UBC Theses and Dissertations

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UBC Theses and Dissertations

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

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THE  1 2  C(p,7) N I 3  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 i n the Department of Physics  We accept t h i s  t h e s i s as conforming  r e q u i r e d standard:  to the  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e  and  study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may by h i s r e p r e s e n t a t i v e s .  be  granted by  permission.  Department of  Physics  The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Date  A p r i l 10,  1974  Department or  I t i s understood that copying or  of t h i s t h e s i s f o r f i n a n c i a l g a i n written  the Head of my  Columbia  s h a l l not be  publication  allowed without  my  abstract  12 The  ninety  degree y i e l d  curve f o r the  r e a c t i o n was e x a m i n e d f o r p r o t o n e n e r g i e s 14 MeV a n d 24.4 MeV u s i n g  13 C(p,T)  (E )  N  between  a 9 9 . 9 % pure carbon-12  target  and  p r o t o n s f r o m t h e U n i v e r s i t y o f W a s h i n g t o n 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 t h e  gamma t r a n s i t i o n t o t h e ground s t a t e  (Yo) was found t o be  c e n t e r e d a t E = 20.5 MeV w i t h a w i d t h T = 4 MeV and a maximum c r o s s'-P.s e c t i o n = 3 u b / s r . I n t e r m e d i a t e s t r u c t u r e o f w i d t h r = 1 MeV was observed a t E = 17.5 MeV and 23 MeV. P IL, 12 "T5(p,Yo)  The  y i e l d curve was compared t o t h e  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 t h a t v a l e n c e n u c l e o n  t r a n s i t i o n s t o t h e ground s t a t e p l a y l i t t l e p a r t i n t h e GDR o f  1 3  N.  Y i e l d curves f o r the t r a n s i t i o n t o the f i r s t state  (Yj)  and t h e sum o f t h e t r a n s i t i o n s t o the second and  t h i r d excited states  (X} ) a r e a l s o +3  where they can be r e l i a b l y e x t r a c t e d . was  excited  observed.  g i v e n i n the r e g i o n s No f i n e s t r u c t u r e  Measured y i e l d s o f t h e 12.71 MeV and 15.11  MeV gamma-rays from t h e 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 . from compound n u c l e a r  P r o t o n decay w i d t h s t o these s t a t e s 13 states i n N are given.  iii A n g u l a r d i s t r i b u t i o n s f o r the (p,Yo) r e a c t i o n were measured a t s i x energies i n the region of the "pygmy resonance" Ep= 10 MeV t o 14 MeV, t o i n s p e c t p r e v i o u s l y reported structure.  fine  Two narrow minima seen i n the n i n e t y degree y i e l d  are found t o be minima 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 s , whereas the shape o f 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.  XV  The  12 13 C(p,Y) N Reaction  table of contents: I  II  III  page  Introduction A  General  1  B  The Dipole Resonance i n Mass-13 cTNuclei  5  Experimental Equipment and Procedure A  General Set-up  B  Gamma-ray Spectrometer  The C ( p , 7 ) N 12  A  13  Y i e l d and Angular Distributions i n the 18  Angular Distributions i n the Region of the Pygmy Resonance  IV  11  Reaction  Region of the Giant Resonance B  9  32  Yields of the 12.71 MeV and 15.11 MeV Gamma-rays from the I n e l a s t i c Reaction 12  cip,p y) T  41  A  Y i e l d of the 15.11 MeV Gamma-ray  44  B  Y i e l d of the 12.71 MeV GammaFray  51  C  Angular Distributions of the 12.71 MeV and 15.11 MeV Gamma-rays  55  V  V  Discussion  VI  Summary a n d  Appendix Bibliography  59  Conclusions  70  72 83  VI  l i s t of tables: I  page  Angular D i s t r i b u t i o n s f o r protons  scattered 12  i n e l a s t i c a l l y t o the 15.11 MeV s t a t e i n II  Calculated  C  gamma-ray a n g u l a r d i s t r i b u t i o n s  12 f o r the C(p,7 ) r e a c t i o n  37  0  III  24  Decay w i d t h s :of t h e 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 o f t h e  12.71 MeV and 15.11 MeV gamma-rays V  Angular d i s t r i b u t i o n s f o r 1  47  to 0 12 gamma-rays f o r t h e r e a c t i o n C(p,p'Y) +  +  where t h e i n t e r m e d i a t e r a d i a t i o n i s unobserved 56  vii  l i s t of figures:  page  1  N a l c r y s t a l spectrometer  12  2  Schematic o f t h e 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 5 6  7  13 C(p,7 )  N gamma-ray y i e l d  0  23.3 MeV 12 13 •~ C(p>Yj) N gamma-ray y i e l d 12 13 CCp,^^) 12  N gamma-ray y i e l d  C(p,Y ) 0  29 30  N gamma-ray y i e l d i n t h e r e g i o n 33  Jo a n g u l a r d i s t r i b u t i o n s i n the r e g i o n of t h e pygmy resonance  11  27  13  o f t h e pygmy resonance 10  22  A n g u l a r d i s t r i b u t i o n s a t 22.4 MeV and  8 9  ~  34  T o a n g u l a r 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 p o l y n o m i a l c o e f f i c i e n t f o r t h e  14 15 16 17  15.11 MeV gamma-ray 12 13 C(p,Vo) N gamma-ray y i e l d from 2.8 MeV t o 24.4 MeV 13 13 N(Y,P) and C(Y,x) c r o s s - s e c t i o n s 11_ 12 c ( p , T ) and 0  C(p,Y ) c r o s s - s e c t i o n s 0  58 60 63 66  Geometric model f o r double s o l u t i o n s t o i n t e r f e r i n g B r e i t - W i g n e r resonance shapes  79  viii  acknowledgment I would l i k e for  to thank D r s . Measday, H a s i n o f f and M u l l i g a n  t h e i r very patient explanations to a novice  in  the  field.  The e x p e r i m e n t w o u l d n o t h a v e b e e n c o m p l e t e d  without  the h e l p of the other graduate students i n  group:  B.  also like  Lim, J . Spuller,  and K. E b i s a w a .  t o t h a n k my w i f e , M a r t a , f o r  l e t t e r i n g and a g r e a t d e a l o f  some  understanding.  the  I would excellent  I  INTRODUCTION A  General  The g i a n t d i p o l e resonance  (GDR), the broad peak seen  i n photo-nuclear c r o s s - s e c t i o n s , i s a phenomenon observed in essentially a l l nuclei.  Many v a r i a t i o n s on the two  b a s i c 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 d e s c r i b e the a b s o r p t i o n process.  Both models have been q u i t e s u c c e s s f u l i n d e s c r i b i n g  most f e a t u r e s o f the g i a n t resonance.  T h i s would seem to i n -  d i c a t e t h a t the two models are n o t as d i f f e r e n t as they a t f i r s t appear, and indeed B r i n k , 1957'!" has shown t h a t , i n some sense, the models are e q u i v a l e n t . The c o l l e c t i v e model, f i r s t proposed by Goldhaber and 2 Teller,  1948, p i c t u r e s d i p o l e p h o t o - a b s o r p t i o n 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 a g a i n s t a l l the neutrons i n the m u c l e u s . e s s e n t i a l l y a q u a n t i z e d hydro-dynamic "fluid"  and a neutron " f l u i d "  This i s  model, whereby a proton  v i b r a t e a g a i n s t each o t h e r .  T h i s c o l l e c t i v e model p o s t u l a t e s ad-hoc  collective  variables,  such as d e n s i t y 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" n u c l e a r medium, r a t h e r than d e a l i n g w i t h the dynamical v a r i a b l e s of  the i n d i v i d u a l n u c l e o n s . The energy o f the g i a n t resonance v a r i e s from 23 MeV f o r  light  n u c l e i to 14 MeV f o r heavy n u c l e i , and i t s width v a r i e s  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 f u n c t i o n of n u c l e a r r a d i u s , and the width of the resonance a r i s e s 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 r a d i u s and other c o l l e c t i v e  can be determined from the low-energy s p e c t r a  parameters  ( i . e . the moment  of i n e r t i a o f 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, a t  p r e s e n t , be c a l c u l a t e d from the m i c r o s c o p i c model, and must be taken from phenomenological s y s t e m a t i c s . Thus, g i a n t resonance shapes and s t r e n g t h s can be c a l c u l a t e d w i t h no f r e e  parameters  and, f o r those heavy n u c l e i where the c a l c u l a t i o n has been c a r r i e d 3 out, reproduce e x p e r i m e n t a l r e s u l t s q u i t e w e l l .  In a d d i t i o n ,  the c o l l e c t i v e model r e a d i l y e x p l a i n s the s p l i t t i n g o f the g i a n t resonance i n t o two peaks f o r deformed n u c l e i .  F o r these n u c l e i ,  the c o l l e c t i v e model i n d i c a t e s two primary modes of v i b r a t i o n — a low frequency mode a l o n g the long symmetry a x i s , and a h i g h frequency mode a l o n g the s h o r t a x i s .  The two f r e q u e n c i e s correspond  to the e n e r g i e s a t which the c r o s s - s e c t i o n peaks.  This  splitting  4 i s v e r y apparent i n such deformed n u c l e i as holmium.'"' developments  Recent  o f . t h e c o l l e c t i v e model i n c l u d e a three f l u i d  p i c t u r e , where the excess neutrons are t r e a t e d as a separate entity. The c o l l e c t i v e model smooths  over n u c l e a r s t r u c t u r e  into  f l u i d s by a v e r a g i n g the c o l l e c t i v e motion o f many nucleons, and so, should be more a p p l i c a b l e to heavy n u c l e i light  nuclei.  ( A > 40)  than to  -3The  independent  p a r t i c l e model (IPM) o f the GDR i s based  on the s h e l l model, and was f i r s t developed by W i l k i n s o n , 1956^ Since the ground s t a t e s o f n u c l e i are w e l l d e s c r i b e d by the s h e l l model, the IPM p i c t u r e s photo-absorption as e x c i t i n g a s i n g l e nucleon  to a more e n e r g e t i c o r b i t a l s h e l l .  g i a n t resonance  cannot be accounted  The width o f the  f o r as the broadening  s i n g l e - p a r t i c l e s i n g l e - h o l e ( l p - l h ) s t a t e , although  calculations  w i t h a f i n i t e p o t e n t i a l w e l l do show some broadening. the g i a n t resonance many l p - l h  of a  Instead,  i s o f t e n viewed as a coherent mixture o f  states.  F i r s t estimates o f the energy  of the GDR u s i n g the IPM  were s i g n i f i c a n t l y below experimental v a l u e s .  Attempts were made  to remove the d i s c r e p a n c y by i n t r o d u c i n g n o n - l o c a l or v e l o c i t y dependent f o r c e s , w i t h l i t t l e  success.  The d i s c r e p a n c y was suc-  c e s s f u l l y removed by i n c l u d i n g a r e p u l s i v e interaction.  T h i s i s simply another way o f d e s c r i b i n g the  a t t r a c t i o n to the nucleons by an e x c i t e d n u c l e o n . energy  particle-hole  o f the GDR.  i n an unclosed  shell  experienced  T h i s " r e p u l s i o n " i n c r e a s e s the c a l c u l a t e d  As B r i n k has showri^ t h i s i n t e r a c t i o n i s a  many body c o r r e l a t i o n which produces a c o l l e c t i v e motion o f neutrons  a g a i n s t 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 w i t h experimental v a l u e s .  Intermediate s t r u c t u r e i n the g i a n t resonance, which i s seen  i n many n u c l e i  (e.g. ^ 0 and ^ S i ) i s viewed a c c o r d i n g t o  the IPM as w e l l - d e f i n e d s h e l l - m o d e l c o n f i g u r a t i o n s (not n e c e s s a r i l y lp-lh states).  In some cases, such a w e l l - d e f i n e d c o n f i g u r a t i o n  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 a n g u l a r d i s t r i b u t i o n of the photo-nucleons (or of the gammar a y s i n the i n v e r s e r e a c t i o n ) . major d i f f i c u l t y of the IPM  T h i s , however, p o i n t s out  of the g i a n t resonance.  a  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 , little,  i f at a l l .  This contradicts?  s t a t e s a c t i n g c o h e r e n t l y , as has  6  1964,  and Tanner, 1965.  7  vary  the n o t i o n o f many l p - l h  been noted by A l i a s , e t . a l . ,  As Tanner's a n a l y s i s  indicates,  the  GDR  s h o u l d p r o b a b l y be r e g a r d e d as a s i n g l e broad resonance,  and  t h u s , the IPM  cannot e a s i l y account f o r i t s w i d t h .  Still,  m i x t u r e s of s i n g l e p a r t i c l e w a v e f u n c t i o n s are f r e q u e n t l y d e s c r i b e the GDR An  i n many t h e o r e t i c a l  used to  calculations.  i m p o r t a n t v a r i a t i o n on these two  models i s the  schematic  g model of Brown and  Bolsterli.  T h i s model i s a g a i n based on  m i x i n g 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  interaction.  By making some r a d i c a l s i m p l i f y i n g assumptions, Brown and show t h a t the c o h e r e n t e f f e c t of the many s t a t e s  e l e g a n t , and  transition  predictions  strength.  g i v e s some i n s i g h t i n t o  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 quantitative  single-  a t the same t i m e , 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 h i s model i s s i m p l e and  Bolsterl  can push a  s i n g l e e i g e n s t a t e to an energy much h i g h e r t h a t the p a r t i c l e e x c i t a t i o n e n e r g i e s , and  the  only w i t h great d i f f i c u l t y .  realistic  the  -5B  The  D i p o l e Resonance  i n Mass-13 N u c l e i  13 The  mass-13 n u c l e i  a valence nucleon  nucleon  does not  Carbon-12  light  an  excitation  strength  indicate  from  of  a  shell  i n the a  GDR  should nuclei  core,  closed  the  subshell. comes  concentration of mechanism  d e s c r i b e Mn  of  nuclei,  the with  wave-functions. of  yield  Recent results 12 in C c a n be m o s t l y  t h e GDR  lp-lh  9  wave-functions.  simplest non-closed some i n s i g h t  i n g e n e r a l , and  nucleus  additional  i n carbon-12  This  to w e l l  structure :  i s affected  by  into  shell  the  structure  in particular, the  addition  into  of  a  nucleon.  