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Measurement of spin asymmetry parameters in the [reaction proton + proton --> proton + neutron + positive… Shypit, Rickey Lee 1983

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c . • MEASUREMENT OF SPIN ASYMMETRY PARAMETERS IN THE pp > pnrr + REACTION By RICKEY LEE SHYPIT B.Sc. The University of Winnipeg, 1979 M.Sc. The University of B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (PHYSICS) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1983 © Rickey Lee Shypit, 1983 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. It i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 1Q\ i i ABSTRACT Measurements have been made of the spin asymmetry parameters ^ L L ' ^SS' ^SL' ^NO a n < ^ ^ON * n t n e ^ n e ^ - a s t i c r eac t ion pp •*• p n f + at inc ident beam energies of 510, 465 and 420 MeV. The measurement of A ^ i s described s p e c i f i c a l l y . This experiment has reported the f i r s t r e s u l t s of a sp in asymmetry measurement with a po la r i zed beam and po la r i zed target i n a reac t ion having a three p a r t i c l e f i n a l s t a te . Neutrons were d e t e c t e d i n an a r r a y of p o s i t i o n s e n s i t i v e s c i n t i l l a t i o n counters while the two charged p a r t i c l e s were detected i n an array of mul t i -wire propor t iona l chambers. Time of f l i g h t was recorded for the neutron. Events were k i n e m a t i c a l l y reconstructed i n the ana lys i s program i n which free and quas i- free s ca t te r ing events were separated by a X 2 test to the k inemat ica l f i t . The unpolar ized background from non-hydrogenous mater i a l i n the target was estimated from unpolar ized data obtained with the target mater i a l replaced by t e f l o n . Results are presented as asymmetries binned against s ing le kinematic v a r i a b l e s . The s t a t i s t i c a l p r e c i s i o n i s 10% on the best data . The data are s u f f i c i e n t l y complete to i d e n t i f y the dominant p a r t i a l wave amplitudes. A comparison i s made with c a l c u l a t i o n s based on a one-pion-exchange A dominance model. Discrepancies from the model are a t t r i b u t e d the neglect of the TTN S 3 1 i n t e r a c t i o n i n the c a l c u l a t i o n s . i i i ACKNOWLEDGEMENTS I would l i k e to thank my colleagues i n the BASQUE group with whom t h i s work has been done. They are D. Axen, D. Bugg, J . Edgington, F . Entezami, M. Comyn, D. Healey, G. Ludgate, N. Stevenson, G. Wait and C. Waltham. As I am perhaps the l a s t student with the BASQUE group, I f e e l fortunate to have worked on th i s experiment. I would also l i k e to thank many at TRIUMF and U . B . C . who have spared time f r e e l y to help me. Thanks go to N. Stevenson and C. Waltham for t h e i r part i n making the analys i s of th i s experiment progress r a p i d l y and to C.W. for c a r e f u l l y checking the manuscript . I thank Professor Bugg for his many valuable suggestions and exper t i se . I e s p e c i a l l y thank Professor Dave Axen, my supervisor for the past four years , for h i s constant encouragement, good advice and good humor. I look forward to working with him aga in . i v TABLE OF CONTENTS Page I. INTRODUCTION 1 1.1 Exchange Nature of the Nucleon-Nucleon Force 1 1.2 Resonance Phenomena i n Nuclear Scattering 2 1.3 Need for Spin Dependent Measurements i n the I n e l a s t i c Channel 4 1.4 The TRIUMF Program 6 I I . THEORY AND FORMALISM 8 I I . 1 The Spin Scattering Matrix 8 11.2 Phase S h i f t Analyses 14 11.3 Matrix Elements of the pp •*• pnrr + Reaction 23 11.4 The Comparison Model 30 I I I . EXPERIMENTAL FACILITY 36 111.1 Cyclotron 36 111.2 Proton Polarimeter 38 111.3 Neutron Collimator 39 111.4 UCLA Bending Magnet 43 111.5 Focussing and Steering Magnets 43 111.6 4C Monitoring System and Beam Defining S c i n t i l l a t o r s 43 III.7a Polarized Proton Target 44 III.7b Background from Non-Hydrogenous Material 46 I I I . 7c NMR P o l a r i z a t i o n Monitor 47 III.7d Independent C a l i b r a t i o n of the Target P o l a r i z a t i o n . 48 III.8 The Forward Angle Chambers 48 V CONTENTS (Continued) I I I . 9 The Neutron Detector 51 IV. DATA ACQUISITION 57 IV. 1 The Configuration 57 IV.2 The Incident Beam Monitor 59 IV.3 The P T T + Component of the Trigger 59 IV.4 The Neutron Component of the Trigger 61 IV.5 The Three P a r t i c l e Trigger 61 IV.6 Data Transfer 65 IV.7 On-Line Monitoring and Setting Up 71 IV. 8 S t a t i s t i c s for the A ^ Measurement 73 V. DATA ANALYSIS 76 V. l Stage I: Reduction to Summary Tapes 77 V.2 Stage I I : x 2 Event Reconstruction 81 V.2a Decoding of the Neutron Array 81 V.2b Least Squares F i t to a pim+ Event 86 V.2c Background Subtractions 90 V.2d Additional Cuts 94 V.3 Stage I I I : Binning and Presentation of the Data .... 98 V.3a The Choice of a Coordinate System 98 V.3b Extraction of A ^ , A ^ , and A Q N 103 VI. RESULTS AND CONCLUSIONS 105 Summary 124 v i Contents (Continued) REFERENCES 135 APPENDIX A: Parameterizat ion of Charged P a r t i c l e Def lect ions i n the Magnetic F i e l d of the Polar ized Target 139 APPENDIX B: C a l c u l a t i o n of the Target P o l a r i z a t i o n by the Method of E l a s t i c Nuclear Scat ter ing 148 v i i LIST OF FIGURES Page 2-la The Orthogonal Unit Vectors £, q, and n in the C.M. Reference Frame ( n o n - r e l a t i v i s t i c kinematics) 12 2-lb The Orthogonal Unit Vectors L, £, and N i n the Lab Reference Frame 12 2-2 Phase S h i f t s of the Proton-Proton System for J<6 21 2-3a Feynman Diagram for A + B->- C + D 29 2-3b D e f i n i t i o n of the Gottfried-Jackson and Triemann-Yang Decay Angles (0 ,$) 29 2- 4 Single Pion Production i n the Reaction pp •* pmr + v i a the P 3 3 and P A 1 Isobars 33 3- 1 The TRIUMF Cyclotron and Experimental Areas 37 3-2 Proton Beam Polarimeter 40 3-3 E l e c t r o n i c Diagram for Proton Beam Monitor 41 3-4 Polarized Proton Target and NMR C o i l 45 3-5 Diagram of a One Meter Multi-Wire Proportional Chamber Used i n the Forward Array 49 3-6 Forward Chamber S c i n t i l l a t o r Hodoscope 52 3-7 Charged P a r t i c l e Veto and i t s Coverage of Neutron Array B i l l e t s 54 3- 8 Hi-Low B i l l e t Timing 55 4- 1 Experimental Configuration 58 4-2 Logic of the prr + Signal 60 4-3 Logic of the Charged P a r t i c l e Veto 62 4-4 Logic of the Neutron Signal 63 4-5 Logic of the Three P a r t i c l e Trigger 64 v i i i Figures (Continued) 4-6a Relative Timing of Individual Components of the Trigger . 66 4-6b Timing of the Chamber Readout Strobe 66 4-7 Computer Gating C i r c u i t r y 68 4-8 Structure of an Event on Tape 70 4-9 Graphic Display of Chamber Hit Locations Projected onto Two Orthogonal Planes 72 4- 10 Transmission Ratio through the Target on a V e r t i c a l Beam Scan 72 5- 1 # of Wire Groups (Representing Possible Hits) Found i n Chamber no. Six 78 5-2 Intercepts of the Tracks F i t t e d through the Chambers at the Target 79 5-3 Timing Spike for the Left Side of One Neutron Array B i l l e t 82 5-4 Decoding of the Neutron Detector 84 5-5 Chronology of the Neutron TOF Measurement 85 5-6 y Peak Isolated from the TOF Spectrum 85 5-7 Sample Fermi Reconstructed Peaks 88 5-8 x 2 D i s t r i b u t i o n for the Polarized Proton Target Data and Normalized Teflon Target Data 92 5-9 Plot of the Reconstructed Neutron TOF Minus the Measured Neutron TOF a f t e r the Cut on x 2 97 5-10 Raw TOF Spectrum at Stage I before Track F i t t i n g and at Stage II a f t e r x 2 Reconstructions and Cuts 99 5-11 Spin/Angle Convention 101 5-12 Momentum Acceptance i n the A Configuration 102 i x F i g u r e s ( C o n t i n u e d ) 6-1 Comparison w i t h the Model 106 6-2 I n v a r i a n t p i r + Mass 107 6-3 ANN' ^ L L ' A S S a S a ^ n s t N e u t r o n T r a n s v e r s e Momentum 110 6-4 ANN' ^ L L ' A S S a 8 a * n s t ^os6 I l l 6 - 5 \ N ' ALL* A S S A G A I N S T * 1 1 2 6-6 Afljj* A ^ ^ , Agg a g a i n s t I n v a r i a n t p i r + Mass 114 6-7 AjgQ> A Q^, Ag^ a g a i n s t N e u t r o n T r a n s v e r s e Momentum 116 6-8 AJJQ, A Q N , A g L a g a i n s t CosG 117 6 - 9 ANO> AON> A S L A G A I N S T * 1 1 8 6-10 A„_, A_„, A__ a g a i n s t I n v a r i a n t p i r + Mass 120 NO ON SL 6-11 I n v a r i a n t Mass of the NN P a i r 122 6-12 AJJJJ, A^JQ, A ^ a g a i n s t I n v a r i a n t NN Mass 123 APP.A-l I l l u s t r a t i o n o f the A n g l e s A s s o c i a t i n g the Measured A s y m p t o t i c T r a j e c t o r y w i t h the True S c a t t e r e d T r a j e c t o r y 140 APP.A-2 I t e r a t i o n o f the C o r r e c t i o n s f o r M a g n e t i c F i e l d D e f l e c t i o n 142 APP.A-3 A n g u l a r Maps of the F u n c t i o n s BDL and BDLV a t 500 MeV/c . 144 APP.A-4 Momentum Dependence o f the F o u r i e r C o e f f i c i e n t s Ag and By 146 APP.B-1 Opening A n g l e and C o p l a n a r A n g l e D i s t r i b u t i o n s 152 APP.B-2 K i n e m a t i c A c c e p t a n c e of the L e f t M o n i t o r 152 X LIST OF TABLES Page I I - l Observables i n Terms of the C o e f f i c i e n t s of the E l a s t i c Scattering Matrix 15 II-2 Symmetry Properties of the Co e f f i c i e n t s of the E l a s t i c Scattering Matrix under Replacement of 9 by ir-6 15 II-3 Relations of the C o e f f i c i e n t s a, c, m, g and h to the M Matrix Elements 22 II-4 Expressions for Observables i n Terms of M Matrix Elements 22 II-5 Matrix Elements of pp + pmr + v i a an Intermediate nA State for a Purely 1D 2 Contribution 26 II-6 Isospin and Angular Momentum States Of The Low Energy irN System 34 I I - 7 Allowed Low Angular Momentum States i n the P a r t i a l Wave Decomposition of pp -»• nA 34 I I I - l Dimensions of the S c i n t i l l a t o r s i n the Primary Beam Polarimeter 42 I I I - 2 Carbon Background Corrections to the Beam Line Polarimeter 42 IV- 1 A l l o c a t i o n of Bits i n the C212 Bitpattern 70 IV-2 Maximum Lab Polar Angles for Neutrons from pp •*• pmr + ... 75 IV- 3 No. of On-Line Triggers i n the A ^ Configuration 75 V- l Distances of the Forward Chambers and S c i n t i l l a t o r Hodoscope from the Target 78 V-2 Error Estimates Used i n the x 2 Reconstructions 89 V-3 Background Subtractions 93 V-4 Selection of x 2 Cuts 95 x i Tables (Continued) V-5 Consistency Check on Background Normalization at 465 MeV 95 V- 6 No. of Events Available for Binning (a f t e r a l l Cuts) ... 101 VI- 1 ^NN» ^ L L ' a n c* ASS a& a^ n s t Neutron Transverse Momentum .. 126 VI-2 A ^ j , A ^ , and A g s against Cos6 127 VI-3 A ^ , A ^ , and A g s against $ 128 VI-4 Dependence of A ^ , A^ L and Agg on Invariant pir + Mass ... . 129 VI-5 A„_, A_.T, and A O T against Neutron Transverse Momentum .. 130 NO ON SL VI-6 A N Q , A Q N , and A g L against Cos0 131 V I ~ 7 ^ 0 ' A0N' a n d ASL a 8 a i n s t • 1 3 2 VI-8 Dependence of &~^Q> and Ag L on Invariant pir + Mass ... 133 VI-9 Dependence of A „ T , A _ and A_„ on Invariant NN Mass .... 134 NN NO ON APP.B-1 Phase S h i f t Solutions for P H And A ^ i n E l a s t i c Scattering at 508.9 MeV 154 APP.B-2 F i t t e d Gaussian Parameters of the Free Hydrogen Signal and Background Carbon Signal 156 APP.B-3 F i t t e d Values for the Analyzing Power of Carbon 156 APP.B-4 F i t t e d Values for the NMR C a l i b r a t i o n Constant CNMR .... 156 1 I. INTRODUCTION 1.1 EXCHANGE NATURE OF THE NUCLEON-NUCLEON FORCE The e x p e r i m e n t a l r e s u l t s r e p o r t e d i n t h i s t h e s i s c o n t r i b u t e i n f o r m a t i o n on the i n t e r a c t i o n of two protons i n the i n e l a s t i c r eac t ion pp •*• pnir"1". These r e s u l t s are new and represent a s i g n i f i c a n t advance i n the understanding of the fundamental nucleon-nucleon (NN) i n t e r a c t i o n . The two nucleon i n t e r a c t i o n mechanism has been studied ever s ince i t was perceived that nuclear matter i s composed of neutrons and protons . A knowledge of the nucleon-nucleon force i s required for an understanding of the propert ies of f i n i t e n u c l e i . In p a r t i c l e physics the NN i n t e r a c t i o n i s c e n t r a l to the understanding of hadronic in te rac t ions i n genera l . A l l s tongly i n t e r a c t i n g p a r t i c l e s are c a l l e d hadrons and are produced i n c o l l i s i o n s between other hadrons. In the laboratory the most acces s ib le hadrons are nucleons and therefore much of the present understanding of hadrons has resu l ted from progress i n the f i e l d of NN i n t e r a c t i o n s . In the experiment described i n th i s t h e s i s , po lar ized nucleons c o l l i d e d y i e l d i n g an a d d i t i o n a l hadron, the if*" meson. The f i r s t major advance toward the present understanding of the dynamic mechanism u n d e r l y i n g the NN i n t e r a c t i o n was made by (Y l ) Yukawa i n 1935. He genera l ized the ideas of electrodynamics in to a strong i n t e r a c t i o n theory where forces of f i n i t e range were mediated by the exchange of a massive v i r t u a l p a r t i c l e . Yukawa used one of the s implest consequences of quantum mechanics, the uncerta inty p r i n c i p l e , to r e l a te the range of the force to the mass of the exchanged p a r t i c l e . The range of the strong force i n n u c l e i was s u f f i c i e n t l y w e l l known to e s t a b l i s h the mass of the exchanged p a r t i c l e to be about 200 e lec t ron masses. The discovery of the pion i n 1 9 4 7 c o n f i r m e d the existence 2 of such a medium mass p a r t i c l e or 'meson'. Furthermore the meson was found to be strongly i n t e r a c t i n g making i t a serious candidate for the exchange p a r t i c l e required by Yukawa's one-pion-exchange (OPE) theory. Since the advent of modern accelerators, pions have been produced copiously i n the laboratory. In fact such a r i c h spectrum of mesons have been observed i n hadron c o l l i s i o n s that elaborate group t h e o r e t i c a l methods have been developed to c l a s s i f y the hadrons i n the hope that a s u c c e s s f u l c l a s s i f i c a t i o n scheme w i l l suggest more fundamental (Cl) ins i g h t s . These heavier mesons have a correspondingly shorter range of i n t e r a c t i o n and thus contribute to the complex structure a t t r i b u t e d to the core part of the NN force, but t h e i r exact role i s not ( L2 ) w e l l understood . However, the o r i g i n a l OPE theory remains successful i n describing the r e l a t i v e l y long range part of the NN , (L3) i n t e r a c t i o n 1.2 RESONANCE PHENOMENA IN NUCLEAR SCATTERING Resonant states of elementary p a r t i c l e systems have frequently been , . , (J1.D1.R1) observed i n nuclear scattering . The pion-proton scattering cross-section exhibits a sharp maximum at a pion k i n e t i c energy (T^) of 195 MeV. The peak at t h i s energy i s evident i n the ir +p e l a s t i c , ir~p _ (C2) e l a s t i c and the IT p charge exchange cross-sections . Bumps also e x i s t i n the cross-sections at higher energies. The bumps are c a l l e d resonances and are interpreted as the formation of short l i v e d states. The dominant peak at T^ =195 MeV i s c a l l e d the A(1236), where the number i n parentheses i s the energy of the state i n i t s own center of mass system ( i e . the invariant mass of the s t a t e ) . The large width and short (L4) l i f e t i m e of t h i s resonance are consistent with the strong decay 3 of an unstable p a r t i c l e . That s ca t te r ing v i a a resonant channel produces (D2) peaks i n the c ro s s - sec t ion was shown, for example, by Dirac The A resonance i s fundamental to the d e s c r i p t i o n of the N N i n t e r a c t i o n since two nucleons can exchange a pion and exc i te the A i n an intermediate s t a t e . From pion-nucleon sca t te r ing i t i s known that A ( F l ) production dominates the TT-N c ro s s - sec t ion up to 400 MeV . Because of the large OPE c o n t r i b u t i o n to the N N i n t e r a c t i o n , the s ca t t e r ing of two nucleons v i a e x c i t a t i o n of the intermediate A state i s expected to be ( B l ) prominent above the threshold for pion production ( B2 ) In the pp pmr + channel , much of the c ro s s - sec t ion proceeds v i a production of a doubly p o s i t i v e charged A + + . A reasonable c r i t e r i o n for i n t e r p r e t i n g any resonance as a p a r t i c l e i s that the resonance must have wel l defined quantum numbers. From TTN s ca t t e r ing experiments i t i s known that the A(1236) ex i s t s i n four charge states and therefore has i s o t o p i c spin 3/2. Its sp in quantum number i s a l so 3/2 and i t s p a r i t y p o s i t i v e ^ ^ . Being a J=3/2 s t a te , the A cannot be reached by s wave pion-nucleon s c a t t e r i n g . The A i s an i n t e r a c t i n g TT-N system i n an L=l or p s tate with t o t a l angular momentum 3/2 and i so sp in 3/2; thus i t i s often c a l l e d the P 3 3 resonance. Many higher mass states of th i s resonant channel ex i s t and are considered to be i n a family because they a l l have the same quantum numbers. Another very important resonance i n p a r t i c l e physics i s the charge doublet N* + (1460) and N ° ( 1 4 6 0 ) with i s o t o p i c sp in 1/2 and spin 1/2 which are the quantum numbers of the nucleon. This resonance can also be exci ted i n p wave TT-N s ca t t e r ing and i s c a l l e d the P ^ resonance. The proton and neutron are considered as the lowest mass doublet i n the family * of N resonances. 4 1.3 NEED FOR SPIN DEPENDENT MEASURMENTS IN THE INELASTIC CHANNEL A phenomenological approach which has been very success fu l i n de sc r ib ing NN sca t te r ing data i s the phase s h i f t ana lys i s (PSA). In th i s approach the vast body of s ca t te r ing data now a v a i l a b l e i s described i n terms of a small number of e m p i r i c a l l y determined parameters. The ult imate goal i s to understand the i n t e r a c t i o n which gives r i s e to the observed phase s h i f t s . The basic p r i n c i p l e s of the PSA are reviewed i n the chapter on theory and formalism ( I I . 2 ) . Above the threshold for pion production the phase s h i f t s i n each p a r t i a l wave or t o t a l angular momentum state are character i sed by an a d d i t i o n a l parameter n, c a l l e d the e l a s t i c i t y parameter. The e l a s t i c i t y parameters account for the loss of p a r t i c l e s from the e l a s t i c channel . They are thus spin dependent. E x i s t i n g PSA are i n general agreement on n i n the dominant i n e l a s t i c p a r t i a l waves but d i f f e r g rea t ly i n t h e i r ( B3 ) determination of n for the low p a r t i a l waves . The low p a r t i a l waves are i n t e r e s t i n g because they provide information on the short range behavior of the NN f o r c e . The i n a b i l i t y of PSA to agree on the n parameters r e f l e c t s the i n s e n s i t i v i t y of e l a s t i c data to th i s parameter and some d i s c r e p a n c i e s amongst e x p e r i m e n t s . In p a r t i c u l a r , the measurements of the t o t a l c ro s s - sec t ion d i f f e rences , AOL and Aa^, have ( S I ) been extremely c r u c i a l for f i x i n g n i n the low p a r t i a l waves , but there e x i s t s some doubt as to the p r e c i s e v a l u e s of Ao^ and ( B3 ) Ao^ . Further improvement i n phase s h i f t analyses can best be achieved by studying the i n e l a s t i c channels d i r e c t l y . (B4 B5 The s t ructures i n AOL a n c * A°T f i r s t observed at Argonne ' ' ( A2 ) A l ) have now been c o n f i r m e d by m e a s u r e m e n t s a t LAMPF , ( A3 ") ( S1 ) S I N V ' , and TRIUMF . The o r i g i n a l h y p o t h e s i s t h a t t h e 5 s t ructure was due to resonances i n the D 2 , F 3 and p a r t i a l w a v e s ^ ^ has not been s u s t a i n e d . A r e c e n t P S A ^ ^ c l a i m s tha t most of the s tructure i n Ao^ comes from the e l a s t i c channel and most of Ao>f i s contr ibuted by the i n e l a s t i c channels . If so, i t i s expected there should be evidence i n the NNTT channel s ince th i s channel dominates the i n e l a s t i c c ro s s - sec t ion above 500 MeV. This needs to be v e r i f i e d . Spin dependent measurements are s ens i t ive to the dynamics of the N N i n t e r a c t i o n and therefore contr ibute to an understanding of the phys i ca l (R2) process . An i l l u s t r a t i o n of th i s ex i s t s i n the l i t e r a t u r e . It had been proposed that IT exchange alone could account s a t i s f a c t o r i l y for the small angle data on pp •>• p m r + ^ ^ and that such a model could reproduce the slope and energy dependece of the d i f f e r e n t i a l cross-s e c t i o n . A subsequent ana lys i s of the same data by d i f f e r e n t authors concentrated on the spin s t ructure of the amplitudes . The ava i l ab l e ( A4) data was from unpolar ized s c a t t e r i n g ; however some information on the spin dependence of the production process can be ca lcu la ted from a knowledge of the angular d i s t r i b u t i o n of the A decay products The authors concluded that the data on pp -»• pmr + could not be explained by TT exchange a lone . This r e s u l t i l l u s t r a t e s the s e n s i t i v i t y of sp in dependent cross - sec t ions to the quantum numbers of the exchange p a r t i c l e , which i s in t imate ly re la ted to the i n t e r a c t i o n mechanism. An improved u n d e r s t a n d i n g of N N dynamics i s v i t a l to the development of r e a l i s t i c N N p o t e n t i a l s . For example, the Par i s group s t i l l (L2) input a phenomenological core much the same as e a r l i e r p o t e n t i a l model c a l c u l a t i o n s . T h e o r e t i c a l models of meson exchange are a lso hampered by the lack of knowledge concerning the core . Their domain of v a l i d i t y remains p e r i p h e r a l , that i s cross- sect ions that do not rece ive s i g n i f i c a n t 6 c o n t r i b u t i o n s from the lowest p a r t i a l waves . Some au thor s have s p e c i f i c a l l y urged that measurements be made of sp in dependent cros s -(Kl) sect ions i n the NNn channel The NA channel i s a l so important for t h e o r e t i c a l d i scuss ions of the hypothet i ca l dibaryon resonance which, i f i t e x i s t s , i s claimed to have a ( HI ^ branching r a t i o to NA of greater than 80% . However, the re su l t s presented i n th i s thes i s w i l l only be compared with a more conventional meson exchange model. 1.4 THE TRIUMF PROGRAM A long ser ies of NN sca t te r ing experiments have been done at TRIUMF by a group of p h y s i c i s t s from Bedford Co l l ege , A . E . R . E . Harwel l , U n i v e r s i t y of Surrey, Queen Mary Co l l ege , and the U n i v e r s i t i e s of B r i t i s h Columbia and V i c t o r i a known as the BASQUE group. These experiments have been designed to provide a unique and unambiguous phase s h i f t s o l u t i o n for . (01,L5,K2,D3,S1) . „ , , pp and np s ca t t e r ing . The experiment described i n th i s thes is i s an extension of that work. Using the po la r i zed beam and po lar i zed proton target ava i l ab l e at TRIUMF, the BASQUE group has measured the spin c o r r e l a t i o n parameters -»-»-A ^ , A ^ , Agg, Ag^, and p o l a r i z a t i o n s A^Q and A ^ N i n the reac t ion pp •*• pmr + at 510, 465, and 420 MeV. The f i r s t subscr ipt denotes the d i r e c t i o n of beam p o l a r i z a t i o n , the second subscr ipt denotes the d i r e c t i o n of target p o l a r i z a t i o n . The a n a l y s i s and r e s u l t s of the A^N» AJJO> a i l d AQJJ measurements w i l l be treated i n d e t a i l i n t h i s t h e s i s . The ALL (S2) and ASL measurements were the s u b j e c t of ano ther t h e s i s However some r e s u l t s of the ALL and ASL measurements not reported p r e v i o u s l y w i l l be p r e s e n t e d here as w i l l r e s u l t s of the Ags 7 measurement. The methods of ana lys i s for a l l four spin conf igurat ions were genera l ly the same with only minor va r i a t i ons i n d e t a i l . Experimental d e t a i l s are described i n chapters III and IV. The experiment was k i n e m a t i c a l l y complete with a l l three p a r t i c l e s being detected . The t r a j e c t o r i e s of the two charged p a r t i c l e s were measured by mul t i -wi re propor t iona l chambers (MWPC) and the neutron was detected i n a p o s i t i o n s e n s i t i v e s c i n t i l l a t i o n bar counter . Time of f l i g h t (TOF) on the neutron was a lso measured. This kinematic over determination allowed clean separat ion of the po la r i zed hydrogen s i gna l from the unpolar ized non-hydrogenous (mostly carbon) background i n the t a rge t . The techniques for data reduct ion and analys i s are descibed i n chapter V. The r e s u l t s are presented and discussed i n chapter V I . The new TRIUMF data on pp • •*• pnir + have s u b s t a n t i a l l y increased the data base for NN i n e l a s t i c s c a t t e r i n g . The combination of the TRIUMF data with the extensive and accurate measurements of the dir + channel made by (G2) the Geneva Group at SIN are helping to complete our understanding ( B7 ) of NN i n e l a s t i c s ca t t e r ing at intermediate energies 8 I I . THEORY and FORMALISM II . 