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The 12C(p,y)13N reaction 1974

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THE 1 2 C ( p , 7 ) I 3 N REACTION by David Berghofer S.B. M.I.T., 1971 A THESIS SUBMITTED IN PARTIAL FULLFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER. OF SCIENCE in the Department of Physics We accept this thesis required standard: as conforming to the In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Physics The University of B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 10, 1974 a b s t r a c t 12 13 The n i n e t y degree y i e l d c urve f o r the C(p,T) N r e a c t i o n was examined f o r p r o t o n e n e r g i e s (E ) between 14 MeV and 24.4 MeV u s i n g a 9 9 . 9 % pure carbon-12 t a r g e t and p r o t o n s from the U n i v e r s i t y o f Washington FN tandem Van de G r a a f f . The g i a n t d i p o l e resonance (GDR) f o r the gamma t r a n s i t i o n to the ground s t a t e (Yo) was found to be centered a t E = 20.5 MeV w i t h a width T = 4 MeV and a 'P. maximum c r o s s - s e c t i o n = 3 ub/sr. Intermediate s t r u c t u r e of width r = 1 MeV was observed a t E = 17.5 MeV and 23 MeV. P I L , 12 The y i e l d curve was compared to the "T5(p ,Yo) C y i e l d curve, and the s i m i l a r i t i e s found i n d i c a t e d that valence nucleon t r a n s i t i o n s to the ground s t a t e play l i t t l e p a r t i n the GDR of 1 3 N . Y i e l d curves f o r the t r a n s i t i o n to the f i r s t e x c i t e d s t a t e (Yj) and the sum of the t r a n s i t i o n s to the second and t h i r d e x c i t e d s t a t e s (X}+3) are a l s o given i n the regions where they can be r e l i a b l y e x t r a c t e d . No f i n e s t r u c t u r e was observed. Measured y i e l d s of the 12.71 MeV and 15.11 MeV gamma-rays from the i n e l a s t i c r e a c t i o n agree w e l l w i t h other recent r e s u l t s . Proton decay widths to these s t a t e s 13 from compound nuclear s t a t e s i n N are give n . i i i Angular d i s t r i b u t i o n s f o r the (p,Yo) reaction were measured a t s i x energies i n the region of the "pygmy resonance" Ep= 10 MeV to 14 MeV, to inspect previously reported f i n e s t r u c t u r e . Two narrow minima seen i n the ninety degree y i e l d are found to be minima i n the integrated cross-sections, whereas the shape of the angular d i s t r i b u t i o n i s r e l a t i v e l y constant. X V 12 13 The C(p ,Y) N Reaction table of contents: page I Introduction A General 1 B The Dipole Resonance in Mass-13 cTNuclei 5 II Experimental Equipment and Procedure A General Set-up 9 B Gamma-ray Spectrometer 11 III The 1 2C(p,7) 1 3N Reaction A Yield and Angular Distributions in the Region of the Giant Resonance 18 B Angular Distributions in the Region of the Pygmy Resonance 32 IV Yields of the 12.71 MeV and 15.11 MeV Gamma-rays from the Inelastic Reaction 1 2 cip,p Ty) 41 A Yield of the 15.11 MeV Gamma-ray 44 B Yield of the 12.71 MeV GammaFray 51 C Angular Distributions of the 12.71 MeV and 15.11 MeV Gamma-rays 55 V V D i s c u s s i o n 59 VI Summary and C o n c l u s i o n s 70 Appendix 72 B i b l i o g r a p h y 83 V I l i s t of t a b l e s : page I Angular D i s t r i b u t i o n s f o r protons s c a t t e r e d 12 i n e l a s t i c a l l y to the 15.11 MeV s t a t e i n C 24 I I C a l c u l a t e d gamma-ray angular d i s t r i b u t i o n s 12 f o r the C(p,7 0) r e a c t i o n 37 I I I Decay widths :of the 12.71 MeV and 15.11 MeV gamma-rays 42 13 IV Resonances i n N found i n the y i e l d of the 12.71 MeV and 15.11 MeV gamma-rays 47 V Angular d i s t r i b u t i o n s f o r 1 + to 0 + 12 gamma-rays f o r the r e a c t i o n C(p,p'Y) where the intermediate r a d i a t i o n i s unobserved 56 v i i l i s t of f i g u r e s : page 1 Nal c r y s t a l spectrometer 12 2 Schematic of the e l e c t r o n i c s 13 3 E f f i c i e n c y and a t t e n u a t i o n c o r r e c t i o n s 16 4 T y p i c a l spectrum 19 12 13 ~ 5 C(p,7 0) N gamma-ray y i e l d 22 6 Angular d i s t r i b u t i o n s a t 22.4 MeV and 23.3 MeV 27 12 13 • ~ 7 C(p>Yj) N gamma-ray y i e l d 29 12 13 8 CCp,^^) N gamma-ray y i e l d 30 12 13 9 C(p,Y 0) N gamma-ray y i e l d i n the r e g i o n of the pygmy resonance 33 10 Jo angular d i s t r i b u t i o n s i n the regio n of the pygmy resonance 34 11 To angular d i s t r i b u t i o n Legendre polynomial c o e f f i c i e n t s 36 12 15.11 MeV and 12.71 MeV gamma-ray y i e l d s 45 13 Legendre polynomial c o e f f i c i e n t f o r the 15.11 MeV gamma-ray 58 12 13 14 C(p , V o ) N gamma-ray y i e l d from 2.8 MeV to 24.4 MeV 60 13 13 15 N(Y,P) and C(Y,x) c r o s s - s e c t i o n s 63 11_ 12 16 c(p,T 0) and C(p,Y 0) c r o s s - s e c t i o n s 66 17 Geometric model f o r double s o l u t i o n s to i n t e r f e r i n g Breit-Wigner resonance shapes 79 v i i i acknowledgment I w o u l d l i k e t o t h a n k D r s . M e a s d a y , H a s i n o f f and M u l l i g a n f o r t h e i r v e r y p a t i e n t e x p l a n a t i o n s t o a n o v i c e i n t h e f i e l d . The e x p e r i m e n t w o u l d n o t have b e e n c o m p l e t e d w i t h o u t t h e h e l p o f t h e o t h e r g r a d u a t e s t u d e n t s i n t h e g r o u p : B . L i m , J . S p u l l e r , and K . E b i s a w a . I w o u l d a l s o l i k e t o t h a n k my w i f e , M a r t a , f o r some e x c e l l e n t l e t t e r i n g and a g r e a t d e a l o f u n d e r s t a n d i n g . I INTRODUCTION A General The giant dipole resonance (GDR), the broad peak seen i n photo-nuclear cross-sections, i s a phenomenon observed in e s s e n t i a l l y a l l n u c l e i . Many variations on the two basic models, the c o l l e c t i v e model and the independent p a r t i c l e model, have been used to describe the absorption process. Both models have been quite successful in describing most features of the giant resonance. This would seem to i n - dicate that the two models are not as d i f f e r e n t as they at f i r s t appear, and indeed Brink, 1957'!" has shown that, i n some sense, the models are equivalent. The c o l l e c t i v e model, f i r s t proposed by Goldhaber and 2 T e l l e r , 1948, pictures dipole photo-absorption as producing a c o l l e c t i v e motion whereby a l l the protons i n the nucleus o s c i l l a t e against a l l the neutrons in the mucleus. This i s e s s e n t i a l l y a quantized hydro-dynamic model, whereby a proton " f l u i d " and a neutron " f l u i d " vibrate against each other. This c o l l e c t i v e model postulates ad-hoc c o l l e c t i v e variables, such as density and v e l o c i t y d i s t r i b u t i o n s , i n the "continuous" nuclear medium, rather than dealing with the dynamical variables of the in d i v i d u a l nucleons. The energy of the giant resonance varies from 23 MeV for l i g h t n u c l e i to 14 MeV for heavy n u c l e i , and i t s width varies from 3 MeV to ;8 MeV. In the c o l l e c t i v e model, the resonant -1- energy i s a function of nuclear radius, and the width of the resonance arises from f r i c t i o n experienced by the i n t e r - penetrating f l u i d s . The radius and other c o l l e c t i v e parameters can be determined from the low-energy spectra ( i . e . the moment of i n e r t i a of the nucleus can be determined from t r a n s i t i o n s between low l y i n g r o t a t i o n a l s t a t e s ) . The f r i c t i o n term cannot, at present, be calculated from the microscopic model, and must be taken from phenomenological systematics. Thus, giant resonance shapes and strengths can be calculated with no free parameters and, for those heavy n u c l e i where the c a l c u l a t i o n has been ca r r i e d 3 out, reproduce experimental r e s u l t s quite w e l l . In addition, the c o l l e c t i v e model r e a d i l y explains the s p l i t t i n g of the giant resonance into two peaks f o r deformed n u c l e i . For these n u c l e i , the c o l l e c t i v e model indicates two primary modes of v i b r a t i o n — a low frequency mode along the long symmetry axis, and a high frequency mode along the short a x i s . The two frequencies correspond to the energies at which the cross-section peaks. This s p l i t t i n g 4 i s very apparent i n such deformed n u c l e i as holmium.'"' Recent developments of.the c o l l e c t i v e model include a three f l u i d p icture, where the excess neutrons are treated as a separate e n t i t y . The c o l l e c t i v e model smooths over nuclear structure into f l u i d s by averaging the c o l l e c t i v e motion of many nucleons, and so, should be more applicable to heavy n u c l e i (A> 40) than to l i g h t n u c l e i . - 3 - The independent p a r t i c l e model (IPM) of the GDR i s based on the s h e l l model, and was f i r s t developed by Wilkinson, 1956^ Since the ground states of nu c l e i are well described by the s h e l l model, the IPM pictures photo-absorption as exc i t i n g a single nucleon to a more energetic o r b i t a l s h e l l . The width of the giant resonance cannot be accounted for as the broadening of a s i n g l e - p a r t i c l e single-hole (lp-lh) state, although calculations with a f i n i t e p o t e n t i a l w e l l do show some broadening. Instead, the giant resonance i s often viewed as a coherent mixture of many l p - l h s t a tes. F i r s t estimates of the energy of the GDR using the IPM were s i g n i f i c a n t l y below experimental values. Attempts were made to remove the discrepancy by introducing non-local or v e l o c i t y dependent forces, with l i t t l e success. The discrepancy was suc- c e s s f u l l y removed by including a repulsive p a r t i c l e - h o l e i n t e r a c t i o n . This i s simply another way of describing the at t r a c t i o n to the nucleons i n an unclosed s h e l l experienced by an excited nucleon. This "repulsion" increases the calculated energy of the GDR. As Brink has showri^ t h i s i n teraction i s a many body co r r e l a t i o n which produces a c o l l e c t i v e motion of neutrons against protons, i . e . the c o l l e c t i v e model. Theoretical 1+ estimates of the energy now agree w e l l with experimental values. Intermediate structure in the giant resonance, which i s seen i n many nuclei (e.g. ^ 0 and ^ S i ) i s viewed according to the IPM as well-defined shell-model configurations (not necessarily l p - l h s t a t e s ) . In some cases, such a well-defined configuration i n the g i a n t resonance can be i d e n t i f i e d by the v a r i a t i o n i n the angular d i s t r i b u t i o n of the photo-nucleons (or of the gamma- rays i n the inverse r e a c t i o n ) . T h i s , however, poi n t s out a major d i f f i c u l t y of the IPM of the giant resonance. Angular d i s t r i b u t i o n s throughout the resonance, f o r the most p a r t , vary l i t t l e , i f a t a l l . This c o n t r a d i c t s ? the n o t i o n of many l p - l h s t a t e s a c t i n g coherently, as has been noted by A l i a s , e t . a l . , 6 7 1964, and Tanner, 1965. As Tanner's a n a l y s i s i n d i c a t e s , the GDR should probably be regarded as a s i n g l e broad resonance, and thus, the IPM cannot e a s i l y account f o r i t s w i dth. S t i l l , mixtures of s i n g l e p a r t i c l e wavefunctions are f r e q u e n t l y used to d escribe the GDR i n many t h e o r e t i c a l c a l c u l a t i o n s . An important v a r i a t i o n on these two models i s the schematic g model of Brown and B o l s t e r l i . This model i s again based on the mixing of l p - l h e x c i t a t i o n s by the p a r t i c l e - h o l e i n t e r a c t i o n . By making some r a d i c a l s i m p l i f y i n g assumptions, Brown and B o l s t e r l show that the coherent e f f e c t of the many s t a t e s can push a s i n g l e eigenstate to an energy much higher that the s i n g l e - p a r t i c l e e x c i t a t i o n energies, and a t the same time, endow t h i s s t a t e w i t h e s s e n t i a l l y a l l of the d i p o l e t r a n s i t i o n s t r e n g t h . This model i s simple and elegant, and gives some i n s i g h t i n t o the more d e t a i l e d p a r t i c l e - h o l e c a l c u l a t i o n s , but y i e l d s r e a l i s t i c q u a n t i t a t i v e p r e d i c t i o n s only w i t h great d i f f i c u l t y . -5- B The D i p o l e R e s o n a n c e i n M a s s - 1 3 N u c l e i 13 13 The mass-13 n u c l e i C a n d N h a v e a v e r y s i m p l e s t r u c t u r e : a v a l e n c e n u c l e o n a d d e d t o a c a r b o n - 1 2 c o r e . I f t h e a d d i t i o n a l n u c l e o n d o e s n o t c a u s e a m a j o r d i s t u r b a n c e i n t h e c o r e , t h e c a r b o n - 1 2 w i l l r e m a i n i n i t s g r o u n d s t a t e , a c l o s e d s u b s h e l l . C a r b o n - 1 2 i s a l i g h t 4n n u c l e u s . The GDR i n c a r b o n - 1 2 comes a t an e x c i t a t i o n e n e r g y E^= 23 MeV. T h i s c o n c e n t r a t i o n o f s t r e n g t h a t a h i g h e n e r g y i s a s c r i b e d t o t h e m e c h a n i s m o f t h e s c h e m a t i c m o d e l , w h i c h seems t o w e l l d e s c r i b e Mn n u c l e i , w i t h e s p e c i a l l y s y m m e t r i c s p a t i a l w a v e - f u n c t i o n s . R e c e n t r e s u l t s 12 i n d i c a t e t h e o v e r a l l s t r u c t u r e o f t h e GDR i n C c a n be m o s t l y 9 d e r i v e d f r o m s e m i - p h e n o m e n o l o g i c a l l p - l h w a v e - f u n c t i o n s . M a s s - 1 3 n u c l e i a r e among t h e s i m p l e s t n o n - c l o s e d s h e l l n u c l e i . T h e i r s t u d y s h o u l d y i e l d some i n s i g h t i n t o t h e s t r u c t u r e o f n o n - c l o s e d s h e l l n u c l e i i n g e n e r a l , a n d i n p a r t i c u l a r , i n t o how a c l o s e d s h e l l n u c l e u s i s a f f e c t e d by t h e a d d i t i o n o f a s i n g l e n u c l e o n . 