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Observation of two-photon emission after pion capture in carbon-12 Mazzucato, Eddy 1979

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OBSERVATION OF TWO-PHOTON EMISSION AFTER PION CAPTURE IN CARBON-12 by EDDY MAZZUCATO B . S c , U n i v e r s i t e de Montreal, 1977 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Physics) We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1979 © Eddy Mazzucato, 1979 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes is fo r f i nanc i a l gain sha l l not be allowed without my written permission. Department of Physics  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 i i ABSTRACT 12 The C(ir ,2y)X re a c t i o n for stopped pions has been investigated at TRIUMF using two large Nal c r y s t a l s (TINA and MINA) and two lead glass Cerenkov counters. A 20 MeV pion beam from the stopped ir/u channel (M9) was used. The incoming pion beam was defined by a 3-counter telescope ^ l ' ^ 2 ' ^ 3 ^ a n ( ^ W a S s t oPP e c^ ^ n a 1*25 cm thick carbon target. The l a s t telescope counter (S^) determined the time of a r r i v a l of the pions. The four y-detectors were located at +55°, +105°, -55°, and -135°, with respect to the incident pion beam. S c i n t i l l a t i o n counters were placed i n front of each y-detector i n order to i d e n t i f y charged p a r t i c l e s . For the Nal c r y s t a l s , t i m e - o f - f l i g h t information was used to separate neutrons and gammas ori g i n a t i n g from the (iT -,nn) and (ir~,nY) reactions. Accidental coincidences from simultaneous (IT -,y) reactions generated by multiple pion stops i n the target were rejected by measuring the energy deposited by the incoming pions i n S^. A t o t a l of 2.5x10"^ pions were stopped, and a f t e r background subtraction, about 500 good YY events were observed at 6 d i f f e r e n t opening angles (0 = 50°, 80°, 110°, 120°, 160°, 170°). The t o t a l branch-12 -5 ing r a t i o f o r the C(TT~,2Y) reaction was measured to be (1.2 ± 0.2)xl0 ; th i s value was found to be very s e n s i t i v e to the low-energy threshold of the Y~detectors. The good energy r e s o l u t i o n (=10%) of the Nal c r y s t a l s permitted the i n v e s t i g a t i o n of the energy-sharing between the two photons at © _ = 120°. The sum energy spectrum of the two photons peaks at 120 MeV i i i and has a width of about 40 MeV. I t s shape indicates that most of the a v a i l a b l e energy i s c a r r i e d o f f by the two photons and that the r e s i d u a l 12 nucleus, most l i k e l y B, i s not highly excited. Detailed t h e o r e t i c a l c a l c u l a t i o n s made by other authors p r e d i c t a t o t a l 2y rate approximately 30% larger than our measured value. No 12 evidence for pion condensates or precondensate e f f e c t s i n C was found. i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS x Chapter 1 Introduction 1 Chapter 2 The o r e t i c a l and Experimental Background 4 12 Chapter 3 Experimental Aspects of the Study of the C(ir ,2y) Reaction 13 Chapter 4 The Experiment 21 4.1 The Experimental Run 21 4.2 Time-of-Flight Spectra and Energy C a l i b r a t i o n s 28 4.,3 The 1 2C(TT ,y) Reaction 38 Chapter 5 Data Analysis 44 5.1 Remarks and Notation 45 5.2 TINA-MINA Coincidences ( 0 ^ = 120°) 46 5.2.1 Sources of Background 46 5.2.2 Background Subtraction 59 5.2.3 Accidental Coincidences Due to Pile-ups 71 5.3 The Other Configurations ^ _ ^ 3 5.4 The Branching Ratio for the C(TT ,2y) Reaction 88 5.4.1 Pile-ups i n the Beam 89 5.4.2 Pair Production 90 5.4.3 Time-of-Flight Cuts 91 5.4.4 The Tot a l Branching Ratio 93 Chapter 6 Discussion of the Results 96 Chapter 7 Conclusion 107 BIBLIOGRAPHY 109 V LIST OF TABLES Page Table I The Nal c r y s t a l s TINA and MINA 15 Table II Raw counting rates 25 12 Table I II The C(ir ,y) reaction 42 Table IV The most probable types of coincidences 58 Table V The background subtraction 67 Table VI The good 2y events at the other angles 74 Table VII Pair production 91 Table VIII TOF cuts 92 Table IX The d i f f e r e n t i a l branching r a t i o 94 v i LIST OF FIGURES Page F i g . 2.1 The TT~ + "IT " 2y mechanism 4 Fi g . 2.2 Born terms for the u p - * e +e n reaction 6 Fi g . 2.3 Angular d i s t r i b u t i o n of 2Y events a f t e r TT capture i n beryllium and carbon (Deutsch et a l . 1979) 9 Fi g . 2.4 Bremsstrahlung graphs contributing to the 2y rate 10 F i g . 2.5 Dominant diagrams i n the u p * YY n process for P-wave capture 12 12 Fi g . 3.1 Photon energy spectrum from TT capture i n C ( B i s t i r l i c h et a l . 1972) 16 Fi g . 3.2 The 1 2C(TT,Y) 1 2 B and 1 2C(IT,Y) U B reactions 17 Fi g . 4.1.1 Lay-out of the experimental area 22 F i g . 4.1.2 Time-of-flight of beam p a r t i c l e s 24 F i g . 4.1.3 Energy-loss spectrum of S^ 24 Fi g . 4.1.4 Diagram of the e l e c t r o n i c s 27 Fi g . 4.2.1 Time-of-flight spectra measured with the Nal c r y s t a l s during a t y p i c a l run with a carbon target 29 F i g . 4.2.2 Time-of-flight spectra measured with the Cerenkov counters during a t y p i c a l run with a carbon target 30 F i g . 4.2.3 Photon energy spectra measured with the Nal c r y s t a l s using a LiH target 33 F i g . 4.2.4 Photon energy spectra measured with the Cerenkov counters using a LiH target 34 v i i F i g . 4.2.5 Energy spectra measured with the Nal c r y s t a l s f o r TT° -»• 2y coincidence events (LiH target) 35 F i g . 4.2.6 Energy spectra measured with the Cerenkov counters for TT° ->• 2y coincidence events (LiH target) 36 F i g . 4.2.7 Coincidental photon energy d i s t r i b u t i o n s for the TT° 2y decay calculated for the two experimental configurations 9 = 160° and 0 = 170° 37 Fi g . 4.2.8 TINA l i n e shape for 129 MeV r a d i a t i v e photons as measured by J. Spuller et a l . (1977) 37 Fi g . 4.3.1 Photon energy spectra obtained with the Nal c r y s t a l s for 12 -the C(ir ,y) reaction 40 Fi g . 4.3.2 Photon energy spectra obtained with the Cerenkov counters 12 -for the C(TT ,y) rea c t i o n 41 Fi g . 5.2.1 TOF spectrum of beam p a r t i c l e s for TINA-MINA coincidence events ( 0 ^ = 120°) 47 F i g . 5.2.2 Energy-loss spectrum of for TINA-MINA coincidence events (0 • =120°) 47 Fi g . 5.2.3 TOF spectra of the Nal c r y s t a l s for TINA-MINA coincidence events 48 F i g . 5.2.4 Two-dimensional time d i s t r i b u t i o n of the TINA-MINA coi n -cidence events 49 F i g . 5.2.5 T^-vs-T^ scatter p l o t for empty target runs 52 Fi g . 5.2.6 Two-dimensional energy d i s t r i b u t i o n of events l y i n g i n the YY window of f i g . 5.2.4 55 v i i i F i g . 5.2.7 Energy-loss spectrum of for high energy coincidence events l y i n g i n the TTNA-MINA yy window 57 F i g . 5.2.8 The background subtraction technique 60 F i g . 5.2.9 TOF d i s t r i b u t i o n s of the events l y i n g i n the y-ray bands of f i g . 5.2.4 62 F i g . 5.2.10 TINA, and MINA y-ray energy spectra for the good 2y events at 9 T M = 120° 65 Fi g . 5.2.11 The TM-vs-T^, scatter p l o t with the d i f f e r e n t regions A, and B^ used i n the background subtraction 66 Fi g . 5.2.12 The d i f f e r e n c e and sum-energy spectra of the good 2y events at Qm, = 120° 68 TM F i g . 5.2.13 Energy-sharing between the two photons ( 0 ^ = 120°) 69 Fi g . 5.3.1 TOF spectra for MINA-C2 coincidence events ( 0 M 2 = 50°) .. 76 Fi g . 5.3.2 T 2~vs-T scatter p l o t 77 F i g . 5.3.3 TOF spectra for TINA-Cl coincidence events ( © T l = 80°) .. 78 F i g . 5.3.4 T 1-vs-T T scatter p l o t 79 Fi g . 5.3.5 T^vs-Tj^ scatter p l o t 80 Fi g . 5.3.6 TOF spectra for MINA-Cl coincidence events = 160°) . 81 Fi g . 5.3.7 T,-vs-T.. scatter p l o t 82 1 M F i g . 5.3.8 TOF spectra f o t TINA-C2 coincidence events ( © T 2 = 170°) . 83 Fi g . 5.3.9 T 2~vs-T T scatter p l o t 84 F i g . 5.3.10 The y-ray energy spectra for the good 2y events at F i g . 5.3.11 The y-ray energy spectra for the good 2y events at i x F i g . 5 . 3 . 1 2 The y-ray energy spectra for the good 2y events at e . 1 2 = 1 1 0 ° 86 F i g . 5 . 3 . 1 3 The Y - r a y energy spectra for the good 2y events at G M 1 = 1 6 0 ° 86 Ml F i g . 5 . 3 . 1 4 The y-ray energy spectra for the good 2y events at e T 2 = 1 7 0 ° 87 12 - 12 -F i g . 6 . 1 The y-ray energy spectra for the C(ir , y ) and C(TT , 2 y ) reactions 97 F i g . 6 . 2 Angular d i s t r i b u t i o n of the 2y events 99 12 F i g . 6 . 3 A n n i h i l a t i o n diagram i n the C(TT , 2 y ) reaction 102 12 F i g . 6 . 4 Dominant bremsstrahlung graphs i n the C(ir , 2 y ) r e a c t i o n for P-wave capture 102 F i g . 6 . 5 Photon energy d i s t r i b u t i o n at 0 = 1 2 0 ° 106 YY X ACKNOWLEDGEMENTS I am pleased to thank my research supervisor Dr. M.D. Hasinoff for h i s help and encouragement during the course of my Master's program. I am i n p a r t i c u l a r very g r a t e f u l to Dr. M. Salomon whose inappreciable help and guidance throughout t h i s work have permitted the successful completion of t h i s experiment. I would also l i k e to express my thanks to Dr. D. Beder and Dr. J.M. Poutissou for t h e i r time and e f f o r t i n reading t h i s manuscript and also for the many f r u i t f u l discussions I had with them. F i n a l l y , I wish to thank the other members of the group, Dr. B. Bassalleck, Dr. T. Marks and Dr. R. Poutissou, for t h e i r valuable assistance. 1 Chapter 1 Introduction The hypothesis that the nuclear force between the protons and the neutrons of a nucleus i s due to the exchange of v i r t u a l pions . was made a long time ago by Yukawa (1935) and was confirmed l a t e r by the discovery of the pion i n 1947. I t i s well established now that the constituents of the nucleus act as a source for a pionic f i e l d which i n turn i s mostly responsible for the long range part of the nuclear force. The one pion exchange p o t e n t i a l (OPEP) derived from the exchange of ir-mesons has proved indeed to be very successful i n the peripheral p a r t i a l wave phase s h i f t analysis of nucleon-nucleon sc a t t e r i n g . The success of the d e s c r i p t i o n of the nucleon-nucleon p o t e n t i a l i n terms of pion exchanges and also of heavier meson (p'j'co) or m u l t i -meson (2 T T , P T T) exchanges i s , however, only an i n d i r e c t evidence for the existence of mesons i n n u c l e i . Experiments that have shown d i r e c t s i g -nature for mesonic structure i n n u c l e i and nuclear exchange currents are, up to now, rather scarce. The c l e a r e s t manifestation of mesonic exchange e f f e c t s i n n u c l e i has been found i n electromagnetic and weak i n t e r a c t i o n processes i n l i g h t n u c l e i . Discrepancies between experiments and con-ventional nuclear models i n the study of processes l i k e the r a d i a t i v e 3 neutron capture by protons and the g-decay of H have revealed the neces-s i t y for including mesonic degrees of freedom' in-".the d e s c r i p t i o n of the J 2 dynamical properties of the nucleus. These mesonic e f f e c t s are now known to a r i s e from the i n t e r a c t i o n of electromagnetic and weak f i e l d s with the v i r t u a l mesons exchanged between nucleons (exchange currents) and to modify appreciably the properties of a nuclear system (e.g. the d i s c r e p -3 "3 ancies obtained i n the magnetic moment of He and H). I t i s therefore of considerable i n t e r e s t to f i n d s e n s i t i v e probes to the nuclear meson f i e l d and more p a r t i c u l a r l y , to look for pion e f f e c t s i n n u c l e i . In t h i s regard, T.E.O Ericson and C. Wilkin suggested a few years ago (1975) that v i r t u a l pions could i n p r i n c i p l e be detected using the c h a r a c t e r i s t i c TT + " i r + " 2y process which would occur i f a IT injected into a nucleus interacted with a v i r t u a l TT"*". This a n n i h i l a t i o n mechanism was believed to probe d i r e c t l y the pion con-tent of the nucleus and to provide more information about the pionic degrees of freedom. Another strong motivation for studying t h i s process was the possible existence of pion condensation i n nuclear matter. I t was pointed out by Migdal i n 1971 that, i f the nuclear density exceeded a c e r t a i n c r i t i c a l value, v i r t u a l pions could be raised to the energy s h e l l and condense as r e a l pions with a f i n i t e p r o b a b i l i t y . Calculations on the value of t h i s c r i t i c a l density have been attempted but are d i f -f i c u l t and ambiguous. There i s at present no agreement on whether nuclear density approaches that value or not. However, M. Ericson and J. Delorme (1978) have shown that an enhancement of the s t a t i c pion f i e l d could occur and possibly be detected even at d e n s i t i e s below but close to the c r i t i c a l density (precondensation e f f e c t s ) . In view of the importance of these fundamental questions of 3 nuclear physics, the study of the (TT ,2y) process i n n u c l e i -the doubly r a d i a t i v e pion capture- has raised i n recent years a great i n t e r e s t among experimentalists and t h e o r i s t s as we l l . I t was t h i s desire to learn more about the nuclear "pioriic f i e l d that prompted our i n v e s t i g a t i o n of the (TT-,2Y) process at the Tri-University-Meson-Facility. 4 Chapter 2 Theoretical and Experimental Background In 1975, Ericson and Wilkin, with the aim of probing the behaviour of r e a l and v i r t u a l pions inside the nucleus, suggested two mechanisms to study: (i) the a n n i h i l a t i o n reactions IT + " i r + " ->• 2y or e +e on v i r t u a l pions i n n u c l e i : and ( i i ) the v i r t u a l T r ° 2y decay ins i d e the nucleus. In analogy with positron a n n i h i l a t i o n on the electrons of a s o l i d , the a n n i h i l a t i o n process TT + "TT +" ->• was believed to probe d i r e c t l y the nuclear pionic f i e l d and i t s coupling to nuclear e x c i t a t i o n s . An e s t i -mate for the branching r a t i o of the 2y a n n i h i l a t i o n mode i n n u c l e i was based on the evaluation of the dominant Born term i n the Coulomb gauge for the IT p -v yyn reaction at low energies (S-capture) . The corresponding diagram i s shown i n f i g . 2.1. F i g . 2.1 The TT + "TT " + 2y mechanism. 5 The rate of the doubly r a d i a t i v e pion capture as depicted i n f i g . -4 2.1, was calculated to be about 10 of the rate of the well known sing l e r a d i a t i v e pion capture IT p yn o n a free proton free 9 —U i . e . -p-— * 1.9 x 10 free R i y -4 i n good agreement with the previous value of 1.4 x 10 calculated by Joseph i n 1960. To obtain an estimate of the rate of the TT + "TT +" 2y process i n n u c l e i , i t was assumed that the r a t i o of the doubly r a d i a t i v e pion capture rate to the s i n g l e rate was not dramatically modified by the presence of other nucleons, that i s : nucl free R2Y .. R2Y ^nucl ^ f r e e ly l y Since for moderately heavy n u c l e i the s i n g l e r a d i a t i v e rate i s about 2-3% of the t o t a l capture rate, t h i s y i e l d s a branching r a t i o for the 2y anni-h i l a t i o n process i n n u c l e i with A — 6 B . F ™ C l = 5 x 10" 6. 2y In c a l c u l a t i n g the r a t i o of the 2y/ly processes, i t was hoped that nuclear e f f e c t s such as the Fermi motion of the nucleons and the P a u l i blocking would be s i m i l a r for both processes, and therefore, that the above estimate would be r e l i a b l e for n u c l e i . If the 2y a n n i h i l a t i o n mechanism on a v i r t u a l pion i s s t i l l the dominant mechanism i n n u c l e i , then the pion content of the nucleus could be 6 probed. The energy balance of the reaction would then i n d i c a t e to which states the pionic f i e l d i s p r e f e r e n t i a l l y coupled. In addition, a large enhancement i n the observed rates would possibly r e f l e c t anomalies i n the pion i c f i e l d (pion condensates and precondensate e f f e c t s ) . In the case of the e + e emission, however, the s i t u a t i o n i s more complicated. It was shown a few years ago by K r o l l and Wada (1955) that, because of the presence of the photon propagator (see f i g . 