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A study of the reaction ²⁸Si (p,γ) ²⁹P Lim, Sim Too 1975

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28 29 A STUDY OF THE REACTION Si(p,y) P By Sim Too Lim B.Sc. Nanyang U n i v e r s i t y , Singapore, Rep. of Singapore, 1969 M.Sc. U n i v e r s i t y of V i c t o r i a , V i c t o r i a , B.C., Canada, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics We accept t h i s t h e s i s as conforming to the the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1975 In presenting th i s thesis in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th is thes is fo r f i nanc ia l gain sha l l not be allowed without my writ ten pe rm i ss i on . Department of Physics  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date <&<3> /P^f '5>7S ABSTRACT 29 The giant resonance region of P has been inve s t i g a t e d by 28 29 means of the r e a c t i o n Si(p,y) P. The y i e l d s have been measured f o r the t r a n s i t i o n s to the ground and the f i r s t f i v e . e x c i t e d s t a t e s . A 29 28 comparison of the (p,Y Q) y i e l d with the Si(.y,p) A l y i e l d show a pos s i b l e i s o s p i n s p l i t t i n g of 2.5 MeV. Angular d i s t r i b u t i o n s have been. measured for the t r a n s i t i o n s to the ground, l S t excited and 5 t h excited states. The angular d i s t r i b u t i o n s are i n t e r p r e t e d i n terms of the dominating dipole t r a n s i t i o n s with interference from the giant quadrupole resonance. A considerable amount of quadrupole strength i s observed i n the ('p,YQ5 and (p,Y^) r e a c t i o n s . The strengths of d i f f e r e n t channels i n term of the c l a s s i c a l d i pole sum are compared with the structure of the low-lying 29 states i n P. Intermediate structure, of width T-200 keV, observed throughout the giant, dipole resonance i s compared to a v a i l a b l e 2p-lh c a l c u l a t i o n s . 29 Higher excited states of P, m the region below the giant resonance, have also been investigated v i a the (p,Y Q) r e a c t i o n . Several narrow resonances with observed widths characterized by the.target thickness 29 (-17 keV) are proposed to.be,T=3/2 stat e s , i . e . analogs of states i n A l . Possible s p i n - p a r i t y assignments to these states are given. Of p a r t i c u l a r i n t e r e s t are the resonances, of width -150 keV, observed at E = 7.25, 7.45 and 8.80 MeV. Evidence f o r p o s s i b l e s p i n -P p a r i t y assignments to the 7.45 and 8.80 MeV states are given. These states are proposed as p o s s i b l e doorway states, such as. 2p-lh s t a t e s . ii TABLE OF CONTENTS Page ABSTRACT i TABLE OF CONTENTS - i i LIST OF TABLES i v LIST OF FIGURES . V ACKNOWLEDGEMENT V i i i INTRODUCTION 1 CHAPTER 1 EXPERIMENTAL.EQUIPMENT AND: PROCEDURE 1.1 Detector system and e l e c t r o n i c s 9 1.2 Rejection of cosmic-rays by a n t i - c o i n c i d e n t s h i e l d i n g 16 - • 1.3Performance'"of •'•the 'NaT spectrometer 19 1.4. Standard line-shapes and spectrum unfolding 23 1.5 Gamma y i e l d curve c o r r e c t i o n 26 1.6 Absolute cross s e c t i o n measurements f o r 28 29 the Si(p,y) P r e a c t i o n 28 CHAPTER 3 EXPERIMENTAL RESULTS 2.1 Analysis of experimental spectra 31 28 29 + 2.2 Y i e l d of the Si(p,Y Q) P(g.s.,l/2 ) r e a c t i o n 40 28 29 2.2.1 Resonances i n the Si(p,Y ) P r e a c t i o n o below GDR region 40 28 ,29 2.2.2 Cross section of the Si(p,Y ) P r e a c t i o n o i n the GDR region 65 2.2.3 The angular d i s t r i b u t i o n measurements of the 28„. . ,29^ _ _„ Si(p,Y ) P r e a c t i o n 72 o 2.3 The S i f p j ^ P(1.38 MeV,3/2 ) r e a c t i o n i n the GDR region 84 2.4 Cross section and angular d i s t r i b u t i o n measurements of 28 29 the Si(p,Y c5 P r e a c t i o n i n the GDR region ...... 90 CHAPTER 3 DISCUSSION 3.1 Possible candidates of T=3/2 states 95 3.2 Dipole sum r u l e s and r a d i a t i v e proton capture reactions 107 3.3 Intermediate structure and po s s i b l e doorway states 121 LIST OF REFERENCES 135 APPENDIX A DIPOLE SUM AND INDEPENDENT PARTICLE MODEL i v LIST OF TABLES TABLE PAGE 2.1 Summary of resonances below the GDR region 42 2.2 Summary of angular d i s t r i b u t i o n measurements at resonances 44 2.3 Width and center of g i a n t dipole resonance i n n u c l e i of mass A between 17 and 42 66 3.1 Coulomb displacement energies i n A=29 n u c l e i 3.2 E ( 1 ) ( A , T ) and E ( 2 ) (A,T) from higher m u l t i p l e t s c c 3.3 Expected energies of i s o b a r i c analog states i n n u c l e i of mass A=29 3.4 Dipole sum expended i n the r a d i a t i v e proton capture reactions and the simple harmonic o s c i l l a t o r model c a l c u l a t i o n s 29 •3.-5 -Energy "levels'-of ' 'P-'for*E < -4".'08 -MeV x 3.6 Comparison of sing l e - n u c l e o n - s t r i p p i n g spectroscopic 29 f a c t o r s for the low-lying states of S i and f r a c t i o n a l . 29 d i p o l e sum f o r the low-lying states i n P LIST OF FIGURES Figure Page 1.1-1 Lay-out of the spectrometer system 10 1.1-2 Bleeder chain f o r the EMI 9758B photo-tubes 12 1.1- 3 E l e c t r o n i c c i r c u i t showing t y p i c a l NIM equipment used i n the system 14 1.2- 1 Energy spectrum of cosmic-rays r e j e c t e d by the anti-coincidence s h i e l d i n g 17 1.2- 2 P r o b a b i l i t y of acceptance of cosmic-rays vs. equivalent gamma energy (or deposited energy) 18 1.3- 1 Response of the Nal spectrometer to a radiothorium source 20 11 12 1.3-2 T y p i c a l spectrum from the B(p,Y) C re a c t i o n 21 1.3- 3 Spectrum obtained by using a c o l l i m a t o r of '-half-angle'8^6° .... ..."22 1.4- 1 E x t r a c t i o n of the standard line-shape f o r the -. 22.40 MeV photo-peak 24 1.5- 1 Detector e f f i c i e n c y and o v e r a l l c o r r e c t i o n f a c t o r f o r the gamma y i e l d curve 27 2.1-1 2.1-2 2.1-3 2.1- 4 2.2- 1 2.2.1-1 2.2.1-2 28 12 I n e l a s t i c gamma spectra from S i and C targets. . . 32 28 29 Si(p,Y) P gamma spectrum at 11.85 MeV 34 28 29 Si(p,y) P gamma spectrum at E = 16.30 MeV 36 JP 28 29 Si(p,y) P gamma spectrum at E = 20.80 MeV 37 P 90° y i e l d of the 2 ^ S i (p,Y Q) 2 % r e a c t i o n f o r i n c i d e n t proton energies from 7.2 to 23.75 MeV 39 90° y i e l d of the 2 8 S i ( p , Y ) 2 9 P r e a c t i o n f o r i n c i d e n t o proton energy range from 7.20 to 13 MeV 41 90° y i e l d of the 2 8 S i (p,y )29P r e a c t i o n over the E = 7.45 MeV resonance 46 P v i Figure PAGE 2.2.1-3 Normalized angular distributions of the (p,y ) reaction at E = 7.35, 7.46 and 7.60 MeV 44 P 2.2.1-4 Resonances near E =8.0 MeV 50 •P 2.2.1-5 Normalized angular distributions of the (p,yo) reaction at E = 8.02 and 8.07 MeV 51 P 2.2.1-6 Detailed 90°yield of the (p,Y0) reaction at proton energies between 8.40 and 9.40 MeV 53 2.2.1-7 Normalized angular distributions of the (p,Y ) reaction at E = 8.67 MeV 54 P 2.2.1-8 Normalized angular distributions of the (p,Y ) o reaction at E =8.78 and 8.80 MeV 55 P 2.2.1-9 Normalized angular distributions of the (p,y ) reaction at E = 9.275 MeV 57 P 2.2.1-10 Detailed 90 yield of the ,(J>,,Y ) reaction in the vi c i n i t y of the E = 9.555 MeV resonance 59 P 2.2.1-11 Detailed 90° yield of the (p,Y0) reaction in the v i c i n i t y of the E = 11.205 MeV 60 2.2.1-12 90° yield of the (p,YD) reaction for incident proton energies between 9.5 and 13.0 MeV 62 2.2.1- 13 Normalized angular distributions of the (p,Yo) reaction at E = 11.55, 11.70 and 12.40 MeV 63 P 2.2.2- 1 Allowed nucleon decay mode of the giant dipole 29 resonance in Si .... 69 28 29 29 28 2.2.2- 2 Si(p,Y o) P yield compared with the Si(y,p) yield in the giant dipole resonance region 71 2.2.3- 1 Normalized angular distributions of the (p,Y ) o reaction in the GDR region 73 28 , , 2.2.3-2 Legendre polynomial coefficients for the Si(p,Y0). angular distributions f i t t e d up.to N=2 74 V X 1 Figure Page 2 2 . 2 . 3 - 3 Relation between R , a„ and cos 6 7 7 i2 2 8 2 . 2 . 3 - 4 Legendre polynomial c o e f f i c i e n t s f o r the Si(p,y ) o angular d i s t r i b u t i o n s f i t t e d up to N=3 7 9 2 . 3 - 1 9 0 ° y i e l d s of the 2 8 S i ( p , Y l ) 2 9 P C l . 3 8 M e V , 3 / 2 + ) and 2 8 2 9 + S i ( p , Y 2 ) P ( 1 . 9 5 MeV,5/2 ) reactions i n the giant d i p o l e resonance region 8 3 2 . 3 - 2 , Normalized angular d i s t r i b u t i o n s of the (p,y^) r e a c t i o n 8 5 2 8 2 . 3 - 3 Legendre polynomial c o e f f i c i e n t s f o r the Si(p,Y^) r e a c t i o n angular d i s t r i b u t i o n s f i t t e d up to N=2 . . . 8 6 2 8 2 . 3 - 4 Legendre polynomial c o e f f i c i e n t s f o r the Si(p,y^) r e a c t i o n angular d i s t r i b u t i o n s f i t t e d up to N=3 . . . 8 8 2 . 4 - 1 9 0 ° y i e l d s of the 2 8 S i ( p , y ) 2 9 P ( 3 . 1 1 M e V , 5 / 2 + ) and 28 29 — S i ( p , Y r - ) P ( 3 . 4 5 MeV, 5 / 2 or 7 / 2 ) reactions i n ...T the--GDR.., r.eg,-ion. .v- .-»-»»... . . . . . •..*•,..,»-.-•-. • ... . , . .» -• . . 9 1 2 8 2 . 4 - 2 • Legendre polynomial c o e f f i c i e n t s f o r the SiCp,Y^) angular d i s t r i b u t i o n s f i t t e d up to N=2 9 3 3 . 1 - 1 Isobaric m u l t i p l e t s i n n u c l e i of mass A=29 3.2- 1 Photonuclear cross sections c a l c u l a t e d from the corresponding inverse (p, y) r eactions 3.3- 1 Intermediate structure i n d i f f e r e n t reactions and ca l c u l a t e d nucleon decay widths of 2p-lh states of J U= l / 2 ~ , 3/2~ and 5/2~ 3.3-2 Intermediate structure i n d i f f e r e n t reactions and ca l c u l a t e d nucleon decay widths of 2p-lh states ir + of J = 9/2 v i i i ACKNOWLEDGEMENTS I take great pleasure i n acknowledging the invaluable guidance and encouragement of Professor David F. Measday. I t i s my pleasure to acknowledge the invaluable assistance and h e l p f u l discussions of Professor Michael D. Hasinoff throughout the course of t h i s work. I would l i k e to thank Professors J.M.McMillan and P.W.Martin f o r t h e i r time and e f f o r t i n reading t h i s manuscript and a c t i n g as members of the supervising committee. I am indebted to Professor W.G.Weitkamp and the members of the Nuclear Physics Laboratory at U n i v e r s i t y of Washington, Se a t t l e f o r t h e i r help and h o s p i t a l i t y and to the U.S.A.E.C. (now E.R.D.A.) f o r making the Van de Graaff f a c i l i t y a v a i l a b l e . I am g r a t e f u l to Dr.T.Mulligan, Dr.K.A.Snover, K.Ebisawa, D.Berghofer, J . S p u l l e r and ,,,-Pw Helmer ..for ...their -.•assistance; during the course of "the "'experiment. I am thankful to the Canadian NRC and Killam Memorial Fund fo r f i n a n c i a l support during t h i s work. This work would not have been completed without the love and companionship of my wife J u l i a n a and daughter Ruth. 1 INTRODUCTION As e a r l y as 1948 Baldwin and K l a i b e r observed the appearance of a high energy resonance at 20 MeV i n carbon and at 16 MeV i n tantalum, i n t h e i r study of nuclear p h o t o - d i s i n t e g r a t i o n . The integrated cross s e c t i o n deduced,-from the experiments was too great to be explained by the motion of a s i n g l e proton or even of a small f r a c t i o n of the protons contained within the nucleus. This highly excited resonance, according to an i n t e r -p r e t a t i o n given by Goldhaber-Teller (1948), must correspond to a nucleus i n which the bulk of the protons move i n one d i r e c t i o n while the neutrons move i n the opposite d i r e c t i o n . This resonance i s known as the "giant dipole resonance". This giant resonance which i s a few MeV broad i n the photon absorption cross section i s centred at about 22 MeV i n l i g h t n u c l e i , decreasing to about 12 MeV i n heavier n u c l e i . Later Wilkinson (1956) showed that the g i a n t d i p o l e resonance (GDR) could be explained i n terms of the shell.model as w e l l . He postulated that the resonance was due to a nucleon being r a i s e d i n energy by one s h e l l spacing. This model gives too low an energy f o r the resonance, e s p e c i a l l y i n l i g h t n u c l e i , but i t was then shown by Brown (1959) that the r e s i d u a l p a r t i c l e - h o l e i n t e r a c t i o n could r a i s e the energy of the resonance almost a f a c t o r of 2. Brink (1957) has been able to show that the Goldhaber-Teller and the s i n g l e - p a r t i c l e p i c t u r e s of g i a n t resonance e x c i t a t i o n are e s s e n t i a l l y the same. Due to the f a c t that the s h e l l model approach i s p a r t i c u l a r l y suited to c a l c u l a t i o n of the decay modes, such as angular d i s t r i b u t i o n s , p o l a r i z a t i o n s and branching r a t i o s , most of the recent attempts at i n t e r p r e t i n g the g i a n t d i p o l e resonance, p a r t i c u l a r l y i n l i g h t n u c l e i , have proceed within the framework of the s h e l l model (e.g. B a r r e t t et al.1975). A d i s c u s s i o n of the general c h a r a c t e r i s t i c s of the giant dipole resonance can be found i n the reviews by Hayward (1970) or Spicer (1969). The photonuclear giant d i p o l e resonance phenomenon has been studied extensively over the l a s t 25 years. Bremsstrahlung beams of photons with a continuous energy spectrum and a well-defined upper energy l i m i t have been used f o r such studies f o r three decades. More r e c e n t l y there has been a development of quasi-monoenergetic photon beams (of energy r e s o l u t i o n - 200 keV) using the a n n i h i l a t i o n - i n - f l i g h t of positrons generated by e l e c t r o n beams from l i n e a r a c c e l e r a t o r s . This improvement.in the energy spectrum of the y-rays made the experimental data more r e l i a b l e and also made po s s i b l e the study of the phenomenon i n greater d e t a i l (review see Berman and F u l t z 1975), even though the beam i n t e n s i t y has been a severe problem. Much work has been done at Livermore where they have studied (y,n) reactions i n p a r t i c u l a r with the a b i l i t y to separate (y,2n) and (Y,3n) rea c t i o n s , as well as to d i s t i n g u i s h (y,n ) from (y,n ). However o x measurements performed with a monoenergetic photon beam have tended to be f o r medium and heavy mass n u c l e i and only a few experiments on l i g h t n u c l e i have been done with adequate accuracy. As a r e s u l t of the large quantity of photonuclear data accumulated i n the l a s t few decades and the exploration of systematic properties of the giant d i p o l e resonance, pr o p e r t i e s such as the energy, width, d i p o l e sum and the s p l i t t i n g i n heavy deformed n u c l e i are i n general known f o r n u c l e i throughout the medium and heavy mass region. I n v e s t i g a t i o n of the giant d i p o l e resonance i n l i g h t n u c l e i v i a r a d i a t i v e proton capture has been aided by the development of the tandem Van de Graaff a c c e l e r a t o r . Many of the measurements done i n e a r l y s i x t i e s are due to the Argonne National Laboratory group using t h e i r tandem VDG and a large Nal c r y s t a l detector of energy r e s o l u t i o n of about 8% (Bearse et a l . 1968 and references t h e r e i n ) . Angular d i s t r i b u t i o n s and e x c i t a t i o n functions over the giant d i p o l e resonance of n u c l e i such as 12 16 20 28 . 24 32 . . , , C, O, Ne, S i , Mg and S were i n v e s t i g a t e d . More r e c e n t l y the Stanford tandem group has measured a rather complete set of (p,y) data i n the GDR r e g i o n . o f , l p ~ s h e l l n u c l e i (e.g. Fisher.. .(1970.).-and the annual report of the nuclear. physics laboratory, Stanford :,University (3 974)). 90 142 Medium and heavy mass n u c l e i such as Zr (Hasinoff et al.1974) and Nd (Hasinoff et al.1972) have a l s o been inve s t i g a t e d by t h i s group. Radiative proton capture into n u c l e i such as 4°Ca, ^ 2Ca and ^ N i (Diener et al.1973, Diener et al.1973a, Diener et al.1971) have been performed a t Stony Brook. The -energy '-resolution - of" i s approximately 5% f o r 20 MeV gamma rays. Radiative proton capture experiments have been able to provide information which i s not obtained from photo-absorption measurements. Since charged-particle a c c e l e r a t o r s are able to provide much better energy r e s o l u t i o n i n the compound nucleus system, a great wealth of structure within the g i a n t d i p o l e resonance has been revealed. For example 40 i n the i n v e s t i g a t i o n of r a d i a t i v e proton capture i n t o the GDR of Ca, f i n e structure about 25 keV wide i s observed throughout the region; but no other f i n e structure can be found even i n a search with 2 keV r e s o l u t i o n (Diener et al.1973). Investigation of r a d i a t i v e proton capture i n t o the 28 GDR of S i (Singh et al.1965) revealed intermediate structure of width =175 keV and f i n e structure of width 50 keV w i t h i n the intermediate s t r u c t u r e . The observed intermediate s t r u c t u r e may represent doorway states. A comparison of the various h i g h - r e s o l u t i o n experiments shows that the width of the f i n e structure decreases with increasing atomic number. The f i n e structure can be i n t e r p r e t e d as the mixing of the compound nuclear l e v e l s i n t o the g i a n t dipole s t a t e . The v a l i d i t y of the concept of i s o s p i n has long been established, p a r t i c u l a r l y , i n l i g h t n u c l e i . The formalism of i s o b a r i c spin, which t r e a t s protons and neutrons as being simply d i f f e r e n t charge states of nucleon, i s treated i n most elementary texts on nuclear physics. Detailed discussions on the a p p l i c a t i o n of the concept to n u c l e i can be found i n the reviews edit e d by Wilkinson (1969). For a nucleus.of mass rd , -> number A, the 3 component T^ of the i s o s p i n operator T has eigenvalue T = (N-Z)/2, where N i s the number of neutrons and Z the number of protons. I f the nuclear i n t e r a c t i o n i s charge independent, then the t o t a l i s o s p i n T of a nuclear system i s a good quantum number and the low-lying energy l e v e l s have minimum i s o s p i n , T= T =T . However higher excited states o z may have an i s o s p i n of T = T + 1. These excited states of higher i s o s p i n are u s u a l l y refered as i s o b a r i c analogue states because they are s i m i l a r (analogous) to the low-lying states i n the neigbouring n u c l e i of mass A having T =±|T o+1J. This means that nuclear structure does not depend too c r i t i c a l l y on whether a p a r t i c u l a r state i s populated by a neutron or a proton because the strong i n t e r a c t i o n i s charge independent and the Coulomb forces are small compared with the nuclear forces (at l e a s t for l i g h t n u c l e i ) . The i s o s p i n s e l e c t i o n r u l e (AT=±1) f o r e l e c t r i c d i p o l e t r a n s i t i o n s was f i r s t i n v e s t i g a t e d by Wilkinson. Isospin s e l e c t i o n r u l e s f o r d i f f e r e n t electromagnetic t r a n s i t i o n s can be found i n the review by Warburton and Weneser (in the book edited by Wilkinson(1969)). The charge dependent i n t e r a c t i o n s i n nuclear system may be expected to introduce i s o s p i n i m p u r i t i e s , p a r t i c u l a r l y , i n t o higher excited states i n n u c l e i . The existence of i s o s p i n impurities i n some of the i s o b a r i c analogue states i n l i g h t n u c l e i permits t h e i r observation i n the r a d i a t i v e proton capture reactions as well as other i s o s p i n forbidden r e a c t i o n s . 29 29 The ground state of P i s a T=l/2 s t a t e . The f i r s t T=3/2 state i n P 29 a t E^=8.38 MeV (i s o b a r i c analogue state of the ground states of A l 29 and- S) has been inve s t i g a t e d i n d e t a i l (e.g. Endt e t a l . 1973 and references t h e r e i n ) . However the highest T=3/2 states were not we l l established before t h i s work. We s h a l l discuss the po s s i b l e i d e n t i f i c a t i o n 29 of these higher T=3/2 states i n P. Useful information has been obtained from the r a d i a t i v e proton capture r e a c t i o n which has established the existence of i s o s p i n s p l i t t i n g i n the giant d i p o l e resonance f o r n u c l e i with i s o s p i n T^ 0. Recent progress i n i d e n t i f y i n g the i s o s p i n of the gi a n t dipole resonance can be found i n 13 13 15 the work of Paul (1973) . For l i g h t nuclei', C- N and N have received 13 considerable a t t e n t i o n . In N the s p l i t t i n g i s rather s o l i d l y e stablished 15 (Measday et al.1965) but i n N (Kuan et al.1970 and Paul 1973) the s i t u a t i o n i s not very c l e a r . There i s no d e f i n i t e i d e n t i f i c a t i o n of i s o s p i n s p l i t t i n g of the GDR i n n u c l e i of mass between 20 and 30. 29 Since P has a h a l f - l i f e of 4 seconds (Azuelos e t al.1975), the giant dipole resonance cannot be studied by the photon absorption 29 29 method. However the d i f f e r e n c e between the S i - P mirror p a i r i s 29 . the valence nucleon. The s i m i l a r i t y between the low-lying s.tates m S i 29 and P in d i c a t e s the e f f e c t s of Coulomb forces on nuclear l e v e l s are 6 small. Based on the concept of i s o s p i n we expect the giant dipole resonances i n these two n u c l e i to be very s i m i l a r . As the ground 28 state of S i i s a T=0 state and the proton has an i s o s p i n of 1/2, the e x c i t a t i o n of the T=3/2 component i n the giant dipole resonance i s strongly suppressed i n the r a d i a t i v e proton capture r e a c t i o n . In t h i s work we inve s t i g a t e the l o c a t i o n and width of the T=l/2 29 29 component of the giant dipole resonance i n P (or S i ) . We hope t h i s w i l l provide information leading to the determination of i s o b a r i c spins 29 of the giant dipole resonance i n S i . 28 Much d e t a i l e d work has been done on S i (Singh et a l . 1965, Caldwell et a l . 1963, Wyckoff et a l . 1965, Bezic et a l . 1968 and Wu et a l . 1970), but only i n a few experiments has the giant d i p o l e resonance 29 i n S i been investigated (Katz et a l . 1954, Fukuda et a l . 1973). The w(Y/ri)'. and •"••(Y7p^ ;-*6"toss^ sec't'i6nrs:'*'haa''b'e'en- measur'ed'-^by *"'-Ka'tz '-et -al;-in sa natural s i l i c o n t arget using a bremsstrahlung photon f l u x . A resonance shaped peak at 20.5 MeV, approximately 6 MeV wide, had been observed 29 28 • 29 i n the Si(y,p) A l r e a c t i o n . The (y,n) cross sections i n the S i 30 and S i isotopes were not distin g u i s h e d and above 17 MeV photon energy 28 (threshold of Si(y,n) reaction) the e x t r a c t i o n of the (y,n) cross sections was not p o s s i b l e . However a considerable amount of di p o l e strength had been observed between the e x c i t a t i o n energies of 12 MeV 29 and 17 MeV. Fukuda et al.- has also reported on the Si(y,n) r e a c t i o n a t low energies (<13 MeV e x c i t a t i o n ) , where some structure was observed. 29 ' ' As the ground state of S i i s a T=l/2 st a t e , according to the AT= ±1 i s o s p i n s e l e c t i o n r u l e the resonances excited.by e l e c t r i c d i p o l e absorption can be T= 1/2 or 3/2. I t i s not c l e a r from these measurements 29 i f i s o s p i n s p l i t t i n g i n the giant d i p o l e resonance of S i e x i s t s . 7 In photo-absorption measurements, only the giant dipole resonance b u i l t upon the ground state can be reached. The r a d i a t i v e proton capture r e a c t i o n allows the study of giant resonances b u i l t upon excited states by detecting y-transitions to these excited states. The spacing of low-lying states i n most l i g h t n u c l e i allows the observation of y-transitions to i n d i v i d u a l states following r a d i a t i v e capture. The center of the giant d i p o l e resonance b u i l t upon excited states i s found, i n several l i g h t n u c l e i , mostly A=4n or even mass n u c l e i , to l i e higher than the center of the ground state giant resonance by an energy approximately equal to the energy of the excited state. However experimental data of t h i s type on odd n u c l e i are scarce. T h i s type of measurement leads to information on both the giant resonance and the low-lying state upon which the giant resonance i s b u i l t (Brown '*1'973). The concept of doorway states (Feshbach 1967) has received much a t t e n t i o n i n the l a s t decade. T h e o r e t i c a l c a l c u l a t i o n s (Payne 1968 and Choi et a l . 