The  nuclei  13 C and  N have been w e l l - s t u d i e d , and  have been documented.^ However,  and  in particular,  has  not  thus  The  MeV.  among t h e  13  levels  state,  simple  I f the  i s a s c r i b e d to the  seems  are  core.  disturbance  semi-phenomenological  closed shell  single  23  structure  T h e i r study  non-closed  how  E^=  spatial  overall  Mass-13 n u c l e i nuclei.  carbon-12  nucleus.  energy  symmetric  the  derived  4n  model, which  especially  N have a very  i n i t s ground  energy  at a high  schematic  to a  cause a major  remain  is a  C and  added  carbon-12 w i l l  at  13  be  13  the  single  been e x h a u s t i v e .  nucleon  Carbon-13  studied directly.  The  the  study  decay  of  is a  stable 13  reactions  of  the  many  the  GDR,  dipole  resonance  i s o t o p e , and 12  CCYjp)  B  can  and  12 C(7,n)  between  C have been  5 MeV  most complete  and  38  study  examined MeV  to  by date.  from  Cook  in  photon  energies  WBy^'Wid t h i s  (Ey)  remains  the  -6Nitrogen-13  w i t h a l i f e t i m e of about examination  P+  i s an u n s t a b l e i s o t o p e , ten minutes.  decaying to carbon-13  The p r e s e n t work i s an  13 in N by means of the i n v e r s e 12 13 capture r e a c t i o n : C(p,Yo) N . This reaction 13 12  of the d i p o l e resonance  r a d i a t i v e proton  N(Y,po)  i s r e l a t e d to the r e a c t i o n  C by the p r i n c i p l e o f  12 d e t a i l e d b a l a n c e . (A s u b s c r i p t 0,1... on the p and 7  indicates  t r a n s i t i o n s l e a v i n g the r e s i d u a l nucleus i n the ground s t a t e , first  e x c i t e d s t a t e , etc.)  In t h i s case, the p r i n c i p l e o f de-  t a i l e d balance i s v a l i d even i f time r e v e r s a l i n v a r i a n c e  is  13 violated.-  While  the p r o t o n t r a n s i t i o n to the ground s t a t e i n  g e n e r a l r e p r e s e n t s the s t r u c t u r e  o f the GDR  f a i r l y well,' d i s t o r t i o n s  14  do o c c u r .  In p a r t i c u l a r , t h i s mode of decay may  a t low e n e r g i e s , but may  be q u i t e  become l e s s important a t h i g h e r e n e r g i e s ,  where more decay channels are e n e r g e t i c a l l y a l l o w e d . (Y,p ) c r o s s - s e c t i o n s G  of the GDR. structure  Thus, the  do n o t n e c e s s a r i l y r e f l e c t the gross shape  Some care must a l s o be taken when i n t e r p r e t i n g i n r a d i a t i v e capture r e a c t i o n s .  t h a t such s t r u c t u r e may states  important  Tanner p o i n t s  be the r e s u l t of weak compound n u c l e a r  i n t e r f e r i n g w i t h the main broad resonance,  r e a l l y representative  out  of the  GDR7  and  thus, not  However, even w i t h these  u n c e r t a i n t i e s , r a d i a t i v e capture has proved a powerful t o o l for  s t u d y i n g the  GDR. 12  U n t i l recently, rather neglected.  the  13 C(p,Y)  Warburton and  the capture gamma-ray Yo  N capture r e a c t i o n has been Funsten were the f i r s t  i n 1962?"^ In 1963,  Fisher, et  to al.  l fi  examined the r e a c t i o n over a wider range.  Both  experiments  detect  were L i m i t e d by the poor energy r e s o l u t i o n o f both the p r o t o n beams (300 keV and 800 keV r e s p e c t i v e l y ) and the s m a l l N a l detectors  ( = 13%).  A more r e c e n t  study by D i e t r i c h was l i m i t e d 17  13 to a s m a l l r e g i o n about the lowest T = '3/2 s t a t e i n  N.  Recent work on the capture r e a c t i o n has been done a t the U n i v e r s i t y of Washington i n S e a t t l e .  Johnson has examined the r e a c t i o n from  18  2.8 MeV t o 9 MeV.  Measday, H a s i n o f f  and Johnson have examined 19 the capture r e a c t i o n from 9 MeV to 16 MeV. The p r e s e n t r e p o r t extends t h i s study t o 2M.M MeV. 13 The  GDR i n  N can a l s o proton-decay to the ground s t a t e  12 or e x c i t e d s t a t e s o f C. Thus, the p r o t o n and gamma-ray c r o s s 12 12 s e c t i o n s from the C(p,p) and C(p,p y) e l a s t i c and i n e l a s t i c 13 T  r e a c t i o n s might a l s o c o n t a i n  information  about the GDR i n  N.  I n the p r e s e n t study, we a l s o examine the y i e l d s o f the 12.71 MeV and  15.11 MeV gamma-rays e x c i t e d i n t t h e i n e l a s t i c  reaction.  P r o t o n 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 r e a c t i o n s f o r i n c i d e n t proton  energies  between 9.4 MeV and 21.5 MeV have 20 12 been measured by Levine and Parker, who a l s o measured the C(p,cx) decay. Data w i t h a p o l a r i z e d p r o t o n beam have been taken by 21 13 Meyer and P l a t t n e r . The neutron decay channel i n N has been 12  12 N r e a c t i o n by d e t e c t i n g p o s i t r o n s 12 22 from decay o f the ground s t a t e o f N by Rimmer and F i s h e r . s t u d i e d v i a the  C(p,n)  16  The  r e s u l t s o f F i s h e r , et„ a l . , showed a peak a t a  proton  energy E^= 13 MeV, s e p a r a t e d from the main resonance near E = 20 MeV.  P  Our r e s u l t s confirm  this.  times been c a l l e d a "pygmy resonance". has  been a p p l i e d s e v e r a l ways i n n u c e l a r  This  lower peak has some-  The term "pygmy resonance" physics.  I n neutron  -8-  capture  spectroscopy,  t h e term a p p l i e s t o broad peaks seen i n 23 c e r t a i n mass r e g i o n s . When r e f e r r i n g t o t h e GDR, "pygmy resonance"  sometimes r e f e r s t o t h a t p a r t o f t h e d i p o l e resonance w i t h t h e 24 lower  a l l o w e d v a l u e o f i s o s p i n (T ) . F o r t h i s r e p o r t , t h e  term "pygmy resonance" w i l l r e f e r o n l y t o t h a t p a r t o f t h e 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 t h a t t h e main s t r e n g t h of the resonance. The  p r e s e n t r e p o r t a l s o i n c l u d e s t h e measurement o f s i x  a n g u l a r d i s t r i b u t i o n s i n t h e r e g i o n o f t h e pygmy resonance, and two a n g u l a r d i s t r i b u t i o n s a t a h i g h e r energy.  We s h a l l  attempt t o view a l l t h e data i n t h i s r e p o r t i n l i g h t o f t h e following 1)  questions: To what e x t e n t does t h e v a l e n c e n u c l e o n d i s t u r b t h e L 2  2)  C  core?  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 t h e v a l e n c e nucleon contribute s i g n i f i c a n t l y t o the dipole resonance?  3)  To what e x t e n t can we i d e n t i f y resonances seen i n o t h e r r e a c t i o n s w i t h t h e GDR?  -9II  EXPERIMENTAL EQUIPMENT AND PROCEDURE  A  G e n e r a l Set-Up 13  The  N nucleus has a s i n g l e v a l e n c e p r o t o n o u t s i d e the 12  closed s h e l l configuration of  c  Tti ,  >  US  the p r o t o n b i n d i n g  energy  13 for  N i s 1.944 MeV  (= Q v a l u e ) , a s m a l l number when compared 12 w i t h the p r o t o n b i n d i n g energy o f 15.9 57 MeV f o r C. To study 13 the f u l l g i a n t resonance r e g i o n o f capture, p r o t o n energies P r e s e n t day Van de  N by r a d i a t i v e proton  from 10 MeV t o 30 MeV would be r e q u i r e d .  G r a f f a c c e l e r a t o r s , w i t h a maximum o f  approximately 25 MeV, cover most, but n o t a l l ,  of this  A study o f the g i a n t resonance through the i n v e r s e has  region.  (p,Y) r e a c t i o n  the advantage o f e x h i b i t i n g more f i n e s t r u c t u r e than i s  p o s s i b l e when examining the d i r e c t (Y,p) or (Y,n) r e a c t i o n s , because the i n c i d e n t beam o f charged p a r t i c l e s possesses f a r b e t t e r energy r e s o l u t i o n than any beam o f photons, a t p r e s e n t . Also,  the d i p o l e resonance f o r u n s t a b l e i s o t o p e s ,  in particular  13 N, which a r e u n a c c e s s i b l e  i n the d i r e c t r e a c t i o n , can be  s t u d i e d by the capture r e a c t i o n . FN  The U n i v e r s i t y o f Washington's  tandem Van de G r a f f can r o u t i n e l y achieve an energy r e s o l u t i o n  o f b e t t e r than 5 keV f o r 15 MeV p r o t o n s , an u n c e r t a i n t y l e s s than the energy l o s s i n the t a r g e t In g e n e r a l ,  even  (= 10 k e V ) .  energy c a l i b r a t i o n was no problem f o r the  12 C  (P>Y)  'spectrao  F o r i n c i d e n t p r o t o n energies  greater  than  E = 17 MeV, the 12.71 MeV and 15.11 MeV gamma-rays from the P  -10i 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 . t i o n was  When below these t h r e s h o l d s , an energy  done f o r low-energy  and the g a i n was  calibra-  gamma-rays from r a d i o a c t i v e s o u r c e s ,  t h e n d e c r e a s e d by a known amount, t o b r i n g  the c a p t u r e gamma-rays w i t h i n ^ the energy range o f the a n a l y z e r . The s i g n a l s from the s p e c t r o m e t e r were a n a l y z e d by a p u l s e h e i g h t a n a l y z e r (PHA)  and s o r t e d 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 . were dumped i n t o an SDS for later analysis.  A t the end o f a r u n , the d a t a  computer and then s t o r e d on magnetic  A v e r s i o n o f the EGG  had been adapted f o r use on the SDS immediate  program (see  tape  appendix)  computer, a l l o w i n g an  o n - l i n e a n a l y s i s w h i l e the d a t a was b e i n g t a k e n .  T h i s i s a g r e a t a i d t o the e x p e r i m e n t e r , p e r m i t t i n g him t o 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. o f a l l d a t a was  Final analysis  done on a t i m e - s h a r i n g IBM computer a t the  U n i v e r s i t y of B r i t i s h  Columbia.  -11B  The Gamma-Ray S p e c t r o m e t e r  The gamma-ray d e t e c t o r used i n t h i s study belonged t o a U n i v e r s i t y o f B r i t i s h Columbia group, b u t r e s i d e d a t the U n i v e r s i t y o f Washington N u c l e a r P h y s i c s L a b o r a t o r y . A d e t a i l e d desc r i p t i o n g o f the s p e c t r o m e t e r has been p u b l i s h e d ( H a s i n o f f - e t a l . , 25 1973  ) , o n l y a b r i e f account w i l l be g i v e n h e r e . The d e s i g n o f t h e s p e c t r o m e t e r and h o u s i n g 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 d i a m e t e r by 25.4 cm. l o n g , .was manufactured by the F r e n c h company Quartz e t S i l i c e .  The response o f the  crystal  t o a 1.33 MeV gamma-ray from a c o l l i m a t e d source moved a l o n g i t s a x i s , was u n i f o r m t o +0.75 %.  A 1 cm. t h i c k n e s s o f l i t h i u m c a r -  bonate and wax surrounds the s i d e s and f r o n t f a c e o f the c r y s t a l , and p r o v i d e s some a b s o r p t i o n o f slow n e u t r o n s .  The a n t i - c o i n -  c i d e n c e s h i e l d c o n s i s t s o f NE 110 p l a s t i c s c i n t i l l a t o r , cm.  10.8  thick. A schematic o f 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 o f the e l e c t r o n i c s i s g i v e n by 26 Lim, 19 74.  Note t h a t the anode s i g n a l i s used f o r b o t h the  l i n e a r s i g n a l and the t i m i n g .  T h i s was found t o be s i m p l e r  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 o f 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 a t t a c h e d t o the power s u p p l y o f the c r y s t a l ' s p h o t o - t u b e s , because the g a i n o f the photo-tubes  Figure 1  RCA 8055 NE HO  EZ2  LEAD  EEH  LI C0 +WAX  RCA 8055  x EMI Nal  3  2  9758 B  X  x »  0  •  »  10  t  1  20 cm  Na  I  PLASTIC ANTI-COINCIDENCE DISC ANNULUS Nal SUM SUM H ANODE HIGH LEVEL SUM DISCRIMINATOR EGG EGG I AN 201/N AN 201/N LRS LRS FAN-OUT ATTEN ORTEC ORTEC 700 n-sec LRS 454 454 DELAY FAST AMP| I 133 B EGG EGG ORTEC DISCRIM. DISCRIM. 454 EGG DISCRIM. CLIP TO TD IOI/N 400 n-sec EGG OR LINEAR  1  [TENNELEQ GATE TC 304  LRS DISCRIM.!  EGG Gl 200/N  I  EGG NAND  ORTEC AMP  PHA ND 2400  zn EGG  ROUTER •  EGG AND J.  EGG DISCRIMJ  EGG Gl 200/N Gl 200/N ACCEPT GATE 6 DELAY GATE a DELAY  Figure 2  REJECT  -14was a n o n - l i n e a r f u n c t i o n o f the c o u n t i n g r a t e .  With the  s t a b i l i z i n g u n i t , t h e g a i n s h i f t was d e c r e a s e d t o about 1 %, w h i c h 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 o f t h e 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 t h e 4.4 3 MeV gamma-ray  from t h e f i r s t e x c i t e d s t a t e o f  12 C..  Cosmic r a y r e j e c t i o n u s i n g t h e 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 t o 1. T h i s spectrometer  has a c h i e v e d  a r e s o l u t i o n o f 3 % FWHM f o r 15 MeV gamma r a y s , u s i n g a c o l l i m a t o r o f s o l i d a n g l e 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 o f s o l i d angle =0.077 s r . , h a l f - a n g l e = 7°. T h i s gave a r e s o l u t i o n (FWHM) = 4 %, w h i c h was more t h a n adequate.  F o r t h e a n g u l a r d i s t r i b u t i o n s , t h e c r y s t a l was moved  back t o maximize the range o f a n g l e s . c o l l i m a t o r , corresponding  The data was t a k e n w i t h no  t o approximately  t h e same s o l i d  angle,  c a u s i n g the energy r e s o l u t i o n t o worsen s l i g h t l y , t o FWHM = 4.5 %. The •v  d e t e c t o r c o u l d be moved between  about 42° and 140°.  The a n g u l a r a l i g n m e n t o f t h e c r y s t a l was checked  b e f o r e each r u n .  R e c e n t l y , o t h e r members o f t h e l a b have t e s t e d  the a l i g n m e n t 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 holder.  mechanically  i n the t a r g e t  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 o f t h e d a t a . f o r t h e y i e l d curve were taken d u r i n g a single run.  