2.2), the i n t e r -2 nal p a i r s o r i g i n a t e predominantly from quasi-real photons (m^ = 0) and so, carry l i t t l e more information than the TT p -> yn r e a c t i o n . Furthermore, i t 2 2 2 i s only f o r massive photons (m >— m ) that the a n n i h i l a t i o n graph of f i g . y 3 TT 2.2 (a) can compete with the process of f i g . 2.2 (b) i n which the photon i s excl u s i v e l y radiated by the nucleon. Fi g . 2.2 Born terms for the TT p e^e n reactio n . In that case, the branching r a t i o f o r the e +e a n n i h i l a t i o n mechanism was estimated to be 2 2 2 -5 B.R + - (m > - m ) - 10 e e y 3 TT that i s , of the same order of magnitude as the value for the 2Y a n n i h i l a t i o n . 7 The second process, the v i r t u a l TTU 2y decay, was at t r i b u t e d to the charge f l u c t u a t i o n s of the pionic f i e l d when a low energy IT propagates i n the nuclear medium. Inside the nucleus, t h i s charged pion can be momen-t a r i l y converted into an off-mass s h e l l TT° v i a v i r t u a l charge exchange (?r •*• "TT°" IT ) . During the short i n t e r v a l of time when the pion finds i t s e l f i n the neutral state, a TT° -* 2y decay can be observable. Ericson and Wilkin (1975) estimated that the branching r a t i o of the 7r° v i r t u a l decay was B . < ° * 1 0 - 6 - 10" 7. 2Y If the v i r t u a l TT° decay could be distinguished from the 2y anni-h i l a t i o n process, then a measurement of the sum energy of the two photons and the momentum balance would give some information about the excited states of the nucleus caused by charge exchange. These, of course, would be d i f -ferent from the states excited through the two-photon a n n i h i l a t i o n mechanism. These processes as suggested by Ericson and Wilkin raised great i n t e r e s t among experimentalists. Stopping a negative pion i n matter and looking at the emission of two y~rays or an electron-positron pair seemed therefore an appropriate way to probe the soft component of the pionic f i e l d 2 2 (momentum transfer q - m ). Although i t was uncertain that pion condensates i n n u c l e i could be detected"*", the processes proposed could hopefully map out 2 the q -dependance of the pion nuclear coupling constant g „._, and, as pointed out by Nyman and Rho (1977), the 2y a n n i h i l a t i o n mechanism could provide a better understanding of the weak coupling renormalization i n n u c l e i . A s i g n a l for pion condensates i s more l i k e l y to occur at a large momentum transfer, q 2 = 2m2. (Ericson and Delorme, 1978). 8 At that time, the only search for the emission of two photons a f t e r nuclear pion capture had been done by Petrukhin and Prokoshkin (1964) who looked for charge-exchange reactions for stopped pions i n several n u c l e i . But since the p u b l i c a t i o n of Ericson's and Wilkin's paper (1975), three experimental groups have investigated these questions: ( i ) l ' U n i v e r s i t e Catholique de Louvain at CERN, ( i i ) the V i r g i n i a Polytechnic I n s t i t u t e and the Indiana Un i v e r s i t y at SREL, and ( i i i ) , a group from the University of B r i t i s h Columbia at TRIUMF (work being presented i n t h i s t h e s i s ) . The f i r s t group to publish a r e s u l t was the Virginia-Indiana c o l -12 laboration (Roberson et a l . 1977). They investigated the TT + C 2y + X reaction at r e s t (X unknown) but could not resolve the true YY events from the background. An upper l i m i t for the branching r a t i o was found to be 1.4 x 10 ^ at a 90% confidence l e v e l . This value was obtained from a c a l -c u l a t i o n of the photon angular c o r r e l a t i o n for the dominant TT p -> YYN mechanism i n a S-pion capture. More recently, the Louvain group (Deutsch et a l . 1979) observed for the f i r s t time the emission of two photons a f t e r TT capture i n bery-l l i u m and i n carbon. Using a high acceptance array of lead glass Cerenkov counters, they measured the angular d i s t r i b u t i o n of the two emitted .'Y-rays (see f i g . 2.3). The branching r a t i o s obtained for photons of energy above -5 -5 25 MeV were (1.0 ± 0 . 1 ) x l 0 i n beryllium, and (1.4 ± 0.2) x 10 i n carbon. A q u a l i t a t i v e s i m i l a r i t y between the sum-energy d i s t r i b u t i o n of the two photons and the y-vay energy spectrum for the si n g l e r a d i a t i v e pion capture i n carbon was also observed. However, because of the poor energy r e s o l u t i o n 9 of t h e i r detectors, no information on the energy-sharing between the two photons was a v a i l a b l e . Also no experimental r e s u l t on the electron-positron emission was reported and the r o l e of the l e s s probable v i r t u a l TT° -> 2y decay was s t i l l uncertain. d N j j < e 1 2 ) / d f i 1 2 (XT6/ Stopped pion-Sterod) • Carbon » Beryllium .-i , , , 0 50 100 150 6^ F i g . 2.3 Angular d i s t r i b u t i o n of 2y events a f t e r ir~ capture i n beryllium and carbon (Deutsch et a l . 1979). The s o l i d l i n e represents the 2y angular c o r r e l a t i o n as calculated by Barshay. In l i g h t of these experimental r e s u l t s , i t seemed very premature to make comparisons with Ericson's and Wilkin's estimate for the 2y anni-h i l a t i o n process. The consideration of the so c a l l e d " s e a g u l l " graph alone ( f i g . 2.1) was open to c r i t i c i s m since i t leads to amplitudes which are not gauge i n v a r i a n t . Furthermore, because the capture of a pion i n n u c l e i l i k e 9 12 Be and C occurs predominantly i n a P-state (-90%), terms dependent on the 10 three-momentum of the pion are expected to s i g n i f i c a n t l y a f f e c t the rate of the 2y emission. To improve the estimate of Ericson and Wilkin, and to remedy the f i r s t objection made above, Beder (1978, 1979a) investigated the IT p -> YYN r e a c t i o n at threshold (S-capture) by considering i n addi t i o n to the seagull graph, the bremsstrahlung diagrams shown i n f i g . 2.4. (a) (b) F i g . 2.4 Bremsstrahlung graphs contributing to the 2Y rate. It was shown that for a t y p i c a l geometry where the inter-photon angle i s 90°, the seagull contribution at threshold was only 2/3 of the t o t a l 2y rate (for S-wave capture). For larger opening angles, the seagull term i s even more suppressed, i n d i c a t i n g the important r o l e played by the bremsstrahlung graphs, The value obtained for the r a t i o of the double-to sin g l e capture rates on a free proton was not, however, much d i f f e r e n t than the previous estimates f o r S-capture: = 1.3 x 10" 4. R i y The e f f e c t of the A resonance (J = 3/2, M = 1235 MeV) i n the TT p * YYN reaction was also considered by Beder, and was found to bring a non-negligible c o r r e c t i o n to the pion-seagull amplitude (+7%). 11 Meanwhile, Barshay (1978) calculated the angular c o r r e l a t i o n of the two photons for the P-wave and S-wave a n n i h i l a t i o n mechanisms on a free proton as well as for the v i r t u a l TT° decay, again assuming only the seagull graph to contribute. The branching r a t i o s he obtained were: q _C B.R = 3.5 x 10 (S-wave) a P -6 B.R = 5 x 10 (P-wave) a for the TT a n n i h i l a t i o n on a v i r t u a l TT+, and 9 P -Q B.R = 2B.R . * 3 x 10 for the v i r t u a l TT° -»• 2y decay. The angular d i s t r i b u t i o n predicted for the free nucleon TT " i r + " a n n i h i l a t i o n process i s compared to the experimental r e s u l t s of the Louvain group (1979) i n f i g . 2.3. The f r a c t i o n of the capture occurring i n the P-state was assumed to be 85%. In connection with the problem of pion condensates, Barshay also proposed a new mechanism i n which two-photon emission i n TT capture could be induced by the meson condensate i t s e l f . According to the author, a clear s i g n a l for pion condensates would then consist of the observation of a very energetic nucleon (-7F- m ) i n coincidence with the two photons, 2 TT At the time when the U.B.C. group started t h e i r experiments i n A p r i l 1978, the s i t u a t i o n of the doubly r a d i a t i v e pion capture re a c t i o n i n r e l a t i o n with the pionic f i e l d and meson condensation e f f e c t s was not c l e a r . The experimental r e s u l t s obtained to that time were two to f i v e times larger 12 than the c a l c u l a t i o n s involving free nucleons. C l e a r l y , more r e a l i s t i c i n v e s t i g a t i o n s and computations of the (TT , 2y) reaction i n n u c l e i were necessary. Since then, more de t a i l e d c a l c u l a t i o n s have been performed by Beder (1979b) and also by C h r i s t i l l i n and Ericson (1979) . These authors have pointed out the f a c t that i n P-wave capture, the doubly r a d i a t i v e pion capture i s dominated by the bremsstrahlung graphs shown i n f i g . 2.5 and not by the a n n i h i l a t i o n graph as i t was believed e a r l i e r ./ (a) (b) F i g . 2.5 Dominant diagrams i n the ir p -> yY n process for P-wave capture. Using a l l diagrams, and considering the e f f e c t s of the A resonance and the v i r t u a l TT° decay i n the TT p * YY n process for both S- and P-wave capture, Beder (1979b) estimated the 2y capture rate i n carbon v i a the impulse approximation and a r e a l i s t i c capture schedule. C h r i s t i l l i n and Ericson (1979) used an e f f e c t i v e Hamiltonian together with energy weighted sum rules 12 over the nuclear spectrum of the f i n a l states i n B to evaluate the t o t a l 2y rate, the inter-photon angular c o r r e l a t i o n , and the y energy spectrum for 12 the C(TT , 2y) r e a c t i o n . The r e s u l t s and conclusions of Beder and Chr i s -t i l l i n and Ericson w i l l be presented i n Chapter 6 where they w i l l be compared to our experimental r e s u l t s . 13 Chapter 3 Experimental Aspects of the Study of the "COrr , 2y) Reaction Experimentally, the task of i n v e s t i g a t i n g the (TT , 2y) reaction i n n u c l e i i s d i f f i c u l t . One simple reason i s the very low p r o b a b i l i t y of occurrence of t h i s process. Not only i s i t necessary to work with high rates of low energy pion beams, but moreover, i f one wishes to get some information about the r e s i d u a l nucleus, i t i s desirable to achieve good energy r e s o l u t i o n —5 —6 and also high detection e f f i c i e n c y . At the 10 -10 l e v e l , i t i s expected that background processes w i l l compete strongly with the above re a c t i o n . Therefore, the choice of target and experimental technique are very important. Cer t a i n l y , the study of the doubly r a d i a t i v e pion capture r e a c t i o n i n hydrogen would provide the most extensive information on the TT "TT +" a n n i h i l a t i o n mechanism on a free nucleon; yet i t presents major background problems. Needless to say, the charge-exchange (CEX) and the r a d i a t i v e pion capture reactions i n hydrogen are highly probable processes (branching r a t i o s of 60.7% and 39.3% respectively) and can produce accidental coincidence 2 rates which are thousands of times larger than the true 2y events. However, i n other l i g h t n u c l e i , r a d i a t i v e pion capture i s le s s probable (B.R^ = 2 % ) , 3 and for n u c l e i heavier than He, the charge-exchange process i s known to be strongly hindered (B.R £. 10 "*) , and even, i n some cases, forbidden at r e s t . TT° A s u i t a b l e target-nucleus for the i n v e s t i g a t i o n of the (TT , 2y) reaction, would therefore be a nucleus for which the charge-exchange reaction i s Despite these experimental f a c t s , the study of H(TT , 2y)n has been proposed at LAMPF. 14 12 preferably endothermic. In t h i s regard, C appears to be a good candi-date since i t s Q-value for the CEX rea c t i o n i s negative, 0- = -8.9 MeV. By l i m i t i n g the incident energy and the energy spread of the pion beam, i t i s therefore possible to suppress considerably the production of r e a l TT 0'S. Furthermore, these neutral pions, i f any, would have a small k i n e t i c energy, and consequently, they would only decay into nearly c o l l i n e a r y-rays i n the laboratory frame. If one disregards the i n - f l i g h t charge-exchange reaction, the other processes that can occur when a negatively charged pion stops i n carbon are: 1. (a) 1 2 C ( 7 r " , 2n) 1 0B (b) 1 2 C ( T T " , n ) n B i2„, - Nio„ 2. C(TT , np) Be 12 - 12 3. (a) ± ZC(TT , Y ) B ... 12„, - .11 (b) C(TT , n Y) B 12 The C(TT , 2n) reaction at re s t has been studied by several groups i n correlated neutron emission measurements (Nordberg et a l . 1968, Bassalleck et a l . 1977, Hartmann et a l . 1978 and references t h e r e i n ) . Despite some serious disagreements between recent experiments (Bassalleck et a l . 1977, Hartmann et a l . 1978), t h i s reaction i s known to occur with a r e l a t i v e l y high p r o b a b i l i t y ( B . I ^ between 13% and 26%), Thus neutrons could y i e l d a large amount of undesirable coincidences i f they are not distinguished from Y _ r a y s - One way to avoid t h i s complication would be to use lead glass Cerenkov counters which are i n s e n s i t i v e to neutrons. However, the bad energy r e s o l u t i o n of these counters (30% or worse) would 15 not permit the extraction of any valuable information on how the two photons and the r e s i d u a l nucleus share the a v a i l a b l e energy. By using two large sodium iodide c r y s t a l s , TINA (46 cm <(> x 51 cm) and MINA (36 cm <f> x 36 cm) which are capable of giving good time and energy r e s o l u t i o n , together with s u i t a b l e s o l i d angles, Y - r a Y s c a n he separated from neutrons by the time-o f - f l i g h t (TOF) technique. The performances of TINA and MINA have been tested previously; table I summarizes the main features of these Nal c r y s t a l s . Table I The Nal c r y s t a l s TINA and MINA TINA (Harshaw Chemical Company, Solon, Ohio, U.S.A.) Size: 46 cm diameter, 51 cm long equipped with 7 RCA 4522 tubes Time r e s o l u t i o n : ~2 ns Energy r e s o l u t i o n : 5% at 100 MeV 4.4% at 144 MeV MINA (Bicron Corporation, Newbury, Ohio, U.S.A.) Size: 36 cm diameter, 36 cm long equipped with 4 RCA 4522 tubes Time r e s o l u t i o n : -2.8 ns (tested with cosmic rays) Energy r e s o l u t i o n : 6% (tested with electron beam) tested with electron beam 16 Reactions 1(b) and 2 are of much l e s s i n t e r e s t here, since we are only concerned with neutral-neutral coincidences. Radiative pion capture i n carbon (reaction 3) has been studied by Davies et a l . (1966) and B i s t i r l i c h et a l . (1972) who detected high energy y - r a y s following the capture of stopped pions. In both experiments, the y i e l d of the r a d i a t i v e capture was found to be about 2% of the t o t a l capture rate ((1.68 ± 0.10)% for Davies et a l . and (1.92 ± 0.20)% for B i s -t i r l i c h et al.) and the y-ray spectrum was observed to peak strongly i n the region of 105-120 MeV. The high-resolution photon spectrum obtained by B i s t i r l i c h et a l . using a pair spectrometer, i s shown i n f i g . 3.1. 50 70 90 110 130 150 E r ( M t V ) F i g . 3.1 Photon energy spectrum from T r " capture i n 1 2 C ( B i s t i r l i c h et a l . 1972). The energy dependance of the y - r a y s appears as a continuous spectrum with a maximum energy between 110 MeV and 120 MeV ( s o l i d l i n e ) on which are superimposed resonance-like enhancements associated with the 12 ground state and excited states of B (reaction mechanism 3(a)). More p r e c i s e l y , these excitations are the 1 and 2 components of t r a n s i t i o n s 17 to analogs of 1 known states i n the Giant Dipole Resonance region of C. The continuum i s very well described by the pole model i n which the quasi-free (QF) capture on a proton i n the nucleus gives r i s e to a three-body f i n a l 12 11 state, i . e , TT + C ->• B + n + y (reaction 3(b)). These two reaction mechanisms are shown schematically i n f i g . 3.2, (a) (b) F i g . 