels. It should be noted that at very high e x c i t a t i o n energies, the compound system i s no longer characterized by the independence of formation and decay (Bohr's postulate 39). Wilkinson had found i t necessary to include a time dependence i n the formation of the compound state which was proportional states which decay so very quickly w i l l not excite a l l the degrees of freedom of the nucleus, and they might be more r e a l i s t i c a l l y c a l l e d intermediate states ( i . e . doorway, hallway configuration, c l u s t e r states, etc.** 0). The c r i t e r i a usually used to d i s t i n g u i s h between compound processes and d i r e c t reactions i s that the l a t t e r i s often characterized by 1. asymmetrical angular d i s t r i b u t i o n s , 2. smooth ex c i t a t i o n curves, and 3« selective e x c i t a t i o n of f i n a l states. The compound system i s often indicated by can be strongly mixed when ^ H ^ ^ D y . At a s u f f i c i e n t l y high e x c i t a t i o n (i^. > Dj ) isospin i s strongly mixed because ^ H J ) S> D t and the states are not well described by a single I t i s easy to imagine that these high energy 48. resonances i n the y i e l d curve and a symmetrical angular d i s t r i b u t i o n . However, these c h a r a c t e r i s t i c s are not t o t a l l y foolproof i n di s t i n g u i s h i n g between these two types of processes. For example, overlapping and i n t e r f e r i n g compound states can have an asymmetrical angular d i s t r i b u t i o n , and the s t a t i s t i c a l compound nucleus i s characterized by a smooth excitation:.function. The y i e l d curve f o r the ( OC,dYu.71 ) reaction c l e a r l y indicates a smooth exclstaion curve, and we conclude that the process i s described by one of the following p o s s i b i l i t i e s : 1. a d i r e c t reaction, 2. a compound nucleus, or 3. a combl.4 natlonioftheses-two .processes. Many authors have reported on the isospin breaking aspects of the (d, oc ) reaction, and t h i s process i s analogous to the ( (X ,d) reaction described i n t h i s paper. It has been found that large v i o l a t i o n of isospin can be interpreted i n terms of mixing i n the compound nucleus. For example, Richards and Smith report on the 1 2C(d,CC ) 1 0B(1.74 MeV; T=l) r e a c t i o n . 4 1 Although t h e i r data exhibit an asymmetrical angular d i s t r i b u t i o n , they f i n d t h i s asymmetry arises from i n t e r f e r i n g compound states i n l i ,'N(E x~20 MeV). J o l i v e t t e , who studied the ^ O t d , o( ) l 4 N * reaction, also found that mixing i n the compound system could explain the population of the f i r s t T=l state i n l £ , ,N(E x = 2.31 MeV). 4 2 J o l i v e t t e ' s findings are not too 4 9 . s u r p r i s i n g , since the po p u l a t i o n of the f i r s t T=l s t a t e of l^N by the (d,C( ) r e a c t i o n r e q u i r e s an unnatural p a r i t y process. As mentioned i n chapter I . , the formation of the compound nucleus i s one way f o r t h i s unnatural process to proceed. Hrejsa and Brown who looked a t the 2 0 N e ( d , (X ) ^ F * r e a c t i o n a l s o found l a r g e I s o s p i n mixing, and, again, i t was found that the mixing was o c c u r r i n g i n the compound nucleus. We note that our data i n d i c a t e that the T=l 15.11 MeV 12 s t a t e of C i s being formed by ( CX ,d) r e a c t i o n a t an e x c i t a t i o n energy of 26 - 28 MeV. (This i s below the t h r e s h o l d f o r the ( 0( .pnY^n ) r e a c t i o n . ) This i s 6 - 8 MeV above the compound s t a t e s which were res p o n s i b l e f o r the i s o s p i n mixing reported by Richards and Smith ^ 1 i n the 1 2C(d,CX )1°B (1.74 MeV) I f the compound nucleus formation was in v o l v e d i n our (C(,d) r e a c t i o n , we expect t h a t there would be l e s s mixing than that seen by Richards and Smith. This f o l l o w s from the above argument on the r o l e that widths and d e n s i t i e s play i n mixing i s o s p i n . Indeed, W i l k i n s o n has ass e r t e d that i s o s p i n would have reasserted i t s i n f l u e n c e at E x ~ 2 7 MeV i n ^ N ( i . e . > Dj ) Hence our data"-have" the p o t e n t i a l f o r being a means of . e x t r a c t i n g the i s o s p i n mixing l n the 12.71 and 15.11 MeV l e v e l s 12 of C. Un f o r t u n a t e l y , we can not "be.certain^that there was the formation of a compound nucleus. Nevertheless, we thought i t u s e f u l t o do a s i m p l i f i e d Hauser-Feshbach c a l c u l a t i o n to remove the e f f e c t s of 50. p e n e t r a b i l i t i e s i n the exit channels and compare the y i e l d s to the 12.71 and 15.11 MeV l e v e l s of l-^C. 4 2- Instead of using o p t i c a l model potentials, we used the phenomenological square well model of Blatt and Weisskopf 4 ^ to calculate the transmission c o e f f i c i e n t s . Since we were not interested i n the absolute cross sections, we thought that the r e l a t i v e y i e l d s would not Lc:. be sensitive to the potentials used. 3 The form of our analysis took where A i s the wavelength i n the exit channel and the Ts are the transmission c o e f f i c i e n t s . We included the p a r t i a l waves up to 1=6 and ignored a l l other exit channels. Figure XIII. on page 51» shows the r a t i o of the two y i e l d s before and a f t e r corrections were made. I t can be seen that the r a t i o has been flattened, and t h i s suggests that the p e n e t r a b i l i t i e s can be removed by t h i s type of c a l c u l a t i o n . As expected, i t was not possible to account f o r the rapid r i s e i n the ( OC ,pnT^,., ) y i e l d . We found that the average value of the r a t i o was 1.2$ f o r the data which were below any contribution from the deuteron breakup process. Since the 12.71 and 15.11 MeV l e v e l s are thought to mix only among themseves (See chapter I. C.), 52. they can be expressed as I12.71) = or.|T=o) + fi\j= 1^ ) 5.n> = J3\J=O) - a|T=i> where oc + P n F i r s t order perturbation theory gives -<T=olKlT=l> « E,- E. E, = 15.11 , £ = 12.7/ Tf)eV J f a = $ . 0 1 2 . We f i n d that <^  |HC) )> = 270 keV, and t h i s should be compared with Braithwaite's 2 8 value of 250 keV and Reisman's value of 260 keV. 2 * (We emphasize that our value of 270 keV represents an upper l i m i t f o r 4^ |HC| ) because there may be some mixing i n the compound nucleus.) The agreement i s good, and we believe i t worthwhile f o r other experiments to be done to determine the deuteron angular d i s t r i b u t i o n . This information would help to determine the reaction mechanism responsible f o r the 1 0 B ( « , d ) 1 2 C ( 1 2 . 7 1 and 15.II MeV). 