Photodisintegration of Helium-3 at Energies between 200 and 600 MEV Citation McDonald, Kirk Thomas (1972) Photodisintegration of Helium-3 at Energies between 200 and 600 MEV. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/E7PT-0T58. https://resolver.caltech.edu/CaltechTHESIS:05092016-154916452 Abstract We have measured differential cross-sections for the two-body photodisintegration of Helium-3, ɣ + He 3 → p + d, between incident photon energies of 200 and 600 MeV, and for center of mass frame angles between 30° and 150°. Both final state particles were detected in arrays of wire spark chambers and scintillation counters; the high momentum particle was analyzed in a magnet spectrometer. The results are interpreted in terms of amplitudes to produce the ∆(1236) resonance in an intermediate state, as well as non-resonant amplitudes. This experiment, together with an (unfinished) experiment on the inverse reaction, p + d → He 3 + ɣ, will provide a reciprocity test of time reversal invariance. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Heusch, Clemens A. Thesis Committee: Unknown, Unknown Defense Date: 24 May 1972 Funders: Funding Agency Grant Number Atomic Energy Commission UNSPECIFIED NSF UNSPECIFIED United States Steel Foundation UNSPECIFIED Record Number: CaltechTHESIS:05092016-154916452 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:05092016-154916452 DOI: 10.7907/E7PT-0T58 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9713 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 10 May 2016 14:41 Last Modified: 01 Jul 2024 22:36 Thesis Files Preview PDF - Final Version See Usage Policy. 41MB Repository Staff Only: item control page

PHOTODISINTEGRATION OF HELIUM- 3 AT ENERGIES BETWEEN 200 AND 600 HEV Thesis by Ki rk T . McDona l d. I n Partial Fulfillmen t of th e Requirement s f or th e Degree of Doctor of Philos ophy California Insti t ute of Technolo gy Pasadena , ·Ca lifornia 1972 (Submi t t e d May 24 , 197 2) ii ACKNOWLEDGEMENTS One of the pleasures of thi s experiment has b een th e opp ortunity to work togeth er with many outs tanding peop l e . My greatest debt is to Cl emens Hcusch who , as my advis e r, h as h a d a p ervasive and s a lut ary influence on all asp ec ts of th is long exp er ime nt, f rom its concep tio n to th e f inal anal ysis . The bus iness of co nducting an experiment was t augh t t o me by Charle s Prescott. The constr.uction of t he appar a tus was p r i marily due to the c raftsmanship of Walter Nilsson. Th e exp eriment al so b e nefitted from the advice and services of engineers Bill Friedler, Hans Grau, Da n Se ll and Joe Ungerer . Barry Lieberman a ss i sted in the c onstruction of special electronics. The hap py tedium of collecting the data was share d by my colleagues Steve Ch eng, Bob Kline , Bill McNeely, Bruce Winstein and St eve Yellin. The contributions of Steve Cheng , Char l es Prescott a nd Leon Rochester to the data analy s~s are mentioned in the te xt . Duane Edgington and Greg Stewa rt assisted in computer programmi ng. Abe Seiden has made important contributions to the interpretation of the results. The spirit of liberation was brought to the data analysis by Ms. Phyllis Nilsson. This experiment was performe d at the Calt ech synchrotron during the final months of its life, The machine was successfully nursed through this period by the operators: Al Neub e iser, Joe Laurinovics, Frank iii Scarlino and George Ynclan, and by the mai ntenance crew: Paul Van-Ligten, Danny Heffington, Art Schmidt and George Talbert. The He 3 target was provided by Victor Perez-Mendez with the technical assistance of Don Hunt. It was kept running smoothly by Earl Emery and Dick Wileman. The production of the thesis was aided by Judi Laurence. For financial support, I am indebted to the Atomic Energy Commission, the National Scie nce Foundation, and the United States Steel Foundation. Concurrent for me with this experiment was ano the r, with ~ancy Schaefer. Are they not of the same conception? feel the irreversibility of time. To be alive one must "There are momen ts when you think you see her grow old and feel yourself growi ng old with her ... If I remember correctly, they call that the irreversibility of time.'' (Jean-Paul Sartre) iv ABSTRACT We have measured differential cross-sections for the two-body photodisintegration of Helium-3, y + He 3+ p + d, between incident photon energies of 200 and 600 MeV, and for center of mass fr ame angles between 30 0 0 and 150 . Both final state particles were detected in arrays of wire spark chambers and scintillation counters; the high momentum particle was analyzed in a magnet spectrometer . preted in terms of amplitudes to produce the The results are inter- ~(1236 ) resonance in an intermediate state, as well as non-resonant amplitudes . This experimen t, together with an (unfinished) experiment on the inverse reaction, p + d + He 3 + y, will provide a reciprocity test of time reversal invariance. v TABLE OF CONTENTS .TITLE PART PAGE I. INTRODUCTION 1 II. EXPERIMENTAL METHOD 11 A. The Choice of Techniques 13 B. Apparatus 15 C. Electronics 26 D. Summary of Data Collected 34 III. DATA ANALY SIS 37 A. Track Reconstruction 38 B. Event Reconstruction 45 C. Background Subtraction 54 D. Efficiency Calculations 61 1. Geometric Efficiency and Momentum Acceptance 62 2. Nuclear Scattering 67 3. Electronic Inefficiences 69 4. Wire Spark Chamber Inefficiencies 70 E. Cross-Sections and Statistical Errors 73 F. Systematic Errors and Resolution 77 IV. RESULT S 80 v. DISCUSSION 95 vi PART VI. TITLE APPENDICES A. Historical Survey of the Reactions y + He 3 ++ p + d B. Electrodisintegration of He3 C. Electromagnetic Multipole Structure 107 116 of y + He 3 + p +.d 122 D. The Photon Beam Spectrum 130 E. Be am Monitoring 133 F. The He 3 Target 137 G. Ca libration of the Analyzing Magne t 1. Principle of the Me thod 2. Orbits in -the Mid-Plane of the Magnet Gap 3. 4. H. I. VII. PAGE 145 146 Propert i es of Orbits not in the Mid-Plane 149 Corre ction for Gravity 151 Example of the Background Subtraction Proc e dure 155 Survey of Possible Reciprocity Tes ts 167 FOOTNOTE S AND REFERENCES 172 vii LIST OF FIGURES FIGURE 1.1 TITLE PAGE ·- Existing Cro s s-S ection Data on y + He 3 ~ p + d a t 90°(c.m.) 8 2.1 Layout of the Experiment 16 2.2 The Magnet Array 18 2.3 A Typical Time-of-Flight Spectrum 21 2.4 The Range Array 23 2.5 The Trigger Ele ctronics 27 2.6 The Pulse Height Analysis Elec tronics · 30 2.7 Examples of the Pulse Height Spectra Di s play 31 2 .8 Examples of the Spark Chamber Display 33 3.1 X-Y Distribution of Event Vertices 43 3.2 Skew Distance Between Tracks 44 3.3 A Raw Coplanarity Distribution 47 3.4 A Raw Missing Mass Distribution 48 3 .5 49 3.6 A Raw Incident Photon Energy Spectrum I A Raw Pulse Height Spectrum in Counter RSl 51 3.7 A Raw Pulse Height Spectrum in Counter MS 3 53 3.8 Effect of the Background Subtraction 59 3.9 Example of the Monte Car lo Efficiency Calculation 4.1 65 He3 Photodisintegration Differential CrossSections in 10 MeV Bins 82 viii FIGURE 4.2 TITLE He 3 Photodisintegration Differential CrossSections in 50 MeV Bins 4.3 90 He3 Photodisintegration Angular Distribution at 550 MeV 4.10 89 He3 Photodisintegr ation Angular Distribution at 500 MeV 4.9 88 He3 Photodisintegration Angul a r Distribution at 450 MeV 4.8 87 He3 Photodisintegration Angular Distribution at 400 MeV 4.7 86 He3 Photodisintegration Angular Distribution at 350 MeV 4.6 85 He3 Photodisintegration Angular Distribution at 300 MeV 4.5 83 He3 Photodisintegration Angular Distribution at 250 MeV 4.4 PAGE 91 Summary of He3 Photodisintegration Angular Distributions and Fits 92 4.11 He3 Photodisintegration Total Cro ss-Sections 94 5.1 Comparison of He3 Photodisintegration Total Cross-Secti0n Data 5.2 96 Comparison of He 3 Photodi sintegration Differen tia l Cross-S ec tion Data at 30°(c. m.) 98 ix FIGURE 5.3 TITLE Comparison of He 3 Photodisintegration Differential Cross-Section Data at 60°(c.m~) 5. 4 . 110 Existing Data on He3 Photodisintegration Total Cross-Sections 6.3 102 Existing Data on He3 Photodisintegration Differential Cross-Sections at 90°(c~m.) 6.2 101 Comparison of He3 Pho.todisintegration Differential Cross-Section Data at 150°(c.m.) 6.1 100 Comparison of He3 Photodisintegration Differential Cross-Section Data at 120°(c.m.) 5.6 99 Comparison of He3 Photodisintegration Differential Cross-Section Data at 90°(c.m.) 5.5 PAGE 111 He3 Photodisintegration Angular Distributions at 109 and 140 MeV 114 6.4 He3 Virtual Photodisintegration Cross-Sections 118 6.5 He3 Photodisintegration Angular Distribution at 75 MeV 119 6.6 Radial Dependence of the Beam Intensi ty 132 6.7 Phase Diagram of He 3-He 4 Solutions 138 6:8 The He3 Targe t 140 6.9 Density vs . Temperature of Liquid He3 at 6;10 Saturation Vapor Pressure 142 Orbits Measured in the Magne t Calibration 147 x FIGURE 6.11 TITLE The Correction for Gravity in the Magne t Calib ration 6.12 PAGE . 154 The Pulse Height Spectrum in Counter RSl for Events with ·Small Coplanarities and Missing 156 Masses 6.13 The Coplanarity Distribution for Foreground and Background Events· 6.14 The Missing Mass Distribution for Foreground and Background Events 6.15 160 The Coplanarity Distribution for Background Events 6.18 159 The Missing Ma ss Distribution for Events with Large Pulse Heights in Counter RSl 6.17 158 The Coplanarity Distribution for Events with Large Pulse Heights in Counter RSl 6.16 157 Gene~ated by the Monte Carlo Calculation 162 The Missing Mass Distribution for Background Events Generated by the Monte Carlo Calculation 163 6.19 The Sebtra cted Coplanarity Di s tribution 164 6.20 The Subtra cted Missing Ma ss Distribution 165 xi LIST OF TABLES TAB LE TITLE 2. 1 Element s of the Magne t Arr ay 2.2 Elements of the Range Array 2. 3 Calte ch- Des i gne d Ele ctron ic s Used in This Ehrpe r i rnent 28 2. 4 Summary of Da ta Collected 35 4.1 Differenti a l Cross - Se ctions for y: + He 3 ->- p + d . 4. 2 Paramet r iz a tion o f t he Cros s -Secti ons f or y + He 3 -+ p + d 6.1 84 93 Angu l ar Distribution Coefficients for t h e React ion y + He 3 ->- p + d. 113 xi i To the memory of my father, J ames E. McDonald. , / -1- I. INTRODUCTION We have measured th e differential c ross-section for the t wo bo dy photodisinte.gration of He lium-3, y + He 3 ->- p + d. The incident photon energy was between 200 and 600 MeV and the scattering angles · varied fro m 30 0 to 150 0 i n t he center of mass fr ame . The energy r ange i ncludes the r egion in which th e fir s t nucleon r esonance , th e 6 (12 36), c an b e produced in an intermediate state . Pas t studi es of this r eac tion have b een conducted almost e xclusive ly at ph oton energies b e low 150 MeV . Appendix A. This work is reviewed in Da t a on th e rel ated process , the electrodisintegration of He 3, are discussed in App end i x B. The pr esent experiment on y + He 3 -+ p + d is intima t ely r e lat e d to a study of the invers e r eac tion, p + d -+ He 3 + y. The cros s-sections for these two r eactions must ob ey a simp le relation (given b e low) in th eir center of mass frame as a consequence of time r eve rsal inva ri ance . . 1 Th e d iscovery in 19 64 of a violation of the combined symmetry CP (cha rge conjugation and parity) in the de cays of th e neutral K mesons has stimulated the search for a violation of time reversal invariance (T). Such a violation is to be exp e cted, given a CP viola- tion, according to the CPT Theorem 2 which claims that all physical processes are invariant under the combined transfo rmat ion of C, P, and T. In particular, Bernstein, Feinberg and Lee 3 noted that the experi- mental evidence for T-invariance in the electromagne tic interaction was very scanty. Thi s is partly due to the fact that in many experiments a time -2- reversal violation would also imply a parity violation, or nonhermiticity or non-conservation of the electromagnetic current. evidence against these effects is considerably greater 4 The We shall not review the present experimental status nor the variety of experiments proposed to test T-invariance. A comprehensive review through 1969 has been given by Henley 5 The me thod of investigation of T-invariance which concerns this experiment is a test of detailed balance. In general, if T-invariance is true, then the cross -s e·c·tfons of the forward and reverse reactions a + b~-+ c + d must be related by dcr drl (a + b + c + d) c P 2 dcr (c + d + a + b) Pa drla (2Sc + 1) C £cL±.J) (2Sa + 1)(2Sb + 1 evaluated in the center of mass frame. Bars hay _G_2 6 in 1966 suggested that the reaction y + d + n + p would be a good place to look for a Tviolation. The source of any potential T-violation would involve a yNA (l236) vertex. This is known to contribute strongly to y + d + n + p as a resonance 'bump' app ears in the cross-se ction near photon energies of 300 MeV . It is necessary to consider the yNA the simpler yNN vertex because the requiremen~ vertex rather than that the electromagnetic current is conserved, and that it conserves parity, forbid any T-violation here. A time reversal violation at the yNA vertex might manifest itself in either (or bot~ ) of two ways . If the magn it~dc of the coupling constant is different for y + N + A than for A + y + N, then the total cross-sections of the forward and reverse reactions will be -3 - di fferent. Howeve r, the e x erimental difficulty i n making a precise absolute norma li zation of a photon b eam intensit y might such an effect . s imul ate Any evidence fo r an e l ectromagnetic T-violation b ased solely on a di screpancy b etween t otal cross-sections should b e re garded war ily. The second poss ibility i s th at th e phase of the c oup ling c onstant ma y b e different for y + N ~ 6 th an for 6 ~ N + y . The n if the a mpli tude to produce th e 6 int erferes with a T-invariant amplitud e , such as one invo lving the yNN v ertex , th e shape o f the differenti a l cro ss -s e ction ma y b e noticeab l y different for th e fo rward and r eve rs e re ac ti ons . Experime nts which inves tig a t e th is possibility are not sensi tive to errors in t he ab solute norma liz a tion of th e cross -s ec tions . Barshay p r oposed a s ear ch for thi s t ype of effe ct . He not e d th at th e cros s- s e ction for y + d ->- n + p in th e r egion of th e 6 resonance h as c ont ributions of about 60 % from the tr ans ition El~ 3P , 0 3 6% fro m Ml~ 1n2 and L1% fro m Ml ~ 1 s . 0 Th e 6 i s prod uced in the Ml ~ 1D2 transition, which c an int erfere with any non-resonant part of the same a mplitude, or also with the Ml~ 1 s amplitude . 0 Howev e r, it cannot interfere with th e strong El ~ 3P transit ion a s the total spins 0 of the final stat es are differen t. suppres sed as Thus, any T-violation i s somewha t it must appear in th e interference b e t ween a strong T- violating amp litud e and a weak T-conserying a mplitude . Nonetheless , a max i ma l violation could cause the ratio A2/Ao to differ by as much as 0.3 between the forwar d and r eve rse reactions, presuming the differential -4- cross-section to be of the form P 2 is the second orde r Legendre polynomial. For completeness, we note that there exist models of a possible T-violation of the electromagnetic current which suggest that the yN6 vertex will be T-invariant, the violation appearing elsewhere. and later Okun 8 Lee 7 consider that the T-violation is due to the existence of certain as ye t unobserved particles whose strong interactions are not charge conjugation invariant. This leads to an electro- magnetic T-violation which, however, conserves isotopic spin . yN6 Since the vertex involves a change by one of the hadron isospin, it would be T-invariant. 9 The second argument , due to Frazer is that the static model bootstrap description of the reaction yN + 6 + NTI requires it to be T-invariant. This reaction appears as part of the mos t reasonable mechanis m for 6 production in y + d + n + p, so the latter reaction should be T-invariant also . Turning to the e x p e rimental situation regarding y + d +-+ n + p, we find that the forward reaction has be e n reasona bly well-studied at energies suita ble for 6 production 10-14 . Investigation of the inverse reaction was stimulated by Barshay ' s work . The reaction is difficult bec a u s e of the background r ~a ction n + p ->- cl + 1r 0 + d + y + y, which has a cross-section roughly seve nty times that of n + p + d + y. first n + p e x perime nt 15 The ' claime d a 2 .5 st a ndard d e viation effect in the discre p a ncy of the r a tio A2 /A 0 comp a red to the y + d r eaction . At -5- the time th e present e xperiment was proposed (1969), the pre liminary analysis of a s e cond n + p experirnent s maller effect. 16 showe d a similar, · if slightly Since that time , the first e xpe rime nt has bee n redone 17 , reducing troublesome spark chambe r inef ficiencies, and the analy s is cornpleted on the s e cond 18 ; as a r es ult, th e effec t has disappeare d. The latter experime nt r eport s the T-violating phase as 4 ± 10 degrees. I Within the last y ear, the interest in reciprocity te sts of Tinvariance has shifted fro m reactions y + d +-+ n + p to y + n +-+ p + TI • While the latter are perhaps conceptually simpler than the former, they are more difficult exp e rimentally. The y+ n reaction must be performe d with a deuterium targe t and corrections made for the 'sp ectator ' proton. The TI + p reaction has an all n e utral final state, and is subject to large backgrounds from n + TI 0 final sta tes. There are sizable discrep- ancies between the data on the forward and reverse reactions, which might indicate a T-violation. The difficulty of the experiments makes it hard to draw firm conclusions at present, and more precise data are need ed to clarify the situation. Donnachie 19 has given a rec ent review of this complex problem, including a good bibliography. We come at length to consider the present experiment. when the data on y + d + n In 1969, + pwereconsistent with a T-violation, the re actions y + He 3 +-+ p + d were propos ed as a good place to verify or disprove the effect. The reaction y y + d + n p + p + n. + He 3 + p + d is slightly more complicated than + p because t h e re exis ts the 3-body breakup re ac ti on y + He 3 + This c an be suppressed by requiring a deuteron to be observe d -6- in the final state . An actual advantage is that both final state par- ticles are charged and can easily be detected, allowing the elimination __ of backgrounds due to pion production, such as y + He3 + d + n + 7T+ • The inverse reaction, p + d + He 3 + y is studied with a charged proton (or deuteron~) beam which can be made with good momentum definition. This provides an important additional constraint to eliminate the backgroun d process p + d -~r He3 + 7To , ( 7To + yy ). The lack of the extra con- straint is a weak point of the n + p -r d + y experiments (which was, . t h e second p rinceton . . l 7) • h owever , somewh at recti. f.ie d in experiment A kinematic disadvantage of the p + d reaction is that the He 3 is produced with fairly low kinetic energies. Since it is doubly. charged, it subsequently loses energy rapidly via multiple Coulomb scattering . If a deuteron beam an d a proton target were used, the He 3 kinetic energies would be much greater in the laboratory for a given center of mass frame energy ( see Appendix I for a more complete discussion). Some additional fe atures of the reactions y + He 3 ~ + d which must be considered are as follows . . 78 is . a b out a First, t h e cross-section factor of ten lowe r than that for y + d ++ n + p, requiring more time to reach a given accuracy. Second , He 3 migh t have an excite d state , He 3*, which would decay to the ground state with the emission of a photon . a state could be produce d by p + d + He 3 bility as p + d -r He 3 + y . Such * + y ~ith roughly equal proba- The He 3 ,.~ , or subsequent He 3 after decay , migh t lead to a final configuration indistinguishable in the experimen tal appara t us from an He 3 produced in the desired reaction. Thus the recipro- -7- city b e t ween th e f orwa rd a n d r evers e r eaction s co u ld b e des troyed witho ut a T- viol a tion . Apparen t l y , th e thr ee nucle on sys t e m is th e on l y multi - nu c l e on sys t em with no k nown e x cit ed states , eithe r bound or virtua 1. A third si gnific an t f e ature is that th e e x citation of th e 6(1236) d oes not a ppear to h a v e su ch a p ronoun c e d effect on y + He 3 -+-r p + d as on y + c1 ~-r n + p. . ting . Th e on 1 y e xis c1a t a 7 8 at e nergi. es a b a ve 200 Me V are ~0° ( c . m. ) diff e r e ntial cross -s e ctio ns . These are shown in Figure 1.1 and indic a te at most a bro a d ri s e n ear 300 Me V above th e cross-section as extrapola t e d fro m loge r ene rgi es . It is of course p ossible th a t the 6 contribution to the 90° cross-section is small. The lack of a 'bump ' can also b e attribut e d to th e fact th at i.sospin cens ervati on requires any interme diate s~ate which contains a 6 to have all th ree baryons unboun d with resp e ct to one anothe r; th a t is, the two nonr esonant nucleons may not form a spectator deuteron. The relative kinetic energies of the three b a ryons smear th e cross-section for 6 production towards higher photon energies . As discussed in more d e tail in Appendix C, th e smearing might be as much as 100 MeV . Recal l that for t he r e ciprocity test to have significar.e inde- penden t of absolut e normalizations of th e cross-sections, the interference between th e 6-producing amplitude and some T-invarian t a mp litude must b e large . As discu ssed in Appendix C, even at energies n ear thresh old several a mplitudes contrib ute to y + He 3. ~ p be produced in several amplitudes. + d. Likewise , a 6 could This is a f avo rable situation in that there ar e more possibilities for int e rf erence . Sp eci fic models (Appendi x C) predict the most likely amplitudes for 6 production are magneti c dipole 20 ,--r -8- 10 1 Reference 73 78 82 x 48 + z 0: 0 0: cc I 1- l w (J) '-... (J) z cc 0: m D cc 2 10- 1 :L I I _L__ L_1 100 _,____L1-__J..._____. i_ _I.__ _1 200 300 400 500 INCIDENT PH OTON ENERGY CMEV) Fi gure 1 . 1 Exi s ti ng Cr oss -S ec tion Da ta on + He 3 + p + d at 90 °( c . rn .) y I 600 -9- trans itions sys t em . leadin~ to either a 4 s 312 or a 2n312 state of the p + d Mos t of the cross-section at energies below 200 MeV is due to transitions to doublet final spin sta tes. If this trend a pplies to the T-invariant part of the cross-section above 200 MeV, the trans ition to the 2 n312 could be small and still h ave a large interference term. Indeed, the interference effect in y + He 3 + p + d might we ll be stronger than in y + d + n + p. At the t ime this experiment was proposed, oth er group s h a d stated their plans to restudy n + d + d + y . Rather than duplicate these efforts , we desired to provide an independen t che ck on the then currently observed failure of the reciprocity test. The reactions y + He 3 .