13 13 The n u c l e i C a n d N h a v e b e e n w e l l - s t u d i e d , a n d many l e v e l s h a v e b e e n d o c u m e n t e d . ^ H o w e v e r , t h e s t u d y o f t h e GDR, a n d i n p a r t i c u l a r , t h e s i n g l e n u c l e o n d e c a y o f t h e d i p o l e r e s o n a n c e h a s n o t b e e n e x h a u s t i v e . C a r b o n - 1 3 i s a s t a b l e i s o t o p e , a n d c a n 13 12 t h u s be s t u d i e d d i r e c t l y . The r e a c t i o n s C C Y j p ) B and 13 12 C(7,n) C h a v e b e e n e x a m i n e d f r o m p h o t o n e n e r g i e s (Ey) b e t w e e n 5 MeV a n d 38 MeV by Cook i n WBŷ'Wid t h i s r e m a i n s t h e m o s t c o m p l e t e s t u d y t o d a t e . - 6 - Nitrogen-13 i s an unstable isotope, P + decaying to carbon-13 with a l i f e t i m e of about ten minutes. The present work i s an 13 examination of the dipole resonance i n N by means of the inverse 12 13 rad i a t i v e proton capture reaction: C(p ,Yo) N . This reaction 13 12 i s r e l a t e d to the reaction N ( Y , p o ) C by the p r i n c i p l e of 12 det a i l e d balance. (A subscript 0,1... on the p and 7 indicates t r a n s i t i o n s leaving the r e s i d u a l nucleus in the ground state, f i r s t excited state, etc.) In t h i s case, the p r i n c i p l e of de- t a i l e d balance i s v a l i d even i f time reversal invariance i s 13 violated.- While the proton t r a n s i t i o n to the ground state i n general represents the structure of the GDR f a i r l y well,' d i s t o r t i o n s 14 do occur. In p a r t i c u l a r , this mode of decay may be quite important at low energies, but may become less important at higher energies, where more decay channels are energetically allowed. Thus, the (Y,pG) cross-sections do not necessarily r e f l e c t the gross shape of the GDR. Some care must also be taken when interpreting structure i n ra d i a t i v e capture reactions. Tanner points out that such structure may be the r e s u l t of weak compound nuclear states i n t e r f e r i n g with the main broad resonance, and thus, not r e a l l y representative of the GDR7 However, even with these uncertainties, r a d i a t i v e capture has proved a powerful t o o l for studying the GDR. 12 13 U n t i l recently, the C(p,Y) N capture reaction has been rather neglected. Warburton and Funsten were the f i r s t to detect the capture gamma-ray Yo i n 1962?"^ In 1963, Fisher, et a l . l fi examined the reaction over a wider range. Both experiments were Limited by the poor energy resolution of both the proton beams (300 keV and 800 keV respectively) and the small Nal detectors ( = 13%). A more recent study by D i e t r i c h was li m i t e d 13 17 to a small region about the lowest T = '3/2 state i n N. Recent work on the capture reaction has been done at the University of Washington i n Seattle. Johnson has examined the reaction from 18 2.8 MeV to 9 MeV. Measday, Hasinoff and Johnson have examined 19 the capture reaction from 9 MeV to 16 MeV. The present report extends t h i s study to 2M.M MeV. 13 The GDR i n N can also proton-decay to the ground state 12 or excited states of C. Thus, the proton and gamma-ray cross- 12 12 sections from the C(p,p) and C(p,p Ty) e l a s t i c and i n e l a s t i c 13 reactions might also contain information about the GDR i n N. In the present study, we also examine the yi e l d s of the 12.71 MeV and 15.11 MeV gamma-rays excited intthe i n e l a s t i c reaction. Proton y i e l d s from the e l a s t i c and i n e l a s t i c reactions for incident proton energies between 9.4 MeV and 21.5 MeV have 20 12 been measured by Levine and Parker, who also measured the C(p,cx) decay. Data with a polarized proton beam have been taken by 21 13 Meyer and Plattner. The neutron decay channel i n N has been 12 12 studied v i a the C(p,n) N reaction by detecting positrons 12 22 from decay of the ground state of N by Rimmer and Fisher. 16 The r e s u l t s of Fisher, et„ a l . , showed a peak at a proton energy E^= 13 MeV, separated from the main resonance near E = 20 MeV. Our re s u l t s confirm t h i s . This lower peak has some-P times been c a l l e d a "pygmy resonance". The term "pygmy resonance" has been applied several ways i n nucelar physics. In neutron - 8 - capture spectroscopy, the term a p p l i e s to broad peaks seen i n 23 c e r t a i n mass re g i o n s . When r e f e r r i n g to the GDR, "pygmy resonance" sometimes r e f e r s to that p a r t of the d i p o l e resonance w i t h the 24 lower allowed value of i s o s p i n (T ) . For t h i s r e p o r t , the term "pygmy resonance" w i l l r e f e r only to that p a r t of the d i p o l e resonance a t an energy s i g n i f i c a n t l y lower that the main strength of the resonance. The present r e p o r t a l s o includes the measurement of s i x angular d i s t r i b u t i o n s i n the regio n of the pygmy resonance, and two angular d i s t r i b u t i o n s a t a higher energy. We s h a l l attempt to view a l l the data i n t h i s r e p o r t i n l i g h t of the f o l l o w i n g questions: 1) To what extent does the valence nucleon d i s t u r b the L 2C core? 2) Do s i n g l e - p a r t i c l e t r a n s i t i o n s i n v o l v i n g the valence nucleon c o n t r i b u t e s i g n i f i c a n t l y to the d i p o l e resonance? 3) To what extent can we i d e n t i f y resonances seen i n other r e a c t i o n s w i t h the GDR? -9- I I EXPERIMENTAL EQUIPMENT AND PROCEDURE A General Set-Up 13 The N nucleus has a single valence proton outside the 12 closed s h e l l configuration of c > TtiUS, the proton binding energy 13 for N i s 1.944 MeV (= Q value), a small number when compared 12 with the proton binding energy of 15.9 57 MeV for C. To study 13 the f u l l giant resonance region of N by ra d i a t i v e proton capture, proton energies from 10 MeV to 30 MeV would be required. Present day Van de Graff accelerators, with a maximum of approximately 25 MeV, cover most, but not a l l , of th i s region. A study of the giant resonance through the inverse (p,Y) reaction has the advantage of exhibiting more fine structure than i s possible when examining the d i r e c t (Y,p) or (Y,n) reactions, because the incident beam of charged p a r t i c l e s possesses f a r better energy resol u t i o n than any beam of photons, at present. Also, the dipole resonance for unstable isotopes, i n p a r t i c u l a r 13 N, which are unaccessible i n the d i r e c t reaction, can be studied by the capture reaction. The University of Washington's FN tandem Van de Graff can routinely achieve an energy resolution of better than 5 keV for 15 MeV protons, an uncertainty even less than the energy loss i n the target (= 10 keV). In general, energy c a l i b r a t i o n was no problem for the 12 C(P>Y) 'spectrao For incident proton energies greater than E = 17 MeV, the 12.71 MeV and 15.11 MeV gamma-rays from the P -10- i n e l a s t i c r e a c t i o n were p l a i n l y v i s i b l e , thus f i x i n g the energy c a l i b r a t i o n i . When below these t h r e s h o l d s , an energy c a l i b r a - t i o n was done f o r low-energy gamma-rays from r a d i o a c t i v e sources, and the gain was then decreased by a known amount, to b r i n g the capture gamma-rays w i t h i n ^ the energy range of the a n a l y z e r . The s i g n a l s from the spectrometer were analyzed by a pulse height analyzer (PHA) and sorted i n t o ACCEPT and REJECT b i n s , as d i s - cussed i n the f o l l o w i n g s e c t i o n . A t the end of a run, the data were dumped i n t o an SDS computer and then s t o r e d on magnetic tape f o r l a t e r a n a l y s i s . A v e r s i o n of the EGG program (see appendix) had been adapted f o r use on the SDS computer, a l l o w i n g an immediate o n - l i n e a n a l y s i s w hile the data was being taken. This i s a great a i d to the experimenter, p e r m i t t i n g him to f u r t h e r i n v e s t i g a t e i n t e r e s t i n g r e s u l t s a t once. F i n a l a n a l y s i s of a l l data was done on a time-sharing IBM computer at the U n i v e r s i t y of B r i t i s h Columbia. -11- B The Gamma-Ray Spectrometer The gamma-ray detector used i n t h i s study belonged to a U n i v e r s i t y of B r i t i s h Columbia group, but r e s i d e d a t the Univer- s i t y of Washington Nuclear Physics Laboratory. A d e t a i l e d des- c r i p t i o n g of the spectrometer has been published (Hasinoff- et a l . , 25 1973 ) , only a b r i e f account w i l l be given here. The design of the spectrometer and housing i s i l l u s t r a t e d i n f i g u r e 1, page 12 . The c e n t r a l N a l ( T l ) c r y s t a l , a c y l i n d e r 25.4 cm. i n diameter by 25.4 cm. long, .was manufactured by the French company Quartz e t S i l i c e . The response of the c r y s t a l to a 1.33 MeV gamma-ray from a c o l l i m a t e d source moved along i t s axis, was uniform to +0.75 %. A 1 cm. thickness of l i t h i u m car- bonate and wax surrounds the sides and f r o n t face of the c r y s t a l , and provides some absorption of slow neutrons. The a n t i - c o i n - cidence s h i e l d c o n s i s t s of NE 110 p l a s t i c s c i n t i l l a t o r , 10.8 cm. t h i c k . A schematic of the e l e c t r o n i c s i s shown i n f i g u r e 2, page 13 . A complete d e s c r i p t i o n of the e l e c t r o n i c s i s given by 26 Lim, 19 74. Note t h a t the anode s i g n a l i s used f o r both the l i n e a r s i g n a l and the t i m i n g . This was found to be simpler Mian?2&s£ng 'the dynode s i g n a l f o r the l i n e a r p u l s e , and caused no l o s s of r e s o l u t i o n . A g a i n - s t a b i l i z i n g u n i t was attached to the power supply of the c r y s t a l ' s photo-tubes, because the gain of the photo-tubes Figure 1 RCA 8055 NE HO Nal E Z 2 LEAD EEH L I 2 C 0 3 +WAX RCA 8055 x X x EMI 9758 B » • » t 1 0 10 20 cm N a I LINEAR PLASTIC ANTI-COINCIDENCE Nal H ANODE SUM I HIGH LEVEL DISCRIMINATOR DISC SUM ANNULUS SUM LRS LRS FAN-OUT ATTEN EGG AN 201/N EGG AN 201/N 700 n-sec DELAY ORTEC 454 LRS FAST AMP| 133 B ORTEC 454 ORTEC 454 CLIP TO 400 n-sec EGG DISCRIM. TD IOI/N [TENNELEQ GATE TC 304 EGG Gl 200/N EGG DISCRIM. 1 I EGG DISCRIM. EGG OR LRS DISCRIM.! EGG AND ORTEC AMP I EGG NAND zn J . EGG DISCRIMJ EGG Gl 200/N PHA ROUTER ND 2400 • GATE 6 DELAY EGG Gl 200/N GATE a DELAY ACCEPT REJECT Figure 2 -14- was a no n - l i n e a r f u n c t i o n of the counting r a t e . With the s t a b i l i z i n g u n i t , the gain s h i f t was decreased to about 1 %, which caused no d i f f i c u l t y i n i d e n t i f i c a t i o n of the l i n e s . The s t a b i l i z e r window was u s u a l l y s e t on the 4.4 3 MeV gamma-ray 12 from the f i r s t e x c i t e d s t a t e of C.. Cosmic ray r e j e c t i o n u s ing the a n t i - c o i n c i d e n c e s h i e l d can be made b e t t e r than 200 to 1. This spectrometer has achieved a r e s o l u t i o n of 3 % FWHM f o r 15 MeV gamma ray s , u s i n g a c o l l i m a t o r of s o l i d angle 0.035 s r . The y i e l d curve i n t h i s r e p o r t was taken w i t h a c o l l i m a t o r of s o l i d angle =0.077 s r . , h a l f - a n g l e = 7°. This gave a r e s o l u t i o n (FWHM) = 4 %, which was more than adequate. For the angular d i s t r i b u t i o n s , the c r y s t a l was moved back to maximize the range of angles. The data was taken w i t h no c o l l i m a t o r , corresponding to approximately the same s o l i d angle, causing the energy r e s o l u t i o n to worsen s l i g h t l y , to FWHM = 4.5 %. The detector could be moved between about 42° and 140°. •v The angular alignment of the c r y s t a l was checked mechanically before each run. Recently, other members of the lab have te s t e d the alignment by p l a c i n g a r a d i o a c t i v e p o i n t source i n the t a r g e t h o l d e r . The measured y i e l d was i s o t r o p i c t o w i t h i n 5 %. Most of the data . f o r the y i e l d curve were taken during a s i n g l e r un. For t h i s run, p a r a f f i n was placed i n f r o n t of the detector to reduce the neutron background. The p a r a f f i n a l s o s i g n i f i c a n t l y attenuates the gamma-rays, as does the f r o n t p l a s t i c used i n a n t i - c o i n c i d e n c e . The a n t i - c o i n c i d e n c e s h i e l d , which s i g n i f i c a n t l y improves the r e s o l u t i o n of the Nal c r y s t a l , causes some of the gamma-rays -15- to be "rejected". These gamma-rays are stored i n a separate bin as the REJECT spectrum. When ca l c u l a t i n g the absolute y i e l d from the ACCEPT spectrum, a correction f o r the percentage of gamma-rays rejected must be applied to the data, i n addition to the various attenuation f a c t o r s . The former correction, c a l l e d the " e l e c t r o n i c e f f i c i e n c y " , i s a function of the gain of the photo-tubes on the p l a s t i c s c i n t i l l a t o r , but also depends on the size of the collimator and on the energy of the gamma-ray i t s e l f . For the 10" by 10" Nal c r y s t a l , approximately 100 % of I S MeV gamma-rays i n t e r a c t , i . e . deposit some energy. Thus, the e l e c t r o n i c e f f i c i e n c y , defined by F , -p- _ # i n ACCEPT L a ' #• i n ACCEPT + # i n REJECT f o r an i s o l a t e d gamma-ray, need only be folded into the attenuation factors to give a t o t a l correction value. A c a l c u l a t i o n of the correction factor f o r the experimental set-up used i n t h i s study has been done. The r e s u l t i s given i n figure 3 on page 16 . The e l e c t r o n i c e f f i c i e n c y i s a smooth f i t to three experimental data points. The p a r r a f i n attenuation curve i s a t h e o r e t i c a l c a l c u l a t i o n normalized to one data point. The f r o n t p l a s t i c curve i s a purely t h e o r e t i c a l c a l c u l a t i o n , derived using the p l a s t i c ' s thickness and chemical composition, 27 and known mass absorption f a c t o r s . The t o t a l correction curve i s seen to vary l i t t l e as a function of gamma-ray energy. From E = IM- MeV to 25 MeV, t h i s correction varies by less than 5 %. EFFICIENCY AND ATTENUATION CORRECTIONS FOR THE 10" X10" No. I CRYSTAL DETECTOR .1*0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 y F R 0 N T PLASTIC ATTENUATION P ARR AFI N ATTENUATION - - ^ • - <Qr E L E C T R O N I C E F F I C I E NCY X T O T A L CORRECTION A E X P E R I MENTAL DATA POINTS 10 12 14 16 1* 20 22 24 G A M M A - R A Y ENERGY (MeV) Figure 3 -17- The absolute u n c e r t a i n t y of t h i s curve i s not more than 10 %, Since the v a r i a t i o n w i t h energy was s m a l l , a constant c o r r e c t i o n at 15.11 MeV, where i t i s b e t t e r known experimentally, was uniformly a p p l i e d to the data. The data p o i n t f o r the e l e c t r o n i c e f f i c i e n c y at 22.4 MeV was taken a t a separate run. There was some discrepancy i n the absolute n o r m a l i z a t i o n f o r d i f f e r e n t runs, and thus the e l e c t r o n i c e f f i c i e n c y curve given i s somewhat i n question. For the worst p o s s i b l e case, the r e l a t i v e y i e l d curves should be t i l t e d , i n - c r e a s i n g the y i e l d a t 22 MeV by 10 %, and l e a v i n g the y i e l d a t 15.1 MeV unchanged. Further s t u d i e s of the e f f i c i e n c y f o r t h i s geometry are being made to remove the p o s s i b l e discrepancy. 