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A measurement of the Panofsky ratio in helium-3 Corriveau, François 1977

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1 A MEASUREMENT OF THE PANOFSKY RATIO IN HELIUM-3 by FRANCOIS CORRIVEAU B.Sc, University Laval, 1975 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 thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1977 (c) Francois Corriveau, 1977 In presenting th is thes is in p a 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 s h a l l make i t f r ee ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i ca t ion of th is thes is for f inanc ia l gain sha l l not be allowed without my wri t ten permission. PHYSICS Department of ' The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date i ABSTRACT The Panofsky r a t i o i n 3He, P3=a)(TT~3He->3HiT0)/u(Tr~3He^3HY) , has been measured experimentally for absorption of negative piohs at r e s t . _ 3 A 30 MeV TT beam was degraded and stopped i n a 1.9 cm thick l i q u i d He target. The high-energy photons, from the i n f l i g h t TT°-^ YY decay and the r a d i a t i v e capture channels, were detected by a large Nal(Tl) c r y s t a l (46 cm (j) x 51 cm). The large distance (2.8 meters) between the c r y s t a l and the helium target provided a good t i m e - o f - f l i g h t s e l e c t i o n of the photons, with a n e g l i g i b l e neutron contamination. A 4.5% r e s o l u t i o n at 135.8 MeV was achieved by the detector and made possible a good separation between the r a d i a t i v e break-up channels (dny + pnny) and the peak of 3 5 in t e r e s t ( Hy)• About 1.1 x 10 photon events were observed i n the data presented i n t h i s work. Af t e r subtraction of the target empty backgrounds, the t h e o r e t i c a l l i n e shapes were folded with the experimental energy r e s o l u t i o n and f i t t e d to the data. The Amado model was used to represent the break-up channels and thus extract the Panofsky r a t i o . A value of P^ = 2.83 ± 0.07 was 3 determined, not including the i n f l i g h t corrections and assuming f or He the i n t e r n a l conversion rate of hydrogen. A general p i c t u r e of the r a d i a t i v e pion capture processes i n 3 3 n u c l e i i s also given, i n which •.i-itHeKt i s a test case for the impulse approximation and the hypothesis of p a r t i a l conservation of axial - v e c t o r current i n n u c l e i . Moreover, a second r a t i o , B^, between the r a d i a t i v e capture pro-cesses ( r a t i o of the break-up channels to the e l a s t i c channel) has been measured to be' Bt. = 1.35 ± 0.11. i i TABLE OF CONTENTS ABSTRACT TABLE OF CONTENT LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENT < CHAPTER 1 INTRODUCTION 1.1 Stopped pion absorption .1 Hydrogen .2 Deuterium .3 A > 2 Nuclei 1.2 Heli u m ^ .1 ir Capture Processes ^ ,2 The Eanofsky Ratio i n He .3 Radiative Break-up 1.3 Previous Results CHAPTER 2 THE EXPERIMENT 2.1 The Pion Beam 2.2 The Helium Target 2.3 Equipment .1 Set-up .2 E l e c t r o n i c s 2.4 The Nal c r y s t a l CHAPTER 3 SPECTRA 3.1 The Time Spectra .1 The RF signal .2 Time-of-flight 3.2 The "T2 neutron" Contamination .1 Helium-3 Runs .2 Background and Contamination 3.3 Raw Spectra .1 Cuts on time .2 Energy Spectra .3 Random Events 3.4 Scalers i i i Page CHAPTER 4 DATA ANALYSIS 4.1 Target Empty Run .1 Estimates f o r each kind of background 50 .2 T2 Neutron Background Normalization 53 .3 Empty Target Background Normalization 57 4.2 F i t t i n g of the Spectra 59 .1 Low-Energy Background^ 60 .2 Lines from the IT + He Reactions 65 .3 The 4-line F i t s 66 4.3 Error Processing and Panofsky. Ratio Calculation70 .1 Corrections and Sources of Errors 70 .2 The Panofsky Ratio - P 3 78 .3 The Ratio B 3 83 CHAPTER 5 CONCLUSIONS 5.1 Absolute Rates 85 5.2 Delayed Events 86 5.3 The Future of the Panofsky Ratio 87 BIBLIOGRAPHY 90 i v LIST OF TABLES Page 3 Table I Experimental branching r a t i o s f o r IT capture on He . 13 Table II Fr a c t i o n of the photons missed by the TOF cuts 43 Table I I I Random and photon counting rates 48 Table IV Scalers for the experiment ........ ..... 49 Table V Extrapolation method f or T2 neutrons 54 Table VI Evaluation of errors involved i n the T2 neutron background with respect to the target empty run 56 Table VII Normalization f a c t o r s f o r the target empty background 58 Table VIII Comparison of reduced chi-squares f o r electron f i t s between 17 and 79 MeV for run #164 64 Table IX Description of the f i t s f o r the f i v e runs 69 Table X Example of error and c a l c u l a t i o n procedures 71 Table XI Sum i n each capture channel f o r each run ............ 77 Table XII External conversion c o r r e c t i v e factors 80 Table XIII Individual Panof sky r a t i o s for each run . .... 81 Table XIV Individual r a d i a t i v e r a t i o s for each run 83 Table XV Summary of experimental and t h e o r e t i c a l r a t i o s ...... 88 V LIST OF FIGURES Page Figure (1.1) Radiative capture spectra i n helium 5 Figure (1.2) Pole model diagram for r a d i a t i v e TT capture 12 Figure (2.1.1) Lay-out of the M9 channel 16 Figure (2.3.1) Lay-out of the target area and cross-section of the helium target .... 19 Figure (2.3.2) Diagram of the e l e c t r o n i c s 22 Figure (2.4.1) 129 MeV photon from n-y coincidence ............. 26 Figure (2.4.2) Nal timing response i n run 168 28 Figure (3.1.1) Time of f l i g h t f o r beam p a r t i c l e s • 31 • Figure (3.1.2) Time-of-flight separation i n run 169 33 Figure (3.1.3) . Energy spectra f o r various time cuts 34 Figure (3.2.1) Time-energy d i s t r i b u t i o n of neutral events from a p a r t i a l He run (#169) .......... 36 Figure (3.2.2) Contour pl o t of f i g u r e (3.2.1) 3 7 Figure (3.2.3) Detailed contour pl o t f o r photon events i n run 168 38 Figure (3.2.4) Time-energy d i s t r i b u t i o n of events from the target empty run 40 Figure (3.2.5) Contour pl o t of f i g u r e (3.2.4) 41 Figure (3.3.1) Raw photon spectrum of run 169 46 Figure (3.3.2) Gainshifted photon spectrum of run 169 — . . 47 Figure (4.1.1) Target empty photon spectrum • 51 Figure (4.2.1) Time-energy d i s t r i b u t i o n of electrons f o r a p a r t i a l He run (#169) . . 61 v i Page Figure (4.2.2) Electron energy spectrum for run 164 ' 63 Figure (4.2.3) F i t of run 169 a f t e r subtraction of the backgrounds ..................................... 67 Figure (4.2.4) Contributions to the f i t of fi g u r e (4.2.3) 68 Figure (5.3) Values of the Panofsky r a t i o i n helium-3 88 v i i ACKNOWLEDGEMENTS Je tiens a exprimer ma viv e reconnaissance au professeur Michael D. Hasinoff pour l ' a i d e et 1 1 encouragement patient q u ' i l m'a apport^s l o r s de l a preparation et de l a redaction de cette these. Je remercie auss i tout spfacialement l e professeur D.F. Measday et l e docteur J.E. Spuller pour de nombreux entretiens au cours desquels i l s ont su m'6ciairer sur l e s v e r i t a b l e s problemes de 1'experience et m'en f a i r e appr£cier l a s i g n i f i c a t i o n physique. Que l e s autres membres du groupe, D. Berghofer, T. Suzuki et l e s docteurs R. MacDonald, J-M. Poutissou, R. Poutissou et M. Salomon, qui par leur temps et leur t r a v a i l ont rendu possible l e succes de cette experience trouvent i c i leur j u s t e part de m£rite et soient remerci£s de cet inappreciable apport. Je suis dgalement reconnaissant au c o n s e i l n a t i o n a l de recherche du Canada pour son appui f i n a n c i e r au cours de ces deux ann£es d'dtudes a Vancouver. 1 Chapter 1 Introduction §1.1 Stopped Pion Absorption Negative pions brought to r e s t i n a material are generally captu-red by an atomic system i n a large quantum number state to form pionic atoms. The pioris then quickly cascade down by X-ray or Auger electron emission to lower l e v e l s from which they i n t e r a c t with the nucleus. In the case of a molecular target, molecular pionic states may e x i s t but they are very u n l i k e l y because of the small o r b i t a l radius required by the mass of the pion. Moreover, i t has been observed that when d i f f e r e n t atoms enter i n the composition of a molecule, there i s a p r e f e r e n t i a l capture by heavier atoms. This process has been measured for example [see J.A. B i s t i r -l i c h et a l . , 1972] i n hydrogenous compounds on the basis of the charge-exchange r e a c t i o n TT p TT°n which i s suppressed i n most atoms except hydro-gen and helium-3: the decrease of t h i s rate with respect to pure hydrogen i s a d i r e c t i n d i c a t i o n of the e f f e c t . Pion absorption occurs mainly from 3s and 4s o r b i t s f o r hydrogen isotopes [M. Leon and H.A. Bethe, 1962], Is and 2p o r b i t s f o r other low-mass n u c l e i but contributions from higher o r b i t s become more and more im-portant as A increases. Because the cascade time and absorption time -12 ( ^10 sec) IH.W. Baer et a l . , 1977] are much smaller than the mean-life —8 time of the free pion (2.6 x 10 sec), most of the stopped pions are absorbed. 2 §1.1.1 Hydrogen The simplest and l o g i c a l f i r s t choice of target f or the study of stopped pion reactions with n u c l e i i s hydrogen. The absorption from the ns o r b i t s proceeds e s s e n t i a l l y through two channels: IT + p -> n + TT° charge-exchange TT + p -> n + y r a d i a t i v e capture The r a d i a t i v e capture re a c t i o n was one of the f i r s t methods used to deter-mine the mass of the pion. The neutral pion from the charge-exchange —16 r e a c t i o n decays mainly i n two photons ( T - 10 sec). In 1951, Panofsky et a l . [W.K.H. Panofsky et a l . , 1951] f i r s t measured the r a t i o P^ of the rates of the strong i n t e r a c t i o n to the electromagnetic i n t e r a c t i o n : o)(ir p -»• mr°) P l =  to (IT p ny ) They were followed by many other experimenters. Among these r e s u l t s , the l a s t two best determinations of the r a t i o were done by Cocconi et a l . [V.T. Cocconi et a l . , 1961] and Spuller et a l . [J.E. Spuller et a l . , 1977] who found 1.533 ± 0.021 and 1.546 ± 0.009'respectively, both using a Nal(Tl) photon spectrometer method. Anderson and Fermi [H.L. Anderson and F. Fermi, 1952] showed that a l i n k e x i s t s between the lew^energy-pien-reactions ( i . e . s c a t t e r i n g lengths) and the pion photoproduction amplitude at threshold. The experi-mental Panofsky r a t i o can therefore be used as a tes t of the charge inde-pendence p r i n c i p l e of the strong i n t e r a c t i o n , the d e t a i l e d balance hypothe-s i s f o r time-reversed reactions and procedures of extrapolation at zero energy. 3 §1.1.2 Deuterium In deuterium, the charge-exchange re a c t i o n proceeds by the emission of the neutrons and a TT°. For negative pions (odd p a r i t y ) captured from the ns o r b i t s , the P a u l i p r i n c i p l e requires that the two 3 neutrons be emitted i n an antisymmetric state, i . e . i n a P state and therefore the TT° must be emitted i n a p-wave to conserve spin and p a r i t y . Since the ir° has a k i n e t i c energy of only 1 MeV, the r e a c t i o n i s g r e a t l y suppressed ( r e l a t i v e to hydrogen, where the ir° has 2.9 MeV and i s emitted i n an s-wave. On the basis of the low binding energy of the nucleus, the impulse approximation and the Panofsky r a t i o i n hydrogen were used to obtain further r e l a t i o n s h i p s between the low-energy pion reactions. The r a d i a t i v e capture r e a c t i o n also represents a two-neutron system for which the n-n scattering length (a ) could be derived i n the approximation of the low momentum di f f e r e n c e between the neutrons. This approximation i s based on the experimental observation that the photons are sharply peaked towards high energies. §1.1,3 A > 2 Nuclei 3 For n u c l e i heavier than He, charge exchange appears to be sup-pressed even when i t i s e n e r g e t i c a l l y allowed. There are also many more possible channels open for the pion i n t e r a c t i o n , with the possible ej e c t i o r of one or more nucleons. The r a d i a t i v e capture r e a c t i o n has a p r o b a b i l i t y of about 2% for the medium-mass n u c l e i i n comparison with 39.5% for hydro-gen [V.T. Cocconi et a l . , 1961], 24.7% for deuterium [J.W. Ryan, 1963] and 4 14.0% f o r JHe I P . Truol et a l . , 1974]. The existence of r a d i a t i v e capture processes i n complex n u c l e i o f f e r s the p o s s i b i l i t y of considering the pion i n t e r a c t i o n with a proton side of the nucleus rather than with the nucleus as a whole. The study of photon spectra, f o r which the experimental energy r e s o l u t i o n i s f a r better than for the neutrons, represents a way of investigationg both the nuclear structure and the mechanisms of pion absorption. For high-resolution detectors, such as the pair spectrometer used at the Lawrence Berkeley Laboratory [J.A. B i s t i r l i c h et a l . , 1972; H.W. Baer et a l . , 1973], which has a 2.0 MeV (FWHM) r e s o l u t i o n , i t i s also possible to study the excited states of the r e s i d u a l n u c l e i i n r a d i a t i v e capture reactions and test the p a r t i a l conservation of a x i a l vector current (PCAC) i n the soft pion l i m i t . 4 Such e x c i t a t i o n s have been studied i n He. The spectrum obtained 4 by B i s t i r l i c h et a l . for r a d i a t i v e capture i n He was well reproduced [J.A. B i s t i r l i c h et a l . , 1970] by assuming the existence of three excited states whose posit i o n s are i n agreement with 4-nucleon system phase-shift analyses. Their calculated curve, folded with the r e s o l u t i o n of t h e i r detector (but with t h e i r e f f i c i e n c y factor removed) i s shown i n f i g u r e ( l . l a ) f o r purpose of understanding the sources of background involved i n our experiment. A general review of r a d i a t i v e pion capture has been given recently by H.W. Baer, K.M. Crowe and P. Trub"l [1977]. 5 Figure (1.1) RADIATIVE CAPTURE SPECTRA IN HELIUM I : 1 1 1 : 1 (a) 4 He(iT ,y) >— cr. CE cr. cn CY. CE (b) 3HeOT,Y) TT° photons break-up 135.8. MeV 0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 m He; the theore-PHOTON ENERGY (MEV) Figure (1.1) . Radiative capture spectra i n helium. (a) t i c a l curve, folded with the r e s o l u t i o n of t h e i r detector, i s from J.A. B i s -t i r l i c h et al.[1970].. (b) i n He; the break-up channels are represented by the Amado model [A.C. P h i l l i p s and F. Roig, 1974]. 6 §1.2 Helium-3 3 The He nucleus, the subject of the present experimental work, represents a l i n k between the simplest basic n u c l e i (H and D) and more complex ones and i s therefore a test case for the a p p l i c a t i o n of the impulse approximation (IA). This i s also the only other nucleus, i n addition to hydrogen, for which the charge-exchange rea c t i o n i s known to occur s i g n i f i c a n t l y and for which the r a d i a t i v e y i e l d i s s t i l l important, even with the presence of non-radiative break-up channels. Moreover, a l l the processes r e s u l t i n g from pion absorption have been observed for t h i s 3-nucleon system: t h i s i s e s p e c i a l l y h e l p f u l i n order to get a coherent pi c t u r e of the system and t b s t e s t i t h e v a l i d i t y of i t s t h e o r e t i c a l d e s c r i p t i o n s . §1.2.1 TT Capture Processes The following channels are allowed by the conservation laws f o r 3 the capture of negative pions at r e s t i n He: charge-exchange (1) e l a s t i c r a d i a t i v e capture (2) (3) } r a d i a t i v e break-up (4) (5) } absorption (6) TT + He -> - ^ 3„ TT + He -> 3 ir + He + TT~ + 3He iT + 3He -»-TT" + 3He -> 3H, + ^° 3H + y 3 F + n + Y p + n + n + Y d + n p + n + n 7 The neutral pion emitted i n the charge-exchange r e a c t i o n has a k i n e t i c energy of 3.89 MeV from the d i f f e r e n c e i n masses, l e s s the binding energy of the TT i n the K - s h e l l (0.016 MeV). The TT° decays with a mean-l i f e of 0.83 x 10 ^ sec. The main decay modes are [ P a r t i c l e Data Group, 1976] : TT° + y Y (98.85 ± 0.05 %) (a) TT° -> Y e + e" ( 1.15 ± 0.05 %) (b) The other modes, including TT° -»- e +e e +e , are at l e a s t four orders of magnitude lower i n p r o b a n i l i t y than the predominant YY mode and are there-fore neglected here. The photons from the two main channels are emitted i s o t r o p i c a l l y i n the center of mass of the TT°, but as the TT° has a v e l o c i t y v = 0.24 c, they are Doppler-shifted i n the laboratory frame to y i e l d a uniform energy d i s t r i b u t i o n between the two l i m i t s , given by 2 m0c E =[., | Y ( i ± e ) where B = v/c, c i s the speed of l i g h t Y = l//(l-.