+-+p '+ d h ave qualit atively equal, and perhaps even greater, sensiti vity to a possible T-violation . They also enjoy the advantage of cleaner b ack- ground separation in both the forwar d and reverse reactions. Indep endent of any considerations of T- invariance , meas ur ement of y + He 3 +-+p + d a t 6 production energies would ex t end the study of the three-nucleon problem to a new kinematic region . While this problem is sufficiently comp lica ted a t low energies , we may hope for simplifications when the energy of the probe ( i . e ., photon) is l arge compared to the binding energy of the nucleons . We have therefore investigated both reactions y + He 3+-+ p + d a t energies near 300 MeV above threshold (in the center of mass frame ). This thesis reports the measurement of the differential cross-section o f the reaction y + He 3 +p + d for incident photon energies between 20 0 -10 - and 600 MeV . The e}i..-periment was performed at the Cal t ech 1 . 5 GeV elect ron synchrotron . The inverse experiment h as b een pe rfo rm2d at the ) 1 84 inch cyclotron of the Lawrence Be rke ley Laborat ory * . The data fro m t he inverse reaction are not y e t comp l e t e ly analy ze d and will b e r eported el sewhere . * Forme rly the Lawrence Ra diation Labo ra t o ry. -11- II. EXPERIMENTAL METHOD In this e xpe riment we wished to measure the differential cros ssection of th e reaction y + He 3 -> p + d at energies such th at an i ntermediate state might contain th e f..(1236) nucleon resonanc e . This could o ccur with photons of energies around 300 :MeV hitting a stationary He3 t arget . In view of time and cost limitations, we measured cross- s ections at c en ter of mass angles 30° , 60° , 90°, 120° and 150°, and to l esser pre cision , at 75 0 0 and 105 , for incident photon energies between 200 and 600 MeV . The main fe atures of th e experimental me thod were : 1. High energy bremss trahlung photons were produced at the Caltech 1.5 GeV electron synchrotron . y 2. The p hotons were incident on a t arget of liq uid Re 3 . 3. Both th e proton and the deuteron produced by th e reaction + He 3 -+ p + d were observed in wire spark chamber arrays . 4. The spark ch ambers were tri ggered b y an appropriate coinci- dence o f signals from scintillation counters interspersed among the s park chambers . 5. One of the arrays also c ontained a bendi n g magnet , yielding a precise measurement of t he moment lun of the detected particle; also measured was the time of fli gh t 6. of the particle in th e array. The da t a were r ecord e d on magnetic t ape u sing an on-line PDP 5 computer. Section A of this ch apter c ontains a discussion of th e motivation -12- of the choice of technique, followed by a more detailed description of the apparatus and procedur e s in Sections B and C. are summarized in Section D. / The data collected -13- A. The Choice of Techniques 'Jihe only copious source of high energy photons is the bremsstrahlung of high energy charge d particles, which produces a b eam of intensity inverse l y proportiona l to the photon energy . bremsstrah l ung beam of the C a l~ech As the cross-section of y We used the synchrotron. + He 3 ->- p + d was expected to be low, it was i mportant to take advantage of the greater density of a liquid t arget as opposed to a gaseous one . This invo lv es some technical diffi- culty as He 3 has the lowest liquefying t emperature of any known sub stance . We were fortunate in obtaining a condensation-type liquid He 3 target on loan fro m the Lawrence Berke l ey Laboratory. The final state of our reastion contains two particles . As the energy of the photon initiating . the reaction was not known , two quant ities must be measured in the final state to provide a comp lete description of the reaction (assuming definite masses for the final state particles ). Rather than observe the energy and angle of only one of the particles, both particles were observed. This is important more for the suppression of backgrounds due to three particle final states than for measurement of the desired reaction. The laboratory production angles of both particles and the momentum of one were measured, thus over -determining the description of a two-particle fin al state by one quantity . The particles' azimuthal angl es play no part i n the description of a two-body final state except that they must differ by 180°. Thi s need not be so when only t wo particles are detected out of a three-body state. -14- The angles were measured in wire chamber arrays, one for each particle. This technique offered the advantages of good angular reso- lution and compute ri ze d processing of the data. One particle was momen tum analyzed in a magnet placed behind the wire chambers. To make full use of the magne t's aperture, a second se t of wire chambers was placed behind the magnet . With the observa tion of t wo angles and a momen tum, there are two independent constraints which can be used to eliminate backgrounds. Scintillation counters were used to trigger the spark chambers and to help identify the particles. For the latter purpose , the pulse heights of the signals from several of the counters were measured for each event. Additionally , the length of the magnet and its array of chambers and counters was sufficient for a measurement of the time of flight of the particle through this array . A very i mportant feature of the experimental method out line d above was that all of the data could be processed by an on-line computer and recorded onto magnetic tape. A detailed description of each event was obtained without photographic techniques, making it possible for subsequent data analysis to be performed by only one person. / - 15- B. Apparatus Thi s experiment was performed in the ' south ' b eam of the synchr otron . The photon beam was produced by the b rems s trahlung of the 700 MeV cir culating electron beam striking an internal t arge t of 0.2 radia t ion lengths of tantalum . The details of the photon beam spectrum are di scussed i n Appendix D. There were two beam pul ses per second wi t h a duty cycle of 12% . Figure 2 . 1 shows the l ay out of the b e am . The beam wa s co lli- mated to a cone of angle roughly three millira di ans by t he t wo lead collima tors . Cha r ged pa rticles we re r emoved fro m the b eams by two magnets : the " r a da r" ma gne t, ·which de flect e d pa rticles v e rtically , followe d by the " sweep" magne t , which de fl e cte d hori zontally . The s we ep magne t was i mme di a tely foll owed by a four inch lea d wall to ab s orb the swept particle s . A helium b a g (t o r e duc e pa ir production ) e x t ende d from the first l ead wall to a second l ead wall e i ghteen inche s b e fore the He 3 t a rget . The aper ture s of the l ead walls we re c ons ide r ably l a r ge r than th e beam cros s -sec t i on . For r uns with the magne t spec t rome te r at the most f orward ang l e s, a l ead pipe thr ee i n che s in di ame t e r was pla ce d b e t ween the second l ead wall and the t arge t to suppres s t he sp r ay of ch a r ged pa rticle s , mos tly e l e ctrons , a t small ang l e s . The l eng th of t his b e am was thirty - three fee t from the t a nta lum targe t t o t he He 3 targe t . inche s in diame t er . The beam spo t a t the targe t was 2- 3/ 8 The beam was thus 5.9 mi ll iradians i n di ame t e r . The beam was continuous l y moni t ored by observing the current outp u t 0 £ a thick pl ate i on chamber intercepting the b e am about thir ty -17- fe et downstream of the He 3 targe t. A de tailed discussion of the use and calibra tion of this beam monitor is given in Appendix E. The target was a cylinder four inches long and three inches in diameter containing liquid He 3 . It s axis was along the b eam line . He 3 was condens e d at the expense of evaporation of liquid He~ The De tails of the operation and monitoring of the target are given in Appendix F. As outline d above, the final state particles were detected in two arrays of wire spark ch amb e rs and scintillation count ers . called the magnet and r ange 2.2 and 2.4 resp ective ly. 21 They are arrays and are illustrated in Figures The measurement of the complet e angular distribution of the reaction y + He 3 + p + d r equired the detectors to be place d at angles ranging from 20° to 145° to the beam. array was limited by space to angles less than 90°. The magnet It was used to detect whichever of the proton or deuteron had the smaller laboratory angle. The range array was used to detect the other particle, be it deuteron or proton, produced at large angles. The eleme nts of the magnet array were four scintillation counters (made of NE102) and ten wire chambe rs, mounted six in front of and four behind the magnet. A lead wall shielded all but the central region of the detectors from th~ target. spray of particles emanating from the At times, a plastic absorb er was placed over the cutout in the lead wall to further reduce the spray. Various dimensions of the array elements are listed in Table 2.1. The bending magnet deflected positively cha r ged parti cles down- SCINTILLATION COUNTERS 3 He TARGET --0---ABSORBER J ~;s~j/f / SCINTILLATION COUNTERS ~ ~'lit LE AD WALL WIRE MS3 8 MS4 ~LEADS~~ " " - - - - - - - SPARK CHAMBERS . Figure 2. 2 I -D The Magnet Array I-' 00 I I 1 -, l(/ -19- Table 2.1 Elements of the Magne t Array Height (iti:ches) Wid th (inches) Thickness (inches) Distance From He3 Target (inches) Plastic Absorber 10 6 O, !-:-4 , 12 31 Lead Wall Cutout 10 6 1 32 Scintillator MS l 15 15 14 40 Wire Chambe r 1 25 9 0.34 43 Wire Chamber 2 " 9 " 51 Wire Chamber 3 " 9 " 59 Wire Chamber 4 " 9 II 67 Wire Chamber 5 II 9- " 75 Wire Chamber 6 II 9 II 83 Scintillator MS2 16 4 14 90 Wire Chamber 7 19 19 0.34 177 Wire Chamber 8 " 19 II 189 Wire Chamber 9 " 19 " 201 Wire Chamber 10 II 19 II 21 3 Scintilla tor MS3 19 19 3/4 21 7 Scintilla tor MS4 " 19 " 218 -20- ward in the l aboratory. 0 The angle of b end of the central r ay was 27 . The gap between the magnet pole tips was fo ur inches wid e . The magnet an d it s array of chambers were mounted on a trolley which could b e rotated about a vertical axis thr ough the He 3 t arge t (see Figu r e 2.1). During the experiment , th e t ro lley was placed at t wenty settings ranging fro m 23° to 82° with respect to the photon beam . The signatur e of a particle in the magnet array was a coincidence of pul ses fro m all f our magnet scintillations count e rs, with appropriate allowance for th e time of fli ght of the particle . However , the kinetic energi es of the protons and deuterons we re low, so that in certain cases , generally at l arger angles, the parti cle s may be absorbed in counter MS3. A coinci dence of only counters MSl , 2 and 3 was · required in these cases . As a check on the identity of the p ar ticle in the magnet array, its time of flight between counters MSl and MS3 was measured. An appropriate bias on the time of flight exclud e dpions, and clearly distinguished protons fro m deuterons. Figure 2.3 shows a typical time of flight spectrum for a run in which both protons and deuterons were obs erv ed in the magnet. For further id entification of the particles, the signal pulse heights in counters MS3 and MS4 were digitized and recorded (cf. Section C). The spark chambers consisted of two planes of wires, yielding x-y coordinate info rmation. The wires were s paced t wenty- five to the 1080~~~~~~~~~~~~~~~~~~~~-,--~~---~~--. S~TTI NG 19 RUN 68 PRSS 1 810 (/) Protons 1- I N f--' I z=::) 5l!O ·o u 270 Deuterons 01-....-~--.!=:~~~-l.~-=-~-'--=:~--'=~~~W=-~~....J.-~~---'-~~---l 0.0 40.0 Figure 2.3 80 .0 TIME LJF FLIGHT 120.0 A Typical Time-of-Flight Spectrum 160 .0 -22- inch, with a gap of 0.34" between planes. They were operated at 10 KV with a gas mixture of 90% neon-10% helium and a small amount of alcohol as a quenching agent. The gas was purified and recirculated by two Lawrence Berkeley Laboratory spark ch amber gas purifiers. The sparks in the wire chambers in front (i.e., upstream) of the magne t served to define a straigh t line along a particle's tr a j e ctory, thus determining its polar and azimuthal ang le with respect to the photon beam. The additional chamb e rs b ehind the magne t define d a second line. These two lines, together with the magnetic field streng th, dete rmined the pa rticle's momentum. Multiple Coulomb scattering limited the accuracy to 0.5 - 1.5%, depending on the setting . The method of the momentum calibration is described in Appendi x G. The second particle in the final state was detected in the r an ge array . This ar r ay was a l s o moun t e d on a trolley, and was set at ang les from 75° to 145° to the photon beam in the course of the experiment. A l ead wall wi th a square aper t ure was f ollowed by five wire spark chambers and three scintil l ation counters . were identical to those behind the magne t. The wire chambers Various dimensions of the ar r ay elements are lis te d in Table 2.2. The signature of a p artic le in the range array dep ended on the partic l e ' s ki neti c energy. for a tri gge r. When low, only RS l o r RS l· RS 2 was required To insure tha t there were suffici en t spari<s to form a reliable line, counter RS l was mounted after the fourth ch amb e r. To i dentify the particles in the range array , the pulse height s SCINTILLATION COUNTERS a RS3 RS2 RS1---~ He3 GRGET _Jl J_~ r}i \____ I N - !J (I) t'i- 111 ) v WIRE SPARK CHAMBERS Figure 2.4 111111 ...... 11 ...... 11-v- - The Range Array WIRE CHAMBER AND CARBON PLATE ARRAY w I -24- Table 2.2 Elements of the Range Array Height (inches) Width (inches) Thickness (inches) Distance From He 3 Target (inches) Plastic Absorbe r 12 12 o, 1/8, ~ 19 Lead Wall Cutout 12 12 1 20 Wire Chambe r 1 19 19 0.34 25 Wire Chamber 2 " 19 " 31 Wire Chamber 3 " 19 " 37 Wire Chamber 4 II 19 " 43 Scintillator RSl 17 17 ~ 47 Wire Chamber 5 19 19 0.34 49 Scintillator RS2 19 19 3/4 53 Scintillato r RS 3 " 19 " 54 / - 25- of the signals of all three counters were measured and recorded . The signature of an event, for which the ch ambers were pulsed , was the coincidence of the separate signatures described above. -26 - C. Electronics Th e electronics used in t his experiment served t wo purposes: to indic ate th e presence of candidates for a y + He 3 ->- p + d event and t o r ecord onto magnetic tap e th e d ata associated with such an event . A bl ock diagram of the electronics u sed t o d efine an event is s hown in Figure 2.5 . Most of the circuits , l abelled LIM, DISC, etc. , were d esigned and built at Caltech . Table 2.3 r e lat es the abbreviations u sed in Figure 2.5 ( and Figure 2.6) to the n ames of th e c ircuits as d escribed i n r eferences 22 and 23. The b as ic signature of an event i s the coincidence of signa ls fro m th e seven scin t illation c ounters RSl-3 and MS l-4. As me ntione d above in Sect ion B, counters RS2, RS3 a nd MS4 were no t u sed in some runs , and h ence l eft o ut of the coincidence . to comp l ete this coincidence . Two more signals were r equired The 'beam gate ' signa l was u se d to su ppress events of co smic ray ori gin . . Finally, a 'veto' signa l indicated th ~t an event h ad not occurre d within th e l as t 0.2 second s , allowing the sp ark ch ambers time to r ec ove r. As the b eam g ate signal was only about 0.1 s ec ond - lon g , the elec tronics allowe d at mos t one coincidence p e r beam pul se of the synchrotron. The output signal from a master coincidence initiated the recording of an event: it triggered the spark chambers, pulse height analyzers , and the comp ut er . It also ~nhib ited the scalers observing the scintillation counting rates and the beam monitors during th e mandatory 0. 2 second d ead-time following an event. corrections were needed for this dead-time . Therefore, no -2 7- I RS I I RS 2 n f'SI .IS3 MS4 MS2 BEAM GATE DISC DISC DI SC GATE ,... GENERATOR MASTER \V COl ~KIDEN CE TO SCALER AN D INTEGRATOR G./.\TE S VETO GENERATOR ' TO P.H . A. GATE S CO M PUTER SPARK CHAMBER K /·~~~~--' TRIGGER TO SPAR K CHA MBER S @ 8 ILJ::::LLL Fig ur e 2.5 =SCALER = PU LSE HE IGHT ANALYZE R = VJ'.'.1.RIABLE DELAY CABLE The Tri gge r Electronic s -28- Table 2 . 3 Calt ech-Des i gne d Electronics Used in This Experiment Name in Figures 2.8, 2.9 Name in References LIM Limiter-3 DISC TVD- 3B COIN TC-6 FAN Limiter-3 Spark Chambe r Trigge r SCT-1 SPHA SPHA- 1 GATE T6 - 3 Fast AMP FA-1 Veto Gener ator not described Ga t e Generator not descri bed -29- The data we re r ecord e d onto magneti c t ape via a PDP 5 comp uter. For each event, 18 3 12-bit words cons titu ted a ' record'. ·ward · Data Run fl Event II Se tting fl Pulse Heights Beam Monitors Spark Coordinates 1 2- 3 4 5-10 11-13 14-183 At the end of each run , three additional records were written. Two con- t ained summary distributions of the pulse heights and the third was a comment record, stored in BCD characters . The analog to digital conversion of the signals fro m the s cintillation counters in the electronics is diagrammed in Figure 2 :6. The pulses from counters RSl , 2 , 3 an d MS4 were shaped into pulses of standard voltage wi th duration proportional to the area ( charge ) of the input pulse in the SPHA-1 circuits . The output pulses were digitize d by a Lecroy Mode l 151 quad digitizer , and then transmi tted to the computer . The pulse height from counter MS 3 and the time of flight of particles between counters MS l and MS 3 were processed in a Nuclear Data Mode l 160-F, 150-M analogue to digital converter . A TVD-3B circui t in its start-reset mode was used to produce a pulse of standard voltage and of duration proportional to the time difference between signals from counters MS l and MS 3. During each run , the computer accumul ated distributions of the pulse heights and displayed them on an oscilloscope. Figure 2 . 7 shows such a display for a run in which it was possible to detect deuterons - 30 - ' ( SI M IL AR LY FOR RS2 1 RS3 AN D MS4) 'V COMPUTE R y ~GATE ~ ' ,,, GATE START / ~r1 RESET 'V CO MPUT E R ' ' C0 1~ PUTE R PU L SE HEIGHT ANALYS IS Figure 2 .6 TI ME OF FLIG HT The Pulse Heigh t Ana l ysis Electronics -31- ,"'. . .. ;. ·. -- ...._ "l'a ... -, ,~ , ·. - . - 1· RS l RS2 Time- cf-Flight Figure 2.7 _. -...::,:._ . - -: ..... -- ·~ RS 3 . ·......--;.:._ --.....~~· MS4 MS3 Examp l e s of the Pulse Heigh t Spectra Display -32- in both the magnet and r ange arrays. The large peak in the time of fligh t spectrum is due to protons , with a smaller peak due to deuterons · at la t er times . The othe r five displays are s c in t illa tion c ounter pulse heigh t spectra . They also show the expected doub l e peaked struc- ture , protons having l ower pulse heights than deuterons . For each event, the cumulative outputs of three beam moni to r s were recorded . Specifically , they were the thick pla t e ion chamber and the two thin plate ion chambers , discussed in Appendix E. A spec i a l circuit was built to interrogate the output of the ion chamber cur r ent integrators and transmit this information to the computer . These data were not used extensively in the later analysis of the experiment. The last block of electronics was for the purpose of converting the signals from the wire chambers to digital form and transmitting the results to the comp uter . These circuits and their operation have been des cribed in de tail by Charles Presco tt 24 • For each event , the compute r displayed the coordinates of the digitized sparks on an oscilloscope . from a good event . Figure 2.8a shows this display (Eowever , some of the se cond fiducials are missing .) The particles ' directions are from left to right . view , the x a side view . They view is a top The first six columns of sparks are from the front magnet chambers ; the next four are from the rear magne t chambers ; the next five are the front range chambers ; and the last t en are the (little used ) rear range chambe rs . Figure 2.8b shows a multiple exposure of severa l events , illustrating the spread of tra cks in the chamb ers. - 33- ..... •. r ·· ·· ·· ·· '··· .... ........ : . ... , ... .. .. >;;: •.•• .... a . An Event tlll ... ." v ....'i:. ....II '·' ..•. . ...... . .• ' ~!:~ !; ~ ~ .. . ·"· ; : : : I : i ....... 1.tt . a: .:., ...... •• 1. ·: .. ,u. .' ..... ; : I ! : I , ... . ..... b . Mult i ple Exposure of Several Event s :Figure 2.8 Examp l es of the Spark Chamber Display -3!,- D. Summary of Data Collected Appro ximate ly 300,000 tri gge rs were collected in t wo months of running . There were 135 runs at a to tal of thi rty-four settings of th e app aratus . The dat a occupy nearly fi fty 2400 foot magnetic t a p e s, r ecorded at 200 bytes p e r inch. Table 2.4 summariz es t he basic parameters of th e variou s settings , and the number o f events c ollected at each . Th e paramet er listed ar e : e c;m. = center of mass ang le o f final proton, Ey = average incident photon energy, 8 Magnet = l ab angle of th e magnet array, 8 Range = lab angle of th e range array . Protons were d etected in the magne t arr ay at settings 1 - 18; while deut e ron s were det ected at th e other settings . In addition , a short run was made at each setting in which the He 3 target was empty, in order to investig ate the possible origin of events in the target walls. -35- Tab l e 2.4 Summary of Data Co llecte d Setting Ey . e c. m. e Magri.et e Range Events . (MeV) 1 250 30° 26.4° 140 .5° 13,5 27 2 250 30° 26.4° 140 .5° 5, 718 3 300 30° 25.4° 138 .0° 10,145 Lf 300 30° 25. 4° 138 .0° 18, 800 5 400 30° 25.0° 135 .9° 8,578 6 400 30° 25.0° 135.9° 19,676 7 200 60° 53 .4° 105.5° 12,919 8 300 60° 51 .9° 102.5° 12'116 9 300 60° 51.9° 102.5° 9,709 10 400 60° 50.7° 99.8° 3,911 11 450 60° 50.7° 99.8° 6,2 69 12 300 75° 46. 8° 91.6° 11,264 13 20 0 90° 82.0° 75.6° 7,6 80 14 250 90° 82.0° 75.6° 5,119 15 300 90° 80.3° 72.7° 4,162 16 300 90° 80.3° 72. 7° 6' 395 17 350 90° 78.3° 70.5° 4,142 18 400 90° 78.3° 70.5° 2,490 19 350 90° 72. 7° 80.0° 4,600 20 400 90° 72. 7° 80.0° 4,097 21 400 90° 70.6° 78.2° 7,121 22 450 90° 70.6° 78.2° 1,081 23 300 105° 59.3° 95.1° 16,015 24 250 120° 48.7° 112. 3° 7 ,172 25 300 120° 46.8° 110.7° 12,975 26 350 120° 46. 8° llO. 7° 4,693 27 350 120° 45.3° 108. 7° 762 28 500 120° 45 . 3° 108. 