53. IV. The 12c( CK , cx Y „ ) 1 Z C Reactions A. The ( oc t oi ) process The y i e l d s f o r the gamma rays from the 12c( cx , cx') 12C* reaction have been shown i n figure VIII. on page 37. Or i g i n a l l y , the main purpose of t h i s experiment was to measure the i s o s p i n mixing between the 12.71 and 15.11 MeV lev e l s i n * 2C. However, our data show that the y i e l d f o r the 12.71 and 15.11 MeV gamma rays has considerable structure, and i t 16 * i s l i k e l y that isospin mixing i s occurring i n 0 . Therefore, we w i l l not use our data to speculate on the mixing of these two l e v e l s . Instead, we reverse the argument and use the fact 16 « that mixing i s occurring i n the compound states of ,0* to deduce some q u a l i t a t i v e features of the peaks i n our y i e l d curves. As mentioned i n seefrion I.D., the formation of an 1 f, * Intermediate state i n -LD0 i s an acceptable mode f o r populating the J T r = l + states i n * 2C v i a the (cx , cx ) process. Since both the alpha p a r t i c l e and the 12C ground state are spinless, they w i l l only populate natural parity states i n l 60* ( i . e . J T r= 1", 2+, 3- , e t c . ) . Furthermore, the incoming channel w i l l only be ef f e c t i v e i n ex c i t i n g the T=0 components of these states (neglecting Coulomb e x c i t a t i o n ) . However, we also see a r e l a t i v e l y strong y i e l d i n the T=l 54. exit channel, and we suspect that the condition of P~ D ~ ^PLj) i s a p p l i c a b l e . 3 7 ' 3 8 Therefore, the i n i t i a l T=0 component l n the intermediate state w i l l be e f f e c t i v e i n mixing isospin to produce other states with large T=l components. This arises from the well known time development of intermediate states through the isospin mixing e f f e c t s of the Coulomb in t e r a c t i o n . We point out that the peaks seen i n the yi e l d s of the 12.71 and 15.II MeV gamma rays d i f f e r i n both the widths and exc i t a t i o n energy. The widths seen i n the 12.71 MeV gamma ray y i e l d are broader than the widths f o r those of the 15.11 MeV gamma ray. This i s not surprising since the population of the 12.71 MeV l e v e l i n 1 2 C i s isospin allowed (although i t has unnatural parity aspects), and the population of the 15.II MeV l e v e l of 1 2 C i s both isospin forbidden and parity unfavored v i a the ( Of , cx) reaction. From t h i s we conclude that nearly a l l the y i e l d f o r the 1 5 . H MeV gamma ray comes from the forming - of T=l components i n the states of 1^0*, and the 12.71 MeV gamma ray a r i s e s from the T=0 components i n 1^0*. j n addition the y i e l d of the l a t t e r could also have some contribution from d i r e c t processes (i.e.AT=0) which do not need the formation of intermediate states to conserve p a r i t y and angular momentum. (See section I.D. f o r a more detailed description of these types of processes.) 55. IV. B^v The 1£C( CX . a Y, > c i5>H Reaction The y i e l d curve f o r the 1 2 C ( c< «cx Y^ ,, ) 1 2 C reaction (See figure VIII. on page 37.) shows four peaks at E x ( l 6 0 ) = 24.4, 25.15, 25.55 and 26.25 MeV. There i s also a rapid increase i n the y i e l d at E x « 2 7 . 2 MeV, but we were li m i t e d to E ^ (lab) = 27.0 MeV and could not pursue the investigation at higher energies. The two peaks at E x = 25.15 and 25.55 MeV were v e r i f i e d by using a 200 ^Cg/cm ( » 5 0 keV fo r E a = 25 MeV) and stepping over the region i n 50 keV (lab) steps. We summarize the position of the peaks seen i n our (cX.cxY^), data i n table IV. A l l the ex c i t a t i o n energies have been corrected f o r the half width of the 500 yug/cm2 target (»60 keV). The widths were estimated from the y i e l d curves and do not include any e f f e c t s from interference e f f e c t s . Figure XIV. shows the y i e l d curves from a series of d i f f e r e n t experiments proceeding through 1^0* which decayed by alpha emission to the i 5 . l l MeV state of 1 2 C Since the 15.11 MeV l e v e l of 1 2 C i s primarily a T=l state (See section 1 fs & I. C ) , we ten t a t i v e l y i d e n t i f y the l e v e l s i n 0 that decay to the 15.II MeV l e v e l i n 12C as being primarily T=l configurations. 