1 THE SPIN SCATTERING MATRIX The s ca t t e r ing of two nucleons can be completely described by a matrix spec i fy ing the amplitudes for t r a n s i t i o n s between inc ident and (WI) f i n a l states of the same t o t a l angular momentum . This matr ix , c a l l e d the sp in s ca t t e r ing matrix M, i s not i t s e l f an observable . Experimental measurements of d i f f e r e n t i a l c ro s s - sec t ions , p o l a r i z a t i o n s , and corre la ted asymmetries i n s ca t te r ing when one or both of the beam and target p a r t i c l e s are po la r i zed are used to reconstruct the matr ix , u sua l ly v i a recourse to phase s h i f t analyses . The spin sca t te r ing matrix for pp (H3) e l a s t i c s ca t t e r ing i s w e l l determined i n the intermediate energy region but very l i t t l e i s known of the i n e l a s t i c s ca t t e r ing matrix i n the pp •*• pnif1" channel . The data presented i n th i s thes i s contr ibutes to the determination of the s ca t t e r ing matrix i n th i s channel , although many more exper iments w i l l be r e q u i r e d f o r i t s complete and unambiguous r e c o n s t r u c t i o n . The formalism presented i n th i s s ec t ion b r i e f l y reviews the r e l a t i o n s h i p between observables and the s ca t t e r ing matr ix . The s p e c i f i c form of the matrix descr ib ing i n e l a s t i c c o l l i s i o n s d i f f e r s from that descr ib ing e l a s t i c c o l l i s i o n s . However the formalism for d i scuss ing the s ca t t e r ing matrix i s the same i n both cases and many r e l a t i o n s can be defined without spec i fy ing the representat ion of M. The de ta i l ed s t ructure of M w i l l be discussed af ter some general r e l a t i o n s of in te re s t to th i s experiment are der ived . The matrix M i s an operator i n two p a r t i c l e sp in space and re la tes the f i n a l state spin wave funct ion Xf to the i n i t i a l sp in wave funct ion X i -X f = M X ± (II.1-1) 9 In general the p o l a r i z a t i o n state for an ensemble of two nucleon systems, prepared for s ca t t e r ing i n the l a b , i s a mixture of the pure spin states i n which any two nucleons can be found. The degree of p o l a r i z a t i o n of a mixture i s s p e c i f i e d by the expectat ion values of the s ixteen operators formed from the P a u l i sp in operators , a, for the two nucleons . <ola*.>, (a,3=0,1,2,3) ( II .1-2) The subscipts a and 8 re fer to the three poss ib le orthogonal d i r e c t i o n s of sp in vector with respect to an a r b i t r a r y coordinate system. aQ i s the uni ty operator whose average value spec i f i e s the normal iza t ion of the state and corresponds to a measurement where the spin component i s not analyzed. To e laborate , the experimenter has no knowledge of Oa 1 ( J 8 2 for any two nucleons (beam and target) which scat ter but rather has only a measure of the expectat ion value <o"a 0g >, averaged over the ensemble of nucleons prepared i n the l a b . To be accurate the average i s not even over the e n t i r e ensemble but only over that f r a c t i o n sampled by the polarimeter or other monitoring dev ice . The dens i ty matrix p i s convenient for descr ib ing such a mixture of pure spin s ta tes . For a s t a t i s t i c a l ensemble of s t a te s , p i s given by P = ^ P n X n x n t ( I I . 1-3) where P n i s the r e l a t i v e p r o b a b i l i t y of f ind ing the system i n state Xn* Xn Is a four component vector representing the pure spin state n . The sum over n can be thought of as a sum over the i n d i v i d u a l states formed by the two sca t te r ing p a r t i c l e s . The average value of any spin operator S for a mixture of states i s re la ted to p by <S> = T r ( p S ) / T r(p) ( I I . 1-4) Since p i s a hermit ian 4x4 matrix i t can be constructed from the s ixteen 10 independent operators °"ctCTB of I I . 1-2. Denoting the base matrices Sy where, S P = ajc 2, , u=l,2,...16 (II.1-5) and the S y s a t i s f y the orthogonality r e l a t i o n Tr(sV) - 4 5 y v (II.1-6) then p has the form p = - J - Z y S U T r ( p S y ) = £ r r (p ) i : p <S y >S U (II.1-7) The r e l a t i o n between incident and outgoing p o l a r i z a t i o n states i s obtained by giving averages of <Su>f i n the f i n a l state i n terms of <S u>i for the i n i t i a l s t a t e . Using I I .1-1 and I I .1-3 the f i n a l state density matrix i s pc = £ P J M x I 1 x n t M t = Mp^M1" ( I I . 1-8) r n n i i Substituting I I .1-7 into I I .1-8 and the r e s u l t into I I .1-4 y i e l d s the desired r e l a t i o n u M M P ^ = i z < s v > T r ( M S v M t s y f T r ( p i ) 4 v i The d i f f e r e n t i a l crosssection i s denoted I , and i s given by I = Z £ | M £ 4 ) ( i i .1-10) T r ( P i ) so that <S y> fI = •J-E v<S V> ±Tr(MS VM +S P) (II.1-11) For a measurement with beam polarized along a, target polarized along g and where none of the outgoing p o l a r i z a t i o n s are a n a l y z e d , the d i f f e r e n t i a l cross-section i s I = yl <a 1a2>Tr(Mo 1a 2M t) (II.1-12) The cross-section for scattering of an unpolarized beam from an unpolarized target, denoted I 0 , i s 11 I - •J-Tr(MM T) ( I I . 1 - 1 3 ) Since the beam and target p o l a r i z a t i o n s are prepared independently, <o la&, = <a l>.<ah. ( I I . 1 - 1 4 ) a 0 i a i 0 i v so that I a g becomes I fl = 7-Tr(MM t) ap 4 + irr(Mala2^ t)<aJ t>.<a2>. (II.1-15) The matrix M i s used to describe a strong i n t e r a c t i o n process and i s therefore required to obey the symmetry p r i n c i p l e s which charac ter ize the strong i n t e r a c t i o n . The condi t ions of invar iance under space r o t a t i o n s , r e f l e c t i o n s , and time r e v e r s a l r e s t r i c t the form of M. A p a r t i c u l a r consequence i s that an a x i a l vector i s required to be combined with the a x i a l vector <o> i n the second and t h i r d terms of I I . 1-15 to form a s c a l a r . Using the most general form of M and taking the required t race , Tr(MoM^), the only a x i a l vector which can be formed i s one normal to the s ca t t e r ing p l a n e . Thus terms two and three depend only on the normal component, <OJJ>, of <o>. They are known as p o l a r i z a t i o n terms. There i s some a r b i t r a r i n e s s i n the choice of a coordinate system. F ig 2-1 shows two commonly used reference frames. In the lab frame i t i s customary to c a l l the axes L , S, and N for l o n g i t u d i n a l , sideways, and ( B8^ normal. In a standard notat ion the trace terms of II.1-15 are c a l l e d r e s p e c t i v e l y Tr(Ma^M^) = IQA^^Q 0"0N Tr(Mo^M' ) = I„A, T r d i a ^ ) = I 0 A A 6 ( I I . 1 - 1 6 ) Equation I I . 1-16 defines the p o l a r i z a t i o n terms AJJO» A.QN and the spin c o r r e l a t i o n tensor A a g . These are observables and measurable i n I 12 F I G . 2-1 a THE ORTHOGONAL UNIT VECTORS P. g_. and n I N THE C. H. REFERENCE FRAME I n o n - r e i a t i v i s t i c k i n e m a t i c s ) F I G . 2-1 b THE ORTHOGONAL UNIT VECTORS L. S. and N I N THE LAB REFERENCE FRAME A 13 the l a b . A knowledge of them i s necessary for the determination of M. Rewrit ing the d i f f e r e n t i a l c r o s s - s e c t i o n , I I .1-15 , i n terms of the new d e f i n i t i o n s gives I = I f t(l+A n P . M + A_ P^.. + A P , P T 0 NO bN ON tN LL bL tL +A P P A P P NN bN tN + SS bS tS + A S L P b S P t L + A L S P b L P t S ) ( II .1-17) where P^ i s the beam p o l a r i z a t i o n , P t i s the target p o l a r i z a t i o n and the subscr ipts L , S, and N denote components along the coordinate axes. The experiment described i n th i s thes i s has measured AQ^, A^Q, A ^ , A ^ , A SS ' a n d A S L ' For a two body r e a c t i o n , A+B •*• C+D, the s ca t t e r ing matrix expressed i n center of mass var i ab le s has the general form % + C + D " W * A>V ° i < 9 > ( I I - 1 " 1 8 ) where 9 i s the center of mass angle between the inc ident p a r t i c l e A and the scattered p a r t i c l e C. The 0^ are the spin operators for the t r a n s i t i o n and Ic are the momentum v e c t o r s . For the case of e l a s t i c s ca t t e r ing the spin operators are combinations of the P a u l i matrices and the uni ty operator contracted with the c m . uni t v e c t o r s . F i g . 2-1 shows the dependence of the c m . uni t vectors on 9, which i s how the dependence on 9 enters i n the 0^. The most general form of M for pp e l a s t i c s ca t ter ing i s M = a + c(ala2) + m(a 1 a 2 ) + g (o 1 a 2 + alaz) + h ( a 1 a 2 - ala2) (II .1-19) v n n ' v n n ' p p q q P P q q The f i ve c o e f f i c i e n t s a, c , m, g , and h are c a l l e d amplitudes . They correspond to the A-£ of I I . 1-18 and can be parameterized as functions of energy and angle . The P a u l i p r i n c i p l e requires that the e l a s t i c s ca t t e r ing matrix be 14 symmetric with respect to the interchange of the two nucleons . This cond i t ion combined with p a r i t y makes AQN and A^o as defined i n II .1-16 equal and genera l ly known as the p o l a r i z a t i o n parameter P. Hence the p o l a r i z a t i o n asymmetry for e l a s t i c s ca t t e r ing i s independent of whether i t i s the beam or target which i s p o l a r i z e d . Another r e s u l t i s that the tensor A a g i s symmetric. Some r e l a t i o n s between observables and amplitudes of the e l a s t i c s ca t te r ing matrix are given i n table I I - l . A complete l i s t i s given i n r e f . (H4). The g e n e r a l i z a t i o n of M to the two body process NN > NA i s treated at length i n r e f . (KI) and w i l l not be recreated here . There are some s i g n i f i c a n t d i f f e r e n c e s . For ins tance , the number of independent amplitudes (the A-^  of I I . 1-18) for th i s case i s s i x t e e n . As w e l l the sca t te r ing matrix for th i s process does not have a sp in independent term corresponding to ' a ' i n I I . 1-19 since one or the other of the nucleons must make a t r a n s i t i o n from a spin 1/2 to a spin 3/2 p a r t i c l e . To connect a l l poss ib le states of spin 1/2 to 3/2, a spher i ca l tensor of rank 2 i s needed. Aside from s p e c i f i c mathematical d e t a i l s the concept of the two body sca t t e r ing matrix and i t s r e l a t i o n to observables remains the same for th i s process . I I .2 PHASE SHIFT ANALYSES The data c o l l e c t e d by s ca t t e r ing experiments are often analyzed i n terms of p a r t i a l waves. The phase s h i f t &LJ , for each p a r t i a l wave with o r b i t a l angular momentum L and t o t a l angular momentum J , provides information on the behavior of the nuclear force i n the outer , intermediate , and core reg ions , depending on the value of L . The p a r t i a l wave expansion i s useful because only a small number of lower p a r t i a l 15 TABLE I I - l OBSERVABLES IN TERMS OF THE COEFFICIENTS OF THE ELASTIC SCATTERING MATRIX I Q - | a | 2 + | m | 2 + 2 | c | 2 + 2 | g | 2 + 2 | h | 2 IQP = 2Re{(a+m)c*} 10Am = I - | a -m| 2 - A | g | 2 I Q A S S = 2Re{(a-m)g* - (a+m)h*cos9 - 2 ich*s in6} it ii ic V^LL = 2Re{(a-m)g - (a+m)h cos 6 + 2ich s i n 6} ii ii I A = 2Re{(a+m)h s in6 - 2 i c h cos 6} TABLE II-2 SYMMETRY PROPERTIES OF THE COEFFICIENTS OF THE ELASTIC SCATTERING MATRIX UNDER REPLACEMENT OF 6 BY ir-0. a( 6) + m ( 6) = - { A ( IT- 9) + m( TT- 9) } a(6) - m(9) = -2g(TT-9) g(9) = - | {a (TT-9) - m(Tr-9)} c(9) = C(TT-9) h(9) = h ( i r - 9 ) 16 waves contr ibute s i g n i f i c a n t l y . This r e su l t s d i r e c t l y from the fact that the nuclear force i s short range and that the phase sh i f t s are re l a ted to the i n t e r a c t i o n d i s t ance . The advantage of th i s parameterizat ion i s that when an accurate set of phase s h i f t s i s known, c a l c u l a t i o n of the sca t te r ing matrix and observables i s s t ra ight forward . The concept of a phase s h i f t i s most e a s i l y understood i n the context of sp inless p a r t i c l e s s ca t t e r ing v i a a s p h e r i c a l l y symmetric p o t e n t i a l . In t h i s approach a s o l u t i o n of the Schrodinger equation i s constructed which, at large dis tances from the s ca t t e r ing center , represents an inc ident plane wave and an outgoing or scattered spher i ca l wave of amplitude f ( 6 ) . i k r Y + e + f ( 6 ) - ( I I .2-1) The most general s o l u t i o n of the Schrodinger equation for the case of spinless p a r t i c l e s and a r o t a t i o n a l l y invar iant p o t e n t i a l i s given by CO Y = I 4 P T ( c o s 6 ) f T ( r ) ( I I .2-2) L=0 r L L where PL(COS 6 ) are the Legendre polynomials , f i , ( r ) are the so lut ions of the r a d i a l wave equat ion, and the AL are constants . At large distances where the p o t e n t i a l i s zero , the s p h e r i c a l Bessel funct ions , J L ( k r ) , are a p a r t i c u l a r s o l u t i o n of the r a d i a l equat ion. Their asymptotic form i s J L ( k r ) = i - r s in (kr -LTr /2 ) . ( I I .2-3) r-»-°° A more general choice of r a d i a l wave functions which leads to the des ired form of the o v e r a l l wave funct ion II .2-1 i s given by f T ( r ) = . e - i C k r - L . / Z ) + i (kr-L i r /2 ) ( I I > 2 _ 4 ) 17 th SL I S the sca t te r ing matrix for the L p a r t i a l wave and i s re l a ted to the matrix M by M(?_f = < 6 f * f Is"1!\*±> ( I I . 2 - 5 ) where k i s the wave number of the r e l a t i v e motion and (0, <f>) are the polar and azimuthal angles of s c a t t e r . The c o e f f i c i e n t s AL i n the expansion of Y must be adjusted to match the inc ident plane wave. For t h i s purpose the inc ident plane wave can be expanded as e i k z = e i k r c o s 6 = ^ 1_ ( 2L+i ) i L P L ( c o s 9 ) s i n ( k r-LTT / 2 ) ( I I . 2 - 6 ) L Using I I . 2 - 6 and I I . 2 - 4 i n I I . 2 - 2 and equating with I I . 2 - 1 gives I A L { - e - 1 < k r " L i r / 2 ) + S L e 1 < k r - L i r / 2 > } P L (cos6) ( I I . 2 - 7 ) = I (2L + 1) i L {e«*x~™'V - e - K k r - L i r / 2 ) } g Q ) + f ( e ) £ l k r L 2 ikr r - i k r Comparing terms i n e f ixes the c o e f f i c i e n t s AL by the r e l a t i o n \ • ' L ( H . 2 - 8 ) . * + i k r , t L - i L i r / 2 . Comparing c o e f f i c i e n t s of e and u s i n g i e =1 g i v e s CO f (0) = I (2L+1) PT(cose){s-l} ( I I . 2 - 9 ) L=0 2 ik L L 2 Below the pion threshold the matrix SL i s un i ta ry (|SL | =1). This ensures that the t o t a l outward p a r t i c l e f lux i s equal to the t o t a l inc ident f l u x . As a uni tary operator , SL can be wr i t ten S T = e 2 i 6 L ( I I . 2-10) t tl where &L * - s t n e phase s h i f t for the L p a r t i a l wave (the subscr ipt J i s absent for sp inless p a r t i c l e s ) . The phase s h i f t i s the d i f ference i n 18 phase between the Incoming spherical wave and the outgoing scattered wave due to the change i n wavelength of the p a r t i c l e while i n the region of the p o t e n t i a l . This can be seen by subs t i t u t i n g II.2 - 1 0 into the r a d i a l wave function II.2 - 4 with the r e s u l t f T ( r ) - _ e - i ( k r - W 2 ) e i ( k r - L , / 2 + 2 6L) where the f i r s t term represents an incoming spherical wave and the second an outgoing sph e r i c a l wave with i t s phase sh i f t e d by 2 6L« The de Broglie wavlength i s longer or shorter depending on whether the po t e n t i a l i s predominantly a t t r a c t i v e or re p u l s i v e . An a t t r a c t i v e p o t e n t i a l i s characterized by p o s i t i v e phase s h i f t s while the phase s h i f t s for a repulsive i n t e r a c t i o n are negative. The cross-section, however, does not depend on the sign of the phase s h i f t . The complexity r e s u l t i n g from the NN i n t e r a c t i o n being neither s p h e r i c a l l y symmetric nor independent of s p i n i s t r e a t e d by H o s h i z a k i ^ H ^ . Only r e s u l t s needed to re l a t e the phase s h i f t s to the scattering matrix are quoted here and again, for s i m p l i c i t y , i t i s the e l a s t i c s c attering matrix which i s considered. Using equation II.2-5 the matrix elements of M i n spin space can be expanded i n terms of phase s h i f t s according to <s mg |M(Pf ,P1)|s'm's> = | £ <8 f* f,s mg | e 2 i S - l | s'mg , 0 ± <t>.> (II.2 - 1 2 ) where s denotes the t o t a l spin of the st a t e . The S matrix can be diagonalized with respect to J and mj by the use of the completeness r e l a t i o n 19 £ iLm^XLm^l =1, which gives L <s m |M(P , : ,P , ) | s , m'> = s 1 —f — i 1 s |£l< 6 f <f>f I L n ^ X L n ^ s mg | Ls Jm ><L1 s' J 'm^ | e 2 i 6 - l | L • s' J 'mp L x a ' s ' J ' i ^ L ' ^ s ' i ' X L ' i ^ l e . ^ ) , (II .2-13) where <6<|)|LmT> = Y™L(6,<()) Ju Li and <LmTsm |LsJmT> are c a l l e d the Clebsch-Gordan c o e f f i c i e n t s and w i l l be L s 1 J denoted C(fh m s ^J ) , with M = nL+m . For e l a s t i c s ca t t e r ing J , s, and M Li S J J L i S J are conserved so that II .2-13 becomes <s m |M|s'm'> = 6 4rk I I I / ( 2 L » + 1 ) / 4TT Yf6,<|>) s s ss 2ik L J = ( L _ S | L , = | j _ s | t x C( m s " m s m s ™s) C( T ° m s m s ) < L s J m ' | e 2 i 6 - l | L ' s J m ' > (II .2-14) L I S J L I S J S S The summations over L and L ' must be taken i n such a way to s a t i s f y the general ized P a u l i p r i n c i p l e which requires ( - ) ^ + s + ^ = - 1 5 with T the t o t a l i so sp in of the s t a te . The non-zero matrix elements of M remaining a f ter summation are c l a s s i f i e d spin s i n g l e t and spin t r i p l e t amplitudes and are denoted M = <OO|M|OO> ss 1 1 M , = <lm |M|lm'> (II .2-15) mm s 1 1 s s s r e s p e c t i v e l y . The important r e s u l t i s that once the phase s h i f t s are known, c a l c u l a t i o n of the M matrix elements involves only a s t r a i g h t -forward a p p l i c a t i o n of angular momentum a lgebra . Obtaining the amplitudes of the M matrix i s a lso s t ra ight forward . For example, operating M on the s ing le t wave funct ion Xs gives MXo = (a-m-2g)x0 (II .2-16) s s 20 Since the s i n g l e t and t r i p l e t wave functions are orthogonal, the only non-zero s i n g l e t matrix element i s M s s = X I M Xs = ( a _ m - 2 8 ) (II.2-17) Similar r e l a t i o n s e x i s t for the t r i p l e t wave functions. They can be solved for the c o e f f i c i e n t s a, c, m, g, and h. The c o e f f i c i e n t s i n terms of M matrix elements are given i n table II-3. The formulas for observables of int e r e s t to this experiment are given In table II-4. The onset of i n e l a s t i c reactions breaks the u n i t a r i t y of the scattering matrix. This requires a modification of S given by 2i5 T S L J = \ j e " " L J «><\j<» > (II.2-18) where ri i s c a l l e d the e l a s t i c i t y parameter and must be determined experim-e n t a l l y . An alternate way of accounting for the loss of p a r t i c l e s from the e l a s t i c channel i s to allow the phase s h i f t s to become complex. A further important point i s that the NN i n t e r a c t i o n has a non-cen t r a l component and therefore the o r b i t a l angular momentum i s not conserved. The conserved quantities are the t o t a l angular momentum J , one of i t s components J z , and p a r i t y . For spin t r i p l e t states with J values greater than 1 there are three L values possible (L=J, L=J+1). The states with L=J+1 have the same J and p a r i t y and are therefore free to couple. The S matrix can s t i l l be diagonalized with respect to J using the following form e J-1,J e ± 6 J + l , J co s 2 ej i s i n Z E j isin2"e cos2,"e e J-1,J e i 6 J + l , J (II.2-19) where <5T T are the nuclear bar-phase s h i f t s and e i s the bar mixing parameter. A table of allowed p a r t i a l waves i n the pp system up to J=6 i s 21 F IG . 2 - 2 PHRSE SH I FTS OF THE PROTON-PROTON SYSTEM FOR J < 6 L S p D F G H I J J 0+ 1~ 2+ 3 " 4+ 5" 6+ 7" 0 V V 1 V 2 V V V 3 4 V V V 5 v 6 V "^6 V V 22 TABLE I I - 3 RELATIONS OF THE COEFFICIENTS a, c, m, g and h TO THE M MATRIX ELEMENTS a = (2M n + M 0 0 + M s g) C = — ( M ^ Q - M Q 1) m = ^<-2M10 + M 0 0 - m g s) g = i < M u + M i _ r M s g) h " 4 c i i e ( M i i " M i - r Moo> = 4iln -e ( M i o + Moi> TABLE II-4 EXPRESSIONS FOR OBSERVABLES IN TERMS OF M MATRIX ELEMENTS i o - r l * u l 2 + T|Mft J 2 + h \ s \ 2 + l\* l 2 + l l M l 2 + | l M I2 ^ ^ 00 4 s s z 10 z 01 z 1-1 I 0P = ^ e f i C M ^ - M o ^ C M ! ^ ^ ^ ^ ) * } ^^ "W = l l M s s | 2 + l l M l l + M l - l | 2 = A I M 0 0 I 2 " i l M s s I 2 " i K l l 2 + jKol 2 + Re<MnM*_i) - jlMlll 2 - 7>ool 2 - i l M s s l 2 + i K l l 2 - l l M 1 0 l 2 + jlMi - x l 2 I O A S L = 4 t a n 0 { l M i r M i - i l 2 - l M o o l 2 l - ^ o t e { | M 0 1 | 2 - | M 1 0 | 2 } 23 given i n f i g . 2-2. The notat ion used i s spectroscopic , each state being 2s+l denoted by L where L = 0 , l , 2 . . . for S , P , D , F . . . e t c . waves. The preceding formalism shows how the s ca t t e r ing matrix can be reconstructed from a knowledge of the phase s h i f t s i n each p a r t i a l wave. The converse i s not t rue . A complete knowledge of M does not a l low a d i r e c t c a l c u l a t i o n of the phase s h i f t s . The equations r e l a t i n g phase s h i f t s to observables are t ranscendenta l . The phase s h i f t s must be extracted using a chi-squared goodness of f i t c r i t e r i o n . In th i s method the phase s h i f t s of the lower p a r t i a l waves are var ied f r e e l y while a l l others are constrained to values ca l cu la ted from OPE. Only very recent ly has a d i r e c t experimental recons t ruct ion of the pp e l a s t i c s ca t t e r ing , v J (H3) matrix been done II. 3 MATRIX ELEMENTS OF THE pp + pnir + REACTION Some f a m i l i a r i t y with the matrix elements of the pp -»• pmr + r eac t ion i s necessary for understanding and i n t e r p r e t i n g the r e s u l t s of th i s experiment. As w e l l , an in spec t ion of the kinematic factors contained i n the matrix elements h int s at the quant i t i e s i n the ana lys i s which may be the most r e v e a l i n g . The purpose of th i s sec t ion i s to demonstrate ways i n which the magnitudes of amplitudes and kinematic d i s t r i b u t i o n s of observables can be used to i d e n t i f y the dominant c o n t r i b u t i n g matrix elements and how t h i s i n turn gives information on the under ly ing dynamical mechanism. The h e l i c i t y amplitude formalism i s convenient for d i scus s ing the sp in s t ructure of matrix elements s ince the h e l i c i t i e s are d i r e c t l y re l a ted to the p o l a r i z a t i o n states of the i n d i v i d u a l p a r t i c l e s . In the h e l i c i t y d e s c r i p t i o n the spin state of a p a r t i c l e i s l a b e l l e d by the 24 p a r t i c l e ' s component of spin along i t s own d i r e c t i o n of motion rather than along a fixed a x i s . The elements of the M matrix i n spin space are now written <y v |M|XXX2> = H y v X i X 2 (II.3-1) and are c a l l e d H matrix elements to emphasize they are h e l i c i t y amplitudes. The h e l i c i t y amplitudes can be expanded i n terms of phase s h i f t s by the use of completeness r e l a t i o n s as was done with eq. II.2-12. A l t e r n a t e l y , more insi g h t into the construction of the matrix elements can be gained by e x p l i c i t l y writing state functions for the i n i t i a l and f i n a l states. A state vector for the incident state with d e f i n i t e value of J and one component X can be constructed from the two p a r t i c l e h e l i c i t y state using the rules for coupling of angular momenta |siXx> B |s 2X 2> B |LmL> = c\)z \j2 * C* ° * | J A > (II.3-2) If i n the f i n a l NA state the neutron i s produced at cm. angles (3,a) and i s quantized along the beam d i r e c t i o n while the A i s quantized along the f i n a l neutron d i r e c t i o n , then the state vector of the f i n a l state i s 13/2 -u> S |L' 0> B J1/2 v> (II.3-3) Rotating the f i r s t two vectors to the beam d i r e c t i o n gives I D 3 / 2 i 3 / 2 x> 8 D V J L ' A-V-X> B 11/2 v> L x,-u' X-v-x,0' 1 x _ v p - u A-v-x L-v 3/2 L' £ ^3/2 L* J * x,-y A-v-x.O | j ' A-v> 8 11/2 v> (II.3-4) where the D's are angular momentum rot a t i o n matrices depending on the angles 8 and a. U n i t a r i t y r e l a t i o n s amongst the D matrices reduce the f i n a l state to 25 J ' X-v> B 11/2 v> amplitude for NN + NA becomes H ( 6, a) = - i e ( iXa) I /(2L'+1)(2L+1) C J y J , ll , L j S X= X i~ x 2 Xi — x 2 x 1/2 1/2 s X 0 X s L J yvXj X 2 x C v X - v X -y o -3/2 L ' J ,(B) H' J , L , s J ' , L ' , X ( II .3-6) 1/2 J ' J X - v , - y In the case of pp + pnif v i a the intermediate nA s t a te , the P 33 resonance can be decomposed into a f i n a l state proton and pion with one uni t of r e l a t i v e o r b i t a l angular momentum. As an example, the matrix elements for pp going to nA i n a r e l a t i v e s wave with subsequent decay of the A in to a proton and pion are given i n table II-5 for a purely c o n t r i b u t i o n . The decay angles , 6 and <(>, are defined with respect to the quant iza t ion axis i n the A rest frame. The f i n a l proton spin has been summed over . The spin c o r r e l a t i o n s A a g as defined i n II .1-16 are c o r r e l a t i o n s of proton spins i n the i n i t i a l s t a te . For any p a r t i c u l a r c o n t r i b u t i o n to the process pp •> nA the , A a g w i l l have d e f i n i t e va lues . For example two protons i n a ^D 2 s tate going to nA i n i n a r e l a t i v e s wave requires A = K-j= A = - 1 . The experimental ly determined values of the A are the r e su l t of such d e f i n i t e values mixed by competing p a r t i a l waves having d i f f e r e n t values of A a g . The degree of mixing i s determined by the r e l a t i v e normal izat ions of the amplitudes i n each p a r t i a l wave and can only be determined by a p a r t i a l wave expansion of the matrix elements. If only a small number of p a r t i a l waves with d i f f e r e n t values of A a g 26 TABLE I I-5 MATRIX ELEMENTS OF pp > pn f + VIA AN INTERMEDIATE s WAVE nA STATE FOR A PURELY : D 2 CONTRIBUTION + ^ , M as • 3 . 