7° 5,41 2 -3 6- Tabl e 2.4 (Cont i nued ) Se tting_ Ey . (MeV) ec.m. e Magnet e Range Events 29 250 150° 24.0° 145.3° 2, 727 30 250 150° 24.0° 145.3° 6,397 31 300 150° 22.9° 144.1° 8,971 32 350 150° 22.9° 144.1° 4,794 33 400 150° 22.2° 142.9° 5,107 34 450 150° 22.2° 142.9° 6,755 -37- III . DATA ANALYSI S The task of analyzing the data in this experiment involves two separate problems . Firs t, true y + He 3 7 p + d events mus t be extracted from all the events collected, and second , the efficiency of the apparatus for collecting such events mus t be determined . Prior to the selection of good events, the tracks of the particles mus t be reconstructed from the spark coordinates in the wire chambers as described in Section A below. The tracks then are used to calculate various quantities needed to comp lete the experimental des cription of a n eve nt (S ection B). The procedure for separating .good events from bad is discussed in Section C. The most important efficiency is the geometric effic iency ( so lid angle ) of the apparatus; including the acceptance of the magne t. This was calculat e d with a Monte Ca rlo c ompu ter program, discussed in Section D. Other efficiences , such as that of the spark chambers and electronics , are also considered in Section D. The conversion of the preceding results into cross - sections is described in Se ction E and the systematic errors and resolution are treated in Section F . -38- A. Track Reconstruction For each event there we re three straigh t tracks to be found in the wir e chambers : one in the six fron t magne t array chambers, anothe r in the four rear magne t chambers , and the third in the five range ar ray chambers. Each chamber provided x and y coordinate information on the sparks within. The b as ic approach to the track fitting follows that of S. Cheng and C. Prescot t in an earlie r experiment with the present wire chambe r system 25 Taking the z axis as perpendicular t o the pl anes of the chambers, straight track projections were found in the x-z p l ane and y-z plane independently. If more than one such projection is found in either p l ane , there is an ambiguity to be resolved as to wha t is the real track in s pace . We did not utilize the common solution to this problem which is to include chambers in the array with wires running a t, 0 say , 45 , to the x and y axes. Conside r first the problem of finding a track projec tion in a single view . Dep ending on the array , there were 4, 5 or 6 chambers with up to four sparks in each . Any pair of sparks in different chambers forms a line segment which potentially belongs to an actual track projection . The procedure was to extend each such line segment int o the other chambers and check if any sparks we re within 0 .1 11 of the resulting points of int erse~tion . as a possible candidate. If not , the line segment was rejected If so, there were three or more sparks lying in a strip of width 0.2 11 , and it was assumed that a real track projection -39- was to be found therein. A straight line was fitted to each group of three or more sparks within the strip, and that line with the minimum chi-square per degree of freedom was taken as the true one. This procedure was tested by comparing the results with a visual scan of the spark data as displayed on an oscilloscope by special playback program on a PDP 8 computer. There was less than 1% disagreemen t in whether or not a track projection was present, and in the dllputed cases, I j udge the above procedure to be more reliable than a visual scan . Thus I estimate the track finding algorithm to be b ette r than 99% efficient a t finding tracks , if they can be found . I believe many of the disputes were caused by events in with a phantom ' s12ark' occurred before the first fiducial , which has the effect of shifting the coordinates of real sparks . The eye tends to be more lenient than the computer in accepting these spurious shif ts. This effec t als o com- plicated the estima tion of the spark efficiency of the chambers , as discussed in Section D below. The relations between the front and rear magne t tracks discus sed in Appendix G allow events to be saved if tracks are missing due to chamber ine fficiencies in one or the other region (but not both ). Because the magnetostrictive wands can suffer ine fficiencies , sparks missing in the x-z and y-z views are not always correlated. As noted in Appendix G, the x-y and y-z vi ews of a track in frcnt of the magnet are inde pende ntly related to the corresponding views of the track behind the magnet . Thus, if there were not enough sparks to define a track projection in the y-z view in front of the magne t, but a y-z vi ew -40- track projection is present behind it, the front track projection can be extrapolated from the rear. To insure this process did not invent spurious tracks, it was required that there be two sparks in the front chambers along the extrapolated track. For the x-z view, the relation between the front and rear track projections depends on the particle's momentum . It is possible to determine the momentum given only a track projection on one side of the magnet and one spark on the other. Again, it was required that two sparks could be found that yielded the same momentum before the missing track projection was declared recovered. These procedures salvaged about 5% more events than would have been possible without them. We now consider the problem of determining the real track when more th an one track projection ap pears in the x-z and /or y-z views. In less than 1% of the event s were there more th an one track projection in both x-z and y-z views of an array , as anticipated when the experiment was designed. However, the circumst ance that one view has more than one track proj ection whi le the other has only one occurred about 10 to 15% of the ti me in the r a nge chambers . This most probably indicated the presence of an electron in the chambe rs, as an electron suffers significant mul tiple Coulomb scattering , so that its path is not very straight . Thus it was possible that such events had a reconstructible track projection in only one view . The :following procedure was used in al l cases when there was a multip le track ambi guity in the front magne t or range ch ambe rs . Each track projection in each view was ex trapolated into the He 3 t arge t, and -41- tho se which missed the target by more than l " were rej ected . Then, for b oth arrays, a track in space was fo rmed by combini.ng one x- y view track projection with one from the y-z view . The 'coplanarity ', or dif ference between the azimuthal angles - 180°, of the two t racks was c alculated. This was done for all possible combinations of track pro- j ections from th e x-z and y-z views , and the combination with the minimum coplanarity was chos en as the 'real' one . As noted above , in most instances when this procedure was necessary , th ere were only t wo combi nati ons , resulting fro m f ive tr ack projections i n the four vi ews i n the front chamber arrays . FurthE::r , most often the ambiguity was in the r ange chambers , which would not affect th e later c a lcula tion of the incident photon energy which is de rived from quanti ties de termine d in the magnet array. Thus I feel that the practical effect of possible mischoices is below the 1% level - the fr ac tion of events where the ambiguity was in the magnet array. In case of an ambiguity in t he r ear magnet chambers , th at track was chosen which whe n comb ined with the other tr acks pre dicted the sma lles t deviation in a calcul ation of the proper ties of the p artic le in the r ange chambers . This choice was necessary l e s s th an 1 % of the time. The tracks in the magnet array were investigated as to whether the work. particl ~ had scatt ered off of the mabnet pole tips or othe r fr ame- This was done by e x trapo l ating th e fr ont tracks to the r ear of the magne t and comparing wi th the observed track . If the comparison -42- was not satisfactory , the event was r ejected. Mul tiple Coulomb scattering rendered this comparison l ess decisive than is desirab le. I feel it would have been wise r to have placed scintillation coun ters around the boundary of the magne t gap , so that any partic le outside the desired region could have been vetoed on the bas is of a signal in these counters. Figures 3.1 and 3.2 illustrate the results of the track reconstruction . The coordinate frame h a d the z-axis along the photon b eam which was horizontal in the l ab ; the x-axis was vertical and the y-axis was horizontal. Figure 3.1 shows the projection of the reconstructed event vertices onto the x-y plane . in radius. The beam spo t was about 1.2 . inches In general, the tracks in the front magne t and range cham- bers did not intersect but are skew , and a ' vertex ' as plotted is the mid-point of the line joining the clos es t points on the t wo tracks. Figure 3 . 2 shows the distribution of the skew distances of closes t approach of the two tracks. In Figure 6.6 of Appendix D, the radial distribution of event vertices is compare d with a curve taken from densitometric analysis of a photo :~raphic plate exposed in the photon beam. / -43 - 1. s . ·' . . . :.. .: ,..... en w I LJ z 0.0 .· t--1 -. - "'--/ >-1 .5 . The cir cle indicates the position of the target walls. -3.0 -3.0 -1.S 0.0 1.S X CINCHES) X-Y DISTRIBUTIO N OF EVENT VERTICES Figure 3.1 3.0 RUN 68 200 .--~~-.-~~~-,--~~-.-~~~-.-~~--,-~~~-,.-~~--,~~~~ 150 ()) f- z 100 ~ ..,..I ..,.. 0 u I 50 ~~.0~~~1-~~~~__::___i_'::~~~~~~~=i.~~~~-::""~~_L_~~~ 1.0 2.0 3.0 4.0 INCHES SKEW DISTANCE BETWEEN TRRCKS - RUN 68 Figure 3.2 -45- B. Eve nt Recons t ruc ti on With a know l e d ge of th e tr acks , a nd the momentum of the p a r t icle in a magne t, fu ther p arame t e r s o f an e ven t c a n b e c a l cula t e d. Event s for which this inf o rma tion i s availab l e are c a lle d ' r ec ons t r uctibl e '. The polar a n d a zimu th a l a ng l e of each p a rticl e with r espe ct to the photon beam are obta i ne d at once . Ca ll th ese 8M and ¢M fo r th e particl e d e tected in the magne t array , a n d 8R and ¢R for the p ar ticle i n the range array. The coplana rity of the t wo p a rticle is d e fin e d by For a sc a ttering with only t wo p a rticle s in th e fin a l state , the coplanarity should be z e ro . However, multipl e sca ttering broade ns the d istribution eve n for re a l events . Figure 3.6 shows the coplanarity di stribution for all reco nstructible events in run 74. A peak of half width about 1° cont a ining the good event s is seen to rise above a broader background. I f t he i d e ntity (and h e nce the mas s ) of the particle in the magnet array is a ss u me d, then the mass of the particle in t he range a ~ray , the inci dent photon energy and the c enter of mass angle of the scattering c an be c alculated. E 8c.m. Thus 2 MH~ - M2 H - ~ + ~ 2(M H ~ + PM c os 8M) = tan -1 ~M· s in e,, y (PMcos 8M - SE ) \ l I I -46- E/(E + ~) 8 where ~I = mass of ~' hi (1-: 8 2) ~+ .p2M ·. ~ • y He3 ~=mass , PM, momentum and energy of the par ticle in the magnet array . MR= mass of particle in the range array. E = incident photon ene rgy . 8c. m. = scattering angle of the proton in the y - He3 center of mass frame . In practice , E was calculated using the exact value of ~ (assuming a c orrect p a rticle id entification) while the calculation of MR was used to s eparate good events from bad. Figure 3.4 shows a distribution of the quantity ~ (calculated ) - ~ (exact ) for all r econs tructible events in run 74 . This is called th e missing mass although it is more precisely a mass ex cess. The good events li e in a peak of width about 20 MeV /c 2 centered at zero while the background events center at 50 MeV /c 2 with a width of about 50, in this case. Fi gure 3.5 shows t he reconstruction of the inciden t photon energy sp ec trum for the s ame run. to b e entirely b a ckg round . Events below 250 MeV will late r prove The number of events at a given incident photon energy is, of course, directly related to the cross-section. Thus th e r emaining effort in proc ess ing th e events is to exc lude bad events fr om this di stribution. All other distributions are secondary in the sens e that whi l e they can aid in th e elimina tion of b ad events, 120 .---~~-.-~~~-r-~~-,-~~~-r-~~--,.~~~~~~~,--~~-. 90 en 1- z ::i 0 .GO I .i:-. ---J I u 30 0 '--~~-'-~~~_.__~~_._~~~-'-~~---L~~~-'-~~~'--~~-' -12.0 -6.0 - 0.0 . COPLRNRRITY CDEGREES) Figure 3 . 3 A Raw Coplanarity Distribution 6.0 12.0 160 .--~-,-~~~~-.--~-.--~--T~~~~~~~ 120 en f- z ::::) 80 I 0 ~ co u I 40 OI - 200 . 0 ~u u- I - 100 . 0 I I 0 .0 I I I 100 . 0 MISSING MRSS EXCESS CMEV/C~~2) Figure 3 .4 A Raw Missing Mass Distribution L,11 I 200 . 0 200 .---~-.-~-.-~--.~~--,--~-.-~--.~~--,--~--. 150 en 1- z~ 100 ..,..I 0 \.0 I u 50 0 0 .0 200 . 0 400 .0 GOO .0 INCIDENT PHOTON ENERGY CMEV) Figure 3.5 800 . 0 A Raw Incident Photon Ener gy Spectrum -so- t hey are not simp ly related to the v a lue of the sca ttering cro ss-sec tion. We h ave so f ar a ssumed the identities of the particles detected l in t he ma gne t and r ange arrays . The various pulse hei ghts and the time of fl ight measurement were u se ful to check t his . intersection of th e First , the points of tracks and the scintillation counter were calcu- lated and a correction applied to the pulse heights f or t he variation of l ight output. as a function of pos ition. Depending on whether a proton or a deu teron was expec t ed in t he magnet array , diff erent pulse h e ight distributions arc most use ful. If a _ proton was in th e magnet array, the width of th e gate in th e time of fli ght circuitry di scriminated against p ositrons and deuterons. Fast prot ons cou ld conceivab l y be confused with s low pions in the time of flight spectrum . Th e pulse heights of t he magnet scintillation coun t ers for such protons and pions ·were in th e s ame rang e . Thus th e electronics of the magnet array provid e d a fairly pure sample of protons , which could not.b e furth er purified by loo k ing at the detai ls of the time of flight spe ctrum or the magnet _scintillator pulse h e ights. A proton in the magne t array should cor·r.es pond to a deuteron in the range array . The deuterons were slow moving compared to the spee d of li ght and consequently had large pulse heights . Figure 3.6 shows the pulse height distribution of particles in count er RSl of the range array, for a run with predominantly protons in the magnet array. Deuterons have pulse heights of roughly 400 or more (arbitrary units). The separation of deuterons from (in all probability) protons with high pu~se h eights is not comp letely clean ; individual events 80 l GO en f- Z ~ 40 I Vl 0 f--' I u 20 OL_l__~j_~~_L_~~_L_~-::-=--1-:-~~___i__::-=..L.L~~~J..U.....l_J-U_.__~~ 0,0 480.0 Figure 3 . 6 960.0 RSl PULSE HEIGHT 1440 .0 A Raw Pulse Height Spectrum in Counter RSl 1920. 0 -52- cannot be positive ly identifi e d as p ~ d fin a l states . Hen ce a back- ground subtraction is nee ded. J In th e case tha t a deu teron is expect ed in the magne t, the situ ation is much simpl er . The time of flight spectrum (see Figure 2.3) allows a clear identification of deut e rons . Th e pulse height in counter MS3 was used to confirm this id entifica tion . Figure 3. 7 shows a spectrum in younter MS3 with deuterons having pul se h eights averaging eighty compared to twenty for protons . With deuterons in the magnet array , protons are expected in the range array . are electrons or pions. The other po ssibilit ies A ba ckground subtraction was made to correct for such spurious events. In summary , a reconstruct ible event is parame trized by i ts 1. Incident photon energy; 2. Center of mass scattering angle ; 3. Copl anarity ; 4. Mass excess of particle in the r ange array; 5. RSl puls e height if a proton was in the magnet array or time of flight and MS3 puls~ h eight if a deuteron was in this array. 440 .--~~-.-~~~-.-~~~--.-~~~.--~~--.-~~~-.-~~~-.--~-.----. SETTING 19 RUN 68 PRSS 1 330 (f) I 1- ll1 w z: 220 ::::) I 0 u 110 00 • 0 lJ:O. 0 '==:r=1 ~ ::::i 80.0 '-' t' MS3 PULSE HEIGHT Figure 3.7 I :1--= 120 .0 A Raw Pulse Height Spectrum in Counter MS3 I I i60 .0 -54- C. Background Subtraction Aside from accidental coincidences , the following y + He3 reactions might contribute to the b ackground of y + He 3 + p + d (only reactions with two charged particle s in the fina l state are listed): y + He3 -+ T + 1T + (1) 0 d + p + 1T } (2) d + n + 1T+ p + p + n p + p + n + 1T } (3) 0 etc. The meagre experimental data 26 on reaction (1) indicate that its cross- sec tion migh t be five time s tha t of y + He 3 -+ p + d , However, the laboratory kinetic energy of the t ritium is s o low a s to make detection difficult , and essenti ally i mposs ible with the apparatus of this experiment. . A survey 27 of y + He 3 reactions using a diffusion chamber detected on ly one-third as many T7r+ events as pd . Reactions of t ype (2) would be the principal source of background in runs where deuterons were detected in the magne t array ; abou t as many events of this type as of the pd final state were observed in the survey experi ment. The p7r 0 o r n1T+ can come from a 1'1+(12 36 ) without the isospin comp li cations pres ent wi th only a pd final state . Thus the cross-sec ti on for these rec:.r:tions might well be much gre<.lte r than for y + He 3 -+ p + d . A rat h er opt1rn1st1c . . . pa per 28 h as pre d icte . d an enh ance' ment of about three orders of magnitude . Of course , thre e-p articles in a fina l state wi ll not be so strongly correlated a s only t wo, and the -5 5- efficiency of the apparatus for detecting two out of three particles i s much less than for two out of two. Reactions of type (3 ) would be the principal background for runs . t h e magnet array . wi. th pro t ons in Tl1ere is . experimenta . 1 evi"d ence 73 that the ppn state is about as like ly as the pd state for incident photon energies below 50 MeV . However, by 150 MeV the ppn states occur about five times as often a s the pd . The previous remark about the lower efficiency for detection of three particle states app lies here also . For photon energies around 30 0 MeV , production of the pnnn + state will probably be of the same order of magni tude as of the ppn state . Thus the b ackg round consists of several different reactions about whi ch even less is known than the reaction being studied . Accordingly, no attempt was made to calculate the background . But instead , an empirical procedure was devised to esti ma te it . The desired result of the background subtrac tion is the true number of events as a functi on of incident photon energy . Howeve r, as seen in the preceding sec ti on , the 'foreground ', or good event sample , stands out from the background most clearly in the distributions of coplanarity, missing mass excess and the pulse heights. the photon energies accepted during plots. Data from all a run are lumped together in such If these distributions were calculated for only a smal l range of photon energies , there would be so few events that the statistical accuracy of any background subtraction would be poor . To overcome this difficulty inherent to experiments with a bremsstrahlung photon beam, we used a procedure devised by Leon -56- Rochester 29 . Tei make an initi a l separation of the foreground from the background, consider the distribution of all events (from a single run) as a function of coplanarity and missing mass excess. This distri- bution can be divided into two regions: the foreground region a t small values of coplanarity and mass excess , chosen to contain a ll foreground events, but having some background contamination; and the background region which consists of the remaining events and includes only background. The problem is to use the events in the background region to estimate the number and the photon energy spectrum of the background events which lie in the foreground re gion. The procedure for t4is t akes advantage of the observed fact tha t background even ts do not h ave strong correlations among the eight parameters which define an e vent: - The (3) coordina tes of the event ori gin in the target. - The (4) coordinates of t he int erse ctions of the p ar ticle's tr a cks with counters MS2 and RSl. - The momentum of the particle meas ure d in the magne t. A collection of ' fake ' events can be constructed by choosing sets of eigh t parameters a t random from those describing the background region . The eight parameters of a 'fake ' even t a r e , in general , drawn from e i ght separate background events by ·a random number gsnerator . If N is the number of events iu the b a ckground region , th en SN independent ' fake ' events can be generated ·. If the ei ght parameters are indeed uncorrelated , the ' fake ' events should r e produce the structure of the -57- background region as a function of coplanarity , mass excess , or photon energy . However, these events are not restricted to the background The ~a t i o of region but populate the foreground region as well . the number of background events in the foreground region t o the numb e r in the background region can be determined from the ' fake ' event sample . Further , a photon energy spectrum for background events in the foregroun d region is generated , and can be properly normalized using the above ratio . This normalized spectrum is then subtracted from the spectrum for all events in the foreground region to yield the corrected numbe r of y + He3 -+ p + d events a s a function of photon energy . The statistical accuracy of this procedure is easily demonstrated . Let NI be the (unknown ) number of b ackground events inside the foreground region, with photon ene.rgies in some given energy interval. The above proc edure estimate s N where N 0 I = N ·M / M o I o number of events outside the foreground region .. M =number of 'fake ' events outside the foreground region . 0 MI number of 'fake ' events inside the foreground region lying in the de sired energy interval. N , M and MI are subjec t to statistical uncertainties , l eading to an 0 0 uncertainty in NI : (cr I/NI) 2 = l/N0 + l/M 0 + l/MI As M and MI can be made arbitrarily large (up to 8N°), N is the main 0 sour ce of uncertainty in NI. 0 In this procedure, N is as l a rge as 0 -58- possible since it is the en tire b ackground region sample, not just those events lying in the energy interval of NI' as would be the case for a more typical method. Hence our method attains the maximum statistical precision available . · Rocheste r has gone to considerab le length in his thesis j ustify the proced ure in general. 29 to We have verified that the eight para- me ters u se d to describe a background event are uncorrelated, and that the resulting ' fake ' events reproduce the structure of the background (cf. Appendix H). We have checked th a t the results are not sys t emat i- cal l y dependent on the size of the background region , so long as true foreground events are not included in it . Also , the subtraction was only 10 to 15 percent , so that the procedure need no t be precise in al l details to yield goo d results. In Appendix H, the subtraction process is pres ented in detai l for a particular run . The resulting corrected pho ton ene r gy spe ctrum is shown in Figure 3.8 . A b ackground problem not ye t considered is the possibility of events originating in the material of the targe t walls , rather than in the He 3 . It is , however , unlikely that reactions in which photons hi t protons , carbon or oxygen nuclei , e tc. , could imitate y + He3 ~ p + d . To be safe , a short empty-targe t run was taken a t each se tting . The resulting event rates were not zero, but very few of them contained enough tracks to reconstruct the event . In th ese , there is no sign of a signal in the distributions of coplanarity or missing mass ex~ess . 