12 A pure carbon£12 t a r g e t (99'.9% c) w a s used throughout t h i s study. The t a r g e t thickness was measured using the narrow 13 ( P = 1.3+.3 keV) T = 3/2 resonance i n N a t proton energy o E = 14.231 MeV. The t a r g e t thickness was found to be 380 ug/cm P +10 %, i n good agreement w i t h previous measurements. For spectrometers of t h i s type, the behaviour of the gamma-ray l i n e shape i n the low energy t a i l r egion has not been determined. The present r e s u l t s have been analyzed by e x t r a p o l a t i n g the t a i l l i n e a r l y to zero energy at zero counts. The a l t e r n a t i v e extreme, e x t r a p o l a t i n g the t a i l h o r i z o n t a l l y , would increase the s t a t e d y i e l d s by 12 % a t E = 24 MeV and by 8 % a t E = 14 MeV. Combining t h i s w i t h the u n c e r t a i n t i e s i n t a r g e t thickness and detector e f f i c i e n c y , we estimate an u n c e r t a i n t y of + 30 % i n our absolute c r o s s - s e c t i o n n o r m a l i z a t i o n s . -18- I I I THE 1 2 C C p , 7 ) I 3 N REACTION A Y i e l d and Angular D i s t r i b u t i o n s i n the Region of the Giant Resonance The n i n e t y degree y i e l d f o r r a d i a t i v e proton capture on 12 C was measured f o r proton energies from 14 MeV to 24.4 MeV 13 ( e x c i t a t i o n energy i n N from E x= 14.87 MeV to 24.47 MeV). i n steps of 100 keV or s m a l l e r . The energy r e s o l u t i o n of the beam, i n c l u d i n g energy losse s i n the t a r g e t , was = 15 keV. The energy r e s o l u t i o n of the measured gamma-rays had a f u l l - width half-maximum (FWHM) = 4 %, although the r e s o l u t i o n worsened f o r cases of low y i e l d coupled w i t h a l a r g e background due to p i l e - up. A t y p i c a l spectrum i s shown i n f i g u r e 4 on page 19. The gamma-ray from the t r a n s i t i o n to the ground s t a t e (Yo) was w e l l defined i n a l l the s p e c t r a . Gamma-rays from t r a n s i t i o n s to the second and t h i r d e x c i t e d x s t a t e s a t E = 3.51 MeV and x 3.56 MeV could not be r e s o l v e d , but t h e i r sum O^+g) was always v i s i b l e , except where i t overlapped w i t h the p r o l i f i c 15.11 MeV or •'.12.71 MeV gamma-rays from the i n e l a s t i c s c a t t e r i n g r e a c t i o n s . A s i g n i f i c a n t background was present i n the region between Yo and T ^ ^ e This background could be somewhat reduced by decreasing the beam c u r r e n t from - 80 nA to - 40 nA-, implying that i t was more p i l e - u p r e l a t e d than neutron r e l a t e d . However, most spectra were taken a t — 80 nA beam, since the background was s t i l l manageable, and decreasing the beam increased running-time p r o h i b i t i v e l y . Most spectra were taken f o r an i n t e g r a t e d current o THOUSANDS CO OF COUNTS —» t O cn 0 V to to CO CO to t o c —I 4 ^ -< T J *—• o > CO "0 m o — i CZ -6T- -20- of 100 pC, w i t h a run time of —20 min/spectrum. Gamma-rays 13 from t r a n s i t i o n s to the f i r s t e x c i t e d s t a t e i n N at E = 2.366 x MeV (Yj) could be discerned above the background only i n the r e g i of the g i a n t resonane ( E p > 20.5 MeV). The data were f i t t e d i n s e v e r a l d i f f e r e n t ways, u s i n g the EGG f i t t i n g program described i n the appendix. For the hig h energy reg i o n (E > 21 MeV), the capture gamma-rays were w e l l separated from the i n e l a s t i c gamma-rays. In t h i s r e g i o n , the three capture gamma-rays (Y©,7^'T^+g) were f i t , together w i t h a fo r c e d quadratic background. The background was of the form: B ( x ) = B o ( x - CUTOFF) 2 f o r x < CUTOFF B ( x ) =0 f o r x > CUTOFF CUTOFF = xo-j^ where x = channel number x o = channel number of Y o B 0 , B ^ = parameters Thus, the background i s a pure quadratic and goes smoothly to zero a t some p o i n t above or below Y 0 . This form has the advantage of r e s t r i c t i n g the amount of background under the photo-peak of the ground s t a t e gamma-ray Y o , and of not a l l o w i n g questionable humps th a t sometimes appear i n a cubic background. The parameter B 0 was always allowed to vary, but B ^ was u s u a l l y f i x e d a t -10. -21- A t lower energies, the "^2+3 o v ^\ o f t e n overlapped w i t h one of the i n e l a s t i c gamma-rays. For these energies, 7o was f i t t e d e i t h e r alone or w i t h 7-^. The f i t t e d region had to be narrowed such that chi-squared was most a f f e c t e d by the l i n e s f i t , r a t h e r that the background. In a l l cases, the forced quadratic background was in c l u d e d i n the f i t . Whenever the 7^ was f i t , i t was necessary to f i x i t s e x c i t a t i o n energy w i t h respec. to the 7 o . I n overlap regions, the data were f i t i n s e v e r a l of the above ways. Re s u l t s were always c o n s i s t e n t w i t h i n the s t a t e d e r r o r s . 12 ^ 3 OOO The C(p , 7 0J N y i e l d curve i s given i n f i g u r e 5 on page f o r proton energy E = 14 SMeV to 24.4 MeV. The absolute nor- P m a l i z a t i o n of the c r o s s - s e c t i o n i s u n c e r t a i n by + 30 %, The r e l a t i v e e r r o r s shown i n c l u d e the s t a t i s t i c a l e r r o r and the un c e r t a i n t y due to background s u b t r a c t i o n as c a l c u l a t e d i n 28 the e r r o r matrix (see appendix and Bevington ) . The main p a r t of the d i p o l e s t r e n g t h appears centered a t E = 20.8 MeV w i t h a width of F = 4 MeV. This roughly c o i n c i d e s w i t h a s t a t e seen i n proton s c a t t e r i n g a t E = 20.8 MeV, w i t h a width r = 1.5 MeV. This s t a t e has been assigned a s p i n and p a r i t y J = 5/2 , based on the a n a l y s i s of p o l a r i z a t i o n cross- 29 s e c t i o n s by Lowe and Watson, and on i n e l a s t i c a l l y s c a t t e r e d 30 proton s c r o s s - s e c t i o n s of Sc o t t e t a l . Lowe and Watson s t a t e t h a t assignments of J u=3/2 +and l / 2 + are a l s o allowed. Scott compares the measured angular d i s t r i b u t i o n f o r proton decay to the 15.11 MeV state i n 1 2C CD TJGO 73 co o c z —1 (D m cn -z. m CD < ro D I F F E R E N T I A L C R O S S - S E C T I O N (Mb /sr) _* ro Co cn T T CEJ 11 CO o o CD > ro O > I 73 —' czT* -< m r - o 1U3 Jco to CO -23- expt(20.5) > Po + 0.1 P 1 ' + 0„8 P 2 - 0.3 Pg - 0 , 3 P^ with angular d i s t r i b u t i o n s calculated f o r decays from states o f / 3/2 + > Po + 0.5 P 2 5/2 + > P n + 0.8 P - 0.1 P ° 2 4 and conclude J = 5/2 i s indicated. However, the calculated angular d i s t r i b u t i o n s of Scott are based on the assumption that d i f f e r e n t channel spins contribute equally to the cross-sections. This assumption i s reasonable i n the sense that, i n the absence of a d e t a i l e d model f o r the reaction mechanism, we can do no better. I t has, however, a very s i g n i f i c a n t e f f e c t on the calculated angular d i s t r i b u t i o n s . Our calculations of the angular d i s t r i b u t i o n s f o r each channel spin are given i n table I on page 24. We see that no combination of channel spins f o r J1T=5/2+ can adequately account for the measured values of both a 2 and a^ (dif f e r e n t channel spins do not i n t e r f e r e ) . Other interference e f f e c t s must be important. A resonance of J = 3/2 can e a s i l y account f o r the large a value. The non-zero value of a., indicates 2 4 interference with a resonance of J ^ 5/2 with po s i t i v e p a r i t y , but t h i s i s not u n l i k e l y . I f t h i s state contributes to the 7 Q y i e l d , as seems l i k e l y , an assignment of J = 3/2 i s strongly indicated. This assignment i s not inconsistant with e x i s t i n g proton scattering data. We cannot rule out the p o s s i b i l i t y that two separate resonances are superimposed. -24- Table I Angular d i s t r i b u t i o n s f o r protons s c a t t e r e d i n e l a s t i c a l l y to the J w= 1 s t a t e a t 15.11 MeV i n c, c a l c u l a t e d i n the channel-spin coupling scheme. J ^ r e f e r s to the compound nuclear s t a t e , L to the s c a t t e r e d proton. S i s the channel s p i n . J*"" L S Angular D i s t r i b u t i o n 3/2 + 2 1/2 % ( Po + P 2) 3/2 4 p Q 5/2 + 2 1/2 6 ( Po + 1.14 P 2 +0.86 P )̂ 3/2 6 ( Po + 0.41 P 2 - 0.97 P )̂ -25- The region E p= 16.5 MeV to 18.5 MeV i n the To y i e l d probably contains further structure. Whether t h i s should be interpreted as two dips or a separate peak i s not c l e a r . The high density of states seen i n i n e l a s t i c proton scattering i n t h i s region"^ would support almost any hypothesis. Angular d i s t r i b u t i o n s i n this region might provide some in s i g h t , however these have not yet been obtained. Whether the slowly increasing y i e l d down to E^= 14 MeV joins smoothly to the pygmy resonance at E = 10 MeV to 13 MeV P or i s a separate bump i s another unresolved question. Further measurements i n t h i s region gave some in d i c a t i o n that the y i e l d reaches a minimum near 14 MeV, but because of time constraints, the s t a t i s t i c s were rather poor and r.did not warrant a d e f i n i t i v e statement. A broad background seems to underlie the entire y i e l d curve. The sharp peak at E' = 14.231 MeV i s a T = 3/2 s t a t e . This very narrow resonance was found i n the ^^B ( He,n)^N reaction, 11 3 13 and also i n the mirror reaction HB ( He,p) C. The anomaly i s 20 also seen i n proton scattering data. A spin-parity assignment of J = 3/2" was confirmed by the C(p,7 0) data of D i e t r i c h 17 31 et a l . Szucs et a l . have measured the f u l l width and found n 3 2 I = 1.3 + 0.3 keV. Adelberger et a l . , 1973, have found P = 0.82 + 0.2 keV by a coincidence ( He,nT) measurement, i n good agreement with the previous r e s u l t . The width, spin and p a r i t y , Ml decay width,cand'iother information about t h i s state .._ 13, a 11 indicate that i t i s the lowest T = 3/2 l e v e l i n N, the -26- 13 13 analogue of the ground s t a t e of B and 0. This resonance was used to measure the t a r g e t t h i c k n e s s . 13 N has two narrow T = 3/2 resonances at E = 17.86 MeV and x 18.46 MeV. These s t a t e s p r i m a r i l y proton decay to the T =11 12 15.11 MeV l e v e l i n C, and are seen i n the y i e l d of t h a t gamma- ray (see s e c t i o n IV A ) . These regions were examined i n 25 keV steps, buifc no corresponding s t r u c t u r e was seen i n the Yo y i e l d . This might i n d i c a t e a*many 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 . The s t r u c t u r e above the main strength of the GDR i s q u i t e i n t e r e s t i n g . I t might be i n t e r p r e t e d as a dip a t E^= 22.4 MeV or as a peak a t E^= 23 MeV. Angular d i s t r i b u t i o n s were performed at E = 22.4 MeV and 23.2 MeV. The r e s u l t s are shown i n f i g u r e 6 P on page 27 , together w i t h the f i t t e d Legendre polynomial c o e f f i - c i e n t s according to the equation: n Y(8) =Ao ( 1 + a i P i(cos9)) by the program LEGFIT (see appendix). An a s t e r i s k (*) above the c o e f f i c i e n t s i n d i c a t e s the f i t was f o r c e d to be non-negative a t e i t h e r forward or backward angles. At these energies, the y i e l d was taken at only f i v e angles between 60° and 124°. S t i l l , the r e s u l t s are q u i t e s t r i k i n g . A l l three capture gamma-rays are strong'ly asymmetric about ni n e t y degrees. The Yo and Yg+g are l e s s asymmetric (smaller a^) a t 23.2 MeV t h a t at 22.4 MeV (the Y^ i s l e s s w e l l d e f i n e d ) . The 15.11 MeV gamma-ray from the i n e l a s t i c r e a c t i o n i s moderately a M s o t r o p i c at 22.4 MeV, but becomes very n e a r l y i s o t r o p i c a t 23.2 MeV. - 2 7 - ANGULAR DISTRIBUTIONS AT "2 2.4 MeV AND 23.2 MeV T a.