0 + i a / 2 +i<t> u 2 2 ° l H+ 3 + 1 ++ = 4 ( l + c o s B ) s m - s i n e e H 3 / 2 0 0 2" 2" - ^ 3 N 0 N - i a / 2 +i<f> 2 2 0 i H + 3 - l ++ = 4- ( l - c o s 3 ) c o s - s i n 6 e e H 3 / 2 0 0 2 2 + ^ , n _ _ « ^ „ 1 + i « / 2 - i * u 2 2 0 1 H _ 3 + 1 + + = 4 : ( l ~ c o s 3 ) c o s - s i n 6 e / : e H 3 / 2 0 0 2 2 —^ 2 2 0 i H _ 3 _ l -H- = " f ( l + c o s 3 ) s i n - s i n 6 e ~ i a / 2 e " 1 * H 3 / 2 „ 0 2" 2 . „ +1 ( 3 c o s 3 - l ) 3 + i a / 2 r - l s i n e +i<j> /2 fli „ i H . , . . = 5 c o s - e {nr—FT- e y r cos 6 j H 2 2 0 +1+1 ++ = /2 2 c o s 2 e " ^ " 7 2 - ^ T / 3 C ° S ° i n 3 / 2 0 0 2 2 -1 (3COS0+1) , 3 - i a / 2 r 1 s i n 9 + i <f> . ^ n l 2 2 0 l H + l - l + + = v T 2 S ± N 2 E W " 7 T e + / 3 ^ 6 } H 3 / 2 0 0 2 2 +1 (3cos3+l) , 3 + i a / 2 r+vT n . 1 1 . Q - i<h 2 2 0 i H _ 1 + 1 = ^ 3 s i n - e { -73- cos 6 +^ s i n 0 e } H 3 / 2 0 „ 2 2 +1 ( 3 c o s 3 - l ) 3 - i a / 2 r+»/2 „ , 1 1 . fi -i<f>i 2 2 0 l H - l - l ++ = 2 C O S 7 6 t 73 C O s 9 + / 3 / 2 S i n 9 6 ' H 3 / 2 0 0 2 2 uv++ 27 contr ibute to the c ro s s - sec t ion i t may be poss ib le to i d e n t i f y which p a r t i a l waves l i k e l y c o n t r i b u t e , though not t h e i r normal i za t ions , without recourse to a p a r t i a l wave expansion. A p o t e n t i a l l y great amount of information i s contained i n the part of the matrix element descr ib ing the A decay. Information on the production of resonances i s contained i n the angular c o r r e l a t i o n s of t h e i r decay products . This r e s u l t s from the fact that the decay of an unstable system depends on the J value of the system and on the magnetic substate populat ions , which i n turn depend on the production process . This suggests the p o s s i b i l i t y of using decay c o r r e l a t i o n s to test for the dominance of a given exchange mechanism as was done i n r e f . (R2). The axes with respect to which the decay c o r r e l a t i o n s are given can be chosen a r b i t r a r i l y , but for the case of per iphera l c o l l i s i o n s (see s ec t . I I .4) there i s a na tura l choice which emphasizes the exchanged system. The na tura l frame i s the rest frame of the unstable system with z^  along the d i r e c t i o n of the inc ident p a r t i c l e as seen i n that frame and y_ normal to the production p lane . Referr ing to the process depicted i n the diagram of f i g . 2-3a, A denotes the inc ident p a r i c l e , C i s the resonance, and E i s the exchange p a r t i c l e . The normal d i r e c t i o n n i s defined by n= DxA/ |DXA | . The choice i s such that the three momentum t r a n s f e r , E=C_-A, i s a n t i p a r a l l e l to a_, the ax i s , i n the rest frame of C (ie.C=0) and the consequence that the r e l a t i v e o r b i t a l angular momentum of A and E cannot have a z component d i f f e r e n t from zero . The polar and azimuthal angles , (6,<|>), defined i n th i s reference frame and shown i n f i g . 2-3b are c a l l e d the GOTTFRIED-JACKSON and TRIEMANN-YANG angles r e s p e c t i v e l y . They are useful for the d e s c r i p t i o n of any two-body decay r e s u l t i n g from a production process such as that depicted i n f i g . 2-3a. 28 The magnetic substate populations of a resonance are s p e c i f i e d by a sp in dens i ty matrix p. In a system at rest the dens i ty matrix i n the |Jmj> basis i s defined to be (11.3-7) P T = I |jmT> p , <Jm'T I V m j J J where m and m' are magnetic quantum numbers r e l a t i v e to the z a x i s . The (Gl) J=3/2 density matrix can be wr i t t en P33 P31 P31 J ~  P 3 3 P3 _1 - i P l _1 i » - i p 3 _ 3 p 3 _i P3 _1 i P l _1 2 " P33 •P31 i P 3 _3 > * P3 _1 » * ~ i P 3 1 P33 (II .3-8) where the subscr ipts on the dens i ty matrix are 2m and 2m' . The elements P 3 3 , p 3 , _ 3 , and P p - i are a l l r e a l . The angular d i s t r i b u t i o n , W(8,<|>), for the p a r i t y conserving two body decay of a 3=3/2 resonance i n terms of the spin dens i ty matrix elements i s given by J a c k s o n ^ 2 ' * W(9,<}>) = | ^ { p 3 3 s i n 2 9 + p n ( l / 3 + c o s 2 e ) - 2/v /3Rep 3,_ 1sin 2ecos2<|> -2//3Rep3 1sin2eCos<t> } ( I I .3-9) This c a l c u l a t i o n again uses the h e l i c i t y formalism. If a s ing le type of exchange mechanism dominates, then not a l l of the magnetic substates w i l l be populated r e s u l t i n g i n a modi f i ca t ion of the angular d i s t r i b u t i o n . Since the axes were chosen so that the o r b i t a l angular momentum has zero z^  component, nonvanishing mj and mj ' values i n the sp in dens i ty matrix must o r ig ina te i n the i n t r i n s i c spins of systems A and E . I f the system E has sp in 0, then mj and mj ' must be less than or equal to the spin of 29 F I G . 2-3a FEYNMAN DIAGRAM FOR A + B -> C + D B D F I G . 2-3b D E F I N I T I O N OF THE G O T T F R I E D " J A C K S O N AND TRIEMANN-YANG DECAY ANGLES (Q,<p) A X A n 0 and * are defined i n the rest frame, of p a r t i c l e C. P i s the momentum of one of the decay products of C, n i s normal to the production plane and P^ i s the momentum of B (the beam) as seen i n 0 C 30 A. If A i s a nucleoli the only non-zero matrix element i s p ^ . Therefore the angular d i s t r i b u t i o n for a spin 0 exchange has a simple l+3cos 2 6 dependence. Other elements of the matrix contribute, for instance, to a decay with the outgoing proton p o l a r i z e d . P o l a r i z a t i o n of the i n i t i a l nucleons l i m i t s the states which can be populated i n the density matrix. Combinations of polarized i n i t i a l states produce a d d i t i o n a l constraints amongst the density matrix elements and can i n p r i n c i p l e be used to reconstruct the J=3/2 density matrix completely. In t h i s way the laws of angular momentum and p a r i t y combine to make spin dependent measurements more s e n s i t i v e to the quantum numbers of the exchanged system. I I . 4 THE COMPARISON MODEL The r e s u l t s of t h i s experiment are compared with model predictions i n chapter VI. The model used for comparison belongs to a general class known as peripheral models, the general aspects of which are described i n the following. Two prominent features i n hadron c o l l i s i o n s at energies of a few GeV are the predominance of small momentum transfers and the frequent observation of dynamically unstable resonances formed i n the f i n a l s t ate. The quasi-two-body production processes share with e l a s t i c s c a t t e r i n g the c h a r a c t e r i s t i c of strong forward peaking. The p r e f e r e n t i a l l y small momentum transfers i n these two body processes can be interpreted as glancing c o l l i s i o n s from the exterior region. These c o l l i s i o n s do not probe the core of the i n t e r a c t i o n but rather are peripheral, that i s s e n s i t i v e to contributions from the longest range forces and thus they require the exchange of r e l a t i v e l y l i g h t mesons. Close c o l l i s i o n s 31 i n v o l v i n g large momentum transfers lead p r e f e r e n t i a l l y to uncorre lated many p a r t i c l e s t a te s . NN s ca t t e r ing data show a r i c h energy and spin dependence at intermediate energies , due i n part to the copius production of p ions . Any r e a l i s t i c model of the NN i n t e r a c t i o n at these energies must provide for the uni tary coupl ing of the e l a s t i c and i n e l a s t i c channels . The model used to compare with data i n t h i s thes i s i s ex tens ive ly documented i n the (K1,K3,K4,D4,S3,S4) ^ ^ , , , l i t e r a t u r e and i s a meson exchange model of the coupled NN and NNir channels . The model employs r e l a t i v i s t i c kinematics and respects two and three body u n i t a r i t y . Coupled NN '•*• NN and NN -»- NN7r amplitudes are ca l cu l a ted using dynamical OPE f o r c e s . P r a c t i c a l c a l c u l a t i o n s done with t h i s model have been reported and published to f a c i l i t a t e comparison with data from experiments. T h e o r e t i c a l work i s s t i l l i n progress . In th i s model the amplitudes T for the process NN •*• NNir are constructed as TNN^NNir = ^ V a G o t TNN+Na ( I I .4-1) a This i s a model of s ing le pion production where a l l of the c ro s s - sec t ion proceeds v i a the i n t e r m e d i a t e i s o b a r s t a t e a. The o n l y i s o b a r s * i n c o r p o r a t e d i n the model are the A(1236) and N ( 1 4 6 0 ) . P i o n production i s the r e s u l t of isobar breakup into NTT. Coupling to the * e l a s t i c channel i s introduced by se t t ing the mass of the N isobar equal to the nucleon mass. In I I . 4 -1 , G a i s a propagator for the isobar and V a i t s decay ver tex . None of the complicat ions of sp in or i s o s p i n have been wr i t t en into th i s equat ion. The forces i n the model a r i s e from TTN in te rac t ions i n the P x l and P 3 3 32 p a r t i a l waves (an is o s p i n and angular momentum decomposition of the low * energy TTN system i s given i n table I I - 6 ) . The coupled NN •*• NN and NN •*• NA amplitudes are calculated by solving three body Blankenbecler-Sugar i n t e g r a l equations with two and three body u n i t a r i t y imposed. At no time are more than three p a r t i c l e s considered. The model dependence of the c a l c u l a t i o n resides i n the construction of 'denominator' functions which are b a s i c a l l y propagators for the isobars. The conditions of u n i t a r i t y are imposed on the T amplitudes through the construction of these denominator functions. Included i n them are unknown vertex functions representative of renormalization e f f e c t s which cannot be ca l c u l a t e d . This i s the same s i t u a t i o n encountered i n e a r l i e r peripheral models where i t was found necessary to introduce empirical form factors (functions of momentum transfer) to compensate for the i n c a l c u l a b l e renormalization e f f e c t s . In the present model a rank 1 separable form i s chosen for the vertex functions for c a l c u l a t i o n a l ease. The constructed TTN amplitudes can then be used to cal c u l a t e T N phase s h i f t s for the and P33 waves. The f i n a l agreement between the model and experimental irN phase s h i f t s i s excellent (K3 ) for P33 but poor for P ^ . F a i l u r e of the model on the P ^ amplitudes can be at t r i b u t e d d i r e c t l y to the exclusion of the physics of the Roper resonance. Improvement i n the model's treatment of the P ^ phases could be achieved by moving to a rank 2 separable p o t e n t i a l but at the expense of admitting more coupled equations into the numerical c a l c u l a t i o n . The authors of t h i s model have compared phase s h i f t s and cross-sections calculated by t h e i r model with experimental data. They have suggested that the i n a b i l i t y of the model to reproduce e l a s t i c cross-sections can be at t r i b u t e d to the non-peripheral component of the cross-33 F I G . 2-4 S I N G L E P ION PRODUCTION IN THE REACTION PP ->Pn7T + V IA THE AND P, , I SOBARS 34 TABLE 11-6 ISOSPIN AND ANGULAR MOMENTUM STATES OF THE LOW ENERGY irN SYSTEM irN STATE I X 3 L2I,2J 3/2 3/2 S31 P31 P 3 3(A++) n+n 3/2 1/2 S31 P31 P 3 3(A+) 1/2 1/2 S l l P l l P13 The states with s i g n i f i c a n t amplitudes below a pion k i n e t i c energy of MeV are underlined. Above 8 0 MeV, the P__(A + +) resonance dominates. TABLE I1-7 ALLOWED LOW ANGULAR MOMENTUM STATES IN THE PARTIAL WAVE DECOMPOSITION OF pp -»• nA PP STATE JP A++CP33) n STATE \ \ F2 3 F F 3 0 ~ 1" 2" 2+ 2" 3" 3P * 0 3 p 5 p P l , P l 3 P 2 , 5 D 2  S2 3 P 2 , 5 F 2  P 3 ^ + P ( S 3 1 ) n STATE S 0 0 + \ 3 p o 0 " \ 3 p l 1~ S l 2+ 3P P2 35 section i n that channel and the neglect of higher mass resonances. They fi n d good agreement with experiment for the spin averaged N N •*• NNTT cross-sections from 500 to 2000 MeV. On the basis of th i s agreement they have claimed that the OPE model c a l c u l a t i o n s e x p l i c i t l y show the peripheral (KI} nature of the N N -»• NNTT amplitude . In a l l cases the model predicts large spin dependent e f f e c t s i n both N N and NNTT channels. 36 I I I . EXPERIMENTAL FACILITY Much of the apparatus used i n the present experiment was b u i l t at the Rutherford High Energy Laboratory and used i n the previous program of pp and np measurements c a r r i e d out at TRIUMF. The neutron detector and large multi-wire proportional chambers and readout are described f u l l y i n previous t h e s e s ^ L " ' > ^ ^ . The polarized proton target used was the ex-( B9) Liverpool U n i v e r s i t y target ' which was brought to TRIUMF i n 1979 ( S l ) f o r the AOL and Aa-p experiment . The primary proton beam polarimeter was i n s t a l l e d and ca l i b r a t e d during one of the e a r l i e s t ( A5) measurements at TRIUMF. The present experiment was commissioned on BL 4C at TRIUMF i n early 1981. In th i s chapter the apparatus used i n the pnTr + measurement i s described at a l e v e l of d e t a i l appropriate to convey how the data was acquired. More detailed descriptions of th i s 4 i i i • « u j i * (C4,W2,W3) equipment are av a i l a b l e i n technical reports I I I . l CYCLOTRON TRIUMF ( T r i - U n i v e r s i t y Meson F a c i l i t y ) i s located on the campus of the U niversity of B r i t i s h Columbia (UBC). The TRIUMF sector focussing cyclotron i s v a r i a b l e i n energy and accelerates H~ ions to extraction energies ranging from approx. 180 to 520 MeV. A proton beam of selected energy i s extracted by intercepting the H~ beam c i r c u l a t i n g i n the tank with a carbon or aluminum s t r i p p i n g f o i l . The energy of the extracted beam i s determined by the r a d i a l p o s i t i o n of the st r i p p i n g f o i l . H~ ions for polarized beam are taken from a Lamb s h i f t polarized ion ( T l ) source and are e l e c t r o s t a t i c a l l y a c c e l e r a t e d to 300 KeV f o r i n j e c t i o n to the cycl o t r o n . The phase acceptance at i n j e c t i o n i s 40 degrees requiring that the d.c. pre-accelerated beam be bunched and F I G . 3-1 THE TRIUIIF CYCLOTRON AND EXPER IMENTAL AREAS ^42 MeV Isotope Production Cyclotron V Interim Radioisotope Laboratory BLI (p) -yr ION SOURCE -H" POLARIZED ION SOURCE Thermal Neutron Facility Two independent beams are extracted for use i n the Proton H a l l and Meson H a l l . The primary requirement of Proton H a l l users i s a low in t e n s i t y polarized proton beam f o r NN physics. 38 chopped before i n j e c t i o n . Reversal of the beam p o l a r i z a t i o n i s ef fected at the ion source. The tank vacuum i s kept below 2 x 10 " 7 t o r r to minimize gas s t r i p p i n g and the magnetic f i e l d i n the tank i s l i m i t e d to 5.8 k i l o -gauss to prevent e l e c t r i c d i s s o c i a t i o n of the H ~ . The radio frequency ( r f ) a cce le ra t ing voltage i s 90 kV. continuous wave at 23.05 MHz., which i s the f i f t h harmonic of the cyc lo t ron frequency. The time s t ructure of the beam i s a burst every 43 nsec of width 2-5 nsec . The macroscopic duty factor i s 100%. III.2 THE PROTON POLARIMETER The proton polarimeter i n BL 4A monitored the i n t e n s i t y and p o l a r i z a t i o n of the beam de l ivered to BL 4C. This device was a symmetric four armed telescope of p l a s t i c s c i n t i l l a t o r s viewing e l a s t i c scat ters from a 1.6 mm C H 2 f o i l suspended i n the beam p i p e . Each arm had two s c i n t i l l a t o r s i n e l e c t r o n i c coincidence to minimize random counts . The s c i n t i l l a t o r telescopes were mounted i n pairs i n the h o r i z o n t a l plane with one pair detect ing i n coincidence protons scattered to the l e f t at 2 6 ° and t h e i r corresponding r e c o i l s while the other pa i r monitored scat ters to the r i g h t . A schematic of the monitor i s shown i n f i g . 3-2 and i t s e l e c t r o n i c l o g i c i s d e t a i l e d i n f i g . 3-3. The sum of the monitor counts for the l e f t and r i gh t arms was propor t iona l to the i n t e n s i t y of the beam, whereas t h e i r d i f ference measured the p o l a r i z a t i o n of the beam. From eq. I I .1-17 , the count r a t e , L , i n the l e f t monitor for beam po la r i zed (Pfc) i n the normal d i r e c t i o n and an unpolar ized target i s given by L = R 0 ( l + P ( + 2 6 ° ) P b ) where R n i s the count rate for unpolar ized beam and P ( + 2 6 ° ) , the equivalent of AJJQ, i s the p o l a r i z a t i o n parameter for e l a s t i c pp 39 scattering at 26° l e f t . The count rate i n the right monitor i s R = R Q(1 + P(-26°)P b) Since P(6)= -P(-6), an asymmetry e can be defined such that L-R e = L+R " P < + 2 6 ° > P b The beam p o l a r i z a t i o n i s thus P b = e/P(+26°). The r e s t r i c t e d kinematic acceptance of the polarimeter supressed the carbon contamination. Correction factors for the carbon contribution to the observed asymmetries have been measured p r e v i o u s l y ^ ^ and are given i n table III-2. The corrections have been applied i n the form of given by CH2* The beam p o l a r i z a t i o n using the corrected asymmetries i s P, = b P(+26°) H I CH_2j L-R L+R P(+26°) H eCH, The value of P at 26° was obtained from a phase s h i f t analysis of the world d a t a ^ " ^ . The monitor has been c a l i b r a t e d for s t a b i l i t y against .(01) beam movement The o v e r a l l accuracy of the p o l a r i m e t e r i s ± 1.5% p o l a r i z a t i o n of the beam delivered to BL 4C was t y p i c a l l y 70 % and was used as an indicato r f o r misaligned beam. < A 5>. The III. 3 NEUTRON COLLIMATOR The neutron collimator was a 25 ton assembly of s t e e l and lead with 11 equally spaced beam ports bored from -3° to +27°. BL 4C i s an extension of BL 4A v i a the 0° port of the neutron c o l l i m a t o r . For th i s experiment a 20 cm long copper plug with a 1 mm hole bored was f i t t e d into the o r i g i n a l 3.5 m long 0° port. By using a quadrupole magnet to defocus the beam on the copper c o l l i m a t o r , the i n t e n s i t y of beam admitted to BL 4C 40 F I G . 3 - 2 PROTON BEAN POLARIMETER LR telescope SCINTILLATOR NOTATION l S t LETTER 2 n d LETTER NUMBER L LEFT F FORWARD 1 FRONT R RIGHT R RECOIL 2 BACK 41 1 1 I t ± ± XX L F I LF 2 LR I LR 2 L F L R RF I RF 2 RR I RR 2 R F R R M SCALER SCALER SCALER SCALER SCALER L+R SCALER S C A L E R ELECTRONIC LOGIC DIAGRAM FOR PROTON BEAM MONITOR F I G . 3-3 42 TABLE I I I - l DIMENSIONS OF THE SCINTILLATORS IN THE PRIMARY PROTON BEAM POLARIMETER HEIGHT WIDTH THICKNESS SCINTILLATOR mm mm mm F l 30 40 3.2 F2 30 50 3.2 RI 50 50 3.2 R2 70 100 3.2 TABLE 111-2 CARBON BACKGROUND CORRECTION TO BEAM LINE POLARIMETER PRIMARY BEAM I r , £„, ENERGY w I r„ n / e r„ (MeV) ^ 2 L H 2 210 4.2 1.031 325 8.4 1.050 427 10.6 1.056 480 12.3 1.057 516 12.1 1.056 = Rate using f o i l X = Measured asymmetry from a CH2 f o i l = measured asymmetry from hydrogen 43 was reduced by a factor of 10 . III.4 UCLA BENDING MAGNET This d ipo le magnet was o r i g i n a l l y part of a proton c y c l o t r o n at U . C . L . A . . The magnet weighs 40 tons and has a pole gap of 49" . Its present use i n BL 4C i s to bend the proton beam through an angle of 3 5 ° . Protons degraded by mul t ip l e s ca t t e r ing i n the co l l imator were swept aside by th i s magnet. For measurements r e q u i r i n g beam po la r i zed i n the l o n g i t u d i n a l d i r e c t i o n , the beam i s f i r s t precessed to the sideways d i r e c t i o n by a solenoid and then i n coming through the bending magnet the proton spins are further precessed to the l o n g i t u d i n a l . Beam po la r i zed i n the normal d i r e c t i o n does not have i t s p o l a r i z a t i o n vector af fected by the UCLA magnet. III.5 FOCUSSING AND STEERING MAGNETS Two sets of quadrupole doublets for focussing the beam were a v a i l a b l e i n BL 4C. These were used minimal ly except to disperse the beam on the co l l imator s ince the beam q u a l i t y was exce l lent without them. V e r t i c a l and h o r i z o n t a l d ipo le s teer ing magnets were s i tuated before and a f ter the bending magnet. These were used to center the beam on the c o l l i m a t o r , monitors , and t a rge t . III.6 4C MONITORING SYSTEM AND BEAM DEFINING SCINTILLATORS Monitors were a v a i l a b l e to check beam focus and center ing at the polar imeter , bending magnet and at the ta rget . These monitors consis ted of mul t i -wire propor t iona l chambers of r e s o l u t i o n 1 to 4 mm. The l a s t monitor (4CM8) was mounted 1 m upstream of the target and had 1 mm wire 44 spacing. The monitor boxes were permanently i n s t a l l e d i n the beamline and evacuated by the beamline vacuum system. The chambers however could be swung i n and out of the beam by remote c o n t r o l . Only 4CM8 was l e f t i n the beam permanently. S c i n t i l l a t o r s placed just upstream of the target were also a v a i l a b l e as monitors of beam centering and movement. A pair of s p l i t s c i n t i l l a t o r s monitored beam movement i n the v e r t i c a l and horizontal d i r e c t i o n s . Each s p l i t pair consisted of two s c i n t i l l a t o r s measuring 2.5 x 1.3 x 1 mm, i n d i v i d u a l l y wrapped and separated by 1.2 cm. Ratios of l e f t - r i g h t and up-down rates were checked a f t e r new beam tunes to ensure the beam had not s h i f t e d . Three s c i n t i l l a t o r s were used to define the incident beam. Two of these ( T l and T2 on diagram 4-1) were placed back to back at a distance of approx. 40 cm from the target. Their dimensions were 4.0 x 3.75 cm and 10.2 x 8.25 cm res p e c t i v e l y , both being 2 mm thick. A veto s c i n t i l l a t o r (V) of dimension 5.1 cm square by 1.6 mm thickness with a c i r c u l a r hole 1.2 cm i n diameter bored through i t was placed 30 cm from the target to veto beam not centered on the target. The coincidence of T l and T2 with V i n anti-coincidence defined the incident beam. III.7a POLARIZED PROTON TARGET The cy l i n d e r containing the target material was a perforated hydrogen free polytetrafluoroethylene (te f l o n ) c e l l measuring 2.4 cm long by 1.5 cm i n diameter. The target composition by weight was 95% butanol (C^HgOH) and 5% H 20 doped with 2-ethyl 2-hydroxybutyric acid - Cr(v) complex (EHBA-Cr ( v ) ) . This alcohol mixture was frozen i n l i q u i d nitrogen to form beads 1.0 to 1.7 mm i n diameter. The density of free hydrogen, found from 4 5 F I G . 