1974) show that there should be intermediate structure 29 i n S i which can be i n t e r p r e t e d as i s o l a t e d doorway s t a t e s . These states are expected to be a few MeV below the GDR region and have considerable nucleon decay width. In the present work we have investigated 29 the possible existence of these doorway states i n P ( the mirror nucleus of Si) One major experimental d i f f i c u l t y encountered i n these measurements was the energy l e v e l spacing between the low-lying states 29 of p which ranges from 300 keV to 1.38 MeV; the other major d i f f i c u l t y 28 29 + was associated with the f a c t that the Q~value of the Si(p,Y Q) S i ( g . s * , ^ ) r e a c t i o n i s only 2.745 MeV which i s lower than most other cases which 8 have been inve s t i g a t e d . The narrow energy spacing means that a detector r e s o l u t i o n of better than 5% i s necessary and the low Q-value means that a proton beam of energy as high as 24 MeV i s necessary to cover the whole region of giant dipole resonances b u i l t upon the ground and the f i r s t f i v e excited states. The high, energy of the protons, causes some problems with neutrons background i n the detector. In summary, then, t h i s work i s po s s i b l e only because we had a v a i l a b l e both the UBC 10" X 10" Nal gamma-ray detector (Hasinoff et a l . 1974) and the three-stage-tandem VDG accelerator at the Nuclear Physics Laboratory, U n i v e r s i t y of Washington, S e a t t l e , Washington (Weitkamp and Schmidt 1974). CHAPTER 1 EXPERIMENTAL EQUIPMENT AND PROCEDURE §1.1 Detector system and e l e c t r o n i c s The gamma-rays were detected by a large Nal c r y s t a l surrounded by an anticoincidence s h i e l d of p l a s t i c s c i n t i l l a t o r . The o v e r a l l design of the spectrometer (Fig.1.1-1) had been described i n d e t a i l elsewhere (Hasinoff et al.1974). The c e n t r a l Nal(T^) c r y s t a l , i s a c y l i n d e r , 25.4 cm i n diameter and 25.4 cm long, and i s surrounded by an anticoincidence s h i e l d , 10.8 thick, made from the p l a s t i c s c i n t i l l a t o r NE110. The purpose of the anti-coincidence s h i e l d i s that i f a s i g n i f i c a n t amount of energy from a gamma-ray shower escapes from the Nal c r y s t a l , then there i s a high p r o b a b i l i t y !"(-150%- *c;harrcef) " t h e f t * these -g-amma^rays wilT'-be - dat'ec;ted-'i:in 'the'-'-pl-astic S c i n t i l l a t o r and that the event can then be routed i n t o a d i f f e r e n t group of the pulse-height-analyzer. This group (or spectrum) i s hereon r e f e r r e d to.as the rejected-spectrum. Hermetically sealed i n an aluminium can, the Nal(TI) c r y s t a l (manufactured by the French company Quartz et S i l i c e of St. P i e r r e l e s Nemours) i s viewed by seven 78 mm photo-tubes of the type EMI 9758B, which has a 65 mm b i a l k a l i photo-cathode and an anode-pulse r i s e time of about 12 ns. The smaller photo-tubes are chosen because of the non-uniform s e n s i t i v i t y of the photo-cathode of a large photo-tube. The gains, of the photo-tubes are matched by adjusting the high voltage on the bleeder..chains so-that the outputs of the photo-tubes are the same f o r a well collimated. gamma-ray source F i g . 1 . 1 - 1 Lay-out of the spectrometer system. 11 incident on the centre of the front face of the Nal c r y s t a l . Average high voltage applied to the photo-tubes i s about 1400 v o l t s . The anode signals from the seven photo-tubes are summed pa s s i v e l y and fed to a-fan-out. A r i s e time of about 20 ns i s observed on the anode s i g n a l . In order to minimize the s e n s i t i v i t y of the gain to the count rate i n the Nal c r y s t a l , the bleeder chain (Fig.1.1-2) f o r the photo-multipliers i s designed such that the base current of approximately 2 ma i s always much bigger than the average s i g n a l current... There are zener diodes between the cathode and f i r s t dynode and also across the l a s t two dynodes and anode i n order to s t a b i l i z e the voltage at these s e n s i t i v e sections. An external feedback system (by William and Harris) i s also connected to the high voltage applied ^ 6 ' * ' * h e - - ^ B B ' t?o - ' m u ^ t d p l l i e r s ' ••.in^or-dar^fco^Ma^ detector. Input si g n a l s f o r the s t a b i l i z e r are taken from the fan-out of the Nal s i g n a l . The s t a b i l i z e r i s adjusted such that a d i s c r i m i -nator xvindow i s set on a l i n e i n the low energy p o r t i o n of the spec-trum, normally the 2.23 MeV l i n e from the capture of thermal neutrons by hydrogen or a strong l i n e corresponding to one of the low-lying states of the target nucleus. The remaining gain s h i f t s are always n e g l i g i b l e compared to the r e s o l u t i o n of the spectrometer. To reduce the p o s s i b i l i t y of neutron f l u x reaching the main c r y s t a l the Nal c r y s t a l i s surrounded on a l l si d e s , except the side viewed by the photo-tubes, by 1/2 inch of self-supporting mixture of l i t h i u m carbonate (80% by weight) and wax (20%). H Z Z! C=0.01JUF C1=0.05juF C2=0.10JUF r=33kn , n = 510a, r'a=5.1 ka R=200kA z=lN5378 (100v MOTOROLA) zi=1N 5388 (200v • • ) z I—£+-1M0 ir-€1 Cl ±c C2 node Q R fckn. z — i C2 OUTPUT +H.V. F i g . 1 . 1 - 2 Bleeder chain for the EMI 9758B photo-tubes. 13 The anti-coincidence s h i e l d consists of NE110 p l a s t i c s c i n t i l l a t o r , 10.8 cm thick, manufactured by Nuclear Enterprises of San Carlos, C a l i f o r n i a , U.S.A.. The s c i n t i l l a t o r NE110 was chosen as i t has a better l i g h t transmission than the more common NE102A and yet i s only 10% more expensive. The thickness of 10.8 cm was chosen to match the photo-cathode of the 12.5 cm diameter 8055 photo-multiplier tubes (manufactured by RCA). This tube i s f a i r l y slow with a r i s e time of 15 ns but i t i s inexpensive. Standard r e s i s t o r - c h a i n s are. used. in..the bases of. these-photo-multiplier . tubes. . . The s c i n t i l l a t o r d i s c , s i t t i n g i n front of the Nal c r y s t a l i s 50.8 cm i n diameter and viewed by two pho t o - m u l t i p l i e r s . The c y l i n d r i c a l p l a s t i c , surrounding the Nal c r y s t a l , was made in t o two halves, ' e'ach viewed";by ;'flir'ee' photo-mul't'ip'ri'ei' 'tubes." "Tire 'jShoto-tfubes on the front p l a s t i c and the c y l i n d r i c a l p l a s t i c are matched f or gain separately. The average high voltage, on the tubes i s 2,000 V . and the average current i s 2 ma. The s i x anode sig n a l s from the annular s h i e l d and the anode signals from the fr o n t p l a s t i c are passiv e l y mixed. The p l a s t i c s i g n a l i s amplified and clipped to 40 ns (Fig.1.1-3). This s i g n a l i s do u b l e - d i f f e r e n t i a t e d then inverted by a timing a m p l i f i e r of type ORTEC 4 54 , such that the timing i n the following updating di s c r i m i n a t o r i s on the cross-over part of the s i g n a l s . The p l a s t i c d i s c r i m i n a t o r i s t y p i c a l l y set j u s t above the noise l e v e l at pulse height corresponding to a gamma ray energy of 50 keV . The count rate of the p l a s t i c s i g n a l i s t y p i c a l l y a few hundred thousand pulses per second. 14 Na I L I N E A R P L A S T I C A N T I - C O I N C I D E N C E H I G H L E V E L D I S C R I M I N A T O R L R S F A N - O U T 7 0 0 n - s e c D E L A Y L R S A T T E N ZZ3ZZ D I S C S U M I A N N U L U S S U M E G G A N 2 0 1 / N J L E G G A N 2 0 1 / N O R T E C 4 5 4 C L I P T O 4 0 0 n - s e c L R S F A S T A M P ! 1 3 3 B ± O R T E C 4 5 4 E G G D I S C R I M . T D 101 / N ••• -. K — > O R T E C 4 5 4 E G G D I S G R I M . I E G G D I S C R I M . P H A s S — i R O U T E R G A T E a D E L A Y N D 2 4 0 0 * — • G A T E a . D E L A Y F i g . 1.1-3 E l e c t r o n i c c i r c u i t showing t y p i c a l NIM equipment used i n the system. 15 Since a f a i r l y large dynamic range i s normally required for the NaT. l i n e a r pulse, a high-low discriminator (HLD of type EG&G TD101) was i n s t a l l e d i n t h i s branch of the c i r c u i t (Fig.1.1-3). This d i s c r i m i n a t o r reduces the time slexjing caused by the r e l a t i v e l y slow Nal ri s e - t i m e (-20 ns), by producing a time s i g n a l from a low-level discriminator (usually a few hundred keV) whereas the h i g h - l e v e l i s usually set at an energy not too f a r below the range of i n t e r e s t (about 10 MeV). This high-low di s c r i m i n a t o r i s i n h i b i t e d f o r 1.5 us following the f i r i n g of the h i g h - l e v e l discriminator i n order to eliminate m u l t i p l e discriminator outputs for the same Nal pulse. The h i g h - l e v e l l o g i c s i g n a l i s then cli p p e d to -5 nsec f o r use i n .the.coincidence l o g i c . The Nal l i n e a r s i g n a l i s amplified and passed through a . :/..^ ; linear-'gafre.'^ •• (Nuclear Data 2400). The l i n e a r gate (Tennelec type TC 304) i s opened by the h i g h - l e v e l d i s c r i m i n a t o r through an i n t e r f a c e module (EG&G Gl 200/N). The gate i s normally open f or -450 ns so that the pile-up e f f e c t s can be reduced: too short a gate worsens the . r e s o l u t i o n as noted previously (Diener et a l . 1970). A f a s t coincidence i s formed between the Nal and p l a s t i c l o g i c s i g n a l s a f t e r which slow l o g i c pulses are produced to route the energy s i g n a l i n t o two groups of the multichannel analyzer. Events i n the Nal c r y s t a l that are coincident with events i n the p l a s t i c s c i n t i l l a t o r are routed i n t o the rejected spectrum of the pulse-height analyzer, while Nal events with no count i n the p l a s t i c s c i n t i l l a t o r are routed i n t o the accepted spectrum as shown i n Fig.1.3-2. 16 §1.2 Rejection of cosmic-rays by anti-coincident s h i e l d i n g Since the spectrometer i s encased i n a lead s h i e l d , 5" thic k , only higher energy cosmic-rays can reach the c r y s t a l . However these cosmic-rays have to pass through the anti-coincidence p l a s t i c s h i e l d . The p r o b a b i l i t y of these cosmic-rays being detect-ed by the p l a s t i c s c i n t i l l a t o r i s high and so almost a l l the events are routed i n t o the rejected spectrum. Good cosmic-ray r e j e c t i o n has been achieved by the present set-up. Figure 1.2-1 shows a spectrum of cosmic-rays rejected by the anti-coincidence p l a s t i c s h i e l d i n g . The energy d i s t r i b u t i o n of the r e s i d u a l cosmic rays shows a peak at about 130 MeV,. of about'-20 'MeV i n width.. The energy of t h i s peak i s determined by the ...diameter. ,p.f.;,,the .NaX-crystal. .. .The ..ov.erall.probability-..of „sa,,cosmic^-ray event f a l l i n g into the "accept" spectrum i s about 1/310. The t o t a l count rate f o r cosmic-rays depositing more...than . 14 -MeV i n •- : the c r y s t a l i s 475 counts per minute. Figure 1.2-2(a) and 1.2-2(b) show the accepted and rejected spectra of cosmic-rays, of equivalent gamma-ray energy range from 14 to 40 MeV, accumulated i n an 10 hour i n t e r v a l . In t h i s energy range, the energy d i s t r i b u t i o n i s e s s e n t i a l l y uniform and a count rate of 168 counts per MeV-hour i s obtained f o r the rejected cosmic-ray events. When a cosmic-ray passes through the p l a s t i c s c i n t i -l l a t o r , the amount of energy deposited depends on the energy of the cosmic-ray. When the pulse height i s close to the dis c r i m i n a t o r s e t t i n g , the p r o b a b i l i t y of the cosmic-ray not being accepted 17 EQUIVALENT ENERGYCIN MeV) OF RES. COSMIC RAY 16 18 20 22 24 26 28 30 32 34 36 38 n ~i 1 r — " — r — — f r ~ — i — — i 1 n 1 r ACCEPTED -J15 10 5 O o '-I m o cr 0-# « • • 0 0 • • • • • • • • •M • • • • •• y REJECTED • • . ^ » « M « • « • « . . . • • • • » • • •• • «• ••» •• • • » » • I n » i • * — • »*——I (J . . .350 x • . • • . . • • ' cn I • •* ; . ' * . . " H200 •300 •250 -1150 ACCEPTED v ACCEPTED'REJECTED _|3 2 _ J I L_ I L I ' ' ' I I I » 120 160 ^ 200 240 CHANNEL NO. Fig. 1 . 2 -2 (a) Accepted spectrum; (b) rejected spectrum; and ; (c) probability of acceptance of cosmic-raya vs. " equivalent gamma energy, (or deposited energy). ! 19 depends s e n s i t i v e l y on the cosmic-ray equivalent energy. In Figure 1.2-2 the average p r o b a b i l i t y , f o r acceptance of a cosmic-ray, i s p l o t t e d against the equivalent energy of the cosmic-ray. A dotted-l i n e has been drawn to guide the eye. The cosmic-rays which feed through into the accepted spectrum never exceed 10 counts/MeV-hour which i s always n e g l i g i b l e i n comparison to the accepted count rate from r a d i a t i v e proton capture i n the target. Possible improvement i n the cosmic-ray r e j e c t i o n depends l a r g e l y on the signal-to-noise r a t i o and the photo-multipliers on the s h i e l d i n g p l a s t i c . §1.3 Performance of the Nal spectrometer The performance of the spectrometer and a comparison with other detectors of the same s i z e has been described i n d e t a i l e l s e -where :;{Hasijioff.ACt._aJ...^19^4)-^-Eig!ure--l."3--l«?shows :the-response 'of the Nal spectrometer to a radiothorium source a few inches away from the f r o n t p l a s t i c . The r e s o l u t i o n of 5.8% i s b e t t e r than r e s u l t s obtained with other Nal spectrometers of the same s i z e and i s g e t t i n g f a i r l y c l o s e to the r e s o l u t i o n obtained i n small Nal c r y s t a l s . The peak-to-valley r a t i o f o r the ^ C o d o u b l e t - l i n e i s seen to be 2.5 . . 11 12 Figure 1.3-2 shows a spectrum from the B(p,y) C r e a c t i o n a t E =7.0 MeV. The count rate i n the c e n t r a l Nal detector was P 30 k/s f o r gamma rays above 1 MeV. The gamma-ray c o l l i m a t o r h a l f -angle was 5° and the diameter of the region subtended on the back face of the Nal c r y s t a l was 13 cm. Figure 1.3-2a shows the response of the spectrometer without the a n t i - c o i n c i d e n t r e j e c t i o n , obtained oz LLI z z: < u cr LLI C L 00 O 1 1 B ( P / r 0 ) 1 2 C Ep=7.0Nl9V H A L F - A N 6 L E=5° COUNT RATE = 35 k/s FWHM = 2.8 % F W T M = 1 2 % Eyo = 22.4MeV 4. + I E y = 17.9MeV i + 160 170 180 CHANNEL NO/ 190 200 TftT 220 -1000 -800 •600 •400 •200 0 100 0 F i g . 1.3-2 T y p i c a l spectrum from the 1 1B(p,Y ) reacti o n . (a) T o t a l spectrum obtained from summing (b) and ( c ) ; (b) accepted spectrum; (c) rejected spectrum. 1500 1200 LU 900h < u LLI 600r C L 00 o u 300-0-150-a-• E p= 7.0 MeV HALF-ANGLE =8.6° COUNT .RATE=33K/S FWHM = 3.9% 140^ T 5 0 T 6 0 ~ ^ 170" C H A N N E L . NO. 190 200 F i g . 1.3-3 Spectrum obtained by using a co l l i m a t o r of half-angle 8.6 23 by summing F i g s . 1.3-2b and 1.3-2c. The accepted and rej e c t e d .-spectra (Figs.l.3-2b and c) are p l o t t e d and the one-escape-peak i s obviously seen i n the rejected spectrum. The f u l l - w i d t h - h a l f -maximum (FWHM) of the 22.4 MeV photo-peak i s 4.8% and 2.8% f o r the t o t a l spectrum (Fig.l.3-2a) and accepted spectrum (Fig.1.3-2b), r e s p e c t i v e l y . The full-width-tenth-maximum of the accepted spectrum i s 12 %. The energy r e s o l u t i o n of the Nal spectrometer also depends on the aperture of the c o l l i m a t o r . Figure 1.3-3 shows a spectrum obtained by using a coll i m a t o r of half-angle 8.6° . The FWHM i s 3.9% f o r the 22.40 MeV photo-peak. §1.4 -Standard line-shapes and spectrum unfolding In a large Nal c r y s t a l , the shower produced by a gamma ray i s u s u a l l y contained within the c r y s t a l . I f a s i g n i f i c a n t amount of energy from a gamma-shower escapes from the c e n t r a l Nal c r y s t a l , there i s a high p r o b a b i l i t y that these gamma-rays or e l e c t r o n s - w i l l be detected i n the anti-coincidence p l a s t i c s h i e l d i n g and the event can be routed into the re j e c t e d spectrum. As a consequence, not only i s the energy r e s o l u t i o n of the detector improved, but also the c h a r a c t e r i s t i c shape (or standard line-shape) f o r a mono-energetic gamma-ray i s much simpler than that of a smaller c r y s t a l and does not depend as much on the t o t a l energy of the gamma-ray. This means that the energy spectrum of the gamma-rays can be unfolded more p r e c i s e l y . 1000H 120 l 1B( P /y) l 2C Ep=7.0 MeV HALF-ANGLE = 5 COUNT RATE = 44 k/s FWHM = 3 % 14 140 16 160 CHANNEL NO. T | 18 180 200 20 22 E^(MeV) 24 F i g . 1.4-1 E x t r a c t i o n of the standard line-shape f o r the 22.40 MeV photo-peak. . 2 5 A computer programme was constructed to analyze the experi-mental spectra i n terms of mono-energetic gamma-rays. A standard chi-square minimization technique (e.g. Bevington 1969) i s used i n the f i t t i n g process and the f i t consists of a sum of a c e r t a i n number of line-shapes. A background, i n the form of a polynomial can also be included i n the f i t and the c o e f f i c i e n t s i n the poly-nomial f u n c t i o n can be eit h e r f i x e d or set as v a r i a b l e s during the chi-square minimization. The line-shapes a p p l i c a b l e to the peaks being analyzed were obtained by i n t e r p o l a t i n g between two standard line-shapes. Standard line-shapes are obtained from various nuclear 11 12 12 12 react i o n s , s p e c i f i c a l l y B(p,Y o) C and " C(p,pY^ -^) C. To describe the determination of a standard line-shape, we show a t y p i c a l 'clean' pulse-height spectrum i n F i g . 1.4-1. The l i n e -shape f or Y Q (energy of 22.4 MeV)around the photo-peak (region 1 i n F i g . 1.4-1) can be determined quite p r e c i s e l y from the spectrum. By f i t t i n g t h i s photo-peak shape and a background (a second order polynomial s e r i e s of channel number) to region 2, the best f i t t e d background can be added to the photo-peak shape to make a better standard line-shape f o r y • Region 2 and region 3 are then f i t t e d by t h i s standard line-shape together with a background. The dashed-l i n e i n the f i g u r e shows the best f i t to a l l the regions. The background provides the lower energy t a i l of the standard line-shape fo r y . The t a i l of the standard line-shape i s then extrapolated to zero at zero energy. D i f f e r e n t t a i l extrapolations produce a v a r i a t i o n of about 10% i n the t o t a l number of counts i n the accepted 26 spectrum (Hasinoff"1970 and Suf f e r t 1973). The f u l l l i n e curve i n F i g . 1.4-1 shows the standard line-shape obtained f o r the 22.40 MeV gamma-ray. §1.5 Gamma y i e l d curve c o r r e c t i o n The e f f i c i e n c y of the spectrometer i s defined by the number of counts i n both the accepted and rejected line-shapes. In f a c t t h i s i s the absolute c r y s t a l detection e f f i c i e n c y and an o v e r a l l c o r r e c t i o n factor should also take i n t o account the absorption of gamma-rays by materials i n fr o n t of the Nal c r y s t a l . 11 12 12 The B(p,Y o) C and C(p,p'y^^ ^ ) reactions have been used to study the energy dependence of the e f f i c i e n c y . Both the ac.cepted.vspectrum. .and, .also . to.tal .spectrum .(obtained .from- .the sum of accepted and rejected spectrum) were f i t t e d with the programme mentioned e a r l i e r . The detector e f f i c i e n c y , TI , i s then determined from the accepted-total r a t i o . The e f f i c i e n c y determined experimentally f o r a c o l l i m a t o r with a half-angle of 5°, with the f r o n t face of the spectrometer 10 inches from the target, i s shown i n F i g . 1.5-1. Figure 1.5-1 also show the o v e r a l l c o r r e c t i o n f a c t o r , £ , for the gamma-ray y i e l d as a function of gamma-ray energy when one takes i n t o account the absorption of the gamma-ray by the materials i n f r o n t of the c r y s t a l , i . e . 4.5 inches of p l a s t i c , 1/8 inch of aluminium, \ inch of wax-LiCO^ mixture and the Nal can. The o v e r a l l c o r r e c t i o n f a c t o r i s a product of the attenuation through the materials between target and c r y s t a l and the detector e f f i c i e n c y curve f o r the NaT spectrometer. The c o r r e c t i o n f a c t o r v a r i e s by 2% between 15.11 MeV 27 OVERALL CORRECTION o o LO ~ i i i i ~ r i — r i i i r LO O LO CO CD LO A0N3I0IJJ3 a0103.13a 28 and 22.4 MeV and i s w e l l represented by a l i n e a r function of gamma-ray i n t h i s energy range. The absorption c o e f f i c i e n t s were taken from Nuclear Data Tables (Storm et.al.1970). 28 §1.6 Absolute cross section measurements f o r the Si(p,y) r e a c t i o n The absolute cross section for a r a d i a t i v e capture r e a c t i o n can be ca l c u l a t e d from the following equation: do Y _ ze A 1 1 dtt ~ N N eft Q " tN " e ' ft p t o where Y = gamma-ray y i e l d obtained from experimental spectrum; ze = e f f e c t i v e charge of incident p a r t i c l e (Coulombs); Q = integrated charge (Coulombs); •• -.• •• •••A"-'!s ..-•ati©miG-.^ weigkt.1.©:fr-£he.t!t'a-rgefc-7nmc-leu-s:; 2 t = target thickness (g/cm ); 23 N = Avogadro's number = 6.023 X 10 atoms/mole; o e = c o r r e c t i o n f a c t o r f o r the gamma-ray y i e l d ( F i g . 1.5-1); ft = detector s o l i d angle (steradians). 28 A self-supporting S i target, having an i s o t o p i c p u r i t y >99%, was used i n the r a d i a t i v e capture studies. The target was mounted across a 1/2 inch hole i n a A l target holder. The target chamber, p a r t l y l i n e d with lead to minimize background from scattered p a r t i c l e s , was c y l i n d r i c a l ' i n shape having.a 4 inch diameter and up to 4 targets could be placed i n a target ladder at one time. Between the analyzing magnet and the target, the proton beam 29 was focused through a 1/8 inch aperture and then a 3/16 inch aperture which were about 1% f t apart. However during the course of data accumulation only the 1/8 inch aperture, which i s about 5 f t upstream from the target, was struck by any beam. This was to reduce back-ground r a d i a t i o n and neutron production. The beam on the aperture was always-negligible i n comparison with the beam passing through the target. A f t e r s t r i k i n g the target, the beam was transported •15 meter to a Faraday, cup, which was surrounded by p a r a f f i n , concrete s h i e l d i n g and boxes of borax powder. The charge i n t e g r a t i o n was accomplished by a Dymec i n t e g r a t o r . An upper l i m i t of 5% could be placed on the current i n t e g r a t i o n e r r o r s . The front face of the spectrometer was normally 10 inches from the target. The s o l i d angle was defined by a lead c o l l i m a t o r ,. . -2 as 2;4 x 10 s r . The uncertainty 'in the s o l i d angle i s estimated to be about 10%. The target thickness was determined by weighing a target of known area and an estimated error of 15% was obtained. The error f o r the absolute cross s e c t i o n depends on the s t a t i s t i c s of the experimental spectrum and also the p o s i t i o n s of the photo-peaks i n the spectrum. F i t t i n g errors u s u a l l y range from 3% to 10% f o r Y a n d from 5% to 15% f o r Yi and Y r - A f t e r a l l possible, o 1 15 errors are taken i n t o account the uncertainty i n the absolute cross s e c t i o n are believed to be better than 20% for the (p,Y Q) measurement at 16 MeV proton energy and better than 25% f o r the (p,Y-^) an<3 (p,Y5) measurements at 18 MeV and 21 MeV r e s p e c t i v e l y . The angular distribution.measurements covered the range of angles from 43 degrees to .125 degrees which-was-made-.possible by moving 30 the detector to 16.5 inches from the target; to economize on beam time, a larger collimator was used to obtain the same solid angle -2 of 2.A xlO sr. Since we. were interested i n the relative yield only for the angular distribution, no absolute cross section was evaluated for these measurements. 31 CHAPTER 2 EXPERIMENTAL RESULTS §2.1 Analysis of experimental spectra Most of .the -experimental gamma spectra on the Si(-p,y) P react i o n were taken with a self-supporting i s o t o p i c a l l y pure (less 2 p 2 than 1% impurities) S i target of thickness 800 Ug/cm . The target material was purchased from the Oak Ridge National Laboratory (U.S.A.) and the targets were made by Micromatter Inc., S e a t t l e . The main experimental d i f f i c u l t y was one of r e s o l v i n g Y^ from Y and of the re s o l v i n g Y from Y . To help resolve these 2 4 5 1 . t r a n s i t i o n s , separated by approximately 400 keV, gamma-ray spectra were taken with the Nal c r y s t a l t i g h t l y collimated. A c o l l i m a t o r with h a l f - a n g l e =5° , 'whrch 'cbli'imateci 'to =:'T2 :5 cm diameter at the back of the 25.4 cm;"x25.4 cm Nal c r y s t a l , was used f o r the 90° y i e l d curves. In a d d i t i o n , the counting rate f o r a l l experimental runs was held w e l l below 30 thousands per second to ensure a r e s o l u t i o n of 3% f o r 20 MeV gamma-rays and 3.3% f o r 15.11 MeV gamma-rays. The other d i f f i c u l t y was.the p i l e - u p of i n e l a s t i c gamma-rays from the target nucleus. Figure 2.1-1 dis p l a y s a spectrum obtained 2 D at a proton beam energy of 20.60 MeV on the S i target. The high l e v e l d i s c r i m i n a t o r was set at approximately 4.0 MeV so that gamma-rays due to i n e l a s t i c e x c i t a t i o n of the target n u c l e i could be seen. 12 A spectrum obtained from a C target i s also shown i n the same fi g u r e with the 15.11 MeV peak height normalized to the corresponding peak i n the ^ ®Si spectrum. From the known thickness of the target i t COUNTS PER CHANNEL P) 3 CTl M s n>' < P-ro cn pj H ro Hi H o g n o 3 rt P-f» rt P.