56. Many experiments have reported on the (Y ,n) and (Y ,p) reactions, and i t i s well known that the incident gamma ray i s e f f e c t i v e i n e x c i t i n g the l p - l h components of the giant dipole resonance. 1*^ However, the (Y »ocY;5|| ) shows the the existence of more complex configurations i n 16Q* than the simple l p - l h states. This i s not surprising i n l i g h t of the need to include many particle-many hole configurations to explain the structure i n the giant dipole region of l 6 0 * # 6 4 Figure XIV. A. shows that the (Y .ocY^,, ) y i e l d i s broad (P TZ. 2 MeV) and has i t s maximum y i e l d at E,,;^25.2 MeV. This agrees f a i r l y well with the maximum y i e l d of our ( ex , o( cf/5 jj ) data, and i t suggests that our data can help elucidate some of the structure seen i n the giant dipole regi of 16Q*. However, we prefer to be cautious, and we w i l l not ascribe c a t e g o r i c a l l y J**=l~ to the le v e l s seen In the ( <X , c* Y.c I I) reaction. We emphasize that the (cX . cV ) process can e a s i l y populate higher spin states than just the J ^ l " states. The 1 3 C ( 3He,c<^£ | ( ) 1 2 G data In figure XIV.B. shows the existence of states i n 1 ^ 0 * ( E x = 24.9, 25.7, 26.0, 26.9 and 27 . 4 MeV),and we note that Weller et a l . have i d e n t i f i e d the l e v e l s at E x = 26.9 and 27 . 4 MeV to be T=l.^ The state at E x = 26.9 MeV d e f i n i t e l y corresponds to a minimum i n our (cX.oC^^ data, and we suspect that t h i s i s the same state seen at E x = 26.7 MeV (J*= 1 + ) i n the l 6 0 ( e , e f ) l 6 0 * reaction. 57. Table IV A. P o s i t i o n of peaks seen i n 1 2 C ( o f ,C*Yc ,,) 1 2C E for*-(MeV) (MeV) (keV) (/xb/sr) 23.1 24.40 750 2.0 24.1 25.15 450 8.5 24.6 25.55 450 6.9 25.5 26.25 450 5.2 B. P o s i t i o n of peaks seen i n 1 2 C ( o r , a ' ) ( a 1 ) l 2 C E E rcrt. /^a-a (MeV) (MeV) (keV) (/Ub/sr) 22.0 23.6 1500 260. 23.4 24.65 (?) 25.6 26.35 1150 90. 58. Figure 14. ^ 2,4 25 2,6 2,7 2,8 2,9 a-V r e f . 50 b. r e f . (51) c. ref . (49) A d ' r e f . (52) e. 59 60 61 The J ^ = l + assignment would preclude the p o s s i b i l i t y of the (of.ofM reaction from populating t h i s l e v e l (e.g. J £ (-1) ) . The other peaks seen l n the 1 3 c ( ^Ee,oi Yj5.11 ) 1 2 C data also do not correspond to peaks i n our ( a , ck Y|$,n ) data, and we can not be sure that the same l e v e l s are being seen i n both reactions. The ^Nfd.ccY^.n ) l 2C, reaction i s isospin forbidden and has roughly 3*1 % of the strength of the isospin allowed 1%(d ,ofY a 7 |) 1 2G'. i |'9 This i s not consistent with the 1% T=0 impurities of the 15.11 MeV state of l 2 C and implies that 1 f\ * isospin mixing i s occurring i n the X D 0 compound nucleus. However, t h i s should be contrasted with our (CX , <% YIS„) and (cf,cX^ i 7 /) data. We f i n d that the former varies from 1 to 20$ of the l a t t e r , and indicates considerably more isospin 1 f * mixing i n the i D 0 compound states than that occurring i n the ^^N(d, (X ) 1 2 C * reaction. Furthermore, a comparison of figure XIV. e:. and D. shows that the (oi toClflSl) reaction exhibits a more pronounced structure than the ^H(A.,<xYis.n )^"2C data. It i s tempting to explain these features i n terms of the nuclear structure and dynamical differences of the two reactions. S p e c i f i c a l l y , we note that r e l a t i v e l y more isospin mixing i n the 0 nucleus occurs i n the (oC,oC) process than l n the (dto( ) reaction. This point helps to exemplify the powerful spectroscopic aspects of the isospin forbidden and parity unfavored 1 2 C ( # . r f ^ ^ C . process. 