{3 2) m 0c 2 = 134.96 MeV, mass of the TT°. i . e . 53.1 and 85.7 MeV for 3He. 3 The e l a s t i c Hy channel y i e l d s a high-energy gamma-ray at 135.8 MeV while the endpoints f o r the two other r a d i a t i v e capture processes are 129.8 and 127.7 MeV for reactions (3) and (4), r e s p e c t i v e l y . One further p o s s i b i l i t y , the i n t e r n a l conversion of the photon from re a c t i o n (2), has to be considered. For hydrogen, the p r o b a b i l i t y (O(TT p->ne+e )/CO(TT p-*ny) has been calculated to be about 1% by Joseph [D.W. Joseph, 1960], but t h i s 3 rate i s not known for He. 8 §1.2.2 The Panofsky Ratio i n ^ He 3 The Panofsky r a t i o P^ i n He i s defined the same way as i t i s i n hydrogen, i . e . the r a t i o of the strong i n t e r a c t i o n to the electromagnetic i n t e r a c t i o n ; however, the i n t e r n a l conversion process i s usually not 3 included f o r He: _„ „ CO(TT He -*• HTT°) (1) p. = = 3 a ) ( T r" 3He + 3Hy ) (2) There have been, to t h i s time, two experimental determinations of t h i s number. 3 Zaimidoroga et a l . [O.A. Zaimidoroga et a l . , 1965] used an He d i f f u s i o n chamber operated at pressures of 17.5 and 6.5 atm. to observe 3 the r e c o i l t r i t o n . In the r a d i a t i v e capture r e a c t i o n (2) the H energy 3 i s 3.28 MeV but i n the charge-exchange reaction(1) the H energy i s only 0.19 MeV. For consistency, because of the r e s u l t i n g short tracks, they determined P^ at d i f f e r e n t pressures. Their measurements yielded P 3 = 2.28 ± 0.18 Trub'l et a l . [P. Truo'l et a l . , 1974] repeated the experiment using a 180° pair spectrometer with a r e s o l u t i o n of 2.0 MeV (FWHM) at 129.4 MeV, providing a good separation of the break-up channels and the e l a s t i c peak i n the photon spectrum. The e f f i c i e n c y of t h e i r detector was low i n the charge-exchange region and very s e n s i t i v e to the spark 3 chamber performance, so that they ran the l i q u i d He target interchangea-bly with a hydrogen target, f o r which the Panofsky r a t i o P^ was already well known. They measured a value, P^ =2.68 ± 0.13, with which they presented an impulse approximation c a l c u l a t i o n . This a n a l y s i s , based on 9 the assumption by Ericson and Figureau [M. Ericson and A. Figureau, 1967] that the r a d i a t i v e capture comes mostly from the Is state of the TT , involves a renormalized Panofsky r a t i o f o r hydrogen; but as t h i s theore-t i c a l value was also used i n t h e i r experimental determination of P^, the comparison of the calculated value of 2.49 with t h e i r measured value 2.68 ± 0.13 was considered as a d i r e c t test of the IA c a l c u l a t i o n . Following t h i s paper, another impulse approximation c a l c u l a t i o n was done by P h i l l i p s and Roig [A.C. P h i l l i p s and F. Roig,1974]. In t h i s a n a l y s i s , d i f f e r e n t percentages of S' and D states were postulated for the 3-nucleon wave functions. A f t e r corrections for capture from the 2p TT state, values of P^ obtained for d i f f e r e n t p a i r s of S',D p r o b a b i l i -t i e s 1(1.8%,0%), 11(1.6%,5%) and 111(1.4%,9%) were 2.51, 2.79 and 2.98, r e s p e c t i v e l y . The advantage of using the r a t i o of the two capture rates i s that the uncertainty of the i n i t i a l state i n t e r a c t i o n applies to both channels and can be neglected i n P^. They estimated that the corrections to these c a l c u l a t i o n s would be of the same order as the e f f e c t s of the v i r t u a l meson i n t e r a c t i o n i n the IA c a l c u l a t i o n f or the B-decay of t r i t i u m , i . e . between.0% and 12%, i n agreement with Truol's value. Other IA c a l c u l a t i o n s have been performed by Mizuta et a l . [M. Mizuta et al.., 1975], y i e l d i n g a 2.63-3.06 range for the value of the Panofsky r a t i o . The p a r t i a l conservation of axi a l - v e c t o r current (PCAC) approach has also been used to determine t h e o r e t i c a l l y the Panofsky r a t i o [see M. Erieson-,and A. Figureau, 1967, 1969; M.Ericson and M. Rho, 1972]. This hypothesis originates from the a p p l i c a t i o n of weak i n t e r a c t i o n to 10 the strong i n t e r a c t i o n . The vector part of the hadronic current of the weak i n t e r a c t i o n i s conserved, but the a x i a l part cannot be, as the mass of the pion, for the pion decay, would have to be zero, thus the idea of p a r t i a l conservation from a small c o r r e c t i o n to t h i s coupling constant. Using the s i m i l a r i t i e s with the weak i n t e r a c t i o n i n u capture [A. F u j i i and D.J. H a l l , 1961], the IT capture i s considered, i n the soft-pion l i m i t , as the inverse of low-energy photoproduction. Both i n i t i a l and f i n a l n u c l e i are treated as elementary p a r t i c l e s . Results obtained by these methods, a f t e r c o r r e c t i o n f o r the p-meson exhange (from t h e i r = 2.70 value [1967]), are 1.9 and 2.1, depending on the method (IA or soft-pion) used to c a l c u l a t e the charge-exchange cross-section. The goal of t h i s experiment was to redetermine the Panofsky r a t i o 3 i n He with a 100% e f f i c i e n t Nal detector which would reduce the experimen-t a l error i n the charge-exchange energy region and hopefully improve the accuracy of the r a t i o i t s e l f . Since theatwo e x i s t i n g values disagree by considerably more than t h e i r quoted errors, a t h i r d accurate measurement should allow one of the early measurements to be reje c t e d . 11 §1.2.3 Radiative Break-up Due to the overlap of the charge-exchange and the elastic radia-tive capture channels with the break-up channels, especially after folding in the experimental Nal resolution, a good knowledge of a l l line shapes is necessary to ascertain their respective contributions. In the Amado model [R.D. Amado, 1963], the f i n a l 3-nucleon state 1 3 comes as a solution of the Faddeev equations in which separable SQ and S^ 2- nucleon interactions are assumed. In these states, one considers a "pair of nucleons with respect to the third nucleon. Both states imply a zero orbital angular momentum between the third nucleon and the pair i t s e l f , but in the f i r s t case the spins of the nucleons of the pair are anti-parallel while they are parallel in the second case. Phi l l i p s and Roig [A.C. P h i l l i p s and F. Roig, 1974] used this model to calculate the relative rates for the break-up and elastic channels and to obtain the shape of the photon energy spectrum. A comparison with experimental data of Truolet a l . [1974] shows a good agreement in the absolute rate and the energy d i s t r i -bution (through the ratios and shape). However, for energies below M.10 MeV, the agreement i s poor due to the off-shell .part df the interaction (i.e. the conservation of energy and momentum i s momentarily broken). The good f i t in the high-energy region does not yield, moreover, any evidence of a 3- nucleon resonance. A general approach for the radiative break-up channels has also been developed by Dakhno and Prokoshkin [L.G. Dakhno and Yu.D. Prokoshkin, 1968]. This"pole-model" (figure 1.2) involves the capture of a negative pion by a quasi-free proton inside of the nucleus. This model seems to provide a much better description of the photon continuum than the Fermi-gas model 12 or a simple phase-space distribution. It was used by Bistirlich et a l . [J.A. Bistirlich et al., 1972], in conjunction with excited states of the final nucleus, to describe the photon spectra for ir absorption on nuclei with 5<A<41. However, there are s t i l l important uncertainties in the know-ledge of i n i t i a l - and final-state interaction between particles or groups of particles involved in the description. Figure (1.2) Pole model diagram for radiative TT capture with neutron emissioni:n neutroa emission. No pole-model calculation was available to us at the time of this work, but the results of such a calculation were presented in 1974 by Truol et al., along with their experimental spectrum. Although a comparison between the information obtained using both the pole model and the Amado model would have been preferable to illustrate the model-dependent effects in the determination of P^ , the Amado model described by Phillips and Roig was used in this analysis. It provided a very good f i t to the data in the high-energy region. The individual and summed shapes of the break-up channels are shown in figure (1.1b) together with the charge-exchange and elastic radiative capture spectral functions. The low-energy part of the radiative break-up channel (<90 MeV) is an extrapolation by the polynomial method described in section (4.2.1) from the data in the 90-120 MeV region. Further comments on this choice will be given later in the analysis. In relation to these radiative break-up channels, another ratio, BQ, is defined between the radiative capture channels, namely the ratio of 13 the two break-up channels rate to the rate for e l a s t i c capture at 135.8 MeV, as a useful parameter of the 3-nucleon f i n a l states. -3 -3 (3) + (4) O)(TT He dny) + CO(TT He -> pnny) 3 (2) w(Tr" 3He -> 3Hy) Depending on the S' and D contributions i n the 3-nucleon wave function, P h i l l i p s and.Roig obtained values f o r B 3 of 0.84(1), 1.10(11) and 1.27(111) (see l a s t s e c t i o n ) . §1.3 Previous Results Table I summarizes previous experimental r e s u l t s f o r the d i f f e r e n t 3 branching r a t i o s f o r TT' absorption i n He. 3 Table I Experimental branching r a t i o s f o r TT capture on He F i n a l state Zaimidoroga et a l . Trub'l et a l . 11965, 1967] [1974] (1) 3HTT° 15.8 ±0.8 17.8 ± 2.3 (2) 3 H Y 6.9 ± 0.5 6.6 ± 0.8 (3) dny 3.6 ± 1.2 (4) pnny (5) dn • 15:9?± 2.?3i (6) pnn 57.8 ± 5.4 } 7.4 ± 1.0 } 68.2 ± 2.6 P 3 = (l)/(2) 2.28 ± 0.18 2.68 ± 0.13 B 3 = [(3)+(4)]/(2) 1.12 ± 0.05 14 Chapter 2 The Experiment The Panofsky r a t i o i n helium-3 Is defined as the r a t i o of the - 3 3 t r a n s i t i o n rate of the charge-exchange reaction TT + He -> H+TT° over the - 3 3 rate of the radiative, capture re a c t i o n TT + He -> H+y. In order to determine t h i s value experimentally, a beam of negative pions was stopped i n a l i q u i d 3 He target. A large Nal c r y s t a l was used to obtain the energy spectrum of the photons emitted from the target, and they were distinguished from neutrons by a t i m e - o f - f l i g h t technique. Thus, good timing response was required from the detector and, because of the presence of two r a d i a t i v e break-up channels, the energy r e s o l u t i o n of the c r y s t a l was c r i t i c a l as how well a l l the d i f f e r e n t channels would be separated out. This experiment was i n many ways si m i l a r to the very precise re-measurement of the Panofsky r a t i o i n hydrogen done recently by J.E. Spuller i n the same location.and using b a s i c a l l y the same experimental equipment. (See J.E. Spuller, 1977). His energy spectra also exhibited the characte-r i s t i c box from 55 to 83 MeV, i n d i c a t i n g the events due to the charge-exchange rea c t i o n TT +p n + T r ° , as well as a high-energy e l a s t i c peak at 129.5 MeV, from the r a d i a t i v e capture reaction TT +p -»- n+y, but without of course any break-up channel. I s h a l l therefore r e f e r the reader to h i s work for a more d e t a i l e d discussion of some points r e l a t i v e to the equipment and analysis procedures. 15 §2.1 The Pion Beam This experiment was performed i n March 1977 at the T r i - U n i v e r s i t y Meson F a c i l i t y (TRIUMF) Project using i t s stopped ir/y channel (M9) i n the meson h a l l . H ions were accelerated up to 500 MeV by the sector-focussed cyclotron. A change of curvature i n the t r a j e c t o r i e s of the ions was induced when the electrons were stripped off the ions by a t h i n carbon f o i l at an outer radius of revolution.>.The proton beam was extracted t h i s way with an e f f i c i e n c y of almost 100% along the beam l i n e 1 (BL1). The proton current i n t h i s l i n e during the corse of the experiment varied between 12 t y p i c a l l y 3 and lOuA, i . e . a f l u x of about from 20 to 60 x 10 protons/sec. At the end of the l i n e the protons were focussed onto a 10 cm Beryllium target (T2), which produced a r e l a t i v e l y large number of negative pions per incident proton. A secondary pion beam was taken at a 135° backward angle with respect to the incident proton beam, as can be seen on f i g u r e (2.1.1). This M9 channel was composed of a succession of f i v e quadrupole magnets and two bending magnets as shown on the diagram. The helium-3 target was positioned at the second focus for t h i s channel. A l l the magnets were set to carry a 30 MeV TT beam (96.3 MeV/c). The l a s t d i pole magnet B3, a 30 cm gap cyclotron magnet, was not used i n t h i s experiment but imposed a 30 tons physical constraint to the p o s i t i o n of the Nal detector. Horizontal and v e r t i c a l s l i t s between the two bending magnets Bl 2 and B2 were set to 2 and 10 cm r e s p e s t i v e l y , r e s u l t i n g i n a vLOxlO cm image of the production target at the helium target p o s i t i o n , with a 15% momentum spread associated to the width of the v e r t i c a l s l i t s . Those 17 conditions were not optimal with respect to the dimensions of the '"'He 2 content of the target (^80 cm ), but on the other hand enabled a high beam f l u x of about 5x10'' p a r t i c l e s / s e c . Neutrons were removed from "the beam by the curvature of the channel but contaminations by u and e were s t i l l present (with energies of 37 and 96 MeV r e s p e c t i v e l y ) . It was estimated, from e a r l i e r experiments with the same momentum for the beam p a r t i c l e s that there were about 20% of the par t i c l e s , of the beam which were electrons while the muons represented 6% of them. The macro-duty cycle of the machine i s e s s e n t i a l l y 100%, but the micro-cycle i s of about 7%. This means that the proton beam onto T2 comes i n bursts at each 43.3 nsec for 3.0 nsec at each time. Also a v a i l a b l e for t h i s experiment was a radio-frequency (RF) si g n a l associated with the beam to be used l a t e r i n the a n a l y s i s . §2.2 The Helium Target The l i q u i d helium target used i n t h i s experiment was developed by J.S. Vincent, and W.R. Smith [J.S. Vincent and W.R. Smith, 1974] for either 3 4 He or He scattering experiments. The primary target c e l l was c y l i n d r i c a l i n shape (10.6 cm ())• x 1.905 cm), i t s axis i n the same plane as the channel, thus o f f e r i n g a 80 cm face area. Good thermal s h i e l d i n g was provided by a f i l m of su p e r f l u i d Sle i n the entrance and ex i t double windows (0.0125 cm) of the c e l l . At an operating pressure of about 135 mm Hg, these windows were 3 s l i g h t l y domed to give to the He a c e n t r a l thickness of about 2.0 cm. Lateral"thermal shi e l d i n g was achieved by two concentric copper shields 18 each wrapped with a few layers of 10 microns aluminized sheets. In fi g u r e (2.3.1) i s reproduced a cross-section of the chamber. The two copper shields were the continuation of two re s e r v o i r s located over the target. The external tank was f i l l e d by l i q u i d nitrogen, and the inner one by l i q u i d Ste, bringing the shields to 77°K and 20°K 3 r e s p e c t i v e l y , by conduction. S t i l l i n s i d e , a t h i r d pumped l i q u i d He reser-3 v o i r was connected to the target by an heat exchanger through which He gas i s cryopumped down to the target c e l l . By t h i s system, the heat load of the target was about 10 mW