-O 3 P-ro i i-3 H 3 J 3 ro ro I_I cn PJ cn M rt OJ p-o P> co ro o rt H PJ Hi Hi O 3 O r O O 4^ -O O o > m <» i — o 03 o JTI o 70 00 p.-P> 3 o f t pj ffi ft cn O o CO o C O o K5 O CD o i ro o. a -4^  ro O + T3 v. CO ro cn 00 T3 C D II ro o o 0) o CD < cn co IE O m m M O -< £ 5 CO C D ro o ro ro ZZ 33 i s p o s s i b l e to estimate that the amount of carbon b u i l t upon the 28 2 Si target i s less- than 20 ug/cm . Gamma rays of i n t e n s i t i e s a few-thousand times stronger than the capture photo-peaks ( i . e . and y ) 2 8 are observed between 4 MeV and 10 MeV i n the S i spectrum. Some of 28 these come from the gamma decay of excited states i n s i , following i n e l a s t i c s c a t t e r i n g . Since there are fewer low-lying l e v e l s and the (p,n) reaction threshold i s higher, the gamma spectrum from the ' C 28 target i s cleaner than that from the S i target. The 6.13 MeV and 6.92 MeV gamma rays (indicated by arrows i n F i g . 2.1-1) from oxygen-16 are also seen i n both spectra. The higher energy t a i l l y i n g below the capture 28 peaks f o r the S i target, are believed to be mainly due to the p i l e -up of two (or more) lower energy gamma rays. 28 29 The low Q-values of the Si(p,y) P re a c t i o n means that almost any material (such A l and Pb) near the target w i l l produce y rays of higher energy. For a proton beam energy below 14 MeV there are i n d i c a t i o n s of the existence of gamma events from the proton capture 27 27 on A l . However the capture cross section on A l i s bel i e v e d to be n e g l i g i b l e when the proton beam energy i s higher than 14.MeV, because 28 one i s above the giant dipole resonance i n S i . Usually the spectra were taken with the high..- l e v e l d i s c r i m i n a t o r (HLD) set at an energy j u s t below the lowest l i n e (e.g. y^ or y^) of i n t e r e s t , and so most of the p i l e - u p events were not analyzed. Even so the p i l e - u p t a i l i s not n e g l i g i b l e i n comparison to the capture photo-peaks when the in c i d e n t proton beam energy i s lower than 17 MeV. Figure 2.1-2 shows a spectrum of capture gamma rays f o r a proton beam energy of 11.85 MeV. The energies of y a n d y^ are 35 14.19 MeV and 12.81 MeV re s p e c t i v e l y and the background underlying i s quite s i g n i f i c a n t / A t the-'lower energy end of the spectrum the HLD cu t - o f f i s also i n d i c a t e d . For proton beam energies below 12 MeV, the y i e l d i s usually weak and the HLD had to be set at an energy j u s t below to reduce acceptance of p i l e - u p events. This means that the Y^ y i e l d may be subject to. suppression from the HLD, and so the Y^ y i e l d f o r proton beam energies l e s s than 12 MeV was not extracted. Figure 2.1-3 shows a spectrum obtained at a proton beam energy of 16.30 MeV. The background under the r a d i a t i v e capture photo-peaks i s now less s i g n i f i c a n t . The spectrum also shows that the e x t r a c t i o n of the Y r y i e l d at t h i s and s i m i l a r energies becomes, almost impossible 5 • • ' 12 because of the superposition of the 15.11 MeV gamma ray from C. Figure 2.1-4 shows a spectrum obtained at proton beam energy of 20.80 MeV. One can see that the background underlying the r a d i a t i v e capture peaks i s completely n e g l i g i b l e . Gamma rays leading to the ground state 29 and to the f i r s t 8 excited states of P are i n d i c a t e d . At many energies i t i s e s s e n t i a l to describe the background under the'peaks c o r r e c t l y i n order to extract the cross s e c t i o n f o r capture with confidence. Thus a background function was included i n the computer f i t of the experimental spectrum, and i t took the form:-2 a + b l + c l f o r a given channel number I where a,b,c are free parameters which are determined by the least-chi-square f i t t i n g programme. As some of the separations i n the f i n a l states are le s s than the i n t r i n s i c r e s o l u t i o n of the Nal spectrometer the separations between the photo-peaks were f i x e d at energies corresponding to the separations of 29 the f i n a l states i n * P throughout the f i t t i n g procedure. This step 36 .120 140 160 160 200 220 240 CHANNEL NO. 28 29 Figure 2.1-3 Si(p,y) P gamma spectrum at E = 16.30 MeV. The 12 P 15;11 MeV l i n e i s from C b u i l t upon the target. 37 160 120 8 Yr 7 r6 r5 i l 28 si(p,r) 0 R=90° E =20.80 MGV 8 0 ID o ( J 4 0 r3 160 180 CHANNEL NO. \ 200 \ Figure 2.1-4 S i ( p , Y ) P gamma spectrum at E = 20.80 MeV. 1? 38 of f i x e d separations and c a r e f u l energy c a l i b r a t i o n i s e s s e n t i a l to e s t a b l i s h which t r a n s i t i o n s are dominant and which of minor importance. Figures: ' 2.1-2, 2.1-3 and 2.1-4 also showed the computer f i t s and the background i n the computer f i t has been included i n Figs.2.1-2 and 2.1-3 . The e r r o r matrix f o r the f i n a l f i t was evaluated and the f i t t i n g e r r o r was p r i n t e d as p a r t of the programme output (see Bevington (1969) f o r a d e t a i l e d mathematical treatment). A l l y i e l d s (except the y i e l d s around the sharp resonances of width l e s s than target thickness) are converted to absolute cross sections using the method described i n the l a s t chapter. Since y i s o always w e l l i s o l a t e d from other photo-peaks, the y i e l d has been studied from 7.20 MeV up to 23.75 MeV. However due to the lack of knowledge of the e f f i c i e n c y below a photon energy of 15 MeV, the uncertainty i n the absolute.' cross .,;sec;bion-;.<f or .-proton,, energies-^ -be-low. l-2--»MeV- -is-:believed to be l a r g e r than 20%, and could be as high as 30%. 28 29 The angular d i s t r i b u t i o n f o r the Si(p,y) P r e a c t i o n has also been measured f o r several proton beam energies. Most of the angular d i s t r i b u t i o n measurements contain 4 points between 43° and o 120 ; some measurements have been repeated with 6 or more data p o i n t s . The data are f i t t e d with a s e r i e s of Legendre polynomials of the form; da r N -——- — A { 1.0 + £ a. P. (cos9) } du o x i Normally we used N=2 but i n some cases N=3. However a l l angular d i s t r i b u t i o n s shown i n t h i s work are normalized angular d i s t r i b u t i o n s , W(8), defined as follows: W(9) = — ^ 2 _ -L_ ' N • dQ. A = 1.0 +• T a.P (cos9) i 10.04 a o 4 6.04 JD 4.0-3 b a -ID 2.0-0.0-10 .1 12 EXCITATION ENERGY IN 2 9 P (MeV ) 14 16 18 20 22 24 26 4?' 9.0 111 | 1 1 I 2 8 s i (p,y 0 ) 2 3 p e v=9o° f 1 ,w, 4 fcM A fit f T » , 7.0 11.0 13.0 15.0 . 17.0 19.0 P R O T O N E N E R 6 Y (MeV) 21.0 23.0 o 28 ' 29 Figure 2.2-1 90 y i e l d of the Si(p,y ) P reaction for incident proton energies from 7.2 to 23.75 MeV.. 25 40 28 29 + § 2.2 Y i e l d of the S i (p,^ ) P(g.s.,l/2 ) r e a c t i o n The 90° y i e l d of the ground state gamma-ray (y ) i s i l l u s t r a t e d i n Figure 2.2-1 f o r proton beam energies from 7.20 MeV to 23.75 MeV 29 (which corresponds to an e x c i t a t i o n i n P of 9.8 MeV to 23.75 MeV). No previous data e x i s t s to compare with these r e s u l t s . The t r a n s i t i o n c l e a r l y e x h i b i t s a pronounced giant resonance, centred at 18 MeV e x c i t a t i o n energy; i n addition there are many sharp resonances i n the low energy region. Since the nature of the sharp resonances i s probably d i f f e r e n t from that of the giant dipole resonance we s h a l l f i r s t present d e t a i l e d r e s u l t s below the giant dipole resonance (GDR) region. 28 29 § 2.2.1 Resonances i n the Si(p,y^ ) P r e a c t i o n below GDR region Figure 2.2.1-1 shows the e x c i t a t i o n function f o r t h i s r e a c t i o n 2 ...using the .8.0.0 ..ug/c.ni . ..target .for.:,pr,oton,.beam-energies- from .7..-20..-Me.V.*to 11.50 MeV. Table 2.1 l i s t s the energies and observed widths of the 29 proton capture resonances i n P from t h i s work. Some of the resonances show r e l a t i v e l y large widths (-150 keV ) while resonances at 8.02, 8.67, 9.275, 9.55 and 11.205 MeV r e l a t i v e l y narrow widths (less than or equal to the target thickness). In order to determine the true nature of the resonances, d e t a i l e d y i e l d curves were measured over some of the resonances, i n d i c a t e d by arrows i n Fig.2.2.1-1, with a thinner 2 target of 400 ug/cm . Angular d i s t r i b u t i o n s were measured at resonant energies to i n v e s t i g a t e p o s s i b l e spin assignments. Resonances of r e l a t i v e l y weak y i e l d were not inv e s t i g a t e d i n fur t h e r d e t a i l . I t i s most i n s t r u c t i v e to show here the expected angular d i s t r i b u t i o n s from d i f f e r e n t types of gamma t r a n s i t i o n . I t seems 9.5. 10.0 10.5 11.0 JL. EXCITATION 11.5 12.0 J J . IN 12.5 29t 13.0 140 145 15.0 15.5 PROTON ENERGY (MeV) Figure 2.2.1-1 o 28 29 90 y i e l d of the Si(p,Y 0> P rea c t i o n f o r incident proton energy range from 7.20 to 13.0 MeV. Target thickness was *800ug/cm2. States l a b e l l e d A are proposed to be analocrue states;. •42 T A B L E 2 . 1 Summary of resonances below GDR region. E (MeV) P E (MeV) X Width (keV) r F-( 2 J + 1 ) ( e V J Possible spin assignment Remark 7 . 2 5 • 9 . 7 4 5 - 1 5 0 could be unresolved resonances 7 . 4 5 9.948' 1 5 0 4 7 . 3 / 2 ~ 8 . 0 2 1 0 . 4 8 8 < 1 7 1.4 3/2 — i. 8 . 1 5 5 1 0 . 6 1 1 <17 1.1 8 . 6 7 1 1 . 1 1 6 <17 1.2 3/2 8 . 8 0 1 1 . 2 4 2 1 4 0 4 6 3 / 2 ~ 9 . 2 7 5 1 1 . 7 0 0 <17 1.3 3/2 9 . 5 6 1 1 . 9 7 5 < 1 5 2 . 7 3/2 9. 7 5 5 1 2 . 1 6 4 = 8 0 9 . 9 5 1 2 . 3 5 2 ' 1 5 0 1 0 . 6 0 1 2 . 9 7 9 1 5 0 presumably unresolved 1 1 . 1 7 1 3 . 5 3 0 1 0 0 . 1 1 . 2 0 5 1 3 . 5 6 4 <15 2 . 7 3/2 , 1 1 . 7 0 1 4 . 0 4 2 1 5 0 r r p Y Uncertainty i n ( 2 J + 1 ) 7-, i s about 3 0 % . 43 reasonable to designate the narrow resonances as T=3/2 analogues of 29 29 29 states i n A l and S. The ground state of P has a s p i n - p a r i t y of + 29 1/2 and the low-lying states i n A l are known to be p o s i t i v e i n * p a r i t y . For Ml t r a n s i t i o n s from £ =0 or I = 2 resonances the angular p p d i s t r i b u t i o n s are as follows (Carr et.al.1972):-I = 0, l / 2 + -5- l / 2 + , W(9) = 1.0; P H = 2, 3 / 2 + - » - l / 2 + , W(G) = 1.0 - 0.5 P (cosG) ; P ^ Angular d i s t r i b u t i o n s expected f o r E2 t r a n s i t i o n s from Z =2 resonances P are as follows :-3/2 + >- l / 2 + , W(.G) = 1.0 + 0.5 P 2(cosG); 5/2 + — l / 2 + , W(0) = 1.0 +0.507 P (cos0) - 0.507 P (,cos8) . On the other hand, for e l e c t r i c dipole (£ =1)' resonances the angular d i s t r i b u t i o n s ' are as follows:- " -. l / 2 ~ ->. l / 2 + , . V7.Ce.) .= .1-0 .; 3/2~ > l / 2 + , W(G) = 1.0 -0.5 P 2(cosG). A summary of angular d i s t r i b u t i o n measurements i s shown i n Table 2.2. Although no d e t a i l e d measurements were made above.and below the resonances to c o r r e c t f o r po s s i b l e i n t e r f e r e n c e from background or nearby resonances, the e f f e c t of interference at the resonant energy i s not expected to change the sign of the a^ c o e f f i c i e n t . A l l the a^ c o e f f i c i e n t s strongly i n d i c a t e dipole (El or Ml) t r a n s i t i o n s and favored the spin assignment of J=3/2. However other information, such as the r a d i a t i v e widths of the resonances, are needed to extract p a r i t y assignment for these resonances. In the following sections we s h a l l discuss these resonances i n d i v i d u a l l y . * Z i s the p a r t i a l wave of the i n c i d e n t proton. 44 TABLE 2.2 Summary of angular d i s t r i b u t i o n measurements at resonances. E (MeV) P '. E (MeV) X a i V p o s s i b l e spin assignment 7.45 9.948 0. 13 ± 0.03 -0.84 ± 0 . 0 6 3/2 8.02 •10.488 0. 27 ± 0.06 -0.60 ± 0.10 3/2 8.67 11.116 0. 19 ± 0.06 -0.66 ± 0.11 3/2 8.80 11.242 0. 19 ± 0.04 -0.81 ± 0.04 3/2 9.275 11.700 0. 06 ± 0.06 -0.60 ± 0.10 3/2 - 9.56 11.975 0. 01 ± 0.08 -0.54 ± 0..10 3/2 11.205 13.564 0. 30 ± 0.10 -0.50 ± 0.12 3/2 Resonance .at E =7.45 MeV P 28 29 The si(PfY ) P e x c i t a t i o n function over the 7.45 MeV 2 resonance measured with the 400 yg/cm.- target i s shown i n Fig.2.2.1-^2 The uniformity of the target has been estimated to be within 15% by focussing the proton beam on d i f f e r e n t sections of the target. The. absolute d i f f e r e n t i a l cross section f o r the r e a c t i o n at a proton beam energy of 7.45 MeV i s 6.511.3 ub/sr. Angular d i s t r i b u t i o n measurements at 3 d i f f e r e n t energies are shown i n Figure 2.2.1-3 . The computer f i t s obtained with, a Legendre polynomial expansion using terms up to, order 2 are also shown i n the f i g u r e and c l e a r l y the angular d i s t r i b u t i o n s do not seem to change. The a^ c o e f f i c i e n t at resonance strongly favors an assignment of J = 3/2 . The t o t a l cross section at the resonance i s obtained as 4 T T - ~ - ^ — — / (1.0 - 0.5a,) = (58115) ub. The t o t a l cross • du'. 2 section may be expressed as i A (2J+1) . r p r Y cr(P,Y0) = 4u* { 2 i + 1 ) ( 2 I + 1 ) -2 F r = — ( 2 > 1 ) where J = t o t a l angular momentum of the resonance; i = proton spin, 1/2; I = t o t a l angular momentum of the target nucleus; 9c = reduced wavelength of the i n c i d e n t proton; e l a s t i c proton width; r_^= gamma width; T = t o t a l width of the resonance; w = (2J+l)/(2i+l) (21+1) Since the t o t a l -width from the y i e l d curve i s 150 keV the value of 46 T I " ~~i 1 \ r Q — i LU < SI SI •< CD Ix! > T — — -f f j | - X J . - L X . | ^ _ i , , I, I j I, ( I t„| , X X X X | - X X X X ^ U L X 7.4 7,5 7.S PROTON ENERGY (MeV) Figure 2.2.1-2 90° y i e l d of the 2 8 S i ( p , Y q ) 2 9 P r e a c t i o n over the E =7.45 MeV resonance. Target thickness -16 keV. 47 10 48 r r P ^ - i s evaluated and l i s t e d i n Table 2.1 . As T /T S 1, the i p gamma width, , f o r t h i s resonance i s expected to be larger than the extreme s i n g l e - p a r t i c l e Ml t r a n s i t i o n (Blatt et a l . 1963) . Thus the t r a n s i t i o n must be E l and so we are able to assign negative p a r i t y to t h i s resonance ( i . e . =3/2 ). Resonance at E =7.25 MeV P Resonances at E = 7.248 , 7.266, 7.279, 7.322 and 7.381 MeV p 28 have been observed i n proton s c a t t e r i n g , p a r t i c u l a r l y i n the Si(p,p^) 28 + S i (1.77 MeV,2 ), measurement. The widths of these resonances range from 6.5 keV t o 20 keV. Except for the E =7.248- MeV resonance (which was P proposed as a candidate for a.T=3/2 state),, these resonances•strongly favored the assignment of- £. =2 (Teitelman et a l . 1969).-"It i s most P i n t e r e s t i n g that we observed a strong gamma y i e l d at E^ - 7.25 MeV i n our (p,YQ} measurements (Fig. 2.2-1 or Fig.2.2.1-1) . The T=3/2 state i s presumably a & =0 resonance (Bearse et a l . 1968a) and the (PfY Q) angular d i s t r i b u t i o n measurement i s expected to be a be t t e r way to v e r i f y the s p i n - p a r i t y of l / 2 + f o r the 7.248 MeV resonance. Unfortunely our target i s too t h i c k to resolve the resonances at 7.248, 7.266 and 7.279 MeV, and therefore no d e t a i l e d i n v e s t i g a t i o n has-been made below a proton beam energy of 7.35 MeV. The E =7.322 MeV resonance observed i n the (p,p* ) r e a c t i o n seems P to correspond to a minimum i n the (p,y ) v i e l d curve (Fig. 2.2.1-2). • o ' I t is- not c l e a r whether the small bump at E =7.40 MeV i n the (p,Y ) p o y i e l d curve i s a s t a t i s t i c a l e f f e c t or the presence of the % —2 resonance at E^=7.381 MeV i n the (p,p') measurements. .However the angular d i s t r i b u t i o n measurements at 7.35 MeV (Fig. 2.2.1-3) show 49 + that the 5/2 (^p = 2) strength i s not playing an important r o l e i n the gamma y i e l d . Resonances at E =8.02 and 8.155 MeV : _£ 28 The e x c i t a t i o n function of the Si(p,y ) re a c t i o n i s shown o i n Fig.2.2.1-4 f o r the region 7.90 MeV < E p < 8 - 5 MeV. Two sharp resonances are observed a t E =8.020 MeV and 8.155 MeV. The uncertainty i n the resonance P energies i s believed to be l e s s than 10 keV. The existence of a weaker resonance i s also seen at E =8.40 MeV. This small bump i s also seen P 2 with the t h i c k target (-800 ug/cm ). The observed width of 15 keV f o r the 8.02 MeV resonance i s instrumental, caused by the target thickness (15 keV) and beam r e s o l u t i o n (better than 5 keV a t a proton beam energy of 14 MeV). The ^to.tal-:width- of ..•••this •••resonance ^ -i-s-'thus -smaller '-than - the ' target 'thickness. Angular d i s t r i b u t i o n measurements f o r t h i s resonance are shown i n F i g . 2.2.1-5 together with the Legendre polynomial f i t . A di p o l e type t r a n s i t i o n i s strongly i n d i c a t e d . Off the resonance, a strong asymmetry i s seen i n the angular d i s t r i b u t i o n s a t E =8.07 MeV. ' P The maximum y i e l d from a t h i c k target around the resonant energy can be expressed as (Snover 1969 and Fowler et a l . 1948) M + M 2TT 2 A 2 r . r v _ 1 2 l f max u (-2-2) M 2 e r where 2J+1 (2i+i)(21+1) R E L A T I V E Y l ELD to -t^  cn Oo t r ] O O O O OS 51 O.D 60.0 120.0 1B0.0 Figure 2.2.1-5 Normalized angular d i s t r i b u t i o n s of the (P»Y ) r e a c t i o n at E =8.02 MeV and 8.07 MeV. The f i t s P are subjected to the r e s t r i c t i o n s - o f W(9)?0.0 and N up to 2. 52 * 2 = 0.209 M, + M„ 1 2 M2 M,E 1 L = p r o j e c t i l e i n a.m.u.; = target mass i n a.m.u.; E = laboratory energy of p r o j e c t i l e (MeV); - M2 ,Ecm M + M E L '" M2 M l + M2 T = t o t a l width i n laboratory system; e = stopping power. This expression neglects e f f e c t s due to f i n i t e beam r e s o l u t i o n and energy st r a g g l i n g i n the target. The maximum.gamma y i e l d c a l c u l a t e d from the .. 90° maximum y i e l d using the angular d i s t r i b u t i o n s ( i . e . a^ c o e f f i c i e n t ) f o r the 8.02 MeV resonance i s Y = 4.45 X 10 gamma per i n c i d e n t proton, max. p Using equation (2.2), to—P ^ i s evaluated and l i s t e d i n Table 2.1 Under the assumption that the resonance width i s n e g l i g i b l e i n comparison r r P Y wxth the thxckness of the target the estimated uncertainty i n w—|r— 1— = 1.4 eV i s better than 0.4 eV. No furth e r i n v e s t i g a t i o n on the other two resonances has been done. Assuming the E^=8.155 MeV resonance to have the same angular r r d i s t r i b u t i o n s as the E =8.02 MeV resonance M P Y for t h i s resonance p r i s c a l c u l a t e d and l i s t e d i n Table 2.1 . Resonances at E =8.67, 8.80 and 9.275 MeV The 90° y i e l d of the ground state gamma ray over the region 8.4.MeVSE <9.4 MeV is. shown i n Fig.2.2.1-6. The ta r g e t thickness i s loooi 800H Q _J LU > LU > f-< _J LU or. SO OH 4004 200 a s 1 ' — ~ T 8.8 4.9 1 < 1 1—1 s j J j r 8.6 8.7 9.0 9.1 PROTON ENERGY (MeV) 9.2 1 r 9.3 Figure 2.2.1-6 Detailed 90° y i e l d of the ' ( p ^ ) reaction at proton energies between 8.40 MeV and 9.40 MeV. Target thickness -15 keV. to 54 55 j : 2 ! 1 — 1 2 approximately 15 keV (=400 ug/cm ) f o r t h i s proton energy range. The d i f f e r e n t i a l cross section a t E^ =8.80 MeV i s 8.011.6 ub/sr (a po s s i b l e error from the target uniformity i s not included). A determination of the exact width f o r .the E = 8.67 MeV resonance P i s not po s s i b l e . A more d e t a i l e d y i e l d using a thinner target i s necessary. However the observed width seems to show that the width of the resonance i s l e s s than the target thickness. Angular d i s t r i b u t i o n measurements (Figure 2.2.1-7) also strongly i n d i c a t e ,a dipole,.... type t r a n s i t i o n . Assuming the width i s much l e s s than the target thickness we are able ' r r P Y to c a l c u l a t e w — ~ — ' — from Eq. (2.2) and the maximum y i e l d of Y = 3.79 X 10 ^  gamma per in c i d e n t proton, max. . Angular d i s t r i b u i i o n measurements f o r the E =8.80 MeV P resonance are shown i n Figure 2.2.1-8. The f i t shown i n the f i g u r e i s W(.6) = 1.0 + 0.19 P 1 - 0.81 V . The t o t a l cross s e c t i o n obtained f o r the r e a c t i o n i s 72 ±15ub. Using a t o t a l width of 140 keV, the r r P Y value f o r G O — - — 1 — i s 27±5 keV from Eq.(2.1). Possible angular momentum and p a r i t y assignment f o r the resonance i s 3/2 as discussed i n the case of the E =7.45 MeV resonance. P The y i e l d curve around the E =9.275 MeV resonance shows P that the width i s l e s s than the experimental energy-resolution . .C-14k.ey)L. The angular d i s t r i b u t i o n measurements (Figure 2.2.1-9). suggests the acceptable spin assignment of 3/2. The gamma y i e l d f o r t h i s resonance is-Y = 4.1 X 10 gamma per inc i d e n t proton max. r r and the value f o r w — j r - . = 1.3 eV. 57 58 'Resonance at E = 9.555 MeV E 28 . , A d e t a i l e d gamma y i e l d of- the S i ( p , y o ) r e a c t i o n i n the v i c i n i of E =9.555 MeV i s shown i n Figure 2.2.1-10 . The observed width of P -t h i s resonance i s approximately equal to the target thickness (=14keV). The angular d i s t r i b u t i o n measurements at 9.56 MeV are well f i t t e d by the function 1.0 + 0.01 'P - 0.54 . The gamma y i e l d f o r t h i s resonance i s Y = 6.43 X 10 gamma per in c i d e n t proton max. r r P Y . . . and the value o-f co—~—•— i s 2.1 ±0.6 eV. A po s s i b l e J assignment i s 3/2. Resonance at E = 11.205 MeV P 'Fig.2.-2.1-ll shows"'the.v'detail'e'a.:-gamma. yield,;'for a .proton beam v 28 energy from 11.05 MeV to 11.40 MeV, f o r the Si(p,y ) r e a c t i o n . A o strong resonance i s observed at 11.205 MeV. The observed width of le s s than 15 keV i s probably an e f f e c t of target thickness (-13 keV) and f i n i t e beam r e s o l u t i o n . This resonance seems to be s i t t i n g on the top of a one hundred keV broad structure centred at 11.17 MeV (Fig. 2.2.1-12). A. Legendre polynomial f i t of the angular d i s t r i b u t i o n measurements i s shown i n Table 2.2. The gamma y i e l d a t 11.205 MeV i s Y = 8.3 X 10 ^ " gamma per in c i d e n t proton, max r r P Y Using Eg. 2.1 the value of — - evaluated i s 2.9 ± 0.8 eV. A possible spin assignment f o r the resonance i s 3/2. 59 1—, j _ — r~ -j s —r-f—— IT "," 1 y——; r •« — 1 — 1 1 e i s U s. 9 . 5 0 9 . 6 0 P R O T O N E N E R G Y ( M e V ) Figure 2.2.1-10 De t a i l e d 90° y i e l d of the (p,Y ) r e a c t i o n i n o the v i c i n i t y of the E = 9.555 MeV resonance. P Target thickness =14 keV. 60 14001 11J05 11.1.0 11.15 11.20 11.25 , 11.30 1155 11.40 P R O T O N E N E R G Y ( M e V ) Figure 2.2.1-11 De t a i l e d 90° y i e l d of the CPfYQ) r e a c t i o n i n the v i c i n i t y of the E = 11.205 MeV resonance. P 61 Other possible resonances Figure 2.2.1-12 shows the gamma y i e l d , f o r the energy range 9.60 to 12.75 MeV, obtained with a 800 ug/cm thick target. -Considerable structure has been observed i n t h i s energy range and the peak energies are l i s t e d i n .Tab.2.1.. Many peaks of width between 30 keV and 150 keV have, been observed i n the e x c i t a t i o n curve f o r the . 