3-4 POLAR IZED PROTON TARGET AND NMR CO IL Perforated fep target holder 46 weighings of the target mater i a l and measurements of the target c e l l volume, was 0.0717 ± 0.0003 gm c m - 3 representing 13.25% of the t o t a l target weight. An operat ing temperature of of 0.5 °K was maintained by a H e 3 evaporation . r e f r i g e r a t o r . Thermal i n s u l a t i o n was provided by a He 4 condenser bath and a l i q u i d N 2 s h i e l d . The target assembly was suspended i n a 25.55 k i lo-gauss magnetic f i e l d produced by two superconducting Helmholtz c o i l s . For the geometry used i n the A j ^ measurement, the c o i l s and target can i s te r r e s t r i c t e d the unimpeded ex i t of p a r t i c l e s emerging from the target to ± 5 0 ° i n the h o r i z o n t a l plane and ± 7 . 5 ° i n the v e r t i c a l p lane . The target was dynamically po la r i zed by i r r a d i a t i o n with microwaves at 71 GHz. Reversal of target p o l a r i z a t i o n was achieved by adjust ing the microwave frequency and could be completed i n ha l f an hour. The target p o l a r i z a t i o n was genera l ly 65%. III.7b BACKGROUND FROM NON-HYDROGENOUS MATERIAL The po la r i zed target contained only 13% free hydrogen g iv ing r i s e to a background of pnTr + events from bound protons i n non-hydrogenous mater ia l s (mostly carbon) i n the t a rge t . To estimate the c o n t r i b u t i o n from t h i s unpolar ized background, data was taken with the po l a r i zed target mater i a l replaced by t e f l o n which has no free hydrogen. The t e f l o n was cut in to small disks and packed into the target c e l l at a dens i ty s i m i l a r to the ac tua l target beads. Aside from the composition of the target , procedures for the background run were exact ly the same as for data taken with the po l a r i zed t a rge t . Separate running periods were used to a l low time to change the t a rge t . 47 111.7c NMR POLARIZATION MONITOR The target p o l a r i z a t i o n was monitored continuously by a micro-( C3 ) p r o c e s s o r based n u c l e a r magnetic resonance (NMR) system . A solenoidal four turn sampling c o i l of 0.05 mm thick copper f o i l was wound on a polymer cylinder 2.0 cm i n diameter e n c i r c l i n g the target c e l l . Radio frequency power was supplied by a Rockland model 5600 frequency synthesizer. The r f driver was programmed to sample 301 frequencies centered on 108.8 MHz i n steps of 1 KHz, repeated at i n t e r v a l s of 20 sec. The NMR probe operated on the p r i n c i p l e of Q meter d e t e c t i o n ^ . Interaction between the probe and nuclear magnetization i n the sample caused r f power to be either absorbed from the c o i l or induced i n the c o i l . Quality factor curves sampled s l i g h t l y off resonance (by adjusting the s t a t i c magnetic f i e l d ) were d i g i t i z e d and stored i n microprocessor memory. The NMR signal sampled during the experiment was d i g i t i z e d and subtracted from the control Q curve by the microprocessor, then forwarded to the on-line data a c q u i s i t i o n system. The difference between the NMR si g n a l at resonance and the Q curve was proportional to the p o l a r i z a t i o n of the target. To determine the constant of p r o p o r t i o n a l i t y , the NMR si g n a l was c a l i b r a t e d at thermal equilibrium where the p o l a r i z a t i o n can be calculated d i r e c t l y from the fundamental Boltzmann Law which requires that the equilibrium populations of energy l e v e l s , Em , are proportional to e m . The equilibrium temperature, T, enters c r i t i c a l l y into the c a l c u l a t i o n s , making a precise knowledge of the temperature e s s e n t i a l . The quantity recorded was the integrated NMR s i g n a l i n units of v o l t s -KHz. 48 III.7d INDEPENDENT CALIBRATION OF THE TARGET POLARIZATION In a d d i t i o n to data on the p n T r + r eac t ion some e l a s t i c s ca t t e r ing data was taken to a l low an independent c a l i b r a t i o n of the target p o l a r i z a t i o n . The NMR measurement of target p o l a r i z a t i o n had good s t a t i s t i c a l accuracy but a large systematic uncer ta inty r e s u l t i n g from the d i f f i c u l t y i n c a l i b r a t i n g the thermal e q u i l i b r i u m s i g n a l . The nuclear s ca t t e r ing asymmetry measurement provided an independent check of th i s c a l i b r a t i o n and reduced the o v e r a l l uncer ta inty i n the target p o l a r i z a t i o n to ± 2 % . The a c q u i s i t i o n of the target c a l i b r a t i o n data together with the ana lys i s and re su l t s of that data were a separate s e l f contained measurement independent of the res t of the experiment and are deal t with separate ly i n appendix B. I I I .8 THE FORWARD ANGLE CHAMBERS The forward angle chambers (F i n f i g . 4 - 1 ) were the same set of s i x mul t i -wire propor t iona l chambers of lm square ac t ive area used i n previous experiments^L~* ^ . A complete d e s c r i p t i o n of these chambers has been v - . ^ u , ( C 4 , W 2 , W 3 ) . . . . . . . . . published . A summary of t h e i r use i n t h i s experiment i s g iven here . The chambers were used to detect both the protons and p o s i t i v e pions emerging i n the forward d i r e c t i o n . The angular coverage obtained with these chambers was approx. ± 2 3 ° i n the v e r t i c a l and h o r i z o n t a l d i r e c t i o n s . The chambers were of the s ing le wire readout type and w e l l su i ted for detect ing two charged p a r t i c l e s s imultaneously . In each chamber a c e n t r a l plane of 5 1 2 p a r a l l e l sense wires was sandwiched between two high voltage cathode planes maintained at t y p i c a l l y 5 kV negative b i a s . The sense wires were made of 2 0 um gold plated 4 9 F I G . 3-5 DIAGRAM OF A ONE METER M U L T I - U I R E PROPORTIONAL CHAMBER USED I N THE FORUARD ARRAY 50 tungsten and held under 50 gm tens ion . They were spaced 2 mm apart but to expedite readout adjacent wires were e l e c t r o n i c a l l y paired g i v i n g an e f f e c t i v e r e s o l u t i o n of 4 mm. The high tension planes were of 122 um bery l l ium copper wires a lso pi tched at 2 mm. The frames supporting the wire planes were assembled with the sense plane orthogonal to the two high voltage planes and separated from them by 8 mm. The ent i re wire assembly was contained wi th in a gas t i ght j acket , the gas envelope having 120 um melinex windows covering the ac t ive area of the MWPC. A 'magic gas' mixture of 50% argon, 46% isobutane, 0.4% freon and 4% methyla l was c o n t i n u a l l y f lushed through each chamber. The s ix chambers with gas handling equipment and readout e l e c t r o n i c s were mounted on a moveable frame. When packed as c l o s e l y as the chamber frames a l lowed, the sense planes were separated by 58 mm. The chambers were mounted with sense planes a l t e r n a t e l y h o r i z o n t a l and v e r t i c a l so that three chambers provided d e t a i l s on ' x ' coordinates and three on ' y ' coordinates . The chamber readout e l e c t r o n i c s d i g i t i z e d a unique wire address for each of the ac t iva ted wires which was then read by the o n - l i n e a c q u i s i t i o n system. Fast e l e c t r o n i c l o g i c derived from s c i n t i l l a t o r pulses was used to t r i gger the readout. Readout was i n i t i a t e d by a strobe s i g n a l which daisy chained through chamber e l e c t r o n i c s s e t t ing latches for each ac t iva ted w i r e . The strobe was fo l lowed, a f ter a preset delay , by a scan s i g n a l which prompted l a t c h e s c o n t a i n i n g data to t r a n s m i t t h e i r addresses. One a l t e r a t i o n to the chambers was necess i tated by the design of the experiment which required that unscattered beam pass through the centers of the chambers. To avoid rate problems, the c e n t r a l region of each MWPC was desens i t ized by weaving 74 um t h i c k disks of mylar in to the plane of 51 the sense wires . The angular coverage of the mylar disks was ± 4 ° viewed from the t a rge t . Subsequently no rate problems i n the c e n t r a l region were encountered under running c o n d i t i o n s . A s c i n t i l l a t o r hodoscope was mounted on the chamber support wagon approx. 75 mm downstream of the s i x t h chamber. The hodoscope was used i n conjunct ion with other detectors to define an event t r i g g e r . The hodoscope cons i s ted of 8 overlapping s c i n t i l l a t o r s forming a 3 x 3 matrix of s i m i l a r l y s ized reg ions . On- l ine e l e c t r o n i c l o g i c determined whether two charged p a r t i c l e s (candidates for the p and TT+) had entered two separate regions of the hodoscope. A b i t p a t t e r n for the hodoscope was w r i t t e n to tape so that o f f - l i n e l o g i c a l deduction could be used to i d e n t i f y which regions of the hodoscope had been a c t i v a t e d . This crude p o s i t i o n a l information was used as a check on the tracks f i t t e d through the chambers, those f a i l i n g to in tercept a s truck region of the hodoscope being immediately r e j e c t e d . The s c i n t i l l a t o r hodoscope i s drawn i n f i g . 3-6. The s c i n t i l l a t o r s were designated A-H with the 9 regions defined by t h e i r overlaps denoted 1-9. The c e n t r a l area (9) defined by the B.E coincidence had a 18 cm hole cut to allow passage of the unscattered beam. III.9 THE NEUTRON DETECTOR Neutrons from the pmr+ reac t ion were detected i n an array of block s c i n t i l l a t i o n counters . The neutron array was placed at a dis tance of 6.2 m from the target and subtended an angle of ± 4 . 5 ° . It was moveable i n the h o r i z o n t a l plane to cover a l l k i n e m a t i c a l l y allowed neutron polar angles . The neutron detector provided p o s i t i o n a l and time of f l i g h t (TOF) information on the neutrons. Both pieces of information were necessary for the kinematic recons t ruc t ion of events described i n sec t . V . 2 b . 52 F I G . 3-6 THE FORURRD S C I N T I L L A T O R HODOSCOPE A B C D E F THE EIGHT SCINTILLATORS ARE DESIGNATED A~H AND THE NINE AREAS DEFINED BY THEIR OVERLAPS 1"9 53 The neutron detector was organized into two v e r t i c a l banks with s i x b i l l e t s of NE110 s c i n t i l l a t o r bars i n each stack. The dimensions of each b i l l e t were 15 x 15 x 105 cm. In the o r i g i n a l design t h i s detector had seven b i l l e t s i n the front bank and seven i n the rear. For t h i s experiment the c e n t r a l b i l l e t s were removed and replaced by wooden blocks to support the remaining counters. This was done to prevent unscattered beam from h i t t i n g an active area of the detector when placed i n the extreme forward region. A l i g h t guide and photomultiplier tube (PMT) were mounted on either end of each s c i n t i l l a t i o n bar. The difference i n a r r i v a l time of l i g h t at the two ends of a b i l l e t was d i g i t i z e d e l e c t r o n i c a l l y to give p o s i t i o n a l information. The p o s i t i o n a l r e s o l u t i o n was l i m i t e d i n the v e r t i c a l d i r e c t i o n by the si z e of the b i l l e t (±7.5 cm) and i n the h o r i z o n t a l d i r e c t i o n (along the b i l l e t ) by the timing r e s o l u t i o n (±4.5 cm). The sum of the a r r i v a l times at the two ends of each b i l l e t was a constant and was used to obtain TOF information independent of the l i g h t t r a n s i t time i n the b i l l e t . Timing of the neutron f l i g h t path was done with respect to the two beam s c i n t i l l a t o r s T l and T2. Absolute c a l i b r a t i o n of the neutron TOF to the detector was obtained from a gamma peak i n the TOF spectrum for each b i l l e t (sect. V.2a). To obtain accurate timing r e s o l u t i o n , the PMT outputs from the neutron array b i l l e t s were discriminated i n a 'high-low' coincidence. The timing of the coincidence was determined by a low l e v e l d i s c r i m i n a t i o n threshold while a high l e v e l discriminator f i l t e r e d noise. With t h i s method, timing independent of pulse height and pulse shape was obtained. Voltage l e v e l s on the PMTs were set such that the high discriminator threshold corresponded to a point on the cosmic muon spectrum equivalent 5 4 F IG . 3 - 7 THE CHARGED P A R T I C L E VETO AND I T S COVERAGE OF THE NEUTRON ARRAY B I L L E T S / M W NVB W Nv/C A-D A-D D-A B-E B-E OF C-F E-B F C \ NwD / \ Nv/E / \ NWF / 55 F I G . 3 - 8 H I - L O U B I L L E T T IM ING 56 to approx. 10 MeV e l e c t r o n energy. Cosmic muons were a l so used to time i n the b i l l e t s r e l a t i v e to each other for on- l ine purposes. Subsequently accurate timings were determined o f f - l i n e from the r e l a t i v e pos i t ions of the Y spikes i n the TOF spectra for each b i l l e t . A charged p a r t i c l e veto (NV) cons i s t ing of a s c i n t i l l a t o r hodoscope was mounted on the front of the neutron de tec tor . The s ix overlapping s c i n t i l l a t o r s i n the veto each measured 365 x 746 x 6 mm. When placed i n the forward reg ion , the neutron counter was i n the shadow of the charged p a r t i c l e acceptance defined by the forward chambers. This would have re su l ted i n the r e j e c t i o n of a l l events with a charged p a r t i c l e s t r i k i n g any por t ion of the ve to , representing a s i g n i f i c a n t loss i n phase space coverage. To obta in data at t h i s kinematic s e t t i n g , the charged p a r t i c l e veto was res tructured into three separate v e r t i c a l reg ions . Referr ing to f i g . 3-7, the top row of s c i n t i l l a t o r coincidences provided veto pro tec t ion for b i l l e t s 1,2,7 and 8, and s i m i l a r l y for the middle (3 ,4 ,9 ,10) and bottom (5,6,11,12) b i l l e t s . This allowed the neutron and a charged p a r t i c l e track to be i n c lose proximity to each other , with the cond i t ion that only neutrons detected i n b i l l e t s not covered by an act ivated region of the veto were accepted as t r i g g e r s . 57 I V . DATA A C Q U I S I T I O N Data taking for the experiment commenced with the successive measurements of the A ^ and A^^parameters followed by the simultaneous measurement of A ^ , A^Q and AQ^, and was completed with the measurement of the A parameter. Data taken i n the A c o n f i g u r a t i o n with the o O IN IN polarized target material replaced by t e f l o n was used to simulate the background from non-hydrogenous materials i n the target. An e l a s t i c s c a ttering asymmetry measurement performed i n the ANN configuration provided an independent c a l i b r a t i o n of the target p o l a r i z a t i o n . The arrangement of equipment and detectors for the experiment i s shown i n f i g . 4-1. There are some d e t a i l s of the apparatus which are s p e c i f i c to data taken on ANN and the p o l a r i z a t i o n s . IV .1 T H E ANN CONF IGURAT ION For data taken i n the ANN configuration both beam and target were polarized i n the normal d i r e c t i o n . Since the cyclotron d e l i v e r s beam polarized i n the normal d i r e c t i o n , the precessing solenoids were not needed i n t h i s configuration and were l e f t unpowered. P o l a r i z a t i o n of the target i n the normal d i r e c t i o n required an arrangement of the target Helmholtz c o i l s such that the magnetic f i e l d was i n the normal d i r e c t i o n . The magnet structure combined with the r e f r i g e r a t i n g canister determined the l i m i t s on the target exit windows and consequently also the l i m i t s on the accessible phase space. These l i m i t s were d i f f e r e n t for each o r i e n t a t i o n of the c o i l s and were g i v e n i n I I I . 7 f o r the ANN configuration. Because of experimental d i f f i c u l t i e s , the side chambers (LI and L2) contributed no useful data i n the ANN configuration. The experiment was kinematically complete with a l l three f i n a l state ;s POLARIMETER \ SOLENOID COLLIMATOR F I G . 4-1 EXPERIMENTAL CONFIGURATION BENDING MAGNET POLARIZED TARGET / / / /////, 59 p a r t i c l e s being detected. The three p a r t i c l e hardware trig g e r required on-l i n e coincidences of the beam s c i n t i l l a t o r s , the forward s c i n t i l l a t o r hodoscope and the neutron detector. The formation of th i s event tri g g e r from i t s constituent parts i s described i n the following sections. E l e c t r o n i c diagrams are included for c l a r i t y . I V . 2 T H E I N C I D E N T BEAM MONITOR T l and T2, shown i n f i g . 4-1, were used to monitor the incident beam. The Tl*T2 coincidence output width was adjusted to give a narrow 4 nsec pulse. A width of 10 nsec was chosen for the veto output, V, so that Tl*T2 was safe l y contained within V thus ensuring the timing of the a n t i -coincidence Tl«T2 «V was determined by the leading edge of the Tl*T2 signal (4-6a). A delayed T l *T2 output of width 70 nsec was put into a n t i -coincidence to re j e c t events i n which there was a beam proton i n either of the two previous r f buckets. The purpose of this delayed veto w i l l be discussed i n sect. 4-5. The f i n a l beam defining coincidence required i n the formation of the on l i n e trigger was T1«T2«(V + T1*T2). This c o i n c i d e n c e was s c a l e d as the counter of beam incident on the target. R e q u i r i n g the T1*T2*(V + Tl*T2) coincidence i n the trigg e r automatically compensated for any rate dependence i n the PMTs for T l and T2. I V.3 T H E PTT+ COMPONENT OF T H E T R I G G E R The p i r + component of the trigg e r was formed from fast l o g i c signals derived from the forward s c i n t i l l a t o r hodoscope. The requirement for a p T r + s i g n a l was h i t s i n two separate regions of the s c i n t i l l a t o r hodoscope, where the nine regions were defined by the overlaps of the eight s c i n t i l l a t o r s ( f i g . 3-6). The l o g i c of the pTr+ signal i s shown i n f i g . 4-2. A B D TDC^C2I2 DISC A.D SCALER o c > c > 1 -j > v A \  N ^V V T T 7 c G H iv v i V W V li A. G > - i I r ? ~< 4 > QIC C B. E B. G C. F D.H E. H *-5 C.G F. H w wW W W W W W W 1 + 2 + 8 1 PULSE ATTENUATOR II + II - P 7 T 61 The s ignals from each s c i n t i l l a t o r were paired i n coincidence with the other s c i n t i l l a t o r s which p h y s i c a l l y overlapped. The coincidence outputs for regions one to eight were summed i n a l i n e a r fan i n (Lecroy model 428F) then attenuated such that at l eas t two of the eight coincidences had to be present at the fan i n to generate a pTr+ output s i g n a l . The coincidence for the n in th area , B ' E , was inverted at the fan i n to bias against events where a charged p a r t i c l e was detected i n the extreme forward region where the e l a s t i c d i f f r a c t i o n peak dominates the NN sca t te r ing c r o s s - s e c t i o n . IV.4 THE NEUTRON COMPONENT OF THE TRIGGER Signals were taken from both ends of each neutron b i l l e t and t h e i r coincidence was used to define a detec t ion i n that b i l l e t ( f i g . 3-8). The r e j e c t i o n of charged p a r t i c l e s detected i n the neutron counter was performed by the charged p a r t i c l e ve to . The l o g i c formation of s igna l s from the charged p a r t i c l e veto and the neutron counter are given i n f i g s . 4-3 and 4-4. The coverage of the neutron b i l l e t s provided by the veto s c i n t i l l a t o r s was i l l u s t r a t e d i n f i g . 3-7. A de tec t ion i n the neutron counter with the absence of a s i gna l from the corresponding charged p a r t i c l e veto formed the neutron component, N*NV, of the t r i g g e r . IV.5 THE THREE PARTICLE TRIGGER The three p a r t i c l e t r igger for the experiment was T 1 * T 2 « ( V + T1~T2) • p T f + « N » N V The l o g i c of the t r igger i s given i n f i g . 4-5. A 10 nsec T l « T 2 » ( V + T 1 ~ T 2 ) pulse arranged i n coincidence with a 20 nsec p T T + pulse ensured that the t iming of t h e i r coincidence was determined by the leading edge of the N 3 N5 N 6 N7 N 8 N9 NIO NI2 NI3 NI4 FIG. 4-4 LOGIC OF THE NEUTRON SIGNAL 64 F IG . 4-5 LOGIC OF THE THREE P A R T I C L E TRIGGER T,.T2-(V+T,.T2) T |.T 2.(V + T|«T2).PTT + T , . T 2 « ( V + T , . T 2 ) » P i r + «N»NV CHAMBER S T R O B E TDC START E V E N T TRIGGER 65 T l «T2 »(V+T1 *T2) s i g n a l . There was no ambiguity i n the timing of the pir"*" s i g n a l with respect to the beam s c i n t i l l a t o r s . The protons detected at the chamber hodoscope had a t y p i c a l 3 of 0.4 over a 120 cm f l i g h t path, corresponding to a 10 nsec TOF. This was much less than the 43 nsec period of the cyclotron r f , thus ensuring that the ptr + s i g n a l i n the s c i n t i l l a t o r hodoscope was correlated with the beam proton which had counted i n T l and T2. The T l »T2 *(V+T1 ~T2) «pTr + output was stretched to 110 nsec to await a r r i v a l of the N*NV neutron s i g n a l . The timing of the f u l l t r i g g e r was determined by the N*NV pulse and more s p e c i f i c a l l y by the leading edge of the signal from the slower side (NL or NR) of the f i r s t non vetoed neutron array b i l l e t making a detection. The acceptance i n TOF of p a r t i c l e s detected i n the neutron counter was l i m i t e d by the timing of the 110 nsec gate r e l a t i v e to the N*NV s i g n a l . The resultant overlap allowed ys (from TT°S created i n the target) to s a t i s f y the coincidence requirement. The r e l a t i v e timings of the components of the three p a r t i c l e t r i g g e r are i l l u s t r a t e d i n f i g . 4-6. A l i m i t i n g factor i n the data taking rate was the random count rate i n the neutron detector, that i s the random association of a p i r + detection i n the s c i n t i l l a t o r hodoscope with an uncorrelated p a r t i c l e i n the neutron counter, which originated from a d i f f e r e n t beam burst than the one giving r i s e to the p i r + s i g n a l . The Tl*T2 delayed anti-coincidence reduced the random count rate by vetoing events whose neutron may have arisen from a previous beam burst. IV.6 DATA TRANSFER The occurrence of an event trig g e r i n i t i a t e d readout of the detectors 66 F I G . 4-6a R E L A T I V E T IM ING OF THE I N D I V I D U A L COMPONENTS OF THE TRIGGER T,.T 2 Y 4 n s T| T 2»(V + TI«T2) P7T+ TI«T2»(V + TI»T2)»P7T 1 > 10ns 10ns 20ns 110 ns N»NV 15ns J TI»T2»(V + TI»T2)»P7T + »N»NV (TRIGGER) \20ns F F I G . 4"6b T IM ING OF THE CHAMBER READOUT STROBE TRIGGER |_ STROBE 67 and transfer of data to temporary storage for blocking before being forwarded to tape. No on-line r e j e c t i o n of events was attempted. While data transfer was i n progress the a c q u i s i t i o n system was i n h i b i t e d from recording further data. The CAMAC crates containing s c a l e r s , TDCs and EG.&G. C212 b i t p a t t e r n units were i n h i b i t e d u n t i l the a c q u i s i t i o n program had completed i t s readout function. Further strobes to the chambers were vetoed to preserve wire information latched into memory from the event of i n t e r e s t . The period during which the a c q u i s i t i o n system was dedicated to event readout was known as computer busy. A separate busy condition s i g n a l l e d by the POLISIS (polarized ion source i n j e c t i o n system) spin c o n t r o l l e r prevented data being taken while the beam spin was being changed. The response of the computer gating c i r c u i t r y to an event tri g g e r i s shown i n f i g . 