8Q r--~-r-~-,--~--,-~~..----~--.--~-,-~--.~---., RUN 74 667 EVENTS 81 GO SUBTRACTED ()) f- z L±O :=J I Vl 0 LJ '°I 20 0 0. 0 · .-, _, .,. ci 400 . 0 GOO. 0 ~ 200 . 0 1 I -- I I I I 0 I I 800 .O INCIDENT PHOTON .ENERGY CMEV) EFFECT OF THE BRCKGRO UND SUBTRRCTICJN Figure 3 . 8 -60- Therefore, we conclude that events originati.ng in the target walls contribute only to the background as discussed earlier in this section. The background subtraction has already corrected for events of this type, so no additional empty-target subtraction was made. -6 1- D. Efficiency Calculations In the previous sections of this chapter , the method of analysing the raw data has been explained . The numbers of even ts of the reaction y + He 3 -+ p + d which result from this analysi s cannot be i mmediately converted into cross-sections . We must know , among other things , with what prob ab ility the apparatus detected such even ts. Several factors influence this probability, or efficiency , as it is called. 1. The solid angle subtended by the apparatus. 2. The momentum acceptance of the magne t. 3. The effect of secondary nuclear interactions which migh t prevent the protons and deuterons from reaching the detectors . 4. The efficiency of the scintillation counters and associa ted electronics . 5. The efficiency of the wire spark chamber system . We now discuss the calculation of each of these effects in turn . The first two are considered together . -62- 1. Geometric Efficiency and Momentum Acceptance. The geometric efficiency of the apparatus is the probability that the final state particles of a y + He 3 + p + d event pass through all the scintillation counters required for the 'signature' of the event (see Chapter II, Section C). This probability depends on basi c kinematic parameters of the event , the photon energy and the scattering angle , as well as the properties of the appara tus . Several featur es complicate the efficiency calculation. The intersection of the photon beam with the He 3 target occupies a finite volume. Particles passing through the magnet have curved trajectories . Mul tiple Coulomb scattering causes s mall deflections in all trajectories an d the energy los s in such collisions could prevent particles from r e aching the de tectors in certain cases . There is a corresponding effec t due to nuclear scattering ; howeve r, it will be considered separately. Finally, as the experimental cross-secti ons are to be · expressed in the y - He3 c enter of mass fr ame, the efficiency calculation must be done in this fr ame also . It is i mpossible to make an exac t ca lculation which t akes the above f ea tures into a ccount. program was used . Therefore, a Monte Carlo compu ter The steps in the calcula ti on of the effici ency ave r aged ove r a 10 MeV bin a t one setting of the appara tus a re: 1. Determi ne an uppe r limi t on t he s olid ane-, le subtende d by count ers MS2 an d RS l as vi ewe d in the y - He 3 center of mass fr ame . It was conveni ent to take this l imit as a region bounded by four sur f aces, -63- two of constant </J, and t wo of constant 8 , in a sphe rical coordinate system with origin at the center of the target and z axis along the photon beam. The surfaces were chosen so as to contain all possible straight lines passing through both the targe t and the counters. 2. Using a random number gene r a tor, events were generate d by choosing - a random photon energy within the 10 MeV bin; - a random event ori gi n with in the target such th a t the radial (in cylindric a l coordina tes ) distribution of events r e produce s the s h ap e given in Appendix D; - a random </J within the limits defined in step l; - a random cos 3. e within the limits def i ne d in step 1. Each event was transformed to the l aboratory fr ame whe re several tests we re app lie d to determine whether it could be de t ecte d: - Did the tracks pass through counters :MS2 and RSl? - Di d the track in the magne t array pass through the pole tips and counter NS 3? To answe r this , the results of the magnet calibration discussed in Appendix G were used. - Did the en ergy loss due to Coulomb interactions prevent the particles from passing through the entire apparatus ? ( For this, the range- ene r gy re lations for protons and deuterons were . b y J anni.30 . ) extracte d f ram ca 1 cu 1 ations 4. The fraction of successful events was multiplied by th e ; solid ang le within the 8 and (/J limits set in step 1. geometric detection efficiency . This number i s the A typica l va lue was 0.005 steradiaas . -64- In the calculation as outlined , no correction was made for the angular deflection of the tracks caused by multiple Coulomb scattering. A separate calculation including this effec t showed that, to within 1%, as many particles would scatter into the apparatus as sca tter out of it. As this calculation was about twice as expensive as the one outlined, it was not performed for all settings. The statistical error of the calculation is given by 1 relative error - /successes where ' attempts ,' · ; failure s attempts - 1 ' successes ' and ' failures ' refer to the numbers of such events generated in the Monte Carlo calculation . This is, of course , the error associated with the d etermina tion of a quantity obeying a binomial distribution. For the same number of attempts , the calculation is more accurate the higher the fraction of successes . choosing the 8 and 0 limits By ( step 1) to be as small as possible , the greatest accuracy per dollar spent was obtained . Figure 3.9 shows the calculated efficien cy as a function of photon energy for setting 14, a t which run 74 was made . The ordinate is not the ef f ective solid ang le of the apparatus , but this qua ntity divided by 4n. ated . For each bin in photon e nergy, 10,000 events were gener- This give s the calculation an accuracy of about 2.5% for the bins with large efficiency . When averages are t aken ove r five adj acen t bins, the accuracy wil l be roughly 1%. There are several sources of systematic uncertainty in the efficiency c a lcula tion : - 655. 0 .-----,-~--.-~-.-~-.-~· -,-~-.-~.-~r----r~---r~-.-~-. :::f'_ I Q ...... RUNS 7l1. 75. 78. 79. 121 h 0:: . 0 i+ u a: 4.0 LL w _J a: u (f) >z ~ 3.d LJ LJ 1--t LL LL I w z I ~' ®¢¢ ~ Q ~ ~ Q 0 1--t r- LJ 2 w ·0 rw .~ D ~ !'.!J t1J 1 .d r!Jr!J [!] [!] c:CJ crfJ 0 .0 100 ~I 200 300 400 500 600 700 IN CI DEN T PHO TON ENERGY IN ME V Fi gure 3.9 Exampl e of t h e Mon te Ca rlo Ef fi c i e ncy Ca lcula tio n -66- 1. 3% due to uncertainty in the defocusing effect of Xhe magnet 's fringe field ( see Appendix G). 2. · 2% due to uncertainty in the effective vertical aperture in the magnet fie ld. 3. 1% due to uncertainty in the target position of 0.05 inches. 4. 0.5% due to possib le error of 0.1 inches in size and position of counter MS2 . 5. 0.5% due to same effect for counter MS 3. The maximum system uncertainty is estimated to be 7%. / -67- 2. Nuclear Scattering A significant fraction of the protons and deuterons produced by the reaction y + He 3 7 p + d scattered off some a tomic nucleus in the detection apparatus. If such a sca ttering caused a large change in the energy or angle of the particle, the y + He3 7 p + d event would go undetected. A correction was made for this inefficiency, as described below. There are four cases to consider: either protons or deuterons An extra complication in lost in either the magne t or range arrays. the case of deuterons is the 'stripping ' process in which the deuteron breaks up into a proton and a neutron. In the magne t array , a scatter of 3 0 or mo re (on the average ) occurring before the magnet causes the event to be lost as the solid angle of the apparatus is very small. 0 For scatters less than 3 , a track can still be reconstructed no ma tt er whe re it occurs. cas es , the co.planarity, or or both,will be in error. In these momen tum (and hence missing mass excess ), However , the deviations are within the widths on the quantities used to define the foreground event . sample. If a deuteron underwent stripping with the resulting proton at less than 3° to the deuteron, the even t is sti ll lost, since the proton would have only roughly half the momentum of the deuteron . after the magne t are no t s o detrimental. Scatters which occur A scatter wh ich occurre d in counters MS 3 or MS4 was harmless; the event would still be detected . There was very little matter between the magnet and counter MS 3 to cause a sc a tter, so for ease of calculation , the 3° criterion was ap pli ed to -68- this region als o. I n the range array , only the deflection of a particle can cause the event to be lost. A stripped deuteron is still detected if the proton goes forward ; the pulse heights in a scintilla tor are the same for a deuteron and for a proton of half the kine tic energy. A deflection of greater tha n 5° was considered to eliminate the event, bas e d on the width of the coplanarity used in defining the fore ground event sample . Also, the scatte r would have to occur before counter RSl to have any effect . To calculate the probability of a scatter , empirical fits t o proton-nucleous and deuteron-nucleous cross-sections were made (pA) A-O.Z 6 (A(pp) + (A-Z )(pn )) (nA) l.2A-O.l?(Z(np ) + (A-Z )(pp )) (dA) ((pA) + (nA))·f0.83 - magne t array (0 . 56 - range array 31 : where A= atomi c number of the nucleus , Z = charge of the nucleus and (pA) proton-nucleus cross-section , et c. Using these fits , the prob ability of nuclear scattering was calcula ted for each setting of the apparatus in steps of 10 MeV incident photon energy . Mos t of the scattering occurred in the magne t a rray, which contained more mate rial. The average correction was about 15% although it reached L.0% fo r a few bins a t 10\v energiE.S and small ang l es . I estimate a 5% accura cy in the fits , so the resulting systemati c error in the y + He3 + p + d cross-sections is a bout 1% . -69- 3. Electronic Inefficiencies In this section , we consider the fraction of even ts which went unrecorded due to inefficiencies in the trigger electronics. The scintillation counters were better than 99 % efficient in the detection of charged particles, and no correction was made for any loss of events in the counters themselves. Likewise, the electronics were reliable in putting out a signal whenever an input was present, provided the input signal did not occur during the dead-time caused by a previous signal. The circuits whose dead-times determined the inefficiencies were the TVD-3B discriminators (see Chapter II, Section C). Their dead-time was twenty n anoseconds. Signals were accepted by the electronics only during the sixty millisecond intervals during which the photon beam was incident on the He3 target. The number of beam pulses in each run and the total counts observed in the various scintil lation counters are combined to pre dict the loss rate. Only c ounters MS l, RSl a nd RS2 experienced high enough coun ting r ates for the loss to be sig nific an t. The average e lectronic ineffici ency for all three counters combined was about 1%, r e aching 3% for runs with the appara tus at small angles to the photon bea m. -70- 4. Wir e Spark Chamber Ine fficiencies The l ast typ e of inefficiency we consider is that of th e wir e l spark chamber system. The sources of p oss ible i nefficiencies were b ackground electrons in the chambers , b a d ch ambe r g as , b ad magne tostrictive ribb ons , maladjusted want a mp lifiers , etc. These effects were n ot c alculated s eparate l y, but r ath er methods were d evi sed that estima t e d th e comb ine d effect of all sources of i nefficiency . Th e measure of ch amber effici ency is define d t o b e t he fr action of foreground events d e tectable by the apparatus which also were r econstructed according to th e pro cedures discus se d in Sections A and B of this ch apter . Since the true n umber of for egroun d events is not known, th e effici ency must b e estimate d by a ssuming it equa l to some measureable qu an tity . The first method of estimation, and the one which was used in th e calculation of the cross-s ec tion, is as follows . First, a s amp le with a high percentage of for eground even ts is cho sen on the basis of a scintillator pulse heights and th e time-of-flight meas uremen t. a certain fraction are also 'reconstructible '. Of these, This fraction is the exact mea s ure of the chamber efficiency for the s ample as defined . We estimate that the efficiency for the entire foreground event sample has the same value. It is quite possible that th e chamber efficiency is different for background th an for foreground events. The sensitivity of our estimate to thi s effect can b e ch ecked by varying the pulse height requir ements of th e t es t sample . The calculated efficiencies of various -71- s amples with fro m t en to ninety pe rcent foreground events v ary by only two p ercent. l That is, th e chamber efficiency i s the same for b ackground and foreground events with similar pulse height s (ionization ). The above method is · th e simplest and :nost direc t , since it b ases the estimate on th e exact , observe d efficiency for a samp l e of events very similar to the desired samp l e . A fu rther advantage of thi s method i s that it inc l ud es t he effect of any possible ineff ic iency in th e tr ack finding computer program . As a measure of th e uncertainty of th e estimate , a st at i s tic a l error i s assigned to th e efficiency as if it were an ob servation of a binomia lly distributed process . The efficiencies es timated by this method v aried fr om 85 % to 30 %, depending on t he run , an d average d abou t 65 %. The statis ti cal un cert a inti es r ange d fro m about 1 % to 10 %, depending on th e numbe r of events in th e p ar ticula r run. As a che ck on thi s method , a s e cond one was de vised. In it, th e inefficiency of each wand was calculated and th e n the sep a rate i ne ffici en cies were combine d in to an overall efficiency . The wand ine fficiency was calculat e d - by ob s erving th e fr ac tion of events for whichno spark was found within 0.1''. of a reconstructe d track. An error was assigned to the de termination , as suming th e process to ob ey a binomial distribution . To estima te the ove r a ll inefficie ncy, at l east th ree sparks were required to defi ne a t .rack . For example, th e indi- vidual wand ineffici encies were us e d to c al culate the prob ab ility that in five chambers the first thr ee h ad sp arks but t he las t t wo did not, -72- and s o on for all possible combinations. the sum of these probabilities . The overall inefficiency is An er ror for this overall inefficiency was calculated by combining in the proper fashion the errors assigne d to the wand inefficiencies. The r esults of the second meth od agreed with those of the firs t to within the assigned errors . The errors were grea ter fo r the second metho d due to the large number of combinations which contrib ute to · the resul t. Further , the second metho d was found to be quite sensi- tive to the choice of 0.1" as the a llowe d discrepancy between a ' good' spark an d a tr a ck. This is somewhat surprising as the spread of sparks from the corresponding tracks in a chamber that was working wel l was about 0. 02 1 ' . I believe the t roub le was due to intermitten t signals prior to the first fiducial signals on certain wands . In any case , it was felt tha t the first method was more reliable than the second , an d the fo rme r was us e d exclusively for the results presented . -73- E. Cro ss-Sections and Statistical Errors In this section, the expre ss ions for calculating the diff erent i a l cross-sections and associated statistical errors are summarized. The data colle cted in this experiment have been grouped into b ins 10 MeV width in inc ident photon energy , and as wide in angle as the 0 acceptance of the magnet array - about 4 . The number of events in such a bin is relate d to the differential cross section by do _N(K, 8) = dQ (K,8 )· NHe3 •Ny (K) 6K·4nn (K, 8), where K c entral photon energy of the bin; 6K lOMeV; 8 =central proton angle of the bin ( c . m. frame); do dQ differential c ross-section in cm 2 _,· number of He 3 nuclei/cm2 , N 1Ie 3 23 6.024 x 10 l ength of target/molar volume of He 3 ; also included are the (small ) effects due to H~ 4 in the He 3 samp le - see App endix F; number of incident photons per uni t energy interval, total energy of beam bremss trahlung spectrum fu nc t ion K max K See Appendices D and E for det ai ls; n(K,8) = efficiency for dete cting an event. o:n:l = geometric efficiency x probability of no nuclear scattering x electronic efficiency x spark chamber efficiency. The factor 4n convert s th e efficiency n, into an effective solid angle . - 74- Analysis of th e experimen t a l da ta does not directly yield t he number of events , N, b ecause of ba ckground proce sses . As discussed in Sec t ion C above , N N where - N ·M / M o I o I number of events inside t he f oreground region, numbe r of events outsid e t h e foreground r egion , M /M ratio of numbe r of background events i nside t he o I fo regroun d r egion t o the numb e r outside ; determine d b y a Monte Car l o ca l culation . The c ross-section f or a s ingl e b in in K and 8 woul d t hen b e -do = N/ NHe 3 · Ny liK •4 1rn . d f;t I n th e exper iment , data f or a sing l e bin were t aken during s everal r uns , which in general h ad differen t va l ues f o r a ll of t he p arameters i n t he above exp r ess ion . Th e pr oper way to combine th e data fr om the s everal r uns i s indica t e d by an app li cation of the maxi mum l ike l ihood me thod . The exp ected numb e r of event s to b e observe d in run i is gove r ned by a Poisson di s tribu t ion : P( N.) (N.) ! l l where o abbrevia tes do / dQ, a nd n,l abbreviates a l l of th e remaining f a ctors re l a t ing N.l and o f or r un i . The probabi li ty of ob.s e rving th e s et o f° v alue s { N. } i s t he l ike l ihood l function L(o ) ==" IJ -on.i Co nl.)_ Ni_. e_ __ _ l ( N. ) ! l -75- The maximum like lihood me thod consi s t s of t aki.ng as the b est estimate of a that value which maximizes· L (cr ). a"' Thus , IN./In .. . 1 1 1 This i s just th e simple r esult tha t the cross -section is given by the ave r age number of events per run divided by the average effi ciency . The statistica l error in the determination of the cross-s e ction may now b e calcula t ed . If the only source of error was that of the st atistics of the Poi sson distribution, the maximum likelihoo d method would imply error= /LN./L n . . 1 1 The othe r sources of error were : 1. The background subtraction - Section C. 2. The geometric efficiency calcula tion - Section D.l. 3. The spark chamber effici ency calculation - Section D.Lf. 4 . . Beam monitoring - Appendix E. 5. Target density fluctuations - App endix F. The comp lete e xpression for (relative error) 2 where i labels the run, and EG = rel ative error in th e geome tric efficiency , -76- / EC relative error in th e ch amber efficiency, E relative error in the b eam monitoring, ET relative error in the target density. B -77- F. Syst ematic Errors and Re s olution There are th ree sources of possible systematic error greater th an 1 %. 1. 7 % in the geometric efficiency calculation (Section D). 2. 5 % in th e absolute c a l ibration of th e b eam monitors ( Appendix D). 3. 