62. The peak a t E x = 24.4 MeV i n the (of ,d^,s.n) data agrees w e l l w i t h the 24.4 MeV sta t e found i n the 13c(3He,X, )l 60 and 16o(e,e*) l 60* r e a c t i o n s . 2 7 W e n o t e t h a t t h e l a t t e r Tr + i n d i c a t e s a J =2 assignment f o r t h i s s t a t e , and t h i s would e x p l a i n the strong d i m i n u t i o n of the y i e l d seen i n the 1 2 C ( of ,oc'V^//)12C channel. The peak at E x = 26.25 MeV seen i n our ( o f . o f ^ ) data does not seem to correspond to any of the s t a t e s seen i n the r e a c t i o n s i n f i g u r e XIV. However, i t does agree very n i c e l y w i t h the l e v e l seen a t 26.3 MeV i n the ( Y , p ) ^ and (y,n)53.5^ r e a c t i o n s . (See t a b l e V.) This gives credence to the idea that the s t a t e s seen i n the (of.of 1) process are s i m i l a r to those seen i n the ( Y .p) and ( y ,n) r e a c t i o n s . However, we b e l i e v e that these two d i f f e r e n t mechanisms f o r forming the s t a t e s i n I^Q* w o u i c ; D e s e n s i t i v e to d i f f e r e n t p a r t i c l e - h o l e c o n f i g u r a t i o n s . Figure XV. shows the y i e l d s of the 1 2 C(tf, Yo ) l 60 4 8 and the C(cf .cf'Yo , C l|) 1 2 c r e a c t i o n s , and i t i s i n t e r e s t i n g to compare these two processes. Both the 1 2 C ( <x *oCY,$.i/) 1 2 C and the E l r a d i a t i o n of the 1 2 C ( a , Yo )l60 are i s o s p i n f orbidden, but they can occur i f there i s i s o s p i n mixing i n the compound s t a t e s of ^O*. The forbiddance of the E l r a d i a t i o n has the p r a c t i c a l consequence of a l l o w i n g the E l and E2 r a d i a t i o n to be of comparable s t r e n g t h , and Snover et a l . 5 8 have indeed found some E2 strengt h around E x = 26.5 MeV. Furthermore, t h e i r data i n d i c a t e that there i s evidence 63. f o r Interference between the J^=l~ and 2 + states of ^O*. We wish to point out the co r r e l a t i o n i n energy between the peaks i n the y i e l d curves of these two d i f f e r e n t process and conclude that both processes are consistent with each other. In conclusion we note that the presence of Interfering l e v e l s i n 0 can move the apparent resonant energy by approximately the width of the state (£ T ). Since the l e v e l s that are observed i n the d i f f e r e n t reaction discussed above have widths of the order of .5 to 1.0 MeV, we do not expect that a l l the reactions w i l l be well correlated even i f the same states are being populated. It i s necessary to do detailed calculations on the r e l a t i v e strengths of the various l e v e l s which are populated, and information gained from t h i s sort of analysis would help to elucidate some of the nuclear 1 f # structure aspects of 1 0 near the giant dipole resonance. 64. IV. C. The 1 2C( Of .cx'y J 1 2 C Reaction The y i e l d curve f o r the 1 2 C ( of ,0f'^ 7 /) 1 2 C reaction has been shown i n figure VIII. on page 3 7 , and structure i s c l e a r l y exhibited i n t h i s reaction channel. As previously mentioned the structure may not be necessarily due to compound nucleus formation, but we believe t h i s to be most l i k e l y . This conclusion i s a consequence of the unnatural parity aspects o f . t h i s reaction. Drentje and Roeders have also found compound nucleus formation i n the unnatural p a r i t y e x c i t a t i o n of a ^ = 3 " l e v e l i n the reaction 2 4Mg( c* ,of ) 2 4Mg*. 