4-7. The data read for each event consisted of a C212 b i t p a t t e r n code (see table IV-1), an NMR p o l a r i z a t i o n i n t e g r a l , wire addresses and TDC values. A l l the TDCs for the experiment were started by the f u l l event t r i g g e r . Stops for the TDCs came from the i n d i v i d u a l counter outputs each delayed a fixed amount. The only information recorded on neutron detections was contained e n t i r e l y i n the TDC data. Any neutron array b i l l e t f a i l i n g to make a detection had i t s TDCs started by the trigger but received no stop signals from either of i t s two PMTs. The absence of a stop resulted i n an overrun s i g n a l l e d by b i t 11 of the TDC being set. The b i l l e t s which had made detections were i d e n t i f i e d by a corresponding l e f t r i g h t TDC pair which had not overrun. The TOF TDC was started by the trigg e r and stopped by a delayed Tl«T2*(V + T1~T2) •pTf + signal which had the timing of T1«T2. The value recorded i n the TOF TDC also depended on the l i g h t t r a n s i t time i n the 6 8 FIG. 4-7 COMPUTER GATING CIRCUITRY EVENT TRIGGER S P I N BUSY FROM P O L I S I S 6 C 2 1 2 B I T 0 EVENT OR S P I N BUSY SYSTEM BUSY VETO C212 STROBE COMPUTER BUSY /TV 0 DUAL GATE START GENERRTOR STOP CHAMBER STROBE m n SCALER I N H I B I T Nin CRATE I N H I B I T FAST SLOW LOGIC INTERFACE BUSY CLEAR FROM COI1PUTER 69 neutron b i l l e t . The decoding and absolute c a l i b r a t i o n of the neutron TOF are deta i l e d i n sect. V.2a. Crude charged p a r t i c l e TOFs were recorded for 7 of the 8 hodoscope s c i n t i l l a t o r s but were not used i n the f i n a l analysis of data taken in the A j ^ configuration. The problem of a short f l i g h t path (120 cm) was compounded by the large s c i n t i l l a t o r s (up to 1 m) with PMTs at only one end which didn't allow a d i r e c t elimination of the dependence on l i g h t t r a v e l time i n the s c i n t i l l a t o r . The TDC and b i t p a t t e r n information transferred for each event was of a fixed length. The wire information however was recorded i n a variable length format and was flagged to indicate an end of wire data condition. Each XY pair of chambers was grouped i n a chamber control unit (CCU). The maximum number of wire addresses accepted from each CCU were 12 and hence 36 wires i n t o t a l were the maximum read. Wire addresses were recorded i n an array of INTEGER*2 variables where the f i r s t byte had values between 0-5 corresponding to the s i x chambers and the second byte was a number between 0-255 i d e n t i f y i n g one of the 256 wires i n the chamber. The C212 b i t p a t t e r n was recorded as an 1*4 variable though only 18 b i t s were assigned. The b i t p a t t e r n code contained information on the beam spin and charged p a r t i c l e h i t s i n the s c i n t i l l a t o r hodoscope. The a l l o c a t i o n of b i t s i s given i n table IV-1. Scaler t o t a l s were accumulated i n 24 b i t KINETIC scalers and transferred to computer memory. The scalers were written to tape i n response to a spin busy from the POLISIS spin c o n t r o l l e r i n d i c a t i n g that the beam spin was changing or when an end of run condition was reached. Scaler blocks were separate from event blocks on tape and were written i n fixed format to s i m p l i f y t h e i r recovery from tape. 70 TABLE IV-1 ALLOCATION OF BITS IN THE C212 BITPATTERN BIT CONTENTS 0 Event 1 Beam spin busy 2 Beam spin up 3 Beam spin down 4 Beam spin o f f 5 -6 -7 -8 Forward s c i n t i l l a t o r A 9 Forward s c i n t i l l a t o r B 10 Forward s c i n t i l l a t o r C 11 Forward s c i n t i l l a t o r D 12 Forward s c i n t i l l a t o r E 13 Forward s c i n t i l l a t o r F 14 Forward s c i n t i l l a t o r G 15 Forward s c i n t i l l a t o r H 16 Left side chamber 17 Right side chamber FIG. 4-8 STRUCTURE OF RN EVENT ON TAPE T DC • Dat a (481*2) \ C212 (1*4) f Polar Int. (1*4) Y MWPC Data (nl*2) ' FFFF ' FLAG 71 IV.7 ON-LINE MONITORING AND SETTING UP The data a c q u i s i t i o n system incorporated a PDP 11/34 computer which handled data transfers and performed the processing required to drive the display devices such as a Tektronix 4010 graphics screen and Decwriter II and III hardcopy teletypes. On-line monitoring of the incoming data was a b u i l t i n feature of th i s a c q u i s i t i o n system. Individual wire histograms for each of the chambers were i n s t a n t l y a v a i l a b l e and proved p a r t i c u l a r l y useful for tracing chamber readout problems. A graphics function which projected the chamber h i t locations onto two orthogonal planes allowed display of the tracks recorded for i n d i v i d u a l events. Used as a guide for 'visual track f i t t i n g ' , t h i s d i splay offered a quick assessment of the i n t e g r i t y of the event information recorded i n the chambers. As a measure of the chamber e f f i c i e n c i e s , the numbers of wires activated i n each chamber per event were monitored as the percentage of times no wires i n the chamber were activated (zeroes), the percentage of times one wire was activated ( s i n g l e s ) , etc.. For the f u l l p n T r + t r i g g e r the c r i t e r i o n for good e f f i c i e n c y was a high percentage of doubles. At the st a r t of each run delay curves were measured for the chambers to determine the amount of delay (D) needed to make the a r r i v a l of the strobe coincide with the a r r i v a l of wire signals at the latches ( f i g . 4-6b) . For the purpose of sett i n g the strobe delay, a trigger requiring only one charged p a r t i c l e was used to trace out a curve of zeroes as a function of strobe delay. The delay curve had a plateau approx. 60 nsec wide. Delays i n the stop l i n e s to a l l the TDCs were adjusted and checked v i s u a l l y using the 4010 di s p l a y . Approximately 60 quantities were scaled on-line and could be accessed 72 FIG. 4-9 GRAPHIC DISPLAY OF CHAMBER HIT LOCATIONS PROJECTED ONTO TUO ORTHOGONAL PLANES HORIZONTAL PROFILE VERTICAL PROFILE FIG. 4-10 TRANSMISSION RATIO THROUGH THE TARGET ON A VERTICAL BEAM SCAN Tl .T2 .9760 .9740 .9720 — .9700 .9680 -100 100 200 CURRENT IN THE VERTICAL STEERJ NG MAGNET (ARBITRARY UNITS) 73 at any time. This feature was used extensively for i n i t i a l t e s t i n g as well as for sytematic checking during data taking. Commonly used r a t i o s of scaled quantities were calculated and displayed on demand. Event rates, asymmetry i n the polarimeter, the p o s i t i o n of the beam on the target, the performance of the i n d i v i d u a l counters, e s p e c i a l l y the veto counters, and random counts i n the neutron array were continuously monitored. Random rates were estimated by delaying a T1*T2*(V + T l »T2) ' p T r + pulse three r f periods and forming a coincidence with N'NV. In order to center the beam on the target, a large s c i n t i l l a t o r (T3) was temporarily placed behind the target to measure the transmission r a t i o , Tl*T2-T3/T1*T2, as a function of beam p o s i t i o n at the target entrance. The attenuation of transmitted p a r t i c l e s was observed as the beam was swept across the target. The beam was positioned at the minimum of the transmission curve, where an attenuation of 3% was observed. The veto counter was mounted on a traversing table with remote drive allowing independent movement i n the v e r t i c a l and horizontal d i r e c t i o n s . The veto counter was scanned through the beam to maximize the p a r t i c l e s passing through the hole. A 24 b i t LED dataway display maintained a v i s u a l check on the latching of bitpatterns into the C212 module. P e r i o d i c a l l y the NMR i n t e g r a l , which read out i n 24 binary b i t s , was displayed to check that the gain and p o l a r i t y b i t s were being set properly. IV.8 STATISTICS FOR THE A m MEASUREMENT The data taking rate was determined by the neutron array which had an acceptance of ±4.5° i n both v e r t i c a l and horizontal planes. To span the range of allowed neutron angles (table IV-2) the neutron detector was 74 pos i t ioned succes s ive ly at 8 ° , 1 7 ° , 2 6 ° and 3 5 ° to the l e f t of the beam. For each neutron array s e t t i n g , data was taken with both p o l a r i t i e s of the t a rge t . The p o l a r i t y of the beam was under program c o n t r o l and cycled through 5 minutes of sp in up, 5 min. spin down and 1 min. sp in off g iv ing i n t o t a l s ix combinations of beam and target s p i n . T y p i c a l t r i gge r rates with the po la r i zed target var ied with the p o s i t i o n of the neutron detector i n accordance with Monte Carlo (S2) pred ic t ions . At 510 MeV a rate of approx. 2.0 t r igger s per sec i n l i v e time per MHz of inc ident beam was observed with the neutron counter at 8 ° , dropping to 0.7 t r i gger s /sec/MHz at 3 5 ° . Only data with unpolar ized beam was recorded with the t e f lon t a rge t . The t r i gger rate with the t e f l o n target was lower than with the po la r i zed target and was a t t r ibu ted to the absence of free hydrogen i n that t a rge t . A summary table of the pmr + data taken i n the A^N conf igura t ion i s given i n table IV-3 . 75 TABLE IV-2 MAXIMUM LAB POLAR ANGLES FOR NEUTRONS FROM pp + pniT + Energy 0 ^ t r o ^ (MeV) | (Deg.) 465 37.1 TABLE IV-3 No. OF ON-LINE TRIGGERS IN THE A r a CONFIGURATION Energy Po la r i zed Beam Neutron Array Angle # Of On Line Tr iggers (MeV) (Deg.) (Thousands) DATA WITH THE POLARIZED TARGET 510 Yes 8 ° 50.0 1 7 ° 58.9 2 6 ° 40.0 3 5 ° 64.0 465 Yes 8 ° 56.7 1 7 ° 76.7 2 6 ° 59.2 3 5 ° 50.0 420 Yes 8 ° 44.4 1 7 ° 39.0 DATA WITH THE TEFLON TARGET 465 No 8 ° 23.7 1 7 ° 25.0 2 6 ° 25.0 3 5 ° 25.0 420 No 8 ° 25.0 1 7 ° 13.0 2 6 ° 13.0 7 6 V. DATA ANALYSIS The analysis procedures and software routines for the pp •*• pmr + data evolved n a t u r a l l y into a three stage process. At the f i r s t stage the o r i g i n a l data tapes were reduced to a more manageable set of summary tapes. The major task performed by the f i r s t stage reduction routines was the f i t t i n g of charged p a r t i c l e tracks through the chambers and the matching of tracks with h i t s i n the s c i n t i l l a t o r hodoscope. The TDC information was scanned and only TDCs with data i n the acceptable range were forwarded to the next stage. Header and scaler block information was transferred to the summary tapes unaltered. Data reaching the second stage was analyzed by a kinematics program whose function was to correlate information from the i n d i v i d u a l detectors and separate v a l i d p n T f + events from spurious data and background. A x2 assessment was made of each event reaching this stage. Analysis of the t e f l o n target data by the same method provided an estimate for the amount of background which could not be rejected by the x2 t e s t . A l l reconstruct-ed events (those for which x2 could be made to converge) were written to a t h i r d tape for further examination. At the f i n a l stage reconstructed events were read o ff tape, selections were made on X > background subtractions were applied and the asymmetries were c a l c u l a t e d . The de s c r i p t i o n of data analysis presented i n t h i s chapter i s organized s i m i l a r l y into three sections which p a r a l l e l the three stages of a n a l y s i s . Pions emerging from the reaction pp •*• pnif1" with momenta as low as 80 MeV/c were accepted by the apparatus. Such pions were deflected through an angle of more than 40° by the 25 kilo-gauss f i e l d of the polarized target. At the reconstruction stage of the analysis i t was imperative to have an 77 accurate parameterization of the charged p a r t i c l e d e f l e c t i o n s to reconstruct t h e i r true momenta and scattering angles. A f u l l d e s c r i p t i o n of the parameterization developed for this purpose i s given i n appendix A. The analysis and res u l t s of the target c a l i b r a t i o n data are given i n appendix B. V . l STAGE 1: REDUCTION TO SUMMARY TAPES The f i r s t step performed i n the decoding of the chamber data involved conversion of the wire addresses into coordinates ( i n mm) i n the plane of the chamber making the detection. The array containing wire addresses was scanned and adjacent activated wires were i d e n t i f i e d and grouped. Each group of activated wires represented a possible coordinate on a charged p a r t i c l e track. The number of wire groups found i n chamber no. 6 for one run i s i l l u s t r a t e d i n f i g . 5-1. There i s a predominance of double groups as expected. Independent str a i g h t l i n e tracks were f i t t e d to coordinates measured-by each of the two orthogonal chamber sets. Two chamber f i t s involving a c l u s t e r (more than 3 adjacent wires activated) i n either coordinate were rejected, as were three chamber f i t s involving a c l u s t e r i n more than one coordinate. It was assumed that these rej e c t i o n s did not bias the data. Each successful f i t yielded a slope and intercept measurement i n the corresponding plane. At t h i s stage the candidate tracks i n the two orthogonal planes were s t i l l completely uncorrelated. Cuts were applied on the intercepts of the tracks at the target to r e j e c t tracks which were not consistent with p a r t i c l e s emerging from the target. The intercepts of the f i t t e d tracks and the positions of the cuts are shown i n f i g . 5 -2 . F i t t e d tracks were also required to intercept the s c i n t i l l a t o r hodoscope within 78 TABLE V - l DISTANCES OF THE FORWARD CHAMBERS AND SCINTILLATOR HODOSCOPE FROM THE TARGET CHAMBER // DISTANCE FROM TARGET (± 4.8 mm)  1 622.8 2 725.3 3 827.8 4 930.3 5 1032.8 6 1135.3 SCINT HODOSCOPE 1214.7 F I G . 5-1 tf OF U IRE GROUPS ( REPRESENT ING P O S S I B L E HITS) FOUND I N CHAMBER no. S I X 250 -£ 125 —1 U J a ec 0 I • I • I • I • I I I I I I I 1 1 2 3 4 5 6 7 8 9 10 11 12 - O F M I R E G R O U P S P E R E V E N T F I G . 5 - 2 INTERCEPTS OF THE TRACKS F I T T E D THROUGH THE CHAMBERS AT THE TARGET INTERCEPT IN THE HORIZONTAL COORDINATE I N T E R C E P T I N T H E V E R T I C A L C O O R D I N A T E 80 the physical extent of the s c i n t i l l a t o r array. The e f f e c t of the target magnetic f i e l d on the t r a j e c t o r y of charged p a r t i c l e s while traversing the chambers was studied by ray t r a c i n g . It was found that an 80 MeV/c p a r t i c l e (the lowest s i g n i f i c a n t momentum i n t h i s experiment) traversing the chambers on a path contained i n a plane perpendicular to the f i e l d axis (which i s the path most affected) experienced a d e f l e c t i o n of 0.34°. The amount of d e f l e c t i o n r a p i d l y became less s i g n i f i c a n t for higher momenta where the curvature of the charged p a r t i c l e tracks i n the chambers became i n s i g n i f i c a n t compared to the wire spacings themselves. The curvature was ignored and straight tracks were f i t t e d through the chambers under the approximation of a f i e l d free region. Up to the completion of track f i t t i n g , r e j e c t i o n s had been made on the components of the tracks without the benefit of the correlated information provided by the s c i n t i l l a t o r hodoscope. The array of stored tracks i n the horizontal plane was paired with tracks from the stores of v e r t i c a l candidates. Only pairs of tracks that combined to give a three dimensional track which intercepted the s c i n t i l l a t o r hodoscope i n an activated region were acceptable candidates. After pairing of h o r i z o n t a l and v e r t i c a l components to determine a set of candidates for charged p a r t i c l e tracks, members of that set were paired with each other to form a set of paired tracks i n three dimensions which were then candidates for a r e a l proton-pion p a i r . For each event, a l l two charged p a r t i c l e track candidate pairs reaching this stage were passed to the reconstruction stage where further selections were made. The o v e r a l l percentage of events rejected because two candidate tracks that matched s c i n t i l l a t o r h i t s could not be found varied at 510 MeV 81 from 80% with the neutron detector at 8 ° to 94% at 3 5 ° . A strong c o r r e l a t i o n exi s ted between tracks recorded i n the chambers and the timing of the chamber s t robe . Track information was lo s t for both fast and slow neutrons (evident i n f i g . 5-10). A second problem resu l ted from the overlaps of the s c i n t i l l a t o r s i n the hodoscope. A small overlap between s c i n t i l l a t o r s A, D and G (< 1 wire spacing) allowed a s ing le p a r t i c l e to f a l s e l y s a t i s f y the coincidences for two separate areas . The i d e n t i c a l problem occurred at the four corners of the hodoscope. V.2 STAGE II: x2 EVENT RECONSTRUCTION The neutron array and TOF TDCs were read from the summary tape and decoded, then combined with the track information to determine whether the event information recorded by the detectors was cons i s tent with a pmr + event occurr ing off a free proton i n the target .The measure of consis tency was the x2 (weighted leas t squares f i t ) . V.2a DECODING OF THE NEUTRON ARRAY A l l the TDCs for the experiment were s tarted i n common and stopped by delayed outputs from the i n d i v i d u a l counters . It was genera l ly poss ib le to determine which neutron array b i l l e t was i n time with the t r i g g e r . The counter pulse cont r ibu t ing to the t r igger l o g i c , and which eventua l ly determined the timing of the t r i g g e r , was fanned through a preset delay and also stopped the TDC af ter an a d d i t i o n a l constant length of t ime. Hence each side (NL and NR) of each b i l l e t had a c h a r a c t e r i s t i c timing spike i n i t s TDC spectrum ( f i g . 5-3) i n d i c a t i v e of the times when that component determined the timing of the t r i g g e r . Since no b i t p a t t e r n was recorded for the charged p a r t i c l e ve to , th i s method was used to d i s t i n g u i s h the neut ra l p a r t i c l e from the charged proton or pion of the 82 F I G . 5-3 T IM ING S P I K E FOR THE LEFT S IDE OF ONE NEUTRON RRRRY B I L L E T 400 H 200 —\ 0 160 r^TTTp>rv iTTvrr f f 190 ^ 220 T O C C H A N N E L S (10 C H / n s e c l IS THE POSITION OF THE TIMING SPIKE IN THE TDC SPECTRUM 83 event, which sometimes struck the neutron array. F i g . 5-4 shows the l o g i c a l structure of the timings recorded by the neutron array TDCs. The conversion from TDC values to p o s i t i o n along the b i l l e t was expressed by the r e l a t i o n where XN was the distance from the center of the b i l l e t i n mm, B i l l e t was the width of the b i l l e t (1050 mm), and Cal was the width i n TDC channels of the d i s t r i b u t i o n TDCL~TDCR. It was only necessary to determine C L - C R + A L - A R a s a single constant. The dependence of the TOF TDC on the l i g h t t r a n s i t time i n the b i l l e t was eliminated using the neutron array TDCs. In p a r t i c u l a r the TOF of the neutral p a r t i c l e to the detector was The chronology of the TOF measurement i s shown i n f i g . 5-5. The absolute c a l i b r a t i o n of the TOF measurement was provided by a Y spike appearing i n the TOF spectrum for each b i l l e t . The dominant cross-section for production of these Ys was the reaction pp •*• p p T ^ with electromagnetic decay of the I T 0 into YY. Figure 5-6 shows the Y peak i s o l a t e d from the rest of the TOF spectrum. The peak shown combines the 12 b i l l e t s and indicates a TOF r e s o l u t i o n with a standard deviation, a, of 1.3 nsec. There was a low l e v e l background assumed to r e s u l t from Ys produced when neutrons h i t the cement shiel d i n g and walls of the experimental area. Cosmic rays were also i d e n t i f i e d i n this background. The leading edge of the Y peak was sharper than the f a l l i n g edge. This e f f e c t was a t t r i b u t e d d i r e c t l y to charged pions from the pnir + reaction a r r i v i n g at the detector 2 nsec slower than the Ys. XN = {[(TDC L-TDC R)-(K L-K R)-(C L-C R+A L-A R)]/2}: x-B i l l e t Cal TOF = constant + [TDCT+TDC_J/2 - [TOF TDC] 84 F I G . 5-4 DECODING OF THE NEUTRON DETECTOR OTHER BILLETS VETO W ( V + T | » T 2 ) * P 7 T + STOP 1 L N»NV TRIGGER TDC START START 1 L" TDC STOP i s the time for the l i g h t pulse to t r a v e l from i t s h i t l o c a t i o n i n the b i l l e t to the l e f t edge of the b i l l e t . i s the time for co l l i m a t i o n i n the l i g h t guide, a m p l i f i c a t i o n i n the PMT, d i s c r i m i n a t i o n , and formation of the hi-low gate defining N L . i s the time for the NIM l o g i c s i g n a l to t r a v e l from i t s formation at NL to the stop input of the l e f t T D C . i s the time for the NIM s i g n a l to propagate from i t s formation at NL through the coincidence and veto boxes to the trigg e r formation and on to T D C L where i t provides the s t a r t . 85 FIG. 5-5 CHRONOLOGY OF THE NEUTRON TOF MEASUREMENT ARE TlflES THAT ARE VARIABLE ARE TIMES THAT ARE CONSTANT IN RS t— ED TO t— tu _i fX INS] —i EC LLI INS] BI ET TI rr UJ o z r— X CO CJ LIGHT •— z CO LIGHT z ROTO LAtl : LIGHT M U l c a. m 11 u a co rr ex co rr ID C3 •X PnTT* EVENT AT TARGET -TOF X HIT ON NEUTRON DETECTOR CONSTANT -X TOF TDC—A Q. O CO REAL TIME 1600 H 800 —\ FIG. 5-6 7 PEAK ISOLATED FROM THE TOF SPECTRUM 10 20 30 TOF(nsec) 86 V .2b LEAST SQUARES FIT TO A pun* EVENT The quantities obtained from experiment were the polar and azimuthal angles of a l l three p a r t i c l e s and the neutron TOF. Five equations of constraint were a v a i l a b l e for checking the consistency of the event information. These were three equations of momentum conservation, one equation of energy conservation, and one equation i n neutron TOF. With the designation that the p a r t i c l e s corresponding to tracks 1,2, and 3 were the neutron, proton, and pion r e s p e c t i v e l y , the f i v e contraints were e x p l i c i t l y Y ( l ) = PF x - P ^ i n O ^ o s ^ - P 2 s i n 6 2cos <t>2 - P 3 s i n 6 3 c o s ((13 Y(2) = PF y - P ^ i n e ^ i n ^ - P 2sin6 2sin<j> 2 - P 3 sin9 3sin<|>3 Y(3) = PF z - P 1 c o s 9 1 - P 2 c o s e 2 - P 3 c o s 6 3 Y< 4> = i n c i d e n t " =1 " *2 " *3 Mn= mass of neutron Y(5) = P x - C c = speed of l i g h t /( c 2 T 0 F 2 / d 2 _ L ) d = distance of f l i g h t A x 2 f i t to the f i v e equations determined the three free parameters P p P 2, and P 3 which minimized the residuals (Y). x 2 was defined by x 2 = Ii=1>5 {Yd)/^} 2 where o\ was the error on equation ( i ) . The quantity PF represented the Fermi momentum of the struck nucleon and was always set to zero i n the x f i t s ( i e . the struck nucleon was assumed f r e e ) . The evaluation of X 2 required estimates of the errors for each of the f i v e constraining equations. The error on the neutron TOF measurement was taken to be the width of the Y peak. The uncertainty i n the energy equation originated mainly from energy losses i n the target. An error of 1 MeV was assigned to this equation, which was about the amount of energy 87 l o s t by the incident proton i n traversing 1/2 of the target length. Error estimates for the momentum equations were more d i f f i c u l t to obtain. In addition to P-^ , P 2, and P3, two of the three components of PF were freed similtaneously r e s u l t i n g i n 5 equations to determine 5 parameters. For scatters o f f free protons, the Fermi momentum of the struck nucleon was zero and hence the widths of the peaks i n the reconstructed components of PF were due e n t i r e l y to experimental r e s o l u t i o n . Protons bound i n carbon generally had non-zero Fermi components r e s u l t i n g i n a broad background. The 'Fermi Recontructions' provided estimates of the experimental momentum reso l u t i o n from the widths of the c l e a r l y v i s i b l e hydrogen peaks. Sample Fermi reconstructed peaks are shown i n f i g . 5-7 and t y p i c a l l y had a standard deviation of 10 MeV/c. The centering of the Fermi d i s t r i b u t i o n s was not an imposed constraint, and provided a useful check on systematics concerning geometry and timing c a l i b r a t i o n s . A l l the error estimates used i n the x 2 reconstructions are given i n table V-2. The experimentally determined angles of the charged p a r t i c l e s were asymptotic angles measured af t e r emergence from the target magnetic f i e l d . The angles required i n the constraining equations were the true scattering angles at the target l o c a t i o n which could not be calculated without a knowledge of the p a r t i c l e ' s momentum. Since the momentum of the p a r t i c l e could not be accurately estimated without knowledge of the actual scattering angles, an i t e r a t i v e procedure was developed to obtain the true scattering angles and momenta simultaneously. The i t e r a t i o n r e l i e d on the magnetic f i e l d parameterization described i n appendix B. To s t a r t the i t e r a t i o n , nominal values were input for P j , P 2, and P3. Corrections for the f i e l d d e f l e c t i o n s were estimated using these values of the momenta and new estimates of the scattering angle were obtained. Using the new F I G . 