28 o 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 i C p ^ ^ ) at 90 f o r proton .beam energies from 10.0 to 12.3 MeV (Cohen and Cookson 1961); t h e i r "resonances" are indicated i n the f i g u r e . Since our target thickness i s approximately 25 keV and the y i e l d curve i s measured, i n some cases', . i n 50 keV steps there i s a p o s s i b i l i t y that we might miss the three narrowest "resonances" observed i n the s c a t t e r i n g experiment. However i t i s obvious that the peaks observed i n the s c a t t e r i n g experiment do not correspond too well to. the s.trueture...,in,,the,;ganuTia ..yield-either -in --energy 'or-^wi'dth. " I t i s i n t e r e s t i n g to note that the peaks observed at E^=10.25 and 10.80 MeV i n the s c a t t e r i n g experiment correspond to dips i n our gamma y i e l d curve. The resonances a t E = 10.6 and 11.7 MeV do seem to correspond; however P i t i s not c e r t a i n whether the structure i s due to a few l e v e l s strongly i n t e r f e r i n g or whether there are many l e v e l s with some r e s i d u a l f l u c t u a -t i o n s causing the st r u c t u r e . In any case the (p,Y Q) r e a c t i o n i s l i k e l y to give a c l e a r e r p i c t u r e because photon s e l e c t i o n r u l e s r e s u l t i n a predominance of spin 1/2 and 3/2 l e v e l s . This i s confirmed by the f a c t that our angular d i s t r i b u t i o n measurements at E = 10.55, 11.70 and 12.40 MeV (Fig. .2.2.1-13) show that dipole type gamma t r a n s i t i o n predominate i n t h i s region. Most of the observed cr o s s - s e c t i o n i n the (p,Y 0) r e a c t i o n a t t h i s energy i s p a r t of the giant d i p o l e resonance which i s centred at E =16 MeV. P 62 600-4001 Q _J LU >-LU > 200 LLI L 10 11 12 P R O T O N E N E R G Y ( M e V ) 13 J 12 13 . " 14 E X C I T A T I O N I N 2 9 P ( M e V ) 15 Figure 2.2.1-12 90 y i e l d of the (p,Y Q) r e a c t i o n f o r i n c i d e n t proton energies between 9.5 and 13.0. HeV. The arrows correspond to resonances seen in. the 28 Si(p,p^) r e a c t i o n . 64 As a conclusion, we give a b r i e f comparison of the d i s t r i b u t i o n 28 29 of E l strength, observed i n the Si(p,Y o) P r e a c t i o n below the GDR region 29 to that observed i n the Si(Y»n) r e a c t i o n . The photoneutron cross section 29 of S i i n the energy range from threshold (>8 '5 MeV) to 13 MeV has been studied by Fukuda ajz$. Okabe (1973) , using a bremsstrahlung beam. They 29 used a S i terget, enriched to 92%; the energy r e s o l u t i o n of t h e i r y i e l d curve was about 600 keV. The photoneutron cross section shows maxima at 10.6 MeV and 12.4 MeV with widths approximately 1 MeV and 600 keV r e s p e c t i v e l y . If we now compare with our r e s u l t s , F i g . 2.2.1-1, we f i n d that i n the E^ - 10.6±0.6 MeV region, with a f a r better energy r e s o l u t i o n , we observed a concentration of E l strength at E^=7.45, 8.80 and presumably 7.25 MeV (. E = 9.94, 11.24 and 9.75 r e s p e c t i v e l y ) . The 29 sharp peaks at E -10.5 MeV i n P would not stand out i n a y i e l d curve •with-poor -energy r e s o l u t i o n . JPhere--,seems -to be -more -than-'one-*peak 28 29 between the e x c i t a t i o n energies of 12 and 13 MeV i n the Si(p,y- ) P e x c i t a t i o n function (Figure 2.2.1-12). However the most prominant peak i n t h i s range i s seen at E^ = 12.30 MeV. Since t h i s type of structure 29 i s observed throughout the giant dipole region of P, we speculate that 29 28 s i m i l a r structure might also be seen i n the •- Si(y,n) S i e x c i t a t i o n function i f a higher resolution-photon'beam were used. Systematic c o r r e l a t i o n between the two e x c i t a t i o n functions i s expected i f t h i s structure has o r i g i n a t e d from some r e l a t i v e l y simple configurations (e.g. 2p-lh configurations).. We note i n passing that there i s some d i f f i c u l t y 13 i n comparing Fukuda's C data with other r e s u l t s on the same rea c t i o n , ' 2 9 and so i t i s quite possible that the S i data i s not completely r e l i a b l e . 28 29 §2.2.2 Cross section of the Si(.p,v ) P re a c t i o n i n .the .giant dipole resonance region The 90° y i e l d of ground state gamma-rays ( Y ) for proton beam energy range from 7.2 to 23.75 MeV was given.in F i g . 2.2-l(p.39). The envelope of the y i e l d curve shows a pronounced ginat resonance; intermediate structure of width =few hundreds :keV i s also robvious throughout the giant resonance region. The nature of t h i s intermediate structure i s l i t t l e known and w i l l be discussed i n a l a t e r s e c t i o n . The y i e l d reaches a maximum of 7.3ub/sr at E = 15.70 MeV (or E = 17.90 MeV). p x The errors shown are f i t t i n g errors obtained from the least-squares spectrum, .unfolding programme. The t o t a l error f o r the cross section at the maximum i s l e s s than 20%. The envelope of the giant d i p o l e resonance has a width of 5 MeV and is- centred at E' =i 16 MeV (.or E = P x 18 MeV). , The width of the giant d i p o l e resonance (GDR) i s an i n t e r e s t i n g 17 19 t o p i c . Studies of odd n u c l e i i n .the 2 s r l d .. s h e l l , such, as F, F, 23 25 27 31 ,Na, Mg, A l .and P, show that a l l these n u c l e i have very broad giant dipole resonances (Table 2.3). In general the giant dipole resonance of a-non-self-conjugate n u c l e i , ( i . e . T=/0) should experience an energy s p l i t t i n g due to the operation of the i s o s p i n s e l e c t i o n r u l e AT=0, 1. This was f i r s t pointed out by Morinaga (.1955) and recently sum r u l e s r e l a t i n g i n t e n s i t i e s and.energy separation of ..the two components have been developed (O'Connell 1969, Leonardi et al.1975, Akyuz et al.1971 and Hayward et a l . 1972). For some cases i n l i g h t n u c l e i , f o r example 13 42 N (Measday et a l . 1965) and Ca(Diener et a l . 1973a), these sum . and energy separation rules, have proven to be quite s u c c e s s f u l , e s t a b l i s h " 66 TABLE 2.3 Width and center of giant dipole resonance i n n u c l e i of mass A between 17 and 42. Nucleus Reaction Width(MeV) Peak (MeV) References 17 160(p,Y) 7 22 Harakeh et a l . (1975) 19 F 19F(Y,n) 7 16 Sherman et al.(1973) 2 0 * T Ne .19F(p,Y) Ne(Y,n) 6 19 Segel e t al.(1967) Woodworth et al.(1975) 23 Na 2 3 , Na (.Y,n) 12 >24 Alvarez et al.(1971) 24 . Mg 24 Mg (.Y,n) 23 Na(p, Y) 10 >20 F u l t z et a l . (1971) Bearse et a l . (1968). 25 Mg-25 • , Mg ( Y,n) 10 24 Alvarez et a l . (1971) 2 6Mg 26 , Mg(Y,n) 14 >19 F u l t z et a l . (1971) 2 7 A 1 27 Al(Y,n) :26 , Mg(p,Y) 13 22 F u l t z et al.(1966) Kurjan et a l . (1974) 2 8 s i 2 8 r - , Sx (.Y,n) 2 7A1 (p,Y) 4. 5 20 Wu et al.(1970) Singh e t al.(1965) ; 2 9 P Sx (p, Y) 5 18 Present work 3 1 P 31P(Y,n) 6 19. 5 G e l l i e et a l . (1973) 32 s 32S(Y,n) 31P(P,Y) 6 18 Wu et a l . (1970) Dearnaley et a l . (.1965) Ar 3^ "Cl(p,Y) 3. 5 19 Kernbach (1970) 3 8 * Ar 37 c i ( p , Y) >7 18 Kernbach (1970) 40„ Ca 40 . , Ca(.Y,n) 39 K(p,Y). 3. 5 19. 5 Wu et a l . (1970) Diener et a l . (1973) Ca 4 1KCp, Y) 5 20. 5 Diener et al.(1973a) 67 ing the concept of i s o s p i n s p l i t t i n g f o r these n u c l e i . A tremendous-amount of data and corraborating evidence Cfor review see Paul 1973) for the existence of two T components i n the giant dipole resonance b u i l t upon the ground state of even-even non-self-conjugate n u c l e i i s now a v a i l a b l e . However most a v a i l a b l e data are on n u c l e i of A£40 and much d e t a i l e d work remains to be done i n l i g h t n u c l e i , e s p e c i a l l y n u c l e i i n the lower 2s-ld s h e l l region. If we apply the concept of i s o s p i n s p l i t t i n g of the GDR to the 29 nucleus P, the (=3/2) and T (=1/2) components are expected to be displaced upward and downward r e s p e c t i v e l y by the symmetry energy term i n .the nuclear i n t e r a c t i o n such that the energy d i f f e r e n c e can be expressed as AE = E - E = — (T+l) > < A . where V has been estimated as a constant, V = 60 MeV, by Akyuz and F a l l i e r o s (1971) and T i s the i s o s p i n of the ground s t a t e . The d i f f e r e n c e , AE = 3.1 MeV, i s the order of the width of GDR b u i l t upon 28 the ground state of S i ( T = 4.5 MeV). The T component i s then expected to: s h i f t downward i n energy by approximately 1/2 of the AE 28 . . with respect to the center of GDR m S i . I t i s also i n t e r e s t i n g to note that other t h e o r e t i c a l p r e d i c t i o n s of V (e.g. Leonardi et al-1975) for medium and heavy n u c l e i are i n good agreement with 60 MeV but the p r e d i c t i o n f or l i g h t n u c l e i i s very d i f f e r e n t . The r a t i o of strengths.in the T+l and T components can be approximately expressed (e.g. Paul 1973) S(,T+1) ^ _1_ = „ S(.T) T i n favor of the T = 3/2 component. Since our experimental r e s u l t s are 28 obtained from a T = 0 target ( Si) and an i n c i d e n t proton of T=h, the. 68 e x c i t a t i o n of the T=3/2 component i n the GDR i s forbidden i n the entrance channel. (The i s o s p i n s e l e c t i o n r u l e suppresses but does not eliminate e x c i t a t i o n of T=3/2 structure as the observation of the T=3/2 analogue states i l l u s t r a t e s ) . The width which we f i n d i n the 28 29 Si(p,Y 0) P r e a c t i o n (5 MeV) i s not the unusually broad width of 19 23 27 25 31 6 MeV, as observed i n F, Na, " A l , Mg and P, and i t can probab-l y be explained i n terms of the i s o s p i n s e l e c t i o n r u l e . The center of 29 the GDR i n P at 18 MeV i s also roughly 2 MeV below the center of 28 . 29 GDR m S i . As P i s not a v a i l a b l e as target, a d e t a i l e d study of 29 the r e a c t i o n Si(y,n) i n the GDR region, to search f o r the stronger T=3/2 component at higher e x c i t a t i o n , would be most i n t e r e s t i n g , since 29 29 low-lying states i n S i and P are very s i m i l a r . I t i s well known that a dipole e x c i t a t i o n of a deformed nucleus r e s u l t s i n a s p l i t t i n g of the GDR i n t o two components, e.g. the K=l/2 and K=3/2 components. The r a t i o of energies of the dipole vibrations-along the two h a l f axes a and b can be ca l c u l a t e d from the simple formula based on the hydrodynamic model (.e.g. Nuclear Models- by Eisenberg arid Greiner, 1970) as = 0.911 (a/b) + 0.089 E a This model also p r e d i c t s the d i s t r i b u t i o n of dipole strengths as- 2:1 i n favor of the upper peak f o r a p r o l a t e nucleus. 29 Since the nucleus P i s believed to have a deformation of 6 = -0.1.5 (Bromley et a l . 1957), the model p r e d i c t s an energy separation of 2.3 MeV between the K=l/2 and K=3/2 components and the r a t i o of the strengths 28 29 as 2:1 i n favor of the component at lower energy. The Si(p,y )" P 69 18.0 17.8 CO cn CN3 2T O < O X L U 12.3-8.5} 0.0 -T = 0 Figure 2.2.2 1 Allowed nucleon decay mode '-.of the giant 29 dipole resonance i n S i . The ^=3/2 component proceeding to.the T=0 states i n 28 S i by neutron decay i s isospin forbidden. 70 cross- section (Fig. 2.2-1) shows marked structure and the p o s s i b i l i t y of several groupings of l e v e l s , . which might be a.consequence.of the influence of nuclear deformation on the cross section . Rigorous c r i t e r i a f o r determining the maxima corresponding to a s p l i t t i n g of the GDR i n l i g h t n u c l e i do not e x i s t . Q u a l i t a t i v e l y i f we assume that the K=l/2 and K=3/2 components each have a width of 4MeV, since the separation has been estimated as 2.3 MeV,we expect a width of 5 MeV f o r the GDR. Furthermore the t r a n s i t i o n s corresponding to K=l/2 and K=3/2 i n the GDR region are l i k e l y to overlap considerably i n l i g h t n u c l e i . The v a l i d i t y of the hydrodynami-c model f o r l i g h t n u c l e i i s very questionable. 29 29 The n u c l e i P and S i are p e c u l i a r as they l i e i n the mass: region where the nuclear deformation s t a r t s to change from a. p r o l a t e shape to an oblate shape and the magnitude of the deformation.is small --in .comparison.--t© -nearby-^iTualei. >-The-*effeet.".of--any i s o s p i n . s p l i t t i n g should therefore be enhanced i n t h i s nucleus i f the concept i s v a l i d f o r t h i s mass region. The most sensible measurement Cs\L to complement t h i s 29 28 29 28 r e s u l t are d e t a i l e d i n v e s t i g a t i o n s of the Si(y,p) ~ A l and. S i ( Y , n ) J S i 28 S i r eactions. The existence of the strong T=3/2 component would be revealed by the dominant decay to T=l states i n the r e s i d u a l n u c l e i 28 28 ( A l or Si) at photon energies above 18 MeV (Fig. 2.2.2-1). In contrast to. the concept of i s o s p i n s p l i t t i n g , the hydrodynamic model pr e d i c t s a weaker K=3/2 component i n t h i s higher e x c i t a t i o n region. In s p i t e of the poor energy r e s o l u t i o n (-1 MeV) i n the 29 28 Si(y,p) measurements obtained by Katz et al.(1954), a 28 29 comparison with our Si(p,Y Q) P measurement i s shown i n Fig.2.2.2-2. 28 29 Since we expect the shape of the Si(p,Y Q) P measurements to be 29 28 • s i m i l a r to that of the Si(y,n) s i r e a c t i o n , our measurements 15-124 o. -Q b "D ^ 3-0 2 9 s i c y , P ) 2 8 A i Si(p^YQ)29P •40 h30 G~(mb) -20 -to 94 1'2 ?4 16 18 20 22 EXCITATION ENERGY (MeV) 2 8 ~ - • ..29_ . • ' ' . . 29 . , ,28 -7— 26 •0 Figure 2.2.2-2 S i ( p / Y Q ) P y i e l d compared with the SiCy,p) A l y i e l d i n the GDR region. 72 in d i c a t e the envelope of the T=l/2 component, centred at E _ = 18 MeV, with a width of 5MeV i s approximately 2.5 MeV below the peak of the 29 28 resonance shape observed i n the Si(y,p) A l channel (Katz et al.1954) This resonance shape i n the (y,p) channel i s presumably the T=3/2 29 component of the giant dipole resonance i n S i , as indi c a t e d i n F i g . 2.2.2-2 . The proton-capture measurements y i e l d the cross; section f o r 28 populating the ground state of S i m the photo-nuclear r e a c t i o n . The dipole sum observed i n the proton capture measurements (see se c t i o n 3.2 f o r d e t a i l e d treatment) sets a lower l i m i t on the t o t a l strength 29 28 i n the T=l/2 component. Thus Si(y,n) S i measurements are necessary to extract the t o t a l strength exhausted i n the T=l/2 component. The 29 30 (y,n) cross sections f o r S i and S i given by Katz e t a l . are unresolv-ed; .^furthermore,.no ..measurement-exists i n - the e x c i t a t i o n 'regioir above 17 MeV. However the d i s t r i b u t i o n of strengths shown i n t h e i r measure^-ments are seen to favor the i s o s p i n s p l i t t i n g concept. 28 29 §2.2.3 The angular d i s t r i b u t i o n measurements of the Si(p,Y I. P re a c t i o n Some angular d i s t r i b u t i o n measurements are presented i n F i g . 2.2.3-1. The e r r o r s on the data points are s t a t i s t i c a l . The c a l c u l a t e d curves were obtained using Legendre polynomial f i t s up to the second order term, a^ F> . Most of the angular d i s t r i b u t i o n s e x h i b i t a s l i g h t l y forward peak ( i . e . a^ £ 0.0) and a negative a^ c o e f f i c i e n t - .The angular d i s t r i b u t i o n c o e f f i c i e n t s are given i n Figure 2.2.3-2 as a function of proton energy. The average value of the a^ c o e f f i c i e n t throughout the GDR region i s -0.76 and the average value f or a^ i n the same region Figure 2.2.3-1 Normalized angular d i s t r i b u t i o n s of the (p,Y ) reaction i n the GDR region. 74 E X C I T A T I O N IN 16 18 20 29, 22 100-75-50-24 ! 26 u _ 28 . , .29 Sx(p,Y Q) P 9 S o o 0 °f! » s ° 0 8 „ »° ° 0 o -0.5H 0 I e • • < » 0 0 v fyfe*/;. ~T—~r—r 1—nr—r-T-—* r ~ r ~— r ~ ™ x -1.0H 13.0 13.0 15.0 17.0 ~T f-19.0 21.0 I ~ T " 23.0 25.0 PROTON E N E R G Y ( MeV ) - 28 29 Figure 2.2.3-2 Legendre polynomial c o e f f i c i e n t s f o r the Si(p,Y o) P angular d i s t r i b u t i o n s f i t t e d up to N=2. i s +0.21 . The c o e f f i c i e n t i s of p a r t i c u l a r importance Because a pure E l t r a n s i t i o n would y i e l d an angular d i s t r i b u t i o n of the simple form (1.0 + a 2 P 2 ^ * I n t h e G D R r e 9 i ° n ' w e expect the E l t r a n s i t i o n to dominate i n terms of i n t e n s i t y . The an a l y s i s of the angular d i s t r i b u t i o n s i n the GDR of other n u c l e i shows that the Ml or E2 e f f e c t s on a^ are always n e g l i g i b l e . Two quite general properties have been observed i n the giant dipole angular d i s t r i b u t i o n s of l i g h t n u c l e i . F i r s t , the a^ c o e f f i c i e n t of the Y 0 giant resonance f o r most n u c l e i remains nearly constant throughout the giant resonance region. The a^ c o e f f i c i e n t f o r l i g h t n u c l e i t y p i c a l l y show l i t t l e or no c o r r e l a t i o n with the structure 27 28 (except the A l (p,T ) S i reactions reported by Singh, et al.(1965}.I 'in'the •gamma y i e l d . ""This i m p l i e s ' t h a t the region of the giant resonance i s dominated by a s i n g l e state or a s i n g l e c o n f i g u r a t i o n whose strength. i s spread out over the underlying s t a t e s . Secondly, the angular d i s t r i b u t i o n s i n the giant resonance region can be in t e r p r e t e d i n terms-of t r a n s i t i o n s from the highest allowable spin state, e s p e c i a l l y i n the v i c i n i t y of the peak of the giant dipole resonance and higher. 28 We consider the S i target as a doubly-closed-s.ubsh.ell nucleus 29 and the ground state of p as a pure ^-s-^/2 s^n9-'-e p a r t i c l e s t a t e . Thus we deal with only 2 p ^ ^ a n d 2p^2 Photon capture i n t o the GDR region. Let E l (1/2 ) and El(3/2 i be the amplitudes of the d i p o l e , t r a n s i t i o n s from state with t o t a l angular momentum J=l/2 and 3/2 r e s p e c t i v e l y proceeding + 29 to the 1/2 ground state of P i n proton capture; then the angular. d i s t r i b u t i o n can be written as (Carr et al.1972).". 76 <* 2 JE1 (l/2~) | 2 + 4.0{ 1.0 - 0.5P2 (cos8) } | E l C3/2~) [ 2 -4.0 |E1 (l/2~) | |E.1(3/2~) | P 2(cos9) cosS _ |El (3/2~) | 2 + 2.0JE1 (.1/2 ~) j |E1(3/2~)[ cos6  Z | E l ( l / 2 ~ ) | 2 + 2.0|E1(3/2~)| 2 where <5 i s the s c a t t e r i n g phase-difference between the J = 1/2 and TT — J = 3/2 p a r t i a l waves. Defining . 2 2.Ox [El (3/2~) ] 2 or | E l ( l / 2 ) | 2 + 2.0|El(3/2")| 2 2 the r e l a t i o n between R and a 2 i s shown i n Figure 2.2.3-3 f o r value of 2 cos 6= 0.5 and 1.0 as i n d i c a t e d . On the abscissa i s p l o t t e d the a 2 2 2 c o e f f i c i e n t and on the ordinate the R . For a given value of cos <5 the curves require that:--0,25- .1 , 1 2,. T - - + T c o s 6 1 1 7 2< a '"S -0.25 + 1 .u 1 2 A + — C O S 0 16 2 Also f o r a l l values of cosS (positive or negative) the curves meet at 2 2 the points (a2=0.0, R =0.0) and (a2=0.5, R =1.0). With the a i d of t h i s diagram a few remarks can be made; (i) the a 2 c o e f f i c i e n t must be l e s s than zero i f cos6 i s p o s i t i v e i n value ( i i ) a predominantly P a r ' t : i a l wave resonance can only give a value of a 2 l e s s than or equal to -0.5 i f cos6>'0; (.iii) a 2= -1.0 only i f cos<5 =1.0. Most measured values of a 2 (figure 2.2.3-2) are l e s s than -0.5 which, means two things. F i r s t that the p c o n t r i b u t i o n i s important and . secondly that cos 5> 0. If we 'assume that.-the .phase s h i f t d i f f e r e n c e , . -<5, does not change change abruptly throughout the g i a n t resonance region then the measured a„ of -1.0 ±0.1 at E = 13.35 MeV . implies--that 2 D K • • 78 0.85 < cos<5 < 1.0 . A s o l u t i o n f o r 6 i n the range of -32° to 32° agrees quite well with the o p t i c a l model's p r e d i c t i o n (Weller et a l . 1975)". In 31 32 the case of the P(P/Y Q) S rea c t i o n i n the GDR region, the only allowed E l matrix elements are the capture of P-jyp a n <3 P3/2 P r o t o n s'- F r o m the r a d i a t i v e capture of p o l a r i z e d protons Calarco et a l . (.1974) showed that the phase d i f f e r e n c e , 6 , between a n d P3/2 P r°tons i n the GDR. region was always l e s s than 20° for the 3 1 P ( p , Y Q ) 3 2 S r e a c t i o n . From the simple independent p a r t i c l e model (Appendix A) the r a t i o of the 2p^^^ bo ^s±/2 t r a n s ;'- t :'- o n a n ^ ^1/2 t C > 2 s l / 2 * - r a n s i t i ° n 2 i s expected to be 2:1 (or R =4/5) i n favor of the higher momentum t r a n s i t i o n . Thus i n the v i c i n i t y of the peak of the giant resonance the p ^ 2 t o sx/2 t r a n s l t ; ' - o n i-s expected to dominate the gamma y i e l d . In the proton beam energy range of 14 MeV to 24 MeV, assuming that cos<5 =1.0, «the almost ..constant.'measured -& • of- -v0.74+0. -2""provides' a • s o l u t i o n of 2 +6% . R = 93% f o r a dominant p c o n t r i b u t i o n . — 2.1-6 . 3 / 2 The value changes smoothly below a proton beam energy of 14 MeV and shows a minimum (a^ = -1.0) at a proton energy of about 13 MeV, which i n d i c a t e s that there i s a. concentration of 1/2 strength i n t h i s region. The c o e f f i c i e n t i n GDR region The a^ term i n the angular d i s t r i b u t i o n i s evidence of an interference between overlapping l e v e l s of opposite p a r i t y . A l l the a^ c o e f f i c i e n t s are s i g n i f i c a n t l y p o s i t i v e i n sign (Figure 2.2.3-3) and its. v a r i a t i o n with energy i s small.and monotonic. The average value for a^ i n the GDR region, i s 0.2 . Evidence from the i n e l a s t i c s c a t t e r i n g of electrons (Nagao 79 14 EXC ITAT ION IN 16 18 20 29, 100-75 JQ 5 OH CL L-b -I L _ 1 1 i. - 1 l_ 22 L _ 24 i 26 fit  0 o .'8 ( 8 ' 0 a 0 o . 0 , 0 >• e • . » * 0 0 o 0 „ 6 •a, 0.5 0.0-0.0 a 2 -0*5"1 -1.0-0.0-CU -0.5-i 1 r r 1 }i f f »» i t r — r n ~ r . f f f i j | 1 j 1 i i i »' . ( i I ! I. I 1 " 1 1 • 1 1 r > - i r-13.0 15.0 17.0 19.0 21.0 —I r 23.0 25. PROTON E N E R G Y ( MeV ) Figure 2.2.3-4 Legendre polynomial c o e f f i c i e n t s f o r the 2 8 S i ( p , y )^ yp o angular d i s t r i b u t i o n s f i t t e d up to N=3. 8 0 e t al.1973), protons ('Lewis et al.1972) , deuterons (Chang et al.1975) and helions (Moss et a l . 1974 and 1975, Arvieux et al.1975) i n d i c a t e the existence of a syst e m a t i c a l l y occuring i s o s c a l a r g i a n t quadrupole resonance (GQR) of a few MeV i n width a t an e x c i t a t i o n energy of about -1/3 63A MeV i n n u c l e i of A >40. In add i t i o n a resonance of = 1 MeV wide a t an e x c i t a t i o n energy 51A 1 / / 3 MeV has been observed i n the l f - 2 p s h e l l n u c l e i (Arvieux et al.1975). Although the i s o s c a l a r GQR does not show up c l e a r l y as a compact resonance shape i n the i n e l a s t i c s c a t t e r i n g reactions from l i g h t n u c l e i of mass A <40, r a d i a t i v e capture of alpha p a r t i c l e s and/or p o l a r i z e d protons shows that the E2 strength i n various-n u c l e i i s d i s t r i b u t e d rather . uniformly over., a broad energy range i n c l u d i n g the GDR region: f o r example 1 6 0 (Snover et al.I973, Snover et 24 26 27 a l . 1974, Hanna et a l . 1974), Mg,, Mg (Kulmann et al.1975), A l 32 40 (Fisher e t al.197'4) , ' S "(Calarcd et"a'l. I97 '4) and •• Ca CBranford 1974).. The'observed p o s i t i v e a^ c o e f f i c i e n t can be i n t e r p r e t e d as the GDR . i n t e r f e r i n g with a giant quadrupole s t a t e . The i n t r o d u c t i o n of a term a-^ Pg to the f i t of the angular d i s t r i b u t i o n measurements tends to reduce the magnitude of the a^ c o e f f i c i e n t while the a^ c o e f f i c i e n t does not change s i g n i f i c a n t l y . The r e s u l t i n g c o e f f i c i e n t s are shown i n Figure 2.2.3-4 . The e r r o r bars for the a^ and a^ c o e f f i c i e n t s are c a l c u l a t e d under the assumption that the a^ c o e f f i c i e n t i s a constant. The average values f o r the a^ c o e f f i c i e n t and the a^ c o e f f i c i e n t are 0.19 and -0.19 respectively.. We t r i e d introducing the a P. term to f i t some of our angular measurements and found that a.-0.0+0.1. 4 4 . 4 The absence of the a^ c o e f f i c i e n t can be regarded as a consequence of the lack of measurements at extreme angles ( 9 < 43° or 9 > 125°) and/or 81 poor s t a t i s t i c s i n the experimental spectrum. Under the assumption that near and above the center of the GDR the E l (3/2 ) term i s dominant, we are able to write the a^ and a^ c o e f f i c i e n t s as follows (Ca'rr and Baglin 1972) { 1.386 E2 (.3/2 ) E l (3/2 + 12.471 E2C5/2 ) E l (.3/2 ) C O S 63/2",3/2 + C O S 63/2",5/2 + } (2.5) and {-8.314 E2(3/2 ) E l (3/2 ) C O S 63/2",3/2 + -5.543 E2(5/2 ) El(3/2 ) C O S 63/2 _,5/2 + (2.6) where E l (3/2 ) and E2 (j"1") represent the amplitudes of dipole and p o s s i b l e quadrupole t r a n s i t i o n s . 6 , represents the d i f f e r e n c e between J and J' J, J wave-phase s h i f t s . -A pure "E2- (-3/2*) - E l (3/2 • •)• i n t e r f e r e n c e -gives ;.a vjja.tio-iof a l / / a 3 ° f - 0 - 1 6 7 ' " i n contrast a pure E2 (5/2 +)-El(3/2 ) interference gives -2.25. I t i s i n t e r e s t i n g to note that the r e l a t i v e sign of the and a^ c o e f f i c i e n t s i n Fig.2.2.3-4. agrees, with the p r e d i c t i o n s . However the r a t i o of a2.^a3 1 S s e e n - b o be -1.0. I t i s d i f f i c u l t to determine. which interence term i s more important i n .the GDR region. To .estimate a lower l i m i t f o r the E2 strength l e t us assume a dominant E2(5/2 +) . and from. Eq. (2.6) we have .. •. "•' . ' 5.543 4.0 E2(5/2 ) E l (3/2 ) C O S 63/2-,5/2 + I t i s seen.that on average a^ = -0.19. Hence E2(5/2 +) | 2 E l t 3 / 2 - ) > 2%. 