at 2°K. The c e l l i t s e l f was surrounded by a 10 ^  t o r r vacuum i n s i d e another larger chamber with 20 cm diameter double windows on each side. Windows 2 represented an o v e r a l l density of 100 mg/cm while l i q u i d helium-3 averaged 2 3 A 3 120 mg/cm (P3jje = 0-08 g/cm ). The He contamination of the He gas was 1%. For the necessary empty target run, i t was possible to evaporate out only 3 the He content of the target, leaving the mylar windows, adjacent material and the 2 mm of He superfluid s h i e l d i n g f i l m on each side. §2.3 Equipment §2.3.1 Set-up A diagram of the lay-out of the experimental area i s shown i n fi g u r e (2.3.1). Upstream to the helium target was a telescope of three p l a s t i c counters (NE102A) C l , C2 and C3 used to define the beam. The small s i z e of C3 (8.8 cm ensured that the incoming p a r t i c l e s would be directed onto the He content of the 10.6 cm <|> c e l l . The counter C4, located behind the target, was used as a veto counter. The C5 counter, between the front ™ 1 meter i i Lead collimator Lead collimator JHe CH2 C4 Figure (2.3.1) Lay-out of the target area and cross-section of the helium target. The counters C1,C2 and C3 were used to define the beam; C4 was. used as a veto i n the stop d e f i n i t i o n and C5 as a charge i d e n t i f i e r . The S i - L i detector was used by another group for mesic X-ray studies C3 C2 Cl OQ C i-i h-1 ro vo to 20 face of the Nal detector and i t s lead c o l l i m a t o r , was used as a charged p a r t i c l e i d e n t i f i e r . The target was a c t u a l l y rotated by a small angle with respect to the beam d i r e c t i o n ; t h i s was permitted by i t s large viewing angle. This also increased the e f f e c t i v e thickness of the target by about 15% and enabled the two detectors present to view the target as well as possi b l e . The S i - L i detector located at backward angle was used by another group f o r mesic X-rays studies. Our experiment was p a r a s i t i c to t h e i r s and there was no room to have the Nal detector at a large angle with respect to the beam i n order to reduce the background due to simple s c a t t e r i n g e f f e c t s . Consequen-t l y , i t was put at the best a v a i l a b l e p o s i t i o n , i . e . at 14° from the beam axis and with the rear end of i t s 15 cm &) collimator at 280 cm from the center of the target, thus sustending a s o l i d angle of 2.3 mstr. A 2.70 cm thick CH^ degrader was placed i n the beam telescope i n order to stop the negative pions i n the target. No optimization by trans-mission measurements was done concerning the chosen thickness but only a rough estimate was made using the energy losses i n the telescope, the mode-rator i t s e l f , the windows of the target and from the range of negative pions i n helium. I t had been observed i n e a r l i e r experiments of t h i s type [J.E. Spuller, 1977; R. MacDonald, 1977; F. Corriveau, 1977] that with the large (15% FWHM) momentum spread of the beam the stopping d i s t r i b u t i o n i s quite uniform or slowly varying, within the range of the mean energy pions. This i s e s p e c i a l l y true for a t h i n target such as we had i n the present ex-periment so that the exact choice of thickness was of no r e a l concern. Many of the incoming pions, however, could be registered as stops, 3 without stopping i n the He content of the target, but i n the windows, or 21 i n the surface of the veto counter (that i s , not deep enough to f i r e i t ) . An empty target run should correct f o r these e f f e c t s . §2.3.2 E l e c t r o n i c s A diagram of the el e c t r o n i c s used i n t h i s experiment i s shown on fig u r e (2.3.2). The data a c q u i s i t i o n system proceeded i n three steps: i d e n t i f i c a t i o n of an event, on-line processing by a PDP 11/40 computer and recording of the data on magnetic tape. The requirements for an event were Cl.C2.C3.C4.Nal; i . e . a possible stop i n the target associated with a count i n the Nal c r y s t a l . This c o i n c i -dence condition was not stringent enough to r e j e c t beam contaminant associa-ted events but t h i s problem was dealt with i n the o f f - l i n e a n a l y s i s . Indeed, the d e l i b e r a t e l y large (70 nsec) C1.C2.C3.C4 gate was chosen to have a better knowledge of random events over an extended period and proved very useful i n l a t e r a n a l y s i s . The timing of the Nal anode s i g n a l was provided through an ORTEC 463 constant f r a c t i o n d i s c r i m i n a t o r . The event d e f i n i t i o n l o g i c was used both to open a f a s t 250 nsec gate for a LRS 2248" ADC CAMAC module and to s t a r t the clock of the LRS 2228 TDC CAMAC module. The ADC integrated the Nal anode signal as a reading of the k i n e t i c energy deposited i n the c r y s t a l . Three stop signals were recorded by the TDC: the RF timing asso-ciated with the proton beam, the C3 counter and the Nal detector. The time of f l i g h t was defined as the time f i f f e r e n c e between the Nal time s i g n a l and C3, placed j u s t i n front of the target and acting as stop time d e f i n i t i o n . Furthermore, the coincidence buffer r e g i s t e r e d i f the p a r t i c l e entering the c r y s t a l was charged, as the counter C5 would have f i r e d . C5 Charge I d e n t i f i e r Nal a Disc. LRS 621 strobe Coincidence Buffer .node, signals Beam Counters: C4 C3 C2 Cl Fan In LRS 127B Fan Out LRS 128 "BEAM" "STOP" Fast Amp. LRS 133B Disc. LRS 621'BL Const. Frac Disc. ORTEC 463 Disc. LRS 621 1 Logic Unit LRS 465 Atte-tauator gate CAMAC ADC LRS 2249 T 3 Disc. LRS 621 Disc. LRS 621 veto Logic Unit LRS 465 "EVENT" D e f i n i t i o n / k - J Disc. tLRS 621 stop Logic Unit LRS 365 istop start 1 Visual Scaler stop CAMAC TDC LRS 2228 RF signal Cerenkov Monitor Output Register Disc. LRS 621 Fan Out LRS 429 * CAMAC Scalers E l l i o t - S R 1608 4 PDP 11/40 COMPUTER C i-f OJ N3 N3 Figure (2.3.2) Diagram of the e l e c t r o n i c s . 23 To summarize, each event contained the following d i g i t a l information: 1. RF time, with respect to an event s t a r t s i g n a l 2. C3 time 3. Nal time, 4. Nal energy 5. Nal charge b i t pattern (0 or 1) The PDP 11/40 computer cycle started with a LAM from the s t a r t s i g n a l of the TDC. A l l CAMAC modules were then i n h i b i t e d i n order for the computer to read them i n . This was followed by a r e s e t t i n g of the units f or the next event taking. Before enabling the system again, the computer processed the acti v e event by adding i t to d i f f e r e n t time and energy histograms with the p o s s i b i l i t y of imposing cuts on some of the parameters. This on-line ana-l y s i s was e s s e n t i a l i n following the progress of the experiment of gains and gates to the study of energy s h i f t s or background changes due to modi-f i c a t i o n s i n the sh i e l d i n g . buffer also contained the scaler information provided by the CAMAC Scaler ( E l l i o t SR 1608 u n i t s ) , both at the beginning and at the end of the group of 74 events. This procedure was set to minimize the p o s s i b i l i t y of l o s s of information on the d i f f e r e n t count r a t e s . The scale r s were: Up to 74 events were recorded i n a buffer by the computer. Each 1. Cerenkov monitor ^ proportional to p beam i n t e n s i t y 2. C1.C2.C3 beam p a r t i c l e s 3. C1.C2.C3.C4 stops 4. Nal counts i n detector 5. C1.C2.C3.C4.Nal events 6. Real time i n seconds 24 These proved useful on-line and afterwards, i n the o f f - l i n e a n a l y s i s , as a general understanding of experimental conditions and.as f i r s t estimates for the background contributions and the counts ra t e s . F i n a l l y , once f i l l e d , the buffer was transfered d i r e c t l y onto a amgnetic tape, i n c o m p a t i b i l i t y with the o f f - l i n e a n alysis system. §2.4 The Nal C r y s t a l The detector used i n t h i s experiment was a large c y l i n d r i c a l Nal(Tl) c r y s t a l enclosed i n a sealed aluminium can. I t was purchased from the Harshaw Chemical Co. of Cleveland, Ohio, U.S.A. Its diameter i s 45.7 cm. and i t s length 50.8 cm. The detector was e s p e c i a l l y designed for an e f f i -c i e n t detection of photons up to a few hundreds MeV. Due to non-uniformities of the photo-sensitive area of large tubes [M.D. Hasinoff et a l . , 1974], seven RCA 4522 phototubes were used to view the c r y s t a l and t h e i r anode pulses were summed to produce a pulse with a 50 nsec r i s e - t i m e . See J.E. Spuller [1977] for a f u l l d e s c r i p t i o n of the balancing of the tubes with cosmic rays. I t should be noted here that e l e c t r o n i c s h i f t s were obser-ved however, which caused changes i n the energy c a l i b r a t i o n of the spectra. This problem had to be handled afterwards i n the data a n a l y s i s , as w i l l be seen i n chapter 3. Two kinds of information were required from the detector: the time at which the recorded photon reached the c r y s t a l with respect to a stop si g n a l i n the target and the energy of the y-ray. Hence the experiment r e l i e d heavily on the performances of the detector, namely i t s energy and timing responses. 25 The energy response of the Nal c r y s t a l was investigated at the time of the measurement of the Panofsky r a t i o i n hydrogen by J.E. Spuller, with the same apparatus i n three d i f f e r e n t conditions. The l i n e shape was ob-tained experimentally f o r the 129.5 MeV photons of the 7r p ->• ny reaction by demanding a coincidence between the Nal detector and a neutron counter (13 cm <j) x 5 cm NE213 l i q u i d s c i n t i l l a t o r ) placed on e i t h e r side of the target, both at r i g h t angles!torn the TT - beam d i r e c t i o n . Two configurations were used: with a 25 cm $ lead collimator at a distance of 91 cm from the target f o r Run(l) and with a 15 cm i f collimator at 193 cm for Run(2). The FWHM resolutions achieved were of 6.0% and 4.9% res p e c t i v e l y . Both response functions exhibited a c l e a r low-energy t a i l which was also confirmed by looking d i r e c t l y at the mono-energetic 11.7 MeV photons from the n B ( p , Y ) 1 2 C * reaction. The empirical l i n e shape of the above mentioned Run(2) i s reproduced i n f i g u r e (2.4.1). I t was estimated that a f t e r removing the accidental coincidences, l e s s than 0.16% of the response function was below 90 MeV. For the purpose of t h i s experiment, where the r a d i a t i v e break-up channels of the TT 3He reaction have to be separated as well as possible from the r a d i a t i v e capture process at 135.8 MeV, the small 15 cm <j> lead collimator was chosen. Although the energy was s l i g h t l y d i f f e r e n t , i t was assumed that the 129.5 MeV l i n e shape could reproduce the response of the detector i n t h i s experiment, considering the small s h i f t i n energy. This was the l i n e shape used l a t e r f o r the f o l d i n g of the t h e o r e t i c a l energy d i s t r i b u t i o n s . The timing response of the Nal detector f o r t h i s experiment showed that the 135.8 MeV photons were detected with a 1.8 nsec r e s o l u t i o n , compared 26 Figure (2.4.1) P H O T O N - N E U T R O N C O I N C I D E N C E FOR RUN2 3 0 0 2 5 0 2 0 0 CO 150 100 5 0 I" 0 •n 50 7 5 100 1 2 5 150 PHOTON E N E R G Y (MEV) Figure (2.4.1) Response function of the Nal c r y s t a l to 129 MeV mono-energetic photons. The data were obtained by n-y coincidence measurement i n the TT p-Hry rea c t i o n for stopped pions. See [J.E. Spuller, 1977]. 27 to 2.2 nsec for the i r ° photons (53-85 MeV), as i l l u s t r a t e d i n f i g u r e (2.4.2). This good timing r e s o l u t i o n , together with the 280 cm distance of the Nal from the helium target, permitted an e f f i c i e n t a p p l i c a t i o n of the time-of-f l i g h t technique to d i f f e r e n t i a t e between photons and neutrons. The small 1.0 nsec walk from high to low energy was a t t r i b u t e d to the e l e c t r o n i c timing of the constant f r a c t i o n discriminator (ORTEC 463). 28 Figure (2.4.2) N f l l T I M I N G R E S P O N S E IN RUN 1 6 8 0 10 20 30 4 0 5 0 C H A N N E L NUMBER Figure (2.4:2) Nal timing response i n run 168. FWHM resol u t i o n s are given on the graph. The bump at the l e f t of the TT° photons are "T2 neutrons" (see section 3.2). 29 Chapter 3 Spectra The data were d i s t r i b u t e d i n runs, according to changes i n the shield i n g or when more degrader was put i n the beam for the i n v e s t i g a t i o n of mes-ic X-rays from muon stops i n the target. We r e l i e d on the p o s i t i o n of the TT° photons and of the e l a s t i c r a d i a t i v e peak to obtain the energy c a l i -b ration of the spectra. However, t h i s was not possible f o r the empty target run and therefore t h i s run was followed by a run with a s o l i d LiH (9.0 cm x 11.5 cm <j>) target sealed i n a s t a i n l e s s s t e e l can. The 3.7% [J.A. B i s t i r l i c h et a l . , 1972] capture rate on the hydrogen provided a s a t i s f a c t o r y spectrum for c a l i b r a t i o n . The o f f - l i n e a n a l y s i s was c a r r i e d at the U n i v e r s i t y of B r i t i s h Columbia Computing Center. The data magnetic tapes were d i r e c t l y compatible with the IBM 370 system a v a i l a b l e there. A set of FORTRAN programs were written and developed to process and handle the data by means of histograms. This chapter w i l l deal with the experimental r e s u l t s per se, presented i n the form of time and energy spectra. §3.1 The Time Spectra E s s e n t i a l l y two types of time information were a v a i l a b l e through the TDC CAMAC module i n t h i s experiment. Both were used to sort out the events of i n t e r e s t f o r the Panofsky r a t i o measurement. The stop s i g n a l of C3, the counter preceding the target, was used as the reference time of the event. 30 §3.1.1 The RF Signal Associated with each proton burst onto the T2 pion production target was an RF signal that was used to select the stopped pion events in helium. The time difference between this signal and the C3 signal was, within a constant, the time of flight of the negative particles along the 8.4 meters of the M9 channel. The spectra of figure (3.1.1) show how the electrons, muons and pions, a l l having the same 96.3 MeV/c momentum but different speeds are positioned relative to each other. It was therefore easy to check directly from the spectra the length of the channel (or vice-versa) , by simple kinematics. The spectra do not, however, represent a valid estimate of the beam contamination as theysare produced for stopped particle events only and the different thicknesses of the degrader were chosen to stop mostly pions (or muons), as seen on the graphs. The 70 nsec width of the stop gate in the electronics was large enough to include some events related to the next proton burst (43.3 nsec lat e r ) . This provided a means of calibrating the TDC module. In the f i r s t step of the analysis, the RF position of the main pion peak was checked a l l through the corresponding runs because i t was observed that the phase of the RF signal with respect to the proton beam changed during the experiment with different tunings of the cyclotron beam. The extent of the shift was determined for each run and sufficiently large cuts were made on the C3-RF histograms. It was -estimated that less than 0.4% of the total number of neutral events (C5 not fired) were muon associated, which i s negligeable for the purpose of this experiment. Figure (3.1.1) TIME OF FLIGHT FOR BEAM PARTICLES CO 2 5 0 0 2 0 0 0 h 1 5 0 0 ° 1 0 0 0 5 0 0 -0 10000 Q000 6 0 0 0 4 0 0 0 2 0 0 0 h 0 - 2 5 . 0 - 1 5 . 0 - 5 . 0 5 . 0 1 5 . 0 2 5 . 0 3 5 . 0 4 5 . 0 5 5 . 0 6 5 . 0 RELATIVE TIME (NSEC) Figure (3.1.1) Time of f l i g h t for beam p a r t i c l e s i n the M9 channel. The data were obtained f o r stopped p a r t i c l e events only. In a muon run (a), a 5.4 cm thick degrader was i n the beam, compared to 2.70 cm for a pion run (b). This amount of degrader reduces the IT f l u x considerably. 