F o r t h i s r u n , p a r a f f i n was p l a c e d i n f r o n t o f t h e  d e t e c t o r t o reduce t h e n e u t r o n 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 a t t e n u a t e s t h e gamma-rays, as does t h e 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 , w h i c h 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 o f t h e N a l c r y s t a l , causes some o f the gamma-rays  -15t o be  "rejected".  These gamma-rays are  as the REJECT spectrum.  stored  When c a l c u l a t i n g the  from the ACCEPT spectrum, a c o r r e c t i o n gamma-rays r e j e c t e d must be  applied  The  percentage  data, i n  of  addition  former c o r r e c t i o n ,  the " e l e c t r o n i c e f f i c i e n c y " , i s a f u n c t i o n  bin  absolute y i e l d  f o r the  to the  t o the v a r i o u s a t t e n u a t i o n f a c t o r s .  i n a separate  of the  gain of  called 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 a l s o depends on s i z e of the  collimator  and  For  by  c r y s t a l , approximately 100  the  10"  10"  Nal  on the energy o f the  gamma-rays i n t e r a c t , i . e . d e p o s i t electronic e f f i c i e n c y , defined  F  ,  -p-  _ '  L a  some energy.  itself.  % of I S Thus,  MeV  the  by  # i n ACCEPT #• i n ACCEPT + # i n REJECT  f o r an i s o l a t e d gamma-ray, need only be factors  gamma-ray  the  to give a t o t a l c o r r e c t i o n  A c a l c u l a t i o n o f the  folded  i n t o the  attenuation  value.  correction  f a c t o r f o r the  set-up used i n t h i s study has  been done.  i n figure  e l e c t r o n i c e f f i c i e n c y i s a smooth  fit  3 on page 16  .  The  to three e x p e r i m e n t a l data p o i n t s .  The  experimental  The  r e s u l t i s given  parrafin  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 n o r m a l i z e d to one The  f r o n t p l a s t i c curve i s a p u r e l y t h e o r e t i c a l  d e r i v e d u s i n g the and  p l a s t i c ' s t h i c k n e s s and 27  known mass a b s o r p t i o n f a c t o r s .  i s seen to v a r y l i t t l e as a f u n c t i o n E = IM- MeV  to 25 MeV,  The  attenuation data  point.  calculation,  chemical composition,  t o t a l correction  o f gamma-ray energy.  t h i s c o r r e c t i o n v a r i e s by  curve From  l e s s than 5 % .  EFFICIENCY AND ATTENUATION CORRECTIONS FOR THE 10" X10" No. I CRYSTAL DETECTOR .1*0  y  0.9  FR0NT  PLASTIC  ATTENUATION  0.8 P ARR A F I N  ATTENUATION  0.7 --^  •  <Qr  0.6  ELECTRONIC  E F F I C I E NCY  0.5  0.4  X  TOTAL  CORRECTION  0.3 A E X P E R I MENTAL 0.2  DATA  POINTS  0.1  10  12  14  16  GAMMA-RAY  1*  20  ENERGY  Figure 3  22 (MeV)  24  -17The  a b s o l u t e u n c e r t a i n t y o f t h i s curve i s n o t more than 10  S i n c e the v a r i a t i o n w i t h energy was at  15.11 MeV,  %,  s m a l l , a constant c o r r e c t i o n  where i t i s b e t t e r known e x p e r i m e n t a l l y , was  u n i f o r m l y a p p l i e d t o the d a t a . The was  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 a t 22.4  taken a t a separate r u n .  There was  MeV  some d i s c r e p a n c y i n the  a b s o l u t e 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 r u n s , and thus the e l e c t r o n i c e f f i c i e n c y curve g i v e n i s somewhat i n q u e s t i o n .  For the w o r s t  p o s s i b l e c a s e , the r e l a t i v e y i e l d curves s h o u l d 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 at  15.1 MeV  unchanged.  by 10 %, and l e a v i n g the  yield  F u r t h e r s t u d i e s o f the e f f i c i e n c y f o r  t h i s geometry are b e i n g made t o remove the p o s s i b l e d i s c r e p a n c y . 12 A pure carbon£12 t a r g e t (99'.9% t h i s study.  The  c  )  used  w a s  throughout  t a r g e t t h i c k n e s s was measured u s i n g the narrow 13  (  P = 1.3+.3 keV)  E = 14.231 MeV. P  T = 3/2 resonance i n  The t a r g e t t h i c k n e s s was  N a t p r o t o n energy found t o be 380 ug/cm  o  +10 %, i n good agreement w i t h p r e v i o u s measurements. For s p e c t r o m e t e r s  o f t h i s t y p e , the b e h a v i o u r o f the gamma-ray  l i n e shape i n the low energy t a i l r e g i o n has n o t been  determined.  The p r e s e n t r e s u l t s have been a n a l y z e d by e x t r a p o l a t i n g the l i n e a r l y t o z e r o energy a t z e r o c o u n t s .  tail  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 i n c r e a s e 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 t h i c k n e s s and d e t e c t o r e f f i c i e n c y , we e s t i m a t e an u n c e r t a i n t y of + 30 % i n our a b s o l u t e cross-section normalizations.  -18III  THE A  1 2  C C p , 7 ) N REACTION I 3  Y i e l d and A n g u l a r D i s t r i b u t i o n s i n the R e g i o n o f the G i a n t 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 p r o t o n c a p t u r e  on  12 C was  measured f o r p r o t o n e n e r g i e s from 14 MeV 13  ( e x c i t a t i o n energy i n i n s t e p s of 100 keV  N from E = x  or s m a l l e r .  14.87  The  MeV  t o 24.4  t o 24.47  MeV).  energy r e s o l u t i o n of the  beam, i n c l u d i n g energy l o s s e s i n the t a r g e t , was The  MeV  = 15  keV.  energy r e s o l u t i o n o f the measured gamma-rays had a  full-  w i d t h half-maximum (FWHM) = 4 %, a l t h o u g h the r e s o l u t i o n worsened f o r cases o f low y i e l d c o u p l e d w i t h a l a r g e background due up.  A t y p i c a l spectrum i s shown i n f i g u r e 4 on page The  was  w e l l d e f i n e d i n a l l the s p e c t r a .  MeV  19.  gamma-ray from the t r a n s i t i o n t o the ground s t a t e  c o u l d n o t be r e s o l v e d , but t h e i r sum  MeV  O^+g)  and  was  always  v i s i b l e , e x c e p t where i t o v e r l a p p e d w i t h the p r o l i f i c 15.11 o r •'.12.71 MeV  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 and T ^ ^ e  (Yo)  Gamma-rays from t r a n s i t i o n s  t o 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 x 3.56  to p i l e -  p r e s e n t i n the r e g i o n between Yo  T h i s background c o u l d be somewhat reduced by  decreasing  the beam c u r r e n t from - 80 nA t o  - 40 nA-, i m p l y i n g t h a t i t was  more p i l e - u p r e l a t e d t h a n n e u t r o n  r e l a t e d . However, most s p e c t r a  were taken a t  — 80 nA beam, s i n c e the background was  manageable, and d e c r e a s i n g the beam i n c r e a s e d prohibitively.  still  running-time  Most s p e c t r a were taken f o r an i n t e g r a t e d c u r r e n t  o  THOUSANDS CO  OF  COUNTS —»  cn  tO  0  to  to  CO  CO  to  V  -<  TJ  *—•  o >  to c —I  CO "0  4^  m o —i  CZ  -6T-  -20-  o f 100 pC, w i t h a r u n time o f  —20  min/spectrum.  Gamma-rays  13  from t r a n s i t i o n s t o the f i r s t e x c i t e d s t a t e i n MeV  N a t E = 2.366 x  (Yj) c o u l d be d i s c e r n e d above the background o n l y i n the r e g i  of the g i a n t resonane ( E > 20.5 p  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 t h e EGG  f i t t i n g program d e s c r i b e d i n t h e a p p e n d i x .  energy r e g i o n (E >  F o r the h i g h  21 MeV), the capture gamma-rays were w e l l  s e p a r a t e d from the i n e l a s t i c gamma-rays.  I n t h i s r e g i o n , the  t h r e e c a p t u r e gamma-rays (Y©,7^'T^+g) were f i t , t o g e t h e r w i t h a f o r c e d q u a d r a t i c background. B ( x ) = B o ( x - CUTOFF)  2  B(x) =0  The background was o f the form: f o r x < CUTOFF f o r x > CUTOFF  CUTOFF = x o - j ^ where x = c h a n n e l number x o = c h a n n e l number o f Y o B , B ^ = parameters 0  Thus, the background i s a pure q u a d r a t i c and goes smoothly t o z e r o a t some p o i n t above o r below Y . 0  T h i s form has the  advantage o f r e s t r i c t i n g the amount o f background under the photo-peak o f the ground s t a t e gamma-ray Y o , and o f n o t a l l o w i n g q u e s t i o n a b l e humps t h a t sometimes appear i n a c u b i c background. The parameter B f i x e d a t -10.  0  was always a l l o w e d t o v a r y , b u t B ^ was u s u a l l y  -21A t lower e n e r g i e s , t h e "^2+3  ^\ o f t e n o v e r l a p p e d w i t h one  o v  o f t h e i n e l a s t i c gamma-rays. e i t h e r a l o n e o r w i t h 7-^.  F o r t h e s e e n e r g i e s , 7o was  fitted  The f i t t e d r e g i o n had t o be narrowed  such t h a t c h i - s q u a r e d  was most a f f e c t e d by t h e l i n e s f i t , r a t h e r  t h a t t h e background.  I n a l l cases,  the f o r c e d q u a d r a t i c background  was i n c l u d e d i n the f i t . Whenever t h e 7 ^ was f i t , i t was n e c e s s a r y t o f i x i t s e x c i t a t i o n energy w i t h respec. t o t h e 7 o . I n o v e r l a p r e g i o n s , the data were f i t i n s e v e r a l o f the above ways.  R e s u l t s were always c o n s i s t e n t w i t h i n t h e s t a t e d e r r o r s . The  12  ^3 C(p,7 J N y i e l d curve i s g i v e n i n f i g u r e 5 on page 0  f o r p r o t o n energy E = 14 SMeV t o 24.4 MeV.  The a b s o l u t e n o r -  P m a l i z a t i o n o f t h e 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 u n c e r t a i n t y due t o 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 m a t r i x  (see appendix and B e v i n g t o n  ).  The main p a r t o f the d i p o l e s t r e n g t h appears c e n t e r e d a t E = 20.8 MeV w i t h a w i d t h o f  F = 4 MeV.  This roughly  coincides  w i t h a s t a t e seen i n p r o t o n 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.  T h i s s t a t e has been a s s i g n e d a s p i n and  parity  J = 5/2 , based on the a n a l y s i s o f p o l a r i z a t i o n c r o s s 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 Scott e t a l . t h a t assignments o f J = 3 / 2 a n d l / 2 u  +  compares t h e measured a n g u l a r the 15.11 MeV s t a t e i n  1 2  C  +  Lowe and Watson s t a t e  are a l s o allowed.  Scott  d i s t r i b u t i o n f o r p r o t o n decay t o  OOO  D I F F E R E N T I A L _* ro  T  C R O S S -  S E C T I O N Co  (Mb  /sr)  cn  T  CEJ 11  CD >  CO  o  o  CD  ro O  > I czT*  73 —'  -< m ro  TJGO  73 1U3  co c  —1  o  z  (D  cn  m  -z. m  Jco CD <  ro  to CO  -23>  expt(20.5)  Po + 0.1 P ' + 0„8 P 1  2  - 0.3 Pg -  w i t h angular d i s t r i b u t i o n s c a l c u l a t e d f o r decays from  0 , 3 P^ states  o f / 3/2  +  5/2  +  >  Po + 0.5 P  >  P  + 0.8 P  n  ° and  conclude J = 5/2  2  - 0.1 P  2  i s indicated.  4 However, the c a l c u l a t e d  angular d i s t r i b u t i o n s o f S c o t t are based on the assumption d i f f e r e n t channel s p i n s c o n t r i b u t e  equally  that  t o the c r o s s - s e c t i o n s .  T h i s assumption i s reasonable i n the sense t h a t , i n the absence of a d e t a i l e d model f o r the r e a c t i o n 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  c a l c u l a t e d angular d i s t r i b u t i o n s .  Our c a l c u l a t i o n s o f the angular  d i s t r i b u t i o n s f o r each channel s p i n are given  i n t a b l e I on page  We see t h a t no combination of channel s p i n s f o r J =5/2  +  1T  adequately account f o r the measured values o f both a ( d i f f e r e n t channel s p i n s do n o t i n t e r f e r e ) . e f f e c t s must be i m p o r t a n t .  can e a s i l y  The non-zero value o f a., i n d i c a t e s 4  i n t e r f e r e n c e w i t h a resonance o f J ^  5/2 w i t h p o s i t i v e p a r i t y ,  I f t h i s state contributes  y i e l d , as seems l i k e l y , an assignment o f J = 3/2 indicated.  and a^  interference  A resonance o f J = 3/2  account f o r the l a r g e a v a l u e . 2  but t h i s i s n o t u n l i k e l y .  Other  2  can  to the 7  i s strongly  T h i s assignment i s n o t i n c o n s i s t a n t w i t h e x i s t i n g  proton s c a t t e r i n g data.  We cannot r u l e out the p o s s i b i l i t y  t h a t two separate resonances are superimposed.  Q  24.  -24Table I Angular d i s t r i b u t i o n s f o r protons scattered i n e l a s t i c a l l y to the J =  1  w  s t a t e a t 15.11  MeV i n  c h a n n e l - s p i n c o u p l i n g scheme.  J ^ r e f e r s t o the compound n u c l e a r  s t a t e , L t o the s c a t t e r e d p r o t o n .  J*"" 3/2  5/2  +  +  c, c a l c u l a t e d i n the  S i s the channel s p i n .  L  S  Angular D i s t r i b u t i o n  2  1/2  % ( Po +  3/2  4 p  1/2  6 ( Po + 1.14  P  2  +0.86  P^)  3/2  6 ( Po + 0.41  P  2  - 0.97  P^)  2  P) 2  Q  -25The r e g i o n E = p  16.5  MeV  contains further s t r u c t u r e .  to 18.5  i n the To y i e l d  MeV  Whether t h i s should be  as two d i p s or a separate peak i s not c l e a r .  probably  interpreted  The h i g h d e n s i t y of  s t a t e s seen i n i n e l a s t i c proton s c a t t e r i n g i n t h i s r e g i o n " ^ would support almost any h y p o t h e s i s .  Angular d i s t r i b u t i o n s i n t h i s  r e g i o n might provide some i n s i g h t , however these have not y e t been o b t a i n e d . Whether the s l o w l y i n c r e a s i n g y i e l d down to E^= j o i n s smoothly to the pygmy resonance  a t E = 10 P  14  MeV  to 13  MeV  or i s a separate bump i s another u n r e s o l v e d q u e s t i o n .  MeV  Further  measurements i n t h i s r e g i o n gave some i n d i c a t i o n t h a t 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 r a t h e r poor and r.did not warrant statement. yield  a definitive  A broad background seems to u n d e r l i e the e n t i r e  curve. sharp peak a t E' = 14.231 MeV  The  T h i s v e r y narrow resonance  was  i s a T = 3/2  state.  found i n the ^^B ( H e , n ) ^ N  11 and a l s o i n the m i r r o r r e a c t i o n  3  reaction,  13  HB ( He,p)  C.  