= 0.80+.04 a 2 =-0.22±.04 Qy 0.6 2+.06 a2=-O4.0+.18 olf- 0.4,5 + .13 Ep=22.4 a = 0.78+.10 al=-0.Q4 + .23 "1 Ep= 23.2 -X- a = 0.65+.20 a 2=-Q36±-21 2+3 Ep= 23.2 a = Q37+.07 a2=-0.0,Vi.18 "15.11 Ep=22.4 ao=-0.32 + .01 r 15.11 Ep=2a2 a2=-0..05+.01 r 12.71 Ep=2 2.4 a9=-0.36+.0 6 IT ' 1Z71 Ep=2a2 a 2=- 0.3.4 +.09 1 45< 90° 135° 180° 45° ANGLE (LAB) 90° 135° 180° (-X-see text) Figure 6 -28- The asymmetry i n the capture gamma-rays i n d i c a t e s that l e v e l s of opposite p a r i t y are i n t e r f e r i n g . Assuming the d i p o l e resonance i s primar i l y j"=3/2" , one could hypothesize that the other l e v e l i s the 5/2" s t a t e a t E. = 22.4 MeV, seen as a broad shoulder i n P the 15.11 MeV and 12.71 MeV y i e l d s (see s e c t i o n IV A) and i d e n t i f i e d through the a n a l y s i s of e l a s t i c s c a t t e r i n g and p o l a r i z a - 29 t i o n c r o s s - s e c t i o n s by Lowe and Watson, 1966. This would give E1-E2 i n t e r f e r e n c e i n t r a n s i t i o n s to the ground s t a t e , and would account f o r the observed angular d i s t r i b u t i o n s (see t a b l e I I on page 37 ) . However, since E1-E2 i n t e r f e r e n c e gives r i s e only to odd legendre polynomials, t h i s i n t e r f e r e n c e would not account f o r a dip i n the ni n e t y degree Y 0 y i e l d . P o s s i b l e explanations f o r t h i s s t r u c t u r e are considered i n s e c t i o n V. The Y ^ n i n e t y degree y i e l d i s given as f i g u r e 7 on page 29 f o r proton energies fro.E = 19.8 MeV to 24.4 MeV. To s i m p l i f y the f i t t i n g procedure, the e x c i t a t i o n energy of the Y ^ was always h e l d f i x e d w i t h respect t o the Y o . A t lower energies, t h i s gamma-ray i s l o s t i n a p i l e - u p a s s o c i a t e d background. The g i a n t resonance i n the y ^ y i e l d i s centered near a gamma-ray energy i£g= 19.5 MeV and has a width f = 2.5 MeV. The y i e l d seems to increase q u i t e sharply a t .E = 20.5 MeV, but the e r r o r bars are l a r g e , and the a c t u a l e f f e c t may not be so dramatic. No f i n e s t r u c t u r e was detected. The Y-2 +g y i e l d i s given as f i g u r e 8 on page' 30 from E^= 19.7 MeV to 24.4 MeV, along w i t h e a r l i e r r e s u l t s of F i s h e r e t a l . , 16 1963, a t higher proton energies. The r e s u l t s of F i s h e r have been re-normalized to agree w i t h the present r e s u l t s . At lower .... - 'y 18 EXCITATION ENERGY IN 20 22 . 1 3 N (MeV) 24 26 T GAMMA-RAY YIELD e - s o - * • l i X 18 20 22 PROTON ENERGY IN LAB (MeV) 24 26 Figure 7 20 T 1 2 C ( P . r 2 + 3 ) l 3 N GAMMA-RAY YIELD 8 r = 9 0 ° E X C I T A T I O N ENERGY IN 22 13 24 N (MeV) T T . • . . FISHER, MEASDAY. NIKOLAEV, KALMYKOV & CLEGG * * PRESENT RESULTS I. I 1 _ J _ I I I i ' I 18 20 22 24 26 PROTON ENERGY IN LAB (MeV) Figure 8 -31- proton energies, the 7^+3 o v e r ^ - a y s t n e i n e l a s t i c gamma-rays, and cannot be e x t r a c t e d r e l i a b l y . No f i n e s t r u c t u r e i s apparent. The y i e l d goes through a minimum near E = 22 MeV. The increase P a t lower energies might i n d i c a t e the presence of the pygmy resonance. A t higher energies, the y i e l d approaches the g i a n t resonance, as seen by F i s h e r . -32- B Angular D i s t r i b u t i o n s i n the Region of the Pygmy Resonance R a d i a t i v e proton capture on carbon-12 i n the region E = P 9 MeV to 15 MeV was p r e v i o u s l y s t u d i e d by Measday, H a s i n o f f , 19 and Johnson, 1973. Measday found two dramatic dips i n the T o y i e l d a t 'E = 10 o62 MeV and 13.12 MeV. T h e i r y i e l d Is r e p r i n t e d as f i g u r e 9 on page 33. The two dips were f i t q u i t e w e l l as narrow resonances of width f = 200 keV i n t e r f e r i n g w i t h the broad Background of the pygmy resonance. However, the n i n e t y degree y i e l d does not t e l l us w i t h c e r t a i n t y whether there i s a dip i n the t o t a l c r o s s - s e c t i o n , or only a r a p i d v a r i a t i o n i n the angular d i s t r i b u t i o n . A l s o , the decrease i n y i e l d could be due to a resonance i n some competing r e a c t i o n channel depopulating the s t a t e . To f u r t h e r understand t h i s phenomena, angular d i s t r i - butions were obtained i n the r e g i o n of the pygmy resonance. Angular d i s t r i b u t i o n s were measured at s i x energies, i n d i c a t e d by arrows i n f i g u r e 9. A t each energy, the y i e l d was measured a t six. angles between 45° and 135°. The angular d i s t r i - butions f o r T o are given i n f i g u r e 10 on page .34. The f i t t e d Legendre polynomial c o e f f i c i e n t s defined by the equation: n Y(Q) = A 0 ( 1 + T a. P. (cosB)) f o r n = 2 are given at each energy. Where values have been pre- ceeded by an a s t e r i s k (*), the f i t has been for c e d to be non- n e g a t i v e . The angular d i s t r i b u t i o n s are a l l peaked near ninety EXCITATION ENERGY IN , 3N (MeV) INCIDENT PROTON ENERGY (MeV) Figure 9 JP ANGULAR DISTRIBUTIONS IN THE PYGMY RESONANCE T T Ep=10.3 1 h AQ= 2.0 + .1 0.19+ .07 -0.70+.13 N 0 3 2l- E =10.65 T 0.231.04 Y - 0 . 7 9 + .09 -Ep= 13.15 ANGLE (LAB) F igure 10 -35- degrees. A l l are s l i g h t l y asymmetric. The f i t t e d Legendre polynomial c o e f f i c i e n t s are p l o t t e d i n f i g u r e 11 f o r the f i t s performed w i t h n = 2 and n = "4. The values f o r the 7 0 angular d i s t r i b u t i o n s measured a t E = 22.4 MeV P and 23.2 MeV have a l s o been i n c l u d e d . The e r r o r s shown are those c a l c u l a t e d i n the e r r o r matrix (see appendix). I n c l u d i n g the t h i r d - and fourth-order Legendre polynomials does not s i g n i f i c a n t l y 28 improve the f i t according to F - t e s t (with the p o s s i b l e exception of the Ep= 13.5 MeV angular d i s t r i b u t i o n ) . The truncated angular region allowed by the experimental set-up does not w e l l define the higher order c o e f f i c i e n t s , which r e s u l t s i n very large e r r o r s f o r the n = 4 f i t . Knowledge of the y i e l d a t f a r forward or backward angles i s necessary to b e t t e r determine the and a^ c o e f f i c i e n t s . The Legendre f i t s w i t h n== 2 were adequate, o v e r a l l . As f i g u r e 11 i l l u s t r a t e s , the a^ and c o e f f i c i e n t s are n e a r l y constant throughout t h i s r e g i o n . The only dramatic v a r i a t i o n occurs i n the A 0 c o e f f i c i e n t , i . e . the dips do occur i n the i n t e g r a t e d c r o s s - s e c t i o n . C a l c u l a t e d angular d i s t r i b u t i o n s f o r Y 0 from r a d i a t i v e proton capture i n the channel s p i n coupling scheme are given i n t a b l e I I on page -37 f o r E l , M l , and E2 r a d i a t i o n , and f o r E l - E l , Ml-Ml, E2-E2, E1-E2, and E l - M l i n t e r f e r e n c e terms. TT + Because the t a r g e t nucleus has J = 0 , the j - j and L-S coupling schemes give d i s t r i b u t i o n s which d i f f e r by only an o v e r a l l n o r m a l i z a t i o n . Assuming t h i s i s d i p o l e r a d i a t i o n , the s t r o n g l y -36- JQ ANGULAR DISTRIBUTION L E 6 E N D R E POLYNOMIAL COEFFICIENTS hi 4 I L_ 10 11 1 T - a 1 0.5 0 0 a 2 -0.5 1 L - 4 1 i I \—JI I 13^ 14 // 22 23 24 1 2 I r • 1 • 1 r- a 1 0.5 0 0 a 2 "0.5 - 1 Q5 °3 0 . - 0.5 -U-JJ L 0.5 r— a 4 0 Q5V t t * ,1 • M " " J Lt | f \ i — \ \\ 1 i , i I // 1 T " ' 1 T > 1 t ' \ \ 1 // 1 . T J 11 12 13 1 4 22 2 3 24 PROTON ENERGY IN LAB (MeV) Figure 11 -37- Table I I 12 C a l c u l a t e d gamma-ray angular d i s t r i b u t i o n s f o r the C(p ,7o ) r e a c t i o n s a s a f u n c t i o n of 1 and j of the incoming proton i n the channel s p i n coupling scheme. 1 j type Angular D i s t r i b u t i o n 0 1/2 E l 2 Po 2 3/2 E l 4 ( Po - 0 . 5 P 2) 1 1/2 Ml 2 Po 1 3/2 Ml 4 ( Po - 0 . 5 P 2) 1 3/2 E:2 4 ( Po + 0.5 P 2) 3 5/2 E2 6 ( Po + 0.57 P 2 - 0.57 P 4) I n t e r f e r e n c e Terms 1 3 type 1 3 type Angular D i s t r i b u t i o n 0 1/2 E l 2 3/2 E l i-2 P 1 1/2 Ml 1 3/2 Ml -2 P 1 3/2 E2 3 5/2 E2 -0.86 ( P 2 - 8 P )̂ 0 1/2 E l 1 1/2 Ml -2 P x 0 1/2 E l 1 3/2 Ml 2 P L 2 3/2 E l 1 1/2 Ml " 2 E l 2 3/2 E l 1 3/2 Ml 2 P l 0 1/2 E l 1 3/2 E2 1.15 P L 0 1/2 E l 3 5/2 E2 1.15 P.3 2 3/2 E l 1 3/2 E2 0.69 ( P r 6 P 3) 2 3/2 E l 3 5/2 E2 6.2 C Pj_ - 0.44 P 3) -38- negative a 2 value indicates J w= 3/2+ for the pygmy resonance. This i s an expected result, as non-spin-flip E l transitions 33 are favored over spin-flip E l transitions. That the measured value a2= -0/75 i s more negative than the predicted a2=-0„5 probably indicates some degree of background, as does the small non-zero a^ value. As the calculated angular distributions i l l u s t r a t e , the integrated cross-section (which depends only on the A 0 coefficient) can be influenced by interfering resonances only i f they have the same angular momentum and parity. Interfering levels with the same parity, but different angular momentum affect the higher order even coefficients. Interfering levels of opposite parity introduce odd Legendre polynomials. Thus, i f the structure is caused by two narrow resonances interfering with the broad pygmy resonance, our results indicate their angular momentum and parity must be 3™= 3/2+, to agree with the pygmy resonance. 19 As noted by Measday et a l . , 1973, the dip at E =10.62 P MeV coincides with a level seen in the elastic and inelastic scattering of polarized protons on carbon-12 by Meyer and 21 Plattner, 1973. This resonance, at E = 11.75 MeV, has a width x T = 250 keV, and was ascribed JTr= 3/2+ by phase shift analysis. Although some;of the results of Meyer and Plattner have been questioned by Measday, this exceptional agreement in position, width, angular momentum and parity of the resonance lends some weight to the interpretation of the dip as an interference effect. -39- We note also that fine structure of approximately this width was seen in thisnregion in the yield of the 4.43 MeV gamma-ray from the inelastic reaction in the earlier data of Adams et a l , 34 1961. The minimum at E^= 14.04 MeV, also as noted by Measday, could perhaps be identified with a level at E^= 13.96 + .05 MeV with T = 150 keV, J u= 3/2+, seen in the elastic scattering data 20 of LeVine and Parker, 1969. The alternative interpretation of the dips being caused by a resonance in some competing reaction cannot be completely ruled out. A competing reaction would not be expected to affect the angular distribution, which i s s t i l l consistent with our results. The only channel open at this energy, besides the entrance 12 9 channel and radiative decay, is C(p,o<) B. This reaction has a threshold of E = 9.5 MeV. Unfortunately, a yield curve in P 20 this region does not exist. LeVine and Parker have examined this reaction near the T = 3/2 resonance at E = 14.231 MeV, but P not at lower energies. They did note several correlations in the (p,pT) and (p, oCT) reactions at higher energies. However, the Ot. decay widths usually never vary as dramatically as would be necessary to account for the minima in the region of the pygmy resonance. The pygmy resonance is often thought to arise from transitions involving the valence nucleon. For a valence nucleon dipole 13 transition to the ground state of N to occur, the incoming proton would have to f a l l into a d q or s,y., shell orbital. -40- The measured angular distributions i n the region of the pygmy resonance are consistent with an incomin d^/v, proton (see table II) , although transitions from a many particle-hole state cannot be ruled out. Some relevant t h e o r e t i c a l calculations are discussed i n section V. -41- IV YIELDS OF THE 12.71 MeV AND 15.11 MeV GAMMA-RAYS FROM THE INELASTIC REACTION 1 2C (p,p t -y) 1 2 c " The two Jv= 1 energy l e v e l s i n C a t 12.71 MeV (T = 0) and 15,11 MeV (T = 1) both have s h e l l model c o n f i g u r a t i o n s - 1 1 12 ( p 3 ^ 2 ) ( p i / 2 ^ * w ^ i e n v i e w e d as l p - l h s t a t e s , w i t h the C core as the vacuum, the 12.71 MeV l e v e l i s symmetric i n the s p i n component of i t s wavefunction,- and anti-symmetric i n i t s i s o - s p i n component, and the 15.11 MeV l e v e l i s anti-symmetric i n s p i n and symmetric i n i s o - s p i n . Together, these l e v e l s exhaust the J = 1 strength i n the l p s h e l l and are w e l l i s o l a t e d from + 2 - 2 the next 1 c o n f i g u r a t i o n — ( s d ) (p) . Table I I I on page 42 l i s t s the known decay widths of these l e v e l s . The 12.71 MeV l e v e l alpha decays mainly to the 2.90 MeV f i r s t e x c i t e d s t a t e (J i r= 2 + , T = 0) i n 8Be, even 4 though the decay i s i n h i b i t e d by a f a c t o r of ~ 10 . (The 12.71 MeV l e v e l i s viewed as a l p - l h s t a t e , whereas alpha decay couples to 4p-4h con f i g u r a t i o n s . ) Decay to the ground s t a t e g i n Be i s p r o h i b i t e d by conservation of p a r i t y and angular momentum, thus gamma decay accounts f o r the remaining 3 % of the t o t a l w i d t h . 85 % of t h i s gamma width i s Ml r a d i a t i o n to the ground 12 s t a t e of C. The t o t a l c r o s s - s e c t i o n f o r e x c i t a t i o n of the l e v e l was c a l c u l a t e d using a branching r a t i o n YyJr = (2.5 + .3) % 3 7 and assuming an i s o t r o p i c angular d i s t r i b u t i o n . Table I I I Decay widths of the 12.71 MeV and 15.11 MeV gamma-rays Energy 3 J T C T ) a t o t a l w i dth T (eV) alpha width ry r c%) gamma-ray to ground decays ( to 4.4.MeV r iv %) to 7.7 MeV r iv yi' y to \ 12.7 MeV fy t / Vy 12.713+.006 l + ( 0 ) 14.6+2.8b 97.1+.3C 2.4+.3b 17.+.3C < 1 0 . c 15,109+.004 1 +(1) 39.4+1.53 3.6+2.8d 95.