32 §3.1.2 Time-of-flight (TOF) The large distance between the target and the Nal c r y s t a l , i n addi t i o n to the good timing response of the detector, were of great use i n d i s t i n g u i s h i n g photons from neutrons by a simple t i m e - o f - f l i g h t technique. This was e s s e n t i a l i n view of the large y i e l d of neutrons from the four 3 d i f f e r e n t break-up channels of He. 3 Figure (3.1.2) i s a TOF spectrum for one of the He runs. The apparent 2.7 nsec r e s o l u t i o n of the gamma-rays i s a combination of the reso-l u t i o n s of the TT° box and r a d i a t i v e capture photons (2.3 and 1^.8 nsec res p e c t i v e l y ) with the 1.0 nsec walk i n the timing response, as seen before. One can see that a good separation of the photon peak was achieved but i t i s superimposed a non-negligible f l a t random time d i s t r i b u t i o n before and a f t e r the time of a r r i v a l of the photons. This was f i r s t a t t r i -buted to s t r i c l y random events. I t turned out that imposition of cuts on time i n those regions revealed, as i l l u s t r a t e d i n f i g u r e (3.1.3), a d e f i n i t e energy structure which moved towards low energies for cuts taken a few nanoseconds later.- The time zero was defined, as being the mean time of a r r i -v a l of the photons i n the c r y s t a l , i . e . 9.3 nsec a f t e r a stopped TT re a c t i o n i n the target. Because of i t s rather uniform time d i s t r i b u t i o n , the s t r u c -ture could not be noticed on-line on the a v a i l a b l e p r o j e c t i o n histograms. The next section deals with the steps taken to i d e n t i f y the nature of the problem. T I M E - O F - F L I G H T S E P A R A T I O N I N RUN 1 6 9 1 0 0 0 0 8 0 0 0 6 0 0 0 -4 0 0 0 2 0 0 0 0 - 2 0 - 1 5 - 1 0 - 5 0 10 1 5 2 0 2 5 3 0 R E L A T I V E T I M E ( N S E C ) Figure (3.1.2) Time-of-flight separation i n run 169 for stopped pion events. 34 Figure (3.1.3) ENERGY SPECTRA FOR VARIOUS TIME CUTS o CJ ISO 75 150 75 150 § 75 CD CJ O CD CJ o CJ CJ 500 1 250 o 50 25 50 25 SO 25 10 30 t= 11.6 ns (g) neutrons / t= 7.6 ns (f) t= 3.6 ns (e) TT° photons I break-up 136 MeV \ I — L I --I t= -0.4 ns . (d) .p-...«" i  L T 1 t= -4.4 As (c) t= -8.4 ns (b) t= -12.4ns (a) r • • i „ • i  50 70 90 110 130 150 ENERGY IMEV) Figure (3.1.3) Energy spectra for various time cuts in run 164. A l l cuts are 2.4 nsec large and taken at 4.0 nsec intervals. Time zero i s defined as the mean time of arrival of low-energy photons. One can see a structure moving in energy for t<0 ("T2 neutrons"). 35 §3.2 The "T2 Neutron" Contamination §3.2.1 Helium-3 Runs In order to observe the behaviour of the energy structure, I decided to look at a two-dimensional (2D) representation of the events, p l o t t i n g the time of f l i g h t of the p a r t i c l e emitted from the. target against i t s energy for each neutral p a r t i c l e entering the Nal detector, thus crea-t i n g a 2D g r i d where the events were d i s t r i b u t e d . Such a dot-plot f or a 3 p a r t i a l He run i s reproduced from a computer printout i n f i g u r e (3.2.1). For reasons of c l a r i t y , a contour p l o t of the same data i s also presented i n f i g u r e (3.2.2). As f a r as the computations are concerned, the data were always handled i n t h e i r r e a l binning. The features observed on t h i s p l o t are, at the so-defined time zero, the energy d i s t r i b u t i o n of the photons (enlarged i n f i g u r e (3.2.3) i n t h i s region of i n t e r e s t ) , with the c l e a r ir° box, the breaknup.channels h i l l and the r a d i a t i v e capture peak. At l a t e r times, are observed a large number of neutrons receeding i n energy as the time goes on, consistent with kinematics and timing response. One can again see the c l e a r time separation between photons and neutrons. Random events are v i s i b l e a l l over the pl o t at high energy, and these i s o l a t e d events are mostly due to cosmic rays. Their number seems to increase towards low energies. However, t h i s i s i n fac t a low-energy background that can be distinguished c l e a r l y only for negative times: these events w i l l be accounted f o r l a t e r i n the a n a l y s i s . The main feature of concern i n the data i s t h i s t a i l going across the photons with a d e f i n i t e time-energy r e l a t i o n s h i p . 36 Figure (3.2.1) TIME-ENERGY DISTRIBUTION OF NEUTRAL EVENTS (He run) i 1 1 r 1 T 1 30 37 a 36 l 35 V 3* X 33 w 32 V 31 u 30 T 29 s 28 R 27 0 26 P 25 0 24 tt 23 H 22 L 21 K 20 J It 1 18 H 17 G 16 F 15 E 1* D 13 C 12 B 11 A 10 V 9 8 8 7 7 6 6 5 5 4 4 i 3 2 2 1 1 0 I I 1 1 1 1 1 I 1 1 1 1 1 1 l > X » C B 5 5 3 2 1 1 3 1 1 1 M i l l I l f l « * l l - 9 8 5 1 1 1 1 ? 1 1 I 1 1 1 1 1 1 1 1 1 2 1 3 » « k E 9 2 4 2 3 1 2 1 1 1 1 1 1 2 1 2 1 1 1 S » « » J 5 » b l l 3 2 1 1 1 1 1 1 1 6 * » * F F B 7 3 1 1 1 3 1 1 1 1 1 1 6 U ' * I H A 6 2 2 1 1 1 2 1 1 1 1 1 1 1 1 1 6 « « » I A G 5 1 4 1 1 1 1 1 2 1 1 1 1 1 4 S » « C l ) K C 7 3 3 1 1 2 1 1 1 7 - * « C j r ) 0 6 3 1 12 t i l l 1 1 1 I I 3 S » » 1 K G 9 6 3 3 2 1 1 1 1 1 1 1 I 5 » » » l M C ; i 1 1 4 1 2 1 1 1 2 1 1 1 1 1 2 P « . Y U C F 9 4 ! I 3 < 3 4 I l l 1 1 t 4 J . . . P G C 4 9 3 6 3 1 2 1 1 1 € P « » « » L M E 4 5 4 31 2 I I 1 1 1 2 1 2 5 M " » I J D « C 7 « 1 2 n i l 2 1 1 1 2 N « < « U J N D 9 7 3 6 3 5 1 3 1 1 1 1 1 1 1 3 L « « < « « H K C f 583 84 2 4 3 11 1 1 I 1 4 C » « < « « X f C A 8 B 6 6 6 4 2 1 1 1 2 1 1 3 r » « . « « l . K G G D F 3 9 7 7 8 1 2 1 1 1 1 1 1 1 6 A « • • » « « S H F I G A P 4 A 3 5 2 2 3 1 1 1 1 l C « « < » » X h l J 9 C 6 F . 8 E t i 9 7 3 6 4 l 2 1 1 1 1 2 B « < < < > T C R K H H 9 [ E 9 : l / i n A 5 5 2 1 1 1 1 l F » 1 « « » « . . V P H E H C K C n F 5 6 2 4 2 3 2 l 1 1 1 H « « . « * » » 2 Y « I I S I P . L F F F P e C 5 7 3 4 3 3 I 1 1 1 D U » < « * » » * • * R N J C C 0 F G H 9 ? 5 9 7 7 2 2 3 1 1 1 1 1 7 j . « , . . . . . . I . V L ; L K E J H D E D I E 6 5 7 8 3 1 2 1 I 1 I 1 1 C P 4 « « » * . « . « » « Y O V K P N h F F 8 K G 5 0 e 9 t 2 5 1 3 1 1 1 1 1 1 5 X » » » » » * » < « » * * » * X R P C 0 I A 7 E I L F 9 A 9 4 5 2 5 5 2 I 5 2 » < • » » * . . « • » z « » Y 1 S S C I N 0 » F F G D C 7 4 6 7 2 1 2 3 2 1 . . . . . . . . t t . . . . • ' « * * S N O P P P P R N c e P C 7 8 6 6 2 1 2 3 2 1 1 K < « « * » < » . * » * « « S » « * C R - 2 » k ^ C F l J I C F 9 5 9 8 5 3 3 1 6 1 1 3 1 X « • . » . . . . * . « . « « • • • • • . . t < x l l C C M G F L D 9 8 9 5 5 3 5 1 1 1 1 2 1 1 1 5 D R « « * * * « « * « * * * * * » * » * * " < : « Y R H S I ' L H I J N * 1 N 7 F F G 0 8 3 5 6 2 1 1 1 1 1 3 E 0 < < « « . » . * . « . . « * . » « . . . . . . » k X Y Z S P » V . J J L L B E 9 C F 8 8 ' . < . < . 2 . 1 1 1 1 4 C H « « * . . . . . . . . . . . . . . . . . . . kz Z U " C U C L C J K 0 E L E F C A 8 4 4 4 4 5 2 1 2 1 2 1 5 9 C < « * » . . . . . * . » » » . » Z « . « « . X Z f J . I C S U H h U O N I C G 3 I 0 G 8 3 6 8 7 3 3 9 1 1 1 1 2 1 1 1 l 2 7 9 . a * * . * * * Z " * Y . * R T R Y T J V X U J X W C S G " - S G T R C L A F n F E I 7 C 6 9 9 7 5 C 3 7 6 3 2 1 I 1 6 5 A N > « k ' T : P V » Z C V 0 1 F K X V G S \ k t f D J L P » C F J U D ! K C H « 0 r . 3 C F . e 3 C 8 6 7 9 6 3 8 3 3 2 1 5 6 6 E I < l v . , < K J L I - I W C K C C C I 1 G C 8 C C 8 7 C 3 8 B C : C C 5 C E EC G C G B P P. 8 9 9 5 7 2 A 3 1 2 4 2 3 3A 1 2 I 1 3 2 7 4 « J J l G D C N D 8 H G A 7 7 F 9 a 3 » A A 4 9 A B B 5 a 3 » C 6 8 C 9 P , 7 3 9 9 5 B 8 5 5 7 ( > 7 6 8 7 5 1 5 4 3 3 3 2 1 2 2 1 3 3 1 2 9 P . e H E C C C . 7 0 P 6 7 A 4 5 4 3 4 6 8 3 5 2 ' . ; E 2 3 8 4 9 2 7 4 9 4 6 3 4 3 3 2 6 1 2 > 4 4 6 4 I 44 I 3 2 5 2 ? 6 5 2 1 2 4 I I I 1 3 1 1 1 5 7 4 ' . 7 G 8 9 7 9 6 3 4 5 4 I 3 1 1 2 3 3 3 4 2 1 4 2 3 1 3 2 2 2 ? 3 5 3 5 3 3 3 1 2 6 4 1 23 1 -, 3 1 3 3 5 5 2 1 ? ? 1 1 1 1 12 1 1 1 1 1 U 6 2 7 4 C 5 F 2 7 5 4 4 3 2 4 2 1 1 12 1 U A S 7 7 6 7 4 3 6 5 1 2 1 1 2 2 2 2 3 2 ( 3 7 7 2 3 6 1 2 1 1 I ' l l 1 1 2 7 3 2 5 5 5 5 4 2 2 1 2 1 1 5 5 5 5 4 2 2 7 1 1 3 1 1 4 7 6 2 6 2 2 5 2 1 1 H i l l 1 1 2 C 5 2 1 2 3 2 1 2 1 2 2 1 2 2 2 1 1 1 1 5 4 2 3 4 5 1 2 3 1 1 1 1 1 1 2 1 4 5 8 1 1 1 1 1 2 2 1 3 1 2 3 1 1 2 1 4 5 8 3 4 6 2 4 4 2 2 1 2 1 1 1 2 U 2 « 5 3 3 2 4 2 2 4 2 1 2 U l 3 7 E 5 5 4 7 5 3 7 2 1 1 3 3 5 1 2 2 1 1 1 2 1 8 4 4 3 3 5 3 5 3 3 6 4 3 5 3 3 2 3 1 1 2 1 3 2 1 1 1 1 2 1 3 1 1 1 1 2 1 1 11 1 12 11 2 1 1 11 2 1 2 3 2 2 2 2 2 1 1 3 2 1 3 11 2 1 2 1 1 1 1 2 1 1 1 2 11 1 1 2 1 1 1 2 1 1 1 1 1 1 1 I 1 1 1 1 I U l 2 2 I I 2 2 1 1 1 2 1 2 2 1 1 1 1 8 3 6 2 6 2 4 4 1 112 1 6 1 1 1 5 2 2 1 1 1 1 1 11 III 1 2 1 1 11 1 1 1 1 1 1 1 1 1 1 1 U 2 6 5 4 C 1 4 E 6 A 8 3 3 2 3 5 2 3 3 3 24 3 5 8 A D A 9 7 B C 8 F S 6 E 6 9 61 3 2 2 4 6 6 1 2 l ^ 7 6 5 t 9 3 3 8 ? 3 3 5 5 3 3 3 1 4 7 6 5 6 E B N U S F P K O P S ' I F G M ( I < F F E e 7 8 A 4 3 1 1 1 2 1 1 2 2 2 1 2 1 1 1 1 3 2 1 5 1 1 4 1 1 3 2 1 1 1 11 1 2 1 E 8 6 4 2 6 3 2 1 S 3 5 6 4 4 2 6 6 1 6 1 f . 7 0 T X C J « » I » W » Y R X X » V S » M Y P H 7 3 I 5 4 2 2 3 4 3 4 4 4 2 3 7 6 6 5 8 8 7 9 7 5 6 8 9 2 8 6 7 9 9 9 6 7 1 3 ) - > 4 1 4 3 1 4 ' ; 4 5 ' 2 3 3 4 24 6 3 4 1 Ii J P1 I L VM J V M J O H C Y XMP<- U3 J E 9 4 22 5 5 2 1 5 I 6 737 74 F C DC 2 B F C L C F 6 6 0 E E I S K N C 1 1 112 3 4 2 3 3 4 1 2 4 2 1 3 322 1 3 - 4 4 6 4 5 6 ^ A 9 6 E eB609CCEFA C 5 C A 9 1 3 4 4 2 5 24 1 2 33 1 4 5 6 8 B 6 0 C H A E A B A 8 9 6 A - < KR 7 9 1 1 - • - - - 4 1 4 5 2 2 3 3 4 7 2 3 2 2 3 7 B A 5 2 1 2 1 221 111 I 2 1 1 2 1 2 1 1 2 1 2 1 1 2 2 4 2 2 1 2 3 1 1 2 1 1 2 2 2 1 5 1 1 2 2 1 1 1 1 2 2 1 1 2 2 1 1 1 4 1 1 1 4 1 1 1 2 4 2 2 1 1 2 2 1 1 1 2 2 1 I • 1 2 2 3 4 1 1 1 1 1 2 2 1 1 1 1 1 1 1 2 1 I 1 1 1 2 1 1 2 1 1 1 121 113 2 12 21 2 23 U l 3 1 11131 1 11 • 2 1211 2 12 1 2 11112 121111 1 1 12 2123 2 11212 1 1 1 11 212 I 1 2} 1 1 1 It 2 2 11 1 . 1 3 1 3 2 5 1 2 3 5 1 1 2 3 2 1 1 2 1 2 1 1 1 1 1 1 1 1 1 2 1 1 2 3 2 1 3 2 2 3 3 4 1 2 4 1 1 1 3 2 2 2 2 2 1 5 4 2 4 3 3 3 1 2 1 1 3 3 1 2 1 2 2 1 1 2 1 2 1 3 1 3 2 4 2 1 1 2 1 11 1 4 1 3 1 2 3 1 1 1 1 11 1 11 1 1 2 1 1 3 1 3 2 2 1 1 2 1 1 1 1 1 1 I 1 1 1 1 1 1 2 3 2 2 3 1 11 2 4 2 3 1 1 1 1 U l 1 1 1 11 1 1 1 4 5 2 2 4 1 2 1 2 1 1 3 1 2 1 1 1 1 1 1 1 12 1 2 2 2 1 1 ? 2 1 1 4 3 2 1 I 1 I 1 1 2 1 1 2 1 1 1 1 2 1 3 4 1 1 2 1 2 2 2 2 1 1 1 1 1 1 1 U l 1 21 1 1 1 2 2 2 3 1 1 2 2 3 1 1 2 1 1 1 11 11 1 212 2 111 1 11 I 1 1 2 11 1 1 1 2 _J I 1 I L 1 1— 20 . 40 60 80 100 120 140 ENERGY (MeV) Figure (3.2.1) Time-energy distribution of neutral events from a partial He run (#169) in the form of a computer printout. The symbols for the number of counts in each bin are explained at the top l e f t side of the graph. ENERGY (MeV) Figure (3.2.2) Contour plot of f i g u r e (3.2.1). The superimposed dashed l i n e s i n d i c a t e the shape obtained for <fctie-3"T2':neutroh" data taken with the B l dipole o f f . Detailed contour plot f o r photon events T 1 1 r 1 1 r 1 i i i i i 1 1 1 20 40 60 80 100 120 140 ENERGY (MeV) Figure (3.2.3) Detailed contour plot for photon events i n run 168. 39 §3.2.2 Background and Contamination Similar two-dimensional pl o t s f or both target f u l l and target empty (figures 3.2.4 and 3.2.5) runs leave no doubt that the t a i l cannot 3 be due to He, nor to scattering from material around the target body. Aside from t h i s problem, the target empty run also exhibited many neutrons (with a s l i g h t l y d i f f e r e n t o v e r a l l time-energy shape due to the disappea-3 4 ranee of the He break-up channels) and the r a d i a t i v e high-energy He channel, at time zero, as expected. Consequently, i t was believed that the observed contamination could only come from the pion production target (T2). This feature was not seen at the time of the measurement of the Panofsky r a t i o i n hydrogen but, since then, the proton current onto T2 was increased (from 0.8 uA to about 5 uA) and a f a r larger number of the neutrons b o i l i n g o f f the target could go through the 4.4 meters of s h i e l d i n g (see f i g u r e 2.1.1). But at the same time the TT beam rate,and hence the stop rate i n the helium target, i s increased so that many more of these T2 neutrons are re g i s t e r e d as events when they enter the Nal c r y s t a l . Indeed, a two-dimensional pl o t f o r a run taken at a proton current of 10 uA shows such a comparatively large increase. There were two ways of checking t h i s hypothesis. F i r s t , from the time-energy slope of the feature, i t was possible to v e r i f y that the t a i l agrees by simple kinematics for neutrons with the distance of the detector from T2. Secondly, another background run with the B l dipole o f f (see f i g u r e 2.1.1) confirmed convincingly the T2 neutron contamination. This l a s t datum i s also indicated i n f i g u r e (3.2.2) for comparison. 40 Figure (3.2.4) TIME-ENERGY DISTRIBUTION OF EVENTS FROM THE TARGET EMPTY RUN(#183) \ T T • ^39 I 3 0 •> 37 36 35 34 33 3? 31 30 29 2S 27 26 25 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -8 -16 T T i 3 * * * 1 8 6 4 2 1 1 2 1 1 1 1 2 1 2 S * * . * 4 K f 3 9 4 2 5 3 3 1 2 3 3 1 4 2 4 Q * * « « « « l < > 7 5 1 1 2 1 1 2 3 2 2 1 2 3 I T » * * « . * | < 7 7 1 1 4 1 3 2 2 3 3 1 3 2 1 2 2 K « ' « » « X C 1 9 5 7 1 3 1 3 5 3 4 1 3 1 I 1 1 1 1 1 1 1 1 3 1 1 1 2 ! » » « • « . I 9 J 7 ) 3 1 1 2 2 2 2 2 2 2 1 4 2 2 1 L N * . . » . . | ( 1 5 1 m 2 2 2 1 3 1 2 1 4 2 12 2 1 1 1 2 I * * * « « * X 9 7 2 7 4 2 3 1 2 3 1 3 1 2 1 1 1 2 1 1 3 1 I 1 2 1 l j . . 4 * . . * P 5 4 4 3 2 2 3 2 1 2 2 1 1 1 1 1 1 1 1 S » * « « « » Y G 8 7 3 3 1 3 2 1 3 3 3 1 2 1 2 1 1 1 1 2 1 0 , ( C 5 4 3 4 1 1 2 3 1 1 2 3 2 1 3 2 2 1 2 8 « » « « « , . 0 0 9 7 3 5 4 2 1 1 2 3 1 2 1 1 I 1 2 1 1 N * * « « * * » » C 6 C 6 1 2 2 2 3 1 1 2 2 3 1 1 1 2 2 2 1 1 1 1 1 E . * * 4 < a . . N L E 7 6 5 2 1 2 5 3 2 1 2 1 1 2 1 1 1 B * » * * . * * » * P H 3 5 4 3 3 1 4 1 3 1 3 1 1 2 1 3 1 1 1 2 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 2 3 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 3 1 2 1 1 1 2 1 1 1 3 1 1 4 1 2 2 1 4 1 2 3 3 2 I 2 2 1 2 1 1 2 1 1 2 1 I 1 1 1 2 2 1 1 1 2 1 2 1 1 2 2 1 2 1 1 1 1 1 2 11 1 2 221 121121 1 I 1 1 1 2 1 1 2 1 1 1 2 1 2 1 1 1 1 11 1 3 1 1 2 I 1 2 1 1 1 1 3 1 1 1 2 1 1 11 11112 11 1 1 1 1 1 1 1113111 2111 1 1 I 1 31 11 I 1 1 I 12 I I 1 U l 12 1 1111 1 1 11 11 2 1121 1 1 11 3 11 1 U l 11 1 2 2 1 21 1 I 1 1 1 21 11 1 1 1 1 1 1 I 1 1 1 1 2 21 1 1 1 1 1 1 11 12 1 I I 1 1 I 1 I I 2 1 11 [ ) » * • • * • . . X Z J F 0 G 4 2 1 3 2 1 1 12 11 2112 i i m i n 1 1 2 3 1 1 1 2 1 6 * * * * * * * * » W 0 1 C A 3 6 4 4 2 1 U 1 1 2 1 1 1 2 1 1 1 1 1 3 2 1 1 1 1 1 6 * * * * » « * * » * * S H C H 8 5 5 3 4 1 2 1 1 1 2 2 1 U l 1 3 2 1 1 1 1 1 1 1 1 A * » « 4 » 4 * * * * * » X P K 9 2 4 4 2 3 3 2 2 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 7 * « * . 4 . * * * • * , . 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C ] N K 5 8 4 7 4 4 1 2 1 1 1 2 1 1 1 1 I . * » « . » , « * » * H K E A 0 E 7 7 8 3 4 4 1 1 1 1 1 « * * • * * * * » . « « * * « * * * . * * * * * * * Z X K Z W M N A H 9 9 2 3 3 2 1 2 1 2 *.«**4**«.****.*****.-.*******.*WXt.»JDCC896462 1 2 . . . • . • f t * * * * * * * * * * * **»*.** + . t f Y V Z O U V U H 9 5 8 5 E 5 7 7 4 3 3 1 21 1 22 11 11 1 I 3 a * * * * » * * * * * « * * * . « * . , I B f f * * * * * * * * * * * * * * * . * 1 2 9 N * * * * * * * * * * * * * * * * * 2 2 C 9V * 4 ******** »>.**** 2 2 4 P . C n 44444******. * * • * * * * * * * * ' * * * * *•» * * * * * * * « Y * * » / * X Z Y * T N C P 1 ) S Q I L 7 G 8 C 6 6 4 3 4 1 1 1 2 2 3 1 | 7 6 C W « * * * * * * * * * * * Z * » 0 t f * * * * i < * * * « - * * T V t f C 9 U U N T U T R S H 7 < T M L H R Q G f J H l H F l A r ) 9 B 2 5 6 8 3 1 ? ? 3 ! | j 1 1 5 6 J S * « * * * * * * * S Z * « N O R O P U S M I M L O L J F J H J M . 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F 0 F 5 5 3 3 7 5 3 3 3 3 4 6 4 9Pl.N'CE.'". 5 7 ' 8 7 4 ? 3 2 1 1 1 2 1 U l 2 3 6 9 4 3 I I H D 7 8 3 3 3 4 ^ 2 3 1 2 1 3 4 4 3 4 3 3 C J J 3 I C 5929H644T«21 2 4 3 4 4 e 7 5 7 C F 7 C G 7 9 7 7 6 1 A a a i > > J l 2 I 1 3 2 9 5 5 1 7 C C G F A 9 6 9 5 3 4 5 ? 3 2 2 l \ s 2 1 U 4 0 8 7 4 4 B C E 9 F A B 6 7 4 6 2 4 6 f*k/i 3 1 1 4 4 6 2 7 6 3 6 5 A 6 7 e 9 7 7 7 8 5 9 2 7 5 4 3 2 4 0 U " t ^ 2 3 2 2 1 2 1 1 2 1 6 3 3 6 4 9 A 7 7 B E 1 8 6 B 8 3 5 9 5 7 4 4 4 7 2 4 2 2 2 2 >J. 2 4 2 1 4 2 3 2 2 1 2 1 1 ! !. 