The anomaly i s  20 a l s o seen i n proton s c a t t e r i n g d a t a . A s p i n - p a r i t y assignment of J = 3/2" was confirmed by the C ( p , 7 ) data of D i e t r i c h  17  et a l .  0  31  Szucs e t a l . have measured the f u l l width and  n  found  3 2  I  = 1.3  P  = 0.82  + 0.3 + 0.2  good agreement  keV.  Adelberger et a l . ,  1973,  have found  keV by a c o i n c i d e n c e ( He,nT) measurement, i n w i t h the p r e v i o u s  result.  The w i d t h , s p i n  p a r i t y , Ml decay width,cand'iother i n f o r m a t i o n about t h i s n N, a 11 i n d i c a t e t h a t i t i s the lowest T = 3/2 l e v e l i .._ 13,  and  state the  -26-  13  analogue of the ground s t a t e of was  used t o measure the t a r g e t  13 B and  0.  T h i s resonance  thickness.  13 N has  two  narrow T = 3/2  resonances a t 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 p r o t o n decay t o the T  =11  12 15.11 ray  MeV  level in  C, and are seen i n the y i e l d of t h a t gamma-  (see s e c t i o n IV A ) .  These r e g i o n s were examined i n 25  keV  s t e p s , buifc no c o r r e s p o n d i n g s t r u c t u r e was  seen i n the Yo y i e l d .  T h i s might i n d i c a t e a*many p a r t i c l e - h o l e  configuration.  The  s t r u c t u r e above the main s t r e n g t h  interesting.  of the GDR  i s quite  I t might be i n t e r p r e t e d as a d i p a t E^=  or as a peak a t E^= a t E = 22.4 MeV and P  22.4  MeV  23 MeV. A n g u l a r d i s t r i b u t i o n s were performed 23.2 MeV. The r e s u l t s are shown i n f i g u r e 6  on page 27 , t o g e t h e r w i t h the f i t t e d Legendre p o l y n o m i a l c o e f f i c i e n t s a c c o r d i n g t o the n Y(8) =Ao ( 1 +  equation: a  i  P (cos9)) i  by the program LEGFIT (see a p p e n d i x ) .  An a s t e r i s k (*)  the c o e f f i c i e n t s i n d i c a t e s  forced  the f i t was  t o be  above  non-negative  a t e i t h e r f o r w a r d or backward a n g l e s . A t these e n e r g i e s , the y i e l d was between 60°  and  124°.  Still,  taken at only f i v e angles  the r e s u l t s are q u i t e  striking.  A l l t h r e e c a p t u r e gamma-rays are strong'ly asymmetric about ninety  degrees.  a t 23.2 The  15.11  MeV  Yo  t h a t a t 22.4  MeV  aMsotropic a t 23.2  The  MeV.  and Yg g are l e s s asymmetric ( s m a l l e r +  MeV  (the Y^ i s l e s s w e l l  a^)  defined).  gamma-ray from the i n e l a s t i c r e a c t i o n i s m o d e r a t e l y a t 22.4  MeV,  b u t becomes v e r y n e a r l y  isotropic  -27-  AT  ANGULAR DISTRIBUTIONS "2 2.4 MeV AND 23.2 MeV  T  Qy 0.6 2+.06 a =-O4.0+.18  a.= 0.80+.04 a =-0.22±.04  2  2  "1 E = 23.2 p  -Xa = 0.65+.20 a =-Q36±-21  olf- 0.4,5 + .13  2  E =22.4  2+3 E = 23.2  a = 0.78+.10 al=-0.Q4 + .23  a = Q37+.07 a =-0.0,Vi.18  p  p  2  r  "15.11  15.11  E =22.4  Ep=2a2  a =-0.32 + .01  a =-0..05+.01  p  o  2  IT ' 1Z71  r 12.71  Ep=2a2  E =2 2.4 p  a =- 0.3.4 +.09  a =-0.36+.0 6  2  9  45<  90°  135° 180° 45° ANGLE (LAB)  Figure 6  1  90°  135° 180°  (-X-see text)  -28The  asymmetry i n the c a p t u r e gamma-rays i n d i c a t e s t h a t 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 t h e d i p o l e resonance  i s p r i m a r i l y j"=3/2" , one c o u l d h y p o t h e s i z e t h a t t h e o t h e r  level  i s the 5/2" s t a t e a t E. = 22.4 MeV, seen as a b r o a d s h o u l d e r 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 t h r o u g h t h e a n a l y s i s o f 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. T h i s would g i v e 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 t o the ground s t a t e , and would  account f o r t h e observed a n g u l a r 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, s i n c e E1-E2 i n t e r f e r e n c e g i v e s o n l y t o odd legendre p o l y n o m i a l s ,  t h i s i n t e r f e r e n c e would n o t  a c c o u n t f o r a d i p i n the n i n e t y degree Y explanations The  rise  0  yield.  f o r t h i s s t r u c t u r e are considered  Possible  i n s e c t i o n V.  Y ^ n i n e t y degree y i e l d i s g i v e n as f i g u r e 7 on page 29  f o r proton energies  f r o . E = 19.8 MeV t o 24.4 MeV.  To s i m p l i f y  the f i t t i n g p r o c e d u r e , the e x c i t a t i o n energy o f t h e 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 e n e r g i e 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.  this The g i a n t  resonance i n the y ^ y i e l d i s c e n t e r e d n e a r a gamma-ray energy i£ = 19.5 MeV and has a w i d t h g  f = 2.5 MeV.  The y i e l d seems t o  i n c r e a s e q u i t e s h a r p l y a t .E = 20.5 MeV, b u t the e r r o r b a r s are l a r g e , and the a c t u a l e f f e c t may n o t be so d r a m a t i c . f i n e s t r u c t u r e was The 19.7  No  detected.  Y-2 g y i e l d i s g i v e n as f i g u r e 8 on page' 30 +  from E^=  MeV t o 24.4 MeV, a l o n g w i t h e a r l i e r r e s u l t s o f F i s h e r e t a l . , 16  1963,  a t higher proton energies.  been r e - n o r m a l i z e d ....  -  The r e s u l t s o f F i s h e r have  t o agree w i t h t h e p r e s e n t r e s u l t s . A t lower 'y  EXCITATION 20  18  GAMMA-RAY  e  ENERGY 22 .  IN  1 3  N  (MeV) 24  26  T  YIELD  -so-  *  18  l  i  20 PROTON ENERGY IN  Figure 7  X  •  22 LAB (MeV)  24  26  EXCITATION 22  20  T  ENERGY  T  C(P.r2+3)l3N  1 2  IN  13 N 24  (MeV)  T  FISHER, MEASDAY. NIKOLAEV, KALMYKOV & CLEGG  GAMMA-RAY YIELD  . •. .  8 =90°  * * PRESENT  RESULTS  r  I.  I  18  1  _  J  20  _  I PROTON  I  22 ENERGY IN  I  Figure 8  i  24 LAB (MeV)  '  I  26  -31-  p r o t o n e n e r g i e s , the 7^+3  o v e r  ^- y a  s  and cannot be e x t r a c t e d r e l i a b l y .  t n e  inelastic  gamma-rays,  No f i n e s t r u c t u r e i s a p p a r e n t .  The y i e l d goes t h r o u g h a minimum near E = 22 MeV. P  The i n c r e a s e  a t lower e n e r g i e s might i n d i c a t e t h e presence o f the pygmy r e s o n a n c e . A t h i g h e r e n e r g i e s , t h e y i e l d approaches the g i a n t r e s o n a n c e , as seen by F i s h e r .  -32B  A n g u l a r D i s t r i b u t i o n s i n the R e g i o n o f the Pygmy Resonance  R a d i a t i v e p r o t o n c a p t u r e on carbon-12 i n the r e g i o n E = 9 MeV  t o 15 MeV  was  P  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 d r a m a t i c d i p s i n the T o  y i e l d a t ' E = 10 62 MeV  and 13.12  o  as f i g u r e 9 on page  33.  The  narrow resonances o f w i d t h  f  MeV.  Their y i e l d Is r e p r i n t e d  two d i p s were f i t q u i t e w e l l as =  200 keV  interfering with  b r o a d Background o f the pygmy r e s o n a n c e .  the  However, the n i n e t y  degree y i e l d does n o t t e l l us w i t h c e r t a i n t y whether t h e r e 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 o n l y 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 c o u l d be  to a resonance i n some competing r e a c t i o n c h a n n e l the s t a t e .  due  depopulating  To f u r t h e r u n d e r s t a n d t h i s phenomena, a n g u l a r  distri-  b u t i o n s were o b t a i n e d i n the r e g i o n o f the pygmy r e s o n a n c e . A n g u l a r d i s t r i b u t i o n s were measured a t s i x e n e r g i e s , 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  measured a t six. a n g l e s between 45° and 135°. b u t i o n s f o r T o are g i v e n i n f i g u r e 10 on page  The  angular  .34.  Legendre p o l y n o m i a l c o e f f i c i e n t s d e f i n e d by the  The  was  distri-  fitted  equation:  n Y(Q) for  = A  0  (1 + T  a. P. (cosB))  n = 2 are g i v e n a t each e n e r g y .  Where v a l u e s have been p r e -  ceeded by an a s t e r i s k (*), the f i t has been f o r c e d t o be negative.  The  non-  a n g u l a r d i s t r i b u t i o n s are a l l peaked near n i n e t y  EXCITATION ENERGY IN  ,3  N  (MeV)  INCIDENT PROTON ENERGY (MeV) Figure 9  JP ANGULAR IN  T  THE T  DISTRIBUTIONS  PYGMY  RESONANCE  T  E =10.3 p  1h A = 2.0 + .1 0.19+ .07 -0.70+.13 Q  0.231.04 Y - 0 . 7 9 + .09  0 3 2l- E =10.65  N  -E = 13.15 p  ANGLE (LAB) Figure  10  -35degrees. The  A l l are s l i g h t l y asymmetric. f i t t e d Legendre p o l y n o m i a l  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. v a l u e s f o r the 7 and  23.2  MeV  0  a n g u l a r d i s t r i b u t i o n s measured a t E = 22.4 P  have a l s o been i n c l u d e d .  c a l c u l a t e d i n the e r r o r m a t r i x t h i r d - and f o u r t h - o r d e r  13.5  MeV  The  (see a p p e n d i x ) .  to F - t e s t  Including  The  the  significantly  ( w i t h the p o s s i b l e  angular d i s t r i b u t i o n ) .  r e g i o n a l l o w e d by the e x p e r i m e n t a l  MeV  e r r o r s shown are those  Legendre p o l y n o m i a l s does n o t 28  improve the f i t a c c o r d i n g o f the Ep=  The  exception  truncated  angular  set-up does n o t w e l l d e f i n e  the h i g h e r o r d e r c o e f f i c i e n t s , w h i c h r e s u l t s i n v e r y l a r g e e r r o r s for  the n = 4 f i t .  Knowledge o f the y i e l d a t f a r f o r w a r d or  backward a n g l e s i s n e c e s s a r y t o b e t t e r determine the a^  and  coefficients. The  Legendre f i t s w i t h n==  2 were adequate, o v e r a l l .  f i g u r e 11 i l l u s t r a t e s , the a^ and constant  throughout t h i s r e g i o n .  o c c u r s i n the A  0  c o e f f i c i e n t s are The  As  nearly  only dramatic v a r i a t i o n  c o e f f i c i e n t , i . e . the d i p s do o c c u r i n the  integrated cross-section. Calculated 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  p r o t o n c a p t u r e i n the c h a n n e l s p i n c o u p l i n g 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  for  E l - E l , M l - M l , E2-E2, E1-E2, and E l - M l i n t e r f e r e n c e t e r m s . TT  +  Because the t a r g e t n u c l e u s has J = 0 , the j - j and L-S  coupling  schemes g i v e d i s t r i b u t i o n s w h i c h d i f f e r by o n l y an o v e r a l l normalization.  Assuming t h i s i s d i p o l e r a d i a t i o n , the  strongly  -36-  JQ ANGULAR LE6ENDRE  POLYNOMIAL  hiI 4  L_  10 1 a  1  11  DISTRIBUTION COEFFICIENTS  4  i  I  12  \—JI  14 //  13^  1  I  22  23  24  T -  0.5  0 0  I  a -0.5  r  2  a  1  1  L -  1  r-  •  0.5  -U-JJ  0 0 a  2  * ,1  L  M""J  •  "0.5  -1  Lt |  Q5 °3  •  1  . - 0.5  >  1  1  i  ,  t '\  i  \  I  //  1  1 // 1 .  0.5 r— a  4  0 Q5  —  \  f  \' \\ 1T  0  i  T"  T J  tt  V  11  PROTON  12  13  ENERGY  14  IN  Figure 11  22  LAB (MeV)  23  24  -37Table I I  C a l c u l a t e d gamma-ray a n g u l a r d i s t r i b u t i o n s f o r the  12  C(p,7o)  r e a c t i o n s a s a f u n c t i o n o f 1 and j o f the i n c o m i n g p r o t o n i n the c h a n n e l s p i n c o u p l i n g scheme. 1  j  0  1/2  El  2 Po  2  3/2  El  4 ( Po - 0 . 5  1  1/2  Ml  2 Po  1  3/2  Ml  4 ( Po - 0 . 5  P)  1  3/2  E:2  4 ( Po + 0.5  P)  3  5/2  E2  6 ( Po + 0.57 P  type  Angular D i s t r i b u t i o n  P) 2  2  2  2  P)  - 0.57  4  I n t e r f e r e n c e Terms Angular D i s t r i b u t i o n  1  3  type  1  3  type  0  1/2  El  2  3/2  El  i-2  1  1/2  Ml  1  3/2  Ml  -2 P  1  3/2  E2  3  5/2  E2  -0.86 ( P  0  1/2  El  1  1/2  Ml  -2 P  0  1/2  El  1  3/2  Ml  2 P  2  3/2  El  1  1/2  Ml  2  3/2  El  1  3/2  Ml  2P  0  1/2  El  1  3/2  E2  1.15  0  1/2  El  3  5/2  E2  1.15 P.  2  3/2  El  1  3/2  E2  0.69 ( P  2  3/2  El  3  5/2  E2  6.2  "  P  2  - 8 P^)  r  6 P)  x  L  l  2 E  l P  L  3  C Pj_ - 0.44  3  P) 3  -38negative a  value indicates J = 3/2 f o r the pygmy resonance. w  2  +  This i s an expected r e s u l t , as non-spin-flip E l transitions 33 are favored over s p i n - f l i p E l t r a n s i t i o n s .  That the measured  value a = -0/75 i s more negative than the predicted 2  a =-0„5 2  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 i n t e r f e r i n g resonances only i f they have the same angular momentum and p a r i t y .  Interfering levels with the  same p a r i t y , but d i f f e r e n t angular momentum a f f e c t the higher order  even c o e f f i c i e n t s .  Interfering levels of opposite parity  introduce odd Legendre polynomials.  Thus, i f the structure i s  caused by two narrow resonances i n t e r f e r i n g with the broad pygmy resonance, our results indicate t h e i r 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 l e v e l seen i n the e l a s t i c and i n e l a s t i c +  scattering of polarized protons on carbon-12 21 Plattner, 1973.  by Meyer and  This resonance, at E = 11.75 MeV, has a width x  T = 250 keV, and was ascribed J = 3/2+ by phase s h i f t analysis. Tr  Although some;of the results of Meyer and Plattner have been questioned  by Measday, this exceptional agreement i n position,  width, angular momentum and parity of the resonance  lends some  weight to the interpretation of the dip as an interference  effect.  -39We note also that fine structure of approximately this width was seen i n thisnregion i n the y i e l d of the 4.43 MeV gamma-ray from the i n e l a s t i c reaction i n the e a r l i e r data of Adams et a l , 34 1961. The minimum at E^= 14.04 MeV,  also as noted by Measday,  could perhaps be i d e n t i f i e d with a l e v e l at E^= 13.96 + .05 MeV T  with  =  150 keV, J = 3/2 , u  +  seen i n the e l a s t i c scattering data 20  of LeVine and Parker, 1969. The alternative interpretation of the dips being caused by a resonance i n some competing reaction cannot be completely ruled out.  A competing reaction would not be expected to a f f e c t  the angular d i s t r i b u t i o n , 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, i s C(p,o<) B. This reaction has a threshold of E = 9.5 MeV. Unfortunately, a y i e l d curve i n  P  20 t h i s region does not e x i s t . LeVine and Parker have examined t h i s reaction near the T = 3/2 resonance at E = 14.231 MeV, but  P not at lower energies.  