3.2 The 1 2 C ( 7 T , y ) 1 2 B and 1 2C ( T r",ny) U B reactions. It i s found that the QF capture dominates the t o t a l r a d i a t i v e capture, The branching r a t i o of processes 3(a) and 3(b) have been mea-sured to be (Q.43 ± ,04)% and (1.49 ± .15)% r e s p e c t i v e l y . Note that for the l a t t e r reaction, n-Y coincidence events can be i d e n t i f i e d by TOF measurements. Furthermore, i t has been observed that the y-ray and the neutron are p r e f e r e n t i a l l y emitted at 180° and that the neutron has a k i n e t i c energy which peaks at about 10 MeV (Lam et a l , 1974). One serious question that a r i s e s i n t h i s context i s the p o s s i b i l -i t y of capture-cascade processes i n which, the emission of the capture photon populates a nuclear State that can i n turn deexcite to a low-lying l e v e l through, a r a d i a t i v e t r a n s i t i o n . These nuclear processes, of course, con-t r i b u t e to two-photon background events that are i n d i s t i n g u i s h a b l e from the true 2y events. In the QF capture, most of the r e s i d u a l energy i s c a r r i e d 18 o f f by the neutron, and the (A-l) nuclear system, for instance, i s l e f t with an e x c i t a t i o n energy of about 5 MeV. A s i m i l a r remark applies to the resonance capture for which the energy of the excited state does not exceed 8-10 MeV. With a t y p i c a l detection threshold of 15 MeV i n each detector, capture-cascade events are mostly eliminated. So f a r , we have discussed the possible processes that can compete with the doubly r a d i a t i v e pion capture but we have not said anything about the experimental constraints that are present i n the study of that rare reaction. When working with high pion beam rates, an appreciable number of accidental coincidences can be generated by multiple TT -stops i n the target. In that case, the p r o b a b i l i t y that two stopped pions each produce a sing l e r a d i a t i v e capture y-ray within the resolving time of the detectors, i s not n e g l i g i b l e when compared to the p r o b a b i l i t y of occurrence of the expected 2y events. For example, i t i s estimated that for a stopping pion rate of 1 x 10 /s at a cyclotron frequency operation of 23 MHz, the f r a c t i o n of multiple to sing l e stopped pions i s about 2%. Assuming a r a d i a t i v e capture p r o b a b i l i t y i n carbon of 2% and taking the value of 1.4 x 10 obtained by the Louvain group f o r the doubly r a d i a t i v e capture (Deutsch et a l , 1979), the r a t i o of accidental to true 2y events i s about ( 2 Y ) a c c . ( 2 % ) 2 x 2% y _ ^  ( 2 Y ) t r u e 1.4 x 10 5 Although most of these accidental coincidences can be removed by imposing a l i m i t on the sum energy of the two photons, i . e . E + E 5_ m Y l Y2 (provided the energy r e s o l u t i o n i s good enough), i t i s desirable to r e j e c t 19 those "pile-up" pions before they stop i n the target. One e f f i c i e n t method of doing t h i s i s to measure the energy deposited i n a s c i n t i l l a t i o n counter which defines the incoming pion beam (see section 4.1), The t o t a l energy loss of the two simultaneous pions should therefore be about twice as large as the energy deposited by a si n g l e pion. In order to c o l l e c t a s a t i s f a c t o r i l y good s t a t i s t i c a l sample of 2y events i n a reasonable amount of time, some compromises must be made, A f a i r l y good TOF separation between neutrons and y _ r a y s can be obtained i n the Nal c r y s t a l s i f the distance from target to c r y s t a l i s s u f f i c i e n t l y large. T y p i c a l l y , the TOF i n t e r v a l between y-rays and 60 MeV neutrons should be at l e a s t 6-7 ns (-1.1m), But high detection e f f i c i e n c y can only be achieved to the detriment of energy r e s o l u t i o n . With a f r a c t i o n a l s o l i d angle of 8 x 10 \ one cannot hope to get better energy r e s o l u t i o n than 8 or 10%. This i s due to the fact that with a large c o l l i m a t i o n , some Y*" r ay s see only the edges of the Nal c r y s t a l . With a stopping pion rate of 1 x 10^/s, the number of 2y events expected (assuming isotropy) should be about n 2 « 2 x 1.4 x 10" 5 x 10 6/s x (8 x 1 0 _ 3 ) 2 _3 = 1.8 x 10 event/s or about 6 events/hour. As we have planned to use two lead glass Cerenkov counters to increase the s t a t i s t i c s and to study the angular c o r r e l a t i o n between the two photons, the t o t a l rate of 2y events, with four detectors (6 d i f f e r e n t angles), should be about 12 events/hour. 20 I t i s d i f f i c u l t to give an estimate of the background/real event r a t i o since t h i s depends strongly on how e f f i c i e n t the TOF separation bet-ween Y - r a y s a n d neutrons i s , and on the rate of random coincidences (slow neutrons from TT-production target, cyclotron and shield i n g s , etc.) Never-theless, since we have shown that 2y accidental coincidences can be mostly eliminated, the remaining background events can be removed by applying pro-per background subtraction techniques. In the next chapter, we s h a l l discuss how the experiment was c a r r i e d out. 21 Chapter 4 The Experiment 4.1 The Experimental Run The experiment was conducted at TRIUMF during a two week run i n September 1978 which followed a short preliminary run i n A p r i l . A 20 MeV TT beam from the stopped ir/y channel (M9) was used. F i g . 4.1.1 shows a diagram of the lay-out of the experimental area. The incoming pions were defined by a telescope consisting of the three s c i n t i l l a t i o n counters S^, 2 S^ and S^, and were stopped i n a 2.30 g/cm thick carbon target located 1.3 metres downstream of the beam snout. The time of a r r i v a l of the incident p a r t i c l e s was determined by S^. The two Nal c r y s t a l s , TINA and MINA, plus the two lead glass Cerenkov counters CI, C2, were placed at +55°, +105°, -55° and -135° with respect to the d i r e c t i o n of the incident pion beam. These y-counters had charge i d e n t i f i c a t i o n counters i n front of them to recognize (e,e) p a i r s . S c i n t i l l a t i o n counters, S,., S,.,, S^, S., and S Q were placed ins i d e and outside the iron shields which surround / o TINA and MINA to r e j e c t Y-rays that could convert i n the col l i m a t o r s . In addition, large p l a s t i c counters covered the c r y s t a l s to reduce the cosmic ray background. Steel s h i e l d i n g between TINA and MINA was also used to reduce cr o s s - t a l k and other sources of background. The i n t e n s i t y of the primary proton beam (BLl) varied between IOWA and lOOuA y i e l d i n g stopping pion rates ranging from 450 K/s to 1.4M/s. With the M9 channel tuned for 20 MeV negative pions, a 10 cm Be production 22 inter-detector angles 8 MINA-C2 : 50° TINA-C1 : 80° C1-C2 : 110° TINA-MINA : 120° MINA - C1 : 160° TINA - C2 : 170° 0 Fe H P b Concrete F i g . 4.1.1 Lay-out of the experimental area 23 target, and the M9 s l i t s open to 10 cm, the r a t i o of pions, muons, and electrons i n the incident beam was approximately 40%/5%/55%. However, almost a l l of the electron contamination was removed by r a i s i n g the thres-hold of the telescope counter di s c r i m i n a t o r s . In addition, a s i g n a l o r i -ginating from the proton beam pulse enabled us to separate c l e a r l y the muons and the electrons from the pions by TOF (see f i g . 4.1.2). The actual pion stop rate was measured by putting a large veto counter (S4) j u s t behind the target, but i t was removed during the data c o l l e c t i n g part of the run to avoid unwanted sources of background. The r a t i o S 2«S 3-S^/S 1'S 2«S 3 was found to be 0.78 ± 0.01 and several con-sistency checks proved that t h i s value remained f a i r l y constant during the ent i r e run. The pions entered the target with a mean k i n e t i c energy of about 10.5 MeV and almost a l l of the pions that triggered S^, S 2, and S 3, stopped i n the carbon target. The spread of the beam at was measured to be Ap/p = 5% (p = 61 MeV/c at S„). I t i s estimated by range c a l c u l a -7T 3 tions that about 30% of the "cloud" muons produced i n the TT-production target also stopped i n the carbon target. The p a r t i c l e s that went through the target consisted mainly of cloud muons, e l e c t r o n - and muon pile-ups, and also muons o r i g i n a t i n g from the i n - f l i g h t IT -»- u + v decay. To i d e n t i f y pion pile-ups, the energy deposited i n by the incoming p a r t i c l e s was measured (see f i g . 4.1.3). The size of t h i s counter (7.6 cm x 7.6 cm x .16 cm) was chosen to be smaller than and S 2 i n order to reduce unwanted neutron background i n the Nal c r y s t a l s while the target was large enough (24.7 cm x 19.7 cm x 1.25 cm) to minimize p a r t i c l e losses due to multiple s c a t t e r i n g i n This s i g n a l was obtained from a non-intercepting beam monitor (capacitive probe) located at the ir-production target (T2) . 24 T I M E - O F - F L I G H T O F B E A M P A R T I C L E S I S D D O -H >• 12000 —\ 3 2 <3O00 - I S O -12.0 PIONS "T" -6.0 o.o 6.0 R E L f l T I V E T I M E IN5) ELECTRONS (x5) 12.0 18.0 F i g . 4.1.2 Time-of-flight of beam p a r t i c l e s . The electrons that appear :'. i n the spectrum are associated with the following pion beam pulse. E N E R G Y L O S S ( M E V ) F i g . 4.1.3 Energy-loss spectrum of S^. This spectrum was obtained for any type .of coincidence events. 25 (mult, scatt. < 1%). A t o t a l number of 2.5 x 10 X J" pions were stopped i n the carbon target during the en t i r e run at an average stopping rate of 7 x 10 5 TT/S. In order to e s t a b l i s h the d i f f e r e n t types of background that were present i n our experiment, several test runs were made: "empty" target runs to observe cosmic rays and ambient slow neutrons, a CR^ target run f o r TT° detection e f f i c i e n c y , and two runs with the collimators of the Nal c r y s t a l s f i l l e d to observe only neutron events. A LiH target was reg u l a r l y used to check the s t a b i l i t y of the detectors and to obtain t h e i r energy c a l i b r a t i o n s (see next s e c t i o n ) . T y p i c a l raw counting rates measured i n the cosmic and y-ray counters with and without the carbon target i n place are shown i n the table below. Table II Raw counting rates Counter Geometrical Rates acceptance — . 1 1 ^ ^ ^ 4TT with C target no target (x 10 ) (S 1-S 2-S 3 = 10 /s) (S 1«S 2«S 3 = 780K/s) TINA 9.02 4.3 K/s 600/s MINA 7.45 2.8 K/s 370/s CI 1.91 l . l K / s 630/s C2 2.82 0.8 K/s 340/s Cosmics 20 K/s 17 K/s 26 These rates depended strongly on the si z e of the counters, on t h e i r geo-metr i c a l acceptance and on t h e i r l o c a t i o n i n the experimental area. For instance, the Cerenkov counters detected some scattered electrons of the beam, while TINA and MINA were more s e n s i t i v e to cosmic rays and also slow random neutrons. The l o g i c and analog e l e c t r o n i c devices d i r e c t l y r e c e i v i n g the signals of the y -detectors and a l l the s c i n t i l l a t i o n counters are shown schematically i n f i g . 4.1.4. The signals of a l l four detectors were viewed by constant f r a c t i o n discriminators (CFD ORTEC 934), but because of the high rate of the incident beam, the telescope counters had f a s t discriminators (LRS 621). TDC (LRS 2228) and ADC (LRS 2249W, EGG QD 410) units interfaced to a PDP 11/40 computer v i a a CAMAC system, converted the t i m e - o f - f l i g h t (TOF) and pulse-height (PH) signals of the y-detectors and into 10 b i t words. The timing signal of the proton beam was also recorded. A v a l i d event was determined by requiring a coincidence between counters S^, and S^, and any pair of y-detectors } i . e . (S^'S2*S.j) • (D J) ) . A coincidence buffer module (EGG C212) was used to tag the cor-responding events with the s p e c i f i e d detectors and the kind of p a r t i c l e s (neutral, charged, cosmic). A l l t h i s information was recorded, event by event, on the magnetic tape by the on-line computer. In addition, the S^*S2 and ^2*^2*^3 r a t e s a n < ^ also the singles counting rates i n the detectors were recorded by CAMAC scalers and written on tape at the beginning and the end of each buffer (1 buffer = 74 events). For c a l i b r a t i o n and s t a b i l i t y test purposes, si n g l e events were also recorded. However, i n order to minimize computer dead time, the rate 27 F i g . 4.1.4 Diagram of the e l e c t r o n i c s . The counters are labeled as i n f i g . 4.1.1. A stands for a m p l i f i e r , CFD for constant f r a c t i o n discriminator, CO for coincidence, C P . for c a p a c i t i v e probe, D for discriminator, F for fan ( i n / o u t , l i n e a r , l o g i c ) , GG for gate generator, SCA for CAMAC scaler and V for CAMAC veto. 28 of the Nal singles CAMAC trig g e r s was reduced by a random coincidence with a pulser gate, whereas the single events i n the lead glass Cerenkov counters were only recorded f o r a short period of time i n each run. The l o g i c was designed i n such a way that the coincidence rate (about 16 events/min) was not affected by the rate of s i n g l e s . 4.2 Time-of-flight Spectra and Energy C a l i b r a t i o n s The TOF spectra of the four y-detectors were obtained by taking the difference between the time measured i n each detector D. and the time I of the telescope counter S^ i . e . : TOFD_ = T Q - T i I 3 The TOF of the beam p a r t i c l e s was defined by TOF BEAM = T S 3 - T p R 0 T ( ) N where T i s the time signal that originated from the proton beam. A l l TOF spectra were c a l i b r a t e d using the 43.4 ns time i n t e r v a l between two consecutive beam pulses (f n ^ = 23.060 MHz). We present i n f i g . cyclotron 4.2.1 and f i g . 4.2.2 the TOF spectra obtained for a l l four y-detectors during a t y p i c a l run with a carbon target. The TOF of the beam p a r t i c l e s has been shown previously i n section 4.1. In each spectrum, the time o r i g i n 29 T O F S P E C T R U M OF T I N R UJ 3ZD • 160 -12.0 600 —i BOO -A az UJ 400 CD 200 -12.0 (a) CARBON TARGET (RUN 114) FIT -S ' 0 ' -3 . 0 Y-RAYS 6.0 TOF (NS) (b) T O F S P E C T R U M O F M I N A CARBON TARGET (RUN 114) NEUTRONS!? L - 6 . 0 TOF (NS) F i g . 4.2.1 Time-of-flight spectra measured with the Nal c r y s t a l s during a t y p i c a l run with a carbon target, (a) TINA, (b), MINA. The s o l i d l i n e s i n d i c a t e the contributions from neutrons and Y - r a y s . 30 T O F S P E C T R U M O F C I (a) CARBON TARGET I I I i I T " i - 6 . 0 - 3 .0 0.0 3.0 6.0 9.0 12.0 1S.0 T O F C N S ) F i g . 4.2.2 Time-of-flight spectra measured with the Cerenkov counters during a t y p i c a l run with a carbon target, (a) CI, (b) C2. The s o l i d l i n e s i n d i c a t e the y-ray contributions. 31 was defined to be the time of a r r i v a l of the pions i n the  ±4"C target. F i g . 4.2.1(a), (b) show the f a i r l y good time separation between gammas and neutrons i n the Nal c r y s t a l s . TINA had a time r e s o l u t i o n s l i g h t l y better than MINA however, and since i t was located at a larger distance from the target than MINA, a better time separation between y-rays and neutrons was achieved i n t h i s c r y s t a l . The s o l i d l i n e s drawn i n each figu r e indicate the contributions from the y-rays (gaussian curve) and the neutrons. The f u l l widths at half maximum (FWHM) of the y-peaks were found to be 2.5 and 3.0 ns i n TINA and MINA re s p e c t i v e l y . The lead glass Cerenkov counters, as shown i n the TOF spectra of f i g . 4.2.2, are i n s e n s i t i v e to neutrons, but because they were placed downstream of the incident beam, they also detected some bremsstrahlung from electrons. Note, i n p a r t i c u l a r , that the time r e s o l u t i o n i n C2 i s much better than i n CI (FWHM = 3.1 ns i n CI and 1.6 ns i n C2). This i s due to the fac t that a faster, photomultiplier was used for C2. The energy c a l i b r a t i o n of the detectors was obtained from the measurement of the energy spectrum of the y-rays produced i n the ^H(TT , T r?)n and ^H(TT ,y)n reactions at re s t using the LiH target. In the CEX re a c t i o n , the neutral pion i s emitted i n an S-wave and has a low k i n e t i c energy of 2.9 MeV. Since the TT° ->- 2y decay i s i s o t r o p i c i n the r e s t frame, t h i s leads to a uniform energy d i s t r i b u t i o n of the y-rays between 55 and 83 MeV. The l a t t e r r e a ction, the r a d i a t i v e pion capture i n hydrogen, produces a mono-energetic y-ray of 129 MeV. However, i n the LiH compound, only about 3.9% of a l l the stopped pions are emitted from the ^H(TT ,y)n reaction (Chabre et a l . 