5-7 SAMPLE FERMI RECONSTRUCTED PERKS 89 TABLE V-2 ERROR ESTIMATES USED IN THE x 2 RECONSTRUCTIONS ENERGY (MeV) ANGLE (DEG) oPF. aPF. dPFr oTOF aE X Y Z (MeV/c) (MeV/c) (MeV/c) (nsec) (Mev) 510 8° 7.7 9.4 12.8 1.3 1.0 17° 8.5 13.9 25.5 1.5 1.0 26° 10.2 13.6 13.6 1.3 1.0 35° 10.2 13.6 13.6 1.3 1.0 465 8° 6.8 11.9 13.6 1.3 1.0 17° 10.2 17.0 23.8 1.3 1.0 26° 10.2 11.9 13.6 1.3 1.0 35° 10.2 11.9 13.6 1.3 1.0 420 8° 10.2 11.9 15.3 1.3 1.0 17° 10.2 18.7 20.4 1.3 1.0 90 estimates of angles, a d i f f e r e n t set of P j , P 2, and P 3 were obtained from a x 2 f i t to the f i v e equations. The new values of momenta were used to recompute the charged p a r t i c l e d e f l e c t i o n s and y i e l d a better estimate of the s c a t t e r i n g angle. This procedure was i t e r a t e d to convergence. Convergence of the so l u t i o n was defined when the change i n momenta between i t e r a t i o n s was less than 1 MeV/c for a l l three p a r t i c l e s . Generally 7 i t e r a t i o n s were required. Since no p o s i t i v e charged p a r t i c l e mass i d e n t i f i c a t i o n had been made yet, the i t e r a t i o n was repeated with charged p a r t i c l e mass assignments reversed. As well the reconstruction procedure was done for each v a l i d combination of charged p a r t i c l e tracks with neutron array h i t s . The combination of tracks and mass assignment having the lowest x 2 was selected and stored. V . 2 c BACKGROUND SUBTRACTIONS P r o f i l e s i n x 2 for data taken with the polarized target were compared with x 2 d i s t r i b u t i o n s obtained for the t e f l o n target data. The t e f l o n target data was reconstructed i d e n t i c a l l y to the polarized target data and u s i n g the same e r r o r e s t imates In the c o n s t r a i n i n g e q u a t i o n s . Normalization of the background subtractions was obtained by comparing the two x 2 d i s t r i b u t i o n s at high x 2 (12<x 2 <96) where the free hydrogen contribution to the polarized target d i s t r i b u t i o n was expected to be n e g l i g i b l e . The polarized target d i s t r i b u t i o n was then compared with the normalized background d i s t r i b u t i o n i n the region of small x 2 to determine the most e f f e c t i v e cut on x and to estimate the amount of background remaining a f t e r the cut. The c r i t e r i o n applied i n choosing the cut on x was minimization of the r e l a t i v e error on the free proton s i g n a l . The error i n determining the free proton signal was dominated by s t a t i s t i c s 91 with the error on the background subtraction of secondary importance by comparison. Therefore, instead of cutting close on x 2 to minimize the background, the x 2 cut was placed to minimize the r e l a t i v e error on the free proton s i g n a l and maximize the s t a t i s t i c a l s i g n i f i c a n c e of the r e s u l t . The error on the hydrogen signal included s t a t i s t i c a l errors on the polarized target data, s t a t i s t i c a l errors on the t e f l o n target data, and s t a t i s t i c a l errors on the normalization of the background. A sample of the x 2 d i s t r i b u t i o n for the polarized target data and normalized t e f l o n target data i s shown i n f i g . 5-8. The dashed l i n e i s not continued past X2=6 for c l a r i t y . It follows the s o l i d l i n e very c l o s e l y beyond that point. Teflon target data for background subtractions was a v a i l a b l e only at 465 and 420 MeV. To obtain normalized background subtractions at 510 MeV, the 465 MeV t e f l o n data was used and normalized to the t a i l of the 510 MeV polarized target d i s t r i b u t i o n . The assumption involved was that the normalization of the carbon background changed from 465 to 510 MeV but not i t s shape, which was observed to be co n s i s t e n t l y f l a t for a l l t e f l o n target data taken. The a v a i l a b i l i t y of t e f l o n target data only with unpolarized beam required the further assumption that the shape of the carbon background was not spin dependent, though i t s normalization could depend on the analyzing power of carbon for the pnTr + r e a c t i o n . At each neutron array s e t t i n g , the av a i l a b l e t e f l o n data was used to normalize the background separately for each of the 6 spin combinations of the polarized beam with the polarized target. The background contributions were evaluated as the r a t i o of reconstructed background events within the l i m i t s of the x2 cut compared to the t o t a l number of reconstructed events inside the cut. Background subtractions calculated for the experiment are FIG. 5-8 2 DISTRIBUTION FOR THE POLARIZED PROTON TARGET DATA AND NORMALIZED TEFLON TARGET DATA 4 0 0 -POLARIZED PROTON TARGET (ALL SPINS) TEFLON TARGET (NORMALIZED AT HIGH X 2 ) 0 2 4 6 8 10 12 14 X 2 ( 2C FIT) 3 0 0 200 -93 TABLE V-3 BACKGROUND SUBTRACTIONS F i r s t Arrow Indicates Target P o l a r i t y , Second Indicates Beam P o l a r i t y ENERGY NARRAY SPIN ASSIGNMENTS ANGLE ++ -K +0 4-0 510 8° 17° 26° 35° 465 8° 17° 26° 35° 420 8° 17° 0.1202 0.0696 ±.0215 ±.0113 0.2068 0.0984 ±.0284 ±.0125 0.2185 0.1280 ±.0614 ±.0327 0.1799 0.1705 ±.0927 ±.0843 0.0661 0.0649 ±.0152 ±.0122 0.2014 0.0950 ±.0344 ±.0142 0.1411 0.1037 ±.0452 ±.0279 0.5114 0.1748 ±.3983 ±.1136 0.1239 0.0827 ±.0292 ±.0180 0.1951 0.0830 ±.0431 ±.0168 0.0756 0.0959 ±.0122 ±.0156 0.1846 0.2059 ±.0243 ±.0283 0.2098 0.1423 ±.0589 ±.0393 0.2326 0.2807 ±.1222 ±.1459 0.0934 0.1066 ±.0169 ±.0214 0.1696 0.1692 ±.0263 ±.0259 0.2699 0.1720 ±.0801 ±.0472 0.3030 * 0.2841 ±.2010 ±.1787 0.0647 0.1187 ±.0141 ±.0278 0.1406 0.1400 ±.0282 ±.0289 0.0669 0.1061 ±.0149 ±.0203 0.1259 0.2170 ±.0200 ±.0395 0.1935 0.1701 ±.0616 ±.0559 0.1364 0.5455 ±.0839 ±.3357 0.0883 0.0866 ±.0236 ±.0232 0.1450 0.1594 ±.0274 ±.0290 0.1379 0.3501 ±.0449 ±.1348 0.1818 0.3788 ±.1516 ±.3343 0.1011 0.0868 ±.0287 ±.0255 0.1102 0.2015 ±.0304 ±.0477 94 given i n table 5-3. A consistency check on the method of normalizing the background at high x 2 was provided by the beam spin off data at 465 MeV. At t h i s energy and with unpolarized beam, the x 2 t a i l of the polarized target d i s t r i b u t i o n a r i s i n g from non-hydrogenous materials i n the target was d i r e c t l y comparable to the t e f l o n target data taken at the same energy. Both d i s t r i b u t i o n s were normalized by the incident beam counts and compared. Table V-5 gives the r a t i o s of normalization factors calculated from scaler normalization and from normalization at high x2« The agreement was s a t i s f a c t o r y though l i m i t e d by the amount of polarized target data a v a i l a b l e with beam spin o f f . In p r i n c i p l e the technique of normalizing the background at high x 2 had the advantage that i t compensated for any small differences i n density between the two targets and any change i n detection e f f i c i e n c y between the two running periods. However these advantages were l a r g e l y cancelled by the l i m i t e d s t a t i s t i c a l accuracy. Additional checks were made by summing over beam p o l a r i t i e s to simulate unpolarized beam and the same general agreement was obtained. V.2d ADDITIONAL CUTS The x 2 reconstructions did not s t r i c t l y demand energy or momentum conservation. As well the neutron TOF was free to deviate from i t s measured value i n a way that minimized x • Cuts were applied on the d i f f e r e n c e i n energy between the known i n c i d e n t s t a t e and the reconstructed outgoing state (DE) and on the d i f f e r e n c e between the measured and reconstructed neutron TOF (DT). Like the cuts on x2> these cuts were calculated at stage II but applied at stage III of the processing. The cut on x provided the s i n g u l a r l y most e f f e c t i v e s e l e c t i o n of free proton events, but the cut on the DT was also b e n e f i c i a l i n 95 TABLE V-4 SELECTION OF X 2 CUTS ENERGY NARRAY X 2 CUT (MeV) ANGLE 510 8° 5.6 17° 2.6 26° 2.6 35° 2.8 465 8° 5.6 17° 1.8 26° 2.6 35° 2.6 420 8° 4.0 17° 4.2 TABLE V-5 CONSISTENCY CHECK ON BACKGROUND NORMALIZATION AT 465 MeV RATIO NORMALIZATION FACTOR AT HIGH x 2 NORMALIZATION FACTOR BY SCALERS NARRAY ANGLE 8° 17° 26° 1.111 ± 0.195 1.029 ± 0.141 1.019 ± 0.214 96 re j e c t i n g some events to which x was i n s e n s i t i v e . For example, the error i n determining the momentum from the TOF measurement (eq. Y(5)) i n f l a t e d r a p i d l y and became singular when the TOF of the detected p a r t i c l e (assumed to be a neutron i n the reconstructions) approached the TOF for ys. As a r e s u l t eq. Y(5) entered the x2 reconstructions with large errors when the p a r t i c l e t r i g g e r i n g the neutron detector was r e a l l y a y or an e l a s t i c proton. Therefore x2 was somewhat i n s e n s i t i v e to the measured TOF for these events and allowed the reconstructed TOF to d i f f e r from the measured TOF, providing a convenient quantity to cut on. F i g . 5-9 shows a plot of DT a f t e r a cut on x2 and demonstrates the use of th i s cut i n making rejections which had evaded the x cut. Probably a more important aspect of the DT and DE cuts was t h e i r function i n the absence of x2 cuts. In normalizing the backgrounds at high X 2, the cuts on DT and DE were l e f t i n place and provided protection against spurious data. The amount of r e a l pnir + background from carbon appearing i n the normalization region was also s u b s t a n t i a l l y reduced. The raw, uncut spectrum i n TOF of the p a r t i c l e s detected i n the neutron array and i n time with event triggers i s shown i n f i g . 5-10 for 510 MeV 8° data. The proton peaks separated by 43 nsec are c h a r a c t e r i s t i c of a l l data taken with the neutron detector at 8°. At t h i s p o s i t i o n the frame of the neutron array and the PMT bases themselves intercepted unscattered beam and protons scattered e l a s t i c a l l y at small angles. This gave r i s e to counts i n the neutron detector due to p a r t i c l e s entering the counter through the side face, thereby evading the charged p a r t i c l e veto. P o s i t i o n a l information from the neutron counter confirmed that the proton peaks i n the TOF spectrum were highly l o c a l i z e d at the right side (near the beam) of the neutron detector. The TOF spectrum for the same data 97 FIG. 5-9 PLOT OF THE RECONSTRUCTED NEUTRON TOF MINUS THE MEASURED NEUTRON TOF AFTER THE CUT ON * 2 98 a f t e r cuts on x > DE, and DT i s also shown i n f i g . 5-10. The raw spectrum was taken from a sing l e run, whereas the spectrum with cuts applied contains a l l the events reconstructed at 510 MeV 8 ° . Of the events reaching the X 2 reconstruction stage, almost a l l were reconstructed. At 510 MeV the cuts on x2> DE, and DT subsequently rejected 50.2% of the reconstructed events for 8° data, 78.5% for 17°, 87.6% for 26°, and 90.4% for 35°. The trend to a higher r e j e c t i o n rate at larger angles i s consistent with the r i s e i n background observed i n the Fermi (S2) reconstructions and with Monte Carlo predictions V.3 STAGE I I I : BINNING AND PRESENTATION OF THE DATA Five quantities are needed to specify completely the kinematics of the pmr + f i n a l state at a given beam energy, i n contrast with the two body f i n a l state reactions which require only one. There are no established conventions governing the se l e c t i o n of these kinematic v a r i a b l e s . Choices can generally be made i n ways advantageous for si m p l i f y i n g the matrix elements of the reaction or for emphasizing p a r t i c u l a r features of the reaction. V.3a THE CHOICE OF A COORDINATE SYSTEM For the purpose of comparing with published c a l c u l a t i o n s , the data from t h i s experiment were binned i n the convention adopted i n the th e o r e t i c a l paper^^^. The coordinate sytem used was the {L,S,N} lab frame depicted i n f i g . 2 - l a . This reference frame was p r a c t i c a l from the experimental point of view since the beam and target spins were prepared i n p o l a r i z a t i o n states along these fixed axes and a l l measurements were ca r r i e d out i n th i s frame. The f i v e kinematic quantities chosen to specify the f i n a l state were the momentum of the proton and the polar and 99 F I G . 5 - 10 RRU TOF SPECTRUM AT STAGE I BEFORE TRACK F I T T I N G AND AT STAGE I I AFTER X 2 RECONSTRUCTIONS AND CUTS 4 8 0 H 2 4 0 H 0 2 0 4 0 6 0 8 0 TOF(nsec) 1 0 0 1 2 0 3 0 0 H 1 5 0 — 2 0 4 0 6 0 8 0 TOF(nsec) 1 ' 1 0 0 1 2 0 1 0 0 a z l m u t h a l a n g l e s o f the two charged p a r t i c l e s . T h e o r e t i c a l p r e d i c t i o n s have been p u b l i s h e d f o r the s i m p l i f i e d case o f i n - p l a n e geometry w i t h the a z i m u t h a l a n g l e s o f the p r o t o n and p i o n f i x e d a t 0 o r TT. Thus f o r c o m p a r i s o n w i t h the model, the e x p e r i m e n t a l d a t a a r e d i s p l a y e d as graphs o f asymmetries a g a i n s t p r o t o n momentum f o r f i x e d p i o n - p r o t o n a n g l e p a i r s . The c o p l a n a r a p p r o x i m a t i o n was p a r t i c u l a r l y a p p r o p r i a t e i n the A ^ N c o n f i g u r a t i o n where the v e r t i c a l a c c e p t a n c e was s e v e r e l y r e s t r i c t e d by the e x i t windows of the p o l a r i z e d t a r g e t . The s p i n / a n g l e c o n v e n t i o n i s shown i n f i g . 5 - 1 1 . A d i s a d v a n t a g e o f the { L , S , N } l a b system i s t h a t the m a t r i x elements c a l c u l a t e d i n t h i s r e f e r e n c e frame do not w e l l r e p r e s e n t t h e u n d e r l y i n g (S3) p h y s i c a l mechanisms such as p i o n exchange . F o r t h i s r e a s o n the d a t a were b i n n e d i n a r e f e r e n c e frame whose axes depended on the p a r t i c l e momentum l a b e l s . T h i s frame was chosen s p e c i f i c a l l y f o r the r e s u l t i n g s i m p l i f i c a t i o n i n the dependence o f the m a t r i x e lements on the decay a n g l e s of the A. T a b l e I I - 5 was an i l l u s t r a t i o n of t h i s p o i n t . The axes o f t h i s r e f e r e n c e frame a r e e x p l i c i t l y d e f i n e d i n c h a p t e r V I . S i n c e the amount o f e x p e r i m e n t a l d a t a a v a i l a b l e f o r b i n n i n g was modest ( t a b l e V - 6 ) , a s e r i e s o f one d i m e n s i o n a l p l o t s were made. I n t h e s e 1 - D p l o t s t he asymmetries were b i n n e d a g a i n s t a s i n g l e v a r i a b l e ( e g . momentum t r a n s f e r ) w h i l e i n t e g r a t i n g o ver the a c c e p t a n c e i n the o t h e r v a r i a b l e s . The a c c e p t a n c e i n a l l v a r i a b l e s was not symmetric o r complete due t o the i n c o m p l e t e phase space c o v e r a g e o f the e x p e r i m e n t . The momentum d i s t r i b u t i o n s of the n e u t r o n , p r o t o n , and p i o n a r e shown i n f i g . 5 - 1 2 f o r a l l the e v e n t s r e c o n s t r u c t e d i n the A ^ N c o n f i g u r a t i o n a t 5 1 0 MeV, and i l l u s t r a t e t h a t t h e momentum a c c e p t a n c e o f the AJJJJ c o n f i g u r a t i o n , p a r t i c u l a r l y f o r the p i o n , was i n c o m p l e t e . T h e r e f o r e the 1 - D p l o t s may be 101 F I G . 5-11 SPIN/ANGLE CONVENTION TABLE V-6 No. OF EVENTS AVAILABLE FOR BINNING (AFTER ALL CUTS) ENERGY (MeV) 510 NARRAY ANGLE 8 ° 1 7 ° 2 6 ° 3 5 ° # OF GOOD EVENTS IN ALL SIX SPIN STATES 4132 2088 607 222 465 8 ° 1 7 ° 2 6 ° 3 5 ° 2024 1420 476 46 420 8 ° 1 7 ° 1307 841 102 F I G . 5 - 1 2 MOMENTUM ACCEPTANCE I N THE A CONFIGURATION AT 510 MeV NEUTRON MOMENTUM (MeV/c) PROTON MOMENTUM (MeV/c) 103 expected to r e f l e c t some s e n s i t i v i t y to the hidden v a r i a b l e s . Ultimately, the 1-D plots proved very i n s t r u c t i v e i n i d e n t i f y i n g the factors of importance i n the pnif"'" reaction. A q u a l i t a t i v e assessment of the data based on the 1-D plots suggested a simple i n t e r p r e t a t i o n of the reaction pp •»• pmf*" and offered some insigh t s into the production mechanism. V.3b EXTRACTION OF A m , A $ 0 i AND AQN The s p i n c o r r e l a t i o n parameter, AJJN, and the p o l a r i z a t i o n s , AJJO and AQN, were extracted from a simultaneous weighted least squares f i t to the six spin dependent cross-sections formed from the 3 combinations of beam spin (+ve, -ve, unpolarized) with the two combinations of target spin (+ve, -ve). From eq. II.2-17, the s i x spin dependent cross-sections were I 1 - I M l + A ^ P J + A Q N P J + A ^ P * } , i=l,...6 £ {++, +-, — — , 0+, 0- }, where the f i r s t vector sign indicates beam p o l a r i t y and the second indicates target p o l a r i t y . In terms of p a r t i c l e rates, I* was the number of reconstructed free proton events a f t e r a l l cuts and background subtractions counted within the l i m i t s of the defined bin for the spin combination i . Each kinematic bin was s p e c i f i e d by i n t e r v a l s on three axes for the model c a l c u l a t i o n s and on only one axis for the 1-D p l o t s , although i n p r i n c i p l e f i v e axes were required to specify uniquely a b i n . 1° was the number of counts expected i n the bin for unpolarized scattering and was expressed as an undetermined geometric constant, representing da/dfi integrated over the s o l i d angle acceptance of the apparatus, times the number i n the incident beam. Therefore s i x equations were a v a i l a b l e to determine four unknowns. However rather than trying to f i t for the geometric constant, t h i s unknown 104 was eliminated by d i v i d i n g eq. 5 by 6, 4 by 5, etc., leaving f i v e equations to determine the three spin asymmetry parameters. The error on the free proton s i g n a l , I, included s t a t i s t i c a l errors on the bin counts combined with background subtraction e r r o r s . To estimate the e f f e c t of uncertainties i n the beam and target p o l a r i z a t i o n s on the determination of the asymmetry parameters, the f i t was repeated with and Pt varied from t h e i r nominal values by the amount of t h e i r measured e r r o r s . These errors were added i n quadrature with the s t a t i s t i c a l errors r e s u l t i n g from the f i t . Since r e p o s i t i o n i n g the neutron detector altered the s o l i d angle acceptance of the experiment, and hence the normalization of 1°, the spin asymmetries were calculated for each of the four positions of the neutron array and weighted averages were calculated for any overlapping bins. 105 VI RESULTS AND CONCLUSIONS The AJ^J, A ^ , Agg, A ^ Q , and A ^ parameters, plotted i n f i g . 6-1 for a fixed pion-proton angle p a i r , are compared with the p r e d i c t i o n s ( D ^ > ^ 6 ) of the model described i n section I I . 4 . The comparison i n f i g . 6-1 i s for a select angle pair at 5 1 0 MeV. The A ^ data i s taken from a previous i crbec ( S 7 ) ( S 2 ) work . A ^ , A ^ Q and are the data descrbed i n the previous chapters. These re s u l t s have been reported previously The agreement between the experimental data and the model predictions i s generally good, but with some d e f i n i t e discrepancies i n evidence. The OPE A dominance model c l e a r l y does not account for some detai l e d features seen i n the data. The spin c o r r e l a t i o n parameters, p a r t i c u l a r l y A L L , tend to be more p o s i t i v e than the model c a l c u l a t i o n s . The pol a r i z a t i o n s are i n general underestimated by the model, and show a d e f i n i t e v a r i a t i o n with kinematics. This v a r i a t i o n i s a feature which i s not reproduced by the model. The data show sim i l a r trends at a l l three energies and over the ent i r e kinematic region sampled by the experiment. The model predictions also show very l i t t l e v a r i a t i o n with energy or kinematic setting within the range accessed by the experiment. At present i t i s not clear how to interpret discrepancies from the model. In order to study the quantitative features of the data, i t was assumed that the dominant process was pp •> nA"1-1", and the asymmetries were plotted against (a) the neutron transverse momentum and (b) angles describing the A decay. An invariant mass plot of the p i T + pair (A++) taken from the A ^ N configuration i s shown i n f i g . 6-2 and supports the notion of a resonant TTN i n t e r a c t i o n i n the intermediate s t a t e . The relevant angles are now defined. The z axis was taken along the beam d i r e c t i o n , y v e r t i c a l and x to 1 0 6 F I G . 6-1 COHPRRISON U ITH THE flODEL THE GRAPHS SHOWN ARE 510 MeV DATA WITH THE NEUTRON DETECTOR AT 8 ° . THE ANGLE PAIR DISPLAYED IS 6p= 10 ° ± 5 ° , 6^ = 20° ±5° (EXCEPT FOR Agg WHERE 9p, 0^ = 0 o ± 1 2 . 5 ° ) . MCMENTUM BINS ARE 50 MeV/c WIDE (100 MeV/c FOR Ass). SOLID LINES ARE MODEL C A L C U L A T I O N S F O R 9p= 10° AND 6^ = 20° AT 500 MeV. 0.0 -02 -0.4 •0.6 -08 -1.0 -1.2 -1.4 0 0 •0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 _L I fl0N J I I I T f l N 0 300 400 500 300 400 500 p (MeV/c PLAB ) 107 F I G . 6 - 2 I N V A R I A N T P T T + M A S S CO £ 375 -J 1050 1090 1130 1170 Pvr + MASS(MeV) 510 MEV OfiTfi 465 MEV DflTfl 1120 MEV DflTH 108 the l e f t . The production angle n and azimuthal angle X for a neutron with center of mass momentum, p n , were defined such that i t had momentum components p = p sinncosX x n p = p sinrisinX y n p = p cos TI r z r n The A decay was described i n a system of axes with z^ along the A d i r e c t i o n in the cm. frame, and axes x' and y' i n the A rest frame such that i i ' was to the l e f t i n the nA production plane and y_' , defined by y'=z' x x', was normal to the production plane. The pion from the A decay, with momentum p-^  i n the A rest frame, was used to define polar and azimuthal angles 0 and <j> such that i p = p sin0cos<|> X TT I p = p s in0sind> y TT t p = p cos 9 Z TT For binning against one dimensional v a r i a b l e s , a center of mass reference frame defined i n terms of the nA production plane was used, with L, being the d i r e c t i o n of the beam, being to the l e f t i n the production plane, and N_= x S normal to the production plane. This set of axes was simply the {x^ y^ JE.} s e t r°tated about z_ through the azimuthal angle X of the neutron. Since the beam and target pol a r i z a t i o n s were prepared along the x, y, and z d i r e c t i o n s , the transformation to axes defined i n the production plane mixed components of the p o l a r i z a t i o n vectors. Thus the asymmetries measured i n t h i s frame f o r data taken i n the ANN configuration depended on an admixture of Ass with ANN given by ( A g ssin 2X + A N N c o s 2 X ) P B P T and on a p o l a r i z a t i o n term (A^ P g + A ^ P ^ c o s X . 109 The projections of the p o l a r i z a t i o n vectors onto the production frame axes were evaluated i n each kinematic bin at each s e t t i n g of the neutron detector. The admixture of Ags i n ANN data was small, generally 12% with the neutron detector at 8° and dropping to < 1% at 35°. Since the measured asymmetries were se n s i t i v e only to the l i n e a r combination and not to AJJN and Ass i n d i v i d u a l l y , these two parameters could not be extracted simultaneously. Therefore a smoothed value for Ass w a s used for the purpose of determining ANN* The smoothed value of Ass input was everywhere equal to -1. The data presented i n the following tables and graphs j u s t i f y t h i s choice. In the ANN configuration the only asymmetries containing a s i g n i f i c a n t component of Ass a r e those calculated from 8° data. For 17° data the c o e f f i c i e n t of the Ass term, <sin 2X>, has dropped to < 4%. The data taken i n the ANN configuration at 8° are strongly correlated with large values of D7T+ mass. The percentage of events at th i s angle (510 MeV data) having a piT + invariant mass greater than 1155 MeV i s 95.7, with the mass d i s t r i b u t i o n peaking at 1170 MeV. The r e s u l t s of the Ass measurement demonstrate that the data demand an Ass value near -1 for large pir + masses. Therefore any perturbations to the ANN data introduced by th i s treatement of the Ass component are i n s i g n i f i c a n t compared to the s t a t i s t i c a l e r r o r s . In tables VI-1, VI-2, VI-3 and f i g s . 