1 % in th e nuclear scattering correction, fro m a 5 % error in a 15 % correction (S ection D.4). Thus the absolute cross -s ections might be in error up to 13%, a ssuming all th e effects h ad th e s ame sign . If the u ncertain ties are combined in qu adrature , th e r esult is 6 %. This unc ertainty does not affect the shape of the di fferential cross-sections. As th e diff erential cross-section is a relatively steep function of energy and angle, poor resolution of th ese quant ities could cause a systemat i c error. Th e question of angular r es olution is the simpler . All even ts accep t e d in one setting of the a pparatus ar e lump e d toge ther into one bin. Including the effect of multiple Coulomb scattering, the resulting bin is at most 5° wide, and the event population i s essentially symme trical about the c enter of th e bin. Hence it is a good approxi- mation to average the cross-section ove r the entire bin and report the r esult as that at th e central angle . As discussed in Sect ion B above, the incident photon energy is reconstructed from th e lab angle and momentum of the particle detected in the magnet array. The d ependence on th e lab ang le is s ma ll ; an -78- error of 0.5 0 due to multiple Coulomb scattering causes only about a 0.1 % shift in the calculated photon energy. However, a 1 % error in the momentum c auses nearly 2% error in the photon energy . There are three pos s ible causes of error in the dete r mination of the momentum; uncertainty in the ma gnetic field strength, the error of the momentum fit, and the multiple scattering a particle suffers between the front and rear magnet sp ark chamber arrays. The magnetic fi eld strength was held constant to within 0.1 % during each run by current r egulated power supplies. The current in the magnet was monitored , rather than the magnetic field its e lf. The hysteresis of the magnet could c ause up to 1 % error in the calculation of the magnetic field strength. This would app ear as a 2% systematic error in the photon energy for all runs at a given setting taken b etween adjustment of th e magnet cur rent. As the cross-s ection v aries rapidly with energy, thi s h as the effect of ca using a slight normalization error between different runs at the s ame setting. The data fr om three runs (out of about 100) were discarded due to anomalous nonnalizations compared to other runs at the same s ett ings. If ·an overall 1 % error r emains in the magne tic field strength ave rag ed over the various runs, this would cause a 3% syst ematic error in the cross-sections, using the obs erved energy dependence of roughly EXP (-0.0l* Ey). This effect would mos t likely affect the shape of the angular dist~ibution s , as it is diffe rent at different settings. The accuracy of the momentum fit is 0.2 % (r.m.s.) as discuss e d in App endix G. Multiple Coulomb scattering causes an error in the momen tum of 0.5 % t o 1.5 % depending on the setting . These errors are -79 - random and produc e only a s li ght systema tic effect . However, as a 1.5 % shift in momentum caused a 10 MeV shift in the photon energy at 300 MeV , the d a t a were binne d into 10 MeV bin s , thi s size b eing commensura te with th e r esolution in photon energy . Another aspect of the experimen tal r eso lution is the observe d spre ad is in the coplanari ty and miss ing mass excess (Section C). This wel l accounted for by the effect of multiple Coulomb scattering . Typical v alues of r.m.s. Co u lomb scatt er ing are 0.5 0 for protons and 1.0° f or deut erons , yi e l ding a r . m.s . width of 1.2° for the cop l anarity a nd about 20 MeV for th e mass excess,us ing th e expression g i ven in Section C for th e latter. The effect on the mass e xcess of uncert ainty in the momen tum of th e particle in the magnet is slight . -80- IV. RESULTS The differential cross-sections for the reaction y + He 3 + p + d have been extracted from the data according to the metho d given in Section E of Chapter III. The systematic uncertainty of the results is about 10%, as discussed in Section F of Chapter III. Figure 4.1 shows the differential cross-section as a function of photon energy at the various center of mas s frame ang les of the proton which were observed. Each point is the average over a 10 MeV spread in energy and 4° in angle , centered at the values as plotted. The vertical error bars are the statistical uncertainties assigned to each cross-section. The cross-sections for each angle have their own log scale on the left, each scale reaching a maxi mum of one microbarn per steradian. The dat a plotted with a circular symbol are . from runs in which a proton was detected in the magne t array ; the square symbols represent data with a deuteron detected in this array . Data for both cases wer e collected at 90°; the cross-sections are seen to agree wel l wi th one another there . The statistical accuracy of the cross-sections as binned in 10 MeV s t eps is not high . To suppress the effect of fluctuations, all fur ther consideration of the data wi ll be for bins of 50 MeV in photon ener gy. way . Figure 4.2 s hows the differential cross-sections plotted in thi s Otherwise , the plot is the same as Figure 4.1. The l ogar thmic scale obscures the true size of the error bars. Table 4.1 lists the cross-sections and statistical errors as a -81- function of angle and photon energy . These are the main results of the experiment. Figures 4.3 th rough 4.9 show the differential cross-sections a s a function of proton center of mas s angle for photon energies from 250 to 550 MeV. Agai n, the results a t a given photon energy are the ave rag e s over the data from ±25 MeV abou t the central v a lue. The units of the ordinate are arbitrary ; the purpose of the figures is to display the shapes of the various angular distribu tions. The smooth curves shown in these figures are fits of the form A+ B cose + sin 2 e(c + D cose + E cos 2 e). The relative values of the five parameters A, ... E are listed in Tab le 4 .2. The fits at 250 and 300 MeV went negative a t the extreme angles if left unconstrained. They have be en required to remain non-negative , wi th the result that the fits go to zero a t large and small angles , as shown in Figures 4 . 3 and 4 .4. These constrained fits are not very good in the x2 sense. All of the cross-sections and the fits are shown on a single sem:ilog graph , Figure 4.10, exce pt for the data at 550 MeV. The fits may be integra ted to yield total cross-sections, which are s hown in Figure 4.11. The value s and sta tistical errors of the total cross-s e ctions are ~lso listed in Table 4 .2. Due to the p a thologie s of the fits a t 7.50 and 300 MeV, the e stimated total cross s ections at the se enersies are very prob ably too s mal l. -8 2- a: LLJ f- ()) 10 ° "-.. ()) z cc 10 0 CD (f 0 a: u Figure 4 . 1 He 3 Photo di s integration Differential Cros s- Sec tions j~ 10 MeV Bins -83- 10 o - - -T -----.---,--- =--~ - ep (c. m. ) =30° 90 ° •----<!}---< 120° ~ >--(!)-----< ~ ~ +- 10-310~0~~~-20~0~-~~-30~0~~~-4-0~0~~~-5~00~~~ · 0 INCID ENT PHOTON ENERGY IN MEV Figure 4.2 He 3 Photodisint egra tion Differential Cross Sections in 50 MeV Bins Table 4.1 Dif f erential Cross-S e ctions for y + He3 -+ p + d in Microbands /Steradian (M~) 30° I 60° 75° 0.7 30± 0. 035 . 200 90 ° proton in magne t 90° deuteron in ma gnet 105° 120° 150° I 0.54 0± 0.0 29 250 0. 348± 0 . 02 7 0.7 01± 0.0 23 0.4 90± 0.022 0.297± 0.0 12 300 0. 546± 0 . 021 0. 46 0± 0 . 012 0. 372± 0 .016 0.1 69± 0.0 07 350 0. 483± 0 . 016 0. 244± 0 . 00 7 0. 153± 0 . 01 0 0. 11 7± 0. 005 400 0. 32 7± 0. 012 0. 158± 0. 005 o. uo± O. Oll 450 0. 215± 0. 010 0.084± 0. 005 0.0 85± 0.017 500 O. ll9± 0 . 009 550 0.0 90± 0.010 0.145 ± 0.013 0.079 ± 0.014 0.127 ± 0.010 0.05 8± 0.006 0.115± 0.012 0.06 9± 0.006 0.055 ± 0.005 0.0 37± 0.004 0 .0 67± 0. 004 0.0 67± 0.004 0.06 3± 0.007 0.042± 0.003 0.021± 0.0 02 0.0 42± 0.004 0.039± 0.0 03 0.068± 0.012 0.032± 0.003 0.016± 0.002 0. 055± 0.005 0.0 32± 0.004 0.027± 0.003 0.020± 0.002 0.010± 0.002 0.0 29± 0.004 0.019± 0.004 0.022 ± 0.003 0.014 ± 0.002 0. 007± 0.002 I 00 ..,.. I 1.0r-~-r~-r~~~~-r~--r~~i---~~~~~~.-~-r-~--.~----. JNCIDENT PHOTON ENERGY = 250 MEV J I 0.5 I 00 V1 I __f r l 0.0 ~~_J_~_L___j___J_~}:-_L_~~_l_itn~-L-=~ 150 180 60 90 120 30 0 PROTON C:M. RNGLE Figure 4.3 He3 Photodisintegration Angular Distribution at 250 MeV \ 1.0 .--~-,-~~-,--~-,-~~-.--~----r-~~-r-~-r~~-,--~---.-~~--,-~---r~~~ JNC1DENT PH~T0N ENERGY = 300 MEV 0.5 --j I co °'I f -P / l!J 0.0 + ===--..; 0 30 Figure 4.4 GO PROTON 90 C~M. 120 -150 RNGLE He 3 Photodisintegration Angular Distribution at 300 MeV 180 1.Q.--~-,-~~-.--~-,-~~,--~-r-~~-,--~-r-~~-,-~--.-~~-,--~--,-~~~ JNC1DENT PH~TCN ENERGY = 350 MEV 0 .5 I co -....J I r 0.0'--~__._~_._~__._~~-'--~__._~_._~__._~~L---~__._~_._~__._~__. 0 30 GO 90 120 150 PROTON C~M. RNGLE Figure 4.5 He 3 Photodisintegration Angular Distribution at 350 MeV 180 1.Q,--~~~~-,--~-r-~~-y---~--,-~~-.-~-,--~~--r-~--r-~~-.-~--,-~~~ INCIDENT PHOTON ENERGY = 400 MEV J 0.5 ~ ~ \ ! I co co I I _j 0 .o 0 _ _l__~_ 30 I 60 90 120 150 PROTON C~M. RNGLE Figure 4.6 He 3 Photodisintegration Angular Distribution at 400 MeV 180 I t .0 f ·· - r [ r · I 1 [ 1 1NC1DENT PHOTON ENERGY = 450 MEV 0.5 I co \0 \T } I l t 0.0'--~_._~_._~~~~_._~_,_~__._~~.i..-~-'-~-'---~~'--~-'--~--' 0 30 60 90 PROT~N C~M. Figure 4.7 120 150 RNGLE He3 Photodisintegration Angular Distribution at 450 MeV 180 1 .0 r - - I \ I I I I INCIDENT PHOTON ENERGY = 500 MEV I I I ~ I i I I 0 .5 f- \ I l '°?i T ~ f I l f ------- I 0 .0 1 I I I 0 30 60 90 120 150 PROTON C .-M. RNGLE Figure 4 . 8 He 3 Photodisintegration Angular Distribution at 500 MeV 180 1 .0 1 I JNCIOENT PHDTDN ENERGY = 550 MEV I 0.5 I I \ I \.0 I k ~T I o.o L 0 30 E)Q 90 120 150 PROTON C: M. ANGLE Figure 4 .9 He 3 Photodisintegration Angular Distribution at 550 MeV 180 ~ -92- r Ry (!) 20 0 + 250 4. 300 J' (MeV) x 350 C!J 400 $ 450 ll( 500 cc w 1- cn '-.... (/")10- 1 z cc a:: QJ 0 cc u 10 - 2 ~-'--'_ _.___~_ o 30 so _._ t __ __._____..1~__.__ _._____.__~ 90 120 PRO TON C.M . AN GLE Fi gur e 4.1 0 1so Summary o f He 3 Ph o t o di s int eg r a tion An g ul a r Dis tributions and Fit s i sr: Table 4.2 Parametrization of the Cross-Sections of y + He 3 + p + d E x2 Deg of Freedom Ey A B c D 250 .003 o.o 1. 2.32 3.17 7.5 2 4.09 + 0.1 300 1. 1.0 -.21 . 71 1.9 27. 2 3.29 + 0.2 350 1. . 85 ·-. 67 -.37 -.37 2.8 3 2.12 + 0.04 400 1. .95 -.68 -.52 -.12 2.4 3 1.39 + 0.03 450 1. .97 -.74 ;...,76 -.39 5.6 3 0.84 + 0.02 -.65 -.26 0.3 3 0.47 + 0.02 -.97 -.95 0.1 1 0.27 + 0 . 02 crT(µb) - - I \.D w I 500 1. .95 ·-.65 550 1. .92 -.65 Note that the coefficients A - E have been normalized to A= 1 (except Ey = 250 for which C = 1). - 94- r-- 10 1 + + (f) z cc a: + CD 0 cc u + 1--1 f- u w (f) (f) (f) t 0 cc u _J cc f f0 f- 10 - l ._______.___ ~--·-~-~. -~~_ _L__ _L.~ 100 200 300 400 500 INCIDENT PHOTON ENERGY IN ME V Figure 4 . 11 He 3 Photodisint eg r a tion Total Cros s-Sections 600 -95- V. DISCUSSION The prominent f ea tures of our data on the reaction y + He3 + p + d are: 1. The total cros s -sec ti on falls with increasing photon energy roughly a s exp(-Ey/100 MeV) above 300 MeV , with an indica tion of a shoulder near 300 Me V. 2. This energy depende nce holds a l so for the differential cros s- sec tions at angles greater than 60 3. 0 (c.m. frame). The data at 30° show a rise from 250 to 300 MeV, after which th ey a l so fall with energy. 4. The angular distributions show a sli ght forward dip a t 250 MeV which changes to a forwar d peak a t 350 MeV and ab ove. We first consider the consistency of these trends with other data on the s ame r eaction. Figure 5.1 summarizes the existing to tal cross-sections for y + He 3 + p + d, including the present work . Our data h ave somewhat highe r values than migh t be extrapola t e d from lowe r energies . We shall consider the possibility that this is due t o !:!. production near photon energies of 300 MeV . Caution is necessary, however, b ecause the tot a l cross-sections are calculated from differe ntial cross-sections observed only at angles between 30 0 0 and 150 . The data at 30° off e r the bes t evidence of !:!. production to the extent that they can be regarded with confidence . The 30 0 data we re among the hardest to analyze due to the greater backgrounds and lower chamber eff iciencies enco un tere d at smaller angles to the beam . HmJe ver , -96- 10 2 Refer ence x 73 ~!+ 82 48 l+ 10 1 (f) I z a:: a: + This Experi ment • ! I I I I • OJ 0 cc ·U ..-1 :L I I I I l I I I I . I 10- 1 0 100 200 300 ijQO 500 INCIDENT PHOTON ENERGY ( MEV) Figure 5.1 Comparison of He 3 Photodisintegration Tot a l Cross-S ecti on Da ta I 600 -97- as seen in Fi gure 5.2, the data point at 250 MeV is in good agreemen t with the trend of the data at lower energies . The data at 300 MeV and above indicate the presence of some new mechanism causing higher crosssections at this angle. 0 0 Figures 5.3 through 5.6 give comparisons of data at 60 , 90 , 120° and 150°, respectively. between 200 and 250 MeV . At 60° there appears to be a shoulder While this feature may be spurious, the trend of the data above 250 MeV is consistently above an extrapolation from l ow energies . The data at 90° and 120° are in reasonab le agreemen t above and below 250 MeV , and give no particular indication of resonance production. At 150 0 the data above 300 MeV are subs tantially hi~her · · t1an l expecte d f rom t h e 1 ow energy t ren d . Un-or f t una t e 1y, tl1e 150° da ~La from this experiment near 250 MeV are not reliable enough to be reported. There is crude evidence of a l arge dip near 250 MeV , but we shall not rely on this in further discussion. In Figure 5.4, it may be noted that our 90° data are one third " k p 1 a te spar k c h amb e r experime - nt 1 ower t h an t h ose o f a Frascati. t h ic in the same energy range . 78 Both sets of da ta may be smoothly extrapolated into the cross -sections below 150 MeV. We have searched extensive ly for possible errors in relative normalization ; however, the source of the discrepancy remains an open question. We may also comp "lrc the shapes of our angula r di3t:ributio ns with those at l ower e n e rgies. The forward dip, and peak near 60° seen / in our 250 MeV data (Figure 4.3), are ~lso pres ent at 109 and 140 MeV (Figure 6.3). The change in shape of the angular distributions nea r - 98 - • 10 1 Re ferenc e 48 t 82 t This Ex perimen t z ([ 1--1 D a::: a: w I- cn 10 "- ° en z a: cc CD 0 a: u 1--1 2: + · 10 - l '--~~~~~~~~~~~~~~~~~ ' ~~~=-_L~~ 0 100 200 300 ~0 0 500 INC IDENT PHOTON ENERGY CME V) Figure 5 . 2 600 Compari so n of He 3 Photodisintegration Differentia l Cross-Se ction Data at 30° ( c . m.) - 99 - 10 1 r-1_--r1-.-1.---...-----r-----r-·--,.---,----~~-~---~ ~ q,? Reference 48 1 t 82 This Experimen t t z a: 1--1 D a: cc w 1- cn '-... en z cc CI m 0 cc 2 10- 1 :L: + 100 200 300 400 500 INCIDENT PHOTON ENERGY CME V) Figure 5.3 GOO Compari s on of He 3 Photodis in tegration Diffe rential Cro ss-Sect i on Data at 60°(c.m .) -100- 10 1 Reference 73 A 78 82 x 48 + z a: This Experimen t + 1--t 0 I a: 0:: w I ! 1(J) ......._ I I i--0-< ~ (J) z 0: a: co 0 0:: u 10-1 1--1 2: ; I + HtL I 10-2 l' I !. 11 0 100 200 300 400 500 600 INCIDENT PHOT~N ENERGY CMEV ) Figure 5 .4 Compariso n of He3 Photodisintegration Diff erent ial Cross-Section Data a t 90°(c.m.) -101- 10 1 Reference ~ 48 82 This Experiment z ++ CI 1--1 D a: a:: w 1()) '-.... ()) z cc a:: CD 0 a: u 10-1 1- 1 J 2:: + + + + 10 - 2 __.~--'~---+~-~~___,_~_,_~_L_~~~_._~~ 0 100 200 300 ~0 0 500 INCIDENT PHOTON ENERGY CMEV) Figure 5.5 600 Comparison of He 3 Photodisinte gra ti on Differentia l . 0 Cross-Section Data at 120 (c.m. ) -102- 10 1 --r-1-·1 I E Reference 48 82 10 z This Experiment ft ° (!) ++ a:: 1--i D l CI cc w 1 I([) "'-... t ([) z cc er co 0 a: u 10-1 l . 1--t L_ .. :>-:: ~~ ~-- }-< ___L ~- t__l____J 10-2 0 100 200 I300 ~00 500 INCIDENT PHOTON ENERGY CMEV ) Figure 5.6 GOO Conmarison of He 3 Photodisintegration Differentia l ' 0 Cro ss -S ection Data a t 150 ( c . m.) -103- 300 MeV suggests th e onset of !':. productio n . While i sospin comp lica tions might bro""den the r egi on of ti produc tion ( cf . Appendi x C), it is ) unlikely to e xtend abo e 400 MeV . The.re is, h owever , little ch ange i n the angular distributi on above 350 HeV . This indic a t es that the non- resonant p ar t of the cross -section may h ave altered considerably in th e energy r egion of ti producti on . A simi l a r featur e is obs e rved in the . r eaction y + d ~ ~ n + p ll We now examine the data in more de tail for evidence of 6 p roduction, using the mod e ls outline d in App end ix C. A sizeable contri- bu tion f rom this process i s nee ded i f the te st of T-inva rian c.:e in the r eactions y + He 3 -<-+ p + d i s to have significance at our energies . Recall , however , t hat the r eciprocity test provides a direct ch e ck of T-invariance independent of any .particular mod e l ; mode ls mere l y provide us with the siz e of expected effects . From the di scussion in Appendix C, 6 production might b e e h.lJec t ed in eith er of t he multipo l e transitions Ml-+ abbr eviated s 3 and DJ respectively . ba ckground might occur in five amplitudes : P , and E2 -+ 312 2 D , resp ective ly. 5 D or 312 2 s 312 or Ml -+ 2D312 , S and D l abel the r e l ative angular momentum of the fina l state proton and deuteron . 2 4 Ml -+ The non-resonant 4 s312 , El -> 2P112 or D , which are abbr evi ate d s , P , P , D and 1 3 3 3 512 The diff erent ial c ross-se ction and polari zed photon cross-sectior1 a symme try resulting fro m _these transi tions are given in e xp ressio ns (C.l) and (C.2) of Appendix C. Recall that th e differential cross-section is expec t e d to h ave th e fo rm A+ B case '- + sin 2 e (c + D case+ E co s 2 e ). -104- We fir s t brie fly di s cus s t h e b eh a vior of the non - re s onant background, which should be the dominant f ea ture outside the r e gion from 250 to 350 MeV. The pertinent di f f erential cross- s e ction da ta are summarized in Tables 4.2 a nd 6.1, while da ta on the cross-section as ymmetry from photodi s i n t egration by pola ri zed photons a re dis cussed in Appendix C. The key fe a ture s are 1. Coefficients A and B a re l arge above 100 MeV; 2. The c ro ss-s e cti on asymme try is pos itiv e but s ma ll from 180 to 280 MeV; 3. Coe ffi ci e nts C and E change s i gns be t ween 250 and 350 MeV. (1) imp lies t he comb inati ons P -P and D5-D3 are b oth non-ze ro. 3 1 Fr om (2) we conclude P3- Pl is large be l ow 280 MeV. The t ren d of the asymme try ( 2) a r gue s t h a t the s i gn ch anges (3) are no t due to P-wave e f f ec t s . I ns t ea d, above 350 MeV, n5 -n 3 i s probab l y dominant, and the nega t ive coefficient E i ndica t es t h at u s i gn ifican t contributi on from t h e canno t be dominan t. 3 is t he l arges t amplit ude . A s 3 amplitude i s no t r u l e~ out, but Beyond these qualitative f eatures , the l a r ge number of possib le amp l i t udes i n conjuncti on wi t h the l imi t ed se t of data make the assignment of precise numerical values for the amplitude s unadvisab l e . Consider now the region between 25 0 and 35 0 MeV, where 6 production may be significant . The transitions s 3 and Dj , considered in Appendix C as candidates for 6 production , lead t o isotropic and 2 + 3 sin 2 G angular distributions , respective l y . cle a rly indicated by the data . Neither of these is The isotropic term is rising from 25 0 t o -105- 350 MeV, but can be attributed to the rise of th e n tr ans itio n . 3 The sin 2 e term is definitely decreasing, which argues against th e importance of the n; transition. · However , th e observed rise in the 30° cross-s ections from 250 to 300 MeV suggests the search for 6 production should be continued. The to a 1 + cos 2 e distribution, if dominant , and n3 transition le ads interference with P -P will add a cos e term, so that its effect is 3 1 greatest at small angles. The ch ange in sign of the sin2ecos2e term between 300 and 350 MeV (Table 4.2) i ndicates a large phase change of D relative to D . 3 5 Thus we conclude that the n 3 transition i s th e most likely candidate for a re s onant amplitude . Recall that n 3 abbreviates the transition E2 + di scussed in Appendix C, the 2 n 312 n 312 . As final state i s possible, and perhaps fav ored ,from interme diate 6 production. initiate 2 An electric quadrupole photon can the excitation N + 6, but this is much more likely to occur . magnetic . d.ipo 1 e ra d.iation . 93 via In the photodisintegration of He 3 , it may be that 6 production by Ml photons is suppressed, although the · mech anism is unclear. . 93 effect in y Since 6 production via E2 photons is a small , this would explain th e lack of any prominent re sonant b ehavior + He 3 ->- p + d compared to, say, the process y + d + n + p. In summary, th e data indicate th at 6 production via magnetic dipole photo ns is unimportant in the photodisintegration of He 3 • The interesting possibility remains that electric quadrupole photons do initiate 6 production in an observable amount . The c ompletion of the inverse experime nt , p + d + He 3 + y, will provide a firmer experimental - 106- b as e for thes e concl us ions. I ndep enden t of the details of the ampl i tudes , the t wo experiments will prov ide a t e st of time reve rsal invariance in the electroma gn e tic interaction. -107 - VI. A. APPENDI CES Histori cal Survey of the Re actions y + He 3 -<- >- p + d He lium- 3, the nucleus consisting of t wo protons and a ne utron, was fir st obs erve d in 19 34 by the Rutherford group 36 . It was produce d by t he r eac tion p + Li6 + He3 + H~ ~ and also by d + d + He3 + n. The ear liest in teres t i n t he phot o- dis i ntegrat i on of lle 3, y + He 3 + p + d, c ent ered on the inve rse r eaction , p + d + He 3 + y , which i s exothermic b~ 5.49 MeV. mutatio n of elements i n st ars . Thus it is a p oss ible st ep in the t rans Indeed , it is th e second r ea ction in the ch ain which converts hydrogen into helium-4; + +v 1. p+p ->· d+e 2. p + d + He3 + y 3. He 3 + He 3 + He 4 + p + p "Men have worshipped things more foolish than reactions 1, 2 and 3." - Fred Hoyle37, The origina l work concerning these re a ctions was th eoretical -108- rather than experimenta l; Bethe 's calculation 38 of the p + d r eac tion rate is correct to within a factor of 2, in the region of astrophysical interest . The p + d reaction was firs t detected in 1939 3 9 More recent i nvestigations are reported in references 40 through 49 These experi- ments show the photons to be emitted predominantly as electric dip ole radiation fo r incident proton energies in the r ange 1 - 50 MeV. The p + d experimen ts inspired various theoretical calculations ,50-64 usual ly in terms of the photodisintegration of He 3 into a proton and deuteron . The calcul ations are gene rally restricted to the elec tric dipole part of the cross-section and to incident pho ton energi es below 40 MeV, corresponding to incident proton energie s below 60 MeV in p + d -+ He 3 + y . Only Carro n 64 considers photon energies above 100 MeV . Various forms are assumed for the He 3 wave function and the data are used to determine which is most realistic . The various theories enjoy some success in fitting the energy dependence , but are poor a t pre dicting the shape of the angular distributi on , b eyon d the sin 2 e contribution from elec tric dipole trans itions. A further .stimulus to experi men tal study of y + He 3 -+ p + d as opposed to the inverse reaction was the derivation of certain sum ru les for electric dipole r adiatio n by Levinge r and Bethe6 5,6~ In particula r, the b remss t rahlung weigh t 2d cross-section should no t b e sensi tive to the details of the nuc lea r forces : fa ( E) dEE NZ a A-1 -109 - where E photon energy ; tota l cross-section du e to electric dipole radiation; 0 a = fine structure constant; A atomic numbe r; Z = charge ; N = A-Z R r.m.s. r adius of th e ch arge distribution in the nucleus . If the photons are produce d by b remsstrah lung , th eir spectrum i s proportional to l/ E, so that the total scattered particle yield fro m a bremsstrahlung beam incid ent on a t a r get is the integ ral given above . However , both th e two-bo dy (y + He 3 -+ p + d) and th e thr ee-body {y + He 3 -+ p + p + n) phot odisintegration of He 3 must be measured to evaluate the inte gral. The fir s t ob servation of the reaction y + He 3 -+ p + d was i n 195.8 67 . 68-82 , followed by seve r a l sub sequent experiments , including obs ervations of the three-body breakup r ea ction y + He 3 -+ p + p + n. Figure 6.1 shows the experimental da t a for the differen tial c rosssection of y + He3 -+ p + d at 90° in th e center of mass fr ame as a functio n of inci dent pho ton energy. on the tota l cros s -s ection . converted 83 Fi gure 6.2 shows t he sparser data Da ta from p + d -+ He 3 + y h a ve b een to that for y + He3 -+ p + d by th e detai l ed balance relation: o(y + He 3 -+ p + d) 3 2 evaluated in th e center of mass frame . p2 ~ y o (p + d -+ He 3 + y) This relation presumes the reactions are invariant under time- reversal . Th e angular distributions c an be we ll-fitted at a ll ene rgies by: - 110- ++ + ++t ,. r ; ~ t ~ t , ., L-~~,~~~--_t__~-LL~-~~._JL.Lj 10 1 10° 102 INCIDENT PHOTON ENERGY (MEV) Figure 6 .1 10 3 Existing Da ta on He 3 Pho todis in t ea r a tio n Differential Cross-Sections a t 90 ( c.m . ) -111- 10 3 Reference * 49 (!) 