1963). Fortunately, the charge-exchange reaction i n ^ L i i s —6 much l e s s probable (B.Ey,^ - 10 ) than i n hydrogen, and so, contributes 32 very l i t t l e to the t o t a l y-ray rate. These features are shown i n the y-ray energy spectra obtained i n the Nal c r y s t a l s f o r which a good energy r e s o l -ution was achieved ( f i g . 4.2.3). F i g . 4.2 . 4 shows the corresponding spectra for the lead glass Cerenkov counters. The geometry used during the experiment also enabled us to measure in coincidence the TT° -> 2y decay following the CEX reaction i n hydrogen. Be-cause of the small k i n e t i c energy of the TT°, the y-rays are emitted nearly c o l l i n e a r l y i n the laboratory frame (0yy 21156°). For the two d i f f e r e n t pairs of detectors, TINA-C2 (0 = 170°) and MINA-C1 (0 = 160o), we have com-pared the y-ray coincidence energy spectra with the calculated energy d i s -t r i b u t i o n folded with the response of the detectors (see f i g . 4.2.5 and 4.2.6). I t must be pointed out here that i n coincidence measurements, the energy d i s t r i b u t i o n of the y-rays from the TT° decay i s no longer uniform but rather depends strongly on the geometry used and on the s o l i d angles of the detectors. The y-ray energy d i s t r i b u t i o n was calculated for the two d i f f e r e n t configurations (0 = 160°) and (0 = 170°) and i s shown i n f i g . 4.2.7. The energy response of TINA was taken from a previous work done by Spuller et a l . (1977) who measured the Panofsky r a t i o i n hydrogen. In that experiment, the l i n e shape of the 129 MeV r a d i a t i v e photon was found to have a FWHM of 4.7% and a t a i l extending to low energies (see f i g . 4.2.8). For MINA and C2, a s i m i l a r response function was assumed; for CI, however, a gaussian d i s t r i -bution was used. We have f i t t e d the calculated y-ray energy d i s t r i b u t i o n (folded with the energy response of the detector) to our data. The r e s o l u t i o n was l e f t as a free parameter. The f i t obtained was reasonably good and the energy resolutions for the d i f f e r e n t counters were 10% i n TINA, 8% i n MINA, about 60% i n CI, and about 50% i n C2. 33 ENERGY (MEV) F i g . 4.2.3 Photon energy spectra measured with the Nal c r y s t a l s using a LiH target, (a) TINA, (b) MINA.. 34 G f l M M f l - R R Y S P E C T R U M O F C I (a) E N E R G Y t h E V ) C H M M A - R A Y S P E C T R U M O F C2 (b) E N E R G Y ( M E V ) F i g . 4.2.4 Photon energy spectra measured with the Cerenkov counters using a LiH target. (a) C l , (b) C2. 35 G A M M A - R A Y S P E C T R U M O F T I N A A (a) O . O 2 0 . 0 <3D .0 6 0 . 0 8 0 . 0 1 0 0 . 0 1 2 0 . 0 1 * 3 - 0 ENERGY (MEV) 0 . 0 2 0 . 0 4 0 . 0 6 0 . 0 8 0 . 0 1 0 0 . 0 1 2 0 . 0 1 <40 . 0 ENERGY (MEV) i g . 4.2.5 Energy spectra measuredrwith the Nal c r y s t a l s ifor TT -»- 2y coincidence events (LiH tar g e t ) . (a) TINA, (b) MINA. The s o l i d l i n e s are the calculated energy d i s t r i b u t i o n s of f i g . 4.2.7 folded with the r e s o l u t i o n of the detectors. 36 G A M M R - R f l Y S P E C T R U M O F C I -0 . 0 2 0 . 0 «*0 . 0 6 0 . 0 B O . O 1 0 0 . 0 1 2 0 . 0 1<U3 .0 ENERGY (MEV) . 4.2.6 Energy spectra measured with the Cerenkov counters f o r TT * 2y coincidence events (LiH tar g e t ) , (a) CI, (b) C2. The s o l i d l i n e s are the calculated energy d i s t r i b u t i o n s of f i g . 4.2.7 folded with the r e s o l u t i o n of the detectors 37 C O I N C I D E N C E G A M M R - R A T S P E C T R U M 54.0 58.0 62.0 6S.O 70.0 74.0 78.0 82.0 ENERGY (MEV) F i g . 4.2.7 Coincidental photon energy d i s t r i b u t i o n s f o r the TT -> 2y decay calculated for the two experimental configurations G = 160° and 0 = 170° . R E S P O N S E F U N C T I O N OF T I N A ENERGY (MEV) F i g . 4.2.8 TINA l i n e shape for 129 MeV r a d i a t i v e photons as measured by J.Spuller et a l . (1977). 38 The energy c a l i b r a t i o n s were applied to a l l four y~detectors for each run using the LiH runs done during the experiment. The Nal c r y s t a l s were c a l i b r a t e d using the following reference points i n the si n g l e y-ray energy spectra of LiH: the zero-energy point, the 55 and 83 MeV edges of the TT° box, and the sharp cut-off near 130 MeV. For the Cerenkov counters, only the zero-energy point and the broad peak near 69 MeV for TT° ->- 2y coincidence events were used. We have estimated that the uncertainty i n these c a l i b r a t i o n s was l e s s than 3% i n the case of the Nal c r y s t a l s and about 10% for the Cerenkov counters. F i n a l l y , the energy deposited by the incoming p a r t i c l e s i n the telescope counter was determined by range c a l c u l a t i o n from measurements done with incident pion beams of 20 MeV and 50 MeV. The energy-loss spectrum i n S„ for any type of coincidence events has already been shown i n f i g . 4.1.2; 4.3 The "^C(TT ,y) Reaction As a check of the s t a b i l i t y of the detectors and the e l e c t r o n i c s , we have measured the branching r a t i o of the well known single r a d i a t i v e pion capture i n carbon. This measurement also enabled us to determine the e f f e c -t i v e s o l i d angle of the lead glass Cerenkov counters. As no lead collimator was put i n front of these detectors i n t h i s experiment, an appreciable f r a c -t i o n of the y-rays h i t only the edges of the lead glass material and did not deposit a s u f f i c i e n t amount of energy to be detected. This resulted i n a 39 diminution of the s o l i d angle of the Cerenvov counters with respect to the geometrical one. With the Nal c r y s t a l s , t h i s problem was not encountered however. Even with a large c o l l i m a t i o n , the Nal detectors s t i l l have a high y-ray detection e f f i c i e n c y (> 99%). We show i n f i g . 4.3.1 and f i g . 4.3.2, the y-ray energy spectra 12 measured for the C(TT ,y) react i o n . These energy d i s t r i b u t i o n s were obtained by s e l e c t i n g from each TOF spectrum of f i g . 4.2.1 and f i g . 4.2.2, events l y i n g i n the y-ray peak. The Nal detectors were found to have an energy spectrum very s i m i l a r to the y-ray energy d i s t r i b u t i o n measured by B i s t i r l i c h et a l . i n t h e i r high-resolution experiment. Of course, the energy r e s o l u t i o n of the Nal c r y s t a l s (8-10%) does not permit us to resolve the excited states of the f i n a l nucleus. With the Cerenkov counters, the energy r e s o l u t i o n achieved i s very poor; nevertheless, the y-ray energy spectra s t i l l e x h i b i t a sharp r i s e near 120 MeV. The energy thresholds of the four y-detectors were t y p i c a l l y 17 ± 2 MeV i n TINA, 16 ± 2 MeV i n MINA, 16 ± 3 MeV i n CI, and 20 ± 3 MeV i n C2. 12 The branching r a t i o f o r the C(TT ,y) reaction i s defined as B.R NY W N ( 1 _ f P P ) . ( ) TT-StOpS 4TT where N^ i s the number of y-rays observed, N i s the number of pions ' J TT-stops stopped i n the carbon target, f ^ i s the f r a c t i o n of y-rays l o s t through external p a i r production in s i d e the target, and Afi/4iT i s the f r a c t i o n a l s o l i d angle of the detector (normalized to unity over the sphere). The evaluation of f ^ w i l l be explained i n more d e t a i l i n section 5.4.2. 40 G A M M A - R A Y S P E C T R U M O F T I N A E N E R G Y I M E V ) G A M M A - R A Y S P E C T R U M O F M I N A 1 5 0 . 0 E N E R G Y ( M E V ) , F i g . 4.3.1 Photon energy spectra obtained with the Nal c r y s t a l s for the 1 2C(TT-,Y) reaction, (a) TINA, (b) MINA. 41 G R M M R - R A Y S P E C T R U M O F C I (a) 12 CO ,Y) Jl 1 ' 1 I .11(1. 0.0 30 .0 60 .0 90 . 0 E N E R G Y ( M E V ) 1 1 I 1 1 1 1 I 1 ' ' J20.0 150.0 210 .0 F i g . 4.3.2 Photon energy spectra obtained with the Cerenkov counters for the 1 2 C ( T r ~ , y ) reaction, (a) CI, (b) C2. 42 The t o t a l number of y-rays detected i n each counter was found by c a l c u l a t i n g the area under the y-ray peak of each TOF spectrum ( f i g . 4.2.1 and f i g . 4.2.2). Table III gives t h i s number for each counter, together with the corresponding geometrical acceptance. Table III The C(TT ,y) reaction Counter N Y AP74TT (xlO 3) ( x l 0 ~ 3 ) TINA 5.18 9.02 MINA 4.36 7.45 CI 12.60 1.91 C2 18.91 2.82 The number of y-rays detected i n TINA and i n MINA i s smaller than i n the Cerenkov counters because of the use of a random pulser gate to . '.•.".< reduce the rate of the Nal singles CAMAC t r i g g e r s . The counting rate of the Nal singles events was reduced i n t h i s way by about a factor 160 ^ p u l s e r _g ^3 x 3 ^ ^ order to obtain the ly-branching r a t i o measured with the Nal c r y s t a l s , the value N must.be replaced by N /e In the 9 above expression. With a t o t a l number of 4.8 x 10 pions stopped i n that 43 -particular run, and with t y p i c a l l y equal to 0.027 independantly of the detector, we f i n d a branching r a t i o of (2.0 ± 0.2)% for both TINA and MINA. This r e s u l t i s i n very good agreement with the value of (1.92 ± 0.20)% obtained by B i s t i r l i c h et a l . (1972). We can then c a l c u l a t e the reduction factor e (i=l,2) f o r the s o l i d angle of the Cerenkov counters by taking the r a t i o of the number of y-rays observed i n CI and C2 to the number of y-rays observed i n the Nal c r y s t a l s , normalized with t h e i r s o l i d angles 1 C i pulser , TINA , MINA N . , 0 =ci= 2 - 3 £ - e • ( - r - + — > l - 1 > 2 TINA MINA Using the values of Table III for N Y and A f t , and correcting (~ +4% ) for the events l o s t because of the high energy threshold (20 MeV) i n C2, one fin d s : e c l = 0.70 ±0.04 and zQ1 = 0.73 ±0.04 Thus both Cerenkov counters had t h e i r counting rate reduced by about 30% due to edge e f f e c t s . This diminution i s not n e g l i g i b l e , and therefore, w i l l have to be taken into account i n the evaluation of the branching r a t i o f o r the (TT ,2y) process. 44 Chapter 5 Data Analysis In t h i s chapter, we s h a l l discuss how the analysis of the (neutral) 4 coincidence events was c a r r i e d out. We remind the reader that our aim i s to 12 study the 2y angular c o r r e l a t i o n i n the reaction TT + C X + y + Y for stopped pions as well as the energy-sharing between the two emitted photons. This can be achieved only i f a l l the competing sources of background are c l e a r l y i d e n t i f i e d and properly subtracted. Since TINA and MINA possess the larges t detection e f f i c i e n c i e s and the best energy resolutions, they are most l i k e l y to provide a better understanding of the d i f f e r e n t background contributions. We s h a l l therefore s t a r t by presenting i n d e t a i l the analysis of the coincidence events obtained with the Nal c r y s t a l s (0 = 120°) and then proceed more r a p i d l y to the other configurations. But before doing t h i s , some remarks are i n order. We have also looked at charged coincidence events, i . e . for the reaction ^C(n~, e + e - ) . The r e s u l t s obtained w i l l be presented elsewhere. 45 5.1 Remarks and Notation We have analysed about 90%"' of a l l data recorded using the carbon target. These were gathered i n 30 d i f f e r e n t runs and for each run the TOF and energy spectra were c a l i b r a t e d i n the same way as discussed i n section 4.2. Neutral-neutral coincidence events were then selected by using the event i d e n t i f i c a t i o n word that was generated by the coincidence buffer unit (see section 4.1). We have retained for data analysis the s i x types of coincidences corresponding to the following configurations: 0 = 50° : MINA-C2 0 = 80° : TINA-C1 0 = 110° : C1-C2 0 = 120° : TINA-MINA 0 = 160° : MINA-C1 0 = 170° : TINA-C2 Since from now on we w i l l mainly deal with TOF and energy spectra, we s h a l l adopt a new convention i n order to s i m p l i f y the notations. The TOF spectra w i l l now be denoted by T^ where i = B, T, M, 1, 2 stands f o r beam p a r t i c l e s , TINA, MINA, CI and C2 r e s p e c t i v e l y , the energy spectra by the inter-detector angles by 0 ^ ( i , j = T, M, 1, 2), and the energy loss i n counter S_ by AE. 10% of the data was rejected because of i n s t a b i l i t y problems i n the e l e c t r o n i c s or the detectors. 46 5.2 TINA-MINA Coincidences (0 = 120°) 5.2.1 Sources of Background We present i n f i g . 5.2.1, 5.2.2 and 5.2.3(a), (b) r e s p e c t i v e l y , the T , AE, T and T spectra for coincidence events obtained with the Nal B T M c r y s t a l s . While the TOF spectrum of the beam p a r t i c l e s (T^) shows almost no presence of muons or electrons, the AE d i s t r i b u t i o n however, exhibits a large contribution to coincidences caused by pile-ups (-15%). Those events are mainly accidental coincidences which can be eliminated by making a cut near AE = 2 MeV. The TINA and MINA TOF spectra measured i n coincidence are i n a sense s i m i l a r to the singles spectra of f i g . 4.2.1. Both TOF spectra show c l e a r l y a y -peak which stands out from the neutron t a i l . As expected, however, the contribution from background coincidences i s r e l a t i v e l y impor-tant compared to the number of Y _ r a y s detected. In TINA p a r t i c u l a r l y , there seems to be an important amount of background events present i n the early time region of the spectrum, very close to the Y-ray peak (T^ ~ 0). These background events have a very broad time structure but cannot be regarded as pure randoms. They are rather events correlated with the incident pion beam. A s i m i l a r background i s also v i s i b l e near T„ ~ 0 i n the TOF spectra of MINA, but i t i s much less prominent than i n TINA. To understand the nature of t h i s background and to see how the coincidence events are d i s -tributed i n time i n both Nal c r y s t a l s , we show i n f i g . 5.2.4 a two-dimen-sio n a l scatter p l o t of T -vs-T . A large scale was chosen i n order to obtain 47 T O F S P E C T R U M O F B E A M P A R T I C L E S 600 2 UJ 6DD GO T. 200 —i TINA - MINA 0 ™ = 120° TM PIONS T ' ' ' I ' 1 1 - L a .o 12.0 -B.O 0.0 6.0 12.0 1B.0 T (NS) B F i g . 5.2.1 TOF spectrum of beam p a r t i c l e s for TINA-MINA coincidence events ( 0 ^ = 120°). E N E R G Y - L O S S S P E C T R U M O F S3 TINA - MINA e ™ = 120" TM F i g . 5.2.2 Energy^-loss spectrum of :S~ .for TINA-MINA coincidence events (0 = 120°). 48 F i g . 5.2.3 TOF spectra of the Nal c r y s t a l s for TINA-MINA coincidence events, (a) TINA, (b) MINA. 10 C 5H ~ OH - 5H -10 JL l ? i l I 12 111 1 I 22 1122121 1231 1 2 2 1 1 4 2 2 3 1125222 21232 1 2 2 3 ) U 2 2 3 U 2 « B « 6 78 7 3 4 * 5 5 7 4616UU6( Ju2 ib7 57F 71C A |t 1? a i 1 2 1 1 2 1 1 1 1 1 l l l l l i 31 | 3 l 2 l 4 2 5 4 2 4 4 3 4 6 H 4 7 S 6 7 i 6 3 5 7 2 5 i b 2 S 4 3 2 S 4 B 4 7 » ' » I * i n , 1 1 12 1 11221 1 2 1 2 1 2 2 2 I 2121 222 2144 \ , 3 34645432 364214 3 1 5 * 4 5 4 5 6 4 4 I I I i 1 1 2 l l l i 1 l i e 11I<!<M I e i f i ccc t m » v J n » " ™ « « * v • * " 1 , 1 I I 11 1 211 I I 21 211 21 2 1 3 1 2 1 111 1 1 1 3 0 . 6 . . 2 7 4 5 3 2 5 3 4 2 2 3 2 * 2 1 ft_ M 4 3 9 * , , i l l R _ n 1 1 1 11 2 2 1 2 21 1 112121 2 2 l l 1 I I H 1 T M 5551 6 2 3 4 3 3 3 l b S 3 ' M « 3 A t t , it | | i 1 T M i l 2 1 1 2 1 1 11121 1 I U I 2 1 M i l l 2 I M 2 I S 5 2 2 2 2 4 J 4 2 2 3 4 2 1 2 2 3 1 6 3 3 2 4 2 3 4 2 4 * 7 I I 11 1 -10 I 1 I 1 M l 1 V M 1 1 I I I u 1 12 I 11 1211 I 1 21 112 121111 1 | i l l l 2 2 1 2 t i 4 4 4 S 2 l 3 2 4 4 3 J 5 2 3 2 , 2 2 | 3 « 2 3 4 6 6 3 2 r 1 , 1 I 1 1 M I l l | 2 1 M 1 1 4 2 2 3 2 3 l l 2 4 2 4 2 3 3 l 2 I 2 3 B 2 3 4 2 ? 