82 In addition i f we assume that the Ml strength i s negligible in the GDR region and E2(3/2+) i s the dominant interfering term, from the average value of a^ and Eq.(2.5) we can estimate E2(3/2 ) El (1/2 ) > 3% (2.7) In order to assess the possible isoscalar E2 strength observed in this experiment we employed the sum rule (Gell-Mann and Telegdi 1953) a(.E2) S „(E2) = ' - I J dE = 0.25 Z 2 A 1< R2> x = 0.22 Z2 A 1 / 3 ub/MeV 2 3 2/3 29 with <R > = — r A and r = 1.2 f i . For P the E2 sum rule equals b o o 16 ub/MeV . Here a(E2) i s the quadrupole photon absorption cross section. Since the E2 strength has been observed as f a i r l y evenly distributed over the entire GDR region in light nuclei, the observed strength may be written as follows E„ o(E2) dE a(E2)•(E 2 - E 1) E l E2 From Eq.(2.7), i t i s a good.approximation that E„ o(E2) • (E 2 - E l - 100 a (El) dE iv. The integral, a (El) dE = 15 mb-MeV, over the GDR region i s evaluated 2 -1/3 in section 3.2 . If we use E, E„ = E where E = 63A i s the excitation 1 2 x x energy of the GQR expected, the observed E2 strength could account for £ 6% of the isoscalar quadrupole sum rule. It i s comparable to what has been observed in radiative polarized protons capture in the GDR region of 2 ?A1 (.3-5%; Fisher et al.1974) and 3 2S(25%; Calarco et al.1974). G3 § 2.3 The 2 8 S i ( p , Y 1 ) 2 9 P ( l - 3 8 MeV,J7T=3/2+) re a c t i o n i n the GDR region In Figure 2.3-1 i s given the 90° y i e l d f o r capture to the f i r s t 29 + excited state of P (1.38 MeV, 3/2 ) f o r a proton energy range from 12 to 23.75 MeV. The envelope of the y i e l d curve shows a broad peak of width of ~5MeV and reaches a maximum of 12.3 ub/sr at E =18.25 MeV P (or E^ = 20.37 MeV). Since the y photo peak i n the gamma spectra s i t s on the low energy t a i l of the Y Q photo peak and i s only 500 keV away from an expected y^ photo peak, the uncertainty i n t h i s y i e l d curve i s expected to be larger than the uncertainty i n the Y Q y i e l d curve. The errors shown i n the f i g u r e are f i t t i n g e rrors from the spectrum unfolding programme.. . Resultant errors f o r the cross section at the maximum of the y i e l d i s approximately 2.4 ub/sr or 20%. The centre of the cr'CE) dE,* 'and 'envelope"determined 'from the integrated- cross' section, a(E) the energy-weight-integrated cross section, dE, i s E =18.38 E — ' p MeV' (or E = 20.5 MeV). Intermediate structure of few hundred keV x broad can-be seen throughout the whole energy range. The maxima i n the cross s e c t i o n of the (p, Y ) a n d (p,Y-. ) 2 J 0 + 1 reactions tend to follow the r a t i o of —rrr. r where J and are 23 + 1 o 1 29 the spins of the ground state and f i r s t e x cited state of P r e s p e c t i v e l y . The center of the Y^ giant resonance i s 2.5 MeV higher than the center of the Yq giant resonance. This energy d i f f e r e n c e i s approximately equal to the 29 e x c i t a t i o n energy(1.38 MeV) of the f i r s t state i n P (also p.108). This type of energy displacement has been observed i n other n u c l e i . The d i f f e r e n c e between the widths of the Y 0 a n d Y-^  giant resonances i s not s i g n i f i c a n t . Some angular d i s t r i b u t i o n measurements are presented i n Figure 2.3-2 . The e r r o r s are s t a t i s t i c a l . The c a l c u l a t e d curves were obtained 2 9 E X C I T A T I O N I N R U 15 16 1 7 18 19 2 0 21 2 2 ' 2 3 2 4 2 5 —i 1 1 1 1 1 1 1 1 1 1 1 i i i I i i i i i I . I CO PROTON ENERGY IN MEV Figure 2.3-1 90° y i e l d s of the 2 8 S i (p, y±) 2 9 p (1.38 MeV,3/2 +) and 2 8 S i (p,Y 2) 2 9P (.1.95 MeV,5/2 +) reactions i n the GDR region. ' 86 using Legendre polynomials f i t up to the second term (.i.e. W(.9) = 1.0 + a^P^ + a 2 P 2 ^ * T ^ e r e s u l b i n 9 a ^ a n d a2 c o e f f i c i e n t s are shown i n Figure 2.3-3. Some of the angular d i s t r i b u t i o n are f i t with Legendre polynomials up to a^P^ term and the r e s u l t i n g c o e f f i c i e n t s are shown i n Figure 2.3-4 . The in t r o d u c t i o n of a a^P^ term tends to reduce the magnitude of the a^ c o e f f i c i e n t i n some cases. However the a^ c o e f f i c i e n t i s not a f f e c t e d by the presence of an a^ c o e f f i c i e n t . Errors f o r the a^ and a^ c o e f f i c i e n t s are c a l c u l a t e d under the assumption that a2 i s constant. The large uncertainty i n a^ i s a consequence of the lack of measurements at extreme angles ( i . e . 9 < 43° and 9 > 125°) and/or poor s t a t i s t i c s i n the experimental spectra. The o v e r a l l average value of . i s -0.36 with a standard de v i a t i o n of 0.15. However the a2 c o e f f i c i e n t s at proton energies above -17-MeV«"are a l l -either' equal to-lor•'-larger"than-—0•.-•36. For proton energy above 17 MeV, the average a2 c o e f f i c i e n t i s -0.47 with a p o s s i b l e :.. deviation of 0.15 . since the s p i n - p a r i t y assignment of the f i r s t 29 + excited state i n P i s 3/2 , we expect 2p_ . , 2p.. and I f . proton 3/2 1/2 b/2 capture to dominate i n the giant dipole resonance region. The expected angular d i s t r i b u t i o n f o r the E l decay from 1/2 , 3/2 and 5/2 states to the 3/2 + f i r s t excited state are as follows (Carr et al.1972) l / 2 ~ -> 3/2 + : W(6) = 1.0 ; 3/2~ 3/2 +: WC9) = 1.0 + 0.4 P ; 5/2~ + 3/2 +: W(9) = 1.0 - 0.4 P 2 . The value of the a2 c o e f f i c i e n t strongly i n d i c a t e s that the E l (.5/2 ) strength i s dominant. The signs of a l l c o e f f i c i e n t s ; are p o s i t i v e and the a^ c o e f f i c i e n t s tend to be negative . This i n consistent with the interference between the giant, dipole and giant quadrupole resonances. 87 E X C I T A T I O N 14 16 18 N 2 9 P 20 22 24 150-125 n q 100-~ 75-oT 50-j b 25i 0.5-j •0.5H 0.0-a 2 --1.0 26 0 >° 0 0 0 0 ? «, a 0 t , 0 » ' 0 10 11.0 13.0 15.0 17.0 19.0 21.0 1 1 ! 1 ) i 1 1 1 ! — — i i r 23.0 25.0 P R O T O N E N E R G Y ( M e V ) 28 29 Figure 2.3-3 Legendre polynomial c o e f f i c i e n t s f o r the Si(p,y^) P r e a c t i o n angular d i s t r i b u t i o n s f i t t e d up to N=2. 88 150-| 125 q 100-— 75-Q T son b 25-a 1 0.5-0.0-o.o-a2 -0.5-- 1 . 0 -o.o-a3 -0.5--1.0-E X C I T A T I O N 14' 16 18 _ J ! l 1 N P 20 . 22 24 26 o s o» 9 a 9 2 9 0, £ 0 o « . 8-1 ' 0 a ' 0 4 ? 0 a ' A" 0 0„ •?«},., fj i) \\\\},} f } •» } 11.0 ~I 13.0 i c j 1 j f——j——i—-~T——T r~ ~i—>—r I I I I' 15.0 17.0 19.0 21.0 23.0 P R O T O N E N E R G Y ( M e V ) •* • 28 . , , 29 Figure 2.3-4 Legendre polynomial c o e f f i c i e n t s f o r the Sx(p,y i) P angular d i s t r i b u t i o n s . f i t t e d up to N=3. 89 Since we know that i n the GDR region the El(.5/2 ) i s dominant, the a 3 c o e f f i c i e n t can be written as follows (Carr et al.1972) { 6.072 E2 (3/2 El(5/2 ) cos 6 , - , + 5/2 ,3/2 -4.868 E2 (5/2 ). E l (5/2 C O S 65/2-,5/2 + -5.737 E2 C7/; E l (5/2 ) C O S < 55/2-,7/2 + } (2.8) .and i f the Ml strength i s neglected, the a c o e f f i c i e n t can be written as follows a. {-2.277 +1.826 + E2(3/2 ) E l (5/2 ) E2 (5/2 +) E l (5/2 ) C O S 6-5/2~,3/2+ C O G 65/2-,5/2 + +17.211 E2(7/2 ) E l (.5/2 C O S 65/2-,7/2 + (2.9) where E l (.J ) and E2(j') represent the amplitudes of dipole and po s s i b l e quadrupole t r a n s i t i o n s , 6 . - + represents the d i f f e r e n c e between the 5/2 , J 5/2 and J + wave phase s h i f t . The non-vanishing a^ c o e f f i c i e n t shows + . + • that E2. strength i s not n e g l i g i b l e . A pure E2(3/2 ) or E2(5/2 ) interference + w i l l give the r a t i o a ^ a 3 °f _°.375 while a pure E2 (7/2 ) interference w i l l give -3.0. Experimentally a ^ / a ^ i s -1. to -10.0 and the average values of a^ and a^-are +0.36 and -0.11. r e s p e c t i v e l y , thus.we.-tentatively conclude that the interference E2'strength-is predominantly, the E2 (7/2 +) strength. If the Ml strength i s n e g l i g i b l e , then a low r l i m i t of th  r a t i o E2(7/2+) 1 2 E l (5/2 ) and Eq. (.2.9). as follows can be obtained from the average value of a^=0.45 90 a l l ~ E2 (7/2 +l 17.211 — 1 El(5/2 1 6.0 or E2 (7/2 +) El(5/2 2 > 2 =6 . This E2 strength, could account f o r > 5% of the i s o s c a l a r quadrupole sum r u l e as discussed i n the previous s e c t i o n . ' For completeness, the value of the 90° Y2 y i e l d , 29 corresponding to t r a n s i t i o n s leading to the second excited state of P TT + (.1.95 MeV,J =5/2 ), i s shown i n Figure 2.3-1. The large errors are a consequence of poor s t a t i s t i c s and the nearby strong y photo peak i n the experimental spectra. In the i n v e s t i g a t e d region, the average cross section at 90° i s 1.0±0.5 ub/sr. The y i e l d tends to show a broad maximum around a proton beam energy of 18 MeV. Gamma decay to the t h i r d excited 29 IT + 28 29 state i n P (2.42 MeV,J =3/2 ), i . e . the y i e l d of the Si(p,Y3) P r e a c t i o n , also has about the same magnitude i n t h i s region. No f u r t h e r work has been done although the r e s o l u t i o n of our detector i s believed to be s u f f i c i e n t to obtain reasonably w e l l determined e x c i t a t i o n functions f o r these t r a n s i t i o n s , were there s u f f i c i e n t i n t e r e s t . § 2.4 Cross section and angular d i s t r i b u t i o n measurements of the 28 29 Si(p,Y r) P r e a c t i o n i n the GDR region. Figure 2.4-1 shows the 90° y i e l d of gamma-ray.leading to the f i f t h 29 TT - -excited state i n P (3.45 MeV, J =5/2 or 7/2 \ i n the r a d i a t i v e proton 28 capture r e a c t i o n on a S i target. Below a proton beam energy-of 16.5 Mey Yc- i s subjected to contamination of the strong 15.11 MeV l i n e i n 12 C; natural carbon b u i l d s upon the target during the course of the 91 a , (M in a i n . urj oJ_| a a - 1 CO r^-R T3 19 E X C I T A T I O N 20 21 J _ J I L 29 I N y P 22 _J L_ 23 _JL_ 24 I 2 8 s K P , y 5 ) 2 9 p . e y = 9 0 ° (p,y4.) o ° o ° o • « o O O r, O , 25 _ i , i. 1E.0 17.0 16.0 19.0 20.0 21.0 22.0 23.0 24.0 PROTON ENERGY IN MEV Figure 2.4-1 90° y i e l d s of the 2 8 S i ( p , y ) 2 9P(3.11 MeV,5/2+) and 28 29 - -Si ( p , y r ) P(3.45 MeV,5/2 or 7/2 ) reactions i n 5 the GDR region. experiment as well as i n the process of target f a b r i c a t i o n . The envelope of the y i e l d has a width of approximately 5 MeV and reachs a maximum of 14.3 ub/sr at E -20.60 MeV ( i . e . E = 22.63 MeV). The errors shown p x are f i t t i n g e r r o r s obtained fron the spectrum unfolding programme. Also shown i s the y i e l d curve f o r gamma decay to the fourth excited state i n 29 + P (3.11 MeV,5/2 ) . The r e l a t i v e l y large e r r o r s are due to the close proximity of the y and y l i n e s which are only 340 keV apart i n the 4 5 . gamma-ray spectrum. The r e s u l t a n t error f o r the yr cross section a t maximum i s estimated to be approximately 3.6 ub/sr or 25%. The (p,y^) cross section i s small and the errors are large. The average cross section i n the investigated region i s approximately 1.3 ±0.5 ub/sr. The y^ i s not properly.resolved by the detector from the y_ peak, b The center of the GDR i n the (p,.Y,-) r e a c t i o n determined from the r a t i o of the integrated-cross-section and the energy-weight-cross-section i s E = 23.2 MeV ( or E = 21.2 MeV). The existence of intermediate x p structure i s l e s s obvious than that f o r the other y i e l d curves but i t i s c l e a r l y present. 29 The exact spin of the f i f t h e x c i t e d state i n P i s not known TT — -(J =5/2 or 7/2 , Endt et.al.1973 and references t h e r e i n ) . However i f the empirical r e l a t i o n of 2J+1 i s used, the r e l a t i v e maximum i n y^ and Y^ give 2J+1 = 4.6 while the maxima i n Y Q a n d Y^ give 2J+1 = 3.9. Both values prefer an assignment of J=5/2 to 3=1/2. The center of the Y- GDR i s 5.3 MeV above the center of the y GDR which can be compared 5 o 29 to energy of the f i f t h excited state i n P which i s 3.45 MeV. Angular d i s t r i b u t i o n measurements have been made.at 6 d i f f e r e n t proton beam energies. Resulting a^ and a^ c o e f f i c i e n t s are shown i n 93 EXCITATION IN 2 9 P ( M e V ) 200-150-20 i 22 _ J L _ 24 J _L 26 6 <P <ja 0 Q. b 50--0; E 8 a 0 - 0 D o 8 o g 0 6 C D 6 D 0 8 0 B 0 6 0 B 0% 0 % »<• ^  6 * i r — - r 1 0,5" 0.0' i ~l r 1 ~r~ 1 r 16.0 1B.0 20.0 22.0 PROTON ENERGY ( M e V ) 24.0 28 29 Figure 2.4-2 Legendre polynomial c o e f f i c i e n t s f o r the S i ( p , Y . . ) P 5 angular d i s t r i b u t i o n s f i t t e d up to N=2 . 94 Figure 2.4-2. The main purpose of these measurements i s to e x t r a c t the a c o e f f i c i e n t f o r the evaluation of the t o t a l cross section. The average value for the a^ c o e f f i c i e n t i s -0.29±.18 and a^ i s 0.31±.10. Although the ambiguity i n spin assignment f o r the f i n a l state creates d i f f i c u l t y f o r the e x t r a c t i o n of d e t a i l e d information from the angular d i s t r i b u t i o n measurements, i t i s always i n t e r e s t i n g to speculate on the p o s s i b l e composition of the GDR. If we assume that the f i n a l state i n the (p,Y^) r e a c t i o n i s a 5/2 state,the allowable E l amplitudes + + + are E l (3/2 ), E l (.5/2 ) and;El(7/2 ). The expected angular d i s t r i b u t i o n s f o r t r a n s i t i o n s i n v o l v i n g only one of these amplitudes are as follows 3/2 + -> 5/2~ : W(0) = 1.0 -0.1P ; 5/2 + ->• 5/2~ : W(S) = 1.0 + 0.457P2 ; 7/2 + + 5/2~ : W(Q) = 1.0 - 0.357P 2. Since a l l the c o e f f i c i e n t s are negative we c a n • t e n t a t i v e l y neglect the E l C 5 / 2 + ) term. The most l i k e l y interference to give a large i s the interference between E l (7/2 +) and E2(9/2~) (Carr et al.1972) i f the interference from a p o s s i b l e Ml term i s n e g l i g i b l e . We speculate that near and above the center of the GDR the El(7/2* ) term i s dominant. However i f the f i f t h excited state has J-7/2 , then from the r e s u l t i n g and a^ we can t e n t a t i v e l y state that E l (9/2 +) i s dominating. 95 CHAPTER 3 DISCUSSION § 3.1 Possible candidates of T = 3/2 states. In T =0 and A=4N n u c l e i the Ml t r a n s i t i o n strength b u i l t upon the ground state i s concentrated strongly i n the lowest few l e v e l s a v a i l a b l e f o r t h i s type of t r a n s i t i o n . In l p s h e l l n u c l e i the strength i s concentrated i n the lowest T=l state, however i n 2s-ld s h e l l n u c l e i , the most intense Ml t r a n s i t i o n s are usu a l l y to the second 25 or t h i r d T=l states (Fagg 1975 and references t h e r e i n ) . In Mg (4N+1 nucleus), where the Ml t r a n s i t i o n from the T=l/2 ground to a T=l/2 low-lying excited state i s i s o s p i n allowed, r e l a t i v e l y strong Ml strength has also been observed i n the higher T=3/2 states other than the lowest T=3/2 state (Fagg et al.1969). The lowest T=3/2 state i n 29 TT "t* TT *t* P (at 8.38 MeV with J =5/2 ) cannot decay to the ground s t a t e ( J =1/2 ) v i a Ml t r a n s i t i o n . We thus expect considerable amount of Ml strength, could be observed i n the higher T=3/2 states. The r a d i a t i v e proton capture r e a c t i o n has been found to be very useful i n the i n v e s t i g a t i o n of T=3/2 states i n l i g h t n u c l e i with. T^ =1/2 f o r several reasons. The T=3/2 states i n A=4n+1 n u c l e i , where n i s an integer, generally have numerous proton and alpha channels which, are e n e r g e t i c a l l y open, but forbidden by i s o s p i n conservation. Hence ' these ' T=3/2 states would be expected to be quite narrow compared to the spectrum of T=l/2 states, of i d e n t i c a l spin and p a r i t y i n the same region of e x c i t a t i o n energy. In a d d i t i o n , the gamma-decay channel leading to the ground state or low-lying T=l/2 states- are i s o s p i n allowed so that the T=3/2 resonances are found to stand out from a smoothly varying .96 background i n the r a d i a t i v e proton capture r e a c t i o n . The resonances observed at E^ = 8.02, 8.155 (Fig.2.2.1-4), 8.67, 9.275 (Fig.2.2.1-6), 9.555 (Fig.2.2.1-10) and 11.205 MeV (Fig.2.2.1-11), or e x c i t a t i o n energies of 10.488, 10.611, 11.116, 11.700, 11.975 and 13.564 MeV r e s p e c t i v e l y , i n t h i s work are a l l suggested as p o s s i b l e candidates for a T=3/2 assignment. These l e v e l s are chosen simply because the widths of these resonances are l e s s than 17 keV, the l i m i t being imposed by the target thickness and beam r e s o l u t i o n . 29 29 The f i r s t T=3/2 states i n the S i - P p a i r had been i d e n t i f i e d and well studied (Endt et al.1973 and references t h e r e i n ) . 29 Information on four presumably higher T=3/2 states i n S i i s a v a i l a b l e 30 3 - 2 9 from the study of the S i ( He,a) S i r e a c t i o n (Detraz et al.1970). On the other hand, no information e x i s t s concerning the higher T=3/2 states 29 in. P .except.the .indication, f o r . a ...passible .T=3/2 state ...E = 9.735.MeV CP < 6.5 keV), among many T=l/2 states i n the nearby region, observed i n 28 the Si(p,p') reactions (Teitelmas et al.1969). A l l these states are shown i n Figure 3.1-1 (column 1 and 2). Much experimental and t h e o r e t i c a l work (Jaffee et al.1960, Bearse et.al.1968 , Jones 1969, Jones et al.1969, Kean et. al.1969, Hirko et al.1971, Jones et al.1971, de Voigt et. al.1972, Goosman et al.1973, Becker et al.1974, Williams et al.1975) has r e c e n t l y been devoted to the 29 study of the low-lying l e v e l s i n A l . Jones et a l . (1971) have been able to f i t a l l these low-lying states with e x c i t a t i o n l e s s than 3.7 MeV into a band p i c t u r e , except f o r the 3.19 MeV state (no d e f i n i t e spin-29 p a r i t y assignment). Information on low-lying states i n S i s not a v a i l a b l e 29 f o r d i r e c t comparison. An energy l e v e l diagram of.law-lying states- i n A l i s shown i n Figure 3.1-1 (.column 3) . The energy scale i s adjusted so 97 3^,554 - : ROTATIONAL BANDS IN A l 11,700 11.11ft. 3,947 JWTS ~ i m = a 5 8 4 Miz^>* imA* 11087 2.873 ' 2.873 10.611 ' ,.,^223__ 2.228 10.488 K=3/2+ NO. 7 1 3% 1.759 1.759 (2'2 ) + (1)+ 9.735 9.630 /MG£__ • U05^ K=1/2V NO.9 8-382 8.291 QQ Q.Q 29P 29Q. 29A1 K=5/2+ ° ' A l NO. 5 . Figure 3.1-1 Isobaric m u l t i p l e t s i n n u c l e i of mass A=29. 11.665 - 3 - « 9 < | r K=1/2* 3.193 R M n 11 1 1 > 3 0 5 3.069(i)H" 98 29 29 that the lowest T=3/2 states i n P (at 8.38 MeV), S i (at 8.29 MeV) 29 and the ground state of A l are a l l aligned. The r o t a t i o n a l band p i c t u r e proposed by Jones et al.(1971) i s a l s o shown i n Fig.3.1-1 (column 4,5,6 and 7) for comparison. The K assignments and Nil s s o n o r b i t numbers are shown below the head of each band (where K i s the p r o j e c t i o n of the spin of the state on the asymmetric a x i s ) . Our a n a l y s i s i n d i c a t e s that the gamma decay from the resonances 29 of i n t e r e s t proceeds to the ground state of P v i a a d i p o l e t r a n s i t i o n . 29 Although many p o s i t i v e p a r i t y l e v e l s are observed i n A l , many are not observed i n our experiment because of the AK= 0,±1 s e l e c t i o n r u l e which only allows states of the K=l/2 or 3/2 bands to decay v i a Ml 29 TT + t r a n s i t i o n s to the ground state of P (J =1/2 , T=l/2). The energy l e v e l s of analog states are subject to energy s h i f t s as has been w e l l established from the low-lying states of mirror n u c l e i (Nolen et a l . 19-69.), 29 29 and so one does not expect exact alignment of l e v e l s i n P, S i and 2 9A1. The resonances a t E = 8.02 MeV (E =10.488 MeV) and 8.155 MeV p x (£^=10.611 MeV) both f a l l i n the region where an analogue of the 2.23 MeV TT + 29 (J =3/2 ) parent state i n A l i s e n e r g e t i c a l l y expected. The expected energy of 10.61 MeV ( i . e . 2.23 MeV plus e x c i t a t i o n of the f i r s t T=3/2 29 state i n P) i s approximately 120 keV higher the 10.488 MeV resonance and agrees i n energy with the 10.611 MeV resonance. However the Thomas-Ehrman e f f e c t (e.g. Nolen(1969)) i s expected to be important and the 29 corresponding T=3/2 state i n P i s most l i k e l y s i t t i n g at a lower e x c i t a t i o n energy ( i . e . the E =10.488 MeV resonance). Futher our spin x assignment (J=3/2) for the E^=10.488 MeV resonance.agrees:-wj-th .the 2.23 MeV 29 29 state in... A l . This f a c t .lead. us., to identify;'the. 10.488 MeV state m P 29 as the analog of the t h i r d excited state of A l . The s p i n - p a r i t y and 99 29 + isospxn assignment f o r the 10.488 MeV state i n P i s J=3/2 and T=3/2. In heavier n u c l e i (in the middle of 2 s - l d s h e l l and above) the Ml strength has been seen to experience considerable s p l i t t i n g , however no such s p l i t t i n g has been reported f o r n u c l e i i n the A=29 mass region. Unfortunately no angular d i s t r i b u t i o n measurements have been done at the E =8.155 MeV (E =10.611 MeV) resonance. I t i s also p o s s i b l e that a low-p x ^ 29 l y i n g state i n A l i s not strongly populated i n those reactions (e.g. 24 29 27 29 30 29 Mg(a,p) A l , A l ( t , p ) A l and S i ( t , a ) Al) which have been 29 used to study the low-lying states i n A l . The resonance at 10.611 MeV i s p o s s i b l y not a T=3/2 sta t e , b u t - l i t t l e can be.stated d e f i n i t e l y u n t i l more experimental information i s a v a i l a b l e . The E =8.67 MeV (E =11.116 MeV) resonance observed i n t h i s P x work f a l l s about 130 keV below the expected energy of 11.25 MeV f o r the 29 -analog-of the 2.-87 MeV • state in••• -Al.--One -should 'note-that«the spin assignment of '3/2 from our angular d i s t r i b u t i o n measurements agrees with 29 the 3/2 assignment to the 2.87 MeV state i n A l . The.spin-parity, and i s o s p i n 29 IT + f o r the 11.116 MeV state i n P i s thus most l i k e l y to be J =3/2, T=3/2. E n e r g e t i c a l l y the E =9.275 MeV (E =11.700 MeV) state i s p x between the expected analog states of the 3.193 and 3.439 MeV states i n 29 A l . The s p i n - p a r i t y of the 3.193 MeV state i s not known. Since the other possible T=3/2 states are seen to have e x c i t a t i o n energies s l i g h t l y lower 29 than the expected energies c a l c u l a t e d from the A l l e v i e s , perhaps t h i s i s a l s o true f o r the 11.700 MeV s t a t e . This means an analog state of the 3.439 MeV. l e v e l i s most l i k e l y . However the angular d i s t r i b u t i o n seems to favor a J=3/2 assignment i n contrast to the parent state spin assignment + + (1/2 ). One possible explanation i s the interference between a 1/2 resonance and the under-lying background. The angular d i s t r i b u t i o n of a l / 2 + resonance i s more s e n s i t i v e (a f a c t o r of 2) to the existence of 100 quadrupole strength. (E2). i n the under-lying background than that of a + + + 3/2 resonance. Interference between the Ml (1/2 ) and the E2 (.3/2 ) can give an c o e f f i c i e n t as follows (Carr et al.1972); 6.928 a2 = 2~ E2 (3/2 +) Ml (1/2*) cos 6„ . + „ . + 1/2 ,3/2 where <5 i / 2 + 3/2 + ^ s t^ l e P h a s e - s h i f t - d i f f e r e n c e between the s-jy2 a n c ^ + ^3/2 P a r t i a- ]- waves. A small amount of E2 (3/2 ) strength ( i . e . E2(3/2 M l ( l / 2 + ) > 3%) i s s u f f i c i e n t to account f o r the observed a^ c o e f f i c i e n t . 