43 A 49 ~ 45 12) 73 x 82 l!i 48 10 2 t t V> z 0:: a: CD 0 -+1 1- 0:: u ::E l t l 10 I - i i 1 00 '--~---'-~~~_J__j_J__Ji....L_~~l__--L-L--L--1-..l-'-l-'--~~L___-----'-----'------'-----'-'-'-~ 10 1 100 10 2 INCI DE NT PHOT ON ENERGY CME V) Fi gure 6.2 Ex i s ting Data on He 3 Photod i sin t e grat i o n Totn l Cross - Se c tions 10 3 -112- A+ B case + C sin 2 e + E sin 2e ca se + D sin2e cos2e . Table 6.1 lists values of the co efficients at r epresentative energies n ormalized such th at C=l. A det ai l ed discussi on of possib le electro- magnetic multipo l e tr ansit ions l eading to this angular di stribut ion i s given in Appendix C. 1. At low energies , three tr ansi tions dominate : Magnetic dipole leading to an S-wave p + d fina l state. Label thi s S. 2. Electric dipole leading to a P-wave , labelled P . 3. Electric quadrupo le l eading to a D-wave , l abelled D. The co rresponding angular dist r ibution is s 2 + sin2 e (p2 + /2 Re P*D case+ D cos 2e ). The data in Table 6.1 show the dominance of the electric dipole t rans ition for photon energies b e l ow 50 MeV . Very near thresho ld, th e magnetic dipole trans iti on h as significant r elative size, primari ly b ecause the electric dipole tr ansition i s suppressed by the angula r momentum 'b arrier' . At photon energies above 50 MeV the electric quadr upole transition is increasingl y important, and h as the effect of shifting th e peak in the di fferential cro ss -section away from 90° towards smaller angles. The highe st energy at which an angular distribution has been measured is 140 MeV. The s e da ta are shown in Figure 6.3, along with a more complete distribution at 109 MeV , The solid curves are fits based on the coefficients in Table 6.1. The expe rimental data may also be used to evaluate the Levinge rBe th e sum rule . This rests principally on t he work of Fetisov , Grobunov ... ·: - ll3 - TABLE 6 . 1 Angular Di s tribution Coefficients f or t he Reac tion y + He 3 ~ p + d The coefficients are normalized such t hat C=l. B D E Reference Ey (MeV) A 5.5 2 0.3 44 5.6 8 0.0 8 43 6.0 0.0 24 43 6.97 0.0 2 0.1 3 45 9.17 0.015 0.25 45 12.11 0.0 13 -0. Lf 9 0.16 49 15.39 0.0 08 -0.59 0.25 Lf9 19.23 0.0 8 -0.27 0.39 49 20.60 0.11 -0.3 0. Lf4 49 42.00 -.01 1. 2 1.32 82 52.00 -0.ll 1.03 1. 46 82 75.00 0.01 1. 94 2.62 82 99.00 -0.0 8 1.85 3.06 82 109.70 o. 715 0.6 43 1. 79 2.51 48 ll9.00 1.07 -0.31 3.42 1. 76 82 139.00 0.05 1.26 -.58 1. 88 82 ~ ..--~--,-~---.~~-.-~---.-~~--..-~--.-~~-,--~--,-~~-.-~---.-~~-.-~--. Reference_ Ey (MeV) z 3 0: 1---1 0 a: a: w I- en '-.. 2 ~a: en r - I -------- ~ T I I 0 a: u r--1 L: 1 o ---~~~___..__~_._~-~~~__._~~~~_._~__.._~~_.__~_._~~_._~_. 0 30 Fi gure 6.3 60 PRCJTCJ ~l 90 120 150 C. M. AN GLE CDEGREES) He 3 Photodisintegration Angular Distributions at 109 and 140 MeV 180 t-' t-' _p.. I -115- and Varfolomeev 73 . They found 1.81 + 0.06 fermis. R r.m.s. This compares well with the result R r. m. s. = 84 85 ' 1.88 + 0.05 fermis obtained from analysis of elastic scattering of electrons with He 3 • For more details and for additional information on the threenucleon problem at low energies , the reader is referred to reviews by Delves and Phillj.ps 86, and by Amado87 .· -116- B. Electrodisintegration of He 3 In this Appendix we inves ti gate the possibility of e x tracting information about photodis integration of Helium-3 , y + He3 + p + ·a, fro m the reaction e + He3 + e' + p + d. If the l a tter reaction involves the exchange of a single photon, we may consider the r e action to take place in t wo steps : e + e' + y follo wed by y + He3 + p + d. The second step is called virtual photodisintegration s ince the photon is off the mass-shell . Hence an ex trapo l a tion to r eal pho t odis integra tion is necessary. If the fi nal state e l ec tron and proton are de t ec t e d in the reaction e + He3 + e' + p + d , we may write 8 8 (in the one-photon approxima tion): dcr dE e 1 d~ e 1 d~ r d~ p p r is t he vi rtua l photon spectrum factor given by E I r a e 2n2 E e 4E E , sin2 K 1 q2 1-t: ' whe re K e e w2 - M2 . He3 w (M2 \) E He3 + 2v e - E e I ee, 2 - (4-rnomentum transfer )2 , real photon energy needed to produce the p + d final s t ate , . ~e 3 - q 2 ) !«2 =mass of p + d system , -117- £ = 1/(1 + 2(1 + .v 2 /q 2 ) tan 2 ee ' polarization parameter. 2 The virtual photodisinte gration cross-section c an be f urthe r expressed do dQ = A+ £B sin 2 8 cos2¢ + £C + 1£(1+£) D sine cos¢, p p p where 8 p ¢ proton angle in the y - He 3 c.m. frame. angle be tween the plane e -+ e' + y and the plane y + He 3 -+ p + d. A, B, C, an d D are functions of q 2 , Wand 8 . p The only data for e + He3-+ e' + p +dare those of Johansson89, at E e 550 MeV' E I e = 443 MeV' and e e The proton laboratory ang les varied from 44° to 62°. 0 I = 51. 7 . . The value s of the vari ous quantities contributing to the flux factor are: K 107 MeV q 2 = 1.85 x 10 74 MeV .667 MeV5 r = 3.57 x 10- 7 Mev- 1 Note that the data were taken a t only a single .q 2 , making any extrapolation to q 2 0 rather uncertain . energy , 74 MeV , is well below the region of The ef fective real photon !:::. production in y + He 3 -+ p + d. To compare these data to those for y + He 3 -+ p + d we need to cast the p + d system into the y - H~ c.rn . frame . lab ang le of the photon is / First , note that the GO~ . ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I :z a:: T 1--1 t 040 a:: 0::::: w i-- c.n '-... c.n I ---.l '' :z CL a:: 1 I CD 1--1 _J _J I f-' f-' I 20 1--1 2.: DO 10 f PROTON C.M. RNGLE COEGREES) HE3 VIRTURL PHOTODISINTEGRRTION CROSS-SECTIONS Figure 6.4 28 co I 12 .--~-.-~~.---~-r-~~-.--~-.-~~-r--~~~~-.--~-,-~~-,--~--,-~--. :z CI i---i 0 CI _J 8 cc w en en f- J T "z cc I CI CD 0 4 cc (_) i I 1--i L: I i-' i-' \0 . J 0 I I I I I 30 I 60 I I 90 I I 120 PROTON C. M. RNGLE CDEGREES) Figure 6.5 I I 1so He 3 Photodisintegration Angular Distribution at 75 MeV I I 180 -120- ey tan -1 E , . sin8 . , e e E - E 1 cos8 , e e e 0 51. 6 • Thus the data for the virtual process y + He 3 + p + d all have small angles between the proton and the virtual photon . The solid ang le trans- formation from the laboratory to the center of mass frame can nmv be calculated. With this, and the factor r given above , Johansson's data can be expressed as virtual photodisintegration cross-sections. The results are shown in Figure 6.4. They c a n be compared with the real photodisintegration data at 75 MeV photon energy of O'Fallon et a1 82 • We consider this energy because the p + d final state produced by y + He3 + p + d has the same invariant mass a s that of the p + d state in e + He3 + e' + p + d. The data are shown in Figure 6. 5, with a fit based on the parametrization given in Appendix A. It is very striking that the real photodisinte- gration cross -se ctions are about four orders of magnitude smaller than those due to virtual photodisintegration , and that the for~er has a forward clip while the latter is strongly peaked a t small angles . The problem now is to explain the l arge expe rimental difference between the two concep tual ly simi l a r photodisintegration reactions . The following argument is due to R. P. Feynman (private communication). The forward peak in the virtual photodisintegration cros s-section suggests that the dominant mechani s m is that a proton inside the He 3 absorb s the virtual photon and recoils along the direction of the photon. If energy and momentum are conserved, there need not be any fina l state interaction. The cross-section for the e l ectrodisintegration of He 3 -121- will then be very near twice that of the elastic scattering of electrons on protons. Since it is not possible for a proton to abs orb a real photon and conserve energy and momentum , this process will not co.n tribute to the disintegration of He 3 by real photons, and the cross-section will be much lower. A refinement of the argumen t recognizes that the proton inside the He 3 need not be on the mass shell , but may have fermi momentum p. The distribution of possible fermi momenta is centered at 0 and has a width of abou t 100 MeV/C. Then if the photon has energy v and momentum Q, conservation of energy and momentum requires 2mv - q 2 = p(p + 2 Q). For Johansson's experiment , this i mplies protons with 20 MeV/c fermi momen tum parallel to the photon 's dire ction can absorb the photon . However , for real photons of 74 MeV, the necessary mome ntum for the proton is 300 MeV/C. It is very unlikely that a proton in He 3 has this high a fermi momentum in the direction of the pho ton. Hence the conclusion is the same as before. As the electrodisintegration process can be we ll ap pro ximated by the elastic scattering of a single proton, this can be used to calcul ate the cross-section. obtain a good fit . See, for examp le, Gibson and West90 , who Conve rsely, we see tha t it will be difficult to ca lculate cros~ -se ctions for the photodisintegration of He 3 at energies well above threshold . ,' - 1 22- C. El e ct romagne t ic Mul tipo l e Struct u re o f y + Ue3 + p + d I n thi s Append i x , t he angul ar di s t ributi on for t h e r eac tion y + He 3 ~ p + d i s p arame t rize d accord i ng to v ar i ous elec t r omagn e tic multi po l es 91 2 He 3 is a t ure of a Bo ck 80 For thi s p urpose , we suppose t h a t th e wave fun ctio n of s11 2 sta t e . 4 n 112 Th e e f fe ct of the ro ughly fiv e p er c en t admi x - sta t e h as b e en con s i d e re d by Ba il ey e t a l 5 8 a n d by Th e eff ec t i s s ma ll a n d d oes n o t int roduce a n y n ew a ngul ar f unctions ; we t h ere for e n eg l ec t i t .' A l i s t o f all p oss i b l e e l ec tric d i p o le , El , ma gne tic d ipo l e , Ml , a nd e l ec tric q uad r upo l e , E2 , t rans i tions i s g i v e n b e l ow . Th e p + d f inal state s are l ab e lle d by t otal angul ar momen tum, t ot a l spin , and r e l ative o r bit a l ang u l ar momen tum. E2 ->- ->- 4 s 312 D' 3 To d e t e r mine which tr ansiti ons ar e likely to be mos t i mp ort a nt, we first cons ide r sca tt e rin g n e ar thr es h o ld. Th e sin 2 e b ehavior ob s erve d there i n dic a t es the domi n a nc e of El t r a ns itions. At low energi es , El trans itions affect th e orbita l angul a r mome ntum but not the s p in. import an t El t r ans iti ons th e r e fore l ead to eithe r the 2 r 112 or the The 2 r 312 -123- final state , abbrevia ted P P 1 1 and P 3 r es p e ctively. Indeed, we expec t = P 3 near threshold. The pre s e nce of a s ma ll isotropic component at low energi.es is very likely due to the magnetic dipole transition to the state, a bbreviate d s3 . 4 s 312 final Oth e r magnetic transitions a re suppressed by the angular momentum barrie r, or the requirement that Ml tr ans itions couple primarily to s pin. At e nergies above a b o ut 25 MeV, the ang ula r distribution shows . pea k ing a t a n g 1 es ra·th e r 1 ess tl1 a n 90°. the E2 transitions l eadi ng to n 3 and D respectively . 5 2 This can be ac count e d for by n312 an d 2 n512 final states , a bbrevi a ted These two are favored over the o ther p 9ssibil- itie s as the sp in wave function is unalt ered by these tr ansitions. At low energies, we expec t D = D , again b ecause e l ec tric radiation couples 3 5 only to orbital angular momentum in this limit. We conside r the five independent transitions P , P , 1 3 s 3 , D3 a nd n5 sufficien t to parametri ze the non-resonant part o f y + He 3 -+ p + d even up to energie s of 50 0 MeV. An evalua tion of the angul ar distri - bution corresponding to th ese transi tions l eads to the form A+ B cose + sin2e (C + D cose + E cos2e ), where A s 2 + (P 3 - P 1 ) 2 + 2 (D 5 -n 3 )2 3 B + 2.fi Re (P 3 - P 1 ) *(D 5 - D ) 3 j + 3 Re P ~P 1 - (D 5 - D 3 ) 2 C 3I 2 P D 5.fi Re P ">'~D 1 5 + 2.fi ReP 3 ~·: ( 2D 5 + 3D 2 ) ... / -12 4- All squa red quantities are to be t aken as absolute squares . I n the low energy limit , we may take P1 = P 3 = /i/3P·) D 3 th en D/ S and s 3 s, A B 0 c p2 D fi P*D E D2 We now cons ider which multipole a mp litudes might contain a L'1 (1236) in an intermedia te state . We suppose that one of the nucleons i n He3 is excited into a L'I by th e absorption of a photon . Th e L'I coexists f or a short time with th e other t wo nucleons b e fore it decays by the e mission of a pion , which must be absorbed by one of th e non-resonant n ucleons as part of the final- sta te interaction yielding a proton and a deuteron . I sospin conservation in the fina l state interaction f orbids t he t wo n on-resonant nucleons from being a deuteron i n t he i ntermediate s tate . A diagram for this p rocess is ~pi He 3 ' p J'TT O d I - - - - -- - - 1 - - - - -- - d The p + d final state has i sospin 1/ 2 , while t he L'I + d s t ate has i sospin 3/ 2 . To c onserve isospin, the two non- resonant nucleons must be in an isospin 1 combination . Th ere is no such state which is bound. Ph ase -12 5- shift analyse s 92 show t he 1 s 0 to b e the strongest unbound nu cleon-nuc l eon sc a tterin g b etween th resho ld and 150 MeV . 1 di agram for photodi s int egrati on of He 3 including a y ~p , sta te in A po ssib le s0 i s p l )1TO ~ : ~~~~~~­ d He 3 '---~ If all thr ee baryons were at rest in th e intermedia te state , th e ef fect of th e 320 MeV . ~ would be c entered at incident photon energi es about Sinc e all three particle s must h ave positive kine tic energi e s r elative to one another, a ny ' peak' in th e cros s-section due to a will b e s meared towards hi gher energi e s . Based o n th e the smearing might well b e on th e orde r of 100 MeV . ~ in y 1 ~ s0 phase shifts~2 The effect of the + He 3 ~ p + d will not be n ea rly as dr amatic as in y + d ~ p + n. In ord er to assign sp e cific multipole transi tions to th e above di agram, fur ther a ssump tions mus t be ma d e . First , suppo se the zero orbital angular momentum relative to th e 1 s0 . Then the p stat e must h ave tot al angular momentum 3/2 and positive parity. are three such states : and 4 n 312 • ~ h as + d final There Referring to the list of transitions earlier in this App endix , all three fin a l states c an be reach ed by eithe r a magnetic dipole or an electric quadrupole tr ansi tion. From data on pion photoproduction, it is known93 that magnetic dipole radi ation dominates the photonuclear production of a ~. In the pres ent · cas e, the multipolarity of th e radiation is with resp e ct to the entire He 3 nucleus a nd not its co nstituent nucleons . We sha ll assume that the -126- magnetic dipo l e radiation relative to the nucleon which is excited into a 6 is also magnetic dipole radiation relative to He 3 . Qualitatively, this can be justified by the model that the He 3 consists of two spectator nucleons in a 1 s 0 state which h as zero relative orbital angular momentum with .respect to the third nucleon . This nucleon absorbs a magnetic dipole photon and becomes a 6 , which will also have zero orbi1 tal angular momentum relative to the s 0 spectator . In summary, a model based on one excited nucleon and a 1 s0 spectator two nucleon system permits 6 production in three amplitudes : Near threshold , the previously abbreviated 4 s312 final state, s 3 , is favored by its low ang ular momentu.m, but this need not be so for photon energies of 300 MeV . By considering two-nucleon correlations ins ide the He 3 , we obtain an indica tion that the Ml + should dominate 6 production. in a 3 2 n312 transit ion, abbreviated DJ' The strongest t wo-nuc l eon interaction is s1 state9 2 , having roughly twice the probability of _a 1 s 0 inter- · action at low energies . It is therefore reasonable to assume that the nucleon which absorbs the photon is in a nucleons ins ide the He 3 . 3 s1 relative to one of the other We suppose this correlation l asts as long as the photodisintegration process, and can thereby affect the ang ular distribution of the final state particles . excites the nucleon into 3 ~. In particular , if the photon which then decays via pion e~ission , the pion is more likely to be absorbed by the partner nucleon of the state than by the thi~d nucleon . can only result in a 1 3 s1 6 production by magnetic dipole photons D state of the two-nucleons af ter the pion has 2 -127- been absorbed. To obt ain a proton and a deuteron in the fi nal state , 1 the third nucleon must combine with a member of the deut eron . y n 2 to form a A po ssib l e di agram for this i s ~ 3 s i"\ 6 -·---=:i=a-=-· I p o~ 1 n J 7T ' 2 n He 3{ _________________ • ----~---- - - -- - - d p The third nucleon must have b een in an S-wave r e l a tive to the othe r t wo , assuming _the He 3 wave fun c tion to b e which c an b e r ea che d are the "2 2 s112 . Thus the final p + d states n312 and the 2n512 . Only the 2 n312 can be obtained from a magnetic dipole tr ans ition of the He 3. A similar argumen t shows tha t 6 production is not poss ibe by a photon hitting one of two nucleons with a 1 s 0 correlation. The con- side r a tion of two-nucleon correlations in the photodisinteg ~a tion of • I heavy nuclei has been called the I quasi~deuteron mo d e 166 • > 94 Experi. 73 mentally observe d angular correlations between final st ate protons and neutrons in the reaction y + He 3 7 p + p + n are evidence of twonucleon correlations insid e the He3. This model could also be applied to the dis cussion of non-resonant amplitudes given in the first part of this Appendix. However, it places no further restrictions on the possible amplitudes already given. We may now give a form for the angular distribution of y + He 3 ->p + d including the amp litude D) for 6 proJuction. ·amplitude 83 is also a candidate for 6 production. distribut ion has th e fo rm A+ B co s8 + sin 2 e (C + Dcos8 + E c os 2 8), Recall that the Again the angular -128- where now A 2 2 s3 + (P3 - Pl) + 2(D5 - D3 B 212 Re (P3 - P1)*(D5 - D3 .- n3) c 2 3/2 P~ + 31eP~Pl - · 4(~ 5 - D3 ) 2 + 3(D 5 - D3 + D') 3 D sl2 Re P 1 *n 5 + 212 Re P3*(2D 5 + 3D 3 ) E 5(D 5 n3) 2 (C. 1) + 2D )2 - 20D 2 3 3 Note that the amplitude Dj int erferes with the amplitude s P , 1 P , D and D , which are observed to be large a t low energi es . 3 3 5 If D' 3 contains a T-violating phase, it could cause a l arge difference between the angular shapes of the cross-sections of the reaction + He3 +-+ p + d. y In the remainder of this Appendix , we give expressions for the angular distributions due to photodisintegration of He3 by polarized photons. We consider photons polarized transversely parallel and per- ·pendicular to the scattering plane leading to cross-sections abbreviated 0 11 and o..1. respectively . The cross-section due to unpolarized photons , given earlier in this Appendix , is abbreviated oT . Let AT, BT ' etc ., label the coefficients of the ang ular functions given previously . o.l. A B c Then and o l\ have the same functional form as oT with coefficients c:i. o II ~ 1\. , AT -2 (D - D - D' ) 2 + 8D ' 2 5 3 3 3 BT 3P 2 + 6ReP *Pl + 8ReD j (D -D )'~ 3 3 5 3 D 0 2DT E 0 2ET -129- Not e tha t CJJ.. + CJ 11 = 2 T" The asymmetry in the scatter of polari ze d photons is define d as . ( CJ II - CJ.L.) I Ccr11 + CJ...1). - At 90°, this is 3 p2 + . 6ReP i> P l .+ 2(D . - D + D')2 - 8n32 . . 3 3 3 . 5 3 (C. 2) 2 2 2S + 3P + 6ReP *Pl + 2(P - P ) 2 + 2(D - D + D' ) 2 + 8D'2 3 3 3 3 1 5 3 3 3 In the limit of l ow energies a s described earlier , this b e c omes p2 8 2 + p2 · The asymmetry a t 90 0 (c. m.) has b een measured energies between 180 and 280 MeV. 95 for photon The values decrease linearly from 0.4 at 180 MeV t o 0.3 at 280 MeV . If the low energy approximation holds a t these energies ; the s term must be twice the p2, which is not in agreemen t with the cross ~ection data presented in this thesis . The more detailed expression for the asymmetry shows that the size of must be roughly twice that of 3P ~ + 6ReP3>'>P l + 2(D5 - D3 + n3 ) 2 Further , D) must be small since the asymmetry is positive . These con- clusions hold at 180 MeV , well below ~ production energies , as wel l a s at 280 MeV , where this proces s migh t contribute substa.1tially . 2 -1 30- / D. The Photon Beam Spectrum The energy of the circula ted electrons was he ld at a n ominal v alue of 700 MeV for the entire experiment. The fluctu a tions a bout this v alue were short-live d compared to an average run, and of o rder of 0.5 %. They h ave b een i gnore d . Thi essen The st an d ard calibration of th e beam energy b y 96 gives the true e nergy as 1.021 + .003 of the nominal value , o r 714 MeV for the present case. Recent work of Mc Nee ly and Yellin 97 confir ms Thiess en ' s calib ration . The diff erential energy sp ectrum of photons in the beam is given by n (K) dK w E ~ ) dK K 0 K = photon energy , wher e E 0 ene rgy of the circulat ing ele ctron b eam (714 MeV for this e xperiment) , w and tot al ene rgy in th e b eam . The function B(K, E ) was calc~lated using a computer program 0 written by Wolverton 98 It is approx i mately equal to unity for K l ess th an E , and is normalized such that 0 fEo B(K, E0 ) dK = E0 . o Wolverton estima tes a systema tic uncertainty of 2%. th e beam monitors a s discussed in Appendix E . W is measured by The possible systematic error in W is 3 %, while its statistical uncertainty is 1 %. Thus t he b eam spectrum is known to a statistical accuracy of 1 % with a maxi mum -131- systematic error of ab out 5 %. This systema tic error wo uld influence the normalization but not the shape of the differential cross-sections measured in this experiment . Beca use the beam di ame ter is large a t the target, the int ensi ty variation across the beam should be taken into accoun t in the Mont e Carlo detection efficiency calculation . measured by Groom99 The beam pro file has been by observing the grain density in photographi c plates exposed in the beam . (A thin copper shee t was used to conver t the high energy photons into ones of wave lengths , mo re suitab l e for photography .) Following Groom , I set the intensity to I ( r ) - cos 2 (!:.) O<r<l.5 3 where r - distance from the beam axis in inches . ( Note that the number of photons at a radius r is given by n (r) dr r I(r) dr .) This intensity function can also be measured using the observed distribution of event vertices in this experimen t. Figure 6.6 shows the result of a typical run to be in re asonable agreement with the above fi t. / 320 r--~--,~~--,---~----.-~~-,-~~-.-~~--,.-~~-.-~---. 240 en 1- z 160 :J I r-' 0 LJ w N I 80 0 0.0 -~ O.S 1.0 1.S 2 .0 RADIUS CINCHES) RRDIRL DEPENDENCE OF THE BERM INTENSITY - RUN 68 Figure 6 . 6 -133- E. Beam Manitor in1r + L ~ ;.I~ ~ l ... _,_ T c; \.