2 6 4 4 5 3 5 1 1 1 1 M 1 1121 u 2 4 2 2 2 3 1 1 121 1 1 1 2 1 4 1 3 3 4 1 1 2 2 2 1 2 65 ' 1 -4- I 2 _ | i _ H_J. 1 J i i ' « ^ l l i l J 2 2 l M 2 1 4 4 3 2 3 4 3 5 , , . ' .  1 1 A^il l lTTT I1TT322TJ21 P152322l352ll 1 . ' , , , 1. . 1 U 2 1 Z H 2 5 1 J H 1 3 2 1 2 1 2 1 2 1 1 2 1 3 1 3 3 2 3 3 3 1 , , " 1 ? ' 1 I ,1 121 1 2 2 2 2 3 3 3 3 * 3 2 2 3 2 1 1 2 2 , 2 1 1 3 3 2 2 2 2 2 2 6 2 1 , » « » « * \ H i l l y y 5 3 2 1 2 2 3 1 2 S l S - 5 5 b 1 1 I M 111 1 112 2 2 M 2 l J T « M 1 3 t « 2 3 1 1 2 3 2 ? 2 2 n _ J f M 6 < ( 1 | I I I I I 11 2 I | M 1 2 1 1 2 ; l M l l l 2 2 M 1 2 112,113 1 M „ u > 1 1 11 11 2 111 21 1 1 1 2 2 2 3 2 3 3 4 2 1 3 2 3 1 2 1 1 2 1 2 1 3 1 1 1 2 2 1 2 3 2 4 3 3 3 I I 1 11 I 1 11112 t 1 2 2 1 2 2 1 2 1 3 3 2 1 1 12 n p i I 1 1 J 1 2 3 1 2 4 4 • 1 1 1 1 I 3 I I 2 2 H U 1 11 1 i l J 3 2 5 4 1 1 2 ' ^ L J l * M l 2 1 2 1 1 2 2 2 22 121 2 2 l i t ii 1 3 1 3 1 2 1 1 1 1 1 1 1 2 2 1 2 2 1 11 l 1 1 ' l i t U M 2 2 1 2 I 1 1 21 1 2 1 1 3 1 2 p- *— -T2 TINA - MINA V 1 2 0 ° 1: 2 event s -5 0 10 Tj. (ns) F i g . 5.2.4 Two-dimensional time d i s t r i b u t i o n of the TINA-MINA coincidence events. 50 a cleaner representation of the events d i s t r i b u t i o n . The two i n t e r s e c t i n g bands drawn on the scatter plot i n d i c a t e where the y - r a y s H e i n TINA and i n MINA. For each d i f f e r e n t region of the p l o t , we have indicated the corresponding most probable types of events: neutrons (n) or y-rays (Y) from 12 the C target, and randoms (R). The en c i r c l e d region represents the back-ground events that occur near T = 0 i n both Nal c r y s t a l s . Since the time o r i g i n corresponds to the a r r i v a l of a pion i n the target, the en c i r c l e d events come obviously too early i n time to be explained as o r i g i n a t i n g from the carbon target. They are rather associated with pions that stopped i n the telescope counters, most l i k e l y i n S^. If t h i s i s the case, then these events should also show up i n runs for which the carbon target was removed. We have therefore investigated the ambient background sources by looking at si n g l e and coincidence events i n the Nal c r y s t a l s f o r "empty" target runs. I t was observed that TINA, unlike MINA, was very s e n s i t i v e to neutrons produced from pions that interacted with the telescope counters S^, or S^. In addition, TINA could see some Y -rays coming from S^, while f o r MINA t h i s was impossible with the geometry used (see experimental set-up i n f i g . 4.1.1). Since the a r r i v a l of the pions was determined by a S^.S2'S3 coincidence, the events o r i g i n a t i n g from S^, or even from the beam snout, were most l i k e l y associated with pion pile-ups. Pile-ups occurring i n S^ or S^ cannot be rejected, and one can therefore expect to observe, when the carbon target i s i n place, an appreciable amount of background events due to accidental coincidences (e.g. a coincidence of a y r a y or neutron 12 produced i n the C target with a neutron produced i n S^ or S^)• This feature appears c l e a r l y i n the scatter p l o t of f i g . 5.2.4. Note for instance, the high concentration of events i n the regions R^n^ or R^Y^ for 51 T 1 -2 ns. In MINA however, the time d i s t r i b u t i o n of the events obtained for empty target runs was found to be f l a t , that i s , consistent with a random background (e.g. slow neutrons coming from the ir-production target T2 and the cyc l o t r o n ) . Thus the i r o n s h i e l d i n g located between MINA and the telescope counters proved to be very e f f i c i e n t i n reducing the rate of back-ground neutrons i n MINA. The region R^Y^ of the scatter p l o t has, indeed, much less background then, f o r example, the region Y^ R^ ,-For coincidence events, i t was found that S^ was the most important source of background when the carbon target was removed from the beam. This i s understandable since both TINA and MINA were not shielded against neutrons that could be emitted a f t e r a pion i n t e r a c t i o n i n S^. The two-dimensional plo t of T^-vs-T^ obtained for coincidence events (no carbon target) i s shown i n f i g . 5.2.5 and exhibits two d i s t i n c t concentrations of events. The events l y i n g i n the upper region of the scatter plot (T^,T^ i l 4 ns) have been 12 associated with neutrons detected i n coincidence from the C ( T T - , 2n) r e -action i n S^. Their energy-time c o r r e l a t i o n was indeed found to support t h i s statement. For example, two 50 MeV neutrons that would be emitted i n coincidence from S^, would reach TINA at T^ - 5 ns and MINA at = 6 ns. Furthermore, the energy deposited i n the Nal c r y s t a l s by these p a r t i c l e s was observed to be p r e f e r e n t i a l l y small ( E ^ + E ^ 1. 90 MeV), as i t should be f o r neutrons. The e a r l y events grouped near T^ - T^ = 0 can only be explained as being associated with Y - r a y s that o r i g i n a t e from the decay of a TT° following a CEX reaction (at re s t or i n - f l i g h t ) on the hydrogen of counter Sg. Since MINA cannot see S^, these Y _ r a y s are not detected d i r e c t l y by the Nal c r y s t a l s but rather v i a the following schedules: 10 0 J -5H -10 1 " EMPTY TARGET" 1 .* , 1 , , i i t i i i i i i i i i i n e u t r o n s u i i i f r o m . S „ 1 T T ° - 21 ( S „ ) ' , 1 1 1 * 11 1 11 1 1 1 1 1 1 1 1 i 1~3 i i i i i i TINA - MINA STM 1 2 0 ° 1 1 1 -10 - 5 0 5 10 Tj. (ns) F i g . 5.2.5 T M~vs-T T scatter p l o t for empty target runs. 53 (i) one y-ray i s detected by TINA; the other one converts i n the i r o n s h i e l d on MINA, produces an electron shower which does not tr i g g e r the s c i n t i l l a t i o n counters S, and S c but b o reaches the Nal c r y s t a l , ( i i ) both y - r a y s convert i n the i r o n shields of TINA and MINA and t h e i r charged p a r t i c l e products h i t the Nal c r y s t a l s without t r i g g e r i n g the s c i n t i l l a t i o n counters S,., S,.», S 6, S y or S g. Both processes ( i ) and ( i i ) simulate neutral-neutral coincidences with the appropriate TOF (T^ ^  0, T^ = 0). However, those Y - R A V S that are converted into a e + e _ pair i n the i r o n shields can only deposit a small amount of energy i n the Nal c r y s t a l s . We have checked that In MINA, the energy was small (E^ ^ _ 60 MeV) while i n TINA, the energy could vary from 15 MeV to 90 MeV. We have also looked at charged p a r t i c l e s and found that with or without the carbon target i n place, most of the events occurring at T^ , - = 0 were associated with a charged p a r t i c l e i n MINA (tr i g g e r from only) and a neutral or y - r a y i n TINA. This scheme i s i n fact the same as schedule ( i ) above. Furthermore, the energy dependance of the e-y pairs was found to be very s i m i l a r to the one observed for the neutral coincidence events near T m = T w = 0. T M Fortunately, the background that occurs near the time o r i g i n of the T^j-vs-T^, scatter plot i s mostly eliminated when one considers only the events that l i e i n the time regions defined by the two bands (see f i g . 5.2.5). There s t i l l remains, however, a large amount of events l y i n g i n the Y -ray band of MINA (T - 3.2 ns) and which have -1 ns ^ _ T 2 ns. 54 These events are not r e a l coincidences o r i g i n a t i n g from or from the 12 C target, but rather, as pointed out e a r l i e r , random coincidences due to 12 pion pile-ups i n or (e.g. a r a d i a t i v e y-ray from the C(TT~, y) r e -action i n the target i s detected by MINA while a neutron produced i n or i s detected by TINA). Pile-ups i n would be rejected by a proper cut i n the AE spectrum. The region of i n t e r e s t , namely the YY window defined by the in t e r s e c t i o n of the 2 bands on the scatte r p l o t , contains d i f f e r e n t types of unwanted coincidences. The most probable background sources are r e a l 12 y-n coincidences from the C taget and R-y accidental coincidences. We include i n the l a t t e r , neutrons produced by a ir-stop i n the telescope counters. The energy d i s t r i b u t i o n of the events situated i n s i d e the yy window ( l . O n s i T 1 5 . 8 ns; 2.2 ns £ T^ , 1 7.2 ns) i s shown i n the E M - v s - E T scatter p l o t of f i g . 5.2.6. The s o l i d l i n e determines a sum energy (E^ + E^) of 126 MeV corresponding to the t o t a l energy that two photons would have i f 12 _ 12 they were emitted from the C ( i r , 2y) B reaction. The dashed l i n e g. s. at E T + E M = 145 MeV allows a 15% spread to account for the energy r e s o l u -t i o n of the detectors. Of course no true 2y events should l i e beyond the 12 145 MeV sum energy dashed l i n e . As the f i n a l state of the C(TT~, 2y) r e -12 action can be any state of B or the product of any break-up channel, one expects that the searched 2y events w i l l be confined anywhere i n the region defined by the 145 MeV sum energy l i n e and the low-energy threshold of each detector. We can d i s t i n g u i s h four d i f f e r e n t energy regions i n the E^-vs-E^ scatter p l o t . These correspond to high- (HE) and low-energy (LE) events i n TINA and MINA (LE: = 15-75 MeV. HE: 1 75 MeV). Among the background events, 150 v v 121 I V 11221 V 1 " 2 1 1 .. 11 1 0 0 -Pile - up" i events > i t > i > a> UJ TINA - MINA 50H i , i > 21 1 1 22 21 V 2 12 J I \ 1 1 1I2I2VM 1 11 1 2 1 J 2 1 N 2 12 V 22 3lU>v II I V 1 . 1 222 1 I 11 1211 Xl» 1 1 > t 1 3 12 32 » 1 2 12111 1 1 \ It ^ " A, 11 2 1 J 2 H 11 111 K V l l V 7 131 112 I II 11 1 \ r " A 2 \ v . 22 11 12 I 13 X S V 1 2 2 1 3 a T f * V 1 1 2 11 11 2 \ A , < l \ I I II I 111) I \ Oj, f 2211 1212 1 1 1 I I I K . 'Vai ^ 12111 1 2 1 1 1 1 2 1 1 X *" v 1 1 It 31 II 1 1 1 1 \ l ' x 1 111131 131 1 II 11 1 1 1 1 1 1 1 1 11111 1 It 1 2 2 \ 1 13 t 12 1 I 12 1 1 1 2 I 11112 1 t i l l 1 2 1 1 1 3 12 I 12 12 2 II 2 1 1 1 1 1 1 1 3 11 12 113 11121 1 2 1 112 21 32212 II 2 I 2 1 3 1 11 12 2 1 1 1 2 11 1 I II II 11111 1 I I '11112221 23211 2 1 1 It ' 2 213 1 t 211 1 121111 1 1 ' 0321 213 112 31 11 I t 1 [l l L 2 j £ l 1 1 2 1 1 I II 1 V , 2 0 ° >11 low-energy thresholds i i i i i i t i i i t 12 2 I I 211 t l 1 l l l l l 21U 3 3 1 1 II I I 2 1 1 l K i I 1 1 1 N . 1 1 1 V 2 1 2 2 l \ 1 11 I I V I I I I 2 i m i x » i i i i i i i . v v l l 2 \ -T" 30 —r-6 0 90 120 150 E T (MeV) F i g . 5.2.6 Two-dimensional energy d i s t r i b u t i o n of events l y i n g i n the yy window of f i g . 5.2.4. 56 n-n or R-R coincidences are most l i k e l y to appear i n the LE^LE^ region, whereas n-y or R-y coincidences are mainly d i s t r i b u t e d i n the LE^,-HE^ or LE M~HE T regions ( r a d i a t i v e y-rays p r e f e r e n t i a l l y have energies above 90 MeV). The events grouped i n the HE^-KE^ region (dashed tria n g l e ) are associated with accidental coincidences of two si n g l e r a d i a t i v e y-rays 12 produced i n the C target from multiple u-stops. Another contribution to t h i s region are cosmic rays, but the p r o b a b i l i t y for such events i s very small. Furthermore, most of the cosmic rays were vetoed (~60%) by covering the Nal c r y s t a l s with large p l a s t i c s c i n t i l l a t i o n counters. The high energy events can be mostly eliminated when the energy deposited i n by the incident pions i s required to be l e s s than 2.1 MeV ( i . e . f o r single pions; see f i g . 5.2.2). Unfortunately, not a l l of these events are rejected by requiring that cut. Since S^ was chosen smaller than S^, S^ and the carbon target, the p r o b a b i l i t y that one of the pile-up pions missed but stopped i n the target, whereas the other one(s) triggered S^, and and also stopped i n the target, i s not n e g l i g i b l e . By looking at the AE spectrum for events l y i n g i n the yy window and with energies between 80 and 120 MeV i n both Nal c r y s t a l s , i t was found that the f r a c t i o n of p i l e -ups that were recorded as s i n g l e s only, was about ^ (see f i g . 5.2.7). This means that inside the energy allowed for the (TT -, 2y) process, there ex i s t s some 2y accidental coincidences due to undetected pile-ups that cannot be distinguished from the true 2y events. Those events must be taken into account i n the background subtraction and we w i l l show l a t e r how t h i s can be done. To better understand the d i f f e r e n t sources of background that were present i n t h i s experiment, we have investigated the energy dependance of 57 events appearing i n the d i f f e r e n t time regions of the scatter p l o t of f i g . 5.2.4. This study i s summarized by Table IV i n which we have l i s t e d the most probable types of coincidences ( r e a l or accidental) together • :'with t h e i r assigned time and energy regions. E N E R G Y - L O S S S P E C T R U M O F S3 9 . 6 H > 7 .2 H o 2 4 H (30 EVENTS) (94 EVENTS) TINA - MINA STM - 1 2 0 HIGH ENERGY EVENTS • . 8 1.6 1 2.<4 3.2 <*.8 S . 6 A E (MEV) F i g . 5.2.7 Energy-loss spectrum of S„ for high energy coincidence events l y i n g i n the TINA-HINA YY window. The events with AE < 2.1 MeV are accid e n t a l coincidences due to pion pile-ups not detected by S^. 58 Table IV The most probable types of coincidences Type of coincidence Time region Energy region r cn OJ o C QJ 13 •H O C •H O o cu Pi OJ 60 a •H r r (TT ,2y) (Tr",2n) (TT ,ny) (TT , T T ° ) 2y i n - f l i g h t 12 12 C(ir~,2n) C(Tr",nY) YT YM N T N M V M ° R V M YT YM YT YM ° R V M YT YM ° r YT nM enc i r c l e d region E T+E M < 145 MeV L V L E M LE T-HE M or HE^-LE^ E T+E M > 110 MeV L E T " L E M LE T-HE M or HE^-LE^ L E T - L E M or HE^-LE^ v. r CO QJ O e cu T3 •H O c •H O O 0 QJ •H O O 4 (TT ,Y)R(TT ,y) (TT , n ) R ( T T ,y) (TT , n ) R ( T T ,n) (TT ,Y)R(TT ,n) 13 13 CO YT YM YT nM ° r V M V M YM HE T-HE M (mostly) LE T-HE > IorHE T-LE M L E T " L E M L E T " H E M (TT~ ,n)R(slow neutron) V or _ n M L E T - L E M (TT" ,Y)R(slow neutron) Y T- or ~ YM LE T-HE M or HE^-LE^ (TT" ,n)R(cosmic) n T " or " ° M L E T - or - L E M (TT" ,Y)R(cosmic) Y T- or _ Y M HE T- or - H E M (TT" ,n)R(e beam) n T " or _ N M L E T " L E M (TT" ,Y)R(e beam) Y T- or _ Y M LE T-HE M or HE^-LE^ 12, R : i n random coincidence — : anywhere 59 5.2.2. Background Subtraction The next step i s , of course, to search for the good 2y events i n the yY window by eliminating a l l the unwanted background events. F i r s t , i n order to reduce these unwanted events, i t i s necessary to impose several constraints to our data, notably: 0<AE 1. 2.1 MeV to r e j e c t pile-ups, -6 £. T < 6 ns to eliminate coincidences generated by D spurious p a r t i c l e s i n the beam, and E T + £ 145 MeV. Second, we w i l l confine ourselves to the time regions defined by the y-ray bands i n the scatter p l o t of f i g . 5.2.4, i . e . : 1.0 ± T M 1 5.8 ns and -10 <_ T T £ 10 ns or 2.2 < T m < 7.2 ns and -10 < T„ < 10 ns. — T — — M — The region of i n t e r e s t , the YY window, i s again defined by the following boundaries: 2.2 £ T T <_ 7.2 ns 1.0 < T„ < 5.8 ns. 60 Now, since the time r e s o l u t i o n of the Nal c r y s t a l s i s about 2.5 to 3 ns, i t i s p l a u s i b l e to assume that the energy dependance of a given type of coincidence ( r e a l or accidental) i s not dramatically affected within a 3-4 ns wide time window. In other words, background events of a same type can be regarded as i d e n t i c a l whether they l i e in s i d e the YY window or j u s t outside, i n the adjacent time regions to the YY window (see figure below). I B2 Y-rays i n MINA B3 A B l B4 I Y-rays | | i n TINA ( F i g . 5.2.8 The background subtraction technique. If the adjacent regions B^, B^, B^ and B^ of f i g . 5.2.8 are not too large compared to region A (YY window), then one can hope that by making the operation A - £ B, , a l l the background events contained i n the k=l R 61 d i f f e r e n t regions B^ w i l l account for the background events of region A, provided the regions B^ are properly chosen. The remaining events would then consist of the true 2y events plus some accidental 2y events due to pile-ups that have not been rejected. Moreover, since TINA and MINA have the same energy r e s o l u t i o n , one should expect the y-ray energy spectra of the good events to be s i m i l a r for both detectors. To determine the regions B, , we project on the T and T axis ° k r J T M the events d i s t r i b u t e d within the two y-ray bands and we perform a f i t to the data i n order to estimate the amount of background that i s present ins i d e and outside the YY window (region A). The two spectra T^ and T^ corresponding to the two y-ray band event d i s t r i b u t i o n s are shown i n f i g . 