+3.6 1,5+.3C 1.5+.2° 0.7+.3c a) Ajzenberg-Selove and L a u r i t s e n , 1968 b) C e c i l et a l . , 1 9 7 4 3 6 '37 c) Riesman et a l . , 1970 3 8 d) Adelburger and B u s o l e t t i , 1973 39 e) Chertok et a l . , 1973 -43- 12 The 15.11 MeV l e v e l i s the f i r s t T = 1 state i n C, the 12 12 analogue of the ground states of B and N. Although the state i s 7.7 MeV above the alpha break-up threshold, alpha decay i s isospin forbidden, and the state decays v i a gamma emission almost e n t i r e l y . The ground state branching r a t i o i s very large ( Vy/ r ^ 92 %) , although there i s some disagreement on i t s exact 37 v40 value (see Riesman et a l . , and Alburger and Wilkinson, 1972 ) . The 15.11 MeV l e v e l could alpha decay v i a some isospin impurity, i . e . mixing of the 12.71 MeV and 15.11 MeV l e v e l s . This mixing 38,41 i s thought to occur with an amplitude of ~ 11 %. S t i l l , the alpha decay branching r a t i o of the 15.11 MeV l e v e l i s probably less than 2 %. For our cal c u l a t i o n s , we assume p / P =1 and derive the angular d i s t r i b u t i o n s from the a^ values given by figure 13 on page 58 . -44- A Y i e l d of the 15.11 MeV Gamma-Ray The 15.11 MeV gamma-ray y i e l d curve i s given i n f i g u r e 12 f o r proton energies from t h r e s h o l d (Ep = 16.39 MeV) to 24.4 MeV. The u n c e r t a i n t y i n absolute n o r m a l i z a t i o n i s + 30 %. Throughout t h i s r e g i o n , the 15.11 MeV gamma-ray i s the most prominent feature of the spectrum. No background s u b t r a c t i o n was necessary when the 15.11 MeV and 12.71 Mev gamma-rays were f i t together. The y i e l d curve d u p l i c a t e s q u i t e t ^ e l l the recent r e s u l t s of Measday 19 42 e t a l . , 1973, and Ebisawa e t a l . , 1973. 13 The narrow T =3/2 resonances i n N a t E = 17.86 MeV and P 18.46 MeV are c l e a r l y seen. These s t a t e s can proton decay to the 15.11 MeV l e v e l , but are p r o h i b i t e d from decaying to the 12.71 MeV l e v e l by i s o s p i n c o nservation. (We would estimate P / P <T 50 % f o r both resonances.) The resonance ' P12.71 ' P l 5 . l l .... 43,35 a t £^=17.3 MeV, p r e v i o u s l y seen by Snover e t a l . , has a s l i g h t l y deformed shape, which i s presumably a t h r e s h o l d e f f e c t . The most prominent features of the y i e l d are the two w e l l defined peaks a t approximately E'̂.= 19.4 MeV and 20.5 MeV, together w i t h the broad shoulder a t about 22.4 MeV. The y i e l d seems to l e v e l o f f a t about 23.6 MeV. The y i e l d a t these energies would inc l u d e c o n t r i b u t i o n s from peaks a t higher energies, i n p a r t i c u l a r the resonance seen a t E = 25.5 MeV i n the DWBA a n a l y s i s of P 30 i n e l a s t i c proton s c a t t e r i n g data by S c o t t e t a l . , 1967, and 44 In agreement w i t h the e a r l i e r gamma-ray data of Measday e t a l . ' GAMMA-RAY DIFFERENTIAL CROSS-SECTION (/ib/sr) — ro o o o o ro o o o o CD o o 00 o o > - Qs ? ro v —» • II £ N CD > '5 \ o K i -THRESHOLD 16.39 MeV CD <0 7 2 o aj <o o > < -<• • e e 0) CX) ro i O Iro ro rn x 52 5! H O z m 2: m :o o -< 2 CD < -46- The y i e l d curve was f i t i n segments w i t h two i n t e r f e r i n g Breit-Wigner resonance shapes, u s i n g the program of Has i n o f f (described i n the appendix). Results of t h i s f i t t i n g are given i n t a b l e IV on page 47 . The p a i r s of values quoted are the "strong" and "weak" s o l u t i o n discussed i n the appendix. The brackets i n d i c a t e resonances f i t as i n t e r f e r i n g p a i r s . Within any b r a c k e t , a l l the f i r s t s o l u t i o n s or a l l the second s o l u t i o n s are s e l f - c o n s i s t e n t (unless otherwise n o t e d ) . The t h i r d v a l u e , i f g i v e n , i s an estimate of the proton widths assuming no i n t e r f e r e n c e and some reasonable background s u b t r a c t i o n . A n o n - i n t e r f e r i n g background i s p o s s i b l y present under some of the f i t t e d peaks. For the 15.11 MeV y i e l d , these are the 19.4 MeV, .20.5 MeV and 22.4 MeV peaks. Rather than t r e a t the n o n - i n t e r f e r i n g background as a fr e e parameter, three s p e c i a l cases were f i t : 1) no n o n - i n t e r f e r i n g background, .2) one-half the maximum p o s s i b l e n o n - i n t e r f e r i n g background, and 3) the maximum p o s s i b l e non<?interfering background. For the peaks i n the 15.11 MeV y i e l d , the maximum background was estimated t o be s — 170 j i b / s r . The proton widths quoted are those that seemed most reasonable, w i t h t o t a l widths most n e a r l y the accepted v a l u e s . However, the quoted e r r o r s i n c l u d e the u n c e r t a i n t y i n the back- ground s u b t r a c t i o n . The peaks a t E. = 17.3 MeV and 17.9 MeV were f i t together, but appear e s s e n t i a l l y n o n - i n t e r f e r i n g . The other T = 3/2 resonance a t E - 18.46 MeV, although c l e a r l y d i s c e r n a b l e , could P not be f i t adequately. (One might guess [~ t̂<C 1*5 keV.) Table IV Resonances i n 1 N found i n the y i e l d of the 12.71 MeV and 15.11 MeV gamma-rays. E (MeV) P E x(MeV) A T ) * t o t a l width T (keV) proton v ground st a t e ?idths (keV) 12.71 MeV l e v e l 15.11 MeV l e v e l 15.27 16.02 7/2 + 102 + 10 % 7 .5 B 4.2 + 10 % 98. 5 10 % 14. + 20 % 17.3 17.9 ? 594 + 5 % 401 .1 5 % 40° 50. +20 % D , 1100"± 30 % A .? , 46 + 20 % 17.9 18.46 3/2^(3/2) 101 + 30:.% 2 5 D 1.8 + 10 % 2.5 + 20 % 18 .8 19.3 •p 500 + 100 % 50 C 320 + 100 % ^ 3640 -± 20 W 260 ± 50 % r i 19.4 19.83 5/2" (1/2) 1000 + 50 % 1500 + 50 % 175 B 21.7 -+ 50 % 230 ± 50 % 230 + 50 % ? 19.46 19.88 3 / 2 +(l / 2 ) 506 ± W.% 730 + 2 % 208B •p 11.4 + 20%^] 32.6. ± 20 % 30 + 20 % 20.5 20.9 15Q4.+ 4 % 200 G 520 + 100 % 300 + 100 % 500 + 50 % 'l69_± 20 % 65 +-20 % 360 + 20 % 22.4 22.6 5/2" F (?) 1300 + 25 % 50 G 240 + 100 %/ ? " / 600 + 50 % 100 + .50 % / 1000~+ 50 % N 160 +"30 % * references are on the f o l l o w i n g page. - 4 8 - References f o r t a b l e IV: a) Given by Ajzenber-Selove unless otherwise noted 20 b) LeVine and Parker c) We estimate P / f* = 10 % p o 2 s 11 d) Divide by s t a t i s t i c a l s p i n f a c t o r g(s) = — g — ^> 1 e) Only c o n s i s t e n t w i t h (~̂= 2300 keV f o r the 19.4 MeV resonance 30 f) Assumed from the o p t i c a l model of Scott e t a l . 29 g) Estimated, see Lowe and Watson h) Only c o n s i s t e n t w i t h |~̂ = 4.00 keV f o r the 20.5 MeV resonance -49- The f i t of the peak a t E^= 19.4 MeV y i e l d e d a width V i= 500.keV to 750 keV, which would i n d i c a t e t h a t the major c o n t r i b u t o r i s the resonance a t E = 19.46 MeV (E .= 19.88 MeV, p x P .= 520 keV). For the s e t of i n t e r f e r i n g s o l u t i o n s given f o r the peaks-at E = 19.4 MeV, 20.5 MeV, and 22.4 MeV, the upper values would seem the most b e l i e v a b l e , being the c l o s e s t to the non-resonant estimates. Note, however, t h a t the second set i s not e n t i r e l y r u l e d out. A value of Ppt= 1000 keV f o r the 22.4 MeV peak seems u n l i k e l y , but the requirement t h a t the 20.5 MeV s t a t e have a width of 400 keV could conceivably r e f l e c t a c o n t r i b u t i o n from the_19.4 MeV s t a t e , i f t h i s was the broader ( P = 1000 keV) j " W 5/2" l e v e l , r a t h e r than the 'Jv= 3/2 + s t a t e , as suggested. A l s o , f o r the 22.4 MeV peak, s u b t r a c t i o n of the n o n - i n t e r f e r i n g background causes considerable u n c e r t a i n t y i n the proton widths, which i s i n c l u d e d i n the s t a t e d errors_._ Note, however, t h a t i f the 22.4 MeV resonance has J = 5/2~, as suggested i n the a n a l y s i s of the e l a s t i c s c a t t e r i n g data by Lowe and Watson, one would not expect to see any i n t e r f e r e n c e e f f e c t s w i t h the p o s i t i v e p a r i t y s t a t e s a t E^= 20.5 MeV and 19.46 MeV i n the n i n e t y degree y i e l d . The s p i n and p a r i t y assignment of the 20.5 MeV l e v e l i s based on the o p t i c a l model phase s h i f t a n a l y s i s of e l a s t i c s c a t t e r i n g and p o l a r i z a t i o n c r o s s - s e c t i o n s done by Lowe and Watson, and i s supported by the 30 i n e l a s t i c s c a t t e r i n g data and a n a l y s i s of Scott e t a l . The s p i n assignment was questioned i n s e c t i o n I I I A, page 23 , -50- of t h i s r e p o r t o The s p i n and p a r i t y of the E = 19.46 s t a t e 20 was determined by Leyine and Parker, by o p t i c a l model phase- s h i f t a n a l y s i s of lower energy s c a t t e r i n g data. We note some disagreement i n the reported values of the / 4-3 energies and widths of the two T = 3/2 s t a t e s . Snover et a l . r e p o r t E^= 18.42 MeV and 18.97 MeV w i t h P .= 66 + 8 keV and 2 3 + 5 ReV r e s p e c t i v e l y , as given by A j z e n b e r g - S e l o v e L e V i n e and P a r k e r 2 0 r e p o r t E^= 18.35 and 18.96 MeV w i t h T ,= 100 keV and 15 keV. We give a value of F = 100 keV f o r the former resonance, but t h i s i s w i t h no background s u b t r a c t i o n . Some background s u b t r a c t i o n seems l i k e l y , and t h i s would lower our value to a b e t t e r agreement w i t h Snover. Our energy s c a l e was c a l i b r a t e d u s i n g the energy of the lowest T - 3/2 l e v e l , which i s q u i t e w e l l known. Our r e s u l t s give the energy f o r t h i s l e v e l as 18.456 + .015 MeV, a l s o i n agreement w i t h Snover. Because of our t a r g e t thickness and the q u a l i t y of our data i n the r e g i o n of the 18.96 MeV s t a t e , we cannot f u r t h e r comment on t h a t discrepancy. -51- B Y i e l d of the 12.71 Mev Gamma-Ray The 12.71 MeV y i e l d curve i s a l s o given i n f i g u r e 12 on page 4-5 f o r proton energies from 14.6 MeV to 24.4 MeV (E = 15.4 MeV to 24.5 MeV) . There i s an u n c e r t a i n t y of approximately + 30 % i n the absolute n o r m a l i z a t i o n . Above a proton energy of 16.8 MeV, the 12.71 MeV gamma-ray s i t s on the t a i l of the 15.11 MeV gamma-ray. These spectra were f i t w i t h only the 12.71 MeV and 15.11 MeV l i n e s , no other background was necessary. This introduced an a d d i t i o n a l u n c e r t a i n t y i n the r e l a t i v e y i e l d of the 12.71 MeV gamma-ray due to u n c e r t a i n t y of the low energy t a i l of the l i n e shape. To judge the e f f e c t of t h i s u n c e r t a i n t y , the spectra were a l s o f i t w i t h only the 12.71 MeV l i n e and a v a r i a b l e quadratic background over a narrower channel r e g i o n . The two f i t s agreed w e l l : a l l s t r u c t u r e was reproduced and the absolute y i e l d s overlapped, d i f f e r i n g by a maximum of 5 % on the hi g h energy side (E > 21 MeV). P — The y i e l d curve of the 12.71 MeV gamma-ray d u p l i c a t e s q u i t e 19 45 w e l l the recent r e s u l t s of Measday e t a l . , and Snover. The peak a t E = 15.27 MeV i s i d e n t i f i e d as the E = 15.22 MeV P P peak seen i n the e l a s t i c s c a t t e r i n g and r e a c t i o n data of Levine and P a r k e r 2 0 (E = 15.98 MeV, Jv= 7/2 +, T= 100 keV) . The peak a t Ep= 16.8 MeV and corresponding d i p a t E p= 17.3 MeV were p r e v i o u s l y seen by Snover. This s t r u c t u r e can probably be accounted f o r by. the two l e v e l s a t E = 16.5 MeV (E = 17.2 MeV, J p x P = 500 keV, seen i n e l a s t i c and i n e l a s t i c proton s c a t t e r i n g -52- 46 data by Daehnick and Sherr ) and a t E = 17.27 MeV (E = 17.88 J p v x. MeV, P = i+OO keV, seen by Snover e t a l . ' ) i n t e r f e r i n g w i t h a broad resonant background. The main st r e n g t h which populates the 12.71 MeV l e v e l l i e s between 18 MeV and 22 MeV. With a b i t of i m a g ination, one can see a shoulder a t E = 18.8 MeV, which P c o i n c i d e s w i t h a resonance seen by Daehnick and Sherr. One might a l s o d i s c e r n two separate peaks corresponding to.resonances at E = 19.14 MeV (E = 19.83 MeV, P= 1000 keV, J u= 5/2", T = 1/2, P * 20 seen by Daehnick and Sherr and by Levine and Parker ) and E = 20.5 MeV (E = 20.9 MeV, P= 1500 keV, ^ = ( 5 / 2 ) * , seen i n P x 30 proton s c a t t e r i n g by S c o t t e t a l . and i n the present 15.11 MeV 19 gamma-ray y i e l d , and t h a t of Measday e t a l . The l a t t e r s p i n assignment has been questioned i n s e c t i o n I I I , page' 23, of t h i s report.) Of course, these i d e n t i f i c a t i o n s a re, a t b e s t , marginal. As i n the y i e l d of the 15.11 MeV gamma-ray, we again see the broad shoulder a t E = 22.4 MeV. P Once aga i n , the y i e l d curve was f i t i n segments w i t h p a i r s of Breit-Wigner shapes. Results are a l s o given i n t a b l e IV on ? page 47. The f i r s t two values given are the "weak" and " s t r o n g " i n t e r f e r i n g s o l u t i o n s . The t h i r d v a l u e , i f g i v e n , i s an estimate of the n o n - i n t e r f e r i n g s t r e n g t h . E i t h e r a l l the f i r s t or a l l the second values of s o l u t i o n s i n brackets are s e l f - c o n s i s t e n t . The peak a t E = 15.3 MeV and the dip a t E = 17.3 MeV were P P f i t as resonances i n t e r f e r i n g w i t h a broad resonant background. For the 15.3 MeV resonance, the strong s o l u t i o n seems u n l i k e l y . -53- The d ip a t 17.3 MeV was f i t very w e l l as an i n t e r f e r i n g resonance, but could not e n t i r e l y account f o r the peak-shape near 16.7 MeV. This peak shape could i n c l u d e i n t e r f e r e n c e e f f e c t s from the E = 16.5 MeV resonance (E = 17.2 MeV, = 500 keV, seen by p x 46 Daehnick and Sherr ) . The f i t t i n g program was not capable of handl i n g three i n t e r f e r i n g resonances, but one might estimate the c o n t r i b u t i o n of the 16.5 MeV resonance to be l e s s than t h a t of the 17.3 MeV resonance, t h a t i s j - 1 < 5 0 keV. The resonances between 18 MeV and 24 MeV were f i t w i t h three n o n - i n t e r f e r i n g backgrounds subtracted: zero background, one-half the maximum p o s s i b l e background, and the maximum p o s s i b l e background = 13 ub/sr i n t h i s case. The proton widths quoted are f o r the f i t which gave f u l l widths i n best agreement w i t h accepted v a l u e s , but the quoted e r r o r s i n c l u d e the uncer- t a i n t y due to background s u b t r a c t i o n . Because the 1 2 . f l MeV and 15.11 MeV s t a t e s are so s i m i l a r i n s t r u c t u r e , we can ask to what extent are they populated by 13 13 the same compound nuclear s t a t e s i n N? Analogue s t a t e s i n N (T = 3/2) would be i s o s p i n forbidden t o decay to the 12.71 MeV (T = 0) s t a t e . However, analogue s t a t e s must correspond to 13 13 e x c i t e d s t a t e s i n B and 0. The resonances we are d e a l i n g w i t h are f a r too broad to be i d e n t i f i e d w i t h the low l y i n g 13 13 e x c i t e d s t a t e s of B (no e x c i t e d s t a t e s of 0 are known, a t p r e s e n t ) . Thus, we assume t h a t the compound nuclear s t a t e s we are d e a l i n g w i t h la&e T - l / 2 s t a t e s . (Measday, Clegg and 49 r - i F i s h e r argue t h a t the broad ( P= 1000 keV) s t a t e a t E = 26 MeV -54- 13 13 i n C and N i s the T = 3/2 component of the GDR, but t h i s i s a t a s i g n i f i c a n t l y higher e x c i t a t i o n energy.) Since t r a n s i t i o n s from these s t a t e s t o the 12.71 MeV l e v e l are not i s o s p i n suppressed, we s h a l l consider those broad compound nuclear l e v e l s known to populate the 15.11 MeV l e v e l and those seen i n proton s c a t t e r i n g data to be p r i m a r i l y r e s p o n s i b l e f o r p o p u l a t i n g the 12.71 MeV s t a t e . To some extent , t h i s i s the best we can do, since the y i e l d of the 12.71 MeV gamma-ray contains few w e l l defined resonance shapes. The s m a l l i n t e r f e r i n g s o l u t i o n f o r the 18.8 MeV resonance i s c o n s i s t a n t w i t h the n o n - i n t e r f e r i n g estimate. The large s o l u t i o n seems u n l i k e l y i n t h a t i t corresponds to a proton width of the 19.4 MeV resonance of 2300 keV, greater t h a t the f u l l width u s u a l l y a s c r i b e d t o t h a t s t a t e ( p= 1500 keV). The f i t t i n g r e s u l t s show t h a t i n t e r f e r e n c e e f f e c t s could reduce the resonant c o n t r i b u t i o n of the E =19.4 MeV peak P by an order of magnitude. I f we i d e n t i f y t h i s as the Jv= S/2~ 46 s t a t e seen i n proton s c a t t e r i n g by Daehnick and Sherr and 20 by Levine and Parker, and i n agreement w i t h i t s w i d t h , one would not expect to see i n t e r f e r e n c e e f f e c t s w i t h the p o s i t i v e p a r i t y s t a t e a t E^= 20.5 MeV i n the n i n e t y degree y i e l d . I n t h i s case, the n o n - i n t e r f e r i n g estimate may w e l l be more accur a t e . The same may be s a i d of the E = 22.4 MeV resonance. P I t should be emphasized t h a t the 12.71 MeV gamma-ray y i e l d from Ep= 18 MeV to 22 MeV can be f i t e q u a l l y w e l l w i t h a s i n g l e broad resonant shape. The proton widths f o r the 18.8, 19.4, 20.5 and 22.4 MeV s t a t e s should be considered an upper l i m i t , a t b e s t . -55- C Angular D i s t r i b u t i o n s of the 12.71 MeV and 15 e l l MeV Gamma-Rays Angular d i s t r i b u t i o n s were taken a t E = 22.4 MeV and 23.2 P 12 MeV, p r i m a r i l y t o i n s p e c t s t r u c t u r e i n the C(p , Y o ) y i e l d . The y i e l d was measured a t f i v e angles between 60° and 124°. Res u l t s f o r the capture and i n e l a s t i c gamma-rays were given i n s e c t i o n I I I A., f i g u r e 6 on page '27 , I n a d d i t i o n , the a 2 Legendre polynomial c o f f i c i e n t , d efined by the equation Y(9) = A 0 ( 1 +.a2 P 2(cos8)) i s g i v e n . The s t a t e d e r r o r s are thos- c a l c u l a t e d i n the e r r o r m a t r i x (see appendix)• C a l c u l a t e d angular d i s t r i b u t i o n s f o r t h i s M l r a d i a t i o n are given i n t a b l e V on page 56 . The angular d i s t r i b u t i o n of the 12.71 MeV gamma-ray remains constant a t these energies. The value a 2= -0»34 i s seen to be c o n s i s t e n t w i t h a P^y2 decay from a J™= 5 / 2 ~ l e v e l . A t t h i s energy, the 12.71 MeV gamma-ray s i t s on the t a i l of the 15.11 MeV gamma-ray. I t should be noted t h a t the gamma-ray r e s o l u t i o n v a r i e s s l i g h t l y w i t h angle ( r e s o l u t i o n worsens f o r backward angles, where the spectrometer i s very near the beam c o l l i m a t o r s ) . This i s a s m a l l e f f e c t on the 15.11 MeV gamma-ray, but t h e s e r r o r s on the 12.71 MeV gamma-ray value f o r a^.ihave been increased to account f o r t h i s i naccuracy. The angular d i s t r i b u t i o n of the 15.11 MeV gamma-ray changes d r a m a t i c a l l y , from Being a n i s o t r o p i c a t 22.4 MeV (a 2= -0.32 + .01) to being very n e a r l y i s o t r o p i c a t 23.3 MeV (a~= -0.05 + .01). -56- Table V + + ~~ Angular d i s t r i b u t i o n s f o r 1 — > 0 gamma-rays f o r the r e a c t i o n 12 C(p»PTlO where the intermediate r a d i a t i o n i s unobserved,, J r e f e r s t o the compound nuclear s t a t e . L.. r e f e r s to the unobserved proton. L.. Angular D i s t r i b u t i o n 1/2 s L / 2-P X/2-P3/2 P Q - 0.5 P ? 3/2 s ^ - P ^ P 0 + 0.4 E 2  d3/2" P3/2 - 2 d5/2- ±5/2 5/2 P 3/ 2- d3/2 d . d , Po + 0.46 P 2 f5/2^ d5/2 f7/2~ g7/2 Po - 0.14 P, - 5 7 - Once again, the d i s t r i b u t i o n a t 22 .4 MeV i s c o n s i s t e n t w i t h a 5/2 resonance. The d i s t r i b u t i o n a t 23 .3 MeV, however, seems more c o n s i s t e n t w i t h e i t h e r a d , .y 2 t r a n s i t i o n from a 3/2 s t a t e or an;,s^y2 t r a n s i t i o n from a l / 2 s t a t e , i f populated p r i m a r i l y through a compound n u c l e a r r e a c t i o n . This mode of po p u l a t i n g the 1 5 . 1 1 MeV s t a t e i s i m p l i e d by the proton s c a t t e r i n g data 30 of S c o t t e t a l . The 55° y i e l d f o r the 1 5 . 1 1 MeV and 1 2 . 7 1 MeV gamma-rays i n t h i s r e g i o n was p r e v i o u s l y s t u d i e d w i t h t h i s same spectro*- 47 _ meter by Ebisawa e t a l . ' This data f o r the 1 5 . 1 1 MeV gamma-ray was normalized t o the present 90° y i e l d , and the a 2 c o e f f i c i e n t throughout t h i s r e g i o n was thus e x t r a c t e d . (This work was 48 done by R. McDonald. ) The r e s u l t s are shown i n f i g u r e 1 3 . The l a r g e e r r o r bars r e s u l t from an u n c e r t a i n t y i n the r e - n o r m a l i z a t i o n , which w i l l h o p e f u l l y be reduced by f u t u r e measure- ments . The value a ^ = - 0 . 5 near 1 9 . 4 MeV agrees w e l l w i t h the assignment of ̂ = 3 / 2 ^ 0 t h a t resonance. The decreased value of a 2 n e a r 20 .5 MeV only d i s a l l o w s the assignment J = l / 2 . The value of a 2 i s seen to become more negative past E p = 22 MeV, which agrees w i t h the a 2 v a l u e a t 22 .4 MeV from the present study. LEGENDRE POLYNOMIAL COEFFICIENT FOR THE 1531 MeV 6AMMA RAY 0.2 5 i— o z : LU >—« o £ -0.2 5 Ll_ LU O O CM o -0.50 -0.75 ••EBISAWA et al . ONORMALIZED RESULTS (present study & Ebisawa) O o T o 1 •o » IT 00 Calculation by R. McDonald 19 20 21 PROTON ENERGY IN LAB (MeV) Figure 13 22 -59- V DISCUSSION This study extends recent measurements, taken at the 12 13 U n i v e r s i t y of Washington, of the C(p ,"¥<>) N r e a c t i o n from E =2.8 MeV to 2'4.I4 MeV. The r e s u l t s have been re-normalized P and are given i n f i g u r e 14 on page 60 . We estimate a 25 % u n c e r t a i n t y i n the r e l a t i v e n o r m a l i z a t i o n of the d i f f e r e n t sets of data, and an equal u n c e r t a i n t y i n the absolute y i e l d . We hope to soon make measurements to bettee determine the r e l a t i v e n o r m a l i z a t i o n s . Johnson has measured the Y0 y i e l d from E^= 2.8 MeV to 9 MevV He has shown, i n p a r t i c u l a r , t h a t the strong i n t e r f e r e n c e e f f e c t near E^= 5.3 MeV can be explained by a coupled channel c a l c u l a t i o n TT + which takes i n t o account the c o n t r i b u t i o n of the J =2 f i r s t 12 13 e x c i t e d s t a t e of C t o the ground s t a t e wave-function of N. The work of Measday, H a s i n o f f and Johnson was described i n s e c t i o n I I I B . The most s t r i k i n g aspect of these r e s u l t s i s the h e i g h t of the g i a n t resonance (E = 20 MeV) r e l a t i v e to the height of the J r pygmy (E = 12 MeV). The two peaks appear to c o n t a i n equal P s t r e n g t h s , making the terms "pygmy" and " g i a n t " seem misnomers. The p l o t t e d r e s u l t s are d i f f e r e n t i a l c r o s s - s e c t i o n s , and p r e l i m i n a r y r e s u l t s i n d i c a t e t h a t v a r i a t i o n s i n the angular d i s t r i b u t i o n of the gamma-rays might enhance the y i e l d near 20 MeV by as much as 25 %. Thus, w i t h the u n c e r t a i n t y i n r e l a t i v e n o r m a l i z a t i o n s , DIFFERENTIAL CROSS" SECTION (pb/sr) to t o CD CP 73 O —) m z m t o c -< — i _> Z ^ > C D cn t o o t o t o t o it . 'i T" I I O o a* T* C D - » j> rO > -< CO -< I — I m r -O X m co m , m i8 z > cn=< o" > C O o X z CO o z m co c : CO o "TV -09- -61- we can s t a t e only t h a t the c r o s s - s e c t i o n f o r the g i a n t resonance cannot be greater t h a t 150 % of the c r o s s - s e c t i o n f o r the pygmy. Even c o n s i d e r i n g the enhancement of low-energy y i e l d s by t r a n s i t i o n s t o the ground s t a t e , mentioned i n s e c t i o n I , t h i s demands an abnormal amount of the d i p o l e strengthk be found a t a very low energy f o r such a l i g h t nucleus. The i n t e g r a t e d c r o s s - s e c t i o n s f o r the inverse r e a c t i o n 13 12 N(T,p Q) C c a l c u l a t e d from t h i s data are: E (MeV) fa dE (MeV-mb) 7 - 1 7 17 - 24.4 11 6 where the r a t i o of these numbers i s u n c e r t a i n by 40 %. These numbers are c o n s i s t e n t w i t h an e a r l i e r c a l c u l a t i o n by Measday whose t a b l e we reproduce: Values of /Q 0"dE (MeV-mb) f o r photonuclear r e a c t i o n s e t a l . , Reaction E (MeV) 17 23.5 32 from 1 3 N ( Y , P o ) 12 22 27 Measday l 3C(Y,n) 21 55 109 49 e t a l . 1 3 c cy,p) 0 16 64 13 Measday*s N(*K,p0) i n t e g r a l s i n c l u d e a c o n t r i b u t i o n of 0.9 13 MeV-mb from the 2.37 MeV f i r s t e x c i t e d s t a t e of N not in c l u d e d i n our estimate. Even though our n o r m a l i z a t i o n i s s i g n i f i c a n t l y lower than Measday Ts, our i n t e g r a t e d cross s e c t i o n s t o 17 MeV i s -62- e s s e n t i a l l y the same. In the present r e s u l t s , the pygmy resonance i s seen t o be broader than i n d i c a t e d by the e a r l i e r r e s u l t s used by Measday, which d i d not extend below E = 10 MeV. Measday Ts 13 13 r e s u l t s f o r C(7,p) and C(Y,n) are c a l c u l a t e d from the data of Cook, 1957. 1 1 13 12 The N(T,p 0) C c r o s s - s e c t i o n derived from a d e t a i l e d balance c a l c u l a t i o n of the present r e s u l t s i s given w i t h the p h o t o - d i s i n t e g r a t i o n data of Cook i n f i g u r e 15, page 63 , 24 together w i t h the t h e o r e t i c a l c a l c u l a t i o n s of A l b e r t e t a l . and Jager e t al«?° The curve l a b e l e d ^C(Y,n) + "*"3C (y,pn) + 1 3C(Y,2n) was c a l c u l a t e d from the experimental 1 3C(Y,n) + l 3C(Y,pn) + 13 13 2 C(Y,2n) r e s u l t s by t a k i n g a h y p o t h e t i c a l C(7,2n) c r o s s - s e c t i o n and c o r r e c t i n g f o r the double-counting of neutrons. This c o r r e c t i o n only a f f e c t s the peak near E = 26 MeV, since the (7,2n) t h r e s h o l d i s 23.7 MeV. T h i s i c o r r e c t i o n has been 13 12 * c r i t i c i z e d by Measday f o r i g n o r i n g the C(V,p T) B decay to e x c i t e d s t a t e s i n boron-12, which can f u r t h e r decay by neutron emission. Thus, Measday argues, the neutron decay c r o s s - s e c t i o n could be lower a t 26 MeV, and the proton decay c r o s s - s e c t i o n h i g h e r . E a s l e a ^ argues t h a t the neutron decay c r o s s - s e c t i o n should be higher a t 26 MeV, on the b a s i s of h i s schematic model 13 c a l c u l a t i o n f o r C u s i n g harmonic o s c i l l a t o r w a v e i f u n c t i o n s . Easlea's c a l c u l a t i o n s show s i g n i f i c a n t s t r e n g t h f o r d i p o l t r a n - s i t i o n s i n the r e g i o n 10 - 17 MeV, but only a f t e r adding an ~ TT + ad-hoc i n t e r a c t i o n to c o r r e c t l y give the energy of the J = 2 12 e x c i t e d s t a t e of C a t 4.43 MeV. This procedure has been - 6 3 - PHOTO-PRODUCTION CROSS" SE CTl ONS T H E O R E T I C A L C A L C U L A T I O N S 10 WITH JGk g z o »—I V— o U J C O i CO CO o cr o Q UJ >- < o U J cr o bJ X •13Cfl.n)+ 1 3C(?.pn) h+ 1 3C(l2n) cr < cr oo cr JA6ER et al. J L T J I 7T7 10 H 18 22 26 31 6 A M M A RAY ENERGY (MeV) Figure 15 -64- c r i t i c i z e d by Measday and o t h e r s . Figure 15 gives the r e s u l t s 24 of a s i m i l a r c a l c u l a t i o n by A l b e r t e t a l . w i t h a more r e a l i s t i c 52 Tabakin p o t e n t i a l and no ad-hoc c o r r e c t i o n . This c a l c u l a t i o n shows some str e n g t h below 17 MeV, but does not adequately account f o r the pygmy resonance. The c a l c u l a t i o n s of Jager e t al.