29 The i d e n t i f i c a t i o n of the 11.975 MeV state i n P as a T=3/2 state i s not too obvious. However our angular d i s t r i b u t i o n 29 measurements i n d i c a t e that the parent state i n A l has to be a member of one of the K=l/2 or 3/2 bands. If the r o t a t i o n a l bands proposed by 29 Jones et a l . are c o r r e c t , then the most l i k e l y parent state i n A l i s + the 3.68 MeV (.3/2 ,K=l/2) state which i s a member of "the band b u i l t upon the 3.44 MeV (l/2 +,K=l/2) s t a t e . Our angular d i s t r i b u t i o n measurements prefe r a J=3/2 assignment' i n agreement with the assumption made by Jones et a l . i n order to f i t i n t o the band p i c t u r e . The energy c a l c u l a t e d f or the expected analog state i s 12.06 MeV which i s 90 keV higher than the 29 observed e x c i t a t i o n energy i n P. The s p i n - p a r i t y and i s o s p i n f o r the 29 + 11.97 MeV state i n P i s thus probably J=3/2 and T=3/2. With the current lack of knowledge of d e f i n i t e s p i n - p a r i t y 29 values for the many higher excited states i n A l • (Endt et al.1973), the i d e n t i f i c a t i o n of a parent state corresponding.to the resonance at E =11.205 MeV (E =13.56 MeV) seems impossible. According to the proposed bands given by Jones e t . a l . the members-of the bands based on N i l s s o n o r b i t NO.8 and 29 NO.14 are expected to appear i n A l at E^ greater than 3.7 MeV. If the s t a t i c and dynamic properties of the bands do not change d r a s t i c a l l y , we 101 + expect the band head based on Nilsson o r b i t NQ.8 CK=3/2 ) and band head based on the Nils s o n o r b i t NO. 14 (K».l/2 ) to appear at approximately 5.5 MeV 29 and 10 MeV r e s p e c t i v e l y i n A l . Based on t h i s simple estimate the 13.56 29 + MeV state i n P may then be an analog of a member of the K=3/2 band b u i l t upon the Nilsson o r b i t NO.8 and the s p i n - p a r i t y and i s o s p i n assignment would then be J 7 r=3/2 +, T=3/2. However we should note* that i t i s poss i b l e that members of a band • based on the o r b i t NO.8 i n t e r a c t with other p o s i t i v e p a r i t y members based on lower o r b i t s , and that they have been pushed down to a lower e x c i t a t i o n energy. Hence, there i s a p o s s i b i l i t y that the 13.56 MeV state 29 i n P i s an analog of a member of a negative p a r i t y band. 27 3 29 In the two-nucleon t r a n s f e r reaction, A l ( He,n) P, three sharp peaks of widths l e s s than 300 keV (to be c o l l a r e d with the o v e r a l l •*energy -resolution .of --250*keV) ^ appear --at.-.excitation-.-energies . of .1-0.13, 11.16 and 11.80 MeV (Greenfield et al.1972). Since i t i s i s o s p i n allowed 29 to reach the T=3/2 states i n P from t h i s r e a c t i o n , the peaks at 11.16 and 11.80 MeV could be from the states as we observe i n the (p,Y ) o r e a c t i o n a t E =11.116 and 11.70 MeV. The peak at 10.13 MeV i s e n e r g e t i c a l l y 29 close to the expected t h i r d T=3/2 state i n P. However the peaks at 10.13 MeV and 11.16 MeV are also e n e r g e t i c a l l y close to the resonances ( of widths =150 keV) at E =9.94 MeV and 11.24 MeV observed i n our(p,y ) x o measurements (Table' 2.1). As no information such as spin, p a r i t y or i s o s p i n 3 are extracted from the (. He,n) re a c t i o n , no d e f i n i t e i d e n t i f i c a t i o n could be made here. In the absence of charge dependent nuclear forces, the mass' di f f e r e n c e within an i s o b a r i c m u l t i p l e t would be j u s t due to electromagnetic e f f e c t s and the neutron-proton mass, d i f f e r e n c e . Within a m u l t i p l e t the 102 Coulomb energy- can be expressed as E (A,T,T ) = E ( 0 ) (A,T) 1 - T E a ) (A,T) + {3T 2 - T(T+l)}»E ( 2 )(A,T) c z c z c z c (3.1) where E ^ ( A , T ) , E ^ ( A , T ) and E ^ ( A , T ) are s c a l a r , vector and tensor c c c "Coulomb" energies and are functions of A and T. This equation r e s u l t s from t r e a t i n g the charge-dependent i n t e r a c t i o n i n f i r s t order perturbation theory and i s derived i n numerous references (e.g. Janecke 1969 and references t h e r e i n ) . Coulomb displacement between two members, T and T , z z of a m u l t i p l e t can be defined as AE (T ,T ) = E (A,T,T ) - E (A,T,T ). (3.2) C Z Z c z c z By s u b s t i t u t i n g equation (3.1) i n t o the right-hand-side of equation (3.2) we obtain AE (T ,T ) = (T - T ) « { - E ( 1 ) (A, T) + 3 (T + T ) ' E ( 2 ) (A,T) } C Z Z Z Z ' C z z c (3.3) Coulomb displacement energies for the m u l t i p l e t s i n the A=29 system (from t h i s work and the compilation of Courtney and Fox (1975)) are shown i n Table 3,1 . In a recent study of coulomb displacement energies within the Id.. . s h e l l (Janecke 1969) the experimental energies of the lowest i s o b a r i c m u l t i p l e t s are well reproduced by the simple r e l a t i o n (Eq.(3.3)) t y p i c a l l y within energies of 10 keV or so. However i t i s seen i n Table 3.1 that the higher i s o b a r i c m u l t i p l e t s experience an energy s h i f t , r e l a t i v e to the lowest T=3/2 m u l t i p l e t . This s i g n i f i c a n t energy s h i f t might be accounted for the change of wave functions from one m u l t i p l e t to another or other p o s s i b l e sources such as the Thomas-Ehrman e f f e c t (Thomas(1958) and Nolen(1969)), second order perturbations on the Coulomb energy 103 TABLE 3.1 Coulomb displacement energies i n A=29 n u c l e i . NO. E x c i t a t i o n Energy (MeV) AE (T ,T ) (keV) C Z Z 2 9A1 Sx 29 P Sx- A l 29 29 , P- A l 0 1 2 3 4 5 6 7 8 9 10 0.0 1.405 1.759 2.228 2.873 3.069 3.193 3.439 3.584 3.647 3.679 8.291 9.630 8.382 5393.5 5327.5 11211.0 10.488 11.116 11089.0 11072.0 11.087 11.305 5316.5 5338.5 11.665 11.700 5328.5 11090.0 11.971 11121.0 TABLE 3.2 E ^ t A / D and E ^ 2 ) (A,T) from higher m u l t i p l e t s . Coulomb displacement energy (keV) Results (keV) Sx- A l 29„ 29 n P- A l NO. AE (.1/2,3/2) c • AE (-1/2,3/2) c E( 1 ) (A,T) c (2) EK ' (A,T) c 4 5316.5 11072 5755.5 73.2 7 5328.5 11090 5761.5 72.2 AVERAGE : 5758.5 72.7. 104 equation, i s o s p i n mixing or charge-dependent nuclear f o r c e s . The systematics of Coulomb energy d i f f e r e n c e may be used to pr e d i c t energies of other i s o b a r i c analog states. From equation (.3.3)., i f ^ E c ^ T z , T z ^ between any two p a i r s of meiubers i n an i s o b a r i c m u l t i p l e t i s measured, we are able to c a l c u l a t e E ^ 1 ^ (A,T) and E ^ 2 ^ (A,T) by so l v i n g two simultanuous l i n e a r equations. M u l t i p l e t s NO.4 and NO.7 i n Table 3.1 both provide E (1/2,3/2) and E (-1/2,3/2) and the r e s u l t i n g E ( 1 N A , T ) and c c c (.2) E ^ (A,T) are shown i n Table 3.2 . The energy s h i f t s observed i n higher i s o b a r i c m u l t i p l e t with respect to the lowest T=3/2 m u l t i p l e t means that the values of E ^ (A,T) and E ^ (A,T) are d i f f e r e n t from those f o r the c c lowest m u l t i p l e t . The two sets of values i n Table 3.2 are i d e n t i c a l within the errors (uncertainties i n a l l energy l e v e l s are 10 keV or so). Under the assumption that' the average values of E ^ (A,T) and E ^ (A,T) i n Table c c ,3. ,2. .are app l i c a b l e ...to.,.all,isobaric ..multiplets ,,,=.except ..for ..the. lowest T=3/2 mu l t i p l e t , we are able to c a l c u l a t e p o s s i b l e energy s h i f t s f o r higher m u l t i p l e t s with respect to the lowest T=3/2 m u l t i p l e t . These are -71 keV, 29 29 29 29 -130 keV and -176 keV r e s p e c t i v e l y f o r the S i - A l , P- A l and 29 29 S- A l p a i r s . In table 3.3 we take these po s s i b l e energy s h i f t s i n t o account and show the expected.energies of the f i r s t 10 i s o b a r i c m u l t i p l e t s . The measured energies (in bracket) are shown f o r comparison. The agreement i s s a t i s f a c t o r y , except f o r the NO.10 m u l t i p l e t . I t i s also i n t e r e s t i n g to note that a p o s s i b l e candidate f o r a T=3/2 state has been observed at o p p p 4 . p p p p 9.735 MeV, i n the Si(p,p') Si(1.77 MeV,2 ). and Si(p,p') S i (4.97 MeV,' 0 +) reactions (Teitelman et a l . 1969), but t h i s i s 78 keV higher than our p r e d i c t i o n . I f the poss i b l e energy s h i f t i s not taken i n t o account, the 29 expected energy of the N0.1 state i n p i s 9.787 MeV which i s 52 keV higher than the observed resonance. In conclusion, we note that the energy 105 . 29 . TABLE 3.3 Expected energies of i s o b a r i c analog states i n S i , 29 29 P and S.(The.measured energies are i n parentheses). M u l t i p l e t EXCITATION ENERGIES (MeV)' NO. 2 9 A 1 S i 2 9 P 2 9 s 0 0.0 8.291 8.382 0.0 1 1.405 9.625 (9.630) 9.657 (9.735) 1.230 2 1.759 9.979 10.011 1.584 3 2.228 10.448 10.480 (10.488) 2.053 4 2.873 11.093 (11.087) 11.125 (11.116) 2.698 5 3.069 11.289 (11.305) 11.321 2.894 6 3.193 11.413 11.445 3.018 7 3.439 11.659 (11.665) 11.691 (11.700) 3.264 8 3.584 11.804 11.836 3.409 9 3.647 11.867 11.890 3.472 10 3.679 11.899 11.931 (11.971) 3.504 106 s h i f t s : used i n our predictions- are .roost.likely an upper l i m i t f o r the higher m u l t i p l e t s . There are t h e o r e t i c a l c a l c u l a t i o n s (HannaC1969). and references therein) on wave functions of i s o b a r i c analog states i n the lower 2s-ld 20 24 s h e l l n u c l e i (e.g. Ne and Mg), but no c a l c u l a t i o n s are a v a i l a b l e 29 29 at present f o r P (or Si) f o r d i r e c t comparison. T h e o r e t i c a l c a l c u l a t i o n s concerning these energy s h i f t s i n higher m u l t i p l e t s and f o r the f a i l u r e • to populate other p o s s i b l e T=3/2 states i n t h i s energy range could be a se n s i t i v e t e s t of the wave functions f o r these T=3/2 st a t e s . 107 § 3.2 Dipole sum r u l e s and r a d i a t i v e proton capture reactions I t was f i r s t emphasized by Wilkinson ("1956) that the independent p a r t i c l e model could describe the nuclear photo-effect. The giant dipole resonance i s ascribed to the e l e c t r i c d i pole absorption of photons by the valence nucleons and by those i n the uppermost f i l l e d s h e l l . These nucleons make t r a n s i t i o n s upward to the next u n f i l l e d s h e l l of opposite p a r i t y according to dipole s e l e c t i o n r u l e A£=±l. Their summed o s c i l l a t o r strength i s equal to the dipole sum r u l e . For the sake of s i m p l i c i t y we s h a l l use a harmonic o s c i l l a t o r p o t e n t i a l Cor wave functions) i n t h i s section f o r c a l c u l a t i o n s of the d i p o l e sum (for d e t a i l s see Appendix A). Although t h i s over s i m p l i f i e d model has a v e r y important q u a l i t a t i v e shortcoming, namely that i t gives the giant ., -1/3 resonance energy as e s s e n t i a l l y 41 A MeV which i s appreciably lower than a l l observed giant resonance energies, nevertheless the dipole sum c a l c u l a t e d from t h i s model i s e s s e n t i a l l y independent of the energy involved. I t i s now p o s s i b l e , using a p a r t i c l e - h o l e r e s i d u a l i n t e r a c t i o n introduced by E l l i o t and Flowers (1957) and pursued by Brown and h i s followers (e.g. Brown 1967 and references t h e r e i n ) , to account f o r .the width and the high energy of the dipole resonance. However the basic idea of giant dipole resonance i s the same as that of Wilkinson. From the p r i n c i p l e of d e t a i l e d balance the r a t i o of the cross section of the r a d i a t i v e proton capture r e a c t i o n and i t s inverse reaction, namely the photonuclear r e a c t i o n , i s q( P,y) • 2 ( 2 V l ) ( E Y / c ) 2 ° ( Y ' P ) " (21+1) ( 2 V l + l ) q 2 108 where I = spin of the f i n a l nuclear state i n the r a d i a t i v e capture A -re a c t i o n ; I . = spin of the target nucleus; E_^_ = photon energy; c = speed of l i g h t ; I = spin of the i n c i d e n t proton (h); q = momentum of the i n c i d e n t p a r t i c l e i n the center-of-mass system; The p r i n c i p l e of d e t a i l e d balance shows that the proton capture, experiment y i e l d s the.. cross . section for.. populating the ground-state.of the r e s i d u a l nucleus i n a (YrP) r e a c t i o n , and thus sets a lower l i m i t on the t o t a l (y,p) cross section. As a consequence, the f r a c t i o n of the dipole sum expended .in a. (P/Y ) r e a c t i o n depends strongly on .the overlap .between'-, the states i n the giant dipole resonance.and the proton-plus-target-nucleus system. Further, the r a d i a t i v e proton capture r e a c t i o n a l s o provides a unique p o s s i b i l i t y of studying t r a n s i t i o n s to excited states of the f i n a l nucleus. A p p l i c a t i o n of the p r i n c i p l e of d e t a i l e d balance to the measured cross sections of the (PfY )r (P/Y-,) and (p,Y,-) reactions (e.g.Figures 2.2.3-3, 2.3-3 and -.2...4-2) O 1 D provide us with the cross sections f o r the inverse r e a c t i o n s . Figure 3.2-1 shows the c a l c u l a t e d e x c i t a t i o n s f o r the inverse reactions of (y ,p ), ' o o 29 (Y-j_rP0) and (Y^ »P ) f o r a P ta r g e t . Spins f o r the ground state, f i r s t and f i f t h excited states used i n the c a l c u l a t i o n s are l / 2 + , 3/2+ and 5/2 respectively.' Instead of the incident proton energies, energies of the emitted photon ( i . e . y i T, and Y r) are shown i n the f i g u r e . The centre O 1 5 of the Y Q giant resonance i s seen to be approximately 1.5 MeV lower than that of Y^  and y r . Perhaps t h i s energy s h i f t i s a consequence of the p e n e t r a b i l i t y e f f e c t of d i f f e r e n t p a r t i a l waves involved i n d i f f e r e n t • channels. The integrated cross sections, a(E) dE.., from .these 10.9 3 2H ft 3 „ « o, « > • • a < o « B a a CD ' P0) Q i — i I—-u CO 0 . US -8 " A « t < i i a a o . °5» / 1 1 "B il ff CO CO o C J 3-4 H 0 • a o « « " i , 0 1, 8 1 0 0 J 6 ' • • . • c i o a fl ° « to 0 6 1 ' ' . C j * . 6 » c o • 0 ( y 0 . p o } 13.0 15.0 17.0 19.0 21.0 23.0 25.0 27.0 PHOTON.ENERGY IN MEV Figure 3.2-1 Photonuclear cross sections c a l c u l a t e d from the corresponding inverse (p, y) r e a c t i o n s . 110 e x c i t a t i o n functions are 15.2 mb-MeV, 16.5 mb-MeV and 10.4 mb-MeV re s p e c t i v e l y and the corresponding f r a c t i o n a l d ipole sum i n terms of the c l a s s i c a l dipole sum r u l e , 60NZ/A mb-MeV, i s shown i n Table 3 . 4 . Since our work spans only the main peak of the y giant dipole resonance, the 5 cont r i b u t i o n of the dipole strength from the unmeasured lower and upper region i s not included i n the i n t e g r a t i o n . To take t h i s p o s s i b l e r e s i d u a l strength into account we have also c a l c u l a t e d the product of the width (5.8 MeV) and the peak value i n the (y^,p) e x c i t a t i o n function ( i . e . 2.1 mb) of 12 mb-MeV. Gamma y i e l d s leading to second, t h i r d and fo u r t h excited 2.9 states i n P, as discussed i n chapter 2, enable us to estimate an upper l i m i t of 0.5% for the dipole sum expended i n these re a c t i o n s . We make the assumption that the target nucleus i n the proton capture r e a c t i o n has a simple c o n f i g u r a t i o n such as a hole i n a closed s h e l l f o r an odd mass nucleus, or a closed s h e l l f o r an even mass nucleus, and so the f i n a l state of the r a d i a t i v e proton capture r e a c t i o n then i s a closed s h e l l and a s i n g l e - p a r t i c l e - s t a t e r e s p e c t i v e l y ; thus we are able to cal c u l a t e the expected f r a c t i o n a l d i p o l e sum, using the harmonic - • . o s c i l l a t o r model (Appendix A), f o r several r e a c t i o n s . i n v o l v i n g n u c l e i i n the l p s h e l l and 2s-Id s h e l l region (Table 3 . 4 ) . The c a l c u l a t e d f r a c t i o n a l d i p o l e sums are seen to be too large (by approximately a fa c t o r of 2) i n comparison with the experimental values. Although p o s s i b l e sources of departure such as the o v e r s i m p l i f i e d wave functions might be important, the simple harmonic o s c i l l a t o r model does not include, the r e s i d u a l i n t e r a c t i o n which e x i s t s between the nucleons i n a nucleus. Since the nuclear absorption of photons i n the giant resonance region takes place through the e x c i t a t i o n of a s i n g l e p a r t i c l e , the excited nucleon may emerge d i r e c t l y without fur t h e r i n t e r a c t i o n and under these circumstances the d i p o l e sum expended and the angular I l l TABLE 3.4 Dipole sun expended i n the r a d i a t i v e proton capture reactions and the simple harmonic o s c i l l a t o r (SltO) model c a l c u l a t i o n s . Configurations Reaction target nucleus f i n a l nucleus dipole sum from the state SHO model and References n B ( p . V 1 2 C ( l p 3 / 2 ) 4 ( 2 s l / 2 M l p 3 / 2 > " 1 ( " 3 / 2 M l p 3 / 2 ) " 1 ( I d ^ X l p ^ ) " 1 7.4 3.7 33.2 A l i a s e t al.(1964) ' U » ( P . T 1 ) 1 2 C T o t a l i 44.3 29. 9. 1 SH(p.Y ) 1 G 0 o dp,,) - 1 Up,,)2 ( 2 s ^ ) ( I p ^ ) " 1 U d ^ H l p . T 1 2.8 13.8 Tanner e t al.(1964) Black e t al.(1967) T o t a l : 16.6 16.4 1 9 F ( p . T o ) 2 0 N e <2s,i)"1 ( 2 S j j ) 2 (2p H) C2s ) j)' 1 ( 2 p 3 / 2 ) ( 2 S . T 1 5.5 11.0 Segel et al.(1967) T o t a l i 16.5 8.3 3.2 2 7 A l ( p , Y 0 ) 2 8 S i d d ^ ) " 1 t l d 5 / 2 » 6 ( 2 p 3 / 2 ) ( l d 5 / 2 ) -1 ( l f 5 / 2 , ( l d 5 / 2 r l  ( l f 7 / 2 , { l d 5 / 2 ' " 1 5.7 1.4 28.5 Singh et al.(1968) 2 7 A l ( p , Y 1 ) T o t a l i 35.6 6. 3 S ( p . T 0 ) 3 2 S (2s^) ( 2 3 ^ 1 2 Up^J ( 2 s ^ ) ' 1 3.4 Dearnaley e t al.(1965) ( 2 p 3 / 2 ) ( 2 s ^ ) _ 1 •7.0 T o t a l : 10.4 3.7 1 2 c ( p , r o ) 1 3 H d P 3 / 2 ) 4 dp,,) 1 <2S|i) C l p ^ ) " 1 .Ud^Hlp.T 1 1.5 7.3 Heasday e t a l . U965) Berghofer et al.(1974) T o t a l : 8.8 9.8 1 2 C t p . T l ) 1 3 N d P 3 / 2 ) 4 (23^ I 1 (2p %) ( 2 s | j ) " 1 ( 2 p 3 / 2 ) C 2 s ^ ) " 1 3.6 7.3 T o t a l : 10.9 *1.2 1 2C(P,T 2+Y 3) >7.0b 2 8 S i ( p . Y o ) 2 9 P ( l d 5 / 2 ) 6 (2 S j j) (2 P l j) ( 2 s l j ) "1 ( 2 p 3 / 2 ) ( 2 s ^ ) - 1 1.8 3.6 Present work T o t a l : 5.4 3.5 a B S l ( p . Y l ) a 9 P ( l d s / 2 ) 6 ( l d 3 / 2 , ( 2 p s ) ( l d 3 / 2 ) - 1 t 2 p 3 / 2 ) ( l d 3 / 2 ) - 1 < l f5/2» ( l d 3 / 2 ' " 1 0.7 0.1 4.5 T o t a l : 5.3 3.8 2 8 S i ( p . T 5 » 2 9 P ( l d 5 / 2 ) 6 ( l f 5 / 2 > ( 2 d 3 / 2 , a f 5 / 2 1 " 1 ( 2 d 5 / 2 ) ( l £ 5 / 2 ) - 1 0.9 0.1 5.5 T o t a l : 6.5 2.4 (2.8) C 2 8 S i ( p , Y n ) i0.5 where n°2,3,and 4. a i Upper l i m i t ot the integrated cross section are 30 MeV or l e s s . b) Since the 2 n d excited state i n 1 3 N i s believed t o be a d p , . - ) - 1 state, wo assume (p.Yj) dominating. ' . Ci Product of the widtn and peak value inmtho (Yj.p) y i e l d (Fig.3.2-1). 112 d i s t r i b u t i o n s r e f l e c t the d i r e c t absorption process. A l t e r n a t i v e l y the excited nucleon may undergo f u r t h e r i n t e r a c t i o n s before i t escapes from the nuclear surface. P a r t i c u l a r l y f o r higher spin nucleons, they may not be able to penetrate the angular momentum b a r r i e r and so they remain i n the nucleus making c o l l i s i o n s and sharing t h e i r energy with the other nuclear p a r t i c l e s . Eventually s u f f i c i e n t energy i s concentrated on a nucleon having low angular momentum and i t escapes but the r e s i d u a l nucleus i s now l e f t i n an excited state. As a r e s u l t , the f r a c t i o n a l dipole sum expended i n the (Y,p ) or (p,Y ) r e a c t i o n i s reduced. Also the l e v e l o o density of. the f i n a l nucleus i n the (.Y,p) re a c t i o n i s expected to increase as the mass number,A, increases. However i t i s not easy to detect such an e f f e c t and i t has not been established i n d e t a i l . The integrated cross section j a(. Y^,p) dE obtained from "the y i e l d of•the inverse r e a c t i o n (p,,y^) i s ' l e s s than'the a(y, ,p) dE 0 f o r most n u c l e i investigated up to date (some examples are shown i n Table 3.4); the former i n t e g r a l average about h a l f of the l a t t e r . Because most of the nuclex xnvestigated have been even-even n u c l e i o f . J =0 , t h i s might be expected as the f i r s t excited states are the most e a s i l y exerted 2 states xn which nucleons i n the uppermost s h e l l are rearranged or nucleons are excited to the next higher ..unfilled -- o r b i t . The-configurations of these 2 + states are. expected to be ..fairly/ s i m i l a r to the ground state. However i t i s shown c l e a r l y i n our measurements on the 28. Si(p,v) r e a c t i o n that the i n t e g r a l s fa(y ,p) dE and J ° . J are approximately equal. ,p) dE 12 Sxnce C xs one of the most well studied n u c l e i , we s h a l l give a short d i s c u s s i o n concerning the GDR b u i l t upon higher states i n this-nucleus, based on some recent experimental r e s u l t s . I t has been 113 shown that states i n the GDR, b u i l t upon the 0 exc i t e d state are not populated i n the ^ B (p,y ) "^C (7.66 MeV, 0 +) r e a c t i o n (Brasard et al.1972) . A more recent i n v e s t i g a t i o n on t h i s r e a c t i o n (Snover et al.1974) using our detector observe a dipole sum of approximately an order of magnitude smaller than that observed i n the (PfY Q) or (P/Y^) rea c t i o n s . The r e s u l t can be explained by considering the 0 + excited••state as mainly a fo u r - p a r t i c l e - f o u r - h o l e state. Since the 1 1 B nucleus i s e s s e n t i a l l y a ^3/2^ ^ hole, the target-plus-proton system would not be expected to overlap strongly with the d i p o l e states i n the GDR b u i l t upon the 4p-4h 3 s t a t e . However m an i n v e s t i g a t i o n on the r a d i a t i v e He capture i n t o 12 * C (Shay et al.1974), structure s i m i l a r to the giant resonance has been observed i n the gamma y i e l d leading to the o"1 . excited state, but-the gamma y i e l d s leading to the ground state and the f i r s t e x cited state (2 +, 4.44 MeV) are seen to be an order of magnitude weaker. S i m i l a r r e s u l t s are also found i n the "^0 nucleus (Chew et al.1975). Among the odd mass n u c l e i , • r a d i a t i v e proton capture 12 13 on C in t o the GDR region of N has been in v e s t i g a t e d i n d e t a i l (.Measday e t al.1965, Measday et al.1973 and Berghofer et,al.1974). The observed sum b u i l t upon the f i r s t e x cited state (2.37 MeV, 1/2') i n the (p,Y-j_) channel i s n e g l i g i b l y small. On the other hand, the i n d i v i d u a l dipole sum expended i n the (p,y ) and the (P'Y2+Y3^ channels each account for -10% and -7% of the c l a s s i c a l d i pole sum r u l e . Up to t h i s point, we have shown that r a d i a t i v e capture in t o the GDRs b u i l t upon the ground state and the exc i t e d states have d i f f e r e n t and i n d i v i d u a l c h a r a c t e r i s t i c s . The f r a c t i o n a l dipole sum expended i n d i f f e r e n t reactions tends to depend on the-structure of the 114 f i n a l states as well as i n i t i a l target nucleus. In order to explain our 28 r e s u l t s of r a d i a t i v e proton capture on S i , an in t r o d u c t i o n to the 29 low-lying states i n P w i l l be given as follows. 29 In the extreme s i n g l e - p a r t i c l e s h e l l model P i s considered 28 as a single proton outside of the doubly-closed-subshell of the S i core and the assignments of 3^/2 anc^ s\/2 t 0 t h e ^-'^ M e V f i r s t excited state and the ground state, r e s p e c t i v e l y , are expected. For t h i s simple 29 approximation, P would have only two low-lying states of even p a r i t y . 29 In actual f a c t , P has f i v e even p a r i t y l e v e l s below the f i r s t odd p a r i t y state (see Table 3.5). 29 Most c a l c u l a t i o n s a v a i l a b l e are f o r S i , the mirror 29 nucleus of P. The energies and gamma t r a n s i t i o n s involved i n the low— 29 l y i n g states i n S i are explained f a i r l y w e ll i n terms of the strong-coupling c o l l e c t i v e model. Bromley and co-workers (19*57) applied a • . . , strong-coupling c o l l e c t i v e model, with a small deformation 6=-0.15 (or n=-3.0), to explain the properties of the low-lying s t a t e s . Since 29 the excited states m P show good correspondence with those of the 29 mirror nucleus, S i , up to the f i r s t odd-parity excited state, the strong coupling model should be ap p l i c a b l e to the low-lying states of 29 P. E j i r i (1964) showed that a strong coupling model with a oblate deformation i s preferable to a weak coupling model to explain the 29 properties of the low-flying states of P. The most s t r i k i n g piece of . experimental evidence a v a i l a b l e f o r the assignment of an oblate shape 29 29 to P (or Si) had been the low-lying negative p a r i t y state ( i . e . TT - - 29 IT - 29 3.45 MeV, J =5/2 or 7/2 i n P and 3.62 MeV, J-=7/2 i n s i ) . For a prolate shape, t h i s l e v e l i s expected to l i e at a higher energy. 29 Strong evidence f o r the existence of r o t a t i o n a l hands i n S i had 115 TABLE 3.5 Energy l e v e l s of P f o r E S 4.08 MeV. x The spins, p a r i t i e s and e x c i t a t i o n energies are taken from the compilation of Endt e t . a l . (.1973).. The r o t a t i o n a l band p i c t u r e i s that of Bromley e t . a l . (.1957) and E j i r i (.1964) . E X J 7 7 K (Nilsson o r b i t No. ) 0.0 V 2 + l / 2 + (No.9) 1.38 3/2 + 3/2 + (No.8) 1.95 5/2 + l / 2 + (No.9) 2.42 3/2 + l / 2 + (No.9) 3.11 5/2 + 3/2 + (No.8) 3.45 (5/2,7/2)" ? (No.10 or 12) 4'. 08 7/2 + + 3/2 (No.8) ' 116 also been reported (e.g. Spear et al.(.1971), P i l t et a l . (.1971) and ' Anantaraman et al.