5.2.9(a), (b). These spectra were obtained by imposing the conditions given e a r l i e r plus one more r e s t r i c t i v e condition, a lower l i m i t on the sum energy E^ + E^, i . e . : 60 MeV <- E T + E M This constraint enabled us to eliminate a large amount of low-energy neutrons without r e j e c t i n g s i g n i f i c a n t l y true 2y events. I t was indeed checked that for coincidence events with a sum energy lower than 60 MeV, no y-ray structure i n the TOF spectra of TINA or MINA was observed. I t w i l l appear clear l a t e r on that t h i s assumption i s correct. Despite the large s t a t i s t i c a l f l u c t u a t i o n s i n the spectra of f i g . 5.2.9, the f i t s obtained are r e l a t i v e l y good. On each spectrum, we have indicated by s o l i d l i n e s the contributions from y-rays, neutrons and randoms. Just l i k e for the singles spectra (see f i g . 4.2.1) we have assumed a gaussian d i s t r i b u t i o n for the Y -rays and a gaussian t a i l f o r the neutrons. 62 T O F S P E C T R U M O F T I N A - 9 . 0 - 6 . 0 - 3 . 0 0 .0 3.0 6.0 9.0 T INS) T O F S P E C T R U M O F M I N A (b) -9! o -e.o -3.0 o.o 3.6 6.6 9.0 T (NS) M F i g . 5.2.9 TOF d i s t r i b u t i o n s of the events l y i n g i n the y-vay bands of f i g . 5.2.4. (a) TINA, (b) MINA. The s o l i d l i n e s show the d i f f e r e n t contributions from neutrons, Y - r a y s a n d randoms. The regions determined from the f i t are shown by shaded areas. 63 The "random" background i n TINA was f i t t e d by using a constant background plus a gaussian d i s t r i b u t i o n centered near the time o r i g i n , while i n MINA, a slowly decreasing background was assumed. Note that region A was chosen as wide as possible i n order to include the maximum number of good 2y events. The d i f f e r e n t regions B^, k = 1, 2, 3, 4, which are represented on the TOF spectra by shaded areas, were determined from the f i t by equalizing the background located outside region A with the one located i n s i d e . As i t was discussed above, the background subtraction technique consists now of subtracting from region A, the events of a l l four adjacent regions B i . e . A - £ B . However, for t h i s method to be e n t i r e l y v a l i d , i t must be assumed k k that the unwanted coincidences are only d i s t r i b u t e d along the y-ray bands. Of course, t h i s i s not the case for R-R or n-n coincidences which are rather spread out i n a l l d i r e c t i o n s on the time scatter p l o t . Fortunately, and due to the 60 MeV lower sum energy cut, these types of coincidences are much less probable than the n-y or R-y coincidences, and therefore, the regions B^ as determined by the f i t should approximately account for the background of region A. The best way to ensure that the background subtraction i s pro-perly done i s to r e l y on the good energy r e s o l u t i o n of the Nal c r y s t a l s . We therefore allow the regions B^ to be s l i g h t l y modified from the ones determined by the f i t u n t i l the A - £ B subtraction gives the best agree-k k ment between the y-ray energy spectra of the two Nal c r y s t a l s . If the assumptions we have made are correct, then the new regions B^ should not be too d i f f e r e n t from the ones determined by the f i t , and i n both cases, one should f i n d about the same number of "good" 2y events. 64 The TINA and MINA -y-ray energy spectra obtained by t h i s method are shown i n f i g . 5.2.10. Spectra (a) and (b) give the energy d i s t r i b u t i o n s for both Nal c r y s t a l s before and a f t e r background subtraction. Note the large number of unwanted coincidences compared to the number of events l e f t a f t e r the subtraction ( r a t i o JL 2). Also, the shape of the raw energy spectra of the Nal c r y s t a l s ( a l l events of region A) d i f f e r appreciably from each other, i n d i c a t i n g that TINA and MINA were s e n s i t i v e to d i f f e r e n t types of background sources. This was expected since TINA detected much more low energy neutrons than MINA. In f i g . 5.2.10(c) and (d), the y-vay energy spectra obtained a f t e r background subtraction are shown with t h e i r s t a t i s t i c a l error bars and have q u a l i t a t i v e l y the same shape. These are peaked at about 90 MeV and exhibit a steep r i s e at low energies. The s i m i l a r i t y between the two Y-ray spectra thus confirms that a good background subtraction was achieved. The t o t a l number of good 2Y events was found to be 204 ± 33, the uncertainty given here being only the s t a t i s t i c a l error. We have shown i n f i g . 5.2.11 the T -vs-T^, scatter plot obtained a f t e r a l l energy cuts were applied, together with the d i f f e r e n t regions B^, B^ and A. To assess the v a l i d i t y of the method used, we have compared i n table V the actual regions B^ to the regions B^ as determined by the f i t as well as the corresponding number of events i n each region. Using the regions B^ i t i s found that the number of events a f t e r background subtraction i s 225 ±33, i n good agreement with the actual value of 204 ± 33 (within the s t a t i s t i c a l u n c e r t a i n t i e s ) . Moreover, the fa c t that the regions B^ as determined by the f i t are quite s i m i l a r to the regions B^ proves that the assumptions made e a r l i e r concerning the background subtraction are correct and that our method i s v a l i d . 65 160 + 1 2 0 + > Z CM 80 + > L U iO-t (a) TINA - MINA • • before backg. subtraction after backg. subtraction (c) 60 > z 40 CM UJ 2 0 U J T i I TINA - MINA V 1 2 0 ° T I I - L I I A 20 80 140 160 + 120 + 5 Z CM l/l I— 2 UJ > UJ 80 + 40 (b) TINA - MINA , 6 =120° TM • before backg. subtraction after backg. subtraction (d) 60 + 5 X 40 (VI UJ 20 UJ 20 140 TINA - MINA 9TM = 1 2 0° _ l H 80 140 EM , M e V ) F i g . 5.2.10 TINA and MINA y-ray energy spectra for the good 2y events-at 0_, = 120° TM 10 5H c - OH -5H -10 -10 i i t i * i i i i i 111221 1<M 2 I II 1 11 1 1 1 I I II 3?21 1112212 1 12II1I212I2213422S6U224231 324 121 3I2I3936B77 11111 II 11112 II 112 31311231355243332312313111121142345568 1 22 1111 112 1 111 211 21224234322123322 1122 223135122225 I I I | 2 1 1 2 2 2 1 1 111 22131211 31421221 121 I 31222 1 1 <*S7 1 1 211 2 11 I 1 1 21 2252312241 41121 12 1 222232532 It 2 12 111 1 1 1 1 1 123 2 11121112 II 32112 12 36J5 2 i u m i i 2 i n i i i i " j | L g l J i i ' i L L a l l a l f } L ' i i n * " J » » « I 1 1 11 1 1 TINA - MINA 6TM 1 2 0 ° Regions Regions 1 : 2events 1 1 I I I I 1 I l i 1 J 1 11 I 1 i r t r - ? i r " T - 2 r 2 - T r - 2 n r n I 1 1 1 1 1 1 2 2 1 u II I i J b 1 i \ ,11 ! MH i i ii I > i i ' 3, i i 12 1 1 1 1 1 1 I 1 I 1 |1 1 121 111 11121 1 II I 1 1 2 1 11 1 2 1 2 I 11 1 3 11 11 1211 2 1 I 1 1 1 1 1 11 1 1 11 1 T l Tl 1 122 111 112111 1 2 12123 21211211 2 1 221112212 U l l 1 111 1 1122221132 1 12 2 1|2 |2 1 1 12 12223 12 I 12 1 21 I 2111122 A 31111111 121 II 122212 M I 3 | 2 1 l l 1111 t|l l|2 121121 2 1311 11 12111121 21 21 1 1 lit 111 1 I l l l l l l 21 21 11 l | l 111 1121 121 1 1 1 1^ I I L I 2 1232I31M p i 111 1 121 1 L 121 12 t i 1122111 1 211122 1 I 1 11 l i t 1 1 1 111 I 11 1 - 5 r 0 I 5 6 1 1 1 1 2 1 2 1 1 \l 1 23323 21124222 13245 1 121231322 2122 1344 I 11 233 2 21111 1 21111 1112 11 U l 11 1111 21 1 1 1 It t I I 1 I t 1 1 1 1 11 1 t l 1 I 1 II t 1 11 It t 2 U l 1 11 I 12 11 1 1 1111 1 1 211 1 111211 1 1 1 21 10 TT (ns) F i g . 5.2.11 The T M-vs-T T scatter plot with the d i f f e r e n t regions A, and B^ . used i n the background subtraction. 67 Table V The background subtraction Region : # events Region # events A 655 A 655 B i 79 B l 90 B2 168 B2 147 B 3 165 B 3 138 B4 39 B4 55 A " ^ B k 204 ± 33 A " I B k 225 ± 33 In addition to the y-ray energy spectra of TINA and MINA shown i n f i g . 5.2.10, we present i n f i g . 5.2.12 the diffe r e n c e and sum-energy spectra obtained for the good 2y events. The E^ , - E^ spectrum i s symmetric with respect to energy zero as i t should be, and shows that the events are p r e f e r e n t i a l l y d i s t r i b u t e d i n regions where the diffe r e n c e i n the energy of the two photons i s about 70 MeV. The sum-energy spectrum i s found to peak at 120 MeV and has a FWHM of about 40 MeV. Note also that the spectrum f a l l s o ff very r a p i d l y below 110 MeV and that almost no contribution to the (TT~,2Y) process i s found below 80 MeV. This feature j u s t i f i e s therefore the low sum-energy cut near 60 MeV and already indicates that the r e s i d u a l v . i nucleus i s not highly excited. 68 30 + > I 20 Z LU 21 1 0 (a) TINA-MINA X •80 H r- 80 iJ- (MeV) 3 60 + 40 + > 20 UJ (9=120 ) TM '(b) 40MeV — t -50 100 150 F i g . 5.2.12 The d i f f e r e n c e and sum-energy spectra of the good 2y events a t e T M = 1 2 0 ° . To see how the a v a i l a b l e energy i s shared between the two photons, we show i n f i g . 5.2.13 a two-dimensional energy scatter plot of E -vs-E^, i n which the number of events observed i n each energy b i n has been indicated by f u l l c i r c l e s of d i f f e r e n t s i z e s . Open c i r c l e s were drawn i n the energy regions for which the subtraction of the background yielded negative c o n t r i -butions. Consistent with the y-ray energy spectra obtained for TINA and MINA ( f i g . 5.2.10), the events are found to be p r e f e r e n t i a l l y concentrated i n the HE^-LE^ or LE^-HE^ regions of the scatter p l o t . The number of 2y 69 140 4 I 80 204 O o • o TINA - MINA 8 T M = 1 2 0 ° • O 204 ± 33 events o o • • o 20 80 E T (MeV) 140 F i g . 5.2.13 Energy-sharing between the two photons ( © T M = 120 ) 70 events observed i s therefore strongly dependent on the experimental low-energy threshold .of the y-detectors and so, one can expect the t o t a l branch-12 -ing r a t i o of the C(TT ,2y) rea c t i o n to be very s e n s i t i v e to t h i s experi-mental constraint. Our conclusion regarding the technique used f o r the subtraction of the background i s the following. By looking at each y-ray band on the time-time scatter p l o t , i t i s possible to estimate the background present i n the yy window. Furthermore, i f t h i s background involves mostly y-rays (e.g. R-y or n-y coincidences), then the good 2y events can be singled out by subtracting from the yy window (region A) events l y i n g i n i t s adjacent regions B^. These regions can be f a i r l y accurately determined by equalizing i n each y-ray band the number of unwanted coincidences located in s i d e region A with the one ju s t outside. This l a s t remark i s important since i t w i l l . permit us to perform a same background subtraction on the data obtained with the Cerenkov counters for which good energy r e s o l u t i o n cannot be achieved. 71 5.2.3 Accidental Coincidences Due to Pile-ups It was pointed out e a r l i e r that because was not 100% e f f i c i e n t i n detecting pion pile-ups i n the beam, some 2y accidental coincidences (two simultaneous y-rays from the (TT -, y) reaction i n the carbon target) were present i n the yy window and could not be distinguished from the true 2y events. Although the number of these accidental coincidences i s expected to be small, i t i s important to estimate i t . We have therefore investigated the events associated with p i l e -ups, that i s , which have AE > 2.1 MeV. Using the same energy and TOF cuts as before, we have performed the background subtraction on these events and found a t o t a l of 44 ± 14 2y events. Most of these are accidental c o i n c i -dences but some are also good 2y events. The branching r a t i o for the 1 2 C ( T T _ , y) reaction i s 2% and i t i s estimated that about 20% of accidental coincidences of two r a d i a t i v e photons would have a sum energy smaller than -5 12 145 MeV. Assuming a branching r a t i o of 1.2 x 10 for the C ( T T - , 2y) process (see section 5.4.4) and remembering that each pile-up event corre-sponds i n fact to two stopped pions, then the r a t i o of true to accidental 2y events i s ( 2 y ) t r u e 2 x 1.2 x 10~ 5 1 (2y) 21 (20%)x(2%)x(2%) a 3 acc Thus, about 11 ± 4 of the 44 events are true 2y events and about 33 ± 11 are accidentals. Since 1/4 of the pile-ups were missed by S^ (see f i g . 5.2.7) then the number of accidental coincidences that could not be 72 i d e n t i f i e d i n our previous analysis i s ~11, i . e . about the same number as the true 2y events rejected by the AE cut. Consequently, no co r r e c t i o n on the value of 204 ± 33 events i s necessary. 73 5.3 The Other Configurations We have analysed the coincidence events obtained with the other pairs of detectors by using the same technique of background subtraction as the one we have j u s t discussed i n the previous section. The s i t u a t i o n regarding the d i f f e r e n t contributions from background processes i s now s i m p l i f i e d by the fact the Cerenkov counters are i n s e n s i t i v e to neutrons. It i s found, for instance, that most unwanted coincidences are associated with electron bremsstrahlung detected by the Cerenkov counters. Cerenkov counter CI was p a r t i c u l a r l y s e n s i t i v e to t h i s type of background because of i t s low energy threshold (16 MeV). Coincidences l i k e n^ ^ "Y^ 2 a r e also present i n the TINA-C1, TINA-C2, MINA-C1 and MINA-C2 configurations, but they can be e a s i l y eliminated by applying proper TOF cuts i n the spectra of the Nal c r y s t a l s . We present i n the next few pages the TOF spectra T_^ , T^ obtained at the d i f f e r e n t angles © „ , as well as the corresponding TOF scatter p l o t s T.-vs-T. ( f i g . 5.3.1 to 5.3.9). The d i f f e r e n t regions A and B. that were 2 1 k used for the subtraction of the background are indicated on each scatter p l o t . For C1-C2 coincidences ( 0 ^ = 110°), the TOF spectra ^ and T 2 have been omitted because of the small number of events detected. Moreover, no background subtraction was necessary for that p a i r of detectors (see f i g . 5.3.5). In the case of the TINA-C1 ( 0 T 1 = 80°) and MINA-C1 ( 0 ^ = 160°) coincidences, the large contributions from bremsstrahlung made the background 74 subtraction very d i f f i c u l t to carry out. The T^ spectra of f i g . 5.3.3(b) and f i g . 5.3.6(b) show indeed that the y-ray peaks are overwhelmed by random coincidences generated by electron bremsstrahlung. For TINA-C2 ( © ^ = 170°) and MINA-C2 ( 0 ^ = 50°) coincidences, t h i s background was much less important and the background subtraction could be performed without d i f f i c u l t y . With the geometry used i n the experiment, TT° 2y decays following i n - f l i g h t CEX reactions on the hydrogen of S^ could be detected by the p a i r of detectors TINA and C2 (.0 - 130°). These y-rays come of course i n the early time region of the T^-vs-T^ scatter plot and can be eliminated by proper TOF cuts (see f i g . 5.3.9). Since MINA could not see S^, no background of t h i s type was observed i n the MINA-C2 configuration. For each pair of detectors, we give i n Table VI the number of good 2y events obtained a f t e r background subtraction, together with i t s s t a t i s t i c a l uncertainty. Table VI The good 2y events at the other angles. e . . 2y 50° 68 ± 16 80° 52 ± 19 110° 8 ± 3 160° 68 ± 19 170° 113 ± 20 75 The y-ray energy spectra E_^ , E^ ., and the sum energy spectrum E_j+E_. of the good 2y events are shown for each angle 0 i n f i g . 