{. L The primary. Tbearo monitor was . a thick plate ion chamber located about thirty feet downstream of the ~e 3 target as shown _in Figure 2.1. --. r - :' -~ ;:~;--r As se condary monitors , there were two thin plate ion chambers upstream of the sweep magnet . In addit ion, the circula t ·L1g e_lectron beam of the synchrotron was monitored with a probe tune d to forty m~gahertz (the fr equency of the R.F. accelerating field ). The cl}ar:&,e _,~-'2.l~ected _by the ion chambers was measured with Littauer-typelOO sqrreni integrator s. The integrators were calibrated daily agains t a precision current source , accu r a te to 0.25%. The resu lts of the integrator calibr at ion vari e d linearly with time . When the v a riation reached abou t 0.5 %, the int egra tors were r eadjusted. Two sources of error r e ndered the integrators less reliable during the first half of the experiment. A leakage current from a faulty ion chamber hi gh vo ltage power supply c aused the integrators to r ead too little by an unknown amo unt o f the order of 1%. The sec ond error was c aused by the relays which tur ned the integr a tors off dur ing the dead-time of the experiment associated with firing the spark chambers . This did not affec t the th ick i on chamber appreciably but did make the thin ion chambers unreliable . Howeve r, the thin chambers we re used mainly during the calibra ti on of the thick i on chamber a s described below . During t his calibration , the relays 1vere disconnected as the spark ch amb ers were not fired the n . The result of the ion chamber calibration fro m the second half of the experiment was use d for the whole experime n t. -134- The measurement of the charge collected by the ion chambers mus t now be related to the energy of the beam . For this, the output of the thick ion chamber was compared daily with that of two Wilson-typelOl quantame t ers. The quantameter const ant is calculatedlOZ to be 13.1 (±3%) x 10 18 T/P MeV /c oulomb . OK t emperature in where T and P - pressure in rnmHg for a gas mixture of 95% argon and 5% co . 2 The 3% uncertainty consti- tutes the systematic error of the quantameter calibration . This result was confirmed by a calibration of one of the quantameters agains t a Faraday cup a t the Stanford Mark II linear accelerator1° 2 . Measurements taken during the experiment showed tha t all three of the ion chamber and quantameters were l eaking slowly. The ion chamber was the wo rst at 1% per month . The qua ntameters were mounted on rolling platforms on t he lea d wal l jus t upstream of the He 3 t a rget (Figure 2 .1). beam , the thick ion chamber was the s hadow . Wh en one was in the Hence the calibration was done using the 40 me probe and the two thin ion chambers as intermediat e standards . This result e d in six ways of calibrating the thick ion chamber agains t the two quant ame ters . was used . The average of thes e six methods The variance of the six calibrations abou t the average was roughly 1% which I take as the sta tistical erro r of the final cal ibration. The sys t ematic error , as noted above , is abo ut 3%. As a sidelight , we c.:in compare the two quantameters , the s ocalled ' s outh ' and ' wes t ' quAntamet e rs . The ratio of the south quanta- - 135- me t e r output t o that o f t h e wes t q uantameter was 0. 867 + .01 whi l e t he rat i o o f the ir gas densitie s was 0. 88 4 + . 004. Thus the south quantame t er constant was about 1 . 5% less than tha t o f t he wes t quantameter. I fee l tha t the west quantamete r i s nearer the truth as i t s gas was a b ove atmospher ic pressure while the south quan t ame t e r gas was below ( although both were apparently leaking !). We now consider the ques tion of the relation between the beam at the He 3 target and the beam at the thick ion chamber . The beam wa s always well centered on the He 3 targ e t , as discussed in Appendix F. The ion chamber was centered on the beam at the beginning of the e x perimen t. If the be am wandered beyond the limits of the ion chamber , thi s would show up as a variation in the cross-calibration of the io n chamber against the quant ame ters , who se position in the b eam was checked at each c a libration . As no such effec t was observed , we conclude the ion chamber consistently monitored the wh ole beam . A furth er question is to what extent the composition of the photon b eam is altered by pair production . 1. There are two effe cts : The beam at the He 3 t arget contains e lectrons and positrons as we ll as photons ; 2. Some of the beam energy is scattered out of the beam and no t measured by the ion chamber. There were abou t 0.05 radiation lengths of ma tt er between the sweep magne t and the ion chamber distributed as follows : -136- Air and He 4 b ag upstre am of t a rget .002 rad i atio n lengths target walls .003 He 3 in target .016 Air downstream of target .025 .046 There wer e 0.01 radiation l e ngths of matter before the c en ter of the t arge t. Thus 99% of the total beam e nergy at the t a rget was in the form of photons. We now consider the second ef fect. The angle of a pair produced e lectron or positron with respe ct to the incident photon is roughly M /E. e 3 From the He t arge t the ion chamber had a n ang ula r radius of abo_ut 0.01 radians . Thus al l electrons and positrons with energies greater than 50 MeV were collected by the ion chambe r. Using the facts tha t the total pa ir production cross-section is very near ly constant for photon energies above 10 MeV and that the energy spectrum of the produced l eptons is flat, we estimate that only 10% of the energy converted into pairs is not collected b y the ion chamber . The 0.05 radiation lengths of matter conver t 5% of the photon energy into pairs , so only 0.5 % of the total b eam energy was unmeasur e d. The two effects of pair production have opposite signs . Thu s the tota l energy in the form of photons at the tar ge t is 99.5% of the total energy collected in the ion chamber . This smal l syJ1tema tic effect has been included in the results of this experiment. / -137 - The He 3 Targe t F. The helium-3 used as a target in this experiment was man-made . It came from the beta deca y of tritium produced by neutron bombardmen t of lithium at the Lawren ce Radiation La boratory at Livermore . Our s amp le contained about 15 mo les of He 3 , roughly one pint when liquid . We first consider the composition of the 'he lium-3 ' . As tritium has a half life of twelve years, there migh t well be a sizeable fraction of tritium remaining. As well as causing a b ackground in the experiment, tritium wo uld be a radiation safety hazard. However , as the boiling point of tritium is 20°K while that of He 3 is 3.19 K, the tritium can be condensed out of a He 3-tritium gas mixture . 0 The tritium . 10 7 103• content o f our samp 1 e was b e 1 ow one part in The only significant admixture to the helium-3 was helium-4. mass-spectrographic analy sis 1 04 of our 98.65% He3 an d 1.35 % He 4. 1 A helium-3' established it to be This admixture mus t be taken in accoun t as He 3 and He 4 can remain in solution even at 0°K. Figure 6 . 7 shows the liquid phase diagra m for He3-He 4 mixtures under saturation vapor pressure 105 106 . ' . As discussed below, the the target was around 1.5°K. and He 4 are still in solution . fluid although the At this temperature of the liquid in temperature , we see that the He 3 Further , the mixture is not a supe r- te mperature is below the A. point for pure He 4. . 4 The correction for t h e pre s e nce of He · a pp e ars in two ways . First , the de nsity of the He 3 -He 4 solution is about 0.5% greater than for pure He3. 0 1.5 K, From Ta ble A7 of reference 105, I e s timate that around a 98.65% s olution h a s a mola r volume 0.17 c.c . l e ss th a n pure f . ~ .. ! -138- t ; i ~- t I. "> I NOT SUPERFLUID I 2.0 !· I . i ( ! f I :z > _J 1 .5 w t REG ION OF THIS EXPER I MEN T 1--t I· l ~ I '-" w 1· cc :::) I SUPER FLUID t- a: cc w 1.0 - a_ 2: w t- 0.5 TWO PHASE BO UNDARY (U NPHYS ICA L REGION ) o.o i .__~~-~~--4-~-L--~-L---'~-'--~_.__~_,___. 0.0 0 .2 0.4 0.6 0.8 1 .0 MOLRR CO NCEN TRATI ON OF HE3 PHASE DIRGRRM OF HE3 - HE~ SOLUTI ONS Fi gure 6 .7 -139- He 3 . Second, the solut{on is only 98.65% He3, so a molar volume contains only 98.65% of a mo le of He3, We now consider the target itself, shown schematically in Figure 6.8. The He3 gas is kept in a closed system consisting of the storage tank (not shown), the condense r, and the target cup. The con- denser is in good thermal contact 1.;rith the reservoir of liquid He 4. The He3 is condensed and cooled by the evapo ration of He 4 from the reservoir . The He 4 lost by eva poration is repl a ced by liquid He 4 fro m a dewar. To reduce the evaporation, a liquid nitrogen jacke t surrounde d the He4 reservoir. Further, a v a cuum was maintained in the regions betwee n the outer wall and the nitrogen j a cket, and between the nitrogen ja~ket and the He 4 r eservo ir. The target cup was suspended f rom the He3 condenser by t wo pipes which also served to circula te the liquid He 3 . The cup was surrounded by a chamb e r of He 4 gas in eq uilibri um with the liquid He 3 in the res ervoir, in order to minimize the chance of a rupture of the cup . This chamber was s urround ed by two concentric vacuum j ackets , whose walls are s hown in Figure 6.8 as heat s hields . The me tal she ll of the targe t was replaced by a my l ar window in the region of the targe t cup to r educe the mult iple scattering o f emerging particles . A particle had to trave rse twenty-three mi ls of my l a r and f our mils of aluminum to escape. The target consumed ab out thirty liters , or 1000 mo l es , of H~ 4 a day . The l aten t h ea t of vaporization of H~ '+is about twen ty calories per mo le , so 20,000 calories a day were lib erate d . Assuming a running -140- TO He 4 DEWAR 4 He ESCAPE TUBE 4 He RESERVO IR ----1--t-N- He 4 GAS 3 CONDENSOR L.--+--1-H--- He RES ISTORS BEAM LINE M-- -TARGE T CUP HEAT SH IELDS Fi gure 6.8 The He 3 Targe t -141- temperature of l.5°K, 200 0 calories were used in cooling the He 4 from its boiling point of 4.21°K. The latent heat of vaporizat ion of He3 at 1. S°K is about ten calo ries per mole so condensing and cooling the fifteen or so moles of He3 took 150 calories. These calories wer e not needed every day, but only after the He3 was entirely boiled . Thus about 90% of the cooling went into various heat losses through the walls of the target. Mos t of the loss occurred in the transfer pipe from the liquid He 4 dewar to the reservoir . If the He 4 supply wer e turned off , it would take a t least twelve hours for the He3 to boi l completely . Hence the heat loss out of the He3 system was only abou t ten calories per hou r. The temperature of the He 3 was monitored by meas uring the resistance of one of eigh t carbon resistors mounted at various places withi n the target (see Figure 6 . 8). The resistors had a nominal value of 300 ohms at room temperature , but a t 1. S°K the resistance woul d be about 200,000 ohms .· The t empera ture versus resistance calibration of the resistors was performe d according to the method of Reference 10 7. The process of monitoring a resistor caused a heat source inside the target due to joule h eating. Therefore , we observed resistor seven , which is in the condenser, rath e r th an resistor two in the cup . The observations could then be made continuously and they we re recorded at several times each run . A ca libr ation of resistor two at3ins t resis tor seven showed the cup to be cooler th a n the condenser by about 0.05% . Figure 6.9 shows the d e nsity of liquid He 3 at saturation vapor pressure as a function of temperature, taken from t ab le AlO of 0 . 1 0 .--~~-,--~~--.~~~-,-~~--r~~~-y-~~-i-~~~~~~~ 0.08 Me a n t emperature duri ng th i s e xperiment "" . " .- 0. 06 u (_) l5 '-" >- - .~ I I-' ~ t: 0 .04 N I (./") z LLJ D 0 .02 o . oo ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 1 2 TEMPERATURE CKELVIN) -· Figu re 6 . 9 3 ,' Dens i ty vs . Tempera tur e o f Liquid He 3 at Saturation Vapor Pre'ssure 4 -143- 0 Reference 105. Maximum density is a t 0.5 K but a gently sloping pla tea u The He 3 targe t was designed to run at l.5°K so that exists up to 2°K. the dens ity would not be great l y affected by temperature changes,. while the expense of maintaining this tempe rature is not prohibitive. An average temperature was calculated for each run using the observat ions described above. The mean over the 100 or so runs was l.S3°K with a 0 variance of 0.03 K. o f 0.0002. The mean density was 0.0802 gm/ cc with a v a riance Var iati ons within a run wer e larger with T r anging between 0 1.45 and 1.6 K (except for brief periods of higher values when the liquid He 4 reservoir needed replenishing ). We estimate the resulting uncertainty in the density for a given run as 1/2%. The t arge t cup was in the shape of a cylinder wi th spherical caps on each end . of the photon beam. The axis of the cylinder was a long the central ray The maximum length of the target was 10 . 4 cm , with the radius equal to 3 .7 8 CM . As the measured cross-sections are inve r se ly proportional to the l ength of the t arge t (for a given number of events collected ), it is i mp ort ant to establish the effective l e ngth accurate ly. By effective l ength , I mean the length of a right circular cylinde r t a rget which produces the same event rate as the actua l one . Using the radial dependence of the beam intensity discussed in Appendix D, and the known shape of the spherical caps, I calculate a n effec tive l ength of 3.94 inches , and estima te the erro r a t 1 / 2% . The beam was checked dai ly to assure that it was centered on the target; it never wandered by more than 0.05 inches . The only uncertainty associ ate d with the target was whether the -144 - liquid He 3 contained bubbles . As the various heat shields prevented the target cup from being observed directly, we must rely on indirec t evidence . That it took at least t we lve hours for the entire liquid He3 to boil entirely without any He 4 cooling argues strongly against bubbling: if the lifetime of a bubble were one second, only 1/40,000 of the He 3 would be in the form of bubbles a t any one time . 0 was operated at 1.7 K below the boiling point. Further, the targe t I estimate the heat generated by ionization of the He 3 by electron-positron pairs in the beam at about one calorie per hour; As the beam was abo ut 2-3 / 8 inches in diameter, this heat source was not localized, and was unimportant . A telescope consisting of three scintillation counters aimed at the t arget was designed to monitor whether the t arge t was full. However , as shi e lding was added around the spark chambers during the course of the experiment, the monitor telescope was blocked. For the portion of the experiment when it was working , the monitor revealed no fluctuat ion from run to run beyond 5% or so . The measured cross-sections a l so show this kind of consistency among the v arious runs. We conclude there was no si gnificant bubbling in the target, and no c orrection for such an effect has been made . - 145- G. Ca lib rat i on of th e Analyzing Nagn~t The c a lib ration of th e analyzing magnet u se d in th e experiment l was done with th e so-called floating wire t ech nique . The computer c ontrolled method of d a t a- t ak ing u sing magnetostrictive wands i s describ ed in d etail in Reference 108. This Appendix di scusses th e p rinciple of the flo ating wire t echnique b r i e fly, summarizes it s applicatio n to th e p!esent e xpe riment, a nd d e rives a correction for the effect of grav ity on the c a libration. l . Principle of the Method The flo a ting wire technique is based on the similarity of t he equation of motion of a charge d particle in a magnetic field, and th e equation for the curvature of a current carrying wire in the same field. For a p a rticle with moment P , v e lo city V and charge e , d P / dt = ev x B - wher e B is th e magnetic field. Letting £ P / P b e the unit tang ent to t he trajectory and d s - vdt be the -arc length, d £ / ds = ( e / P) £xB- Cc . l ) Neglecting gravity, a wir e -under ( u niform ) tension T , carrying curren t I obeys d £ / ds = ( I / T ) £xB- (G. 2 ) Thus the " orbit " of a wire suspe nded in the field exactly fo l lows a p ossib l e trajectoryof a particle with momentum P = eT / I I n practical units , this i s P(MeV/c ) ._ = 2 . 9398 T ( grams )/ I(amps ) ( G. 3 ) -146- Note that in a field free region, both a particle's trajectory and wire "orbit" are straight lines. A correc tion for the effect of gravity is discus s ed in Section 4. 2. Orbits in the Mid-Plane of the Magnet Gap The momentum analyzing properties of a magnet can be investigated by measuring r epresent a tive floating wire orbits. Only orbits lying in the mid-plane of the magnet gap were .measured . Corrections for orbits not in this plane were made using a proce dure discussed in Section 3. Fi gure 6.10 illustra t e s the or bit parame ters which were measured . Two r ec t angular coo r dinate fr ames were defined , one on either side of the magnetic field region . The z-axes were i n the di rection of the particle 's fli ght, and the x-axes l a y in the mid-plane of the magnetic field . For each orbit cons idered, the s lopes and int e rc ep ts of the s traight line segmen ts of this orbit were determined , a s we ll as its eq uivalent momen t um , calculated fro m equat ion (G.3). Thus for each orbit, five parame t ers were measured : P, x , tan e , x , t a n e whe re 1 2 2 1 the x. are the intercepts a nd t a n e. are the s lop e s. i i An orbit in the mi d-plane is comp l ete ly determined by three parameters so th a t a ny two may be expressed as a function o f the other three . the x . and e. are known and Pis desired. i data , i In this experiment To take fu ll advantage of the e1 and e2 were combinP.d int o e = e1 -e 2 , and P was expressed as a fourth orde r po l ynomial in x l' x 2 and tan e. p = p 0 + a 1 x.l + a 2 x 2 + a 3 tan e ..... +a 34 x 1 x 2 tan 2 e The orbit which w'ould h ave al l s l opes and intercepts ze ro is ca lled the MAGNETIC Fl ELD REGION ~. Bi RAY C ENTRt.L I \ ~ X1 - 7 \ " ~ ORBI T I I-' "~ '-.../ .I Figure 6 . 10 Orbits Measured in the Magnet Calibration . -148- c entral orb it, and its equivalent momentum is called the central momentum, which is j ust the constant P , 0 Dur ing th e experi ment , t wenty-seven dif ferent magnetic fi e ld st rengths were u sed ranging from 2.8 to 11.1 kilogauss , only th e constant P 0 In principle , should change from setting to setting while th e 3 4 a. ' s remain fi xed as th ey depend only on th e shape of the fi eld . l To t est this , approximately 180 orbits were measured at each of four field strengths and the thirty-five constants calculated by a l east-squares fit. By c onsidering f',P = (r-P )/ P , one magnet setting c ould b e 0 The r. m.s. v a lu e for 8 = f'iP c ompared against th e oth er . f'iP measure 0 c a 1 cu 1 ate d - cl was ty pically 0.3 % for any one setting, and using the c oefficients a . fr om one s e tting t o c a lculate f'iP for another also gave an l r. m.s. value of 8 = 0.3 %. Hence th e a ssumption th at th e shape co e ffici ents a. are i ndependen t of P l 0 i s jus tified. The orbit s f rom all fou r s e ttings were t hen c ombined to c alcul ated ~p = a 1 x 1 + a 2 x 2 + .... a 34 x 1 x 2 tan2 8 A l east squares fit u sing 432 out of 5 42 o rbits g ave 8r . m. s .= 0.2 %, which is t aken as the accuracy of the fit. The value of P 0 must b e known for the othe r twenty- thr ee s e ttings o f the field strength to comp l ete the analysis . o rbits were measured , and P s ettings disc usse d above. 0 At each s et ting , six c a lculat e d using the a . from the four 1 Also , at all settings, an NMR prob e measured t he field strength which is proportional to P . o The propor- t ionality cons tant was calculated for all settings and fo und to be th e s ame to within 0.2 %. -149- In addition to fitting P as a function of x , x and t a n 8, fit s 1 2 were made to x and 8 2 2 as functions of x ,8 and 1 1 ~ P. These fits are used in the geometric effi ci en cy calculation to determine the acceptance of the magne t. 3. Properties of Orbits not in the Mi d-Plane If a particle trajectory does no t lie in the mid-plane of the magnet, it will in general follow a helical path. Defining a as the ang le of the helix with respect to the mid-p l ane , equation (G.l) shows tha t the projection of the orbi t onto the mid-p l ane is exac tly tha t of a p art icle with momentum Pees a whose orbit is in the mid-plane . if x , x ,e and 1 2 1 Thus e 2 are measured for a helical orbit, an d P is calculate d using the fit J escr ib e d in the previous sec tion, a correction P = Pf. -i t mus t be made . radi a ns. a / cos a In the pre sent experimen t, a was limited to la 1$'. .04 This correction is at most 0.1% . In making this correction, need not be determined precise ly. The difficulty in measuring a fields of the magne t cause thr ough them . is that the non-uniform fringe la I to incr eas e as the p a rticle p as ses Thus the s lope with respect to the mid- plane of the straigh t segments of a particle tr a j e ctory is diff erent before and af ter it passe s through the field . mining the particle ' s This effect is not important in dete r- mo 1 nelJ ~um , accep t ance of the magne t. but is very important in determining the The "Jefocusing" which occurs in the direction perpendicular t o the mid-plane reduces the effective widt h of the magne t gap . A 5% e rror in this dlmens ion will manifest itself as a -15 0- systematic 5% in the final scattering cross - section. 109 . . I n ear 1 ier ca l"b i rations o f t h e magne t , a f"irst or d er t h eory was used to rel ate the properties of orbits outside the mi d-pl ane to those lying in it of the magnet. 110 . Let they axis be perpendicular to the mid-plane The theory relates the slope and intercept of an orbit projected into the y - z plane after the magnet to the projected slope and intercept before it. There are six constants to be determined, and in the firs t order theory , the f i ts for x 2 and e 2 in terms of x 1 , e1 and 6P give six relations involving these constants. In addition , fou r of the six par ameters can be determined to within abou t 1% from the physical dimensions of the magnet . The consistency among these ten relatio ns for the six constants is not good . Ta king different subsets of the relations , the predictions for the defocusing effect vary by 5% . In face of t his discrepancy, the above use of the first order theory was abandone d. As an alternative , it wa s conceived that the obs ervation of particles in the magnet in the course of the experiment it s elf cou ld be u sed to calculate the defocusing . This was possible b e c ause the wire spark chamb e rs d e termine d the particles ' tracks both before and afte r the magnet. In pra ctice , this was difficult b e c aus e of multiple Coulomb sca ttering . An add itional complication was that the " fan " veto counters on the pole f ace s were removed in this exper i men t. This left the q ues ti on of whet h e r the particles s c attere d off the pole tip s to be a n swere d by the slope s and intercepts of the tr ack s in the wire chambers . Agai n, mu ltiple scattering made the app ro.a ch less rel i able than desired . To calculat2 the defocusing effect , cle a n tracks were used from - 151- t wo runs i n which the par ticles ' momenta were hi gh , and h e nce mul tiple Coulomb scattering was minimized . A r easonable first order fit was achieved of the fo rm = 1.14 y (a t target ) + 162.0 y' (at t a rget ) y(exit of magne t) The R. M.S. deviation of ob serve d and predict e d v a lues was 0.17". l ast previous c alib ration of th e magne t y (exit) = 109 Th e used th e fit 1. 