6 0 It i s i n t e r e s t i n g to compare the 1 2C(of , oiYix^j) 1 2 C reaction to other i s o s p i n allowed 12C( of , c* )12 C* reactions which are not i n h i b i t e d by spin and par i t y factors. Nakamura's data f o r the l 2C(of , or') 1 2C* reaction at (lab) = 28 .5 MeV shows evidence f o r the exci t a t i o n of both the 12 .71 and 4.44 MeV le v e l s of 1 2 C . 6 1 The 4.44 MeV (J^ = 2 4 ) l e v e l of 1 2 C i s the 12 f i r s t excited state of C and i s very strongly populated i n the ( a , a ) process. We integrated the dO"(^V)/dft and &r(ll.7l)/&Q. of Nakamura and found 6>( 1 2 . 7 1 ) 2 : 1 mb and 0"T (4.44)2:400 mb. Our data f o r the 12C(o< , ofYa^12C reaction f o r Ea ( l a b ) s : 2 7 . 0 MeV indicates that Or( 1 2 . 7 1 ) 2 : . 7 mb, and th i s agrees very well with Nakamura's r e s u l t s . We note that Nakamura found no evidence f o r the e x c i t a t i o n of the 15.11 65 MeV l e v e l of C, and t h i s i s undoubtedly due to background which would mask the low y i e l d to the 15.11 MeV state (ffT2:60 /xb). Mikumo et a l . have also looked at the l 2 C ( a ,a reaction f o r Ea (lab) =28.4 MeV and found evidence f o r the formation of the 12.71 MeV l e v e l of 1 2 C . However, his data indicate 0 7 ( 1 2 . 7 1 ) ^ : 1 0 mb, and we are quite c e r t a i n that he has wrongly i d e n t i f i e d t h i s state. It appears that he was measuring the y i e l d to the j n'=4 + state at E x = 14.00 MeV and not the 1 + state at 12.71 MeV. Morgan and Hobble have studied the 1 2 C ( a , a ) l 2C(4.44-MeV) reaction f o r 19^, E^ ^ 3 0 MeV and f i n d *:L. -\ that t h i s l e v e l has d C / d T i ^ . 1 0 to 20 mb/sr. Furthermore, they state that 1 £> * they f i n d no evidence f o r formation of states i n 0 but admit t h e i r data would have d i f f i c u l t y revealing resonances due to the dominance of the d i r e c t i n t e r a c t i o n . They also f i n d that the y i e l d f o r populating the 4.44 MeV state i s consistently greater than the e l a s t i c process. Hence, we fi n d that the y i e l d to the 12.71 MeV state v i a { a , a ) i s in h i b i t e d by at least a f a c t o r of 10 and at most a factor of 400. The strong peak seen i n our 1 2 C ( or ,ory w 7) l 2C data at E x = 23.6 MeV may correspond to the J =1 l e v e l found i n the 1 2C(of ,Y0 ^ 8 reaction. (See figure XV.) The l a t t e r reaction i s Isospin forbidden and indicates that T=l Impurities are introduced l n t h i s region, and our (of.or^ )^ data v e r i f i e s 66 that there are a l s o T=0 components i n t h i s r e g i o n . Although the p opulation of the 15.11 MeV l e v e l of 1 2 C i s k i n e m a t i c a l l y p o s s i b l e , i t would be s t r o n g l y suppressed due t o p e n e t r a b i l i t y e f f e c t s . We have a l s o found s t r u c t u r e near E x = 24.65 MeV but the y i e l d curve i s ambiguous l n t h i s r e g i o n , and 1 6 * t h i s s t r u c t u r e may not correspond to a s t a t e i n i O 0 . However, a t E x = 26.4 MeV there does seem to be s t r u c t u r e which can be i n t e r p r e t e d i n terms of a compound s t a t e i n X D 0 . We note that Snover et a l . J have found a J =2 i n t h i s regit I t i s i n t e r e