6-3, 6-4 and 6-5, the data have been summed into one dimensional plots against (a) the neutron transverse T momentum P n = P n s i n n , (b) cos 9 and (c) <(>. The tables and plots demonstrate that over almost a l l kinematic regions ANN> &LL»  an^ Ass a r e l a r g e and n e g a t i v e . T h i s r e s u l t i s compatible w i t h a domination by the i n i t i a l NN st a t e . As mentioned i n chapter I I , i f onl y pure s i n g l e t s c a t t e r i n g i s considered, then \m=  A-ti  = ^<i<z~ ~*>  t n e 110 FIG. 6 - 3 A w, Aft, A.„ RGRINST NEUTRON TRANSVERSE MOMENTUM KM LL S3 510 MeV 0.0 A -0.5 H - 1 . 0 H t - 1 . 5 0.0 -0.5 —\ - i . o H - 1 . 5 0.0 • -0.5 H -1.0 H -1.5 P'ltteV/c) n 465 HeV * 4> * 4> 25 125 225 25 125 225 P'lrieV/c) n 420 MeV 25 125 225 pjineV/c) n I l l F I G . 6-4 A M H »  A L L > A s s fiGfllNST COS(0) 510 MeV o.o H -o.s H -i.o H -1.5 o.o H -0.5 H -1.0 -1.5 o.o H s - o . s -1.0 + 465 MeV • H • 4 420 ri-cV + •i.o o.o i.o COS(0) - i . 5 - | 1 ' - i r -1.0 0.0 1.0 -i.o 0.0 1.0 cos (a ) cos (e ) 112 F I G . 6 - 5 A N N ' A L L > A s s AGAINST cp 510 MeV 465 rieV 420 MeV o.o - 0 . 5 H -1.0 H T - 1 . 5 0.0 -\ - 0 . 5 — \ -i.o H - 1 . 5 0.0 - 0 . 5 t - 1 . 0 H - 1 . 5 T i r T 1 r 4> 4 n r + •0 9 0 180 2 7 0 p(deg) 1 1 1 r -0 9 0 180 2 7 0 1 1 1 -0 9 0 180 2 7 0 113 l i m i t i n g value. The NN *D2 p a r t i a l wave i s the only NN i n i t i a l state that couples to nA i n a r e l a t i v e s wave, and hence would be expected to contribute strongly i n a process dominated by A production and at energies where there i s l i t t l e k i n e t i c energy a v a i l a b l e to be shared amongst the f i n a l state p a r t i c l e s . Deviations of the spin c o r r e l a t i o n parameters from -1 a r i s e from t r i p l e t s c a t t e r i n g or from s i n g l e t - t r i p l e t i n t e r f e r e n c e . It can be (B7) , i i shown that interference between 1D 2 and either ^Pj^ or F 3 , which could give r i s e to a 0 and <$> dependence, does not contribute to A N N , A L L * o r Agg. A dependence on 9 and tt) could s t i l l r e s u l t from interference between 1D 2 and 3 P 2 or 3 F 2 . The trend i n the data i s towards no dependence on 9 and $, which suggests that nA production from the i n i t i a l states 3 P 2 and 3 F 2 i s not strong. The departures of A ^ , A T T ,and Agg from -1 can be explained by t r i p l e t scattering proceeding from the i n i t i a l states 3P^ and 3 F 3 . If a comparison with the related process pp -»• dir + i s allowed to serve as a guide, then, on the basis of t h e o r e t i c a l p r e d i c t i o n s by N l s k a n e n ^ ^ and B l a n k l e i d e r ^ a n d an ( B7 ) amplitude analysis of experimental data by Bugg , one would expect close to threshold a strong amplitude for NN 3p •*• nZ"1-*" (s wave) where Z"1-** stands for an i n t e r a c t i n g TTN system i n the S 3 i s t a t e . From scattering data the S 3 i amplitude i s known to be important i n the low energy irN system (table I I - 6 ) . At higher energies i n e l a s t i c i t y i n the dir + channel i s overtaken by growing amplitudes for NN 1D 2 and 3 F 3 •*• nA"1-*". The dependences of A ^ , A ^ » and Agg on the invariant mass, M , of the PIT + pair are plotted i n f i g . 6-6 and show c l e a r l y that a l l three asymmetries move more p o s i t i v e for low mass values of the i n t e r a c t i n g irN system. Scattering 114 FIG. 6-6 Aww, A„, A M RGRINST INVARIANT Pn* flRSS 510 fleV 465 HcV 420 HcV a 0 . 0 -- 0 . 5 --1.0 -- 1 . 5 o.o - 0 . 5 -•i.o --1.5 0 . 0 -- 0 . 5 -- 1 . 0 -- 1 . 5 t t T r , 1 r 1 0 8 0 1 1 2 0 1 1 6 0 1 2 0 0 Pfr* MASS(MeV) 1 0 8 0 1 1 2 0 1 1 6 0 1 2 0 0 PIT* MASS(MeV) 1 1 r 1 0 8 0 1 1 2 0 1 1 6 0 1 2 0 0 PTT* MASS(MeV) (a) C l e a r l y A, N N 1 and A, A * " m A s s m o v e more p o s i t i v e for low mass values. On the A mass, A ^ * * ^ = A g g - l n d i c a t i n g NN •»• NA(s wave) dominates. Off the Amass, the r i s e of a competing t r i p l e t wave becomes evident. SS (b) 3 P 0 and 3P, are candidates to couple to NNn v i a an S,, TTN state. ' P Q alone requires A ^ " _1 and A j^= Agg= 3 P j alone requires A ^ = +1 and A N N = A g g E 31 +1 (not supported by the data). 0 (consistent with the data). We see the domination of the NN *D2 at high pit"*" masses and the r i s e of the 0 P j at low masses. This i s analagous with the dir channel where i t i s known that i n e l a s t i c i t y s t a r t s i n the 3P, at threshold. 115 from the 3 P i or 3 F 3 states alone would give = +1 and A N N=Ag S= 0, and the data are b a s i c a l l y i n accord with this at low mass values. By s i m i l a r arguments the data are contradictory to a large contribution from the NN 3 P Q i n i t i a l state which would require A L L = - 1 and A ^ = A ^ = +1, whereas the data exhibit an A^ which i s co n s i s t e n t l y more p o s i t i v e than A N N or Ags« There i s a l s o no i n t e r f e r e n c e between the NN 3 P Q p a r t i a l wave and either NN ^2 or 3P^ i n any of A ^ , Agg, ^ N0' ^ 0N' ° r ^SL* n t* i e P r°d u ction amplitudes for nA or nZ. The absence of a strong contribution from NN 3 P Q i s supported by a recent phase s h i f t a n a l y s i s ^ D ~ ^ of pp e l a s t i c s c a ttering data which f i t t e d very small i n e l a s t i c i t i y i n the 3 P Q wave. The parameters A ^ Q , AQ^, and Ag^ are c l o s e l y related since I ^ A ^ Q and 1° A Q ^ depend on the imaginary part of Interference between p a r t i a l waves, and I^AgL receives contributions from the r e a l part of the same interference terms. Agj^ also receives contributions from the modulus squared of 3 P 2 and 3 F 2 amplitudes (but not 3P^ or 3 F 3 ) . The dependences of AJJO and A O N o n the neutron t r a n s v e r s e T momentum P n , cos9 and <(> are plotted i n f i g s . 6-7, 6-8, and 6-9. The p o l a r i z a t i o n s show a d e f i n i t e strong dependence on the neutron t r a n s v e r s e momentum and on the azim u t h a l angle <|> . The maximum pol a r i z a t i o n s observed are much larger than those predicted by the OPE isobar model as was already evident i n f i g . 6-1. In sect. II.4 reference was made to the i n t e r p r e t a t i o n that glancing c o l l i s i o n s mediated by l i g h t meson exchange (and characterized by small momentum transfers) are p r e f e r e n t i a l l y manifested i n the quasi-two-body channels, often involving a resonance i n the outgoing state. It can be remarked that the best agreement between the data and the model c a l c u l a t i o n s i s found at small FIG. 6-7 AM 0 , Am, A„ AGAINST NEUTRON TRANSVERSE MOMENTUM O H ' s i o n c v 0.0 --0.5 -S -i.o -1.5 1.0 0.5 -8 o.o --.5 0.5 -0.0 --0.5 -1.0 25 125 225 pjlMeV/c) It 465 MeV •••I P'(neV/cl n 420 MeV M 1 ' — 25 125 225 pj l fleV/c) n (a) The p o l a r i z a t i o n s depend strongly on the neutron transverse momentum. A very prominent feature i s that A N Q = - A Q n . This i s required i f waves of of the opposite p a r i t y Interfere to produce the p o l a r i z a t i o n s , whereas interference between waves of the same p a r i t y would require A N 0 - + A Q ^ . This i s not seen i n the data and suggests that the p o l a r i z a t i o n s a r i s e from interference between the dominant *D2 and t r i p l e t P or F waves. (b) Ag L i s everywhere near 0. Since A g L receives contributions from | 3 P 2 I 2 » the simplest i n t e r p r e t a t i o n i s that the 3 P 2 amplitude i s not strong. 117 FIG. 6-8 A N 0 , A w , A , , AGAINST cos(0) 510 HeV 465 HeV 420 HeV o.o H -0.5 H o X -i.o —\ -1.5 i.o H 0.5 H o.o H - .5 0.5 H o.o H -0.5 H -1.0 T <j>4> • • 1 1 -1.0 0.0 1.0 -1.0 0.0 1.0 cos (e ) cos (e ) ! 4> • 1 1 •1.0 0.0 1.0 cos (e ) 118 F I G . 6 - 9 AN0> AON> A S L AGAINST cp 510 MeV 465 MeV 420 MeV o.o H -0.5 H o X -i.o H -1.5 1.0 0.5 H o.o H - . 5 0.5 H 0.0 H rf -0.5 H -1.0 • i 1 r 4> • t i r 4> i r • 4 H T 1 r -0 90 180 270 1 1 1 r -0 90 180 270 t i t -I 1 1 r -0 90 180 270 P(deg) p(deg) 119 values of neutron transverse momentum and at prr + masses approaching the A threshold, where the spin c o r r e l a t i o n parameters are nearest -1 and the p o l a r i z a t i o n s have t h e i r smallest values. The model c a l c u l a t i o n does well i n reproducing what i s apparently the OPE NA isobar contribution to the NNir channel. However the departures of the data from the predictions of the model indicate that the NNir channel receives contributions i n addition to those a r i s i n g from NA production v i a pion exchange. The non-resonant TTN i n t e r a c t i o n i n the S^^ p a r t i a l wave i s a candidate for t h i s contribution. Throughout the data, the p o l a r i z a t i o n s A ^ Q and A Q n are approximately equal i n magnitude but opposite i n sign. This r e s u l t can be understood i n terms of interference between states with opposite p a r i t y which requires AJ^Q = - A Q n « Interference between states of the same p a r i t y would give A ^ Q = + A Q^. The suggestion i s that the p o l a r i z a t i o n s a r i s e l a r g e l y from interference between the dominant *D2 and t r i p l e t P or F waves. The model ( KI) c a l c u l a t i o n predicts small but s i g n i f i c a n t amplitudes for 3 P 2 -*• nA and 3 F 3 -»- nA which can i n t e r f e r e with iD 2 to produce the p o l a r i z a t i o n asymmetries. However the model does not contain an amplitude for the NN 3 P i -»• nZ"*-*" (s wave) t r a n s i t i o n (P and P g 3 are the only i n t e r a c t i n g irN state incorporated i n the model) which may explain why the predicted p o l a r i z a t i o n s are smaller than the experimentally observed p o l a r i z a t i o n s . There i s a small but d e f i n i t e value of A ^ Q + A Q ^ discernable i n the data which presumably arises from interference between two t r i p l e t waves. In f i g . 6-10 the p o l a r i z a t i o n s are plotted against the invariant mass of the P T T + p a i r . One clear observation i s that the p o l a r i z a t i o n s increase i n magnitude as one moves away from the A mass threshold. The behavior of the p o l a r i z a t i o n s against invariant Pir + mass together with the behavior of A ^ j , A ^ L , and A<,g indicate that at high mass values the dominates 120 F I G . 6 - 10 A N 0, A w , RGf l lNST INVf lR I f lNT P T T + MASS 510 tleV 465 MeV 420 HeV o.o .-0.5 H -1.0 H -1.5 • + • i r i.o H 0.5 H 0.0 H - . 5 i r 0.5 H o.o H -0.5 H -1.0 t f • • + • i r + 1 1 r 1080 1120 1160 1200 PTT* MASS(MeV) 4> i r i r 1 1 r 1080 1120 1160 1200 PTT* MASS(MeV) + 1080 1120 1160 1200 PTT* MASS(MeV) 1 2 1 giving spin c o r r e l a t i o n parameters near -1 and small p o l a r i z a t i o n s . However, i n moving off the resonance mass a s i g n i f i c a n t contribution from a t r i p l e t p a r t i a l wave becomes evident i n the decreasing values of ^NN' ^LL' a m * ^SS a n < * ^ n t* 1 6 l n c r e a s l n 8 values of the p o l a r i z a t i o n s . Since the S 3 I TTN amplitude i s known to be strong i n the low energy TTN system, i t s c o n t r i b u t i o n to the pp •»• pmr + process may be expected to be most v i s i b l e at the lower TTN i n t e r a c t i o n energies before the A resonance begins to dominate. The NN 3 P^ i s a t r i p l e t state which couples to the pmr + f i n a l state v i a an S 3 I TTN i n t e r a c t i o n i n the intermediate state and i s therefore a candidate for the t r i p l e t wave which causes A ^ , A ^ and Ag<, to deviate from -1 and the p o l a r i z a t i o n s to increase. The r e s u l t s f o r AgL do not d i f f e r s i g n i f i c a n t l y from zero over the entire kinematic region where data e x i s t s . This suggests that the 3 P 2 and 3 F 2 amplitudes, which contribute as modulus squared terms, and the 3 F 3 , which contributes through interference with I D 2 , are not strong. Fig 6-11 shows the invariant mass d i s t r i b u t i o n of the NN pairs for data taken i n the AJJN configuration. The large narrow peak i n the energy spectrum just above the threshold for two nucleon masses i s a signature of strong f i n a l state i n t e r a c t i o n s occurring between the neutron and proton i n either of the 1 SQ or 3 states. Only four t r a n s i t i o n s are possible from an NN i n i t i a l state to a pnrr+ f i n a l state with the neutron and proton i n a r e l a t i v e s state and the pion i n either an s or p state r e l a t i v e to the o v e r a l l center of mass. These are as follows. N N ( 3 P I ) •*• n p ( 3 S I ) TT +(S wave) N N ^ S Q ) -»• n p ( 3 S 1 ) Tr +(p wave) N N ( I D 2 ) •»• np( 3 S A ) Tr +(p wave) N N ( 3 P Q ) •»• np( x S Q ) TT +(S wave) 122 FIG. 6-11 I N V A R I A N T M A S S O F T H E N N P A I R 7 5 0 H w 5 0 0 —| o S 2 5 0 H 1880 1800 1320 1840 INVARIANT BASS OF THE NN PAIR lltEV) 510 HEV ORTA 4 5 0 H 3 0 0 150 H 3 7 5 H 2 5 0 H 1 2 5 ieeo isoo 1820 1 6 8 0 1800 1820 « S S HEV OATA «20 HEV OATA 123 F I G . 6 - 1 2 A J J J J , A W O , A 0 N RGf l lNST INVf lR I f lNT NN HRSS 510 tieV 465 MeV 420 fieV 0.0 -0.5 H -1.0 H -1.5 • i r o.o A -0.5 H -i.o H -1.5 i r 5 i.o A 0.5 0.0 -.5 4> 4> + i r i r • i r • • \ i r i i r • i r + + i r 1870 1300 1930 1960 1870 1900 1930 1960 <870 1900 1930 1960 NN MASS(MeV) NN MASS(MeV) NN MASS(MeV) 1 2 4 The data ( f i g . 6 - 1 2 and table V I - 9 ) show that A J J N does not change between the two lowest mass bins as the N N f i n a l state i n t e r a c t i o n comes into play. A l t e r n a t e l y , the p o l a r i z a t i o n s do drop to t h e i r lowest values at the N N threshold. The fac t that AJJJJ remains large and negative In the lowest bin (which was chosen to bracket the peak) indicates that the N N f i n a l state i n t e r a c t i o n i s taking place i n amplitudes o r i g i n a t i n g from an i n i t i a l N N s i n g l e t state. The two candidates are the N N 1 S Q and 1D 2 . However the ^ 2 i s favored since A S Q does not couple to nA i n a r e l a t i v e s wave. In addition a strong 1 S Q amplitude competing with would make A ^ Q tend towards +AQ^, and t h i s i s not seen i n the data. The implication i s that the strong *D2 amplitude results from a cooperative enhancement caused by both the T T N ( A) i n t e r a c t i o n and the N N f i n a l state i n t e r a c t i o n . P u b l i s h e d data from LAMPF on pp •*• pmr + also e x i s t at 6 5 0 and 8 0 0 MeV^^"^ for exclusive kinematics. These data have been compared to the model of Dubach et a l . , with good agreement r e s u l t i n g . At these two energies the p o l a r i z a t i o n s , A^o and AON> have both changed sign i n accordance with the model. SUMMARY The i n e l a s t i c reaction pp -»• pmr + has been studied using a polarized beam and polarized target. This i s the f i r s t time that a three body f i n a l state has been studied using a polarized target. The free proton events were s u c c e s s f u l l y separated from the background of q u a s i - e l a s t i c events by a x 2 test to the so l u t i o n of f i v e constraining equations. The measurement of A ^ , A ^ and A ^ and the data analysis has been described. The r e s u l t s have been combined with measurements of A^> A( S S and A at energies of 5 1 0 , 4 6 5 and 4 2 0 MeV and give d e t a i l e d information L>JU on the p a r t i a l wave amplitudes for the process NN NNir. 125 The measured values of A ^ , A^and Agg are near -1 i n most kinematic regions. This i s at t r i b u t e d to the dominance of the NN AD 2 amplitude. The decrease i n these parameters at low prr + masses can be explained by a strong 3P^ •* nZ"*"*" amplitutde, analogous to that observed i n pp •*• drr + near threshold. Interference between these two strong amplitudes may be the source of the large A J J O and A O N values. The simplest explanation for the small values of A S L i s that the 3 P 2 and 3 F 3 amplitudes are small. Corroborative evidence for a small 3 P 2 amplitude i s the absence of a dependence on $ i n A ^ , A ^ and Agg. A sizeable contribution from the 3 P Q wave i s ruled out since A L L i s con s i s t e n t l y more p o s i t i v e than ^NN ° r ^SS a m * t* i e l a t t e r f a i l t o exhibit large p o s i t i v e values i n any kinematic region. The data display a strong NN f i n a l state i n t e r a c t i o n peak. The dependence of A ^ , A ^ and A^ on t h i s peak indicates that the NN f i n a l state i n t e r a c t i o n cooperates with the irN (A) i n t e r a c t i o n i n producing the dominant 1D 2 amplitude. The work described i n t h i s thesis has been the f i r s t to undertake a systematic analysis of the NNir p a r t i a l wave amplitudes. It has contributed four important points to our knowledge of the NN i n t e r a c t i o n i n the NNrr channel up to 510 MeV. (1) The iD 2 amplitude i s dominant. (2) The 3 P Q amplitude i s ruled out by the data. (3) The 3 P 1 amplitude i s strong at low prr + masses. (4) The 3 P 2 amplitude does not contribute strongly. A quantitative f i t to the data by Dr. R.R. Sil b a r and Prof. D.V. Bugg i s progressing with an extension to the model of Dubach et a l . including an adjustable amplitude f or 3 P^  -*• nZ and adjustable phase parameters. A l l the data are a v a i l a b l e on summary tapes for further t h e o r e t i c a l analyses. 126 TABLE VI-1 A M , A L L and Ag g AGAINST NEUTRON TRANSVERSE MOMENTUM pJCMeV/c) A m (510 MeV) A m (465 MeV) A m (420 MeV) bin l i m i t s  25. 75. -0.673 ± .097 -0.758 ± .147 75. 125. -0.845 ± .123 -0.794 ± .222 125. 175. -0.909 ± .439 175. 225. 225. 275. 25. 75. -0.879 ± .128 - -0.742 ± .153 75. 125. -0.841 ± .099 -0.619 ± .113 -0.607 ± .131 125. 175. -0.706 ± .129 -0.583 ± .140 -0.564 ± .170 175. 225. -0.664 ± .180 -0.477 ± .212 -1.018 ± .388 225. 275. -0.261 ± .272 -0.482 ± .507 P^MeV/c) A L L (510 MeV) A L L (465 MeV) A L L (420 MeV) bin l i m i t s  25. 75. -0.597 + .085 -0.535 ± .066 -0.693 ± .115 75. 125. -0.489 ± .071 -0.469 ± .058 -0.539 ± .082 125. 175. -0.255 ± .079 -0.408 ± .079 -0.180 ± .152 175. 225. -0.345 ± .111 -0.172 ± .161 -0.180 ± .353 225. 275. -0.088 ± .242 +0.161 ± .498 P^(MeV/c) A s s (510 MeV) Agg (465 MeV) A g s (420 MeV) bin l i m i t s  127 TABLE VI-2 Am, A T T and A ™ AGAINST COS (6) cos(9) A M (510 MeV) A m (465 MeV) A m (420 MeV) bin l i m i t s  -1.0 -0.6 - - --0.6 -0.0 0.2 0.4 -0.4 0.6 -0.947 ± .235 -0.481 ± .243 -0.655 ± .224 0.6 0.8 -0.728 ± .090 -0.563 ± .098 -0.661 ± .131 0.8 1.0 -0.775 ± .091 -0.618 ± .106 -0.642 ± .123 cos(9) A L L (510 MeV) A L L (465 MeV) A L L (420 MeV) bin l i m i t s  -1.0 -0.6 -0.573 + .116 -0.477 + .203 -1.068 + .262 -0.6 -0.0 -0.380 + .089 -0.408 + .141 -0.454 ± .207 0.2 0.4 +0.048 + .164 -0.029 + .236 -0.109 + .192 0.4 0.6 -0.312 + .100 -0.062 + .120 -0.410 + .113 0.6 0.8 -0.466 + .065 -0.489 + .062 -0.611 + .091 0.8 1.0 -0.526 + .066 -0.555 + .051 -0.714 + .110 cos(9) Agg (510 MeV) Agg (465 MeV) Ag g (420 MeV) bin l i m i t s -1.0 -0.6 -0.527 ± .374 -0.699 ± .231 -0.6 -0.0 -0.709 ± .108 -0.644 ± .075 0.2 0.4 0.4 0.6 -0.294 ± .384 0.6 0.8 -0.254 ± .222 -0.474 ± .345 0.8 1.0 -0.924 ± .081 -0.916 + .132 128 TABLE VI-3 Am, A L L and Agg AGAINST $ • (deg) k m (510 MeV) A M (465 MeV) A M (420 MeV) b i n l i m i t s -45. 45. -0.480 ± .138 -0.727 ± .174 45. 135. -1.279 ± .133 -0.714 ± .294 135. 225. -0.723 ± .300 -0.655 ± .619 225. 315. -0.578 ± .126 -0.980 + .210 -45. 45. -0.751 ± .089 -0.610 ± .099 -0.553 ± .122 45. 135. -0.810 ± .192 -0.767 ± .231 -0.727 ± .387 135. 225. -0.859 ± .111 -0.578 ± .251 -0.757 ± .143 225. 315. -0.606 ± .163 -0.643 ± .224 -0.679 ± .266 <|>(deg) A L L (510 MeV) A L L (465 MeV) A L L (420 MeV) b in l i m i t s -45. 45. -0.488 ± .083 -0.395 ± .059 -0.363 ± .095 45. 135. -0.502 ± .083 -0.484 ± .067 -0.630 ± .115 135. 225. -0.781 ± .169 -0.213 ± .235 -0.891 ± .529 225. 315. -0.427 ± .061 -0.570 ± .066 -0.593 ± .095 (Kdeg) Agg (510 MeV) A g S (465 MeV) Agg (420 MeV) bin l i m i t s 129 TABLE VI-4 DEPENDENCE OF A M , A L L and A gg ON INVARIANT Prr + MASS M(PTT+) MeV A M (510 MeV) A M (465 MeV) A M (420 MeV) bin l i m i t s  1080. 1100. 1100. 1120. 1120. 1140. +0.119 ± .323 -0.905 ± .239 1140. 1160. -0.671 ± .132 -0.830 ± .144 1160. 1180. -0.823 ± .095 1080. 1100. +0.056 ± .425 +0.080 ± .397 -0.826 ± .450 1100. 1120. -0.407 ± .224 -0.402 ± .178 -0.518 ± .142 1120. 1140. -0.616 ± .166 -0.632 ± .124 -0.719 ± .117 1140. 1160. -0.777 ± .109 -0.650 ± .108 1160. 1180. -0.903 ± .102 M(PTT+) MeV A L L (510 MeV) A L L (465 MeV) A L L (420 MeV) bin l i m i t s  1080. 1100. +0.038 ± .239 -0.214 ± .246 +0.177 ± .195 1100. 1120. -0.008 ± .136 -0.147 ± .127 -0.359 ± .104 1120. 1140. -0.166 ± .089 -0.393 ± .061 -0.729 ± .087 1140. 1160. -0.379 ± .070 -0.582 ± .050 1160. 1180. -0.673 ± .074 M(PTT+) MeV Agg (510 MeV) A g s (465 MeV) A g s (420 MeV) bin l i m i t s 130 TABLE VI-5 A N 0 , A Q N and A g L AGAINST NEUTRON TRANSVERSE MOMENTUM P^MeV/c) A N Q (510 MeV) A N Q (465 MeV) A N Q (420 MeV) bin l i m i t s  25. 75. -0.265 ± .035 - +0.027 ± .044 75. 125. -0.330 ± .036 -0.343 ± .044 -0.093 ± .054 125. 175. -0.520 ± .055 -0.575 ± .062 -0.350 ± .075 175. 225. -0.704 ± .081 -0.641 ± .095 -0.511 ± .190 225. 275. -0.486 ± .145 -0.585 ± .260 P*(MeV/c) A Q N (510 MeV) A Q N (465 MeV) A Q N (420 MeV) bin l i m i t s  25. 75. +0.150 ± .048 - -0.104 ± .074 75. 125. +0.312 ± .050 +0.316 ± .071 +0.084 ± .092 125. 175. +0.421 ± .079 +0.379 ± .093 +0.241 + .120 175. 225. +0.443 ± .125 +0.175 ± .154 +0.542 ± .304 225. 275. +0.657 ± .211 +0.620 ± .347 P^(MeV/c) A g L (510 MeV) A g L (465 MeV) A g L (420 MeV) bin l i m i t s 25. 75. -0.026 ± .053 -0.032 ± .046 -0.055 ± .078 75. 125. +0.104 ± .053 +0.145 ± .073 +0.053 ± .115 125. 175. +0.163 ± .087 +0.087 ± .113 175. 225. -0.074 ± .209 -0.051 ± .328 225. 275. -0.022 ± .635 +0.056 ±1.673 131 T A B L E V I - 6 A N 0 , A Q n and A G L A G A I N S T C O S ( 6 ) cos(6) A N Q (510 MeV) A N Q (465 MeV) A N 0 420 MeV) bin l i m i t s  -1.0 -0.6 --0.6 -0.0 -0.2 0.4 -0.4 0.6 -0.349 ± .106 -0.245 ± .093 -0.034 ± .082 0.6 0.8 -0.346 ± .031 -0.233 ± .036 -0.014 ± .046 0.8 1.0 -0.367 ± .031 -0.416 ± .041 -0.169 ± .049 cos(6) A Q N (510 MeV) A Q N (465 MeV) A Q N (420 MeV) bin l i m i t s  -1.0 -0.6 --0.6 -0.0 - -0.2 0.4 -0.4 0.6 -0.040 ± .156 40.039 ± .158 -0.126 + .138 0.6 0.8 +0.250 ± .044 +0.193 ± .058 -0.090 ± .076 0.8 1.0 +0.308 ± .045 +0.193 ± .061 +0.218 ± .080 cos(6) A G L (510 MeV) A G L (465 MeV) A G L (420 MeV) bin l i m i t s  -1.0 -0.6 --0.6 -0.0 - - -0.2 0.4 +0.200 ± .169 -0.212 ± .205 +0.331 + .805 0.4 0.6 +0.004 ± .091 -0.047 ± .088 -0.065 ± .154 0.6 0.8 +0.008 ± .049 +0.051 ± .048 -0.026 ± .091 0.8 1.0 +0.115 ± .058 +0.032 ± .055 +0.015 ± .107 132 TABLE VI-7 A N 0 , A Q N and A g L AGAINST 4 A N Q (510 MeV) A N Q (465 MeV) A N Q (420 MeV) -0.478 ± .034 -0.459 + .041 -0.214 ± .051 -0.328 ± .079 -0.565 ± .082 +0.151 ± .148 -0.232 ± .033 -0.212 ± .107 +0.033 ± .044 -0.397 ± .071 -0.355 ± .106 -0.237 ± .113 A Q N (510 MeV) A Q N (465 MeV) A Q N (420 MeV) +0.369 ± .050 +0.351 + .063 +0.290 ± .086 +0.369 ± .106 +0.160 ± .144 -0.456 ± .258 +0.173 ± .046 -0.031 ± .164 -0.139 ± .074 +0.242 ± .097 +0.258 ± .166 -0.003 ± .190 A g L (510 MeV) A g L (465 MeV) A g L (420 MeV) -0.081 ± .080 -0.007 ± .067 +0.097 ± .157 +0.125 ± .057 +0.091 ± .061 +0.029 ± .132 +0.194 ± .162 +0.134 ± .181 -0.384 ± .510 +0.066 ± .058 +0.005 ± .059 -0.055 ± .097 133 TABLE VI-8 DEPENDENCE OF A N Q , A Q N and A g L ON INVARIANT Prr + MASS M(Prr+) MeV A N 0 (510 MeV) A N Q (465 MeV) A N Q (420 MeV) b in l i m i t s  1080. 1100. -0.086 ± .244 -0.335 ± .214 -0.321 ± .226 1100. 1120. -0.457 ± .110 -0.548 ± .084 -0.308 ± .062 1120. 1140. -0.606 ± .078 -0.509 ± .051 -0.005 ± .036 1140. 1160. -0.465 ± .043 -0.203 ± .034 1160. 1180. -0.291 ± .029 M(PTT+) MeV A Q n (510 MeV) A Q N (465 MeV) A Q N (420 MeV) bin l i m i t s  1080. 1100. +0.292 ± .429 +0.284 ± .276 +0.132 ± .326 1100. 1120. +0.398 ± .176 +0.298 ± .130 +0.258 ± .102 1120. 1140. +0.302 ± .105 +0.368 ± .081 -0.051 ± .062 1140. 1160. +0.345 ± .062 +0.101 ± .053 1160. 1180. +0.237 ± .041 M(Prr+) MeV A g L (510 MeV) A g L (465 MeV) A g L (420 MeV) b in l i m i t s  1080. 1100. -0.082 ± .271 -0.277+ .208 -0.327 ± 1 . 4 1 8 1100. 1120. +0.166 ± .135 -0.012 ± .107 -0.196 ± .148 1120. 1140. +0.016 ± .085 +0.090 ± .065 -0.018 ± .072 1140. 1160. +0.072 ± .062 -0.007 ± .043 1160. 1180. +0.032 ± .050 J 134 TABLE VI-9 DEPENDENCE OF A M , A N Q and Ag N ON INVARIANT NN MASS M(NN) MeV A M (510 MeV) A M (465 MeV) A ^ (420 MeV) b in l i m i t s  1877. 