22 y ( target ) + 17 4 . 0 y' (t arget ) The magne t's pole tips di f f ere d sli ghtly fro m the pr esent conf i gura tion when thi s fit was made . The most r easonab le fit obtaine d by using fi rst order magnet theory for th e pr esent configura tion was y(exit ) = Lll y(t arget ) + 1 66 .0 y' (t arge t ) The first fit was u sed in the da t a anlysis . Based on th e discrepancy between it and t he third fit , th e p oss ible systema tic error i s t aken as 3%. 4. Correc tion for Gr avity .Both equa tions (G.l) and (G.2) mus t b e c orre cted for the effect of gravity. Howeve r, th e correction to (G.l) i s neglible since all the protons and deuterons in the experiment h ad v e locitie s greater than 0.1 c, and a part icle traveling at 0.1 c for a di s tance of twenty fe e t falls _13 about 10 meter. Equation (G.2) in the presenc e of gravity b e comes dT T d .Q. + dS Q, - pgx + I Q.XB = 0 ds A A - where, for thi s s ecti on, x is vertical, and the y-z plane horizontal . In the pr esent case , Q, li es in th e x-z plane , and ~ is in dire ction y . The v ec tor equation may b e dec ompos e d into compo nents along the (orthogona l) dir ections Q, and d.Q. / ds yielding -15 2- dT ds =Pg sin 8 (along £. ) T d8·= pg cos e - IB (along d£./ds) ds where 8 i s the angle between Q, and Q and d8/ds and lc1 £. /ds j By noting th at ds = sin e dx, the first equation can be inte grated to give T(x) = T (1 + Q_g_ x) T o Since Q__g_ T _ 0 10 - 6 0 -1 cm and x $ 2 0 cm this effect will b e negl ecte d. The second equation can be written _ d8 = IB _ 2..£ ds T T cos 8 (G J;) Since the radius of curvature of the orbit is R = -l /( d8/ds) , it var ies with 8 and is slightly l arger th an in the absence of gravity. Asp g/T is small, it is a good approximation to replace cos 8 by its average. In this approximation, d8/ds is cons t ant so that the orbit is circular. By comparing with equation (G.l), the equivalent momentum of the wire in the pr esence of gravity is p = p 1 1 ( 1 - p -1 B where P 1 = 2.94 T/I. pg .2 . 94 T ) . (co s e) ave The size of this effect is about 0.1 % for this experiment . Summing up, th e effect of gravity on the wire inside the magnetic field is to fl atten the orbit slightly so as to make the equivalent momentum higher. Out s ide of the magne tic field r egion, t e wire orbit no longer consists of straight lines , but of ca t ena ries , as illustrated in Figure -153- 6.11. Inside the magnet , the orbit is circular to a good app roxima tion but outside the catenary orbit rises above the ideal straight line extension of the orbit inside the magne t. equation (G.4) with B = 0. The catenary is described by If we take T and cos 8 to be constant, the catenary is approximated by a parabola. Defining D(s) as the perpen- dicular displacer.1ent between the ideal orbit and the actual parabolic orbit, D (s ) = 1/ 2 s 2 e__g_ T cos 8 where S is measured from the effective edges of the magne t fiel d. In practice, the wire orbit ana lysis was done by fitting a straight line to the parabola by sampling the orbit at four points. Corrections to the slope and interc ep t we re made using a fit to the expression for D(s) at the s ame four points . The corrections to the slope were of the order of five millir a di a ns , while the intercepts changed by as much as 0.2 inches. 1 "' MAGNE T IC FIELD REGION /ACTUAL CATENARY s I <~--- f-' \ \Jl ..,.. .1 IDEAL STRA IGHT ORBIT THE ORBIT IS CIRCULAR INSIDE THE MAGNETIC FIE LD Figure 6.11 The Correction for Gravi ty in the Magnet Calib r a tion ,, -155- H. Example of the Background Subtraction Procedure We illustrate the subtraction procedure by considering it for a particular r un , number 74, in detail . In this run, the proton was detected in the magne t array. The firs t step is to use the pulse height in counter RS l (see Figure 3.6) to throw out events in which no deuteron was observed in the range a rray. To obtain a clear indication of the minimum pulse height c ause d by a deuteron , the RS l spectrum was plotted for events having a coplanarity within +1° and a missing mass excess within +10 MeV / c 2 , as in Figure 6.12. The ratio of for eground to background events in this sampl e is very high . For this case , a pulse h e ight of 35 0 was taken a s the minimum for deuterons . In the remaining steps of the subtraction process , only events with RS l pul se heights ab ove this minimum were considere d. There were 944 such events in run 74. Figures 6 . 13 and 6.14 show distributions of copl ana rity and mass excess for these events . Nex t, the extent of the values of coplanarity and missing mas s excess for foreground events is determined . By considering only events with a very high RSl pulse hei ght, the b ackground can be suppressed. Figures 6.15 and 6.16 s how the coplanarity and mass excess for events with RSl pulse heigh t greater than 800. From this foreground , events were cons ervative ly estimated to have coplanarities within ~5° and mas s excesses within +60 MeV/ c . All events lying outside these limits are taken as belonging to the background and constitute the samp le N0 . discussed earlier . The r e were 277 such even ts, leaving 667 events as the 40 30 en f- z 20 ~ I 0 f-' lJ1 u °'I 10 0 0.0 480 .0 Figure 6 . 12 960 .0 RSl PULSE HEIGHT 1440.0 The Pulse Height Spectrum in Counter RSl for Events with Small Coplanarities and Missing Masses 1920. 0 eo .--~~-,.-~~-,-~~~~~~-,-~~--,~~~-..-~~---.-~~--. RUN 74 60 ()) f- z uo ::) . I I-' 0 \Jl '-.I u I 20 O lo II D DI ~l ['l['~lr:t' ~l r:' - 12 .. o -6 . 0 I I -0 . 0 I ICI IC "JI!· c=-,c1 6 •0 DEGREES Figure 6.13 The Coplanarity Distribution for Foreground and Background Events I ! 12 . 0 120 90 ~ ' ~ RUN 74 ~ I r (.)) I I' ~ 60 ~ I- - 1 I 0 u r 30 ~ I I I o.__._._~~..__---'_,_._._-'-'-'-~.......__._~~_J_~~-'--'-'-U~-LI.-~~~~-" - 300.0 Figure 6.14 -150.0 0.0 MRSS EXCESS IN MEV 150.0 The Missing Mass Distribution for Foreground and Background Events 300.0 I I-' lJl 00 I J 40 I 30 I r -1 en 1- 320 o I I f-' I .I (_) ln \.0 I I i I iJ. Q rI 0 • - 12.0 l -6.0 Figure 6.15 -0.0 COPLRNRRIT Y COEGREES) 6 .0 The Coplanarity Distribution for Events with Large Pulse Heights in Counter RSl 12 . 0 80 ~~~~~~~~~~~~~~__,--~~~---. GO en f- z~ L!O I f-' 0 (]\ u 0 I 20 o~.._._.__._._._~..__._._._.__._.__~~_.___~_.___~~~~~ -200. 0 - 100 .0 0 .0 100 . 0 MISSING MRSS EXCESS CMEV/CX~2) Figure 6 . 16 200.0 The Missing Mass Distribution for Events with Large Pulse Heights in Counter RSl -161- mixture of for eground and background to be separated . l The 277 definite background events were u sed to simulate the entire b ackground samp l e by a Monte Carlo c alcul ation . Lists were made of the intersections of th e tracks with counters RSl and MS2 , and of the momenta measured in the magne t. Multiple Coulomb scattering c ause d the r econstruct ion of event vert ic es i n the He3 target to b e uncertain for most runs . . Therefore , a l ist of possib l e event vertices was made up using a r andom number generator on a computer , with the res triction that the v ertices must l ie within the boundaries of the target , and h ave a r adial dist ribution as that given in Appendix D. From these lists , 50 00 ' events ' were cons tructed by choosing at r andom one va lue from each li st and combining th ese i nto a single event . eight lists of l eng th 277 , t h e re are 8 b e constructed in this way . 277 As there were di fferent ' events ' which might Figure 6.17 and 6.18 show the coplanarity and mass excess di stributions for these 50 00 ' eve nts '. These h ave shapes as migh t b e inferred for th e background events in Figur es 6.13 and 6.14. Of the simu l ated b ackground events , 1132 we r e i ns ide t he f ore- ground r egion as defined abqve , and 38 68 outside . Thus 277·1132/3868 81.1 backgro und events are predi cted to lie in the for eground r egion . Figures 6.19 and 6 . 20 show the r esults of the backg round subtraction in coplana rity and missing mass excess . The s pe ctra of Figures 6 .17 and 6 .1 8 h ave b een no rmali zed to 81.1 events i nside the for eground region and then subtracted fro m the sp e ctra of Fi gure s 6.13 Fin~ lly, we c an obtain t he co rrected di stribution of events as 4 0.--~~-.-~~--,c--~~--.-~~----.~~~-,-~~---..~~~-.-~~--. 30 I n _J I I I n 1 10 0 - 12c.O -6. 0 -0.0 6.0 DEGREES Figure 6.17 The Coplana rity Distributi on for Background Events Generated by the Monte Carlo Calculation 12. 0 ,c CJ'\ N I 80 r-~~-,.-~~--,-~~~-,--~~--,-~~~r--~~-,--~~--.-~~---. 60 ()) 1- :z C!O =i I I-' 0 w °' I u 20 0 - -- - 300 .0 -150.0 Fi gure 6.18 0.0 MRSS EXCESS f N MEV 150.0 The Missing Mass Distribution for Background Events Generated by the Monte Carlo Calculation 300.0 RUN 74 667 EVENTS 50 81 SUBTRACTED Cf) 1- z::J 30 I I-' D O"I u ~ I 10 Q l=P-L:J l=:J , r'l : - 1 2~0 LFJ , 'l :J I IL>d I ,..I I '™..,.d - -6.0 - " - -0 . 0 ' d I ::f ' ...i 6.0 DEGREES Figure 6.19 The Subtracted Coplanarity Distribution 'l 1' L I I ,. ' i..., r' I :J ' c I 12.0 RUN 74 sor 667 EVENTS l I 81 SUBTRACTED J I I en I I I J ~ 50 1 8 I Vl I - -l I' I 20~ 0 iI I f-' (J\ r1 -300.0 q n =~ ,. . ., I - 150.0 L I 6 d ~ ...., ~I I L. I '"' ---1 '=LI U - 0.0 MRSS EXCESS IN MEV Figure 6.20 I ..,..... 9 I u L= r " - - - - - - - - - --1 150.0 The Subtracted Missing Mass Dis Frib ution 300. 0 -166- a function of photon energy. Figure 3.8 shows the distribution of all 667 events in the foreground region and (in black) the distribut ion of the 81.1 background events. The difference between these distributions is the final result of the background subtraction procedure. The subtraction process is very similar for runs in which deuterons rather than protons are detected in the magnet array . The only difference is that the values of the time of flight and MS3 pulse h eight play the role of the RSl pulse height discussed above . / -167 - I. Survey of Possible Recip ro city Tests In general, a reciprocity test of time r eversal invariance in t he electromagne tic int eraction compa res the forward and r everse r eac tions Y +A-<-+ B + C. Particle A must be a stable (or long-lived nucleus ) with no bound excited states . A* As noted in Chapter I, if a bound excited state exists the reaction B + C -+ A* + y followed by the decay A* -+ A + y c an b e experimentally confused with B + C ->- A + y, and might inva lid ate the reciprocity t est . Th e possible t arge t nuclei are p, n (in deuterium), d, H~ 3 , t (half-life -12 ye a rs ), H~ 4 and Li 6 . The pos sibi lities for B and C are the same as for A with the addition of charged pions . All reactions B + C -+ A + y will be subject to t he background B + C -+ A + TI 0 • It wi ll b e much easier to eliminate the b ackground if the. b eam particle B is charged, so that a beam of wel l-defined momentum may be used. All reac tions with a neutron t arget will actually have to b e obs erved with a deut erium t arget , making a sub tr ac tion for th e unwanted proton reaction. This is di £°ficult and would t end to obs cure th e signi- ficance of the r eciprocity t es t. In all re acti ons B + C ->- A + y in wh ich B is a nucl eus , there . 0 is a maximum laboratory angle for particle A, gene rally ne ar 10 . Measurement of _the extreme cent e r of mass frame angl e s requires detection of par ticle A at very s mall lab an gles. 1his is much eas ier with a bea;a of s mall sp atial dimensions , whi ch i s simp ler to ob t ai n with a charged than with a neutral beam . As discuss ed in Chapter I, any T-violaticn must invo l ve the -168- pro duction of a nucleon resonance , of which th e 6 (1236 ) is the lightest . The 6 decays into a nucleon and a pion , so th a t if p art icle B (or C) is not a pion, a final state interaction i s necessary to absorb the pion permi tting B and C to be nuclei. It would appear that reactions with an external pion would have strongest contributions due to 6 production, and th erefore provid e the best t est of T-invariance. re actions prove to b e rather difficult experimentally. However, all such Of th e r eact ions where B and C are b oth nuclei, I f ee l th at reasonably strong 6 product ion can occur if th e 6 can coexist with either B or C in an intermediate state; the only fina l state interaction needed is t he . absorption of a pion by the spectator nucleus . We now cons ider the possible re ac tions i n turn . The remarks apply to b eam energies suitable f or 6 produc tion. 1. y + p +-+ n + 7f+ The forward r eaction is probab l y .th e most well measured of all r eactions und er conside ratio n. Howeve r, in inverse reaction, ++n + 7f p + y i s quite difficult for two r easons : (a) a deuterium target must be used, and (b) th e protons have ve ry low kinet.i c energy, equivalent to a range of only 0.1 gram at the worst angle. A complete angular distribution is impos s ible. 2. y + n + p + 7f A deuterium correction must be made for the forward r ea ction, but this is somewh at simplified in that the entire final state can be measured and from th is t he neutron fermi momentum can be calculated . The inverse r eacti on has a neutral final state , and th e neutrons -169- produced a t large angles have low kinetic energies (15 MeV at eC.M.= 140°). Because of these experimental complications , it is hard to evalua te the presen tly observed 111 d iscrepancy in t e rms of a T-violation. 3. y + d +-r n + p The forward reaction has been wel l measure d, as men tione d in Chapter I. To eliminate backgrounds y + d + n + p + TI 0 or p + p + TI - , e ither the neu tron should be observed, o r a ' synchrotron subtraction' performe d. The inverse re act ion must .be performed with a n e utron beam , which can be obtained with only fair momentum resolution. 4. y + He 3 + p + d Both the forward an d inverse reactions ar e more accessible than for reactions (3) since the p and d are charged . . Disadvantages are the lowe r cross-section and le ss prominent appearance of the 6 . In observing the inverse reaction , it is advant ageous to use a deuteron beam and a proton target rather than the opposite . This is because a deuteron beam of 900 MeV is needed for 6 production whi le a proton beam need only be 450 MeV. Ther efo re , the l a boratory ene rgies of the He 3 and y are much larger , and more easily observable , if a deuteron beam is used . The maximum l a b angle for the He3 is only 9° in this case, s o the d e uteron beam mus t be we ll collimate d if the smal l ang le He 3 are to be detected . 5• y + He 3 -+->- TI+ + t While these re actions should have a l arge 6 production , they a re difficult experimentally . ' In the forward reaction , the tritium mus t be detected to have confidence that the reaction occurre d . However , -170- the maximum kinetic energy of the tritium is 50 MeV, and it would be almost impossible to measure a complete angular distribution. Likewise, in the inverse reaction the He 3 has a maximum energy of 53 MeV. 6. y + t -+ n + d Measurement of the forward reaction would involve the radiation hazard of a tritium target. (3). over reactions 7. These reactions offer no advantages y + t -+ TI-+ He3 These re ac ti ons suffer from the same disadvantages of r ea ctions (5), with the addition of t he radiat i on safety problem. 8• y + He 4 +-+ p + t These reactions appea r the mos t pro mising pos sibility for a n ew reciprocity t es t. Base d on data 78 is abou t 0.1 t ha t of reactions due to !::. production. 0 a t 90 (c .m.), the cross-section (3), with an even mo re p rominen t 'bump ' The tritium is produced with fairly low ene rgy ( 40 MeV ) i n th e forward reaction, requiring care. For the inverse r eac tion it i s advantageous to use a trit ium beam (1200 MeV ) rather than The maximum lab angle of the He 4 wou ld then be 6.5°. a proton beam . 9. y + He 4 ++ d + d While these reactions are quite accessible to experimen t, they have a very low cross-section. The indistinguisha bility of the two spin-one deuterons forbids them from forming the 1 P, state neede d i for electric dipole tr ansit ions. i mportan t for !::. While this transition is probab ly no t production , the latt er is suppresse d by a complicate d final-state i nteraction needed to absorb the decay pion internally. -171 - 112 An experiment at a photon energy of 265 MeV reports a cross-sect ion 60 times :smaller th an that for y +He 4 10. y + Li 6 -<- >- d + Hetf 11. y + Li 6 +->- He 3 + t ->- p + t. While all of these reactions have measureable values of their kinematic parame ters, it i s unlikely th at 6 production i s very important i n th em as c omplicated f inal state interactions are necessary . Based on this survey , I reconunen d the r eactions y + He 4 +-+ p + t a s the best c andidate fo r an additional r eciproci ty t est of T-i nvari ance . They appear to h ave a st rong signal du e t o 6 p r oduction an d are experimentally tractable. 'hot ' e xperiment s. Finally , as tritium is involved , they would b e v ery -172- VII . 1. FOOTNOTES AND REFERENCES J. H. Chr istenson, J. W. Cronin , V. L. Fi tch and R. Turlay , Phys. Re.v . Lett e rs 13 , 138 (1964). 2. G. Luders, Annals of Physics 1_, 1 (1957). 3. J. Bernstein , G. Feinberg and T. D. Lee, Phys. Rev. 139, Bl650 (1965). 4. The evidence for parity conservation is no t at all conclusive for interac ti ons involving virtual photons . A kinematic factor of q 2 (q = 4-momentum of photon ) in a possible parity violating amp litude suppresses any effect in mos t experiments . A search for an asyrmne try in the inelas tic scattering of polarized electrons with unpolarized protons would be the mos t sensitive experimental tes t of parity non-conservation independen t of the question of t ime reversal violation. 5. Ernes t M. Henl ey , Annual Review of Nuclear Science 11_, 36 7 (1969 ). 6. S. Barshay , Phys . Rev . Le tters lZ_, 49 (1966 ). 7. T. D. Lee, Phys . Rev . 140 , B959 (1965 ). 8. L. B. Okun, Physics Lett e rs Q , 595 (1966 ). 9. William B. Fraze r, Phys. Rev . 150 , 1244 (1966). lo . J . C. Keck and A. V. Tollestrup , Phys . Rev . 101 , 360 (1956). 11. R. Kose , W. Paul , K. Stockhorst and K. H. Kiss l er , Ze i tschrift fu r Physik 202 , 364 (1967). 12. J. Buon , V. Gradco , J. Lefrancois , P. Lehmann , B. Merkel and P. Roy , Physics Letters ·26B, 595 (1 968 ). -173- 13. D. I. Sober, D. G. Casse l, A. J. Sadoff , K. W. Chen and P. A. Crew, Phys. Rev . Letters~. 430 (1969). I 14. R. L. Anderson , R. Pr epost and B. H. Wiik , Phys . Rev. Letters ~, 651 (1969). 1,5. D. F. Bartlett, C; E. Friedberg , K. Goulianos, I. S. Hammerman and D. P. Hutchinson , Phys . Rev . Letters l1_, 893 (1969). 16. B. L. Schrock, J. F. Detoeuf , R. P. Haddock , M. J. Longo, K. K. Young, S. S. Wilson , D. Cheng, J. Sperinde and V. Perez-Mendez, in High-Energy Physics and Nuclear Structure, edited by S. Devens (Plenum Press, New York, 1970). 17. D. F. Bartle tt, c. E. Frieberg , P. E. Goldhagen and K. Goulianos , Phys. Rev. Letters J:]_, 881 (1971). 18. Bryce L. Schrock, Roy P. Haddock, Jerome A. Helland, Michael J. Longo, Stephen S. Wilson , Kenneth K. Young, David Cheng and Victor Perez-Mendez, Phys . Rev. Letters ~ ' 1659 (1971). 19. A. Donnachie , in Proceedings of the 1971 International Symposium on Electron and Photon Interactions a t High Energies, edi ted by N. B. Mistry (Laboratory of Nuc l ear Studies, Corne ll Universi ty, 1972 ). 20. This statement is, however, a sub j ect of controversy among nuclear physicists. For a recent summary of the experimenta l situation see K. H. Bray , S. N. Bunker , Mahavir Jain, K. S. Jayaraman, G. A. Moss , W. T. IL van Oers , D. O. Hells and Y. I. Wu , Phys. Rev. / C3, 1771 (1970 ). 21. The ' range ' array is so-called because it was originally intende d -174- to observe the range of the par ticle in carbon. To this end, a sandwich of t en plates of carbon and ten wire chambers was cons tructed behind counter RS3 (Figure 2.4). However, most deuterons would neve r reach the sandwich. Further, the chambers proved troublesome. Data were taken wit h the sandwich when protons were detected in the range array, but not used in l a ter analysis ; the corresponding deuteron in the magne t was s o clearly i dentified that the proton range information was superf luous. In a momen t of imagination it was even conceived that the nuclear scattering of protons in the carbon migh t be used to obtain information on the spin polarization of the protons. 22 . Alvin V. Tollestrup , CTSL Internal Report No. 31 (196 7), unpublished. 23. Alvin V. Tollestrup and Ricardo Gomez , CTSL Internal Repor t No . 35 (196 7), unpublished . 24 . Charles Y. Prescott , CTSL Internal Report No . 38 ( 1~68 ), unpublished . 25 . Shiu-uh Cheng , Ph.D Thesis , CalTech (1970), .unpublished. 26. J. R. O'Fallon , L. J. Koester , Jr. , J. H. Smith and A. I . Yavin , Phys . Rev . 141, 889 (1966). 27. G. Goggi , G. C. Mantovani , A. Piazolli, D. Scannicchio, A. Piazza and R. Rinzivillo , Nuovo Cimento SSA , 901 (1968 ). 28 . R. Guardiola and J, L. Sanchez-Gomez , Nuovo Cimen to lA, 24 3 (1971). 29 . Leon Rochester , Ph.D Thesis, CalTe ch (1968), unpublishe d. 30. Joseph F. J anni, Technical Report AFWL-TR-65-150 , National Techni- -175- cal Infonnation Service, Springfield, Virginia (1966). 31. Fits for the (pp) and (np ) cros s-s ections as a function of kinetic energy were made using data comp iled by MacGregor et a1 32 . The (pp) cross-secti on was fitte d assuming the angu l a r distribution to be flat using the value a t 90 0 (center of mas s frame). This c auses only about a 1% discrepancy between the fit and the . criteria that the · scatter~ng occur at angles greater than 3 5°. 0 The total cross-s ect ion was us ed for (np ) scatte ring . or The 0 26 -coefficient A- · in the (pA) cross-section reflects the fact that r oughly an A 213 dependence is to be expe cted. It was deter- mined from proton-nucleus scattering data taken by Johansson et a1 33 , and is independent of the proton 's k i net ic energy in the range 10 - 600 MeV. The coefficient 1.2 A-O.l 7 in the (nA) cross- sections holds only for A greater than 2 ; for A less than 2, it is 1. 0. It was determined from the neutron-nuc leus scatt ering data of Ashmore e t a1 10 - 350 MeV . 34 and applies to neutron kinetic energ ies In calculating the (dA) cross-sections from those for (pA) and (nA), the proton and neutron kinetic energies are taken as 1 / 2 that of the deutero n. The two factors 0 . 83 and 0.56 come from using the appropriate combinations of the elasti c, inel as tic an d stripping cross-sections for deuter6n--carbon scattering a t 650 MeV given in reference 35; this is the only data in the literature containing the necessary information on deuteron-nucleus scattering . 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