1 2 1 1 2 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 3 2 3 1 1 2 2 1 2 4 2 1 1 1 2 2 2 1 1 1 2 1 3 4 4 5 9 5 E 5 E 7 6 8 7 G 8 3 6 9 6 9 C A 9 4 3 A 8 6 7 4 2 V 3 J 4 J 2 2 5 2 2 2 2 1 3 2 2 1 2 2 2 2 1 2 1 2 2 3 2 5 5 7 5 3 I 3 3 7 D 6 D C E E 3 7 7 8 E 4 A A C 5 8 3 7 8 5 J 6 | ~ 1 5 5 3 2 5 5 5 4 8 1 6 3 4 7 4 6 F D 3 9 C 6 A A E F A E 3 A 7 E 7 O T B 3 " ' 2 2 4 >*"<3 0 5 A 6 A 6 4 6 7 0 E 8 A 9 E 8 9 A 0 G E E 8 9 9 9 I A E 3 A 9 ' 1 2 2 i i l l 2 i 1 1 1 2 1 ! 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" 2 3 1 3 3 J 11 1 1 1 5 2 3 4 2 2 3 5 3 1 1 1 2 2 3 2 1 2 ' »4 <32 3 5 4 6 5 9 9 6 5 8 5 3 5 7 3 A 6 7 6 B A 2 5 2 3 2 1 21 2 5 2 1 4 3 1 1 3 2 2 3 3 2 1 1 1 3 3 4 * < 7 6 3 7 8 7 7 4 5 8 C 8 8 A 9 7 6 3 4 5 6 8 5 2 1 1 2 2 2 5 4 i ; i 4 2 2 1 1 1 1 1 I 1 1 3 3 3 T , S 2 5 4 6 6 5 2 e A 76 » B 8 6 3 3 4 A 2 4 5 4 4 4 3 1 2 3 1 1 1 1 5 5 4 1 2 2 3 4 3 1 4 1 1 2 2 1 1 1 1 1 3 2 3 2 1 ^ 2 3 1 2 5 4 2 6 1 4 9 A4 7 4 3 3 A 2 3 3 6 2 5 3 3 3 2 1 4 4 1 6 4 2 5 1 1 1 1 2 1 2 1 1 3 1 31 1 1 I 3 1 2 1>1£2 1 7 3 7 4 3 8.567 2 5 5 3 5 4 5 5 5 7 4 4 1 2 2 2 7 5 2 3 2 4 2 2 1 3 1 1 1 1 1 1 1 1 3 1 2 1 1 1 2 I 2 2 2 > ^ 3 1 4 6 3 3 7 9 3 5 9 5 9 5 6 8 9 9 5 2 3 4 4 7 2 1 1 1 " 1 4 4 6 6 8 2 4 5 2 6 6 2 1 4 4 2 2 2 2 2 2 2 1 2 1 1 1 1 2 2 1 I U ^ 2 5 5 4 3 1 6 4 5 B 5 2 3 5 4 4 4 3 4 4 7 6 1 3 2 1 3TN?V 5 4 4 5 4 2 2 4 2 3 2 2 2 1 1 3 4 2 1 2 2 1 2 1 2 2 1 1 1 3 2 i r V , l 1 3 2 1 U 3 2 5 U 2 2 2 3 2 2 3 2 2 3 2 1 3 2 6 2 4 5 4 1 1 1 2 3 2 2 2 4 1 1 1 1 2 2 U 1 1 1 ^ * < 2 1 3 1 2 3 2 1 4 3 1 2 2 2 3 1 2 2 1 " 2 1 2 3 5 3 5 5 6 7 3 2 1 3 2 2 2 2 1 2 2 3 1 1 2 1 2 2 1 1 1 1 1 I 1 1 2 1 1 1 1 1 1 1 3 2 1 2 2 2 2 1 1 f - 2 8 1 4 1 6 3 7 7 4 5 2 6 3 2 1 4 1 1 1 11 3 1 1 2 1 1 1 1 3 2 2 1 3 1 2 ^ * 2 1 1 1 1 2 1 2 2 1 1 3 1 2 1 3 3 1 2 N 2 2 1 4 3 5 4 2 2 2 2 3 2 1 2 3 4 3 2 1 3 2 1 2 1 1 1 1 1 2 1 2^*, 1 1 1 1 1 1 1 1 2 2 1 1 1 1 2 1 2 3 7 1 2 3 1 2 3 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 3 1 1 2 4 4 6 1 1 3 2 1 2 2 1 2 1 2 1 1 1 1 1 1 1 1 20 40 60 80 100 120 140 ENERGY (MeV) Figure (3.2.4) Time-energy d i s t r i b u t i o n of events from the target empty run (#183). The s o l i d lines^iefine the shape of the T2 neutron t a i l i n t h i s run. The dashed l i n e s represent the t a i l i n run 169, thus showing the RF s h i f t . 20 40 60 80 100 120 140 ENERGY (MeV) Figure (3.2.5) Contour pl o t of f i g u r e (3.2.4) 42 Such a background happened to be quite troublesome, even once understood, and turned out to be the most important source of uncertainty i n t h i s experiment. I w i l l d e t a i l i n the next chapter the means used to do i t s subtraction. Furthermore, i t should be noted here that there i s al s o , i n t h i s contamination, a time s h i f t independent of the time of f l i g h t of 3 the photons and neutrons from the He target. Moreover, t h i s s h i f t i s 3 s i g n i f i c a n t l y v a r i a b l e from one He run to another, with respect to the target-empty run. This was also a t t r i b u t e d to the RF i n s t a b i l i t y during the experiment so that the T2 neutrons were at d i f f e r e n t p o s i t i o n s i n time from one run to another when the TOF c a l i b r a t i o n was kept constant. This i s i l l u s t r a t e d i n f i g u r e (3.2.4). 43 §3.3 Raw Spectra §3.3.1 Cuts on Time Using the TOF spectrum (figure 3.1.2), i t could not be seen exactly how to make the time cuts i n order to produce the energy spectra f or gamma-rays and at the same time estimate the contamination of r e a l events by neutrons. However the two-dimensional pl o t s (figures 3.2's) showed d i r e c t l y how the data were d i s t r i b u t e d . Accordingly, the cuts were made t i g h t enough to reduce the con t r i b u t i o n from the T2 neutrons as much as possible without l o s i n g more than a very small f r a c t i o n of the r e a l events. As a compromise, a 7.6 nsec wide time cut was chosen. The cut was centered d i f f e r e n t l y from low to high energies to account for the time walk but was maintained at the same width for consistency i n neutron and random back-3 grounds between the He runs and the target empty run. An estimate of the v a l i d i t y of the cuts was made by producing time spectra f o r photons i n the TT° box region and for the higher-energy gammas (as for f i g u r e 2.4.2). Results are shown i n the next table: Table II F r a c t i o n of the photons missed by the TOF cuts ( i n %) Energy region: (MeV) 50-88 88-130 1 130-145 run 164 .06 .03 .04 run 168 .14 .10 .03 run 169 .11 .03 .04 run 170 .05 .02 .03 run 173 .05 .04 .04 run 183 .13 .04 44 In addition to these very small corrections f or photons which l i e outside of the time cuts, the TOF cuts also included some neutrons from r e a l events. For t h i s problem, the two-dimensional pl o t s give a d i r e c t answer: above 30 MeV, the separation i n time i s such that the possible neutron background i n the time cut i s n e g l i g i b l e . The TOF neutrons sum up to l e s s than 0.2% of a l l the events i n the cuts, and they are are the low-energy end of the spectra, so that t h e i r c o n t r i b u t i o n to the photon counts from the charge-exchange r e a c t i o n i s n e g l i g i b l e . §3.3.2 Energy Spectra The time cuts f or each run were determined from the sum of the data i n that run. The data, however, were analysed by s l i c e s i n s i d e each run a f t e r i t had been observed, during the on-line a n a l y s i s , that s i g n i f i c a n t s h i f t s i n energy were occuring. A two-dimensional pl o t was produced for each s l i c e and the time cuts were applied on the i n d i v i d u a l p l o t s . A s l i c e of t y p i c a l l y f o r t y thousand events would produce a photon spectrum with s u f f i c i e n t s t a t i s t i c s to evaluate the energy s h i f t but not so large that good energy r e s o l u t i o n would be worsened by g a i n s h i f t s during t h i s sub-run. S t a t i s t i c a l l y speaking, the r a t i o (events/photons) was t y p i c a l l y 10 i n our data. This s l i c i n g procedure confirmed the important changes i n the energy c a l i b r a t i o n , which were i n one case as large as 5 MeV for the highest-energy peak (135.8 MeV). To compensate for the s h i f t s i n the e l e c t r o n i c s of the apparatus, a g a i n - s h i f t i n g procedure was applied before adding i n d i v i d u a l spectra of the sub-runs. I t was necessary to keep as good energy r e s o l u t i o n as possible i n order to separate out the 135.8 MeV peak from the break-up channels. 45 The energy response of the Nal detector i s e s s e n t i a l l y l i n e a r . This was confirmed afterwards when the f i t t i n g of the spectra produced a s e l f - c o n s i s t e n t l i n e a r c a l i b r a t i o n . Two numbers, defined as the "zero" (channel #) and the sgainVt(channels/MeV) can then describe t h i s c a l i b r a t i o n c o r r e c t l y f o r the energy histograms. The "gain" i t s e l f could riot be e s t i -mated for a sub-run because of the low s t a t i s t i c s , but the summed spectra proved afterwards that i t remained constant within 0.5%. It was also f e l t that a clean separation at high energies was more important and that, i f needed, a l i t t l e worse r e s o l u t i o n could be tolerated at low energies to account f o r keeping the "gain" constant. The g a i n s h i f t i n g procedure consis-ted then i n f i n d i n g the centroid of the high-energy e l a s t i c peak for a l l the s l i c e s of a run, s h i f t i n g them accordingly by a f r a c t i o n a l number of channels and f i n a l l y adding them up together. Losses or mathematical bias i n the computation (less than 0.1%) were n e g l i g i b l e . Two sub-runs, represen-t i n g 6% of the t o t a l analysed data, had to be discarded i n the process because of s h i f t s within themselves that were judged unacceptable due to large d r i f t s i n the e l e c t r o n i c s . Figure (3.3.2) represents the raw spectrum thus obtained for one 3 of the f i v e He runs considered i n t h i s t h e s i s . A comparison with f i g u r e (3.3.1) shows that there i s a considerable improvement i n the o v e r a l l energy r e s o l u t i o n while the g a i n s h i f t i n g , at low energies, produces a s l i g h t smoothing e f f e c t . In any case, the energy r e s o l u t i o n was never worsened and, i n f a c t , a 4.5% performance had been c l e a r l y achieved by the Nal detector. R A W P H O T O N S P E C T R U M O F R U N 1 6 9 5 0 0 4 0 0 3 0 0 2 0 0 -1 0 0 h 0 1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 P H O T O N E N E R G Y ( M E V ) Figure (3.3.1) Raw photon spectrum of run 169. G H I N S H I F T E D P H O T O N S P E C T R U M . RUN 1 6 9 4 0 0 3 0 0 C O ZD O L J 2 0 0 1 0 0 0 s • V 1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 09 C H U J O J r O P H O T O N E N E R G Y ( M E V ) Figure (3.3.2) Gainshifted photon spectrum of run 169. The data given below are estimates of the "T2 neutron" and "target empty" backgrounds, appropriately s h i f t e d and normalized with respect to the .target empty run they are taken from (section 4.1). 48 §3.3.3 Random Events The random events, i.e. events which originate externally to the experimental set-up as a whole, are mainly cosmic rays. They are easy to see at high energies on the two-dimensional plots where they are spread out uniformly. At lower energies, there are other accidental counts but their origin i s different and they w i l l be treated in the next chapter. The two-dimensional plots were used to estimate the number of random events by merely counting the events scattered at high energies outside of the photon or neutron structures. One then gets their average number per unit time per unit energy, for later corrections to the Panofsky ratio. They are liste d in table III, where AE = 1 MeV and At = 1 nsec. Th^rt agreement wven the rardom rate increases with t o t a l pno--cn xate. Table III Random and photon counting rates (per unit energy/per unit time) Run no. Randoms Photons * 164'' 0.241 23.7 168 0.464 28.7 169 0.312 23.9 170 0.443 32.6 173 0.305 23.5 183(BKG) 0.238 5.0 *: the stop gate was narrower for this run 49 §3.4 Scalers The scalers recorded .for.each run'during the experiment are summarized in table IV. Although they generally cannot be reliable for precise calculations, they provide a good idea of the experimental conditions, given the set-up. Table IV Scalers for the experiment Run# Target Real Time (sec) Cerenkov Beam Monitor xlO 9 Incident Beam 1.2.3 xlO 9 "Stops" Nal Events Counts total in photon 1.2.3.4* rate stop.Nal TOF cuts xlO' xlO 164 3He 5210 1.444 1.542 1.099 1.304 241960 25745 168 3He 14747 2.933 4.401 2.045 2.331 371595 31925 169 3He 5176 1.824 2.558 1.380 1.557 260023 26197 170 3He 8712 2.271 3.120 1.729 1.809 337876 35718 173 3He 4290 1.653 2.254 1.248 1.298 285297 25766 183 empty 10632 1.697 5.090 1.550 1.730 163375 5425 50 Chapter 4 Data Analysis §4.1 Target empty Run §4.1.1 Estimates for each kind of background The same physical configuration as described in section 2 was used for a l l the runs. The only minor changes were the addition of some shielding of the beam telescope on the side of the Si - L i detector and the 3 repositioning, also after the f i r s t (#164) of our He runs, of the veto counter. A large electron contamination was expected and observed at the Nal detector due to i t s small 14° angle from the beam direction. The main concern about the background was however the target i t s e l f , with i t s steel and CH^ rings, copper side thermal shielding and mylar windows, as well as 4 3 the He superfluid film on the entry and exit windows of the He c e l l . 3 It was possible to remove the He content of the target and the results of the run taken with an "empty" target are presented in figure (4.1.1). The spectrum displays clearly both the low-energy T2 neu-tron.- contamination and the high-energy gammas from the target i t s e l f . When compared to the Ste spectrum observed by B i s t i r l i c h et a l . [J.A., B i s t i r l i c h et a l . , 1970] (see figure 1.1a), the target empty background shows evidence of contributions from other materials. These are mainly carbon and nitrogen in the windows and the CR^ ring surrounding the target c e l l . As these nuclei are heavier and more complex than He, their photon distribution i s further flattened on the low-energy side, but their contributions remain less important due to the low probability of radiative capture (^1% for A=25). T A R G E T E M P T Y P H O T O N S P E C T R U M 10 3 0 5 0 7 0 9 0 1 10 1 3 0 1 5 0 P H O T O N E N E R G Y ( M E V ) Figure (4.1.1) Target empty photon spectrum (run 183). The two l i n e s are estimates of the shapes of the T2 neutron and target empty backgrounds. 52 The main problem a r i s e s i n considering the background subtraction. There are two backgrounds here, of equal importance but of d i f f e r e n t o r i g i n s , thus r e q u i r i n g d i f f e r e n t normalizations with repect to each of the target f u l l runs. The number of photons coming d i r e c t l y from the target i s proportional to the number of TT stops (excluding the scattered pions which miss the veto counter) while the number of T2 neutrons detected depends d i r e c t l y on the proton beam by means of the accidental coincidence r a t e . The two backgrounds had therefore to be separated from each other i n t h e i r overlapping region. Several time cuts i n regions where only the T2 neutrons are pre-sent showed that within s t a t i s t i c s t h i s c o n t r i b u t i o n could be represented by a gaussian energy function (see f i g u r e 3.1.3). I t i s a reasonnable assumption for t h i s i s also about the shape of the proton beam p r o f i l e . 4 The low-energy side of the He r a d i a t i v e capture spectrum was estimated by 4 generously f o l d i n g the He shape [J.A. B i s t i r l i c h et a l . , 1970] with the Nal response function. This s a t i s f i e d the common slow decrease feature from many reactions of that type [J.A. B i s t i r l i c h et a l . , 1972; H.W. Baer et a l . , 1973] and provided a good extension of the actual shape. A small low-energy backgroung contribution was estimated from the target empty data and removed i n a manner described i n section (4.2.1) of t h i s chapter. The r e s u l t s of these estimations are superimposed to the target empty run data, i n f i g u r e (4.1.1). 