They did note several correlations i n the  (p,p ) and (p, oC ) reactions at higher energies. T  T  However, the  Ot. decay widths usually never vary as dramatically as would be necessary to account f o r the minima i n the region of the pygmy resonance. The pygmy resonance i s often thought to arise from transitions involving the valence nucleon.  For a valence nucleon dipole 13  t r a n s i t i o n to the ground state of proton would have to f a l l into a  N to occur, the incoming d  q  or s,y., s h e l l o r b i t a l .  -40-  The measured angular d i s t r i b u t i o n s i n the region of the pygmy resonance are consistent with an incomin d^/v, proton (see table II) , although t r a n s i t i o n s from a many p a r t i c l e - h o l e state cannot be r u l e d out.  Some relevant t h e o r e t i c a l c a l c u l a t i o n s are discussed  i n s e c t i o n V.  -41IV  YIELDS OF THE FROM THE  INELASTIC REACTION  The two J =  1  v  and 15,11 MeV 3  p  2  15.11 MeV GAMMA-RAYS 1 2  C (p,p y) t-  energy l e v e l s i n  1 2  c"  C a t 12.71 MeV  (T = 0)  (T = 1) b o t h have s h e l l model c o n f i g u r a t i o n s  1 1 ( i/2^ *  (p ^ )  12.71 MeV AND  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  core as the vacuum, the 12.71 MeV  l e v e l i s symmetric  12 C  i n the s p i n  component of i t s wavefunction,- and a n t i - s y m m e t r i c i n i t s i s o s p i n component, and the 15.11 MeV s p i n and symmetric the J = 1 +  i n iso-spin.  Together, these l e v e l s  exhaust  s t r e n g t h 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 n e x t 1 c o n f i g u r a t i o n — ( s d ) Table I I I on page 42 these l e v e l s . 2.90  l e v e l i s anti-symmetric i n  (p)  .  l i s t s the known decay w i d t h s o f  The 12.71 MeV  l e v e l a l p h a decays m a i n l y t o the  MeV  f i r s t e x c i t e d s t a t e (J = 2 , T = 0) i n B e , even 4 though the decay i s i n h i b i t e d by a f a c t o r o f ~ 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 a l p h a ir  +  8  decay c o u p l e s t o 4p-4h c o n f i g u r a t i o n s . ) Decay t o the ground s t a t e g i n Be i s p r o h i b i t e d by c o n s e r v a t i o n of p a r i t y and a n g u l a r momentum, thus gamma decay accounts f o r the r e m a i n i n g 3 % of the t o t a l width.  85 % o f t h i s gamma w i d t h i s M l r a d i a t i o n t o the 12  s t a t e of l e v e l was  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  calculated using a branching r a t i o n  Y Jr = (2.5 + .3) %  37  y  and assuming an i s o t r o p i c a n g u l a r d i s t r i b u t i o n .  ground o f the  Table I I I Decay w i d t h s o f t h e 12.71 MeV and 15.11 MeV gamma-rays  Energy  3  J CT) T  a  %)  total  alpha  gamma-ray decays (  width  width  to  to  to  to \  T (eV)  ry r c%)  ground  4.4.MeV  7.7 MeV  12.7 MeV  C  2.4+.3  d  95.+3.  12.713+.006  l (0)  14.6+2.8  b  97.1+.3  15,109+.004  1 (1)  39.4+1.5  3  3.6+2.8  +  +  a)  A j z e n b e r g - S e l o v e and L a u r i t s e n , 1968  b)  Cecil et a l . , 1974  c)  '37 Riesman e t a l . , 1970  d) e)  3 6  A d e l b u r g e r and B u s o l e t t i , 1973 39 C h e r t o k e t a l . , 1973  38  r iv b  6  17.+.3  r iv yi'  C  1,5+.3  C  <10.  c  y  1.5+.2°  fy t / Vy  0.7+.3  c  -43The  15.11  MeV l e v e l i s the f i r s t T = 1 s t a t e i n  12 analogue o f the ground s t a t e s o f s t a t e i s 7.7  12  C, the  12 B and  N.  Although the  MeV above the alpha break-up t h r e s h o l d , alpha decay  i s i s o s p i n f o r b i d d e n , and the s t a t e decays v i a gamma emission almost e n t i r e l y . ( Vy/ r ^  The ground s t a t e b r a n c h i n g r a t i o i s v e r y l a r g e  92 %) , although there i s some disagreement  on i t s exact  v40  37  v a l u e (see Riesman e t a l . , and A l b u r g e r and W i l k i n s o n , 1972 ). The 15.11 MeV l e v e l c o u l d alpha decay v i a some i s o s p i n i m p u r i t y , i . e . mixing o f the 12.71  MeV and 15.11  MeV l e v e l s .  T h i s mixing  38,41 i s thought  to occur w i t h an amplitude  of  ~ 11 %.  the alpha decay b r a n c h i n g r a t i o o f the 15.11 l e s s than 2 % .  Still,  MeV l e v e l i s probably  F o r our c a l c u l a t i o n s , we assume  p  /P  =1  and d e r i v e the angular d i s t r i b u t i o n s from the a^ v a l u e s g i v e n by f i g u r e 13 on page  58 .  -44A  Y i e l d o f t h e 15.11 MeV Gamma-Ray  The 15.11 MeV gamma-ray y i e l d c u r v e i s g i v e n i n f i g u r e 12 f o r p r o t o n e n e r g i e s from t h r e s h o l d ( E p  =  16.39 MeV)  t o 24.4  The u n c e r t a i n t y i n a b s o l u t e n o r m a l i z a t i o n i s + 30 %.  MeV.  Throughout  t h i s r e g i o n , the 15.11 MeV gamma-ray i s the most prominent f e a t u r e o f the spectrum.  No background s u b t r a c t i o n was n e c e s s a r y when  the 15.11 MeV and 12.71 Mev gamma-rays were f i t t o g e t h e r .  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 r e c e n t r e s u l t s o f Measday 19 42 e t a l . , 1973, and Ebisawa e t a l . , 1973. 13 The narrow T =3/2  resonances i n  18.46 MeV a r e c l e a r l y s e e n . 15.11 MeV MeV  N a t E = 17.86 MeV P  and  These s t a t e s can p r o t o n decay t o the  l e v e l , b u t are p r o h i b i t e d from d e c a y i n g t o the 12.71  l e v e l by i s o s p i n c o n s e r v a t i o n .  P / P <T ' 12.71 ' P l 5 . l l  (We would e s t i m a t e  50 % f o r b o t h resonances.)  P  The resonance .... 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, w h i c h i s presumably a t h r e s h o l d e f f e c t . The most prominent f e a t u r e s o f the y i e l d a r e the two w e l l d e f i n e d peaks a t a p p r o x i m a t e l y E'^.= 19.4 MeV and 20.5 MeV, the b r o a d s h o u l d e r a t about 22.4 MeV. o f f a t about 23.6 MeV. contributions  together w i t h  The y i e l d seems t o l e v e l  The y i e l d a t these e n e r g i e s would i n c l u d e  from peaks a t h i g h e r e n e r g i e s , 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 o f 44 I n agreement w i t h the e a r l i e r gamma-ray d a t a o f Measday30e t a l . ' i n e l a s t i c p r o t o n s c a t t e r i n g d a t a by S c o t t e t a l . , 1967, and P  GAMMA-RAY DIFFERENTIAL CROSS-SECTION (/ib/sr) — o  ro o  o  ro o o  o  v  > Qs ?  00  CD  o o  o o  o o  CD  -  ro  —» •  0)  II £ N CD >  '5  -THRESHOLD 16.39 MeV  <0  72  o  > < -<•  rn  x 52  o aj <o  5!  CX) H  O  z  m  2:  \  K  • e  o  e  m ro :o iO o -<  Iro ro  2  CD <  i  -46The 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 B r e i t - W i g n e r resonance shapes, u s i n g t h e program o f H a s 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 o f v a l u e s quoted a r e t h e " s t r o n g " and "weak" s o l u t i o n d i s c u s s e d brackets  i n the appendix.  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 .  The Within  any b r a c k e t , a l l t h e f i r s t s o l u t i o n s o r a l l t h e 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 ( u n l e s s o t h e r w i s e n o t e d ) .  The t h i r d  value,  i f g i v e n , i s an e s t i m a t e o f t h e p r o t o n w i d t h s assuming no i n t e r f e r e n c e and some r e a s o n a b l e 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 p r e s e n t under some of the f i t t e d peaks.  F o r the 15.11 MeV y i e l d , these a r e t h e  19.4 MeV, .20.5 MeV and 22.4 MeV p e a k s .  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 f r e e parameter, t h r e e cases were f i t :  special  1) no n o n - i n t e r f e r i n g background, .2) o n e - h a l f  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) t h e maximum p o s s i b l e non<?interfering  background.  F o r t h e peaks i n  the 15.11 MeV y i e l d , t h e maximum background was e s t i m a t e d t o be s—  170 j i b / s r .  The p r o t o n w i d t h s quoted a r e those t h a t seemed  most r e a s o n a b l e , w i t h t o t a l w i d t h s most n e a r l y t h e a c c e p t e d  values.  However, t h e quoted e r r o r s i n c l u d e t h e u n c e r t a i n t y i n t h e background 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 t o g e t h e r , 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 o t h e r T = 3/2  resonance a t E - 18.46 MeV, a l t h o u g h c l e a r l y d i s c e r n a b l e , c o u l d P n o t be f i t a d e q u a t e l y . (One might guess [~^<C 1*5 keV.) t  T a b l e IV Resonances i n 1 N f o u n d i n t h e y i e l d o f t h e 12.71 MeV and 15.11 MeV gamma-rays. E (MeV) P  E (MeV) x  AT)*  15.27  16.02  7/2  17.3  17.9  ?  17.9  18.46  +  3/2^(3/2)  total  p r o t o n v?idths (keV)  width  ground  12.71 MeV  15.11 MeV  T (keV)  state  level  level  102 + 10 %  7.5  4.2 + 10 % 98. 5 10 % 14. + 20 %  594 + 5 % 401 .1 5 %  40°  101 + 30:.%  B  50. + 2 0 % , 1100"± 30 %  .? , 46 + 20 %  D  A  2  5  D  1.8 + 10 % 2.5 + 20 % 320 + 100 % ^r 3640 -± 20 W 260 ± 50 %  18 .8  19.3  •p  500 + 100 %  50  19.4  19.83  5/2" (1/2)  1000 + 50 % 1500 + 50 %  175  B  19.46  19.88  3/2 (l/2)  506 ± W.% 730 + 2 %  208  B  20.5  20.9  15Q4.+ 4 %  200  G  22.4  22.6  1300 + 25 %  50  +  5/2" (?)  F  * r e f e r e n c e s a r e on t h e f o l l o w i n g page.  C  G  i  21.7 -+ 50 % 230 ± 50 % 230 + 50 %  ?  •p  11.4 + 20%^] 32.6. ± 20 % 30 + 20 %  520 + 100 % 300 + 100 % 500 + 50 % 240 + 100 %/ ? " / 600 + 50 %  'l69_± 20 % 65 +-20 % 360 + 20 % 100 + .50 % / 1000~+ 50 % 160 +"30 % N  -48References f o r t a b l e IV:  a)  G i v e n by A j z e n b e r - S e l o v e  b)  LeVine and P a r k e r  c)  We e s t i m a t e  unless otherwise noted  20 P  / f* = 10 % po  d) e)  2 s 11  f)  D i v i d e 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 Only c o n s i s t e n t w i t h (~^= 2300 keV f o r the 19.4 MeV 30 Assumed from t h e o p t i c a l model o f S c o t t e t a l .  g) h)  E s t i m a t e d , see Lowe and Watson Only c o n s i s t e n t w i t h |~^= 4.00 keV f o r t h e 20.5 MeV  resonance  29  resonance  -49The  V  f i t of the peak a t E^=  19.4  MeV  yielded a width  i= 500.keV t o 750 keV, w h i c h 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 p P  .= 520 k e V ) .  MeV  (E .= 19.88 x  MeV,  F o r the s e t o f i n t e r f e r i n g s o l u t i o n s g i v e n  the p e a k s - a t E = 19.4  MeV,  20.5  MeV,  and  22.4  MeV,  for  the upper  v a l u e s would seem the most b e l i e v a b l e , b e i n g the c l o s e s t t o  the  non-resonant e s t i m a t e s .  N o t e , however, t h a t the second s e t i s  not e n t i r e l y r u l e d out.  A value of  Pt p  =  1000  keV  f o r the  22.4  MeV  peak seems u n l i k e l y , b u t the r e q u i r e m e n t t h a t  20.5  MeV  s t a t e have a w i d t h o f 400 keV  a c o n t r i b u t i o n from the_19.4 MeV ( P = 1000  keV)  as s u g g e s t e d .  j " W 5/2"  could conceivably  s t a t e , i f t h i s was  l e v e l , r a t h e r t h a n the  A l s o , f o r the 22.4  MeV  the  'J = v  reflect  the b r o a d e r 3/2  +  state,  peak, s u b t r a c t i o n o f  n o n - i n t e r f e r i n g background causes c o n s i d e r a b l e  uncertainty  the in  the p r o t o n w i d t h s , w h i c h i s i n c l u d e d i n the s t a t e d errors_._ N o t e , 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 o f the e l a s t i c s c a t t e r i n g d a t a by Lowe and Watson,  one would n o t e x p e c t t o see any  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^= 19.46  MeV  i n the n i n e t y degree y i e l d .  assignment o f the 20.5  MeV  The  20.5  MeV  interference and  s p i n and p a r i t y  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 o f 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 cross-sections  done by Lowe and Watson, and i s s u p p o r t e d 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 o f S c o t t e t a l . The s p i n assignment was q u e s t i o n e d i n s e c t i o n I I I A, page 23 ,  -50of t h i s r e p o r t o  The  s p i n and p a r i t y o f the E = 19.46  state  20 was  determined by L e y i n e and P a r k e r ,  by o p t i c a l model phase-  s h i f t a n a l y s i s o f lower energy s c a t t e r i n g d a t a . We note some disagreement i n the r e p o r t e d v a l u e s of the / 4-3 e n e r g i e s and w i d t h s o f the two T = 3/2 s t a t e s . Snover e t a l . r e p o r t E^= ReV  18.42  MeV  and 18.97  MeV  P .= 66 + 8 keV and  with  r e s p e c t i v e l y , as g i v e n by A j z e n b e r g - S e l o v e L e V i n e  Parker  2 0  r e p o r t E^=  and 15 keV.  We  18.35  and 18.96  MeV  with  T  ,= 100  23+5 and  keV  g i v e a v a l u e o f F = 100 keV f o r the former  r e s o n a n c e , b u t 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 v a l u e t o a b e t t e r agreement w i t h Snover.  our  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 o f the l o w e s t T - 3/2 l e v e l , w h i c h i s q u i t e w e l l known.  Our r e s u l t s g i v e 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 o f our t a r g e t t h i c k n e s s and the q u a l i t y o f our i n the r e g i o n o f the 18.96 on t h a t  discrepancy.  MeV  s t a t e , we  data  cannot f u r t h e r comment  -51B  Y i e l d o f t h e 12.71 Mev Gamma-Ray  The 12.71 MeV y i e l d curve i s a l s o g i v e n i n f i g u r e 12 on page 4-5  f o r p r o t o n e n e r g i e s from 14.6 MeV t o 24.4 MeV (E =  15.4 MeV t o 24.5 MeV) .  There i s an u n c e r t a i n t y o f a p p r o x i m a t e l y  + 30 % i n t h e a b s o l u t e n o r m a l i z a t i o n .  Above a p r o t o n energy  of 16.8 MeV, t h e 12.71 MeV gamma-ray s i t s on t h e t a i l o f the 15.11 MeV gamma-ray.  