(1974)I. In terms of the strong coupling model (Table 3.5), the 29 ground state of P i s the band head of a K=l/2 band CNilsson o r b i t number 9) and the.wave function i s a simple c o n f i g u r a t i o n of 2s, H with a small f r a c t i o n of d and d . The excited states at 1.95 MeV(5/2 +) 3/2 b/2 and 2.42 MeV (3/2 +) are members of t h i s K=J2 band. The f i r s t excited state at 1.38 MeV (3/2 +) i s the band head of a K=3/2 band (Nilsson o r b i t number nd + st + 8) while states a t 3.11 MeV (2 5/2 ) and 4.08 MeV (1 7/2 ) are members of t h i s band. According to the Nilsson energy l e v e l s f o r s i n g l e p a r t i c l e , the expected f i r s t negative p a r i t y state at 3.45 MeV i s a 7/2 state (orbit No. 10) and the next higher s i n g l e p a r t i c l e state (orbit No.12, K=5/2 ) i s expected to be only few hundred keV away. Both states o r i g i n a t e -from a I f / p a r t i c l e 'and "are 'Unbound."The ^ correction"due to- the- C o r i o l i s force (e.g. Eisenberg and Greiner 1970) i s expected to be important, so 29 that the p o s s i b i l i t y of having the 5/2 state i n P at a lower e x c i t a t i o n than the 7/2 state can not be excluded. Unfortunately i t i s not yet possi b l e to assign a unique spin to t h i s state (Endt e t a l . ( 1 9 7 3 ) and references t h e r e i n ) . Based on the f a c t that the nuclear absorption of photons i n the giant resonance region takes place through the e x c i t a t i o n of a si n g l e p a r t i c l e , the dipole states b u i l t upon the low-lying excited states i n v o l v i n g core e x c i t a t i o n are expected to be more complicated ( i . e . many-particle-many-hole state) than those b u i l t upon s i n g l e - p a r t i c l e -states. Radiative proton capture i n t o these complex states i s not expected without i n v o l v i n g e x c i t a t i o n of the target nucleus. In terms of the dipole 117 sum (.shown i n Table 3.41, our measurements show that the (p,Y QK (PrY-j^ 28 and (p,Y r) reactions-on S i are about an order of magnitude, l a r g e r than 5 the (p,Y2^' (P/Y-j) a n <3 (Pz-Y^) r e a c t i o n s . This means that the heads of the r o t a t i o n a l bands (Table 3.5) are better s i n g l e - p a r t i c l e - s t a t e s than the other members of the bands. Much experimental and t h e o r e t i c a l work has r e c e n t l y been devoted to the study of the wave functions of the low-lying states i n 29 S i . Sophisticated s h e l l model c a l c u l a t i o n s have been made i n order to 29 understand the low-lying states i n S i . A l l studies suggest that some states are well described by a s i n g l e p a r t i c l e c o n f i g u r a t i o n and others 28 are r e l a t e d to e i t h e r the c o l l e c t i v e e x c i t a t i o n of the S i core or more complex p a r t i c l e - h o l e configurations (Johnston et al.1973, DeVoigt e t . a l . 1972, V7ildenthal e t al.1973, Coker e t al.1974 and Boyd et.al.1975). A . 28 29 29 s h e l l model c a l c u l a t i o n on the low-lying states i n S i and S i Cor P) done under the assumption of a c l o s e d - s h e l l "^0 core i s now a v a i l a b l e . 28 . (Wildenthal et al.1973). Wave functions of the low-lying states m S i 29 29 and S i (or P) have been given by Wildenthal and McGrory (.1973) i n terms of a l i n e a r sum of the configurations (ld_ . . ) n i ( 2 s , ) n z (Id ) n 3 5/ Z • -5 5/1 with a c l o s e d - s h e l l "^O core. This set of wave functions (for p o s i t i v e p a r i t y states only) also provides a p i c t u r e s i m i l a r to the strong coupling model c a l c u l a t i o n s . Despite evidence f o r the existence of l p - l h • configuration i n the "*~^0 core- (Morsch et al.1975), the s h e l l model c a l c u l a t i o n enjoys some success i n the i n t e r p r e t a t i o n of the properties of the low-lying states below the f i r s t 0 + excited state (.4.98 MeV). i n 28 S i . Experimentally the angular d i s t r i b u t i o n s of the (.d,p) reactions leading to the 2 n d and 3 r d excited states (.2.03 MeV",5/2+ and 2.34 MeV, 118 + 29 3/2 r e s p e c t i v e l y ! i n P can he reproduced i f a two-step re a c t i o n mechanism (e.g. coupling-channel c a l c u l a t i o n s by Coker et.al.1974) i s applied to the t r a n s f e r r e a c t i o n . Analysis of the proton-gamma-angular-28 29 + c o r r e l a t i o n measurements of the Si(d,p) Si(2.03 MeV,5/2 ) re a c t i o n also strongly i n d i c a t e s . t h a t a two-step r e a c t i o n mechanism is. needed to reproduce the experimental r e s u l t s (Boyd e t al.1975). Complex configurations are expected f o r these excited s t a t e s . This i s i n agreement with the s h e l l model c a l c u l a t i o n of Wildenthal et a l . . The small cross s e c t i o n f o r the (pfY^), ( p , ^ ) and (PJY ) 28 reactions on S i may also be explained i n terms of the wave functions 29 of the target nucleus and that of the f i n a l states i n P. Since the configurations of the di p o l e states i n the GDP. region may be regarded as the e x c i t a t i o n of a single p a r t i c l e in- the 2s-ld s h e l l , the overlap 28 between - these^ states 'and the-'conf i g u r a t i o n =of'the ground state of S i plus a i n c i d e n t proton of i£=2p or I f i s a good measure of the expended. dipole sum i n r a d i a t i v e proton capture. I t is'expected from the published amplitudes f o r d i f f e r e n t configurations i n the ground state and f i r s t 29 excited state of p that the overlap i s large. On the other hand, the overlap of the dipole, states b u i l t upon the.second,.third and. f o u r t h excited states are expected to be n e g l i g i b l e . From the published amplitudes f o r d i f f e r e n t configurations of these l a s t set of excited states, we are able to estimate that the dipole sum expended i n the (p.,Y^) > (p, -^) and (p,Y ) reactions w i l l be l e s s than 20% of those i n the (p,Y Q) or (p,Y^) reactions. In conclusion, we show the t h e o r e t i c a l (.Wildenthal et a l . 1973) and experiemntal (Merrnaz et al.1971) one-nucleon-tranfer spectroscopic 29 f a c t o r s f o r the low-lying states i n . S i to compare with the dipole sums 119 TABLE 3.6 Comparison of single-nucleon-stripping spectroscopic 29 f a c t o r s f o r the low-lying states of S i and f r a c t i o n a l 29 dipole sum f o r the low-lying states of P. Sx 2 9 P . 28„. .29 . .Sx(d,p) Sx spectroscopic f a c t o r s F r a c t i o n a l dipole sum 28 . , • , E Sx(p,y ) x (MeV) E J 7 1 t h e o r e t i c a i a experimental^ x S S (MeV) 3 toj . g.s. l / 2 + 0.5 0.53 0.65 l / 2 + g.s. 1.27 3/2 + 0.59 0.74 0.72 3/2 + 1.38 2.03 5/2 + 0.11 0.12 <0.09C 5/2' 1.95 2.43 3/2 + 0.03 0.012 <0.09C 3/2 + 2.42 •3.07 5/2 + 0.02 0.06 <0.09 5/2 + 3.11 3.623 7/2~ 0.38 0.37 (5/2,7/2)~3.45 a i - Wildenthal et al.(1973) b: Merrnaz; et al.(1971) c: Assume the simple harmonic o s c i l l a t o r c a l c u l a t i o n = 5.4% of the c l a s s i c a l d i pole sum r u l e as i n the case of (p,y ) or (p,Y^) shown i n Table 3.4 . 120 28 observed i n the SrCp/y)- reactions. (Table • 3.61. The values shown 28 i n the column e n t i t l e d Si(p,Y n) are obtained from the observed dipole sums divided by the simple harmonic o s c i l l a t o r c a l c u l a t i o n shown i n Table 3.4 . The (p,y) measurements provides a p i c t u r e s i m i l a r to that . of the spectroscopic f a c t o r s and o f f e r one of the few ex c e l l e n t examples which shows c l e a r l y the structure dependence of the dipole sum expended i n the r a d i a t i v e proton capture r e a c t i o n . 121 § 3.3 Intermediate structure and po s s i b l e doorway states The occurence of intermediate structure i n the e x c i t a t i o n functions f o r nuclear cross sections and the i n t e r p r e t a t i o n of the structure using the concept of doorway states has a t t r a c t e d much att e n t i o n i n the past few years. Extensive discussion can be found i n the reviews by Mekjian (1973) and Mahaux (1973). Although many experimental examples of intermediate structure have been reported, e i t h e r only one re a c t i o n channel was studied or else the i n t e r p r e t a t i o n of the measurements i n terms of doorway states i s not unique. To give a. b r i e f explanation f o r the concept of doorway states we consider a doubly-closed-shell (or Op-Oh) target and an in c i d e n t nucleon. In t h i s case the inc i d e n t nucleon c o l l i d e s , through the two body r e s i d u a l i n t e r a c t i o n , with a target nucleon, and ex c i t e s i t , leading thus to a 2p-lh e x c i t a t i o n , or doorway st a t e . Further c o l l i s i o n s can then lead to 3p-2h, 4p-3h etc., which have been c a l l e d hallway states ( F e r r e l l et al.1966). Two widths are attached to a doorway st a t e . The f i r s t one, r , i s c a l l e d the escape width and i s r e l a t e d to the p r o b a b i l i t y that the doorway state decays i n t o channel c. The other one, the spreading width, V , i s connected with the p r o b a b i l i t y of reaching more complicated configurations, e.g. 3p-2h, etc.. The t o t a l width of the doorway state i s the sum of the escape widths f o r a l l channels, plus the spreading width. The necessary conditions to observe i n channel c intermediate structure corresponding to a doorway state are, t (i) the escape width T i s larger than or comparable to the spreading c 4-width r ; and ( i i ) the doorway state i s i s o l a t e d , i . e . the distance, D , i n energy from the c l o s e s t doorway state i s greater than the t o t a l width. 122 T h e o r e t i c a l c a l c u l a t i o n s about the e f f e c t of doorway states on the structure i n giant dipole resonance have concentrated mainly on even-even n u c l e i . The concept of doorway states has proved to be 12 16 28 40 quite successful f o r n u c l e i such as C, O, S i and Ca (e.g. Shakin et a l . 1971 Marangoni et al.1971 and Bar r e t t et a l . 1973). A p a r t i c u l a r l y u s e f u l study was made by Payne (1968) who c a l c u l a t e d p a r t i c l e emission widths of the 2p-lh states reached from neutron s c a t t e r i n g o f f a se r i e s c a. n • • 28„. 32^ , 40^ 54„ 62 . 92„ 120^ ^ 208^ of target n u c l e i , v i z S i , S, Ca, Fe, Ni, Mo, Sn and Pb. 2 8 For the neutron-plus- S i system Payne concludes that the density of 2p-lh states i s small at low energies (incident neutron energies l e s s than 3 MeV.or E < 11.40 MeV) and i s o l a t e d resonances of intermediate x structure should be seen. At higher energies, the density of 2p-lh states i s large so that structure i n the cross section i s then produced by fl u c t u a t i o n s i n l e v e l width and l e v e l density (Fig.3.. 3-l£ on p.129 shows the ca l c u l a t e d 2p~lh states having nucleon decay widths greater than 30 keVL. Recently, Weller et al.(1975) have also predicted numerous 2p-lh states (Fig.3.3-lf and 3.3-2c) o f considerable decay width in.the - proton energy 28 range of 15 to 22 MeV f o r the proton-plus- S i system. This e x c i t a t i o n 17 region was not covered by Payne. For F, Harakeh e t al.(1975) have included 2p-lh e x c i t a t i o n s and have been able to p r e d i c t c o r r e c t l y the d i s t r i b u t i o n of E l strength i n and j u s t below the giant dipole resonance. Isolated doorway states (or intermediate structure) are expected to e x i s t a few MeV below the giant dipole resonance region. In general, these doorway states are d i f f e r e n t from channel to channel and only o c c a s i o n a l l y w i l l a doorway state be prominent i n several channels. • Lane (1971) proposed that a pygmy resonance may be a prominent common doorway for nucleon and photon channels. Doorway state s , other than 2p-lh 123 configurations (Payne 1968), such as nucleon-plus-vibration-core or nucleon-plus-rotational-core (e.g. Choi et.al.1974) are also predicted. Two resonances at E =7.45 MeV and 8.80 MeV (or E =9.94 MeV p x 28 29 and 11.24 MeV r e s p e c t i v e l y ) are observed i n the Si(P/Y Q) p r e a c t i o n (Fig. 2.2.1-2 and 2.2.1-6). The widths are shown to be 150 keV and 140 keV r e s p e c t i v e l y . Although these resonances are probably seen i n other reactions, no d e t a i l i n v e s t i g a t i o n has been done. E x c i t a t i o n 28 functions and angular d i s t r i b u t i o n s f o r the Si(p,p^) r e a c t i o n have been investigated i n a few MeV i n t e r v a l s by Greenless et al.(1958) and Oda et a l . (1960) i n t h i s energy region. Prominent changes i n the angular d i s t r i b u t i o n near E =7.50 MeV were observed. A more d e t a i l e d y i e l d curve f o r 45° P proton s c a t t e r i n g from the 2 +(1.77 MeV) state shows a prominent anomaly at E^=8.78 MeV (Oda et.al.1960). Furthermore, Hardekopf et a l . (1972) • showed'that the •'analysing power -for protons '•elastically scattered -by 28 o S i at 155 drops abruptly from an average value of 0.3 to -0.6 at E ~ 7.70 MeV. The analysing power tends to show a maximum (-0.72) at E^~ 8.80 MeV i n comparison to an average of 0.6 (with an uncertainty of ±4%). Unfortunately i n a l l these measurements the energy r e s o l u t i o n (between 70 keV and 200 keV) i s much l a r g e r than i n our measurements. From our cross section and angular d i s t r i b u t i o n measurements on the 28 Si(p,Y o) r e a c t i o n , we are able to assign a p o s s i b l e angular momentum to these states of 3/2. Since the resonances.are not s i g n i f i c a n t i n the (p,p ) r e a c t i o n , the r a t i o T /T i s believed to be f a i r l y P o small. From our measured values of (coF T )/T ( i n Table 2.1) P o Y i t i s seen that tor > Y 47 eV at E = 7.45 MeV; P 46 eV at E = 8.80 MeV. P 124 The enhancement of the r a d i a t i v e widths are obvious and the most l i k e l y p a r i t y assignments of these states are negative ( i . e . E l t r a n s i t i o n s ) . 27 3 29 In the two-nucleon t r a n f e r r e a c t i o n , A l ( He,n) P, three l e v e l s at E = 10.13, 11.16 and 11.80 MeV are strongly populated (Greenfield et al.1972). These l e v e l s appear as strong ;peaks with widths of l e s s than 300 keV, which must be compared with the experimental energy r e s o l u t i o n of =250 keV. Presumably only 2p-.lh states are strongly populated i n t h i s r e a c t i o n . Since i t i s i s o s p i n allowed to reach, the T=3/2 states 29 i n P the l e v e l s at 11.16 and 11.80 MeV could be the same states as we observe i n the (p,v ) r e a c t i o n at E = 11.116 and 11.70 MeV (section o x 3.1 of t h i s work). The l e v e l at 10.13 MeV i s . e n e r g e t i c a l l y c l o s e to 29 the expected t h i r d T=3/2 state i n P. However the p o s i t i o n s and widths of the l e v e l s at .10.13 and 1.1.16 MeV a l s o agree, wi t h i n e r r o r , with the structure we observed at 9.94 .MeV and .11 .,2.4 MeV (i.e.. = -7.-45 .and p 8.80 MeV r e s p e c t i v e l y ) . G r e e n f i e l d e t . a l . are not able to extr a c t information such as spin, p a r i t y or i s o s p i n f o r these l e v i e s . 29 For S i Payne (1968) proposed three negative p a r i t y 2p-lh states, i n the e x c i t a t i o n energy range 10 to.12.50 MeV, v i z E = 11.57 MeV (l/2~ , r ' t = 33 keV), 11.64 MeV ( l / 2 ~ , r + = 33 kev) and 12.30 MeV (3/2~, T*=55 keV) , Using a rotator-particle-model, Choi et al.(1974) proposed three p-wave resonances at E^= 9.16 MeV(3/2~,r f= 103 keV), 9.70 MeV(l/2~ , r f = 72 keV) + and 10.921 MeV (.3/2 ,T « 1 keV) . I t i s most encouraging that the resonances at E =9.94 and 11.24 MeV observed i n t h i s work are wi t h i n x the predicted energy region, i n which i s o l a t e d doorway states are expected. 29 Several experiments on S i have proposed doorway states i n t h i s energy region (Jackson et al.1972, A l l e n et al.1973, Fukuda et al.1973 and . 29 Medsker et al.1974). Hopefully the extension to P of these doorway 125 state c a l c u l a t i o n s , i n c l u d i n g the gamma decay, w i l l provide d e f i n i t e i d e n t i f i c a t i o n of t h i s intermediate structure. Intermediate structure i n the cross sections of proton s c a t t e r i n g 28 of a S i target are experiemntally well known. In the l a s t few years many measurements have been done to inv e s t i g a t e the nature of t h i s 29 intermediate structure (=250 keV i n width) i n the compound nucleus P by 28 .proton -scattering from a S i target f o r e x c i t a t i o n energies i n the giant dipole resonanee region. Angular d i s t r i b u t i o n s have been measured 28 by Shotter et.al.(1970) f o r the " Si(p,p') r e a c t i o n , i n the proton energy range 12 to 15 MeV with a beam r e s o l u t i o n of 100 keV i n 100 keV i n t e r v a l s . T o t a l cross sections were determined f o r a l l r e s i d u a l states 28 from 0.0 to 8.25 MeV. Cross sections f o r the r e s i d u a l S i i n the + + ground state and the lowest 2 , 4 states are shown i n Figure 3.3-lc. Shotter et .al ...observe..that ..the. .structure, .appears to,be .correlated .in d i f f e r e n t reaction: channels and also d i f f e r e n t angles, which i s the pr e d i c t i o n of the doorway state concept (Feshbach et al.1967, also Hsu 1972). However i t i s well, known that at bombarding energies such that the mean l e v e l width (.<]> ) i s much greater than the mean l e v e l energy spacing (<D>) of compound states, the nuclear r e a c t i o n cross sections e x h i b i t f l u c t u a t i o n s as described by the s t a t i s t i c a l model of Ericson (1966). These f l u c t u a t i o n s a r i s e from interference between the overlapping states r e l a t i v e to that of the average cross s e c t i o n . According to t h i s model the cross s e c t i o n should be c o r r e l a t e d over an energy range of about Tir and the degree of f l u c t u a t i o n i n the cross section depends • la r g e l y on the r a t i o <T>/<D>. The model also p r e d i c t s that the average energy spacing, <K> between two neigbpring '-maxima, .in . the e x c i t a t i o n functions i s r e l a t e d to the mean l e v e l width <F>. For <T>/<D> i n the 126 range of 1 to 5 the r a t i o <T>/<K> var i e s slowly and monotonically from 0.3 to 0.55 (Dallimore et al.1966 and Branford et al.1973). That i s <r> - 0.5 <D> U - ° (3.4) Shotter et a l . estimate <T>/<D> as 2.0 f o r i n c i d e n t proton between 12 28 to 15 MeV and have been able to reproduce c o r r e l a t i o n s i n the. Si(p,p') reactions with the s t a t i s t i c a l model. I t could not be determined whether the intermediate structure i n the e x c i t a t i o n functions was due to doorway states or s t a t i s t i c a l f l u c t u a t i o n s . Over-the in c i d e n t energy range 16 to 18.2 MeV Kemper et a l . (1972) measured e x c i t a t i o n functions f o r proton s c a t t e r i n g from the lowest 0 +, 2 + and 4 H i n 2 8 S i at laboratory angles of 60°, 80° and 120° with an energy r e s o l u t i o n of 30 keV.(The 80° measurements are shown i n Fig.3.3-ld .and 3.3-2b f o r comparison)..The ..structure a l l appears to be cor r e l a t e d i n d i f f e r e n t reactions and at d i f f e r e n t angles, since t h i s energy range i s above the (p,n) threshold (Q=-15.5 MeV), the l e v e l density of compound states i s expected to be high. According to the s t a t i s t i c a l model of Ericson the c o r r e l a t i o n s and f l u c t u a t i o n produced by these compound states should disappear i f <T>/<D> >10 (Branford et.al.1973). Since no d e t a i l e d i n v e s t i g a t i o n has been done, the a p p l i c a b i l i t y of the s t a t i s t i c a l model i n t h i s energy range i s not c l e a r . Analysing powers for e l a s t i c a l l y scattered protons at 160° by 28 S i has been investigated by Hardekopf et a l . (1972) f o r a proton energy from 5 to 15 MeV with, an energy r e s o l u t i o n of 150 keV. Considerable f l u c t u a t i o n s i n the analysing power are observed. The analysing power, over the energy range of 12 to 15 MeV i s shown i n Figure 3.3-le. The most prominent structure i s the drop i n an i n t e r v a l =100 keV, from 127 0.6 to 0.0 at =12.2 MeV and then the r i s e back to the average value of 0.6 at E =12.6 MeV. P Based on conclusion given by Payne (.1968) , we speculate that 29 i n the giant dipole resonance region of P the number of 2p-lh states i s so high that overlapping between doorway states i s expected. The compound states considered i n the work of Shotter et a l . are presumably the 2p-lh states c o n s t i t u t i n g the doorway states which lead to the c o r r e l a t i o n between the channels. To i n v e s t i g a t e these p o s s i b l e doorway. states i t i s c l e a r l y more i n t e r e s t i n g to f i n d data which disagree rather than agree with the p r e d i c t i o n s of the s t a t i s t i c a l model. Naturally more s e l e c t i v e reactions must be chosen so that only a c e r t a i n c l a s s of doorway states can be reached or enhanced. Since r a d i a t i v e proton capture i n the giant d i p o l e resonance 29 + region-leading to ground state of P (1/2 ) proceeds e s s e n t i a l l y through, the dipole gamma t r a n s i t i o n s , then i f doorway states are involved i n the reaction, only doorway states with s p i n - p a r i t y of 1/2 and 3/2 are expected to modify the envelope of the giant dipole resonance. S i m i l a r l y , i n the GDR region of the (p,Y^) r e a c t i o n only doorway states of 1/2 , 3/2 and 5/2 are s i g n i f i c a n t , and so some c o r r e l a t i o n between the (p,Y Q) and (p,Y ) reactions i s expected. However the p a r i t y of the 5 ^ excited state i n 2 9 P i s d i f f e r e n t from the ground and f i r s t excited states, and so we expect to populate a d i f f e r e n t .'set of doorway states i n the (p,Y,_) r e a c t i o n . In contrast, a large number of p a r t i a l waves? are expected to contribute i n the s c a t t e r i n g measurements and the t o t a l number of associated 2p-lh. states i s expected to be larger than the r a d i a t i v e proton capture re a c t i o n s . 128 Figures 3.3-la and 3.3-lb are'obtained by drawing a smooth l i n e through the y i e l d curves- shown i n Figures- 2.2.3-2 and 2.3-3 r e s p e c t i v e l y . In spite of the f a c t that the r a d i a t i v e capture e x c i t a t i o n functions-have a slowly varying background ( i . e . the envelope of the giant dipole resonances) intermediate structure of several hundred keV.in width i s c l e a r l y seen i n the cross sections. The peak to v a l l e y r a t i o of the structure i n the tp,Y ). and (p,Y^). y i e l d s i s . i n general l a r g e r than those observed i n the e l a s t i c s c a t t e r i n g measurements (Fig.3.3-lc and 3.3-ld). Dotted l i n e s are drawn through the prominent peaks i n the r a d i a t i v e y i e l d s f o r comparison with structure i n others, channels. The f i g u r e demonstrates that there appears- to be a c o r r e l a t i o n between the structure i n d i f f e r e n t channels. Structure observed at 13.70 MeV i n the (P/Y ) channel could be due to p o s s i b l e experimental errors C-10%i, but t h i s structure i s seen prominently i n the (p,p') 'channels. S i m i l a r l y the structure at E^= 17.80 MeV shows c l e a r l y i n the (p,p^) and (.P/P^ ) channels, but might be a r e s u l t of experimental errors .in the r a d i a t i v e capture channels. Assuming that the structure r e s u l t s from i n t e r f e r e n c e between overlapping compound l e v e l s , then to c a l c u l a t e the mean l e v e l width, we count the number of maxima i n the e x c i t a t i o n functions and use the . expression i n Eq.(3.4). The mean l e v e l width from the (P»Y ) y i e l d and (•PfY^). y i e l d s i n the proton energy range of 12 to 22 MeV i s 588 keV. Since the energy r e s o l u t i o n i n our measurements i s better than 20 keV, there i s no appreciable i n d i c a t i o n i n the cross s e c t i o n of further structure having a width between 20 keV and 250 keV, which i s approximately the width of the intermediate st r u c t u r e . In contrast, i n v e s t i g a t i o n of 28 28 28 25 the Si(p,n) p and Si(p,a) A l reactions over the proton energy range of 16 to 18.2 MeV (Gunn et al.1974) has shown f l u c t u a t i o n s i n the • EXCI TATION IN 2 9 P PROTON ENERGY IN MeV Figure 3.3-1 Intermediate structure i n di f f e r e n t reactions and calculated nucleon decay widths of 2p-lh states of J 1 I=l/2 ,3/2~ and 5/2~.. Ca) and (bl are from present work; Cc) 2 8 S i ( p , p from Shotter et al.C1970); Cd) 2 8SiCp,p n , , ) at 80° from Kemper et a l . 0-972); U r 1 f ^  r Ce) asymmetries in e l a s t i c scattering (Hardekopf et al.1972); Cf) nucleon decay widths of 2p-lh states from Payne (1968) and Keller et al.(1975). 