53 §4.1.2 T2 Neutron Background Normalization This type of background, involved not only a normalization problem but a s h i f t ambiguity as w e l l . The shirfr/ o f the RF s i g n a l , mentioned i n s e c t i o n (3.1.1), meant that although the TOF cuts were of the same width 3 i n the He runs and i n the targetcempty run, they did not sel e c t the same energy T2 neutrons with respect to the RF. Therefore the l o n g i t u d i n a l and l a t e r a l (time and energy: see the two-dimensional plots) kinematic ex-pansions of the T2 neutron t a i l are also d i f f e r e n t at that cut. The changes of c a l i b r a t i o n from one run to another are part of the observed s h i f t . I t was not possible to make a proper RF cut for t h i s background because of even greater complications when the t a i l mixes with r e a l neu-trons from the target. Because of the l o w - s t a t i s t i c s of the t a i l i t s e l f and the evidence of only slow changes i n i t s dispersion, the double kine-matic expansion was neglected. The r e l a t i v e time s h i f t was compensated for by a corresponding energy s h i f t following the same assumptions and knowing that a gaussian shape remains (see f i g u r e 3.1.3). As a check to insure of the v a l i d i t y of those assumptions, the 3 normalization factors for each He run were calculated using the informa-t i o n on the t a i l i t s e l f provided by the two-dimensional time-energy p l o t s . It was easy to i d e n t i f y the t a i l before the time of a r r i v a l of the photons since i n that region i t was well separated from the low-energy background. Interpolation to the photon a r r i v a l time using both the " e a r l y " time and the " l a t e " time data was unfortunately not possible because of the a r r i v a l of neutrons from r e a l target associated events r i g h t afterwards and 54 because of the mixing with low-energy background. However, some kind of extrapolation was f e a s i b l e . The neutrons of the t a i l were counted f o r each time bin, the r a t i o s of these values with the corresponding time b i n of the target empty run were found and extrapolated down to the middle of the low-energy time cut. Table V i s an example of these c a l c u l a t i o n s f o r one run. Time zero i s the time of a r r i v a l of the photons. Table V Extrapolation method f or T2 neutrons (run #169) Time b i n (nsec) -10.2 -9.4 -8.6 -7.8 -7.0 -6.2 -5.4 -4.6 Run 169 ( 3He) 109 124 120 144 136 132 144 136 Run 183 (BKG) 124 166 177 167 216 227 191 198 Ratio .88 ± .12 .74 ± .09 .68 ± .08 .86 ± .10 .63 ± .07 .58 ± .06 .75 ± .08 .68 ± .08 0.0 l i n e a r extrapolation .53 ± .22 55 S i m i l a r l y , the estimate of the energy s h i f t was done by extrapo-l a t i n g the centroid of the t a i l along the time bins down to the middle of the time cut. This method dealt d i r e c t l y with channels, thus disregarding the changes i n c a l i b r a t i o n . The uncertainty was - 3 or 4 channels over 200 channels for the whole spectrum, i . e . about 2.5 MeV. This rather large value i s an i n e v i t a b l e consequence of the low s t a t i s t i c s and the fla t n e s s of the t a i l . A second method used to obtain the normalization factor was to consider i t as a fr e e parameter and optimize i t with respect to the other parameters i n the f i t t i n g program. Here we f i n d an inconsistency, as the values extracted i n t h i s way are systematically about one standard devia-t i o n lower than the extrapolated numbers f o r which the f i t i s poorer i n the low-energy region. Three factors could p a r t i a l l y explain the d i s c r e -pancy: the problem of determining the actual amount of low-energy photon background i n the large bump of the T2 neutrons, the width of the t a i l , which could vary from one run to another due to the i n s t a b i l i t i e s of the RF s i g n a l (indeed, run 173, the shortest run but with the highest current, shows a c l e a r remnant of a bump at the extrapolated p o s i t i o n , that cannot be completely eliminated i n the background subtraction), and f i n a l l y the p o s s i b i l i t y of an unclear time-dependent e f f e c t on the shape of the t a i l along the time bins as the fac t o r that agrees best with the extrapolated 3 value comes from the longer He run (#168). I chose to use the factors yielded by the parameter method, as they never completely disagreed with the predicted ones. The errors were assigned as the d i f f e r e n c e between the two values. I t was decided to add l i n e a r l y , l a t e r on, a l l u n c e r t a i n t i e s concerning the T2 neutrons ( i n the energy s h i f t and normalization). 56 The numbers obtained are also compared with the r a t i o s of the Cerenkov s c a l e r s , as a rough i n d i c a t i o n of the kinds of normalisation that were expected. As the Cerenkov monitor was located near the production target i n the beam l i n e , the scalers should be proportional to the i n t e n s i -ty of the proton beam, but they also depend on how well the beam i s focussed onto the T2 target, from which the ir beam emanates. Table VI summarizes the estimates of errors involved i n the whole T2 neutron procedure. Table VI Evaluation of errors involved i n the T2 neutron background with respect to the target empty run (#183) Run no. RF s h i f t Compensation Cerenkov Extrapolated F i t t e d (nsec) ( i n energy ch.) r a t i o s Norm,, factor Ratios 164 2.0 -12 + 3 0.85 1.1 + .3 .77 + .33 168 2.9 -18 + 4 1.73 1.0 + .4 .93 + .33 169 1.0 -7 + 3 1.08 0.5 + .2 .31 + .22 170 2.5 -15 + 4 1.34 1.6 + .4 1.05 + .45 173 2.9 -18 + 4 0.97 2.0 + .5 1.55 + .45 57 §4.1.3 Empty Target Background Normalization This background also required some s h i f t i n g due to the changes i n energy c a l i b r a t i o n from one run to another. But as those f l u c t u a t i o n s were well known (section 3.3.2, feed-back method), the proper d i s p l a c e -ment could be accurately made. An estimate of the normalization factors was a v a i l a b l e through the s c a l e r s . It was not possible to estimate d i r e c t l y how many pions stopped i n the empty target because j t the scattering of the p a r t i c l e s was expected to be d i f f e r e n t due to the absence of a large part of the 3 scattering m a t e r i a l . However, the small thickness of the He content when the target was f u l l , the corresponding slow change i n the stopping d i s t r i b u t i o n f or the pions, and the f a c t that the beam moderator was not s u f f i c i e n t to l e t the slope of the stopping d i s t r i b u t i o n change sign allowed us to use the C1.C2.C3 sc a l e r s , i . e . the number of incoming p a r t i c l e s , for normalization. The s t a t i s t i c a l uncertainty of the target empty data was 2%. The choice of the function, e s p e c i a l l y for i t s e s t i -mated shape on i t s low-energy side, was ascribed a 3% error, added l i n e a r l y . Another method of f i n d i n g the correct normalization factor was again through the f i t t i n g i t s e l f . In the energy region above the TT° box where the background i s observed (95-125 MeV), there are e s s e n t i a l l y three contributions: the break-up channels, the t a i l of the 135.8 MeV peak and the background. A f i t to reproduce the data i n t h i s region was impractical not because of the s t a t i s t i c s , but mostly the s l i g h t l y unre-l i a b l e low-energy behaviour of the t h e o r e t i c a l break-up channels shape [A.C. P h i l l i p s , 1977]. The alternate s o l u t i o n I chose consisted i n 58 i t e r a t i v e f i t t i n g of the whole energy spectrum with v a r i a t i o n of only the parameter of i n t e r e s t . The normalization factor was then given by the best general f i t i n t h i s region f o r each s e r i e s , while i t s uncertainty was ascertained by the v a r i a t i o n needed to observe a deviation of about one of the l o c a l x 2 ( i n the 110-125 MeV range). (See next section about t h i s method). The r e s u l t s are shown i n table VII for t h i s normalization of the high-energy background. The extracted values are seen to check with the i n i t i a l estimates of the beam s c a l e r s . The former, being more r e l i a b l e , were used i n the error a n a l y s i s . Table VII Normalization factors, f o r the target empty background Run no. Ratio of scalers Factor from f i t s 164 .30 ± .02 .30 ± .04 168 .86 ± .04 .85 ± .05 169 .50 ± .03 .50 ± .03 170 .61 ± .03 .58 ± .03 173 .44 ± .02 .44 ± .02 59 §4.2 F i t t i n g of the Spectra In order to obtain the Panofsky r a t i o , simultaneous f i t t i n g of a l l of the l i n e s involved was necessary so that the s i g n i f i c a n c e of the overlaps could be estimated q u a n t i t a t i v e l y . The subtraction of the two target empty backgrounds was done f i r s t , i n the manner explained i n the 3 l a s t section (4.1). Four remaining l i n e s were then considered i n the He spectrum: a low-energy background, the TT° square box, the break-up channels and the r a d i a t i v e capture peak. Other contributions were treated as corrections and are described i n the following section (4.3). I s h a l l comment here on t h i s procedure. Due to the poor i n i t i a l knowledge of the background normalization factors and the self-consistency of the data, i t was not possible to carry out the a n a l y s i s i n a s t r a i g h t -forward fashion. Only by using the information obtained i n the analysis could the energy c a l i b r a t i o n converge on i t s correct value and the norma-l i z a t i o n s a s c e r t a i n t h e i r own ranges. The former was important i n the computation of the area under each l i n e (by the choice of the f o l d i n g resolution) while the l a t t e r stressed the understanding of the backgrounds. The f i t t i n g program used was derived from the "non-linear l e a s t squares" method described by P.R. Bevington [P.R. Bevington, 1969]. There were two parameters assigned to each l i n e : i t s amplitude ( i . e . integrated area) and i t s p o s i t i o n i n terms of i t s channel number i n the 200 channel histograms. The p o s i t i o n parameters were used at f i r s t to get the correct c a l i b r a t i o n and i n the end were f i x e d at the r i g h t energy. By simulta-neously f i t t i n g the four l i n e s , the program also provided errors on the d i f f e r e n t parameters, corresponding to a change of one i n the t o t a l c h i -square when a parameter "a" was varied by an amount equal to i t s standard 60 deviation " 0 " , i . e . such that x 2 ( a + ° " ) X 2(a) + !• Also, as each l i n e was required to be continuous, a n a l y t i c a l or pseudo-analytical expressions had to be provided f o r i t . §4.2.1 Low-Energy Background The main source of the low-energy background i n t h i s experiment was the lead c o l l i m a t o r s . This was deduced [J/E. S p u l l e r , 1977] when data, taken with d i f f e r e n t lead arrangements around the target, were analysed: i t turned out to be e s p e c i a l l y dependent on the s i z e of the lead collimator for the front face of the Nal c r y s t a l . This i s because the f r a c t i o n of the edge of the collimator (of radius "r") over the subtended s o l i d angle follows a 1/r r e l a t i o n s h i p ; hence the increase i n the low-energy background f o r a small c o l l i m a t o r . Most of these photons, registered i n coincidence with a stop gate, are l i k e l y due to the i n t e r a c t i o n of high-energy gamma-rays i n the lead: there i s mainly p a i r production, followed by bremsstrahlung of the electron and positron. The high-energy electrons of the beam also produce brems-strahlung to which the Nal detector was very s e n s i t i v e because of i t s f o r -ward p o s i t i o n , but these counts were rejected by the s e l e c t i o n of pion associated events on the basis of the RF s i g n a l . As the phenomena r e l a t i v e to electrons and low-energy background photons are linked, i t was assumed that they wbuMihave a s i m i l a r energy dependence and therefore that the electron shape could be used to represent t h i s background. A two-dimensional p l o t (figure 4.2.1) was produced f o r exactly the same s l i c e of events as f o r figure (3.2.1), but t h i s time with the opposite requirement of a charged p a r t i c l e entering the detector. The considerable 61 Figure (4.2.1) • ^39 t 38 * 37 36 35 34 33 32 31 30 29 20 27 26 25 24 23 22 21 20 19 IB 17 16 15 14 13 12 11 10 9 -8 L -16 TIME-ENERGY DISTRIBUTION OF ELECTRON EVENTS I T T I i 112 21 1 12 3 13 12 312 1 11 1 31 1311 221 232 12 24 12 1213 33 2 131 1 1 341 235431 1 12 2 11 11 1 112 11 1 21 1223 1232 2131 1 31 3 11 1 1 1 1 I 1 1 1 11 1 2 1 11 221 1 11 1 3 4 2 2 2 3 1 3 1 1 1 1 1 1 1 1 1 2 3 2 1 3 1 2 3 1 1 1 2 3 1 1 1 6 7 2 2 1 2 1 1 2 4 1 2 1 1 1 2 1 1 1 1 2 4 1 3 5 2 4 2 1 1 2 1 1 2 1 3 1 2 3 3 2 3 3 3 1 2 2 1 3 1 1 I 1 3 2 1 I 1 1 1 1 4 1 5 2 2 2 1 2 1 1 1 4 2 1 1 2 2 2 2 1 1 11 1 3 3 3 2 1 2 2 2 3 2 1 1 1 2 4 2 3 1 1 1 5 1 2 2 2 2 2 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 3 1 3 1 1 1 2 2 2 2 1 1 1 2 1 3 1 1 1 2 1 2 1 1 1 t 1 1 2 3 3 2 1 1 2 4 2 1 1 1 1 1 2 1 2 1 2 1 2 2 1 2 3 1 1 1 2 1 2 1 5 1 1 1 1 1 2 1 1 3 1 1 1 1 1 1 1 1 12 1 1 1 1 1 3 1 2 I 1 1 1 121 1 22 2 1 1 1 1 1 1 1 1 13 1 1 1 1 21. 1 3 2 1 1 1 2 1 1 2 1 1 121 1 1 1 1 11 1 1 1 1 1 1 2 11 1 1 1 t 1 1 1 1 1 11 II 11 21 2 122 1 1 13 1 11312 1 2 2 1 122221 1 1 215 122 11 2441361 21 34 1344512354451 1 1 1 1 1 1 .31 1 2 2 3 2 1 1 1 1 1 1 2 4 3 4 4 5 3 5 2 1 5 5 6 9 6 3 4 9 7 4 5 1 1 3 3 5 2 1 2 1 1 1 4 1 4 5 1 1 3 5 2 4 5 1 7 5 3 3 2 2 3 3 2 5 2 5 5 4 4 2 2 6 3 2 3 4 4 2 3 2 1 1 1 1 2 3 I t 2 1 2 2 1 2 3 7 1 3 5 3 2 3 4 4 2 2 3 2 6 4 2 1 2 3 5 2 2 2 3 1 4 1 1 2 1 2 2 1 2 2 2 2 5 2 2 1 2 2 2 1 2 2 2 3 2 1 1 2 1 1 2 1 1 1 1 2 1 2 2 2 1 1 1 1 1 12 2 2 1 2 1 3 1 II 1 2 11 31 1 2 1 1 1 1 11 1 1 11 1 1 21 1 1 1 1 1 1 _L 20 40 60 80 100 ENERGY (MeV) 120 140 Figure (4.2.1) Time-energy d i s t r i b u t i o n of electrons f o r a p a r t i a l He run based on the same data as i n f i g u r e (3.2.1) except f o r the charged p a r t i c l e requirement. 62 drop i n the count rate i n the neutron region, compared to the subs t a n t i a l d i s t r i b u t i o n i n the photon TOF cut, shows how the former are probably a l l random events but i t confirms the connection of the l a t t e r to the low-energy photon background. The electron events were recorded on tape during the experiment but they were assigned a s p e c i a l b i t - p a t t e r n . Figure (4.2.2) shows one of the electron spectra for a f u l l run. No s i g n i f i c a n t contribution from external conversion of the photons of the I T 0 decay or d i r e c t l y from the TT° -> ye +e~ decay could be observed i n any of the runs. The external conversion (mostly by pa i r production) would take place i n the material 3 l y i n g between the He content of the target and the detector, i . e . the 4 s u p e r f l u i d He f i l m i n the w a l l of the e x i t side of the target, the mylar windows and the veto counter (see section 4.3.2). In an e a r l i e r experi-ment, J.E. Spuller [1977] observed, with much better s t a t i s t i c s , a d e f i n i t e bump i n the electron energy spectrum, i n the region of the charge-exchange TT° photons. These electrons were a t t r i b u t e d to mostly e* pa i r s from the TT° •+ ye +e~ decay but the presence of electrons from external conversion and the importance of the low-energy background i t s e l f did not permit the deduction of an accurate branching r a t i o for the s p e c i a l decay. In t h i s experiment the contamination l e v e l of the low-energy photons was considerably higher because of the p o s i t i o n of the Nal detec-tor and i t s small collimator and there was no s i g n i f i c a n t evidence of the two phenomena mentioned above. Accordingly, a simple f i t to the electron data was done i n order to extrapolate the low-energy background under the ir° photon box. A few parameter polynomial, given s t a t i s t i c a l weights, was f i r s t t r i e d , but i t never reproduced the slow decrease of the E L E C T R O N E N E R G Y S P E C T R U M F O R RUN 1 6 4 0 2 5 5 0 7 5 1 0 0 1 2 5 1 5 0 E L E C T R O N E N E R G Y ( M E V ) Figure (4.2,2) Electron spectrum f o r run 164. The three l i n e s are d i f f e r e n t f i t s to the data. See table VIII for. an explanation of the symbols. 64 data towards high energies well enough. I decided to use an exponential form of the polynomial with, f o r s i m p l i c i t y , equally weighted points. The r e s u l t s were greatly improved and indeed the best or nearly best f i t f o r each run was provided by the exponential of a cubic polynomial; (exp(a + bx + c x 2 + dx 3) with four parameters). Table VIII shows the ef f e c t s of the d i f f e r e n t f i t s on the. electron spectrum. The exponential of a fourth order polynomial was not retained because of the c r i t i c a l smallness of the f i f t h parameter i n the computations. Table VIII Comparison of reduced chi-squares f o r electron f i t s between 17 and 79 MeV for run #164 (85 data points) Number of parameters Polynomial. EXP(poly.) " t i " "Pn" "En" 2 4.94 0.70 3 1.08 0.51 4 0.52 0.39 5 0.42 0.38 Figure (4.2.2) shows the r e s u l t s of three of these f i t s , i d e n t i f i e d by the notation used i n table VIII. 65 §4.2.2 Lines from the IT +3He Reactions There are four r a d i a t i v e channels f o r helium-3, and they show up i n three l i n e s of the energy spectrum. The Doppler-shifted photons from the TT° decay i n the charge-exchange re a c t i o n have a uniform energy d i s -t r i b u t i o n between 53.1 and 85.7 MeV. The e l a s t i c photons from the r a d i a -t i v e pion capture r e a c t i o n TT + 3He 3H + y occur at 135.8 MeV. The Amado model, f o r reasons given i n the introduction, was chosen to represent the break-up channels. A pseudo-analytic function for i t was obtained by f i t t i n g the t h e o r e t i c a l shape [A.C. P h i l l i p s , 1977] with polynomial-type expressions i n segments c l o s e l y adjoining each other. Few-parameter polynomials or exponentials of such were t r i e d , following the method described i n l a s t section. Whichever f i t t e d the theory best was taken for each segment. Two functions were a c t u a l l y s u f f i c i e n t to reproduce the accuracy of the t h e o r e t i c a l data a v a i l a b l e : the exponential of a cubic polynomial c l o s e l y followed the curve between 119 and 90 MeV and i t s smooth decrease to p r a c t i c a l l y zero at zero energy was taken as a low-energy extrapolation (see f i g u r e 1.1b); a fourth order polynomial reproduced the 119-128 MeV region. The errors associated with t h i s break-up l i n e come i n the low-energy part of the model which i s s e n s i t i v e to the high-momentum components of the 3-nucleon wave'function [A.C. P h i l l i p s and F. Roig, 1974]. These errors are discussed i n section (4.3.1). The low-energy background shape was not folded with the r e s o l u t i o n function because, being derived from the data, i t already contained i t ; 3 but the three He l i n e s were. To account f o r the gradual l o s s of r e s o l u t i o n towards low energies, the response function was widened by a small amount 6 6 through a simple streching process. Within 0 . 