s t i n g that our data shows an asymmetry i n the shape of the y i e l d f o r the s t a t e at E x = 26.4 MeV, and t h i s i s most l i k e l y due to an i n t e r f e r e n c e phenomenon. The i n t e r f e r e n c e could a r i s e from the 1~ and 2 + s t a t e s 16 * i n 0 . However, we note that Moldauer has shown that i t i s p o s s i b l e f o r compound s t a t e s which are s t r o n g l y coupled to the continuum t o have i n t e r f e r e n c e w i t h a d i r e c t r e a c t i o n v 65 channel ( i n the o p t i c a l model sense), and t h i s would a l s o e x p l a i n an asymmetry i n the y i e l d . We would not expect to observe t h i s e f f e c t i n the y i e l d to the T=l 15.11 MeV l e v e l 12 of C because the compound s t a t e s would have to mix i s o s p i n , and t h i s r e q i r e s a rearrangement (time development) of the i n i t i a l T=0 s t a t e . 67. V. Conclusions It has been shown that the yi e l d s to the 12.71 and 12 15.11 MeV states i n C v i a the (#,<-/) process indicate 1 6 * the presence of both T=0 and T=l states i n •L"0 with large alpha widths. We have found T=l ( E x = 24.4, 25.15, 25.55 and 26.25 MeV) states to be narrow i n comparison with the T=0 structure ( E x = 23.6, 24.65 and 26.35 MeV), and t h i s i s consistent with the requirement that the T=l states are 1 6 * being formed by isospin mixing i n the 0 compound nucleus. Our y i e l d curves have Indicated that there i s substantial v i o l a t i o n of iso s p i n i n t h i s region, and t h i s i s i n disagreement with the prediction of Wilkinson. He had stated that the dynamical condition of PJ ^  ( H c ^ would be applicable f o r ^ 0 * ( E x ^ 2 5 MeV), and t h i s would imply an e f f e c t i v e conservation of isospin. 16 * / > \ The large isospin mixing i n 0 i n the (cx »C< ) process indicates that there i s a strong coherence i n the compound states being formed, and t h i s allows these states to l i v e long enough to be perturbed by the Coulomb forces. I t appears 16 ^ that t h i s mixing results i n 0 (T=l) states with large alpha widths, and our data may indicate the presence of alpha c l u s t e r i n g . Robson has pointed out that the nuclear surface region i s very e f f e c t i v e i n mixing isospin (asymptotic 66 67 mixing) , and Dalton and Robson ' have explained the mixing 68. o * i n Be within t h i s context. They, used an alpha c l u s t e r model to get a better description of the asymptotic region than that provided by s h e l l model wavefunctions. The 1 2 C ( oi ,p) 1%(T=3/2 l e v e l s at 11.61 and 12.51 MeV) reaction was not detected i n our spectra, even though i t has a large branching r a t i o f o r decay to the ground state of by gamma emmission. (We estimate that we would be sensitive to 6>&50 /*b.) It appears that the nuclear structure of the T=l states seen i n our (or , ex ) data are only weakly coupled to these T=3/2 states. I t i s believed that the 11.61 MeV (J 1 1" = 1/2) state of i s a 23^ /^2 nucleon outside a J1*" =0+ T=l core-, and the 12.52 MeV state (J 1 1" =5/2+) i s a l d ^ g nucleon outside a T=1,J^=0+ c o r e . ^ Hence, i t i s not surprising that we do not see these states i f our reaction ( cn , ol) to T=l states i s described by a cl u s t e r i n g e f f e c t . Similar e f f e c t s would also be observable i n other one nucleon exit channels. Our 1 0B(cx ,dY ) 1 2 C data did not show any conclusive evidence f o r formation of compound states i n N . 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