0,1,2 130 e x c i t a t i o n functions over the e n t i r e range with a width'of 100 keV and 48 keV for the neutron and alpha channels, r e s p e c t i v e l y . However, the states i n the (p,Y) and (p,ct) reactions may involve d i f f e r e n t J-values; higher J-values are present i n the (p,a). r e a c t i o n f o r . which a smaller width i s expected (Vonach et al.1965). According to Payne's c a l c u l a t i o n s , i n the e x c i t a t i o n energy 29 range from 14.5 to 17.3 MeV i n S i there are 13 2p-lh. states- of J=l/2 and 3/2 having considerable nucleon decay width (>30 keV as shown i n F i g . 3 . 3 - l f . This means an average energy spacing of 357 keV between two neigboring s t a t e s . S i m i l a r l y Weller,et a l . p r e d i c t (F i g . 3 . 3 - l f , E >15 MeV) an average energy spacing of 465 keV f o r the i n c i d e n t proton P energy range of 15 to 21 MeV. I t i s l i k e l y that the intermediate structure i s a r e s u l t of the existence of doorway states.,: As the observed widths of the. 'intermediate -structure "range °f rom -150- keV --to - 700 keV - i n the (p, Y^).' and (PfY-^) reactions there i s a p o s s i b i l i t y of overlapping between these intermediate structures. The c o r r e l a t i o n between the (p,Y Q) and (p,Y-^) y i e l d s i n the proton energy range of 12 to 15 MeV would then be explained as intermediate structure of 1/2 and 3/2 stat e s . However a strong c o r r e l a t i o n i s not expected i n the region where the inc i d e n t proton energy i s higher than 15.5 MeV since the (p,Y ) r e a c t i o n i s then dominated by the 3/2 o resonance while the (p,Y^) re a c t i o n i s dominated by the 5/2 resonance. Although non-correlated structure i s seen i n t h i s range, the c o r r e l a t e d structure a t E = 17.30 MeV and E = 18.30 MeV could be explained as the P P existence of common 3/2 state(s) a t these energies. A lack of information on the gamma decay aspect of the c a l c u l a t e d 2p-lh states means a d i r e c t comparison with the r a d i a t i v e proton capture 131 reactions is. impossible. However the energy d i s t r i b u t i o n of the 1/2 and 3/2 2p-lh states seem to show a p i c t u r e s i m i l a r to that observed i n the (P/Y ) y i e l d curve, that i s a higher density of intermediate structure between 12 and 14 MeV i n c i d e n t proton energy. No c a l c u l a t i o n on 5/2 2p-lh states above E = 17.5 MeV i s a v a i l a b l e . However i n the x (p,Y^) y i e l d curve the intermediate structure i n t h i s energy range i r -r e l a t i v e l y simple. Perhaps only a small number of these 5/2 states- are observable i n the (p,Y^) channel. Although a d i r e c t comparison with, the analysing power i s not possible the existence of intermediate structure i n the measurements,^ i s quite c l e a r . We note i n passing that intermediate structure of v a r i a b l e widths from 300 keV to 1.5 MeV has been observed i n the analyzing power e x c i t a t i o n functions f o r i n e l a s t i c s c a t t e r i n g of p o l a r i z e d protons-26 27 •from 'Mg and A l (Glashausser et al.1975). These structures are not shown s i g n i f i c a n t l y i n the e x c i t a t i o n functions f o r i n e l a s t i c s c a t t e r i n g , of unpolarized protons. Perhaps, to understand these intermediate structures, i t would help to study more s e l e c t i v e r e a c t i o n such as the asymmetry measurements o f the angular - d i s t r i b u t i o n i n the r a d i a t i v e capture of p o l a r i z e d protons. The i n t e r p r e t a t i o n of the r a d i a t i v e capture measurements i s b e l i e v e d to be more s t r a i g h t forward than that of the i n e l a s t i c s c a t t e r i n g measurements. F i g . 3.3-2a i s obtained by drawing a- smooth l i n e through the . 28 29 y i e l d of the S i ( p , y 5 ) P(5/2 or 7/2, 3.45 MeV) shown i n Fig.2.4-2. The presence of intermediate structure at E =17.20 MeV and 17.80 MeV P i s c l e a r l y shown. Fig.3,3-2b i s obtained from the work of Kemper e t a l . (1972). The structure at =17.80 MeV appears,tobe c o r r e l a t e d i n d i f f e r e n t channels. The c a l c u l a t e d proton decay widths of 2p-lh states EXCITATION I N 2,2 29r 1 1 1 ! 1 1 ! 1 1 16 17 P R O T O N E N E R G Y ( M e V ) Figure 3.3-2 Intermediate structure i n d i f f e r e n t reactions and calculated nucleon decay widths of TT + 28 28 2p-lh s t t t e s of J =9/2 . (a) SiCPrY-) y i e l d from t h i s work; (b) Si(p,p ) from Tf + 0/lf2 Kemper et al.(1972); (c) nucleon decay widths of J =9/2 2p-lh states (Weller et al.19751 133 + having s p i n - p a r i t y of 9/2 shown i n Fig.3.3-2c i s ' t h e work of Weller et al.(1975). A p o s s i b l e 15% experimental er r o r i n our e x c i t a t i o n function 28 f o r the Si(p,Y 5) r e a c t i o n means that some of the intermediate structure between E = 18 and 24 MeV.could be a r e s u l t of t h i s e r r o r . However the P 2p-lh state at E^= 19.50 MeV, of decay width approximately 550 keV', predicted by Weller et a l . , i f i t e x i s t s , does not stand out s t r o n g l y i n the (p,Y^) r e a c t i o n . Ofcourse i t i s p o s s i b l e that the states- decay very slowly to the giant dipole state or that the. gamma decay- width. 29 to the f i n a l state i n P i s very small. It i s i n t e r e s t i n g to compare the structure i n our r e s u l t s 27 28 with the structure within GDR observed i n the A l (p,y) S i (.Singh et 23 24 31 32 al.1965), Na(p,Y) Mg (Bearse et al.1968) and P(p,Y) S (Mason et al-:l»969) "-react-ions.' Two c h a r a c t e r i s t i c widths, -a - f i n e - structure - about 60 keV to 75 keV wide and an intermediate structure few hundred keV wide, 24 28 32 are revealed within the GDRs of Mg, S i and S. The f i n e structure c o n s i s t s of Ericson f l u c t u a t i o n s due to the actual l e v e l s of the compound 28 nucleus, while the intermediate structure i n S i i s i n t e r p r e t e d as-a r i s i n g from "doorway states". The absence of f i n e structure i n n u c l e i of mass 20 or l i g h t e r has been in t e r p r e t e d by Segel et a l . (1967).who suggested that the intermediate states that connect the GDR state to the compound nucleus states are i n d i s t i n g u i s h a b l e from the a c t u a l .• 29 compound nucleus st a t e s . Since P i s an odd mass nucleus, perhaps the unpaired nucleon has played an important r o l e i n the compound nucleus system such that the c h a r a c t e r i s t i c s of the compound, states strongly, deviate from those i n an even-even compound nucleus such as 2 4 , » 2 8 o - -, 3 2 ^ Mg, S i and S. 134 Ov e r a l l i t would be i n t e r e s t i n g i f c o r r e l a t e d f i n e structure representing more complex configuration such as 3p-2h states can be found within the intermediate structure i n higher r e s o l u t i o n measurements (viz better than 10 keV or so), but the high density of 2p-lh states i n t h i s energy region means that the studies of the configurations of these doorway states w i l l be very d i f f i c u l t . However the extension of doorway state c a l c u l a t i o n s to the gamma decay aspect i s now j u s t i f i e d . 135 LIST OF REFERENCES Akyuz,R.O., and F a l l i e r o s , S . , Phys.Rev.Lett. 27,1016 (1971) Alias,R.G., Hanna,S.S., Meyer-Schiitzmeister,L., and Segel,R.E., Nucl.Phys. 58_, 122 (1964) . ' . Allen,B.J., Macklin,R.L., i n Proc. of the International Conference on Photonuclear Reactions and A p p l i c a t i o n s , Asilomar, Edited by BermanmB.L.,(Lawrence Livermore Lab., Univ. of C a l i f o r n i a , Livermore, 1973) . Alvarez,R.A., Berman,B.L., Lasher,D.R., Phillips,T.W., and Fultz,S.C., Phys.Rev.£4,1673 (1971). Azuelos,G., Kitching, J.E., Phys.Rev.Abstr. 6_,No. 14,17 (.1975) . Anataraman,N., Draayer,J.P., Gove,H.E.f and Trentelman,J.P., Phys. Rev.Lett. 33,846 (1974). Arvieux,J., Buenerd,M., Cole,A.J., DeSaitigonon,P. and Perrin,G., Horen,D.J., Nucl .Phys .A247, 238 (.1975) . Baldwin,G.C., and Klaiber,G.S., Phys.Rev. 73,1156(1948). Barrett,R.F., Biedenharn,L.C., Danos,M., Delsanto,P.P., Greiner,W., and Washweiler,H.G., Rev.Mod.Phys. 45,44 (1973) Bearse,R.C, Meyer-Schutzmeister,L., and Segel,R.E., Nucl.Phys. A116/682(1968). Bearse,R.C, Youngblood,D.H., and Yntema, J.L., Phys.Rev. 167,1043 (1968a). Becker,F.A., Byrski,T., Costa,G., and Engelstein,P., Nucl.Phys. A218,2I3(1974). Berghofer,D., M.Sc.Thesis, U n i v e r s i t y of B r i t i s h Columbia (1974). also Berghofer,D., Hasinoff,M.D., Lim,S.T., and Measday,D.F., (to be published). Berman,B.L., and Fultz,S.C., Rev.Mod.Phys. 47_, 713 (1975) . Bevington,P.R., "Data reduction and error a n a l y s i s f or the p h y s i c a l sciences",McGraw-Hill (1969). Bezic,N., Jamnik,D., Kernel,G., K r a j n i k , J . , and Snajder,J., Nucl. Phys. A117,124 (1968). Black,J.L., O'Connell,J.S., Hanna,S.S., and Latshaw,G.L., Phys.Lett. 25B,405(1967). B l a t t , J M., and Weisskopf,V.F., "Theoretical Nuclear Physics", John--Wiley, 7th p r i n t i n g (1969) . 136 Boyd,R.N., Kaminstein,J., Arking,H., and Clement,H., Phys.Rev. C12,14(1975). Branford,D., P a r t i c l e s and Nuclei j5,127 (1974). Branford,D., and Newton,J.O., I n s t i t u t e of Advance Studies Report, A u s t r a l i a n National U n i v e r s i t y , ANU-P/583 (1973). Brassard,C, Shay,H.D., Coff i n , J . P . , Scholz,W., and Bromley,D.A., Phys.Rev. C6,53(1972). Brink,D.M., Nucl.Phys. 4_, 215 (1957) . Bromley,D.A., Gove,H.E., and Litherland,A.E., Can.J.Phys. 35,1057 (1957). Brown,G.E., and B o l s t e r l i , M . , Phys.Rev.Lett. 3_,472 (1959) . Brown,G.E., "Unified theory of nuclear models and forces", North-Holland, Amsterdam(1967). Brown,G.E., "Microscopic models", Proceeding of International Conference on Photonuclear Reactions and A p p l i c a t i o n s , edited by Berman,B.L., page 57 (1973). Calarco,J.R., Hanna,S.S., Kuhlmann,E., and Mavis,D.G., Nuclear. Physics Laboratory Annual Report, Stanford U n i v e r s i t y (1974). Caldwell,J.T., Harvey,R.R., Bramblett,R.L., and Fultz,S.C., Phys.Lett. 6^,213(1963). Carr,R.W., and Baglin,J.E.E., Nucl.Data Tab. A10,143 (1972) . Chang,C.C., Ber trand, F . E. , and Kocher,D.C, Phys. Rev. L e t t . 34, 221 (1975) . also Progress Report, Cyclotron Lab.,Univ. of Maryland(1974). Chew,S.H., Lowe,J., and Nelson,J.M.-, Nucl.Phys. A229,241 (1974) . Choi,B.H., Divadeenam,M., Nuovo Cimento L e t t . 9_, 375 (1974) . Cohen,A.V., and Cookson,J.A., Nucl.Phys. 24,529 (1961). Coker,W.R., Udagawa,T., and Hoffmann,G.W., Phys.Rev. CIO,1792 (1974). Courtney,W.J., and Fox,J.D., Atomic and Nuclear Data Tables 15,141 (1975). Dallimore, P. J . , and H a l l , I . , Nucl.Phys. 88,193 (1966):. Dearnaley, G., Gemmell,D.S. , Hooten,B.W. , and Jones,G.A., Nucl.Phys-. 64,177(1965). D e t r a z , C , and Richter,R., Nucl.Phys. A158_, 393 (1970) . DeVoigt,M.J.A., Glaudemans,P.W.M., DeBoer,J., and Wildenthal,B.H., Nucl.Phys. A186,365 (1972). 137 Diener,E.M., Amann,J.F., Blatt,S.L., and Paul,P., Nucl.Instr. and Meth. 83_, 115 (1970) . Diener,E.M., Amann,J.F., and Paul,P., Phys .Rev. C3_, 2303 (1971) . Diener,E.M., Amann,J.F., and Paul,P., Phys.Rev. C7,695C1973). Diener,E.M., Amann,J.F., and Paul,P., Phys.Rev. C7,705(1973a). Eisenberg,J.M., and Greiner,W., "Nuclear Models", (1970); " E x c i t a t i o n mechanisms of the nucleus", (1971); "Microscopic theory of the nucleus",North-Holland (1972). E j i r i , H . , Nucl.Phys. A52 f578 (1964). E l l i o t t , J . P . , and Flowers,B.H., Proc.Phys.Soc. (London) Ser. A242,57 (1957). Endt,P.M., and van der Leun,C., Nucl.Phys. A214,1 (1973). Ericson,T., and Mayer-Kuckuk, Ann.Rev.Nucl•Sci. 16,198(1966). Fagg,L.W., Bendel,W.L., Jones, E . C , Kaiser, H.F., and Godlove,T.F., Phys.Rev. 187,1384(1969). Fagg,I,.W., Rev.Mod.Phys. 47,683 (.1975) . Ferrell,R.A., and MacDonald,W.M., Phys.Rev.Lett. 16,187 (1966). Feshbach,H. f Kerman,A.K., and Lemmer,R.H., Ann.Phys. (NY) 41,230(1967). Fisher,G.A., Ph.D. t h e s i s , Dept.of Phys.,Stanford U n i v e r s i t y (1970). Fisher,G.A., Kurjan,P.M., Calarco,J.R., Glavish,H.F., and Kuhlmann,E., Nuc1.Phys.Lab., Annual Report,Stanford U n i v e r s i t y (1974). Fowler,W.A., Lauritsen,C.C., and Lauritsen,T., Rev.Mod.Phys. 20, • 236 (1948). Fukuda,K., and Okabe,S., J.Phys.Soc.(Japan) 34,315 (1973) . Fultz,S.C., Caldwell,J.T., Berman,B.L., Bramblett,R.L., and Harvey,R.R., Phys.Rev. .143,790(1966) . F u l t z , S.C, Alvarez,R.A. , Berman,B.L., Kelly,M.A., Lasher,D.R., Phillips,T.W., and McElhinney,J., Phys.Rev.C4,149 (1971). Gellie,R.W., Lokan,K.H., and Sherman,N.K., Proc. of In t e r n a t i o n a l Conference on Photonuclear Reactions and Applications,Asilomar, edited by Berman,B.L.(1973). Gell-Mann,M., and Telegdi,V., Phys.Rev. -91,160 (.1953) • Glashausser,C., Robbins,A.B., Ventura,E., Baker,F.T., Eng,J., and Kaita,R., Phys.Rev.Lett. 35,494 (1975). Goldhaber,M., and T e l l e r , E . , Phys.Rev. 74,1046 (1948). 138 Goosman,D.R., Davids,C.N., and Alburger,D.E., Phys.Rev C8,1331(1973). Greenfield,M.B., Bingham,C.R., Newman,E., and Saltmarsh,M.J., Phys.Rev. C6_, 1756 (1972) . Greenless,G.W., Kuo,L.G., Lowe,!,.-, and Petrauic,M., Proc.Phys.Soc. (London) 71,347(1958). Gunn,G.D., Kemper,K.W., and Fox,J.D., Nucl.Phys. A232,176(1974). Hanna,S.S., "Isospins i n Nuclear Physics",edited by Wilkinson,D.H., page 591, North-Holland(1969). Hanna,S.S., Glavish,H.F., Avida,R., Calarco,J.R., Kuhlmann,E., and LaCanna,R., Phys.Rev.Lett. 32,114 (1974). Harakeh,M.N., Paul,P., and Snover,K.A., Phys.Rev. Cll,998 (1975). a l s o Harakeh,M.N., Paul,P., and Gorodetzky,Ph., Phys.Rev. Cll,1008 (.1975) . Hardekopf,R.A., Armstrong,D.D., and Keaton,J.W.Jr., Nucl.Instr. and Meth. 103,425(1972). Hasinoff,M.D., Ph.D. t h e s i s , Department of Physics, Stanford Univ. (1970). Hasinoff ,M.D., Fisher,G.A., and Hanna,S.S., Nucl.Phys. A.195 (1972) . Hasinoff,M.D., Fisher,G.A., and Hanna,S.S., Nucl.Phys. A216, (1973) . -•"Hasinoff ,M .D., \LimyS; T., "Measday, D-.F., •-•and - Mulligan ;T. J ;y Nucl .-Tnstr. and Meth. 117,375(1974). Haywa.rd,E., "Photonuclear Reactions", National Bureau of Standard Monograph 118, U.S.A.(1970). Hayward,E., Gibson,B.F., and O'Connell,J.S., Phys.Rev. £5,846(1972). HirkOfR.G., Lindgren,R.A., Howard,A.J., Pronko,J.G., Sachs,M.W., Bromley,D.A., P a r t i c l e s and Nuclei .1,372 (1971). Hsu,C.C, Phys.Rev.Lett. 28,45 (1972) . Jackson,H.E., and Toohey ,R.E., Phys .Rev.Lett. 29_, 379 (1972) . Jaffee,A.A., Des Barros,F., Forsyth,P.D., Muto,J., T a y l o r , I . J . , and Ramavataram,S., Proc.Phys.Soc. (London) ,76,914 (1960). Janecke,J., "Isospins i n Nuclear Physics", edited by Wilkinson,D.H., North-Holland(1969). Johnstone,I.P., and Castel,B., Nucl.Phys. A213,341 (1973); also Can.J.Phys. 51,988(1973). Jones,A.D.W., Phys.Rev. 180,997 (1969). Jones,A.D.W., Becker,J.A., and McDonald, R.E. , Phys.Rev. 187,1388 (.1969) . 139 Jones,A.D.W., Becker,J.A., and McDonald,R.E., Phys.Rev. C3,724 (1971). Katz,L., Haslam,R.N.H., Goldemberg, J . , and Taylor, J.G.V., Can.J. Phys. 32_, 580 (1954) . Kean,D.C., Carter,K.W., Piluso,C.J., and Spear,R.H., Nucl.Phys. A132,241 (1969). Kemper,K.W., Fox,J.D., and Oliver,D.W., Phys.Rev.C5,1257 (1972). Kernbach,K.G., Nuovo Cimento L e t t . 3_,461 (1970) . Kuan,H.M., Hasinoff,M., O'Connell,W.J., and Hanna,S.S., Nucl.Phys. A151,129(1970). Kuhlmann,E., Ventura, E'., Calarco, J.R., Mavis,D.G., and Hanna,S.S., . Phys.Rev.Cll, 1525(1975). Kurjan,P.M., Fisher,G.A., Calarco,J.R., Kuhlmann,E., Glavish,H.F., and Hanna,S.S., Annual Report,Nucl.Phys.Lab., Standard Univ. (1974) Lane,A.M., Ann. Phys. (NY). 63,171 (1971). Leonardi,R., and L i p p a r i n i , E . , Phys.Rev. Cll,2073Q975); also Leonard!,R., and Rosa-Clot,M., Phys.Rev.Lett. 23,874(1969)1. Lewis, M.B., and Bertrand, F . E. , Nucl.Phys. A196, 337 (.1972) . Mahaux,C, Ann.Rev.Nucl.Sc.i. 23_, 193 (1973) . ' . Marangoni,M., and Saruis,A.M., Nucl.Phys. A166,397 (1971). Mason,W.M., Tanner,N.W., and Kernel,G., Nucl.Phys. A135,193(1969). Mason,W.M., Tanner ,N.W., and Kernel,G., Nucl.Phys. A138_, 253 (1969) . Measday,D.F., Clegg,A.B., and Fisher,P.S., Nucl.Phys.61,269(1965). Measday,D.F., Hasinoff,M.D., and Johnson,D.J., Can.J.Phys. 51,1227 (1973) Medsker,L.R., Jackson,H.E., and Yntema,J.L., Phys.Rev. C9,1851 (1974). Mekjian,A., "Advances i n Nuclear Physics", edited by M.Baranger and E.Vogt 1_, 1 (1973) . Merrnaz,M.C., Whitten,C.A.Jr., Champlin,J.W., Howard,A.J., and Bromley,D.A,, Phys.Rev. C4,1778 (1971). Morinaga,H., Phys.Rev..97,444(1955). Morsch,H.P., Dehnhard,D., and Li,T.K., Phys.Rev.Lett. 34,1527(1975). Moss,J.M., Rozsa,C.M., Bronson,J.D., and Youngblood,D.H., Phys.Lett. 53B,51(1974). Moss,J.M., Rozsa,C.M., Youngblood,D.H., Bronson,J.D., and Bacher,A.D., Phys.Rev.Lett. 34,748(1975). Nagao,N., and Torizuka,Y. , Phys .Rev .Lett. ,30_, 1068 (1973) and references t h e r e i n . Nolen,J.A., and S c h i f f e r , J . P . , Ann.Rev.Nucl.Sci. 19,471 (1969). 140 Oda,Y., Takeda,M., Yamazaki,T., Hu,C, K i k i c h i , K . , Kobayashi,S., Matsuda,K., and Nagahara,Y., J.Phys.Soc. (Japan) 5_, 760 (1960) . O'Connell, J.S.., Phys.Rev.Lett. 22,1314 (1969) . Paul,P., "Isospin s p l i t t i n g of the giant d i p o l e resonance", Proc. of Int. Conf. on Photonuclear Reactions and A p p l i c a t i o n s , edited by Berman,B.L.(1973). Payne,G.L., Phys.Rev. 174,1227 (1968). Pilt, A . A . , Spear,R.H., E l l i o t , R . V . , and Kuehner,J.A., Can.J.Phys. 49,1263(1971). Segel,R.E., Vager,Z., Meyer-Schutzmeister, Singh,P.P., and Alias,R.G., Nucl.Phys. A93,31 (1967) . Shakin,C.M., and Wang,W.L., Phys.Rev.Lett. 26,902(1971). Shay,PI.D., Peschel,R.E., Long,J.M., Bromley,D.A., Phys.Rev. C9, 76(1974). Sherman,N.K., Lokan,K.H., and Gellie,R.W., "Proc. of Int. Conf. on Photonuclear Reactions and A p p l i c a t i o n s " , A s i l o m a r , C a l i f o r n i a , edited by Berman,B.L. (1973). Shotter,A.C., Fisher,P.S., and Scott,D.K., Nucl.Phys. A159, 577 (.1970) . "Singh,P.P., Segel,R.E., Meyer-Schutzmeister,L., HannafS.S., and A l i a s , R . C , Nucl.Phys. 65,577(1965). also Meyer-Schutzmeister rL., Vager,Z., Segel,R.E., and Singh,P.P., Nucl.Phys. A108,180(1968). Snover,K.A., Ph.D. t h e s i s , Dept. of Physics, Stanford University(1969). Snover,K.A., Adelberger,E.G., Brown,D.R., Lim,S.T., Annual Report, Nuc1.Phys.Lab., Univ. of Washington, Seattle,Washington(1973). Snover,K.A., Adelberger,E.C., and Brown,D.R., Phys.Rev.Lett. 32,114 (.1974) . Snover,K.A., and Paul,P., Annual Report, Nucl.Phys.Lab., Univ."of Washington,Seattle,Washington(1974). Spear,R.H., Cairns,J.E., Elliott,R.V.,Kuehner,J.A., and P i l t , A . A . , Can.J.Phys. 49,355(1971). Spicer,B.M., "Advances i n Nuclear Physics", edited by M.Baranger and E.Vogt,2_,l (1969) . Storm,E., and Isreal,H.I., Nucl.Data Tab. A7, 565 (.1970) . Suffert,M.,"Proc. of Int. Conf. on Photonuclear Reactions and A p p l i c a t i o n s " , edited by Berman,B.L. (.1973) . 141 Tanner,N.W., Thomas,G.C., and Earle,E.D., Nucl.Phys. 52, 29 (.1964) . Teitelman,B., and Temmer,G.M., Phys.Rev. 177,1656 (.1969) . Thomas,R.G., Phys.Rev. 81,148 (1951); Phys.Rev. 88_, 1109 (1952) ; als o Lane,A.M., and Thomas,R.G., Rev.Mod.Phys. 30, 257(1958). Vonach,H.K., and Huizenga,J.R., Phys.Rev. 138,1372 (1965). Weitkamp,W.G., and Schmidt,F.H., Nucl.Instr. and Meth. 122,65 (1974). Weller,H.R., and Divadeenam,M., Phys.Lett. 55B,41(1975) and references t h e r e i n . Wildenthal,B.H., and McGrory,J.B., Phys.Rev. C7,714(1973). Wilkinson,D.H., Physica 22,1039(1956); also Ann.Rev.Nucl.Sci. 9_,1(1959). Wilkinson, D. H., e d i t o r , "Jsospins i n Nuclear Physics", North-Holland (.1969) . Williams,J.R., Nelson,R.O., Gould,C.R., and Tilley,D.R., Phys.Rev. £11,1111(1975). Woodworth, J.G., Jury,J.W., Lokan,K.H., and Sherman,N.K. ,. Can. J.Phys. 53,795(1975) . Wu,C.P., Firk,F.W.K., and Phillips,T.W., Nucl.Phys. A147,19 (1970). Wyckoff, J.M., Ziegler,B., Koch,H..W., and Uhlig,R., Phys.Rev. 137, .576(1965). 142 APPENDIX DIPOLE SUM AND INDEPENDENT PARTICLE MODEL Following the independent p a r t i c l e model of nuclear photo-e f f e c t suggested by Wilkinson (Wilkinson 1956 and Hayward 19701 i t . i s -i n s t r u c t i v e to show that the giant resonance i s ascribed to the e l e c t r i c dipole absorption of photons by the valence nucleons and those i n the uppermost f i l l e d s h e l l . These p a r t i c l e s make transitions- upward to the next u n f i l l e d s h e l l of opposite p a r i t y according to the di p o l e s e l e c t i o n r u l e A.£=±l . The e l e c t r i c d i pole t r a n s i t i o n p r o b a b i l i t y .for a s i n g l e p a r t i c l e to proceed from state ¥ • to Y 2 i s ~2 2 D = q T z Y d r (A.l) where q i s the e f f e c t i v e charge of the sing l e p a r t i c l e and z may be written as / — r Y , „ m term of the s p h e r i c a l harmonic function Y , „ . / 3 10 ^ 10 Assuming that the i n i t i a l state i s a c l o s e d - s h e l l nucleus, and for convenience introducing'a harmonic o s c i l l a t o r p o t e n t i a l so that a l l nucleons i n the s h e l l of spin j have the same r a d i a l wave function R^ , then the t o t a l p r o b a b i l i t y f o r a nucleon i n the j s h e l l (of t o t a l 2j^+l nucleons) to proceed to the s h e l l of j i s 4TT 2 . i m i m 2 2"'"2' "101 3 i m i > r R R 2 dr Applying the Wigner-Eckart theorem to the summation over m^ , the z pr o j e c t i o n of the t o t a l spin j , we obtain 4TT 2 . I . 2 <5 2||Y 1||j >• q X. < D 2 m 2 1 0 | n 2 m 2> -•- • -m2 2 j 2 + 1 r R ] L R 2 d r 143 where ^ <j.m210| j ^ 2 = J _ < J 2 l | Y 1 l | j 1 > = (2j 1+l) C j ^ l O j ^ ) 2 ^ -2 More e x p l i c i t l y D may be expressed as 2 D 2 = - 2 - (.2j.,_+!) <J 1 3sl0| j 2^> 2 dr r R R 2 (A.2J as the p r o b a b i l i t y f o r a nucleon to be excited from the closed j s h e l l v i a E l photo-absorption. Since we assume that the independent p a r t i c l e model i s applicable to t h i s nucleus, then the p r o b a b i l i t y f o r a p a r t i c u l a r s i n g l e nucleon to be excited i s 2 (• D 2=-^- <J^10| j ^ > 2 j r 3 R l R 2 dr 2 ........ For an u n f i l l e d s h e l l , i f there are n nucleons i n the s h e l l the p a r t i a l p r o b a b i l i t y contained i s D 2 _ ng . <J13-5.io| jh>2 r R 1R 2 dr CA.4) The e l e c t r i c dipole absorption can be r e l a t e d to the p r o b a b i l i t y as follow a- (E) dE = A 2 4TT E He k (A. 5) where E i s the energy spacing between state 4* and ¥ . For the simple - 1 / 3 harmonic o s c i l l a t o r , a l l the t r a n s i t i o n s have the energy =41 A MeV 2 and by summing the t r a n s i t i o n p r o b a b i l i t i e s , D , over a l l nucleons one can show (at l e a s t f o r l i g h t nuclei) that 2 wz M A Mw The integrated absorption cross section i s then , 2 2 , x n 2-rr e H NZ 0(E) dE = — Mc A NZ 60 - i — mb-MeV . A (A. 61 144 This r e l a t i o n i s known as the c l a s s i c a l dipole sum r u l e and the quantity on the right-hand-side i s u s u a l l y r e f e r r e d to as. the. t o t a l dipole sum. b u i l t upon a s t a t e . This sum r u l e a p p l i e s not only f o r the simple harmonic o s c i l l a t o r p o t e n t i a l but also for other p o t e n t i a l s . D e r i v a t i o n of the sum r u l e based on a more general i n t e r a c t i o n may be found i n some standard text book (such as Eisenberg and Greiner 1970). The p a r t i a l dipole sum f o r a p a r t i c u l a r nucleon may also be evaluated by using Eq.(A.3) and the values, a f t e r d i v i d i n g by the t o t a l dipole sum (.Eq. CA.6)) are shown i n Table 3.4 for several n u c l e i . I l l u s t r a t i v e c a l c u l a t i o n s are shown at the end of t h i s appendix. The observed integrated t o t a l cross section of photon absorption f o r n u c l e i of A >28 generally exhausts the c l a s s i c a l dipole sum r o l e to within 10 to 20 percent when the i n t e g r a t i o n i s extended over tile g iant d i p o l e resonance up to 30 MeV or so. Example: To c a l c u l a t e the f r a c t i o n a l d i p o l e sum f o r the E l t r a n s i t i o n s of 29 the 2s. proton i n P. From Eqs. (A.3) and (A.5) we have,. a, (E) dE k 4 IT E, 2 He r R R dr 4TT 2 q Mc - < i ^ l 0 | . j >s> MID Ls 2 O r R l R 2 d r where j -h. F r a c t i o n a l d i p o l e sums f o r the 2s, -*2p. and 2s, -y 2p ,„ 1 h. h h *- 3/2 t r a n s i t i o n s are J 1 4 9 0 0 rj(E) dE = 39.86 (-—- )Z< hh 1 0 | h h> I (mb-MeV) "14 9 I 9 9 a(E) dE = 39.86 (-^- ) < h h 1 0 | 3/2 \> I (mb-MeV) 2 m r e s p e c t i v e l y and I = - ° n j r R 1 R 2 d r Using tables shovm at the 145 end of t h i s appendix f o r the Clebsch-Gordan c o e f f i c i e n t s and the r a d i a l i n t e g r a l s we obtain 1.8% and 3.6% of the c l a s s i c a l dipole sum r u l e 29 r e s p e c t i v e l y . The c l a s s i c a l dipole sum r u l e , 60 NZ/A mb-MeV, f o r P i s 434 mb-MeV. J 2 <J1^IO1J2'5> j l + 1 ( j 1+ 3s) (J 1+3/2) H ( 2 j ^ - l ) j l h h(h+1)\h V 1 j l ( 2 ^ + 1 ) MOJ o j . - -2 f 3r r R o R „ dr J n i £ l V? n 2 = n and l2 = £ 1 + 1 . (n 1 + l1 + h)h n 2 = n +1 and V=V-i 

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