1 % d i f f e r e n c e s , the best f i t s revealed a 4 . 5 % r e s o l u t i o n f o r the 1 3 5 . 8 MeV photons, 5 . 2 % f o r the break-up channels and 6 . 2 % at the TT° box, roughly agreeing l i n e a r l y with the 7 . 7 % r e s o l u t i o n observed f o r monoenergetic 1 1 . 7 MeV photons [J.E. S p u l l e r , 1 9 7 7 ] . The chosen response function was the one obtained by n-y c o i n c i -dences, taken with the same collimator and shown i n f i g u r e ( 2 . 4 . 1 ) . It was s l i g h t l y smoothed to p a r t i a l l y compensate for the s t a t i s t i c s , before f o l d i n g . The e l a s t i c peak from the ir p ny sin g l e experiment, with i t s good s t a t i s t i c s , could not be used because of evidence of g a i n s h i f t s during t h i s r u n ( 2 ) , which resulted i n the d i s t o r t i o n of the l i n e shape. The error i n the choice of the response function l i e s mainly i n the t a i l and i s further discussed i n the next section. I t e r a t i v e f i t t i n g s made possible the adjustment of the f o l d i n g resolutions f o r each l i n e i n each run and the convergence of the c a l i b r a t i o n . § 4 . 2 . 3 The 4 - l i n e F i t s One of these best f i t s i s shown i n f i g u r e ( 4 . 2 . 3 ) , . a f t e r the target empty backgrounds have been subtracted. The o v e r a l l agreement with the data i s seen to be quite good. A d e s c r i p t i v e l i s t f o r t h i s f i t and the four others i s given i n table IX. The i n d i v i d u a l contributions of the l i n e s to the f i t are also shown i n f i g u r e ( 4 . 2 . 4 ) . F I T O F RUN 1 6 9 M I N U S B A C K G R O U N D 4 0 0 3 0 0 -CO o 2 0 0 -1 0 0 h 0 10 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 P H O T O N E N E R G Y ( M E V ) Figure (4.2.3) F i t of run 169 a f t e r subtraction of the T2 neutron and target empty backgrounds. C O N T R I B U T I O N S T O T H E F I T P H O T O N E N E R G Y ( M E V ) Figure (4.2,4) Contributions to the f i t of figure (4.2.3) by the four l i n e s : the low-energy background, the TT° photons, the break-up channels and the 136 MeV photons, a l l folded with the experimental response - function. 69 Table IX Description of the f i t s f o r the f i v e runs Run no. S h i f t i n channels Normalization f a c t o r s Number of free Reduced T2 neutrons T2 neutron Target empty parameters v 164 -12 ± 3 0.77 ± .33 0.30 ± .04 169 1.083 168 -18 ± 4 0.93 ± .33 0.85 ± .05 159 0.875 169 -7 ± 3 0.31 ± .22 0.50 ± .03 161 0.677 170 -15 ± 4 1.05 ± .45 0.58 ± .03 163 1.068 173 -18 ± 4 1.55 ± .45 0.44 ± .02 167 0.634 The program calculated .theaajreaeunderheachtbf theafolded-'theoretical l i n e s , t a i l s included, but i t was judged best to go into the computation i n an hybride way. The low-energy background and the break-up channels shapes were used d i r e c t l y and subtracted from the data. Because of the d i f f i c u l t y of f o l d i n g r e s o l u t i o n p r e c i s e l y , and i n order to reduce the bias due to the response function as much as possible, the two l i n e s remaining i n the "subtracted f i t " (charge-exchange and e l a s t i c r a d i a t i v e capture channels) were determined from the remaining data. A problem a r i s e s i n the t a i l contributions because of the enhancement of s t a t i s t i c a l e f f e c t s and t h i s lower part was cal c u l a t e d from the knowledge of the t a i l computed i n the f i t , i . e . the normalized folded l i n e shape (see fi g u r e 4.2.4). Thus the r e s u l t s are not completely independant of the choice of the response function. 70 §4.3 Error Processing and Panofsky Ratio C a l c u l a t i o n In order to compute the Panofsky r a t i o , the contributions from the charge-exchange and r a d i a t i v e capture channels, including the d i f f e -rent corrections and e r r o r s , have to be evaluated. In t h i s section, the errors on the backgrounds previously discussed i n section (4.1) are presented. An example of the procedure followed i s given i n table X for one of the runs. §4.3.1 Corrections and Sources of Errors  Step 1: the f i t The three l i n e s considered i n the photon spectra are: the charge-exchange (CE) , the break-up(BU) and the e l a s t i c peak(EP). Their basic numbers are given by the f i t s of the spectra with the proper r e s o l u t i o n folded into each l i n e (section 4.2.2). The errors quoted are the ones pro vided by the f i t s and they contain the s t a t i s t i c a l uncertainty and the correlated error for each l i n e with respect to the three others using the standard d e f i n i t i o n of a change of 1 i n the t o t a l x 2 (see section 4.2) Step 2: the subtracted f i t To minimize the bias due to the l i n e shape (as commented upon i n the l a s t s e c t i o n ) , a p a r t i a l l y subtracted f i t for the charge-exchange and e l a s t i c peak l i n e s was used to provide an absolute c o r r e c t i o n to the numbers. I t was estimated that t h i s "subtracted f i t " method covered an 71 Table X Example of error and c a l c u l a t i o n procedures Step no. RUN #169 1 F i t (x 2 =0.677) 2 Subtracted f i t 3 Response function 4 TOF corrections Q,L Charge-exchange Q 14226 ± 130 +13 Q +21 ± 48 Q +16 ± 5 5 Low-energy background Q 6 High-energy randoms Q 7 Target empty norm. Q 8 T2 neutron s h i f t L 9 T2 neutron norm. L ± 21 + 7 ± 44 ± 138 Break-up 3708 ± 77 +6 ± 73 +1 ± 1 -50 ± 9 ± 61 ± 1 ± 1 Radiative capture 2543 ± 58 +8 +4 ± 19 +1 ± 1 -32 ± 6 ± 5 ± 1 ± 0 10 Break-up function L 11 I n f l i g h t corrections ? 12 SUM quadratic errors l i n e a r errors -17 ± 17 + 14259 Q L ± 141 ± 199 +55 ± 55 ? 3720 ±123 ± 57 2524 ± 62 ± 1 13 ir° decay factor x 1.0058 Internal conversion x 14 External conversion x 1.0052 1.0059 ? .993(H) 1.0060 72 average of 96% of the counts i n the charge-exchange region and 8 3 % i n the e l a s t i c peak region. The remainder had to be estimated from the f i t s due to s i g n i f i c a n t overlaps of the shapes. Step 3: the response function The s t a t i s t i c a l error of the response function i t s e l f , obtained i n a n-y coincidence measurement (see section 2 . 4 ) , was 1.96% and i t applies f u l l y to the break-up l i n e . For the other two l i n e s , the uncertain-ty associated with the response function i s the s t a t i s t i c a l error of the f r a c t i o n a l contributions obtained from the f i t s (^4% for CE, M.7% for EP), times t h i s f r a c t i o n applied to the t o t a l number of counts under the l i n e ( i . e . -an average of 0.4% of the t o t a l f o r CE, 0.9% for E P ) ( e r r o r s ) . Moreover, a c o r r e c t i o n must be made due to the fa c t that the r e s -ponse function misses about 0.15% of the events i n i t s low-energy t a i l . An uncertainty of 30% was assigned to t h i s c o r r e c t i o n [J.E. Spuller, 1 9 7 7 ] . I t should be.noted that t h i s l i n e shape was obtained from a coincidence measurement at 129.4 MeV with hydrogen, but we chose to use i t 3 on the basis of the small energy d i f f e r e n c e with the He l i n e at 135.8 MeV (EP) and the good agreement with the data i n a l l the runs i n s p i t e of the 12 months time lapse between the two experiments. Step 4: events missed by TOF cuts In section ( 3 . 3 . 1 ) , i t was estimated that the t i g h t cuts necessary i n the t i m e - o f - f l i g h t technique used to separate photons from neutrons caused a small f r a c t i o n of the events to be missed: t y p i c a l l y 0.08% for the charge-exchange box, and 0.04% for both the break-up and the e l a s t i c 73 structures. The associated errors represent the range of the unsure events, which could be r e a l or random, and t h i s should also account for the over-laps of the three l i n e s . Step 5: the low-energy background An argument based on the s i m i l a r i t y of the energy dependence was given i n section(4.2.1) f o r the use of the electron shape to represent the low-energy background. Although t h i s seems p l a u s i b l e and there i s good agreement i n the f i t s , no experiment has been performed to confirm i t d e c i s i v e l y and there may be a systematic uncertainty i n the choice of the function. The f i t s gives a correlated error for t h i s l i n e (V3.2%, t y p i c a l l y ) as for the three other l i n e s , as i n s t e p ( l ) . To account for the choice of t h i s background function, i t was thought reasonnable to double i t , i . e . to add again the uncertainty i t brings to the counts of the charge-exchange channel. Step 6: the high-energy randoms The low-energy background l i n e extend to higher energies but i t s contribution-.becomes very small under the e l a s t i c peak. At that point, the high-energy random events, mainly cosmic rays, are the most s i g n i f i -cant source of background. I t was observed, by looking at two-dimensional dot-plots (section 3.3.3), that these events were quite uniformly d i s t r i -buted i n energy and time and could be represented by a f l a t d i s t r i b u t i o n i n s i d e the region of the TOF. cuts. 74 I d e a l l y , i t would have been preferable to subtract these random events before the f i t , but i t was not possible to determine t h e i r d i s t r i -bution at lower energies because of the low s t a t i s t i c s and the dependence on the count ra t e s , nor could t h i s c o n t r i b u t i o n be f i t t e d by extending the low-energy background at a constant l e v e l past the point where both are about equal (-100 MeV) because the low-energy background amplitude was given by the f i t , and was therefore v a r i a b l e . The procedure used was to d i s t r i b u t e the random cont r i b u t i o n above 90 MeV between the break-up and the e l a s t i c channels according to t h e i r r e l a t i v e importance and to subtract from these estimates the corresponding parts of the low-energy background l i n e . The errors are a quadratic combination of the uncertain-t i e s on the cosmic rays and on the low-energy background i n t h i s region. Step 7: the target empty normalization The error on t h i s background subtraction was obtained from the f i t s , i . e . the e f f e c t on the d i f f e r e n t channels of the change i n the nor-malization f a c t o r which increased the l o c a l x 2 by 1. A l l f a c t o r s agreed with the predictions from the scalers (section 4.1.3). The dif f e r e n c e s i n the contributions of the l i n e s were taken as the corresponding erros f or each channel. Steps. 8&9: the "T2 neutron" background There was a s i g n i f i c a n t number of neutrons coming from the pion production target (T2) through the concrete s h i e l d i n g and r e g i s t e r i n g a coincidence with a stop s i g n a l . The problem of removing these events 75 involved a two-fold uncertainty, in the correction of the RF shift and in the extraction of the normalization factor. Both evaluations were made by the extrapolation method, and since the flatness of the T2 neutron energy distribution made the shift d i f f i c u l t to estimate and for reasons given in section (4.1.2), a consistent discrepancy was observed between the predicted normalization factors and the ones obtained by the f i t s . The uncertainties due to these two problems were given by the difference between f i t s for each line when the input shift or factor was changed by an amount equal to i t s standard deviation. Because there is no doubt that these errors are systematic in nature, both were treated linearly in further computation, instead of in quadrature. Step 10: the choice of the break-up function The two break-up channels were represented by the Amado model. In our data as for the data from Berkeley [see A.C. Ph i l l i p s and F. Roig, 1974], the agreement i s good for energies above ^ 105 MeV but the theore-t i c a l line consistently l i e s a l i t t l e too low in the 90-100 MeV region (see figure (4.2.3) and section (1.2.3) for comments). In an attempt to correct for this model dependant discrepancy, an average difference was calculated above 93 MeV, where the charge-exchange contribution is negli-gible, and over a range of about 8 MeV, main region of the v i s i b l e d i f f e -rence. The result was an increase between 14% and 19% in this region for a l l the runs and was applied to the break-up from 100 MeV to zero energy, corresponding to a total increase of 1.2-2.1% for the break-up line. This also brought a negative correction to the total number of counts in the charge-exchange channel, ranging from 0.09% to 0.17%, depending on the run. 76 One might argue on the hazards of t h i s method and the already extrapolated shape of the break-up from 90 MeV down to zero. Concerning the second point, the shape we used and which i s reproduced i n f i g u r e (1.1b) shows that below 100 MeV there i s about 12% of the t o t a l number under the l i n e , which i s small and subject to minor changes only with the condition of converging to zero at 0 MeV, and therefore acceptable f o r a M.5% i n -crease i n t h i s region. F i n a l l y , t h i s was judged the best p r a c t i c a l way to compensate for the observed discrepancy. I t was decided however to ascribe the value of the c o r r e c t i o n to the error and to add l i n e a r l y t h i s uncertainty i n a l l c a l c u l a t i o n s as i t i s of a systematic kind. Step 11: the i n f l i g h t corrections They were not done i n t h i s experiment since they were found to be <0.5% i n the hydrogen case. Step 12: the sum for each channel The number of counts under each l i n e i s the s t a r t i n g number from the f i t , to which are added a l l the corrections l i s t e d above (see table X). The d i f f e r e n t errors are summed separately depending on whether they are s t a t i s t i c ( Q ) or systematic(L) i n nature, as explained above: the f i r s t ones are added i n quadrature and the others l i n e a r l y , which produces two numbers for each of the three channels at the end of t h i s step i n table X. 3 Furthermore, table XI summarizes these r e s u l t s f o r the f i v e He runs. 77 Table XI Sum i n each capture channel f o r each run Run no. Charge-exchange. Break-up Radiative capture Q L Q L Q L 164 13984 ±145 ±140 3402 ±122 ±83 2467 ±63 ±1 168 16044 ±157 ±223 3938 ±148 ±80 2809 ±63 ±2 169 14259 ±141 ±199 3720 ±123 ±57 2524 ±62 ±1 170 19457 ±177 ±217 4453 ±151 ±89 3472 ±76 ±1 173 12877 ±142 ±214 2640 ±144 ±39 2239 ±60 ±1 78 § 4 . 3 . 2 The Panofsky Ratio - P^ 3 The Panofsky r a t i o for IT absorption i n He has been defined i n section ( 1 « 2 . 2 ) as the r a t i o of the charge-exchange rate to the e l a s t i c r a d i a t i v e r a t e : _ OJ(TT He + HTT°, [ T T ° ^ Y Y ( 9 8 . 8 % ) , T\°+ye e ( 1 . 2 % ) ] ) p = . 3 - 3 3 (TT He -> Hy) (la) + (lb) ( 2 ) as numbered i n s e c t i o h ( 1 . 2 . 1 ) . I f i s defined as the number of photons i n the charge-exchange l i n e and N the number of 1 3 5 . 8 MeV photons, a f i r s t approximation f o r P^ would be: P' = ( 0 . 5 ) x ( N 1 / N 2 ) where the 0 . 