These s p e c t r a were f i t w i t h o n l y the  12.71 MeV and 15.11 MeV l i n e s , no o t h e r background was  necessary.  T h i s i n t r o d u c e d an a d d i t i o n a l u n c e r t a i n t y i n t h e r e l a t i v e  yield  o f the 12.71 MeV gamma-ray due t o u n c e r t a i n t y o f t h e low energy t a i l o f the l i n e shape.  To judge t h e e f f e c t o f t h i s u n c e r t a i n t y ,  the s p e c t r a were a l s o f i t w i t h o n l y t h e 12.71 MeV l i n e and a v a r i a b l e q u a d r a t i c background over a n a r r o w e r c h a n n e l The two f i t s agreed w e l l : absolute y i e l d s overlapped,  region.  a l l s t r u c t u r e was r e p r o d u c e d and the d i f f e r i n g by a maximum o f 5 % on t h e  h i g h energy s i d e (E > 21 MeV). P — The y i e l d curve o f t h e 12.71 MeV gamma-ray d u p l i c a t e s q u i t e 19 w e l l t h e r e c e n t r e s u l t s o f Measday e t a l . ,  45 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 t h e 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 d a t a o f L e v i n e and P a r k e r  2 0  (E = 15.98 MeV, J = v  a t Ep= 16.8 MeV and c o r r e s p o n d i n g p r e v i o u s l y seen by Snover.  7/2 , +  T=  100 keV) .  The peak  d i p a t E = 17.3 MeV were p  T h i s s t r u c t u r e c a n p r o b a b l y be  a c c o u n t e d f o r by. t h e two l e v e l s a t E = 16.5 MeV (E = 17.2 MeV, p x J  P  = 500 keV, seen i n e l a s t i c and i n e l a s t i c p r o t o n s c a t t e r i n g  -5246 d a t a by Daehnick and S h e r r ) and a t E = 17.27 p J  P = i+OO keV, seen by Snover e t a l .  MeV,  a b r o a d r e s o n a n t background. the 12.71 MeV of  '  MeV  v  (E = x.  ) interfering with  The main s t r e n g t h which  l e v e l l i e s between 18 MeV  and 22 MeV.  populates With a b i t  i m a g i n a t i o n , one can see a s h o u l d e r a t E = 18.8 MeV, P  c o i n c i d e s w i t h a resonance  (E =  MeV  19.14  19.83  which  seen by Daehnick and S h e r r .  might a l s o d i s c e r n two s e p a r a t e peaks c o r r e s p o n d i n g at E = P  17.88  MeV,  P=  1000 keV, J = u  One  to.resonances 5/2",  T =  1/2,  *  20 seen by Daehnick and S h e r r and by L e v i n e and P a r k e r E = 20.5 MeV  (E = 20.9 MeV,  P  P=  1500 keV, ^ = ( 5 / 2 ) * ,  ) and seen i n  x  30 p r o t o n s c a t t e r i n g by S c o t t e t a l .  and i n the p r e s e n t 15.11 19  gamma-ray y i e l d , and t h a t o f Measday e t a l .  The  MeV  latter spin  assignment has been q u e s t i o n e d i n s e c t i o n I I I , page' 2 3 , o f t h i s report.) marginal.  Of c o u r s e , these i d e n t i f i c a t i o n s a r e , a t b e s t ,  As i n the y i e l d o f the 15.11 MeV  see the broad s h o u l d e r a t E  =  22.4  gamma-ray, we  again  MeV.  P Once a g a 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 B r e i t - W i g n e r shapes. page  47.  The f i r s t two v a l u e s g i v e n are the "weak" and " s t r o n g "  interfering solutions. of  R e s u l t s a r e a l s o g i v e n i n t a b l e IV on ?  The t h i r d v a l u e , i f g i v e n , i s an e s t i m a t e  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 o r a l l  the second v a l u e s o f s o l u t i o n s i n b r a c k e t s 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 d i p a t E = 17.3 MeV were P P f i t as resonances F o r the 15.3 MeV  i n t e r f e r i n g w i t h a broad r e s o n a n t b a c k g r o u n d . resonance, the s t r o n g s o l u t i o n seems u n l i k e l y .  -53The  d i p a t 17.3 MeV was f i t v e r y w e l l as an i n t e r f e r i n g r e s o n a n c e ,  b u t c o u l d n o t e n t i r e l y a c c o u n t f o r t h e peak-shape n e a r 16.7 MeV. T h i s peak shape c o u l d 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 t h e E = 16.5 MeV resonance (E = 17.2 MeV, p x 46 Daehnick and S h e r r  = 500 keV, seen by  ) . The f i t t i n g program was n o t capable o f  h a n d l i n g t h r e e i n t e r f e r i n g r e s o n a n c e s , b u t one might  estimate  the c o n t r i b u t i o n o f t h e 16.5 MeV resonance t o be l e s s t h a n t h a t o f t h e 17.3 MeV r e s o n a n c e , t h a t i s j The  -1  < 5 0 keV.  resonances between 18 MeV and 24 MeV were f i t  with  t h r e e n o n - i n t e r f e r i n g backgrounds s u b t r a c t e d : z e r o background, one-half  t h e maximum p o s s i b l e background, and t h e maximum  p o s s i b l e background = 13 u b / s r i n t h i s c a s e .  The p r o t o n w i d t h s  quoted a r e f o r t h e f i t w h i c h gave f u l l w i d t h s i n b e s t agreement w i t h a c c e p t e d v a l u e s , b u t t h e quoted e r r o r s i n c l u d e t h e u n c e r t a i n t y due t o background s u b t r a c t i o n . Because t h e 1 2 . f l MeV and 15.11 MeV s t a t e s a r e so s i m i l a r i n s t r u c t u r e , we can a s k t o what e x t e n t a r e they p o p u l a t e d by 13 13 the same compound n u c l e a r 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 f o r b i d d e n t o decay t o t h e 12.71 MeV (T = 0) s t a t e .  However, analogue s t a t e s must c o r r e s p o n d t o 13  excited states i n  13 B and  0.  The resonances we a r e d e a l i n g  w i t h a r e f a r t o o b r o a d t o be i d e n t i f i e d w i t h t h e low l y i n g excited states of present).  13  Fisher  13  0 a r e known, a t  Thus, we assume t h a t t h e compound n u c l e a r  we a r e d e a l i n g w i t h 49  B (no e x c i t e d s t a t e s o f  la&e  T - l/2 states.  states  (Measday, C l e g g and  r-i  argue t h a t t h e b r o a d ( P=  1000 keV) s t a t e a t E = 26 MeV  13 in  13 C and  -54-  N i s t h e T = 3/2 component o f t h e GDR, b u t t h i s i s  a t a s i g n i f i c a n t l y h i g h e r 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 t h e 12.71 MeV l e v e l a r e n o t i s o s p i n s u p p r e s s e d , we s h a l l c o n s i d e r those b r o a d compound n u c l e a r l e v e l s known t o p o p u l a t e the 15.11 MeV l e v e l and those seen i n p r o t o n s c a t t e r i n g d a t a t o 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 t h e 12.71 MeV state.  To some e x t e n t , t h i s i s t h e b e s t we can do, s i n c e t h e  y i e l d o f t h e 12.71 MeV gamma-ray c o n t a i n s few w e l l d e f i n e d 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 t h e 18.8 MeV resonance  i s consistant with the n o n - i n t e r f e r i n g estimate.  The l a r g e 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 c o r r e s p o n d s t o a p r o t o n w i d t h o f t h e 19.4 MeV resonance o f 2300 keV, g r e a t e r t h a t t h e f u l l w i d t h 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 k e V ) . 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 c o u l d  reduce t h e r e s o n a n t c o n t r i b u t i o n o f the E = 1 9 . 4 MeV peak P by an o r d e r o f magnitude. I f we i d e n t i f y t h i s as the J = S/2~ 46 s t a t e seen i n p r o t o n s c a t t e r i n g by Daehnick and S h e r r and 20 v  by L e v i n e and P a r k e r ,  and i n agreement w i t h i t s w i d t h , one  would n o t e x p e c t t o see i n t e r f e r e n c e e f f e c t s w i t h t h e 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 t h e n i n e t y degree y i e l d . In t h i s case, the n o n - i n t e r f e r i n g estimate accurate.  may w e l l be more  The same may be s a i d o f the E = 22.4 MeV r e s o n a n c e . P  I t s h o u l d be emphasized t h a t t h e 12.71 MeV gamma-ray y i e l d from Ep= 18 MeV t o 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 b r o a d r e s o n a n t shape. 20.5  The p r o t o n w i d t h s f o r t h e 18.8, 19.4,  and 22.4 MeV s t a t e s s h o u l d be c o n s i d e r e d  an upper l i m i t , a t b e s t .  -55C  A n g u l a r D i s t r i b u t i o n s o f the 12.71 MeV and 15 e l l MeV Gamma-Rays  A n g u l a r d i s t r i b u t i o n s were t a k e n 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 t h e  C(p,Yo)  yield.  The y i e l d was measured a t f i v e a n g l e s between 60° and 124°. R e s u l t s f o r the c a p t u r e and i n e l a s t i c gamma-rays were g i v e n 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 p o l y n o m i a l c o f f i c i e n t , d e f i n e d by t h e e q u a t i o n Y(9) = A i s given.  0  ( 1 +.a  2  P (cos8)) 2  The s t a t e d e r r o r s a r e thos- c a l c u l a t e d i n t h e e r r o r  m a t r i x (see a p p e n d i x ) •  Calculated 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 a r e g i v e n i n t a b l e V on page 56 . The a n g u l a r d i s t r i b u t i o n o f t h e 12.71 MeV gamma-ray remains constant a t these e n e r g i e s . c o n s i s t e n t w i t h a P^y  2  The v a l u e a = -0»34 i s seen t o be 2  decay from a J™= 5 / 2 ~ l e v e l . A t t h i s  energy, t h e 12.71 MeV gamma-ray s i t s on t h e t a i l o f t h e 15.11 MeV gamma-ray.  I t s h o u l d be n o t e d t h a t t h e 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  a n g l e s , where t h e s p e c t r o m e t e r i s v e r y n e a r the beam c o l l i m a t o r s ) . T h i s i s a s m a l l e f f e c t on t h e 15.11 MeV gamma-ray, b u t t h e s e r r o r s on t h e 12.71 MeV gamma-ray v a l u e f o r a^.ihave been i n c r e a s e d t o account f o r t h i s i n a c c u r a c y . The a n g u l a r d i s t r i b u t i o n o f t h e 15.11 MeV gamma-ray changes d r a m a t i c a l l y , from B e i n g a n i s o t r o p i c a t 22.4 MeV ( a = -0.32 + .01) 2  t o b e i n g v e r y n e a r l y i s o t r o p i c a t 23.3 MeV (a~= -0.05 + . 0 1 ) .  -56Table 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 t h e r e a c t i o n  12 C(p»P lO where t h e i n t e r m e d i a t e r a d i a t i o n i s unobserved,, T  J r e f e r s t o t h e compound n u c l e a r s t a t e .  L.. r e f e r s t o t h e  unobserved p r o t o n . L..  Angular D i s t r i b u t i o n  1/2  s  3/2  s ^ - P ^  5/2  L/2  -P /2-P3/2 X  d  3/2" 3/2  d  5/2- 5/2  P  P  Q  P  0  - 0.5 P  ?  + 0.4 E -  2 2  ±  P / - 3/2 d  3  .  d  2  ,  f  5/2^ 5/2  f  7/2~ 7/2  dd  g  Po  + 0.46 P  Po  -  2  0.14 P,  -57Once a g a i n , t h e d i s t r i b u t i o n a t 2 2 . 4 MeV i s c o n s i s t e n t w i t h a 5/2  The d i s t r i b u t i o n a t 2 3 . 3 MeV, however, seems  resonance.  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  o r an;,s^y2 t r a n s i t i o n from a l / 2 s t a t e , i f p o p u l a t e d p r i m a r i l y t h r o u g h a compound n u c l e a r r e a c t i o n .  T h i s mode o f p o 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 t h e p r o t o n s c a t t e r i n g d a t a 30 of Scott e t a l . The 55° y i e l d f o r t h e 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 s p e c t r o * 47 meter by Ebisawa e t a l . ' T h i s d a t a f o r the 1 5 . 1 1 MeV gamma-ray was n o r m a l i z e d t o t h e p r e s e n t 90° y i e l d , and t h e a c o e f f i c i e n t _  2  t h r o u g h o u t 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 a r e shown i n f i g u r e 1 3 .  )  The l a r g e e r r o r b a r s r e s u l t from an u n c e r t a i n t y i n t h e r e n o r m a l i z a t i o n , w h i c h w i l l h o p e f u l l y be r e d u c e d by f u t u r e measurements . The v a l u e a ^ = - 0 . 5 n e a r 1 9 . 4 MeV a g r e e s w e l l w i t h t h e assignment o f ^ = 3 / 2 ^ 0 t h a t r e s o n a n c e . of a  n 2  The d e c r e a s e d v a l u e  e a r 2 0 . 5 MeV o n l y d i s a l l o w s t h e assignment J = l / 2 .  The v a l u e  of a  2  i s seen t o become more n e g a t i v e  p a s t E = 22 MeV, p  w h i c h agrees w i t h t h e a v a l u e a t 2 2 . 4 MeV from the p r e s e n t s t u d y . 2  LEGENDRE  0.2 5  i—  z:  o  POLYNOMIAL  COEFFICIENT  FOR THE 1531 MeV 6AMMA RAY  ••EBISAWA et a l . ONORMALIZED RESULTS (present study & Ebisawa)  O  o  LU >—«  o  £ -0.2 5  Ll_ LU O O  CM o  o  T  1  •o » -0.50 Calculation by R. McDonald  -0.75 19  20 PROTON  ENERGY IN Figure 13  21 LAB  22 (MeV)  IT 00  -59V  DISCUSSION T h i s study extends r e c e n t measurements, t a k e n a t 12  U n i v e r s i t y o f Washington, o f the E =2.8 P  MeV  t o 2'4.4 MeV. I  The  13 C(p ,"¥<>) N r e a c t i o n from  r e s u l t s have been  and are g i v e n i n f i g u r e 14 on page  the  60 .  We  re-normalized  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 o f the d i f f e r e n t s e t s o f d a t a , and an e q u a l u n c e r t a i n t y i n the a b s o l u t e y i e l d . hope t o soon make measurements t o b e t t e e determine the  We  relative  normalizations. Johnson has measured the Y He has  0  y i e l d from E^=  2.8  MeV  t o 9 MevV  shown, i n p a r t i c u l a r , t h a t the s t r o n g i n t e r f e r e n c e e f f e c t  n e a r E^=  5.3  MeV  can be e x p l a i n e d by a c o u p l e d c h a n n e l c a l c u l a t i o n TT  +  w h i c h t a k e s i n t o a c c o u n t the c o n t r i b u t i o n o f the J =2 first 12 13 e x c i t e d state of C t o the ground s t a t e w a v e - f u n c t i o n o f N. The work o f Measday, H a s i n o f f and Johnson was  described  in  section I I I B . The most s t r i k i n g a s p e c t o f these r e s u l t s i s the h e i g h t the g i a n t resonance (E = 20 MeV)  r e l a t i v e t o the h e i g h t o f  of  the  Jr  pygmy (E = 12 MeV). P  The  two peaks appear t o c o n t a i n e q u a l  s t r e n g t h s , making the terms "pygmy" and The  " g i a n t " seem misnomers.  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  preliminary  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 a n g u l a r d i s t r i b u t i o n o f the gamma-rays might enhance the y i e l d n e a r 20 MeV 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  by as much as  normalizations,  DIFFERENTIAL  C R O S S " SECTION  (pb/sr) a*  to  T*  T"  to  C D  j>  II  O  - »  rO  o  > -<  CD  CO  -<  m r O  CP  I—I  -  73  O —)  m z mto c  —i  X  -<  _>  it  Z ^ > C D  cn  o co i8 z m CO z> o cn=< z o" m > m , m  to o  to to  . 