1884. -0.868 ± .114 -0.669 ± .127 -0.759 ± .147 1884. 1900. -0.896 ± .112 -0.662 ± .125 -0.671 + .132 1900. 1920. -0.595 ± .112 -0.498 ± .130 -0.345 ± .173 1920. 1940. -0.558 ± .169 -0.386 ± .212 -0.587 ± .468 M(NN) MeV A N Q (510 MeV) A N Q (465 MeV) A N Q (420 MeV) bin l i m i t s  1877. 1884. -0.243 ± .034 -0.149 ± .041 +0.039 ± .044 1884. 1900. -0.352 ± .038 -0.310 ± .047 -0.131 ± .052 1900. 1920. -0.558 ± .049 -0.580 ± .059 -0.368 ± .080 1920. 1940. -0.544 ± .081 -0.510 ± .102 -0.263 ± .254 M(NN) MeV A Q N (510 MeV) A Q N (465 MeV) A Q N (420 MeV) bin l i m i t s 1877. 1884. +0.140 ± .046 -0.019 + .061 -0.179 ± .075 1884. 1900. +0.330 ± .055 +0.373 ± .079 +0.241 ± .088 1900. 1920. +0.410 ± .069 +0.309 ± .088 +0.148 ± .131 1920. 1940. +0.417 ± .112 +0.254 ± .156 +0.132 ± .342 135 REFERENCES A l I.P. 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J . Lombard and W.M. K loe t , LAMPF r e p r i n t LA-UR-81-2342. 54 R.R. S i lba r and W.M. K l o e t , N u c l . Phys. A 338, 317(1980). 55 R . L . Shypi t , M . S c Thes i s , U n i v e r s i t y of B r i t i s h Columbia(1981). 56 R.R. S i l b a r , pr ivate communication. 57 R. Shypit et a l . , Phys. L e t t . 124 B, 314(1983). T l TRIUMF, Annual Report 1975, 25(May 1976). WI L . Wolfenstein and J . Ashkin , Phys. Rev. 85, 947(1952). WI G. Waters et a l . , Basque MWPC Readout System, RHEL-HEP E l e c t r o n i c s Group Report(1974). W2 G. Waters et a l . , N u c l . In s t . Meth. 153, 401(1978). Y l H. Yukawa, Proc . Phys. Math. Soc Japan 17, 48(1935). 139 APPENDIX A: PARAMETERIZATION OF CHARGED PARTICLE DEFLECTIONS IN THE MAGNETIC FIELD OF THE POLARIZED TARGET ( S5) The parameterization described i n this appendix had i t s o r i g i n i n the TRIUMF AOL and Aa-p experiment and was upgraded for use i n the present experiment. A parameterization was required which would provide a one to one mapping between the measured asymptotic t r a j e c t o r y of a charged p a r t i c l e emerging from the target magnetic f i e l d and the t r a j e c t o r y the p a r t i c l e had when i t scattered at the center of the target. The term t r a j e c t o r y r e f e r s only to the slope vector of the p a r t i c l e ' s momentum without regard to i t s intercepts, which i n t h i s experiment were altered only minutely by the target f i e l d . To ex p l o i t the c y l i n d r i c a l symmetry of the Helmholtz c o i l f i e l d , the d e f l e c t i o n of a charged p a r t i c l e was viewed i n a preferred reference frame. The axes defining the the preferred frame {xx, YY, ZZ} were chosen with ZZ_ along the d i r e c t i o n of the c e n t r a l f i e l d a x is, YY perpendicular to ZZ_ i n the plane defined by ZZ_ and the t r a j e c t o r y of the scattered p a r t i c l e , and XX given by the cross product YY x ZZ_. In t h i s reference frame the asymptotic t r a j e c t o r y of the charged p a r t i c l e was obtained from the scattered t r a j e c t o r y by two successive r o t a t i o n s , one through an angle defined i n the scattering (YY ZZ) plane and one through an angle defined i n a plane perpendicular to the s c a t t e r i n g plane. These rotations are l a b e l l e d ATHETA and APHI i n f i g . APP.A-1. The rotations were e a s i l y inverted and applied to the asymptotic t r a j e c t o r y to give the actual scattered t r a j e c t o r y . The advantage of transforming to the preferred frame was that the rotations required to correct for magnetic d e f l e c t i o n were independent of an azimuthal angle. The parameterization developed i n this way assumed a knowledge of the 140 FIG. RPP. fl-1 ILLUSTRATION OF THE ANGLES ASSOCIATING THE MEASURED ASYMPTOTIC TRAJECTORY UITH THE TRUE SCATTERED TRAJECTORY ZZ A 4^ 4 * 141 true scattered t r a j e c t o r y which was required to e s t a b l i s h the axes of the preferred reference frame, whereas the quantity a v a i l a b l e from experiment was the asymptotic t r a j e c t o r y . In the p r a c t i c a l a p p l i c a t i o n of th i s parameterization a s e l f consistent i t e r a t i o n was implemented wherein an estimate of the true s c a t t e r i n g t r a j e c t o r y was used to e s t a b l i s h the preferred frame, then corrections for magnetic d e f l e c t i o n calculated i n th i s frame were applied to the asymptotic t r a j e c t o r y to y i e l d a better estimate of the scattered t r a j e c t o r y (see f i g . APP.A-2). With the updated estimate a new preferred frame was established and a further correction applied. When the estimate of the scattered t r a j e c t o r y coincided with the actual scattered t r a j e c t o r y , the rotations applied to the asymptotic vector simply gave back the same scattered vector. Starting with the asymptotic vector used to approximate the the true scattered t r a j e c t o r y , rapid convergence was obtained (3 i t e r a t i o n s ) . The r o t a t i o n angles (ATHETA, APHI) required to correct for the magnetic d e f l e c t i o n were used to define two functions BDL and BDLV by the re l a t i o n s ATHETA = BDL(P,THETA) APHI = BDLV(P,THETA) with the r o t a t i o n angles measured i n radians, P the momentum of the p a r t i c l e i n MeV/c, and .3 representing the e l e c t r i c charge e. Thus the vari a b l e THETA on which the parameterization depended was chosen to be defined by the projection of the asymptotic vector into the scattering plane rather than by the true polar angle (THETA1) of s c a t t e r . The reason for this choice was that the experimentally measured quantity was the asymptotic t r a j e c t o r y and the angle THETA provided a d i r e c t l i n k to this 142 FIG. APP. A-2 ITERATION OF THE CORRECTIONS FOR MAGNETIC FIELD DEFLECTION DASHED LINES INDICATE HOW ROTATION APPLIED TO THE ASYMPTOTIC VECTOR IN THE PREFERRED FRAME LEAD TO A NEW ESTIMATE OF THE TRUE SCATTERED TRAJECTORY 143 quantity. A TRIUMF Library ray tracing program using Runge-Kutta 4th order i n t e g r a t i o n techniques was used to generate maps of the functions BDL and BDLV. The ray tracing program calculated the path of a charged p a r t i c l e from the center of the target out to the f i e l d free region. The angular mapping of BDL and BDLV was done at a fixed momentum by successively t r a c i n g 315 separate paths of a charged p a r t i c l e scattered with angle THETA1 incremented at regular i n t e r v a l s from 0 to TT. F i g . APP.A-3 shows the angular maps of BDL and BDLV at a momentum of 500 MeV/c. The maps for the lower momenta had the same general shape but more pronounced curves. The angular maps of BDL and BDLV were generated at 44 momenta spaced at 10 MeV/c i n t e r v a l s from 80 to 510 MeV/c, and at 26 momenta from 550 to 1175 MeV/c i n steps of 25 MeV/c. At each momentum the angular dependence was f i t t e d to a Fourier series expansion. A n , 1 v . ,iTTHETA. , .iifTHETA. BDL(THETA)p ^ = ^ + U ± c o ^ — ^ - ) + a. 8in<—573—) 12 b n , r v ,iirTHETA. , _ . .inTHETA. BDLV(THETA)p f ± x e d = ^ + J * ± c o s ( — ^ — ) + B. 8 x n ( — 5 7 5 — ) Both functions had a periodic angular dependence with period IT/2. BDLV was symmetric and BDL antisymmetric. Though a l l 25 c o e f f i c i e n t s were used i n the f i t , the a c o e f f i c i e n t s produced by the f i t to BDL were completely n e g l i g i b l e as were the b c o e f f i c i e n t s i n the f i t to BDLV. Hence the angular maps at 70 momenta were reduced to 70 sets of 13 A c o e f f i c i e n t s for BDL and 12 B c o e f f i c i e n t s for BDLV which were stored on disk. To obtain the necessary 25 Fourier c o e f f i c i e n t s at an a r b i t r a r y momentum (between 80 and 1175 MeV/c) the e x i s t i n g set of c o e f f i c i e n t s at fixed momenta were interpolated using Legendre polynomial i n t e r p o l a t i o n through 144 FIG. RPP. fi-3 ANGULAR HAPS OF THE FUNCTIONS BDL AND BDLV RT 500 MeV/c THE FOURIER FIT IS DRflUN THROUGH THE CROSSES (xlO*) D CD 1.6 0.8 -3 0.0 -d -0.8 - 3 -1.6 i 11 11 | 11 i i 350.0 (X1CT1) (xlO'J (x10"a) THETAt rad) 145. the 4 data points nearest i n momentum. Therefore i n the complete d e s c r i p t i o n of BDL and BDLV, the angular dependence of each function was parameterized by a Fourier series with momentum dependent c o e f f i c i e n t s obtained by Legendre polynomial i n t e r p o l a t i o n . BDL(P,THETA) - M £ > + J A.(P) c o s ( ^ | T A ) BDLV(P,THETA) = I B. (P) s i n ( 1 ^ " f ^ ) i= l ' As an i l l u s t r a t i o n of the accuracy achieved, the momentum dependence of the c o e f f i c i e n t s A g and B 7 i s shown i n f i g . APP.A-4 i n the range of momenta between 80 and 510 MeV/c. The crosses are the values of these c o e f f i c i e n t s f i t t e d at the 44 discre t e momenta and the s o l i d l i n e i s a polynomial i n t e r p o l a t i o n through the points. An i t e r a t i v e loop u t i l i z i n g the parameterized functions BDL and BDLV corrected for the magnetic f i e l d d e f l e c t i o n experienced by a p a r t i c l e with assigned momentum P. The assignment of the p a r t i c l e ' s momentum was determined ext e r n a l l y on the basis of kinematic measurements (sect. V.2b). Therefore the procedure of reconstructing the true scattering angles and momenta from the measured asymptotic t r a j e c t o r i e s of the three p a r t i c l e s i n the pnTf+ f i n a l state required a cooperative e f f o r t between the outer loop which assigned estimates of the momenta and the inner loop which corrected for the def l e c t i o n s of the charged p a r t i c l e s . Convergence of the i t e r a t i o n resulted i n a s e l f consistent s o l u t i o n , s i g n a l l e d when further corrections for f i e l d d e f l e c t i o n yielded the same t r a j e c t o r i e s and hence the assignments of momenta remained unchanged. The f i n a l event reconstruction routine was operational i n a l l of 3-D space (4TT coverage) and could handle an a r b i t r a r y o r i e n t a t i o n of the f i e l d 146 FIG. RPP. R-4 noriENTun DEPENDENCE OF THE FOURIER COEFFICIENTS R 9 RND B 7 - 1 . 6 Illllll -1 1 t 1 1 1 | 1 1 1 1 I120.D 1 1 1 1 i 11 i 11 180.0 • i i 1 1 I • i 1 1 240.0 • 11 i 11 i • i i 300.0 i i 1 I I | 1 I I I 360.0 I I i I i | i i i i 420.0 480.0 Illllllllllllllllllllllllll \ »• nOHENTUH ( f l eV /c ) 147 axis (the three orientations s i g n i f i c a n t to the experiment were L, N, S). Since the corrections for f i e l d d e f l e c t i o n were always made i n a preferred reference frame depending only on the cen t r a l f i e l d axis and the scattered t r a j e c t o r y , only the transformation matrices from the lab to the preferred frame changed for d i f f e r e n t orientations of the f i e l d . In a test using actual data the corrections calculated with the parameterization reproduced those calculated using the ray tracing program to an accuracy of generally 0.0001 radians. 148 APPENDIX B: CALIBRATION OF TARGET POLARIZATION BY THE METHOD OF ELASTIC NUCLEAR SCATTERING The e l a s t i c scattering asymmetry measurement employed i n the present (S5) experiment was previously applied with success i n the A O L and Aoj- experiment. The d e t a i l s of the measurement are described i n t h i s appendix. The adaptation of the three p a r t i c l e trigger (sect. IV.1) for the e l a s t i c s c a ttering measurement was straightforward. The condition of a double NIM l e v e l at the pulse attenuator ( f i g . 4-2) was relaxed to the requirement of a single detection i n the forward s c i n t i l l a t o r hodoscope. The r e c o i l protons from e l a s t i c scatters i n the target were detected i n two 8" delay l i n e chambers, L l and L2, shown on f i g . 4-1. The hodoscope el e c t r o n i c s were combined with the side chamber s c i n t i l l a t o r s and beam counters to define an on l i n e trigger given by T1«T2'(V + T1~T2)«(L1 + L2)'HODOSCOPE . , singl e In this way right and l e f t e l a s t i c scatters were monitored simultaneously, with the forward chambers recording the tracks of scattered protons and the side chambers providing track information on the corresponding r e c o i l protons• Analysis of the e l a s t i c scattering data c l o s e l y p a r a l l e l e d the method developed for the pnir + data. Tracks were f i t t e d through the forward and s i d e chambers. Since the s i d e chambers provided o n l y p o s i t i o n a l information on each detection, the tracks projected through the side chambers were assigned intercept coordinates coinciding with the center of the target. In choosing a pair of charged p a r t i c l e tracks which could represent the scattered and r e c o i l protons, only c o r r e l a t i o n s of the 149 hodoscope area 4 with side chamber l e f t or area 8 with side chamber right were accepted. These two c o r r e l a t i o n s consistently accounted for greater than 76% of the on-line tr i g g e r s taken. A summary tape was written containing the f i t t e d track information. A x 2 event reconstruction analogous to the X 2 assessment of pnTr+ events was implemented for the e l a s t i c data. The e x i s t i n g three body kinematics program was reduced to accommodate two body kinematics. The four a v a i l a b l e constraints (3 equations of momentum conservation and one of energy conservation) were f i t t e d for each event to determine the momenta of the scattered and r e c o i l protons. Fermi reconstructed peaks were again used to estimate the uncertainty i n momentum resol u t i o n for the three momentum equations. Corrections for magnetic f i e l d d e f l e c t i o n s were applied using the method developed for the pmr + reconstructions. A tape containing reconstructed events was written to expedite the f i n a l stage of processing. Both l e f t and r i g h t scatters were f u l l y reconstructed. However the r e c o i l chamber of the r i g h t monitor suffered from an obstruction which was i d e n t i f i e d as a magnet support post i n the target assembly. The rate of detections i n the r i g h t monitor was down by a factor of ten compared with the l e f t monitor. Added to the diminished s t a t i s t i c a l accuracy was a d e f i n i t e degradation i n the r e s o l u t i o n obtained i n kinematic quantities such as the opening angle and Fermi reconstructed peaks, which prompted the righ t monitor data to be discarded i n further a n a l y s i s . An accurate determination of the target p o l a r i z a t i o n from the spin asymmetry measurement required an asymmetry that was s e n s i t i v e to the target p o l a r i z a t i o n and r e l a t i v e l y i n s e n s i t i v e to other f a c t o r s . The asymmetry chosen for t h i s purpose i s defined in the following equation. 150 M M B B + small LARGE + °fcPCtPB+-PB+] small (APP.b-1) M was the number of reconstructed counts i n the l e f t monitor, B was the incident beam count, Pg was the beam p o l a r i z a t i o n , P^ was the target p o l a r i z a t i o n , Pg was the analyzing power of hydrogen, Pc was the analyzing power of carbon (mostly due to (P,2P) events), AJN was the spin c o r r e l a t i o n parameter for pp e l a s t i c s c a t t e r i n g , was a geometric acceptance factor for hydrogen events, and o<c was the acceptance factor for events o ff carbon. The superscript arrow indicates the p o l a r i t y of the beam and the subscript arrow designates target p o l a r i t y . Note that only beam spin up data appears i n the equation. Since the beam p o l a r i z a t i o n was stable and c e r t a i n l y not correlated with the target p o l a r i z a t i o n , the f i r s t and t h i r d terms of eq. APP.b-1 were near zero. Therefore the asymmetry defined by th i s equation was d i r e c t l y s e n s i t i v e to the target p o l a r i z a t i o n . The successful a p p l i c a t i o n of Eq. APP.b-1 required an accurate determination of the acceptance factor o^. The asymmetry used was se n s i t i v e to both o^j and and was given by + = ct {4 + P [p + +p + +P + 1 + P [p + +P + +P* +P + 1 H ^  H L B+ B+ B+ B + J H L T+ T+ T+ T+ J small small + Aim[<PBPT)^PBPT)t+(PBPT>I+(PBPT)t^ + " c <4 + P C [PBVPBVPBVPB" + ] } small small (APP.b-2) 151 The analyzing power of carbon was an unknown factor i n the small term at the end of eq. APP.b-1. The asymmetry used to determine a mean analyzing power for the d i s t r i b u t i o n of background carbon events was M M T M M B B B B W PBV PBV P BV PBV (APP-b-3) where a s e l e c t i o n on carbon events was made by applying kinematic cuts to exclude the hydrogen s i g n a l . The approach adopted i n this- analysis was to determine e m p i r i c a l l y the parameters of the free hydrogen signal and the background carbon si g n a l needed i n APP.b-1 by using using eqs. APP.b-2 and APP.b-3. For t h i s purpose i t was desirable to have the background c l e a r l y v i s i b l e so a se l e c t i v e cut on x 2 was not made. The acceptance factors and CLQ were expanded as the d i r e c t product of two gaussians i n the lab opening angle 9 and the coplanar angle <|>. (APP.b-4) One dimensional plots of the opening angle and coplanar angle are shown i n f i g . A P P . B - 1 . The mean values 9Q and <|>Q of the gaussian d i s t r i b u t i o n s were obtained from these histograms. To cover the kinematic range of the sampled d i s t r i b u t i o n s , 46 bins i n 9 from 75° to 98° and 80 bins i n $ from 80° to 100° were used giving a two dimensional g r i d of 3680 bins. The gaussian forms of ot^  and given by A P P.b-4 were inserted into A P P.b-2. The analyzing power of hydrogen and the spin c o r r e l a t i o n parameter A^N were evaluated event by event for the d i s t r i b u t i o n of events i n each of the 3680 bins. In t h i s way the v a r i a t i o n i n analyzing power of the monitor was folded i n with the 152 FIG. APP.B-1 OPENING ANGLE AND COPLANAR ANGLE DISTRIBUTIONS 4000 H - 2000 — \ fi.= 85.973 10000 5000 H 7 2 7 9 8 6 9 3 100 LAB OPENING ANGLE(deg) <p,= 89.875* 7 6 i n—""-^ 8 3 90 9 7 104 LAB COPLANAR ANGLE(deg) FIG. APP.B-2 K INEMAT IC ACCEPTANCE OF THE LEFT MONITOR 1000 5 0 0 —\ 0 0 2 5 LL CM. SCATTERING ANGLE(deg) 153 kinematic d i s t r i b u t i o n of events i n the i n d i v i d u a l bins. Values of and AJJN were obtained from a phase s h i f t a n alysis of the world sc a t t e r i n g d a t a ^ " ^ and are recorded i n table APP.b-1 at i n t e r v a l s spaced by 2.5° i n the center of mass between 20° and 60°. The errors quoted include an i n f l a t i o n a r y factor to account for discrepancies i n normalization between the world data sets. Polynomial i n t e r p o l a t i o n was used to obtain values of Pg and A ^ N at a r b i t r a r y s c a t t e r i n g angles. An estimate of the uncertainty i n the cm. scattering angle was obtained using the departure of the measured opening angle from 180° i n the cm. The e r r o r s on Pg and A ^ N c o n t r i b u t e d by the f i n i t e p r e c i s i o n estimate of the cm. scattering angle were added i n quadrature with the the errors a r i s i n g purely from phase s h i f t determinations of P^ and AJ^N* A r e s t r i c t i o n was imposed to l i m i t the acceptance of the measurement to scatters at cm. angles greater than 32°. This was desirable since A ^ N i n e l a s t i c scattering has only been measured from 34° to 9 0 o ^ ^ , B ^ " ^ and extensions to the lower angles purely on the basis of phase s h i f t analyses are tenuous. A x 2 f i t was made to eq. APP.b-2 to determine the s i x gaussian parameters o'H(eo»<l)o)' aC( 60» *0) » PH» &C> H^> and Y C. The sm a l l term depending on the analyzing power of carbon was ignored i n th i s f i t which was chosen for i t s s e n s i t i v i t y to and OQ. The av a i l a b l e data (80369 events) was grouped into three independent data sets and hence provided three independent determinations of the set of s i x parameters which were then combined as weighted averages. The r e s u l t s of the f i t are given i n table APP.b-2. The f i t t e d 3 and y for the hydrogen signal were c l e a r l y much larger than for the carbon s i g n a l , enabling an e f f e c t i v e exclusion of hydrogen 154 TABLE APP.b-1 PHASE SHIFT SOLUTIONS FOR P H AND A M IN ELASTIC SCATTERING AT 508.9 MeV CM. SCATTERING ANGLE P, (deg) 1 20.0 0.4105 22.5 0.4410 25.0 0.4659 27.5 0.4852 30.0 0.4990 32.5 0.5076 35.0 0.5112 37.5 0.5103 40.0 0.5052 42.5 0.4966 45.0 0.4848 47.5 0.4702 50.0 0.4533 52.5 0.4342 55.0 0.4133 57.5 0.3906 60.0 0.3663 ERROR ANN ERROR ±.0119 0.1140 ±.0237 ±.0101 0.2022 ±.0234 ±.0074 0.2852 ±.0231 ±.0048 0.3602 ±.0223 ±.0020 0.4257 ±.0217 ±.0014 0.4807 ±.0221 ±.0020 0.5250 ±.0215 ±.0031 0.5591 ±.0212 ±.0038 0.5838 ±.0210 ±.0040 0.6002 ±.0222 ±.0039 0.6096 ±.0226 ±.0033 0.6133 ±.0227 ±.0028 0.6124 +.0226 ±.0022 0.6082 ±.0219 ±.0017 0.6013 ±.0204 ±.0011 0.5927 ±.0190 ±.0011 0.5828 ±.0169 155 sig n a l i n the f i t to P c using eq. APP.b-3. A cut on coplanar angle was placed to exclude data between 87° and 93° by which point the f i t t e d parameters for the hydrogen s i g n a l indicated a hydrogen contribution down to 1 0 " 1 1 of i t s peak value. The f i t t e d values for the mean analyzing power of carbon over the d i s t r i b u t i o n of events sampled i s given i n table APP.b-3. Though the NMR measurement of target p o l a r i z a t i o n was believed to be s t a t i s t i c a l l y r e l i a b l e , i t s u f f e r e d from a l a r g e n o r m a l i z a t i o n uncertainty. The e l a s t i c s c a ttering asymmetry measurement was used to ca l i b r a t e the NMR measurement by expanding the target p o l a r i z a t i o n as P_.. = ±CNMR x (10~ 5) x NMR INTEGRAL T T r where the c a l i b r a t i o n constant CNMR was the parameter to be determined. A t o t a l of 50667 events were accumulated and f i t t e d to the form of APP.b-1 as three independent data sets with the re s u l t s of the f i t given i n table APP.b-4. Errors on CNMR due to errors on Py and A^ were estimated by repeating the f i t with P replaced by P+6P and A J J N replaced by A N N + ^ N N ' These e r r o r s were added i n q u a d r a t u r e w i t h the s t a t i s t i c a l errors on the f i t which were by far the dominant e r r o r . With an u n c e r t a i n t y of approx. ±4% i n Afljj and on l y ±1.5% i n beam p o l a r i z a t i o n , eq. APP.b-1 was i n s e n s i t i v e to errors i n the beam p o l a r i z a t i o n which were ignored. The weighted mean of the three determinations of CNMR was CNMR = 5.0250 ± 0.1239 An a d d i t i o n a l c a l c u l a t i o n s i m i l a r to the one already described was also c a r r i e d through, but with the emphaisis on eliminating the background 156 TABLE APP.b-2 FITTED GAUSSIAN PARAMETERS OF THE FREE HYDROGEN AND BACKGROUND CARBON SIGNAL Parameter F i t t e d Value From Data Set 1 F i t t e d Value From Data Set 2 F i t t e d Value From Data Set 3 aH(60,<|>0)x10+8 H^ 65.240 ± 0.922 0.3157 ± .0050 2.6068 ± .0424 63.942 ± 1.745 0.3241 ± .0100 2.4678 ± .0787 64.452 ± 1.556 0.3089 ± .0084 2.6237 ± .0735 a c(e 0,<)) 0)xlO+ ! 0.9258 ± .0219 0.0077 ± .0005 0.0122 ± .0008 1.2469 ± .0511 0.0175 ± .0009 0.0302 ± .0015 1.1388 ± .0436 0.0153 ± .0008 0.0277 ± .0014 TABLE APP.b-3 FITTED VALUES FOR THE ANALYZING POWER OF CARBON Parameter F i t t e d Value From Data Set 1 F i t t e d Value From Data Set 2 F i t t e d Value From Data Set 3 0.3027 ± .0292 0.2187 ± .0405 0.1834 ± .0375 TABLE APP.b-4 FITTED VALUES FOR THE NMR CALIBRATION CONSTANT CNMR Parameter F i t t e d Value From F i t t e d Value From F i t t e d Value From Data Set 1 Data Set 2 Data Set 3 CNMR 5.0191 ± .1684 5.1251 ± .2730 4.9564 ± .2462 157 t o t a l l y rather than separating the signal into i t s free hydrogen and carbon background components. A hard cut was placed on x so that there remained no v i s i b l e signs of background i n the opening angle or coplanar angle histograms. Again the data was grouped into three independent sets giving three independent estimates of CNMR. The estimate of CNMR r e s u l t i n g from that measurement was 4.9595 ± 0.1225. The agreement between the two methods i s excellent and the fact that the second method produced a s l i g h t l y smaller estimate of the target p o l a r i z a t i o n can be understood i n terms of a small remaining contribution from the unpolarized carbon background, which could not be eradicated by the x 2 cut and which d i l u t e d the measured asymmetries and e f f e c t i v e p o l a r i z a t i o n of the sample. 

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