5 factor accounts for the two photons i n the TT° decay channel a f t e r charge-exchange. But what we r e a l l y have i s : N x = 2 (la) + (lb) N 2 = ( 2 ) Step 1 3 : inherent corrections to P^ The Panofsky r a t i o , with simple algebra, can be rewritten i n terms of P' and a m u l t i p l i c a t i v e c o r r e c t i o n . 1 + p' P = P' x { } = P' x C 3 1 + ( p ' / 2 ) P where p' i s the r a t i o ( l b ) / ( l a ) so that becomes the pion decay m u l t i -p l i c a t i v e c o r r e c t i o n . From the P a r t i c l e Data Group tables [ 1 9 7 6 ] , one fi n d s that the r a t i o of the two main decay mode p r o b a b i l i t i e s f o r the neu-t r a l pion gives p' = 0 . 0 1 1 6 3 , hence a m u l t i p l i c a t i v e factor = 1 . 0 0 5 7 8 . 79 One can also show that the introduction of the relative rate of 3 internal conversion for photons in He, to (IT 3He -> 3H e + e ) p = r - 3 3 OJ(IT He. H y ) introduces another multiplicative correction = (1/(1+P3^e)) to the Panofsky ratio P^. This branching ratio p has been calculated by D.W. Joseph ID.W. Joseph, 1960] in the hydrogen case (p = 0.00710) but i t is H 3 not known for He. Nevertheless, i t was decided, in a f i r s t approximation, to assume the hydrogen value for P3g e as a minimum correction to P^. Therefore the correction factor used i s C. = 0.99295. l Step 14: external conversion The photons produced in the target had a small probability of undergoing external conversion by pair production in the materials placed in their path to the Nal detector. These were the mylar windows of the 3 4 He target, the thermal shielding film of superfluid He in the walls of the c e l l and the veto counter through which the photons had to pass. This effect i s small (0.5%) compared to the f i n a l errors, but non-negligible in this experiment. Let N be the number of counts in any one of the channels. By pho-ton absorption in a given material, N is changed by a multiplicative factor exp(-a£), where a is the cross-section in terms of the inverse of the radiative length (L^) and I the thickness of material in units of radiative length. From the Particles Data Group tables [1976], one finds: 80 for E * 70 MeV, a = 0.57 L 1 Y r E ^ 120 MeV, a = 0.65 L - 1 Y r E ^ 136 MeV, a = 0.66 L _ 1 Y r Therefore each material introduces a m u l t i p l i c a t i v e factor to the Panofsky r a t i o . The c o r r e c t i v e factors C f or external conversion are written at e the bottom of table X,for each channel. Table XII summarizes those c a l c u -l a t i o n s , f o r which the net c o r r e c t i o n obtained f o r P^ i s only C* 0 t = ( 1 - 0.00082). Table XII External conversion c o r r e c t i v e factors Material Thickness Radiative (cm) length (cm) Corrective factors for B„ for P, mylar windows 0.04 28.7 l i q u i d 4He 0.20 755 veto counter 0.32 42.9 (NE102A) (1 - 0.00001) (1 - - ) (1 - 0.00007) (1 - 0.00013) (1 - 0.00002) (1 - 0.00067) Step 15: the r a t i o P 3 Using the two m u l t i p l i c a t i v e f a c tors obtained i n t h i s section (C for TT° decay and C for external conversion), a t h i r d one (C., for p e i i n t e r n a l conversion) being unknown but given, i n f i r s t approximation, the value f o r hydrogen, the Panofsky r a t i o i n helium-3 i s simply the r a t i o , divided by 2, of the charge-exchange contribution to the r a d i a t i v e sum of step(12). 81 Due to the systematic nature of some of the un c e r t a i n t i e s , the errors are s t i l l treated separately i n the d i v i s i o n : the r e l a t i v e s t a t i s -t i c a l errors(Q) are added i n quadrature and the r e l a t i v e systematic errors are added l i n e a r l y . The r e s u l t s for the f i v e runs are l i s t e d i n table XIII. Table XIII Individual Panofsky r a t i o s f o r each run Run no. P„ S t a t i s t i c a l Systematic unc e r t a i n t i e s u n c e r t a i n t i e s 164 2.828 + 0.078 (2.76%) + 0.030 (1.04%) 168 2.850 + 0.070 (2.45%) + 0.042 (1.46%) 169 2.819 + 0.075 (2.64%) + 0.042 (1.47%) 170 2.796 + 0.066 (2.37%) + 0.032 (1.14%) 173 2.870 + 0.082 (2.90%) + 0.049 (1.71%) Based on a reasonable confidence i n the estimates of the uncer-t a i n t i e s , and on the good agreement of the r e s u l t s with themselves, i t was decided to take t h e i r weighted average. However, because of the small inconsistency i n the T2 neutron handling, the d i s t i n c t i o n was main-tained between s t a t i s t i c a l and systematic e r r o r s . For the weighted avera-ge of the Panofsky r a t i o , with the corresponding reduction of the s t a t i s -t i c a l e r r or, the following value was obtained: P^ = 2.830 ± 0.033 (1.17%). To t h i s o v e r a l l s t a t i s t i c a l error was added the average of the systematic 82 uncertainties, weighted by themselves: ± 0.037 (1.29%) to finally obtain, adding the two errors linearly: P 3 = 2.83 ± 0.07 (2.46%) This result is considered to be fairly realistic. For the purpose of comparison only, i f the errors of individual runs had been added linear-ly before taking a weighted average, we would have obtained P^ = 2.83±0.05, which is considered to be too optimistic. Furthermore, i f the internal conversion factor (C/) had been completely ignored in this calculation (instead of assuming the hydrogen value), a l l individual and final ratios would have been increased by 0.020 and we would have obtained P^ = 2.85. The main sources of errors in this experiment were the T2 neutrons: there were too few of them to extract them well but too many of them to be considered negligible. 83 §4.3.3 The Ratio B 3 A second r a t i o between the r a d i a t i v e capture processes was defined i n section (1.2.3), namely the r a t i o of the break-up rates to the e l a s t i c channel rate: -3 -3 O)(TT He -> dny) + to (IT He -> pnny) B3 = I 3 3 wOrr He ->• Hy) (3) + (4) (2) as numbered i n section (1.2.1). The i n t e r n a l conversion processes have not been considered at-^all here due to the absence of any knowledge of the 3 i n t e r n a l conversion p r o b a b i l i t y f o r r a d i a t i v e capture on He i n any of the three channels involved i n the r a t i o B^. The values calculated f o r B^ from the numbers obtained i n step(12) and with c o r r e c t i o n factors from steps(13&14) are l i s t e d i n table XIV. The errors were calculated i n the same double way as i n the l a s t section. Table XIV Individual r a d i a t i v e r a t i o s f o r each run Run no. B„ S t a t i s t i c a l Systematic unc e r t a i n t i e s u n c e r t a i n t i e s 164 1.379. + 0.061 (4.40%) + 0.034 (2.48%) 168 1.402 + 0.061 (4.c38%) + 0.030 (2.10%) 169 1.474 + 0.061 (4.12%) + 0.023 (1.57%) 170 1.283 + 0.052 (4.04%) + 0.026 (2.03%) 173 1.179 + 0.072 (6.08%) + 0.018 (1.52%) 84 The unmistakably large spread i n the data i s such that a weighted average was not applicable. The reason for t h i s wide range of values i s l i k e l y to be the f a c t that, apart from r e l a t i v e l y small corrections, the basic number for the contribution i n the break-up channel comes from the f i t . It was possible to apply the subtracted f i t method (section 4.2.3) to a l l l i n e s but t h i s one and therefore i t might be a f i t t i n g problem. This hypothesis i s confirmed by the closeness of the i n d i v i d u a l Panofsky r a t i o s within themselves. That the simultaneous f i t t i n g of four l i n e s does not give s e l f -consistent numbers emphasizes the need for a better i n i t i a l knowledge of the long low-energy part of the break-up channel to avoid the correlated discrepancies, which were discussed e a r l i e r and among which there might be part of the T2 neutron normalization problem. This would of course also avoid the "corrections" to the break-up channel>.0(step 10) . For these reasons, although a weighted average provided a value f o r of 1.348, i t was decided the maximum of the encountered errors f o r both the s t a t i s t i c a l and the systematic unc e r t a i n t i e s , so that adding the two of them l i n e a r l y f i n a l l y gives: B 3 = 1.35 ± 0.11 85 Chapter 5 Conclusions §5.1 Absolute Rates 3 Of the s i x main channels f o r tr absorption on He, two were not ac c e s s i b l e i n t h i s experiment: the non-radiative absorption processes yielded neutrons which were detected i n the Nal c r y s t a l , but i t was not possible to extract these neutrons from a l l the other neutron y i e l d s from the r a d i a t i v e break-up channels. Also, a discriminator threshold was placed at 20 MeV to reduce the noise and the low-energy background counted i n the ADC. 3 In order to get the absolute stopping rate i n the He content of the target, complete range c a l c u l a t i o n s would have to be done, using the approximate knowledge of the momentum disp e r s i o n of the beam and the thicknesses of the degrader materials. But as t h i s was only estimated and not computed accurately, we had to r e l y on the scaler information (see section 3.4). I t turned out that t h i s was also impossible because of the unre-l i a b i l i t y of the "stop" s i g n a l . Although most of the beam p a r t i c l e s stopping i n the target are a c t u a l l y pions, many of them, and also a large number of muons and electrons, are scattered by the target material and do not f i r e the veto counter C4 (less than 4ir coverage). What makes the c a l c u l a t i o n s impossible i s the important d i f f e r e n c e i n the s c a t t e r i n g when the target i s empty compared to when i t i s f u l l . For a stop rate normalized to the number of beam p a r t i c l e s from the target empty run 86 to any of the JHe runs, the number obtained, for example, i n the e l a s t i c r a d i a t i v e capture channel y i e l d s an absolute branching r a t i o of 2.21% with a r e l a t i v e l y small di s p e r s i o n (not uncertainty) of ± 0.14%. This means that the scalers concerned are s e l f - c o n s i s t e n t but that t h e i r abso-l u t e information i s not v a l i d . -3 3 If we assume however that the branching r a t i o f o r the TT He -> Hy r e a c t i o n i s of the order of the value measured by Zaimidoroga et a l . (6.9±0.5%) [O.A. Zaimidoroga et a l . , 1965] or. by Trub'l et a l . (6.6±0.8%) 9 _ [P. Truol et a l . , 1974], t h i s provides a rough estimate of 1.1 x 10 TT 3 stops i n He for the f i v e runs presented i n t h i s work. §5.2 Delayed Events It was suggested to our group that the p o s s i b i l i t y of delayed events i n the TT absorption should be considered [R.M. Pearce, 1977]. These would be caused by the trapping of a few percent of the negative p a r t i c l e s i n a slow cascade channel of a high quantum number atomic state (n,l) i n such a way that the absorption would occur a few nanose-conds l a t e r . Indeed, t h i s could be a s i g n i f i c a n t c o r r e c t i o n to the abso-l u t e rates, but i t does not a f f e c t the Panofsky r a t i o , P^ or the r a d i a -t i v e r a t i o , B^. The problem i n using pions i n t h i s experiment instead of muons (in the mesic X-rays experiment) i s the i m p o s s i b i l i t y of s e l e c t i n g only c i r c u l a r o r b i t s f o r which the delay i s expected to be large and also the l i f e - t i m e of the TT (26 nsec) , which i s of the same order as the kind of delay sought. 87 To make sure that no neutrons would enter the data, a cut was applied over the energy range of 130-140 MeV and the t i m e - o f - f l i g h t spec-trum was studied f o r possible delayed events. No s p e c i a l structure was observed a f t e r the time of a r r i v a l of photons (defined as the time zero). There was a small increase from the random events before and a f t e r the zero time but i t could not be a t t r i b u t e d to aby delayed events beyond the 1.5% l e v e l . The main reason i s that the same kind of data taken with ba-s i c a l l y the same equipment was a v a i l a b l e f o r hydrogen, i n which case no delayed events are possib l e , and a time t a i l was s t i l l noticeable, very l i k e l y due to the e l e c t r o n i c response of the equipment. The search f o r delayed events with pions was therefore inconclusive. §5.3 The Future of the Panofsky Ratio A summary of experimental and t h e o r e t i c a l r e s u l t s f o r the Panofsky r a t i o , P^ and the r a d i a t i v e r a t i o , i s given i n table XV and pictured i n f i g u r e (5.3). For a b r i e f discussion, the reader i s refered to the section (1.2.2) of the introduction. 88 Figure (5.3) Values of the Panofsky r a t i o i n helium-3 T l 169]' o o E l E2 I • 1 T4 o 2 * T l [67] 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Figure (5.3) Values of the Panofsky r a t i o i n helium-3 Table XV E,T E l E2 E3 This work [1977] Summary of experimental(E) and the o r e t i c a l ( T ) r a t i o s Group Zaimidoroga et a l . [1965] TruOl et al.[1974] Technique D i f f u s i o n chamber Pair spectrometer Nal spectrometer 2.28±0.18 2.68+0.13 2.83±0.07 1.12±0.05 1.35±0.11 T l Ericson et Figureau PCAC hypothesis [1967] [1969] T2 Truol et al.[1974] T3 P h i l l i p s and Roig [1974] T4 Miztuta et a l . [1975] no p-exch. c o r r e c t i o n 2.70 1.9, 2.1 Impulse approximation "2.49" IA for P„ Amado for B„ IA I II I I I 2.51 2.79 2.98 2.63-3.06 0.84±0.08 1.10±0.08 1.27±0.08 89 While t h i s new measurement of the Panofsky r a t i o i s again c o n s i -derably l a r g e r than the value of Zaimidoroga et a l . , i t i s also s l i g h t l y larger than the value of TruOl et a l . . A c l e a r increase i s also observed from t h e i r s u r p r i s i n g l y good r a t i o B^. The agreement of the two numbers obtained the 3-nucleon wave functions with non-zero S' and D state proba-b i l i t i e s i s e x c e l l e n t . Naively, i t seems that an increase of the pnny contribution to the t o t a l break-up channels would help to explain the low-energy disagreement and bring up s l i g h t l y the comparative r a t i o B^. Experimentally, two straightforward modifications to the set-up would, with the same basic apparatus, improve our r e s u l t s . In order to minimize the accidental detection of the "T2 neutrons", the s h i e l d i n g of the Nal detector should be increased, but even more important the detector should be put c l o s e r to the target, keeping a good TOF separation, thus s i g n i f i c a n t l y increasing the r e a l event r a t e . The obvious change i n the equipment would be to have a t h i c k stopping target instead of a t h i n scattering target, to increase the count rate and allow a precise eva-l u a t i o n of the stopping rate i n order to obtain the absolute absorption r a t e s . 90 BIBLIOGRAPHY H.L. Anderson and E. Fermi, Phys. Rev. 86, 794,(1952). H.W. Baer, J.A. Bistirlich, K.M. Crowe, N. deBotton, J.A. Helland, and P. Truol, Phys. Rev. C i8, 2029 (1973). ar. H.W. Baer, K.M. Crowe, and P. Truol, in Advances in Nuclear Physics, vol. 9 edited by M. Baranger and E. Vogt, Plenum Press^(1977). P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences McGraw-Hill (1969). J.A. 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MacDonald, Ph.D. thesis, University of British Columbia,(1977)' Phys;, RevJ; Lett. 138,^ 7,4:6 (1977) • ."Phys . f ^ * v. I-It- _3£ , M. Mizuta, Y. Kohyama and A. Fujii, in Abstracts of contributed papers to VI Int. Conf. on High-Energy Physics and Nuclear Structure, Santa Fe (LASL, Los Alamos, 1975), p. 175. 91 W.K.H. Panofsky, R.L. Aamodt, and H. Hadley, Phys. Rev. 81_, 565 (1951). R.M. Pearce, TRIUMF, Vancouver, private communication (1977). A.C. P h i l l i p s , and F. Roig, Nucl. Phys. A234, 378 (1974). A.C. P h i l l i p s , p r i v a t e communications (1977). P a r t i c l e Data Group, Rev. Mod. Phys. 48_, No. 2, Part I I , 1 (1976). J.W. Ryan, Phys. Rev. 130, 1554 (1963). J.E. Spuller, Ph.D. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia (1977), (re s u l t s rr published i n Phys. Rev. Lett.)67B, 479 (1977). P. Truol, H.W. Baer, J.A. B i s t i r l i c h , K.M. Crowe, N. deBotton, and J.A. Helland, Phys.Rev. L e t t . 32_, 1268 (1974). J.S. Vincent, and W.R. Smith, Nucl. I n s t r . and Meth. 116, 551 (1974). O.A. Zaimidoroga, A.M. Kulyukin, R.M. Sulyaev, I.V. Falomkin, A.I. F i l i p p o v , V.M. Tsupko-Sitnikov, and Yu.A. Shcherbakov, Sov. Phys. JETP: 21, 848 (1965); 24_, 1111 (1967). 

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