5.3.10 to 5.3.14. Because of the poor energy r e s o l u t i o n of the Cerenkov counters and also the small number of good events observed at these angles, no precise information about the energy-sharing of the two photons can be obtained. Nevertheless, the sum-energy spectra are found to peak at an average energy of about 130 MeV and to have a shape s i m i l a r to the one observed for the TINA-MINA good events. Furthermore, for small opening angles = a n ( ^ ®xl = » t ^ i e Y-ray energy spectra of the Nal c r y s t a l s resemble c l o s e l y those obtained at 0 ^ = 120°. For the large opening angles = 160° and = 170°) however, these no longer present a steep r i s e at low energies but show rather a broad energy d i s t r i b u t i o n centred near 70 MeV. This feature i s also observed for the Cerenkov counters. A possible explanation for the pe c u l i a r behaviour of the y-ray energy spectra at wide angles w i l l be given i n Chapter 6 where our experimental r e s u l t s w i l l be discussed. H O CO 1 3 2 (B > n » r t i-h O i-i a t> o to o o H-o H* 3 o fD fl> < fD 13 ho o o NUMBER OF E V E N T S CD " N U l cn J> w 11111111111111 I 111111111111111111 NUMBER OF E V E N T S z > O -n co ~D m o — i ID cz o o r o « w u * 10 J> 0) U) I I I I I I I I I I I I I I I I I H I I I I I I I I I I I I I I I o CO -o m o — i ZD 5 -10 MINA - C2 9 = 50° M2 1 : 2events i i i i i 2 t i i I I I i t i t i t t i t 2 1 I t 1 1 11 1 I 1 1 I 1 1 1 I I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 1 1 1 1 1 1 1 111 1 1 1 1 1 22 2 1 1 1 111 1 12 1 1 1 I 1 1 - - » • -1 1 1 21 "I I 1 1 I 1 I I l i t ' 1 1 1 1 i 21 1 1 1 1 1 1 1 1 1 1 11 1 1 U 2 1 1 2 I 1 11 J * I 1 1 2 1 1 1 11 1 1 1 -5 — i 0 T M (ns) 10 Fig. 5.3.2 T 2-vs-T M scatter plot. 78 T O F S P E C T R U M O F C I A (b) TINA - Cl F i g . 5.3.3 TOF spectra for TINA-Cl coincidence events (e j = 80°). (a) TINA, (b) C l . Fig. 5.3.4 T.-vs-T scatter plot. C1 - C2 02--11O° -5 0 — i 5 (ns) 10 15 Fig. 5 . 3 . 5 T 2-vs-T 1 scatter plot. 81 co i— z UJ > •se-en UJ 3Z-CD is-H (b) T O F S P E C T R U M O F C I [U n MINA - CI III Y-RAYS Lf BREMSSTRAHLUNG BREMSSTRAHLUNG " T " - 1 0 . 0 - 5 . 0 0.0 5.0 10.0 1 1 1 I IS.0 20.0 T. (N5) F i g . 5.3.6 TOF spectra for MINA-C1 coincidence events ( 0 ^ = 160 ). sp (a) MINA, (b) CT. Ml 20 10H in c OA -10 -10 MINA - C1 1 : 2 events -5 1 1 1 r U . 4 . . _ _ t _ 4 , 1 1 i t i i i ! 1 i i i i < 1 11 i i ! 11 i i i 1 1 i 1 1 11 i i 1 1 i 1 11 i 1 1 i 11 1 1 211 1 1 1 1 1 1 1 1 1 1 11 1 11 1 1 1 1 I ! 1 1 I 1 1 11 1 1 1 1111 1 1 11 1 1 1 11 1 II U l I 21 I 2 12 I 2 1 1 1 « 1 1 1 1 1 11111 11 1 1111 II 2 111 1 1 11 1 1 1 11 1 II 1 11 U 1 11 1 1 2 11 II I 1 I 1 112 II 1 1 11 2 11 11 1 11 1 1 1 2 1 21 111 " T i l l 12 1 1 II 2 1 t i l l 111 211111211 1 1 111 I 1 111 1 11 11 1 1 12 1 1 1 1 111 1 1 12 1 II I II 1 1 1 1 1 1 1 I 1 1 1 U l 1 1 U l l 1 11121 1 211 13 12 11212211 I 211 I 1 212 1 111 212 II 11 11 - 4 1 II 1 0 T M (ns) 5 10 oo K3 Fig. 5.3.7 T..-VS-T scatter plot. 83 T O F S P E C T R U M OF T I N A 6 4 H l iJ 3 2 — | m n z 1 6 -(a) TINA - C2 11111111111 • 1111111111* 111111111111 • i»[' i - 9 . 0 - 6 . 0 - 3 . 0 Y-RAYS from S,. n/l i i i I i i o. o Y-RAYS from C NEUTRONS i i i i i i i [ i i i i i i i i i | i i i i i i i i i | i ' ' ' ' ' ' 1 3 . 0 6 . 0 (NS) T O F S P E C T R U M OF C2 (b) - 6 . 0 - 3 . 0 0 . 0 3 . 0 6 . 0 9 . 0 1 2 . 0 1 5 . 0 T 2 INS) F i g . 5.3.8 TOF spectra for TINA-C2 coincidence events (0 2 = 170 ). (a) TINA, (b) C2. 15 1CH in c 5H C M 0 -5 -10 i i i i i i i i i n i i t i i TINA - C2 V 1 7 0 ° i i i t i TT - 2Y ' (S, 1 : 2 events i i m i 2 2 " i n i 11 22 1 1121 11 21 ' 2 1 211 II 11 A l> 11 121II 1 / 1 1 M i l 1 II 1 • 1 1 t I 21 1 I l i l t I 111 1 1 1 It 1212 22111 1 2 2112)231)1 t 2 2311222 11 1 1 1211 1 1 1 I 1 11 1 11 / I 1111 \ / 211 321 I 1 >*L L J 1 11 1 12 1 11 21 1 1 1 1 1211 1 1 212 1 1 1 U l 11 I 21 11 2 1 13 11 1 11 1 1 11 111 11 II 1 1 1 |2 111 I 11 11 U l 31 1 II 1 II 1 1 U 1 II 1 1 - 5 — i 0 T T (ns) 10 oo Fig. 5.3.9 T„-vs-T scatter plot. 85 F i g . 5.3.10 The y-ray energy spectra for the good 2y events at 0 M2 50^ TINA - C1 ( 6 T 1 = 80 ) 5 to 15+ 10 + UJ 5 ' TINA C1 Lfl L-. so; 80 H O E T , E 1 (MeV) 20 + 1 15 o (SI z UJ > UJ 10 + 5 + '20 — I — 100 • E 180 1 (MeV) F i g . 5.3.11 The Y-ray energy spectra for the good 2y events at 6 ^ = 80° 86 5* ^ 3 + * 2 + UJ > UJ 1 + 20 C1 - C2 — C1 — - C2 80 ^ 2 (MeV) <e12«iio°> uo 5 + 4 + > o (SI - 3 + to I— z > UJ 2 + 1 + 20 100 (MeV) 180 F i g . 5.3.12 The y-ray energy spectra for the good 2y events at 9 ^ = H 0 C 30+ — M I N A — CI 2~ 2 0 CNI C/> » -l 10 UJ 20 MINA - C1 80 U0 E M , (MeV) (6 =160°) Ml 30 + > QJ Z 20 o CNI I/) 5 1 0 > UJ 20 hoo (MeV) 180 F i g . 5.3.13 The y-ray energy spectra f o r the good 2y events at Q ^ =160 87 TINA- C2 40 1 $ 3 0 2 : oo 2 0 + i — LU > 10 + T I N A C 2 r - T i i 20 E T , E 2 - • — i -80 J (MeV)1—5 U0 < e T 2 = i 7 0 ° ) 40 1 £ 3 0 21 o (M LU > 2 0 1 10 + 2 0 100 E T + E 2 (MeV) 1B0* F i g . 5.3.14 The y-ray energy spectra for the good 2y events at 0 _ =170 88 12 5.4 The Branching Ratio for the C(ir , 2y) Reaction dB.R We define the d i f f e r e n t i a l branching r a t i o -r-r L(6 ) for the dft YY 12 -C(ir ,2Y) rea c t i o n as YY d B " R 2 , ( 0 ) = ^ ! 2 x ( e , . J L . !&i!u2 - ( - u i i ; 4TT An. An. dft Y Y dfl.. J 9 „ E / / I N > • J Tr-stops i j 4ir 4TT where N (0 ) i s the number of 2y coincidence events observed at an i n t e r -2Y i j photon angle 0 = 0 between a p a i r of detectors i j ( i , j=T,M,l,2) ; N ^ ^ ^ i s the t o t a l number of pions stopped i n the carbon target; e i s a co r r e c t i o n factor (e.. < 1.0) which accounts f o r events l o s t through p a i r 1 3 ~ An. . production, TOF cuts, e t c . ; i s the e f f e c t i v e s o l i d angle (normalized to unity) of detector i , j , and dft = dft. . = 2Trsin0. .d©. .. The factor 2 YY i J i j 13 a r i s e s i n the denominator to avoid double counting. Before we compute the d i f f e r e n t i a l branching r a t i o f o r each angle 0 ^ , i t i s necessary to estimate the corrections that must be taken into account i n the evaluation of the e f f i c i e n c y e.., and also i n the t o t a l 13 number of stopped pions N . The most important of these are the ir-stops corrections f o r pile-ups i n the beam, pair production of Y -rays i n the carbon target, and TOF cuts. 89 5.4.1 Pile-ups i n the Beam Because the rate of the incident pion beam was r e l a t i v e l y high i n t h i s experiment (~9 x 10^ TT/S i n S^) , there was a non-negligible p r o b a b i l i t y that two or more pions triggered simultaneously (within a beam pulse) the telescope counters, and therefore, that only one ir-stop was recorded. The p r o b a b i l i t y of observing n pions i n a beam pulse of width At i s given by the Poisson d i s t r i b u t i o n e(-At/x) n P (At,T) ( ^ ) n n J T where x i s the mean time i n t e r v a l between pions. With a beam microstructure of 4 ns beam pulses every 43.4 ns (f , =23.060 MHz) and an average pion rate of 9 x 10 5 TT~/S, the r a t i o cyclotron _ A t  m = ~ i s 4ns m = = 0.04 __4ns_ 1 k43.4ns ; ^ 5, ; 9x10 Is If one considers only si n g l e and double pions, one finds that the f r a c t i o n of pile-ups i n the beam ( i n S^) i s about P-L(m) 2 90 that i s ~2% of the t o t a l incident pion rate. We have also considered TT-U pile-ups i n the telescope counters as well as pile-ups i n the detectors or i n the e l e c t r o n i c s (e.g. i n the coincidence buffer u n i t ) , but the t o t a l contribution from these e f f e c t s was found to be very small ( S 2 % ) . 5.4.2 Pair Production Here we have evaluated the f r a c t i o n of true 2y events that were l o s t when at l e a s t one of the two y-rays converted e x t e r n a l l y into a e +e pair e i t h e r i n s i d e the carbon target or i n the s c i n t i l l a t i o n counters placed i n front of the y-detectors. For a p a i r of detectors i j , t h i s f r a c t i o n i s £pp /-PP- , -pp- \ f.. = n(cr. x. + a. x.) i j i i 3 3 3 where n i s the number of carbon atoms per cm i n the target or i n the s c i n t i l l a t i o n counters, a?^ i s the t o t a l cross-section for the pair production process^ averaged over the y-ray energy spectrum (of the good 2y events) measured i n detector i , and x. i s the mean thickness of material i n the See e.g. A.I. Akhiezer and V.B. B e r e s t e t s k i i . Quantum e l e c t r o -dynamics, Interscience Publishers, New-York - London-Sydney, 1965. 91 d i r e c t i o n of counter i . The value f ? p calculated for each experimental configuration i s given i n Table VII Table VII Pair-production 0.. 13 f P P 13 50° 0.055 80° 0.043 110° 0.045 120° 0.050 160° 0.045 170° 0.059 5.4.3 Time-of-Flight Cuts The TOF cuts that determined regions A and (k=l,2,3,4) f or the subtraction of the background had the e f f e c t of r e j e c t i n g some good 2y events that extended outside these cuts. To-estimate the f r a c t i o n of good events l o s t i n t h i s way, we have f i t t e d a two-dimensional gaussian d i s t r i b u t i o n to each y-ray peak of the d i f f e r e n t TOF scatter p l o t s . 92 In our c a l c u l a t i o n , we have also taken into account the fact that the t o t a l number of good events observed a f t e r background subtraction i s equal to the number of good 2y events of region A minus the t o t a l number of good 2y events of the four regions ( i . e . A - 1 ^ ) . Table TOF k VIII gives for each configuration the f r a c t i o n f of good 2y events rejected due to TOF cuts and background subtraction. Table VIII "."TOF: cuts e . . 13 fT0F i j 50° 0.09 80° 0.12 110° 0.00 120° 0.18 160° 0.06 170° 0.22 93 5.4.4 The Total Branching Ratio With these corrections i n mind, we can now compute the dB -R„ 2Y d i f f e r e n t i a l branching r a t i o — (0..) for each angle 0... The t o t a l dfi. . i i i i i j number of pions stopped i n the carbon target was determined from the number of S^.S^.S^ trig g e r s recorded i n the experiment. Only 78% of these t r i g g e r s corresponded to the stop of a pion i n the target (see section 4.1). In a d d i t i o n , i t was calculated that about 0.5% of the incident pions underwent reactions i n and that about 3% of the p a r t i c l e s that stopped i n the target consisted of muons. With a pro-b a b i l i t y of 2% for pion pile-ups, the t o t a l number of stopped pions i s N = N n„„ x 0.78 x (1+0.02) x (1-0.005) x (1-0.03) TT—stops 123 - 0.77.N 1 2 3 where i s t h e n u m b e r o r S]_ , S2* S3 t r i S 8 e r s recorded i n the experiment ( N 1 2 3 = 2.83 x 1 0 1 1 for TINA-MINA coincidences and N ^ = 2.59 x 1 0 1 1 for the other c o n f i g u r a t i o n s ) . The e f f i c i e n c i e s e . . have been calculated from the values ^TOF , £pp . .. . f . and f . given e a r l i e r : • u - a - f j f j . a - f j j , 94 Table IX gives for each angle 0 , the t o t a l number of 2y events observed, N , the number of pions stopped i n the carbon target, ° . .Aft. . Aft. N , the e f f i c i e n c y e . ., the detection e f f i c i e n c y (-;——) • ( 7 — ! ) , u-stops' 13 ,„ „ 4lT 47T 2Y and the d i f f e r e n t i a l branching r a t i o -j-- with i t s uncertainty. i j This l a s t one includes the s t a t i s t i c a l uncertainty on N^, as well as other systematic errors 9%). Table IX The d i f f e r e n t i a l branching r a t i o Aft. Aft. (xlO" 5) dB.R e . . 13 N_ (0. .) 2y 13 N TT-StOpS ( x l O 1 1 ) 13 1 J 6 (xlO °) 50° 68 ± 16 2.0 0.86 1.5 1.05 ± 0.27 80° 52 ± 19 2.0 0.84 1.2 1.03 ± 0.38 110° 8 ± 3 2.0 0.96 0.28 0.59 ± 0.23 120° 204>± 33 2.2 0.78 6.72 0.70 ± 0.13 160° 68 ± 19 2.0 0.90 1.0 1.50 ± 0.44 170° 113 ± 20 2.0 0.73 1.9 1.62 ± 0.32 The t o t a l branching r a t i o B.R i s rela t e d to the d i f f e r e n t i a l dB.R2 2 Y branching r a t i o — (0 ) by the expression dft YY YY 95 dB.R B.R 2y dft YY (0 ) • 2Trsin0 d0 YY YY YY To c a l c u l a t e t h i s value from our experimental data, we approximate the i n t e g r a l above by a weighted sum: B.R 2Y 4TT dB.R Y ^-(0..) • 2irsin0. .A0. . . ^ . d f t . . ^ x, x, Aii : Y 2iTsin0. .AO. . . . i i l ] where A0 i s the inter-detector angular acceptance determined by the i3 s o l i d angles Aft. and Aft.. Using the values of Table IX, we f i n d a t o t a l 12 -5 branching r a t i o for the C(ir - , 2 y ) reaction of ( 1 . 2 ± 0 . 2 ) x 10 . 96 Chapter 6 Discussion of the Results 12 In regard to the C(TT , 2y) process, we are now i n a p o s i t i o n to discuss the information which can be extracted from the experimental r e s u l t s presented i n the l a s t chapter. We already know from the i n -spection of the y-ray energy spectra obtained with the p a i r of Nal c r y s t a l detectors ( © ^ = 120°) that the above process favours the emis-sion of two photons with unequal energies (see f i g . 5.2.13). As pointed our e a r l i e r , t h i s means that the p r o b a b i l i t y of observing y-ray i s strongly dependent on the experimental low-energy threshold of the de-tectors . A second important remark regards the fa c t that at a l l angles 0 „ the sum-energy spectra of the two photons are well peaked near 120-140 MeV (FWHM ^ 40 MeV). This indicates that the 1 2 C ( i r ~ , 2y) r e -action does not leave the r e s i d u a l nucleus i n a highly excited state. To better understand now what are the most probable f i n a l nuclear states of 12 • the C(TT , 2y) reaction, we have compared i n f i g . 6.1 the sum-energy spectrum of the 2y events obtained at 0 ^ = 120° with the si n g l e r a d i a t i v e y-ray energy spectrum measured with the Nal c r y s t a l s . The processes that dominate the si n g l e r a d i a t i v e capture i n carbon are well known to be the 12 11 12 _ 12 C(TT , ny) B and the C(TT , y) B reactions (see discussion i n chapter 12 11 3) . The break-up channel TT + C B + n + y contributes mostly i n 12 12 the 50-115 MeV region of the photon spectrum whereas the C(TT _, y) B 97 reaction produces energetic y-rays (E > 100 MeV) which are associated 12 with the low-lying states of B. Since the sum-energy spectrum of the 2y events f a l l s o f f very r a p i d l y below 100 MeV, one has a good i n d i c a -12 t i o n that the r e s i d u a l nucleus i n the C(TT~, 2 y ) r e a c t i o n i s most 12 l i k e l y B and that the l a t t e r has a low p r o b a b i l i t y f o r breaking up. Moreover, the small s h i f t 10 MeV) towards higher energies i n the sum-energy spectrum r e f l e c t s the fa c t that, i n contrast with the si n g l e r a d i a t i v e capture, the two-photon emission leaves the r e s i d u a l nucleus 12 B i n i t s ground state with a r e l a t i v e l y high p r o b a b i l i t y . 12C<TT".2S) PHOTON ENERGY (MeV) " - 12 -F i g . 6.1 The y-ray energy spectra for the C(TT ,y) and ^ C ( i r - , 2 y ) reactions. The s o l i d l i n e i s the normalized r a d i a t i v e photon energy spectrum as measured with the Nal c r y s t a l s . 98 We next present i n f i g . 6.2 the angular d i s t r i b u t i o n of the 2y events as a function of the inter-photon angle 0 . Our r e s u l t s are YY compared with those obtained by the Louvain group (Deutsch et a l . 1979) and also with the upper l i m i t measured at 0 = 90° by the V i r g i n i a -Indiana c o l l a b o r a t i o n (Roberson et a l . 1977). The 2y angular d i s t r i b u -t i o n observed i n our experiment has a shape very s i m i l a r to the one found by Deutsch et a l . . In both cases, the angular c o r r e l a t i o n of the two emitted photons exhibits a clear r i s e for backward d i r e c t i o n s ( 0 ^ > 150°). There e x i s t s , however, a s l i g h t disagreement between the values of the branching r a t i o s obtained by the two groups. The Louvain group measured a t o t a l branching r a t i o of (1.4 ± 0.2) x 10 ^ for y-rays with energies higher than 25 MeV. This i s to be compared to our ex-perimental r e s u l t of (1.2 ± 0.2) x 10 ^ obtained with an average low-energy threshold of about 17 MeV. From the discussion made e a r l i e r about the s e n s i t i v i t y of the branching r a t i o to the experimental energy thres- ! hold of the detectors, these two r e s u l t s , at f i r s t , seem incompatible. One should indeed expect our value of the branching r a t i o to be higher than the Louvain r e s u l t . However, such a comparison i s d i f f i c u l t to make since the energy resolutions achieved i n the two experiments were very d i f f e r e n t . Yet, our r e s u l t i s consistent with the upper l i m i t of 1.1 x 10 measured by Roberson et a l . , assuming uncorrelated photons. Their value for the low-energy cut-off was not mentioned i n t h e i r paper, but presumably i t was about 20-25 MeV.