'i  co c: CO  C O  o "TV  to  -09-  X  -61-  we can s t a t e o n l y t h a t t h e c r o s s - s e c t i o n f o r t h e g i a n t resonance cannot be g r e a t e r t h a t 150 % o f t h e 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 t h e enhancement o f low-energy y i e l d s  by t r a n s i t i o n s t o t h e 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 o f t h e d i p o l e s t r e n g t h k be f o u n d a t a v e r y 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 t h e i n v e r s e 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 d a t a a r e : E (MeV)  fa dE  7-17  11  17 - 24.4  6  (MeV-mb)  where t h e r a t i o o f these numbers i s u n c e r t a i n by 40 %.  These  numbers a r e 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 et a l . ,  whose t a b l e we r e p r o d u c e : V a l u e s o f /Q 0"dE (MeV-mb) f o r p h o t o n u c l e a r r e a c t i o n s Reaction  from  1 3  Measday  l3  49  et a l .  1 3  E (MeV) 17  23.5  32  N(Y,Po)  12  22  27  C(Y,n)  21  55  109  0  16  64  cy,p)  c  13  Measday*s  N(*K,p ) 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 o f 0  0.9  13  MeV-mb from t h e 2.37 MeV f i r s t e x c i t e d s t a t e o f i n our estimate.  N not included  Even though o u r 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  l o w e r than M e a s d a y s , o u r i n t e g r a t e d c r o s s s e c t i o n s t o 17 MeV i s T  -62e s s e n t i a l l y the same.  I n the p r e s e n t r e s u l t s , the pygmy resonance  i s seen t o be b r o a d e r 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 u s e d by Measday, w h i c h d i d n o t e x t e n d below E = 10 MeV. results for  13  C(7,p) and  d a t a o f Cook, 1 9 5 7 . 13 The  13  Measday s T  C(Y,n) are c a l c u l a t e d from the  11  12 N(T,p ) 0  C c r o s s - s e c t i o n d e r i v e d from a d e t a i l e d  b a l a n c e c a l c u l a t i o n o f the p r e s e n t r e s u l t s i s g i v e n w i t h p h o t o - d i s i n t e g r a t i o n data o f Cook i n f i g u r e 15, page  the  63 , 24  t o g e t h e r 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 o f A l b e r t e t a l . and J a g e r e t al«?° 13  C ( Y , 2 n ) was  The  curve l a b e l e d ^ C ( Y , n ) + "*"C (y,pn) + 3  c a l c u l a t e d from the e x p e r i m e n t a l C ( Y , n ) + 13  13 2  l3  C(Y,pn) +  13 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 d o u b l e - c o u n t i n g o f n e u t r o n s . T h i s c o r r e c t i o n o n l y a f f e c t s the peak n e a r E = 26 MeV, 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 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  since been  decay t o  e x c i t e d s t a t e s i n boron-12, w h i c h can f u r t h e r decay by n e u t r o n emission.  Thus, Measday a r g u e s , the n e u t r o n decay c r o s s - s e c t i o n  c o u l d be lower a t 26 MeV, higher.  Easlea^  and the p r o t o n decay c r o s s - s e c t i o n  argues t h a t the n e u t r o n decay c r o s s - s e c t i o n  s h o u l d be h i g h e r a t 26 MeV,  on the b a s i s o f h i s s c h e m a t i c model  13 calculation for Easlea's  C u s i n g harmonic o s c i l l a t o r  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, ~  waveifunctions.  b u t o n l y a f t e r a d d i n g an TT  ad-hoc i n t e r a c t i o n t o c o r r e c t l y g i v e the energy o f the J = 2 12 e x c i t e d state of C a t 4.43 MeV. T h i s procedure has been  +  -63-  PHOTO-PRODUCTION THEORETICAL  CROSS" SE CTl ONS CALCULATIONS  WITH  10 • Cfl.n)+ C(?.pn) 13  13  h+ C(l2n) 13  JGk  g z o »—I  V—  o UJ CO i  CO CO  o cr o  Q  UJ  >-  < o  UJ  cr o bJ X  cr < cr oo  cr  10  JA6ER  J  et al.  L  TJ  I  7T7  H 18 22 26 31 6AMMA RAY ENERGY (MeV) Figure 15  -64c r i t i c i z e d by Measday and o t h e r s .  F i g u r e 15 g i v e s t h e r e s u l t s  24 o f 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 s t r e n g t h below 17 MeV, b u t does n o t a d e q u a t e l y account f o r t h e pygmy r e s o n a n c e .  The  c a l c u l a t i o n s o f J a g e r e t al.^,°  u s i n g semi-phenomenological w a v e - f u n c t i o n s , g i v e b e t t e r agreement w i t h our r e s u l t s i n t h e r e g i o n o f the pygmy r e s o n a n c e , a t t h e expense o f 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  b o t h c a l c u l a t i o n s s u p p o r t Measday s argument t h a t the 26 MeV T  resonance i s an i s o s p i n T = 3/2 component o f t h e g i a n t r e s o n a n c e . J a g e r g i v e s a t a b l e o f 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 t o t h e d i p o l e s t a t e s i n h i s model. The  most i m p o r t a n t 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) a r e : ( C  core)  12  from  CP / )~" (P /2) ( 5/ ) L  3  2  1  2  „  1  2  (P )- (P ) (d ) , .-2, 2 _ >1 &V2)l/2 3 / 2  Jager  d  1  2  l / 2  1  5 / 2  v  50  ( P  }  ( 2 s )  13 I n the simple 13  s h e l l model p i c t u r e , t h e ground s t a t e s o f T2 1  C and  N would be ( C core) (P-jy ) > i . e . t h e v a l e n c e n u c l e o n . 2  We see t h a t none o f 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 o f the v a l e n c e n u c l e o n .  Only t h e f i r s t c o n f i g u r a t i o n , w h i c h c a r r i e s  most o f t h e 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) n u c l e o n s c o n t r i b u t e v e r y l i t t l e , and a c o n f i g u r a t i o n  12 (  -65-  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 o n l y 0.05 MeV-mb a t E = 24-.1 MeV.  Thus, J a g e r s T  c a l c u l a t i o n v i e w s t h e v a l e n c e n u c l e o n as a s p e c t a t o r , even i n the r e g i o n o f t h e pygmy r e s o n a n c e .  T r a n s i t i o n s i n v o l v i n g the  v a l e n c e n u c l e o n s h o u l d be seen most s t r o n g l y i n t h e i n v e r s e r a d i a t i v e - c a p t u r e r e a c t i o n , w h i c h l e a d s us t o s p e c u l a t e  whether  the peak seen a t E = 23 MeV ({[E^ 23.2 MeV) c o u l d be i d e n t i f i e d p  w i t h J a g e r * 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 s u p p o r t t h e v i e w t h a t t h e v a l e n c e n u c l e o n does n o t p l a y an i m p o r t a n t r o l e i n d i p o l e t r a n s i t i o n s t o t h e 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 t h e C(p,V<>) N ~ IT. 12 r e a c t i o n t o the cross-section f o r o(p,Yo) C measured by 53 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, b u t t h e y have n o t been d i s torted.  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 ,  t h r e e bumps i n t h e r e g i o n o f t h e g i a n t r e s o n a n c e .  containing  The energy  shifts are: (MeV)  E 1 2  Z \  12,  X  c  E  + p -- >  1 3  25.5  22 .5  19.3  23.2  20.8  18.0  2.3  1.7  N is  + 2 MeV.  1.3 We t h e n  12 t o c o r r e l a t e t h e p e a k s , we must s h i f t t h e  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 % . energies  Since the e x c i t a t i o n  a r e d e t e r m i n e d by t h e shape o f t h e p o t e n t i a l w e l l i n  -66-  RADIATIVE PROTON CAPTURE YIELDS FOR B AND C 11  1 2  i i—i—r~i—i—r  f—i—i—i—i—|—i 1 1  B(p,T ) C Q  1 2  U ALLAS et a I.  J L  16 1ft 20 22 EXCITATION ENERGY IN  24 C  1 2  26 (MeV)  2ft  I—1—I—l—r  C(p,T ) N present results 12  J  I  14  I  I 16  L  I 18  L-J  C  20  EXCITATION ENERGY IN Figure 16  1 3  i 22  0  I  I 24  N (MeV)  13  1  L 26  w h i c h the n u c l e o n s r e s i d e , w h i c h in\:turn a r i s e s from the  sum  t o t a l o f n u c l e o n - n u c l e o n i n t e r a c t i o n s , the d i s t o r t i o n o f the energy s c a l e by the e x t r a n u c l e o n does n o t seem i m p r o b a b l e . The Qkvalue f o r  1  L  B + p  >. C i s + 15.96 MeV. I2  q u e s t i o n a r i s e s whether the bump i n the  (p,To)  The  cross-section 13  a t E = 17.5 MeV  c o u l d be r e l a t e d t o the pygmy resonance i n  b u t c u t o f f by t h r e s h o l d e f f e c t s .  N.  Were t h i s the c a s e , one  might  e x p e c t t o 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 c o n c l u d e s t h a t the a d d i t i o n o f the v a l e n c e n e u t r o n t o the 12 C core causes a major r e s t r u c t u r i n g o f the g i a n t resonance s t r e n g t h . T h i s 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 p r e s e n t results. 12 and  However, D i x o n , 1973,  55  has n o t e d t h a t the  12  C(Y,p)  C ( V , p ) c r o s s - s e c t i o n s and a n g u l a r d i s t r i b u t i o n s a r e 0  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 regions. This discrepancy i s caused by p r o t o n decays t o e x c i t e d s t a t e s i n  Similarly,  we would argue t h a t the r e - d i s t r i b u t i o n o f d i p o l e strength i n  13  C compared t o  12  C  transition  n p t e d by B e r g s t r o m  i s caused  12 m a i n l y by t r a n s i t i o n s t o e x c i t e d s t a t e s i n TT  t h e s e are';.transald.ons t o the J = 2 a c o n f i g u r a t i o n (^C  C.  s t a t e a t E^=  core) ( P / ) ""^U?l/2^ ^» 3  Since most o f  +  2  t h e  4.4 MeV,  with  ^distribution  o f s t r e n g t h f o r t h e s e t r a n s i t i o n s caused by the presence o f a v a l e n c e n u c l e o n i n the P-^/2  s n e  H  n o t  a t  a  H  surprising.  Our r e s u l t s s t r o n g l y s u p p o r t the view t h a t v a l e n c e n u c l e o n t r a n s i t i o n s t o the ground s t a t e from the GDR  carry very  little  -68s t r e n g t h i n t h e r e g i o n E = 17 - 25 MeV ( and perhaps i n the r e g i o n E = 7 - 17 MeV). x I n B e r g s t r o m s d a t a , the pygmy resonance (near E = 14- MeV) T  13 in  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 a n g l e E^= 106 MeV, 0 = 75°. I n t h e c o r r e s p o n d i n g 12 C d a t a , a r a t h e r b r o a d s t r u c t u r e appears between E = 9 MeV and 13 MeV.  We s u g g e s t t h a t t h i s may be the "analogue" o f the pygmy  resonance i n mass-13 n u c l e i .  This i s , of course, only  conjecture,  and a t p r e s e n t we cannot r u l e o u t 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 t h e pygmy resonance i n v o l v e s m a i n l y v a l e n c e n u c l e o n t r a n s i t i o n s . 11 12 I f t h e resemblance o f t h e 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 c o i n c i d e n c e , then t h e resonance 13 a t E = 23.3 MeV i n  N s h o u l d have a c o n f i g u r a t i o n i d e n t i c a l t o 12 the E^= 25.5 MeV resonance i n C w i t h a s p e c t a t o r p r o t o n added. q  The  comment o f B r a s s a r d e t a l .  t h a t t h e 25.5 MeV. resonance i n  12 C i s u n e x p l a i n e d i n the c o n t e x t o f l p - l h s t a t e s i s v e r y interesting i n this light. A good d e a l o f u n c e r t a i n t y e x i s t s c o n c e r n i n g 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 ) C p r o t o n T  decay a t 0°. I n t h e 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 n o t have a s t r o n g e f f e c t on t h e p o l a r i z a t i o n o f the scattered proton. unlikely.  They n o t e , however, t h a t t h i s i s n o t e n t i r e l y 59 A peak was seen by P a t t e r s o n e t a l . , 1966, i n the  150°  y i e l d p r o t o n decay t o t h e ground s t a t e i n  12  C.  They s p e c u l a t e  t h a t i t may be t h e b r o a d 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 t h e coulomb b a r r i e r . The He 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 s u p p o r t t h i s p o s s i b i l i t y . I n t h e C(p,n) N (P ) C 60 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 J  and  23 MeV.  shifted. 23.2  I n t h i s r e a c t i o n , t h e 22.4 MeV s t a t e s h o u l d n o t be  50 The c a l c u l a t i o n o f J a g e r e t a l . g i v e s a s t a t e a t 12  MeV, p r i m a r i l y o f t h e c o n f i g u r a t i o n  ^• 3/2^ p  ^- l/2^  ^°  p  ( C core)  T h i s s t a t e has J = 3 / 2 . 7r  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  +  .  v  However, i t has  contributing.  Some l p - l h s t r e n g t h would be n e c e s s a r y 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 . J ,T  However, J a g e r a l s o c a l c u l a t e s a  = 3 / 2 , l / 2 s t a t e s h o u l d have E = 2411 MeV.  1T  +  This state  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 t h e 23.2 MeV s t a t e c o u l d be p o p u l a t e d v i a some i s o s p i n m i x i n g w i t h t h e 24.1  MeV s t a t e . 61 S h a k i n 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 in  0 c a l c u l a t i o n s quite 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 t h e 23 MeV  .13 resonance xn 25.5  N  m  a  y  w  e  l l  be a 3p-2h s t a t e , and a n a l o g o u s l y , t h e  MeV s t a t e i n C might be e i t h e r 3p-3h o r 2p-2h. 1 2  the p r e s e n t r e a s o n i n g has been by no means r i g o r o u s , 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 .  Although these  -70VI  SUMMARY AND CONCLUSIONS 12 We have measured gamma-rays from the  C(p,Y)  13 N reaction  and from the i n e l a s t i c r e a c t i o n s t o the 12.71 MeV and 15.11 MeV 12 states i n  C. f o r p r o t o n e n e r g i e s between 10 MeV and 24.4 MeV.  I n t e r m e d i a t e s t r u c t u r e was found i n the Yo y i e l d i n the r e g i o n 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 o f t h e  B(p,Y ) 0  C yield.  T h i s has  l e d us t o s p e c u l a t e t h a t t h e v a l e n c e n u c l e o n i n n i t r o g e n - 1 3 i s l a r g e l y a s p e c t a t o r i n t h e r e g i o n o f t h e GDR.  