̂ ,° us i n g semi-phenomenological wave-functions, give b e t t e r agreement w i t h our r e s u l t s i n the regio n of the pygmy resonance, a t the expense of l o o s i n g s t r e n g t h near the E = 20 MeV peak. Note t h a t both c a l c u l a t i o n s support Measday Ts argument t h a t the 26 MeV resonance i s an i s o s p i n T = 3/2 component of the g i a n t resonance. Jager gives a t a b l e of a l l s h e l l model c o n f i g u r a t i o n s c o n t r i b u t i n g s i g n i f i c a n t l y to the d i p o l e s t a t e s i n h i s model. The most important c o n f i g u r a t i o n s (those c o n t r i b u t i n g s t r e n g t h ^> 5 MeV-mb) are: from ( 1 2C core) C P 3 / 2 ) ~ " L ( P 1 / 2 ) 1 ( d 5 / 2 ) 1 ( P 3 / 2 ) - 2 ( P l / 2 ) 2 ( d 5 / 2 ) 1 Jager „ , .-2, v 2 _ >1 50 & V 2 ) - ( P l / 2 } ( 2 s ) 13 I n the simple s h e l l model p i c t u r e , the ground s t a t e s of C and 13 T2 1 N would be ( C core) (P-jy2) > i . e . the valence nucleon. We see t h a t none of these c o n f i g u r a t i o n s i n v o l v e e x c i t a t i o n of the valence nucleon. Only the f i r s t c o n f i g u r a t i o n , which c a r r i e s most of the o v e r a l l s t r e n g t h , i s a l p - l h s t a t e . E x c i t a t i o n of (Is) nucleons c o n t r i b u t e very l i t t l e , and a c o n f i g u r a t i o n -65- 12 1 ( C core) (dg^p * i . e . e x c i t a t i o n of the valence nucleon, c o n t r i b u t e s only 0.05 MeV-mb a t E = 24-.1 MeV. Thus, J a g e r T s c a l c u l a t i o n views the valence nucleon as a s p e c t a t o r , even i n the re g i o n of the pygmy resonance. T r a n s i t i o n s i n v o l v i n g the valence nucleon should be seen most s t r o n g l y i n the inverse r a d i a t i v e - c a p t u r e r e a c t i o n , which leads us to speculate whether the peak seen a t E p= 23 MeV ({[E^ 23.2 MeV) could be i d e n t i f i e d w i t h Jager*s J^yT = 3/2 +,l/2 s t a t e a t E^= 24.1 MeV. To f u r t h e r support the view t h a t the valence nucleon does not play an important r o l e i n d i p o l e t r a n s i t i o n s to the ground ~~ 12 13 s t a t e , we compare our measured c r o s s - s e c t i o n f o r the C(p,V<>) N ~ IT . 12 r e a c t i o n to the c r o s s - s e c t i o n f o r o(p,Yo) C measured by 5 3 A l i a s e t a l . i n f i g u r e 16 on page 66 . The e x c i t a t i o n energy s c a l e s have been s h i f t e d by 2 MeV, but they have not been d i s - t o r t e d . The e x c i t a t i o n f u n c t i o n s appear q u i t e s i m i l a r , c o n t a i n i n g three bumps i n the r e g i o n of the g i a n t resonance. The energy s h i f t s are: 12, 1 2 c E (MeV) X 25.5 22 .5 19.3 23.2 20.8 18.0 Z \ E 2.3 1.7 1.3 + p-- > 1 3N i s + 2 MeV. We then 12 to c o r r e l a t e the peaks, we must s h i f t the C e x c i t a t i o n energy s c a l e by 4 MeV and s t r e t c h i t by about 20 %. Since the e x c i t a t i o n energies are determined by the shape of the p o t e n t i a l w e l l i n - 6 6 - RADIATIVE PROTON CAPTURE YIELDS FOR 1 1 B AND 1 2 C f —i— i — i — i — | — i i i—i—r~i—i—r 1 1 B ( p , T Q ) 1 2 C U ALLAS et a I. J L 16 1ft 20 22 24 26 2ft EXCITATION ENERGY IN 1 2 C (MeV) I — 1 — I — l — r 1 2 C(p ,T 0 ) 1 3 N present results J I I I L I L-J C i I I 1 L 14 16 1 8 20 22 24 26 EXCITATION ENERGY IN 1 3 N (MeV) Figure 16 which the nucleons r e s i d e , which in\:turn a r i s e s from the sum t o t a l of nucleon-nucleon i n t e r a c t i o n s , the d i s t o r t i o n of the energy s c a l e by the e x t r a nucleon does not seem improbable. The Qkvalue f o r 1 L B + p >.I2C i s + 15.96 MeV. The question a r i s e s whether the bump i n the (p,To) c r o s s - s e c t i o n 13 a t E = 17.5 MeV could be r e l a t e d to the pygmy resonance i n N. but cut o f f by t h r e s h o l d e f f e c t s . Were t h i s the case, one might expect to see a bound s t a t e "pygmy" resonance i n i n e l a s t i c 12 54 s c a t t e r i n g r e a c t i o n s on Q. Bergstrom e t a l . have done 13 12 e l e c t r o e x c i t a t i o n measurements on C and C. Bergstrom concludes t h a t the a d d i t i o n of the valence neutron to the 12 C core causes a major r e s t r u c t u r i n g of the g i a n t resonance s t r e n g t h . This i n t e r p r e t a t i o n seems i n c o n f l i c t w i t h the present 55 12 r e s u l t s . However, Dixon, 1973, has noted t h a t the C(Y,p) 12 and C ( V,p 0) c r o s s - s e c t i o n s and angular d i s t r i b u t i o n s are s i g n i f i c a n t l y d i f f e r e n t , i n l o c a l i z e d r e g i o n s . This discrepancy i s caused by proton decays to e x c i t e d s t a t e s i n S i m i l a r l y , we would argue t h a t the r e - d i s t r i b u t i o n of d i p o l e t r a n s i t i o n 13 12 s t r e n g t h i n C compared to C npted by Bergstrom i s caused 12 mainly by t r a n s i t i o n s to e x c i t e d s t a t e s i n C. Since most of TT + these are';.transald.ons to the J = 2 s t a t e a t E^= 4.4 MeV, w i t h a c o n f i g u r a t i o n (^C core) ( P 3 / 2 ) ""^U?l/2^ ̂ » t h e ^ d i s t r i b u t i o n of s t r e n g t h f o r these t r a n s i t i o n s caused by the presence of a valence nucleon i n the P-̂ /2 s n e H n o t a t a H s u r p r i s i n g . Our r e s u l t s s t r o n g l y support the view t h a t valence nucleon t r a n s i t i o n s to the ground s t a t e from the GDR c a r r y very l i t t l e -68- s t r e n g t h i n the regio n E = 17 - 25 MeV ( and perhaps i n the re g i o n E = 7 - 17 MeV). x I n Bergstrom Ts data, the pygmy resonance (near E = 14- MeV) 13 i n C i s most v i s i b l e i n the form f a c t o r f o r e l e c t r o n energy and s c a t t e r i n g angle E^= 106 MeV, 0 = 75°. I n the corresponding 12 C data, a r a t h e r broad s t r u c t u r e appears between E = 9 MeV and 13 MeV. We suggest t h a t t h i s may be the "analogue" of the pygmy resonance i n mass-13 n u c l e i . This i s , of course, only c o n j e c t u r e , and a t present we cannot r u l e out the a l t e r n a t i v e i n t e r p r e t a t i o n t h a t the pygmy resonance i n v o l v e s mainly valence nucleon t r a n s i t i o n s . 11 12 I f the resemblance of the a and C r a d i a t i v e capture c r o s s - s e c t i o n s i s more t h a t a coincidence, then the resonance 13 a t E = 23.3 MeV i n N should have a c o n f i g u r a t i o n i d e n t i c a l to 12 the E^= 25.5 MeV resonance i n C w i t h a spectator proton added. q The comment of Brassard e t a l . t h a t the 25.5 MeV. resonance i n 12 C i s unexplained i n the context of l p - l h s t a t e s i s very i n t e r e s t i n g i n t h i s l i g h t . A good d e a l of u n c e r t a i n t y e x i s t s concerning the p o s s i b l e 13 resonance a t E = 23.2 MeV i n N. A bump a t t h i s e x c i t a t i o n 56 10 3 12 ̂* energy was seen by S c h i f f e r e t a l . i n B( He,p T) C proton decay a t 0°. I n the sam r e a c t i o n , Kuan e t a l . , 1 9 6 4 ^ found " 58 no anomaly. Simons e t a l . , 1967, found t h a t , i f a s t a t e e x i s t s , i t does not have a strong e f f e c t on the p o l a r i z a t i o n of the s c a t t e r e d proton. They note, however, t h a t t h i s i s not e n t i r e l y 59 u n l i k e l y . A peak was seen by Patterson e t a l . , 1966, i n the 12 150° y i e l d proton decay t o the ground s t a t e i n C. They speculate t h a t i t may be the broad 22.4 MeV l e v e l (see s e c t i o n IV) which comes a t E~ =0.5 MeV, i . e . below the coulomb b a r r i e r . The JHe resonance would be d i s t o r t e d by t h r e s h o l e f f e c t s , and t h e i r 12 12 + 12 c a l c u l a t i o n s support t h i s p o s s i b i l i t y . I n the C(p,n) N (P ) C 6 0 r e a c t i o n , Rimmer and F i s h e r , 1968, f i n d s m a l l peaks a t E = 21 MeV and 23 MeV. I n t h i s r e a c t i o n , the 22.4 MeV s t a t e should not be 50 s h i f t e d . The c a l c u l a t i o n of Jager e t a l . gives a s t a t e a t 12 23.2 MeV, p r i m a r i l y of the c o n f i g u r a t i o n ( C core) . v ^•p3/2^ ^ - p l / 2 ^ ^° This s t a t e has J 7 r=3/2 +. However, i t has i s o s p i n T = 3/2, w i t h no l p - l h c o n f i g u r a t i o n c o n t r i b u t i n g . Some l p - l h s t r e n g t h would be necessary t o see t h i s s t a t e i n a proton capture r e a c t i o n . However, Jager a l s o c a l c u l a t e s a J 1 T,T = 3/2 +,l/2 s t a t e should have E = 2411 MeV. This s t a t e does have a s i g n i f i c a n t l p - l h c o n t r i b u t i o n , and so the 23.2 MeV st a t e could be populated v i a some i s o s p i n mixing w i t h the 24.1 MeV s t a t e . 61 Shakin and Wang have shown t h a t i n c l u d i n g 3p-3h s t a t e s 16 i n 0 c a l c u l a t i o n s q u i t e s u c c e s s f u l l y e x p l a i n the intermediate s t r u c t u r e i n t h a t GDR. Our r e s u l t s i n d i c a t e t h a t the 23 MeV . 1 3 resonance xn N m a y w e l l be a 3p-2h s t a t e , and analogously, the 25.5 MeV s t a t e i n 1 2 C might be e i t h e r 3p-3h or 2p-2h. Although the present reasoning has been by no means r i g o r o u s , these conclusions remain an i n t e r e s t i n g p o s s i b i l i t y . -70- VI SUMMARY AND CONCLUSIONS 12 13 We have measured gamma-rays from the C(p ,Y ) N r e a c t i o n and from the i n e l a s t i c r e a c t i o n s to the 12.71 MeV and 15.11 MeV 12 s t a t e s i n C. f o r proton energies between 10 MeV and 24.4 MeV. Intermediate s t r u c t u r e was found i n the Yo y i e l d i n the region of the g i a n t resonance. We note the s i m i l a r i t y between t h i s 11 12 y i e l d curve and t h a t of the B(p , Y 0 ) C y i e l d . This has l e d us to speculate t h a t the valence nucleon i n nitrogen-13 i s l a r g e l y a spectator i n the regio n of the GDR. This p o s s i b i l i t y i s supported by the t h e o r e t i c a l c a l c u l a t i o n of Jager e t a l . , who used semi-phenomenological wave-functions. Jager's r e s u l t s i n d i c a t e t h a t the valence nuclfeon i s a spectator even i n the region of the pygmy resonance. F o l l o w i n g t h i s l i n e of thought, we f u r t h e r speculate t h a t the pygmy resonance i n the mass-13 system may have a r e l a t e d "analogue" s t r u c t u r e i n carbon-12. We p o i n t out s t r u c t u r e i n e l e c t r o e x c i t a t i o n data of carbon-12, measured by Bergstrom e t a l . t h a t may correspond to t h i s "bound s t a t e pygmy resonance". Our measurements i n d i c a t e t h a t , f o r the (p ,Yo) r e a c t i o n , the pygmy resonance c a r r i e s s trength approximately equal to the GDR. On the b a s i s of angular d i s t r i b u t i o n measurements, we v e r i f y the existence of two narrow minima super-imposed on the pygmy resonance, and agree i n f u l l w i t h the suggestions -71- of Measday et a l . concerning t h i s s t r u c t u r e . We derive from our data y i e l d curves f o r the 12.71 MeV and 15.11 MeV gamma-rays from the i n e l a s t i c r e a e t i o n , which agree w e l l w i t h other recent r e s u l t s . We l i s t proton decay widths 13 from compound nuclear s t a t e s i n N to these s t a t e s . The (p,7^) and ( p , 7 2 + 3 ) y i e l d s are a l s o given f o r the regions i n which they can be r e l i a b l y e x t r a c t e d . No f i n e s t r u c t u r e i s seen. The next step i n determining the r o l e of the valence nucleon i n the mass-13 system might be to compare i n d e t a i l 11 12 angular d i s t r i b u t i o n s of the BCp,To) and C(p,y 0) r e a c t i o n s throughout the GDR. We hope to complete measurement of the l a t t e r q u i t e soon. Extending recent measurements of the (d,T G) N r e a c t i o n beyond E — 23 MeV might a l s o prove i n t e r e s t i n g . We f u r t h e r suggest t h a t a t h e o r e t i c a l c a l c u l a t i o n of the e x c i t a t i o n energy d i s t o r t i o n caused by the a d d i t i o n of a valence nucleon would prove v a l u a b l e . -72- APPENDIX The numerical r e s u l t s presented i n t h i s report were, f o r the most part, calculated using the following computer programs:. 1) EGG - f i t s gamma-ray l i n e shapes to a given spectrum 2) POLFT - f i t s a Legendre polynomial expansion to a given angular d i s t r i b u t i o n . 3) INTER - f i t s i n t e r f e r i n g Breit-Wigner resonance shapes to a given y i e l d curve. 4) FIND - locates approximately the second solution f o r INTER. The f i r s t three programs were based almost e n t i r e l y on the methods described i n "Data Reduction and Error Analysis f o r the 28 Physical Sciences" by P h i l i p R. Bevington. The author made only minor changes to each of these programs. The fourth was conceived and written by t h i s author. A numerical program to apply e f f i c i e n c y corrections to the data and do a d e t a i l e d balance c a l c u l a t i o n was also written, but i s straightforward and w i l l hot be described. A) EGG The EGG program w i l l f i t up to ten gamma-rays to a given spectrum. The f i t t i n g routines are those described by Bevington. The program was adapted f o r use by M. Hasinoff and J . Spnller\r (who named i t . ) - 7 3 - The program f i r s t accepts two l i n e shapes, creates up to 20 energy b i n s , and generates a l i n e shape f o r each b i n by l i n e a r i n t e r p o l a t i o n . This allows the user to vary the r e s o l u t i o n of the l i n e shape w i t h energy, or h o l d i t f i x e d . EGG ex t r a p o l a t e s the l i n e shape to zero energy l i n e a r l y to zero counts a t zero energy, or w i t h a h o r i z o n t a l s l o p e , or w i t h any slope i n between, as i n s t r u c t e d . The program w i l l f i t up to ten gamma-rays simultaneously, and w i l l vary p o s i t i o n s and amplitudes as d e s i r e d . The program w i l l a l s o add and vary a v a r i e t y of backgrounds, i n c l u d i n g t h a t described i n s e c t i o n I I I . Another u s e f u l option allows the user to h o l d the e x c i t a t i o n energy of any number of gamma-rays f i x e d w i t h respect to the f0. The program v a r i e s the allowed parameters to minimize the reduced chi-squared, defined by: 1 where Y = # of degrees of freedom I n order to minimize , the program does a Taylor S e r i e s expansion: Using the method of l e a s t squares, the optimum values f o r the parameter increments are those f o r which This r e s u l t s i n simultaneous l i n e a r equations which can be solved as a matrix equation P = SQ * CD where P and $a are row matrices and tX i s a Y X V square matrix e ^ J k Equation (1) i s solved by matrix i n v e r s i o n , done i n t h i s case by rearrangement. The inverse of the curvature matrix iX i s c a l l e d the e r r o r matrix £ . 