^ K. Gotow, private communication. 99 F i g . 6.2 Angular d i s t r i b u t i o n of the 2y events. The experimental r e s u l t s of Deutsch et a l . and the upper l i m i t obtained by Roberson et a l . are compared to our observed angular d i s t r i b u t i o n . The s o l i d l i n e s are the c a l c u l a t i o n s of C h r i s t i l l i n and Ericson f or cut-o f f s of 17 and 25 MeV. The dash-dotted l i n e i s the c a l c u l a t i o n made by Beder (15 MeV cut-off) f o r the nucleonic process. 100 I t was pointed out i n section 5.3 that the y-vay energy spectra obtained at 0 ^ = 160° and Q ^ ~ 170° had a shape quite d i f f e r e n t from the one observed at a l l the other angles (see fig.5.3.13(a) and f i g . 5.3.14(a). This peculiar behaviour i n the photon spectra and also the r i s e observed at wide opening angles i n the 2y angular d i s t r i b u t i o n have prompted us to consider the p o s s i b i l i t y of background processes that could have yielded 2y events ind i s t i n g u i s h a b l e from the true ones. For instance, i n - f l i g h t charge-exchange reactions i n the carbon target with the following decay of the TP would enhance the 2y angular d i s t r i b u t i o n at wide angles and would account for the photon spectra of f i g . 5.3.13(a) and 5.3.14(a). We have therefore investigated t h i s source of background by looking at the AE spectra obtained at 0 ^ = 160° and = 170°. By imposing proper cuts i n the AE spectra, i t was possible to separate events associated with low-energy incident pions (T ^ 10-15 MeV) from those events corresponding to pions of higher energy (T 'v* 20-25 MeV) . As the cross-section of the CEX reaction f o r the energy range considered here i s about proportional to the k i n e t i c energy of the pion, then the rate of the 2y events that would be generated by t h i s process would exhibit a dependance on the energy of the incident pions. No such e f f e c t was found and thus we came to the con-clusio n that the number of 2y events due to i n - f l i g h t CEX reactions i n the target was n e g l i g i b l e even at large inter-photon angles. A second p o s s i b i l i t y for background events of t h i s sort could be explained by charge-exchange reactions due to the presence of some hy-drogen contamination ins i d e the carbon target. Small traces of the order of 50ppm would be s u f f i c i e n t to account for about h a l f of the 2y events 101 observed at © w, = 160° and © m„ = 170°. This estimate i s of course very Ml T2 crude because of the uncertainty about the form i n which the hydrogen i s present i n the target (gas, water vapor...) and about the pion capture rate i n the hydrogeneous compound. Using the Nuclear Magnetic Resonance technique, we have detected the presence of hydrogen i n s i d e the target, but unfortunately, i t was impossible to estimate i t s amount. In view of these r e s u l t s , i t i s d i f f i c u l t to assess the v a l i d i t y of the data obtained at 0 = 160° and 0 = 170° and hence to YY YY determine the shape of the 2y angular d i s t r i b u t i o n at wide opening angles. On the other hand, the exclusion of these two r e s u l t s from the angular d i s t r i b u t i o n of f i g . 6.2 would not change appreciably the value of the t o t a l branching r a t i o (^  1.1 x 10 V In regard to t h i s problem, a g s i m i l a r observation was made by Deutsch et a l . who also a t t r i b u t e d part of the r i s e i n t h e i r photon angular d i s t r i b u t i o n to possible hydrogen contamination. 12 -We turn now to the de t a i l e d c a l c u l a t i o n s for the C(TT , 2y) reaction recently performed by Beder (1979b) and by C h r i s t i l l i n and Ericson (1979). These authors have pointed out the importance of the pion capture schedule i n t h i s process: while the S-capture i s p a r t i c u l a r l y s e n s i t i v e to the TT- "TT+" a n n i h i l a t i o n graph of f i g . 6.3, the pion capture from a P-state i s dominated by the pion bremsstrahlung of sing l e r a d i a t i v e 12 capture ( f i g . 6.4). Since i n C the capture of a pion takes predominantly place from the 2P atomic state, the bremsstrahlung diagrams of f i g . 6.4 are therefore found to bring the largest contributions to the doubly g Deutsch et a l . , p r i v a t e communication. F i g . 6.4 Dominant b r e m s s t r a h l u n g graphs i n t h e C(TT ,2y) r e a c t i o n f o r P-wave c a p t u r e . 103 9 r a d i a t i v e capture. Moreover, the fa c t that the two photons emerge from d i f f e r e n t v e r t i c e s i n the bremsstrahlung graphs implies that the v i r t u a l pions ins i d e the nucleus cannot be d i r e c t l y probed through the 12 C(TT , 2y) reaction. In the works of Beder and of C h r i s t i l l i n and Ericson, the ca l c u l a t i o n s were c a r r i e d out from a f i r s t d e t a i l e d i n v e s t i g a t i o n of the T7~p->YYn process on a free nucleon. The extension of these r e s u l t s to the 12 s p e c i a l case of C has followed, however, a d i f f e r e n t approach i n each work. Beder has calculated the R„ /R, r a t i o i n carbon v i a a crude im-2y l y pulse approximation and a r e a l i s t i c capture schedule. C h r i s t i l l i n and Ericson used an e f f e c t i v e Hamiltonian plus the closure approximation together with a r e a l i s t i c shape of the nuclear e x c i t a t i o n energy spectrum 12 of B to predict the branching r a t i o , the 2y angular c o r r e l a t i o n and the 12 photon energy spectrum i n the C(IT , 2y) reaction. Both computations have indicated that the important contributions of the bremsstrahlung 12 diagrams to the C(TT , 2y) process make the 2y rate very s e n s i t i v e to the photon energy cut- o f f . This, indeed, i s i n agreement with our experimental observations. Using a 15 MeV cut-of f , Beder has estimated the r a t i o of -4 observed 2y/ly events i n carbon to be about 18 x 10 . Combined with a 2% p r o b a b i l i t y f o r the sin g l e r a d i a t i v e capture, t h i s r e s u l t y i e l d s a -5 12 branching r a t i o of 3.6 x 10 for the C(TT , 2y) reacti o n . For a 25 MeV low-energy c u t - o f f , the branching r a t i o reduces to 2.6 x 10 ~\ That Beder's The v i r t u a l charge-exchange process was also considered by these authors but was found to be numerically unimportant. 104 c a l c u l a t i o n s give such large estimates for the branching r a t i o i s not s u r p r i s i n g i n view of the uncertain v a l i d i t y of h i s crude impulse approximation which neglects nuclear structure e f f e c t s . On the other hand, C h r i s t i l l i n and Ericson have obtained values much closer to the present experimental r e s u l t s . For 17 and 25 MeV c u t - o f f s , t h e i r values for the branching r a t i o i n carbon are 1.6 x 10 ^ and 1.15 x 10 r e s p e c t i v e l y . These authors predict thus a 2y rate s l i g h t l y larger 30%) than our experimental r e s u l t . This discrepancy, however, can be accounted for by the large uncertainties i n the experimental t o t a l widths for the IS and 2P IT atomic states. The photon angular c o r r e l a t i o n s calculated by C h r i s t i l l i n and Ericson f o r the two experimental low-energy thresholds of 17 and 25 MeV, are shown by s o l i d l i n e s i n f i g . 6.2. In the same figu r e appears also the L=l angular c o r r e l a t i o n for the TT -p->-YYn process as computed by Beder using a 15 MeV cut-off (dash-dotted l i n e ) . This l a s t curve has been normalized so that the t o t a l branching r a t i o i s 1.2 x 10 While C h r i s t i l l i n ' s and Ericson's c a l c u l a t i o n s predict a slowly decreasing angular c o r r e l a t i o n i n the background d i r e c t i o n , the 2y angular d i s t r i b u -t i o n obtained by Beder exhibits a r i s e at large opening angles i n q u a l i t a t i v e agreement with our experimental r e s u l t s . I t was argued by Ericson and C h r i s t i l l i n " ' " ^ , however, that the enhancement at wide photon angles i n the nucleonic Tr-p->YYn process i s suppressed when nuclear structure e f f e c t s , such as the P a u l i blocking, are taken into account. Private communication. 105 12 The y-ray energy d i s t r i b u t i o n i n the C(TT , 2y) reaction has also been computed by C h r i s t i l l i n and Ericson. The shape of the photon spectrum was found to be the same at a l l opening angles and to e x h i b i t a c h a r a c t e r i s t i c i n f r a r e d divergence for small photon energies. In f i g . 6.4, we compare the average y-ray energy spectrum of TINA and MINA obtained at 0 = 120° with the corresponding calculated energy d i s t r i b u -t i o n , folded with the response function of the detectors. The t h e o r e t i c a l curve represented by the s o l i d l i n e i n the fi g u r e was computed using a 17 MeV cut-off on the energy of each y-ray, and was normalized to our data. The agreement between experiment and theory i s , i n t h i s case, p a r t i c u l a r l y good. For 0 ^ 1 2 0 ° , the conventional nuclear model developed by YY C h r i s t i l l i n and Ericson seems thus to reproduce quite well the energy 12 dependance of the emitted photons i n the C(TT , 2y) reaction. Moreover, i f one disregards the experimental r e s u l t s obtained at the large opening angles, the shape of th e i r 2y angular d i s t r i b u t i o n i s i n q u a l i t a t i v e l y good agreement with ours. Consequently, i f the enhancement observed at the wide angles i s r e a l l y due to hydrogen contamination i n the target, one could then assume that the (TT-, 2y) process i n carbon can be f a i r l y w e l l understood v i a a conventional nuclear p i c t u r e . Otherwise, new features would have to be added to the t h e o r e t i c a l model of C h r i s t i l l i n and Ericson i n order to account for the "anomalous" photon angular c o r r e l a t i o n at the backward d i r e c t i o n . 106 12 C(TT .2K) 0 W = 120° 20 50 80 110 U0 PHOTON ENERGY (MeV) Photon energy d i s t r i b u t i o n at 0 = 120 . The s o l i d curve i s the normalized energy d i s t r i b u t i o n calculated by C h r i s t i l l i n and Ericson assuming a 17 MeV cu t - o f f . The histogram i s the average y-ray energy spectrum of TINA and MINA. 107 Chapter 7 Conclusion In l i g h t of the recent experimental and t h e o r e t i c a l r e s u l t s presented i n the previous chapter, the s i t u a t i o n regarding the doubly r a d i a t i v e pion capture i n carbon can be summarized as following. Our experimental r e s u l t s together with those obtained by the Louvain group have shown that the (IT , 2Y) process i n n u c l e i e x i s t s at a l e v e l of about 10 that i s , s l i g h t l y larger than the o r i g i n a l predic-t i o n of Ericson and Wilkin (~5x 10 ^ ) . The pion capture schedule i s now known to play an important r o l e i n determining d e t a i l s of t h i s process. While the capture from an S-state i s p a r t i c u l a r l y s e n s i t i v e to pio n i c e f f e c t s ( a n n i h i l a t i o n diagram), the P-wave capture i s dominated by the 12 pion bremsstrahlung of r a d i a t i v e capture. In the p a r t i c u l a r case of C, most of the absorption takes place from the atomic 2P state and therefore, the bremsstrahlung mechanism makes the la r g e s t contribution to the t o t a l 12 2y rate. As a consequence, the C(TT ,2y) reaction cannot be used as a t o o l f o r probing d i r e c t l y the nuclear pion f i e l d . The i n v e s t i g a t i o n of the 4 (TT ,2y) process i n very l i g h t n u c l e i , He f o r example, would be more l i k e -l y to provide such information since the capture of the pion occurs mainly from an S-state. Unfortunately, an experiment that would search f o r t h i s process i n gas or l i q u i d targets would be rather d i f f i c u l t to carry out. The good energy r e s o l u t i o n obtained with the Nal c r y s t a l s has permitted us to investigate the energy-sharing between the two photons at an opening angle 0 = 120°. The y-xay energy spectrum of the 2y events 108 was observed to exhibit an equal energy dip c h a r a c t e r i s t i c of nuclear structure e f f e c t s , whereas the sum-energy d i s t r i b u t i o n was found to be well peaked near 120 MeV, i n d i c a t i n g that the r e s i d u a l nucleus, most 12 12 -l i k e l y B, i s not highly excited through the C(ir ,2y) react i o n . The energy dependance of the photons i n t h i s reaction has also indicated the high s e n s i t i v i t y of the t o t a l 2y emission rate to the low-energy threshold of the detectors. The r e a l i s t i c t h e o r e t i c a l model developed by C h r i s t i l l i n and Ericson assuming no anomaly i n the nuclear pion f i e l d has been success-f u l i n reproducing the photon energy d i s t r i b u t i o n at 120°. Despite a discrepancy of about 30% i n the value of the t o t a l branching r a t i o f o r 12 the C(TT ,2y) reaction, the shape of the two-photon angular d i s t r i b u -t i o n f o r opening angles 0 ^ <: 120 , i s also found to be i n q u a l i t a t i v e l y good agreement with our measurements. At the large opening angles, the r i s e i n our experimental angular d i s t r i b u t i o n can probably be accounted for by the presence of some hydrogen contamination in s i d e the carbon target. As pointed out by C h r i s t i l l i n and Ericson (1979), a p r e f e r e n t i a l enhancement i n the backward d i r e c t i o n of the TT "TT +" a n n i h i l a t i o n mechan-ism due to possible pion precondensation e f f e c t s i s u n l i k e l y since these 2 2 would be expected to occur at larger momentum transfers (q - 2m^  , Ericson and Delorme 1978). Before assessing the v a l i d i t y of the conventional approach used by C h r i s t i l l i n and Ericson to describe the doubly r a d i a t i v e pion capture 12 i n C, i t would be i n t e r e s t i n g to c l a r i f y beyond doubt the question of the r i s e at large angles i n the experimental 2y angular d i s t r i b u t i o n . 109 BIBLIOGRAPHY A. I. Akhiezer and V.B. B e r e t e t s k i i , Quantum electrodynamics, Interscience Publishers, New-York - London - Sydney (1965). S. Barshay, Phys. L e t t . 78 B, 384 (1978). B. Bassalleck et a l . , Phys. Rev. C 1_6 , 1526 (1977). D. Beder, TT p'-»- YYN a t threshold, U n i v e r s i t y of B r i t i s h Columbia preprint, (1978). D. Beder, Nucl. Phys. B 156 , 482 (1979a). D. Beder, Radiative TT - capture from L=l states, contributed paper to the 8^ International Conference on High Energy Physics and Nuclear Structure (Vancouver, 1979b). J.A. B i s t i r l i c h et a l . , Phys. Rev. C _5 , 1867 (1972). M. Chabre et a l . , Phys. L e t t . _5 , 67 (1963). P. C h r i s t i l l i n and T.E.O, Ericson, CERN preprint TH2694 (1979) and con-tributed paper to the 8 International Conference on High Energy Physics and Nuclear Structure (Vancouver, 1979). H. Davies et a l . , Nucl. Phys. 78. C, 673 (1966). J. Deutsch et a l . , Phys. L e t t . 79^  B, 347 (1979). M. Ericson and J . Delorme, Phys. L e t t . 76. B, 182, (1978). T.E.O. Ericson and C. Wilkin, Phys. L e t t . _5_7 B, 345 (1975). R. Hartmann et a l . , Nucl. Phys. A 300 , 345 (1978). D.W Joseph, Nuovo Cimento, 1_6 , 997 (1960). N. K r o l l and W. Wada, Phys. Rev. 98 , 1355 (1955). W.C. Lam et a l . , Phys. Rev., C 10 , 72 (1974). A.B. Migdal, Zh. Eksp. Teor. F i z . , 61_ , 2210 (1971) and Sov. Phys., JETP, 34 , 1184 (1972). M.E. Nordberg et a l . , Phys.Rev. 165 , 1096 (1968). . 110 E.M. Nyman and M. Rho, Nucl. Phys., A 287 , 390 (1977). V.I. Petrukhin and Yu.D. Prokoshkin, Nucl. Phys., 54 , 414 (1964). P.L. Roberson et a l . , Phys. L e t t . , 70 B, 35 (1977). J. Spuller et a l . , Ph.D thes i s , U n i v e r s i t y of B r i t i s h Columbia (1977) and Phys. Rev. L e t t . , 67 B, 479 (1977). H. Yukawa, Proceedings of the Physico- Mathematical Society of Japan, 1_7 , 48 (1935). 

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