This p o s s i b i l i t y  i s s u p p o r t e d by the t h e o r e t i c a l c a l c u l a t i o n o f J a g e r e t a l . , who used semi-phenomenological w a v e - f u n c t i o n s . J a g e r ' s r e s u l t s i n d i c a t e t h a t the v a l e n c e nuclfeon i s a s p e c t a t o r even i n the r e g i o n o f t h e pygmy r e s o n a n c e .  F o l l o w i n g t h i s l i n e o f thought,  we f u r t h e r s p e c u l a t e t h a t t h e 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 o u t 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 d a t a o f carbon-12, measured by Bergstrom e t a l . t h a t may c o r r e s p o n d t o t h i s "bound s t a t e pygmy r e s o n a n c e " . Our measurements i n d i c a t e t h a t , f o r the (p,Yo)  reaction,  the pygmy resonance c a r r i e s s t r e n g t h a p p r o x i m a t e l y e q u a l t o the GDR.  On t h e b a s i s o f a n g u l a r d i s t r i b u t i o n measurements,  we v e r i f y the e x i s t e n c e o f two narrow minima super-imposed on t h e pygmy r e s o n a n c e , and agree i n f u l l w i t h t h e s u g g e s t i o n s  -71o f Measday e t a l . c o n c e r n i n g t h i s  structure.  We d e r i v e from our d a t a y i e l d c u r v e s 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 , w h i c h agree w e l l with other recent r e s u l t s .  We l i s t p r o t o n decay w i d t h s 13  from compound n u c l e a r s t a t e s i n The (p,7^) and ( p , 7  2 + 3  N t o these s t a t e s .  ) y i e l d s a r e a l s o g i v e n f o r the  r e g i o n s i n w h i c h 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 n e x t s t e p i n d e t e r m i n i n g the r o l e o f the v a l e n c e n u c l e o n i n the mass-13 system might be t o compare i n d e t a i l a n g u l a r d i s t r i b u t i o n s o f the throughout the GDR. l a t t e r q u i t e soon. (d,T ) G  11 12 BCp,To) and C(p,y ) 0  reactions  We hope t o complete measurement o f the E x t e n d i n g r e c e n t measurements o f the  N r e a c t i o n beyond E — 23 MeV might a l s o prove  interesting.  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  o f 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 o f a v a l e n c e n u c l e o n would prove v a l u a b l e .  -72APPENDIX  The n u m e r i c a l r e s u l t s p r e s e n t e d i n t h i s r e p o r t were, f o r the most p a r t , c a l c u l a t e d u s i n g the f o l l o w i n g computer programs:. 1)  EGG  - f i t s gamma-ray l i n e shapes to a g i v e n  spectrum  2)  POLFT - f i t s a Legendre p o l y n o m i a l expansion t o a g i v e n 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 B r e i t - W i g n e r resonance  to a g i v e n y i e l d 4)  shapes  curve.  FIND - l o c a t e s approximately the second s o l u t i o n f o r INTER.  The f i r s t t h r e e programs were based almost e n t i r e l y on the methods d e s c r i b e d i n "Data Reduction and E r r o r A n a l y s i s f o r the 28 P h y s i c a l Sciences"  by P h i l i p R. B e v i n g t o n .  The author made  o n l y minor changes to each of these programs. conceived and w r i t t e n by t h i s a u t h o r .  The f o u r t h  was  A n u m e r i c a l program t o  a p p l y e f f i c i e n c y c o r r e c t i o n s t o 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  a l s o w r i t t e n , but i s s t r a i g h t f o r w a r d and  will  hot be d e s c r i b e d . A)  EGG  The EGG spectrum.  program w i l l f i t up t o t e n gamma-rays to a g i v e n  The f i t t i n g r o u t i n e s are those d e s c r i b e d by  The program was (who named i t . )  Bevington.  adapted f o r use by M. H a s i n o f f and J . S p n l l e r \ r  -73-  The program f i r s t a c c e p t s two l i n e shapes, c r e a t e s up t o 20 energy b i n s , and g e n e r a t e s a l i n e shape f o r each b i n by linear interpolation.  T h i s a l l o w s the u s e r t o v a r y the r e s o l u t i o n  o f the l i n e shape w i t h e n e r g y , o r h o l d i t f i x e d .  EGG e x t r a p o l a t e s  the l i n e shape t o z e r o energy l i n e a r l y t o z e r o counts a t z e r o e n e r g y , o r w i t h a h o r i z o n t a l s l o p e , o r w i t h any s l o p e i n between, as i n s t r u c t e d . The program w i l l f i t up t o t e n gamma-rays s i m u l t a n e o u s l y , and w i l l v a r y p o s i t i o n s and a m p l i t u d e s  as d e s i r e d .  The program  w i l l a l s o add and v a r y a v a r i e t y o f 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 t o h o l d the e x c i t a t i o n energy o f any number o f gamma-rays f i x e d w i t h respect t o the  f. 0  The program v a r i e s t h e a l l o w e d parameters t o m i n i m i z e t h e reduced c h i - s q u a r e d , d e f i n e d by:  1  where  Y  = # o f degrees o f freedom  I n order t o minimize expansion:  , the program does a T a y l o r S e r i e s  U s i n g the method o f l e a s t s q u a r e s , the optimum v a l u e s f o r t h e parameter increments  a r e those f o r w h i c h  This r e s u l t s i n  simultaneous  s o l v e d as a m a t r i x  equation  P =  *  SQ  l i n e a r e q u a t i o n s w h i c h can be  CD  where P and $a are row matrices and tX i s a Y X V square matrix  ^  e  J Equation  (1) i s s o l v e d by m a t r i x i n v e r s i o n , done i n t h i s case by The i n v e r s e o f the c u r v a t u r e m a t r i x iX  rearrangement. the e r r o r m a t r i x 6  k  =C<  i s called  £ . or  c*  = 1  The e r r o r s i n the v a r i e d parameters d e t e r m i n e d by the e r r o r m a t r i x ((T •= 3  f- • •) i n c l u d e s b o t h the s t a t i s t i c a l e r r o r and the ^ 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 o t h e r v a r i e d parameters.  Thus, the m i n i m i z a t i o n i s a c h i e v e d by f o l l o w i n g the  downward c u r v a t u r e o f the J £  hyper-surface  the v a r i e d parameters as c o - o r d i n a t e s .  i n a space h a v i n g  -75The program has been adapted  t o produce p l o t s of the f i t  and the d a t a , which a l l o w s the u s e r t o see the q u a l i t y of the fit.  The program can f i t a s e r i e s of s p e c t r a from tape, or  p i c k out i n d i v i d u a l s p e c t a a .  B)  POLFT  The POLFT program can p r e s e n t l y f i t an a n g u l a r d i s t r i b u t i o n w i t h Legendre polynomials up t o f o u r t h o r d e r .  The  input required  i s e s s e n t i a l l y the a n g l e s , y i e l d s and v a r i a n c e s , t o g e t h e r w i t h the number of polynomials t o be used and v a r i e d , and 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 e r r o r s and m i n i m i z i n g ~£ previous s e c t i o n . the f i t .  initial  as d e s c r i b e d i n the  I t can a l s o produce a p&ot o f the data  and  The program has a wide range of o p t i o n s which were n o t  used i n this, s t u d y .  C)  INTER  T h i s program, adapted by M. H a s i n o f f , uses the s e a r c h technique d e s c r i b e d i n s e c t i o n A. f u n c t i o n w i t h two  YCE) =  S  A  INTER f i t s a g i v e n e x c i t a t i o n  i n t e r f e r i n g B r e i t - W i g n e r resonance  + S  2 Q  2 e ? 1  denA  +  ^ denB  (2)  shapes:  -76-  denA  X  +  denB  2  cosf  (denA denB)'  rr A  G  CE-E ) (E-E ) +  I  A  G  - 2 s i n f \ -A (E-E ) -  (E-Ej/  r  2  b  2  where A^ = s t r e n g t h o f resonance A _  , 7,2pin p o u t , i  E^ = energy o f resonance A 1"^ = f u l l w i d t h o f resonance A <P = r e l a t i v e phase between the resonances in 1^  = w i d t h o f i n c o m i n g c h a n n e l o f resonance A  Tout  =  w i d t h o f o u t g o i n g c h a n n e l o f resonance A  A denA = E-E^+i  TA—  and s i m i l a r l y f o r resonance G. The program i s c a p a b l e o f v a r y i n g t h e s t r e n g t h , w i d t h , and c e n t r o i d energy o f each r e s o n a n c e , and t h e 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(_ m i n i m i z i n g procedure 2  d e s c r i b e d i n s e c t i o n A, and produces p l o t s o f t h e d a t a and t h e f i t ,  -77An e x c i t a t i o n f u n c t i o n w i t h two f i t w i t h two  peaks can f r e q u e n t l y  e n t i r e l y separate sets of parameters.  further described  be  This i s  i n the f o l l o w i n g s e c t i o n .  D) FIND F i t t i n g two  i n t e r f e r i n g B r e i t - W i g n e r resonance shapes t o  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 T h i s type o f f i t t i n g was (T^)  sets of s o l u t i o n s .  f i r s t done f o r the case of a narrow  analogue s t a t e i n t e r f e r i n g w i t h a b r o a d ( T ^ )  the two  s o l u t i o n s have been c a l l e d the " s t r o n g "  state,  and  s o l u t i o n , cor-  r e s p o n d i n g t o a s t r o n g 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  s t a t e ) , 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 s t r o n g background. the two  Thus,  s o l u t i o n s are c h a r a c t e r i z e d by v e r y 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. F o r 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  usually  been d e t e r m i n e d t o 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 t o o t h e r a v a i l a b l e i n f o r m a t i o n ^ a b o u t the We two  p r e s e n t a s i m p l i f i e d p i c t u r e t o e x p l a i n the o r i g i n of  s o l u t i o n s , and  been f o u n d . vectors  resonance.  t o l o c a t e the " o t h e r "  F i r s t , we  =  S,  e If  has  p i c t u r e the two B r e i t - W i g n e r shapes as  i n the complex p l a n e .  Y(E)  s o l u t i o n a f t e r one  Then 2  where t h e v e c t o r s a r e o b v i o u s l y d e r i v e d from e q u a t i o n ( 2 ) . The v e c t o r s a r e , o f c o u r s e , energy dependent. I n p a r t i c u l a r  A  YCE ) = G  2  si  w i t h Z^E  e  *r  1 S,  +  2  (3)  = (E - E ) G  A  The angle f  i s n o t a c t u a l l y the a n g l e between t h e v e c t o r s  because t h e v e c t o r s themselves c o n t a i n i m a g i n a r y In fact,  S*  <f  S^" p o i n t s a t an a n g l e P*" where  G  = 0 , R  P  l  i s o r i e n t e d a l o n g the i m a g i n a r y  = a r c cos  a  &  - a r c s i n denA,  E + if^/2 .  v  -  i v  —  Then  *-j^  i s i n t h e f o u r t h quadrant  E p o s i t i v e , and t h e t h i r d quadrant f o r ^ E  for ~ *f  a x i s , and f o r  r•A/2  ^ E 3.  where denA^  factors.  negative.  —1 i s then t h e a n g l e w h i c h v e c t o r  i n i t i a l position. vector  i s r o t a t e d from t h i s  We r e - n o r m a l i z e e q u a t i o n  has the norm A^.  (3)  such t h a t  We s e e , t h e n , t h a t f o r a g i v e n  y i e l d and a g i v e n s t r e n g t h f o r resonance G, a s t r e n g t h f o r resonance A can be f o u n d f o r any phase a n g l e —1  vector  <f  a t t h i s energy.  The  W9  t r a c e s o u t an e l l i p s e as <f i s v a r i e d t h r o u g h 2TT.  T h i s s i t u a t i o n i s d e p i c t e d by t h e 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 t h e y i e l d a t a l l e n e r g i e s . We now l o o k a t t h e c o r r e s p o n d i n g  equation f o r the y i e l d a t  -79-  6E0METRIC MODEL FOR DOUBLE SOLUTIONS TO INTERFERING BREIT-WIGNER RESONANCE SHAPES  -80-  —2 S  energy E . The s i t u a t i o n i s s i m i l a r , b u t v e c t o r -2 p o i n t a l o n g the i m a g i n a r y a x i s and the v e c t o r a  does n o t  points 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 b o t h e n e r g i e s , we must r o t a t e t h i s system so t h a t overlays —2 « A g a i n we  at <P = 0 and also re-normalize  can determine a s o l u t i o n f o r  S  S  =  r  A  f o r any v a l u e o f <p , and  2  l o c u s o f s o l u t i o n s t r a c e s a second e l l i p s e . dashed l i n e s i n f i g u r e 17 ( a ) .  the  These are t h e  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 , c o r r e s p o n d i n g s o l u t i o n s f o r the r e l a t i v e phase f  t o two  and the s t r e n g t h A^,  f o r the  same s t r e n g t h A^.. Of c o u r s e , f o r b o t h s o l u t i o n s t o 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 t h r o u g h 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^ v e r s u s  the two e n e r g i e s E the s o l u t i o n f o r  and E  a  <?  and f o r an a r b i t r a r y e n e r g y .  for  Since  S^ must be p e r i o d i c i n <p ( p e r i o d = 2-rr) f o r  any e n e r g y , the s o l u t i o n s f o r S^ must c r o s s t w i c e i f they c r o s s at a l l .  They can be n o n - i n t e r s e c t i n g o r t a n g e n t .  However,  i f one p a i r o f e l l i p s e s i n t e r s e c t f o r a g i v e n y i e l d , i t seems plausible that  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 s i m p l e program was  w r i t t e n making use o f t h i s p i c t u r e .  F o r the two r e s o n a n t e n e r g i e s , s o l u t i o n s  f o r the .strength o f one  resonance was c a l c u l a t e d f o r v a l u e s o f  between 0 and 2TT,  h o l d i n g the s t r e n g t h o f the o t h e r resonance f i x e d a t the o f the f i r s t s o l u t i o n f o u n d by INTER.  value  The second s o l u t i o n ,  LEAF 81 OMITTED IN PAGE NUMBERING.  -82-  where t h e s t r e n g t h s o f A^ a r e e q u a l f o r a g i v e n ^ by i n s p e c t i o n .  , was  found  These new guesses f o r A^ and (J? were then  s u p p l i e d t o 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 o t h e r s o l u t i o n a p p r o x i m a t e l y 75 % o f the t i m e .  Some o f the d i f f i c u l t i e s a r e  thought t o a r i s e from the s i m p l i f i e d assumptions t h a t the v a l u e s o f A„, H , P_, the p h y s i c a l s i t u a t i o n . tests.  made, i . e .  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