6 =C< or c* = 1 The e r r o r s i n the v a r i e d parameters determined by the e r r o r matrix ((T •= f- • •) i n c l u d e s both the s t a t i s t i c a l e r r o r and the 3 ^ 33 u n c e r t a i n t y caused by r e l a t i v e u n c e r t a i n t i e s i n the other v a r i e d parameters. Thus, the mi n i m i z a t i o n i s achieved by f o l l o w i n g the downward curvature of the J £ hyper-surface i n a space having the v a r i e d parameters as co- o r d i n a t e s . - 7 5 - The program has been adapted to produce plots of the f i t and the data, which allows the user to see the quality of the f i t . The program can f i t a series of spectra from tape, or pick out i n d i v i d u a l spectaa. B) POLFT The POLFT program can presently f i t an angular d i s t r i b u t i o n with Legendre polynomials up to fourth order. The input required i s e s s e n t i a l l y the angles, y i e l d s and variances, together with the number of polynomials to be used and varied, and i n i t i a l guesses f o r the c o e f f i c i e n t s . POLFT uses the same procedure f o r c a l c u l a t i n g errors and minimizing ~£ as described i n the previous s e c t i o n . I t can also produce a p&ot of the data and the f i t . The program has a wide range of options which were not used i n this, study. C) INTER This program, adapted by M. Hasinoff, uses the search technique described i n section A. INTER f i t s a given e x c i t a t i o n function with two i n t e r f e r i n g Breit-Wigner resonance shapes: YCE) = S A + S Q 2 e 1 ? + ^ 2 denA denB (2) - 7 6 - denA denB + (denA denB)' X 2 cosf I CE-EA) (E-E G) + rArG - 2 s i n f \ -A (E-E r) - ( E - E j / 2 b 2 where A^ = str e n g t h of resonance A _ , 7 , 2 p i n p o u t , i E^ = energy of resonance A 1"̂  = f u l l w idth of resonance A <P = r e l a t i v e phase between the resonances i n 1 ^ = width of incoming channel of resonance A Tout = A width of outgoing channel of resonance A TA denA = E-E^+i — and s i m i l a r l y f o r resonance G. The program i s capable of v a r y i n g the s t r e n g t h , w i d t h , and c e n t r o i d energy of each resonance, and the r e l a t i v e phase, as d e s i r e d . The program f o l l o w s the j(_2 minimizing procedure described i n s e c t i o n A, and produces p l o t s of the data and the f i t , -77- An e x c i t a t i o n f u n c t i o n w i t h two peaks can f r e q u e n t l y be f i t w i t h two e n t i r e l y separate sets of parameters. This i s f u r t h e r described i n the f o l l o w i n g s e c t i o n . F i t t i n g two i n t e r f e r i n g Breit-Wigner resonance shapes to a y i e l d curve f r e q u e n t l y r e s u l t s i n two sets of s o l u t i o n s . This type of f i t t i n g was f i r s t done f o r the case of a narrow ( T ^ ) analogue s t a t e i n t e r f e r i n g w i t h a broad ( T ^ ) s t a t e , and the two s o l u t i o n s have been c a l l e d the "strong" s o l u t i o n , cor- responding to a strong analogue s t a t e i n t e r f e r i n g w i t h a weak background (the state) , and the "weak" s o l u t i o n , i . e . a weak analogue s t a t e i n t e r f e r i n g w i t h a strong background. Thus, the two s o l u t i o n s are c h a r a c t e r i z e d by very d i f f e r e n t r a t i o s f o r A^/A^, and u s u a l l y a v a r i a t i o n i n the r e l a t i v e phase. For t h i s e type of i n t e r f e r e n c e , the weak s o l u t i o n has u s u a l l y been determined to be the p h y s i c a l s o l u t i o n by comparing r e s u l t s to other a v a i l a b l e information^about the resonance. We present a s i m p l i f i e d p i c t u r e to e x p l a i n the o r i g i n of two s o l u t i o n s , and to l o c a t e the "other" s o l u t i o n a f t e r one has been found. F i r s t , we p i c t u r e the two Breit-Wigner shapes as v e c t o r s i n the complex plane. Then D) FIND Y(E) = S, e If 2 where the ve c t o r s are obviously d e r i v e d from equation ( 2 ) . The vec t o r s a r e , of course, energy dependent. I n p a r t i c u l a r YCEG) = A 2 si e*r + S, 1 2 (3) w i t h Z^E = (E G - E A) The angle f i s not a c t u a l l y the angle between the vect o r s because the ve c t o r s themselves c o n t a i n imaginary f a c t o r s . I n f a c t , S*G i s o r i e n t e d along the imaginary a x i s , and f o r <f = 0 , Ŝ " p o i n t s a t an angle P*" where ra/2 R l ^ E P = arc cos & -arc s i n •A denA, 3. v - i v — * - j ^ where denA^ E + i f ^ / 2 . Then i s i n the f o u r t h quadrant f o r E p o s i t i v e , and the t h i r d quadrant f o r ̂ E n e g a t i v e . ~ —1 *f i s then the angle which v e c t o r i s r o t a t e d from t h i s i n i t i a l p o s i t i o n . We re-normalize equation (3) such t h a t v e c t o r has the norm A^. We see, then, t h a t f o r a given y i e l d and a given s t r e n g t h f o r resonance G, a str e n g t h f o r resonance A can be found f o r any phase angle <f a t t h i s energy. The —1 W9 v e c t o r t r a c e s out an e l l i p s e as <f i s v a r i e d through 2TT. This s i t u a t i o n i s depicted by the s o l i d l i n e s i n f i g u r e 17 ( a ) . Of course a good s o l u t i o n must h o l d f o r the y i e l d a t a l l energies. We now look a t the corresponding equation f o r the y i e l d a t -79- 6E0METRIC MODEL FOR DOUBLE SOLUTIONS TO INTERFERING BREIT-WIGNER RESONANCE SHAPES - 8 0 - —2 energy E a . The s i t u a t i o n i s s i m i l a r , but v e c t o r S does not -2 p o i n t along the imaginary a x i s and the v e c t o r p o i n t s i n a d i f f e r e n t d i r e c t i o n f o r <f = 0 . To determine a s o l u t i o n good —2 a t both energies, we must r o t a t e t h i s system so t h a t overlays at <P = 0 and also re-normalize —2 S A  = r« Again we can determine a s o l u t i o n f o r S 2 f o r any value of <p , and the locus of s o l u t i o n s t r a c e s a second e l l i p s e . These are the dashed l i n e s i n f i g u r e 17 ( a ) . We see t h a t the two e l l i p s e s w i l l u s u a l l y i n t e r s e c t a t two p o i n t s , corresponding to two s o l u t i o n s f o r the r e l a t i v e phase f and the s t r e n g t h A^, f o r the same st r e n g t h  .. Of course, f o r both s o l u t i o n s to be good s o l u t i o n s thay must h o l d a t a l l e n e r g i e s , i . e . many e l l i p s e s must pass through these two p o i n t s . I n f i g u r e 17 (b) , we p l o t s t r e n g t h A^ versus <? f o r the two energies E and E a and f o r an a r b i t r a r y energy. Since the s o l u t i o n f o r S^ must be p e r i o d i c i n <p (period = 2-rr) f o r any energy, the s o l u t i o n s f o r S^ must cross twice i f they cross a t a l l . They can be n o n - i n t e r s e c t i n g or tangent. However, i f one p a i r of e l l i p s e s i n t e r s e c t f o r a given y i e l d , i t seems p l a u s i b l e t h a t e l l i p s e s w i l l i n t e r s e c t f o r a l l energies. A simple program was w r i t t e n making use of t h i s p i c t u r e . For the two resonant en e r g i e s , s o l u t i o n s f o r the .strength of one resonance was c a l c u l a t e d f o r values of between 0 and 2TT, h o l d i n g the s t r e n g t h of the other resonance f i x e d a t the value of the f i r s t s o l u t i o n found by INTER. The second s o l u t i o n , LEAF 81 OMITTED IN PAGE NUMBERING. - 8 2 - where the strengths o f A^ are equal f o r a given ̂  , was found by i n s p e c t i o n . These new guesses f o r A^ and (J? were then s u p p l i e d to the INTER program. The program FIND s u c c e s s f u l l y l o c a t e d the other s o l u t i o n approximately 75 % of the time. Some of the d i f f i c u l t i e s are thought to a r i s e from the s i m p l i f i e d assumptions made, i . e . th a t the values of A„, H , P_, E.A , and E„ remain unchanged i n the p h y s i c a l s i t u a t i o n . The program i s being s u b j e c t to f u r t h e r t e s t s . -83- b i b l i o g r a p h y : 1 B r i n k , D.M., 1957, Nuc. Phys. 4, 215 2 Goldhaber, M., and E. T e l l e r , 194-8, Phys. Rev. 74, 1046 3 Danos, M., 1973, Asilomar I n t . Conf. on Photo-nuclear Reactions and A p p l i c a t i o n s , p. 43 4 Danos, M., and E. G. F u l l e r , 1965, Ann. Rev. of Nuc. S c i . , 15, 29 (see page 52) 5 W i l k i n s o n , D.H., 1956, Physica 22, 1039 6 A l i a s , R.G., S.S. Hanna, L. Meyer-Schutzmeister, R.E. Segel, P.P. Singh, Z. vager, 1964, Phys. Rev. L e t t . 13, 628 7 Tanner, N.W., 1965, Nuc. Phys. 6_3, 383 8 Brown, G.E., and M. B o l s t e r ! ! , 1959, Phys. Rev. L e t t . 3, 472 9 Bra s s a r d , C:i, H.P. Shay, J.P. C o f f i n , W. Scholz, and D.A. Bromley, 1972, Phys. Rev. C6, 53 10 Ajzenberg-Selove, F., 1970, Nuc. Phys. A152, 1 11 Cook, B.C., 1957, Phys. Rev. 106, 300 12 Von B u t l a r , H., 1968, I n t r o d u c t i o n to Nuclear P h y s i c s , Academic Pr e s s , M.Y,, N.Y. 13 Henley, E.M., 1969, Ann. Rev. of Nuc. S c i . 19, 367 14 Segel, R.E., Asilomar I n t . Conf. on Photo-nuclear Reactions and A p p l i c a t i o n s , p. 899 15 Warburton, E.K., and H.O. Funsten, 1962, Phys. Rev. 128, 1810 16 F i s h e r , P.S., D.F. Measday, F.A.. N i k o l a e v , A. Kalmy.kov, and A0B«, Clegg, 1963, Nuc. Phys. 45, 113 -84- 17 D i e t r i c k , F.S., M e S u f f e r t , A.V.. Nero, S.S. Hanna, 1968 Phys. Rev. 16_8, 1169 18 Johnson, D.L., 1974, D o c t o r a l t h e s i s , U n i v e r s i t y of Washington (unpublished) 19 Measday, D.F.,M. H a s i n o f f , D.L. Johnson, 1973, Can. J . of Phys., 51, 1227 20 LeVine, M.J., and P.D. Parker, 1969, Phys. Rev. 186, 1021 21 Meyer, H.O., and G.R. P l a t t n e r , 1973, Nuc. Phys. A199, 413 22 Rimmer, E.M., and P.S. F i s h e r , 1968, Nuc. Phys. A108, 561,567 23 Motz, H.T., Ann. Rev. of N u c l . S c i . , 20_, 1 24 A l b e r t , D.J., R.F. Wagner, H. U b e r a l l , and C. Werntz, 1969, High Energy Phys. and N u c l . S t r u c t u r e , Ed. Devons, p. 89 25 H a s i n o f f , M.D., S.T. Lim, DliF. Measday, T.J. M u l l i g a n , 1974, N u c l . I n s t , and Methods, to be published Ann. Report, N u c l . Phys. Lab., U. of Wash., p. 19 26 Lim. S.T., 1974, D o c t o r a l t h e s i s , U n i v e r s i t y of B.C. 27 Photon Cross S e c t i o n A t t e n u a t i o n C o e f f i c i e n t s and Energy C o e f f i c i e n t s from 10 keV to 100 GeV, UvS. Dept. of Commerce, NSRDS, NBS#29, Aug. 1969 28 Bevington, P.R., Data Reduction and E r r o r A n a l y s i s f o r the P h y s i c a l Sciences, 1969, McGraw-Hill, N.Y., N.Y. 29 Lowe, J . , and D.L. Watson, 1966, Phys. L e t t . , 23_, 261 Erratum: :24B, 174 30 S c o t t , D.K., P.S. F i s h e r , and N.S. Chant, 1967, Nuc. Phys. A199, 177 -85- 31 Szucs, J . , J.E. C a i r n s , N.W. Greene, J.A. Kuehner, 1973 Physics i n Canada 29_, 4 32 Adelberger, E.G., A.B. McDonald, C L . Cocke, C.N. Davids, A ".-.P. Shukla, H.B. Mak, D. Ashery, 1973, Phys. Rev. C7, 889 33 W i l k i n s o n , D.H., 1959, Ann. Rev. of Nuc. Phys. 1,1 34 Adams, H.S., J.D. Fox, N.P. Heyderiburg, and G.M. Temmer, 1961, Phys. Rev. 124, 1899 35 Ajzenberg-Selove, F. and T. L a u r i t s e n , 1968, N u c l . Phys. A114, 1 36 C e c i l , F.E., L.W. Fagg, W.L. Bendel, E.C. Jones, 1974, Phys. Rev. C9, 798 37 Riesman, F.D., P.I. Connors, and J.B. Marion, 1970, N u c l . Phys. A153, 244 38 Adelberger, E.G., and J.E. B u s s o l e t t i , 1973, Ann. Report, Nuc. Phys. Lab., U. of Wash., p. 30 39 Chertok, B.T., C. S h e f f i e l d , S.W. Lightbody, S. Penner, and D. Blum, Phys Rev C8, 23 40 A l b u r g e r , D.E., and D.H. W i l k i n s o n , 1972, Phys Rev, C5, 384 41 B r a i t h w a i t e , W.J., J.E. B u s s o l e t t i , F.E. C e c i l , arid G.T. Garvey, 1972, Phys. Rev. L e t t . 2 9 , 276 42 Ebisawa, K., M.D. H a s i n o f f , D.L. Johnson, S.T. Lim and K.A. Snover, 1973, Ann. Report, Nuc. Phys. Lab., U. of Wash., p. 102 -86- 43 Snover, K.A., E.G. Adelberger, and R e i s s , 1968, B u l l . Am. Phys. Soc. 13, 1662 44 Measday., D.F., P.S. F i s h e r , A. Kalmykov, F5;A. N i k o l a e v , and A.B. Clegg, 1963, Nuc. Phys. -45, 98 45 Snover, KsAv, 1973, p r i v a t e communication 46 Daehnick, W.W. and R. Sherr., 1964, Phys. Rev. 133, B934 47 Ebisawa, K., M. H a s i n o f f , S.T. Lim, D.F. Measday, T.J. M u l l i g a n , and J.E. S p u l l e r , 1973, Ann. Report, Nuc. Phys. Lab., U. of Wash.', p. 100 48 McDonald, R.', 1974, p r i v a t e communication 49 Meaaday, D.F., A.B. Clegg, P.S. F i s h e r , 1965, Nuc. Phys. 61, 269 50 Jager, H.U., H.R. K i s s e n e r , R.A. Eramzhian, 1971, Nuc. Phys. A171, 16 51 E a s l e a , B.VR•, 1962, Phys. 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