π⁻ Photoproduction from Deuterium and a Partial Wave Analysis of π⁺ and π⁻ Photoproduction in the Energy Region 500 to 1250 MeV Citation Scheffler, Paul Erick (1972) π⁻ Photoproduction from Deuterium and a Partial Wave Analysis of π⁺ and π⁻ Photoproduction in the Energy Region 500 to 1250 MeV. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/T5Y8-PR50. https://resolver.caltech.edu/CaltechETD:etd-09222005-113106 Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Single [...] and [...] photoproduction rates from deuterium have been measured at the Caltech 1.5 GeV electron synchrotron at 32 photon energies between 585 and 1250 MeV and for 13 CM pion angles between 6 and 160° at each energy. The cross section for the reaction [...] has been calculated via the [...] ratio from deuterium and via the spectator model for the deuteron. A partial wave analysis has been done on the reactions [...] and [...] in the region of the second and third photoproduction resonances using the model of R. L. Walker. The results show some disagreements with recent quark theories. A case is made for the possibility that the [...] (1535) is excited by isoscalar photons, in agreement with some results of [...] photoproduction experiments, and in disagreement with quark theory. Finally, the helicity 3/2 component of the [...] (1688) resonance in [...] photoproduction is seen to be small, but not zero as predicted by the quark model. 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): Walker, Robert Lee Thesis Committee: Unknown, Unknown Defense Date: 24 January 1972 Record Number: CaltechETD:etd-09222005-113106 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-09222005-113106 DOI: 10.7907/T5Y8-PR50 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3691 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 23 Sep 2005 Last Modified: 02 Jul 2024 21:00 Thesis Files Preview PDF (Scheffler_pe_1972.pdf) - Final Version See Usage Policy. 8MB Repository Staff Only: item control page

mt “PHOTOPRODUCTION FROM DEUTERIUM, ; “+ ~ AND A PARTIAL WAVE ANALYSIS OF a AND ov PHOTOPRODUCTION IN THE ENERGY REGION 500 to 1250 MeV | Thesis by ‘Paul E. Scheffler In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1972 (Submitted January 24, 1972) ii ACKNOWLEDGMENTS I appreciate the help and encouragement of Professor Robert L. Walker in the conception and execution of most caspects of this experiment, and especially his suggestions for the partial wave analysis of the data. ' The experiment would have been impossible without the help provided by the synchrotron crew and operators, especially by Earl Emery and by Al Neubieser. Assisting-in the setup for data runs and in recording data were Craig Maxwell, Chip Smith, Gary Murata, and William Metcalf. I appreciate the advance results of the 1 polarization experiment: done:by..William Metcalf. Finally, most helpful of all was Patrick Walden, my partner in this experiment. Mr. Walden was responsible for most of the data reduction and cross section corrections, relieving me of much tedious work, I am grateful for his many suggestions and explanations, Lii ABSTRACT Single ne and 1 photoproduction rates from deuterium have been measured at the Caltech 1.5 GeV electron synchrotron at 32 photon energies between 585 and 1250 MeV and for 13 CM pion angles between 6 and 160° at each energy. The cross section for the reaction yn > ™ ? has been calculated via the aw fnt ratio from deuterium and via the spectator model for the deuteron. A partial wave analysis has been done on the reactions Yp > nn and yn + 1 p’ in the region of the second and third photoproduction resonances using the model of R. L. Walker. The results show some disagreements with recent. quark theories. A case is made for the possibility that the S, 01535) is excited by isoscalar photons, in agreement with some results of n photoproduction experiments, and in disagreement with quark theory. Finally, the helicity 3/2 component of the Fy, (1688) resonance in 1 photoproduction is seen to be small, but not. zero as predicted by the quark model. iv TABLE OF CONTENTS. List of Figures List of Tables I. Il. III. Iv. Introduction . A. Previous Data - or Lack Thereof B. Preparation of Experimental Apparatus C. Division of Work on the Experiment The Deuterium Problem A. The Spectator Model of Photoproduction from Deuterium B. Bound Nucleon Momentum C. Energy Resolution of the 1 Photoproduction Experiment — : oN -D. Reduction of Energy Resolution Width by Using a "Recoil Counter" to Detect the Second Charged Particle E. The Glauber Effect F. Final State Interactions Calculation of the m-> 1 p Differential Cross Section A. Methods B. Elimination of Competing Reactions Results A. The w/w Ratio B. The Ratio Cross Sections C. Direct nt Cross Sections from Deuterium D. Direct 7 Cross Section (pion only detected) from Deuterium E. Direct 1 Cross Section (both pion and recoil proton detected) from Deuterium F. Accidentals and Dead Time at Backward Pion Angles , G. Backgrounds Page vi ix 10 11 11 12 14 25 27 27 32 35 35 36 37 39 40 AL Al TABLE OF CONTENTS (continued) H. Final 1 Cross Sections (yn > 7 p) I. Total Cross Section, 0° cross Section, 180° Cross Section J. Comparison With Other Experiments V. Partial Wave Analysis A. Model for Partial Wave Analysis B. Fitting Procedure C. Results of Partial Wave Analysis Vi. Conclusions Appendices I, Notes on Kinematics - II. Beam Energy Monitoring III. Experimental Apparatus IV. The Hulthen Wave Function V. Notation and Helicity Formalism for Partial Wave Analysis VI. Partial Wave Amplitudes VII. Born Terms and Resonances VIII. Fitting Procedure IX. Final Helicity Element Fits References Page 93 94 130 137 140 144 146 188 190 191 193 203 220 221 228 235 240 249. 294 10, ll. 12. 13. 14, -15. 16, 17. 18, vi ‘LIST OF FIGURES . te : Total Cross Section for 7 Photoproduction Schematic of Beam Line and Experimental Area Hulthen Momentum Magnitude Probability Density Experimental Spectator Momentum Distribution for Hilpert et al. (38) Monte Carlo Analysis - Spectrum of Magnitude of Target Nucleon Momentum with and without Recoil Counter , ; Monte Carlo Analysis - Spectrum of Total CM Energy with and without Recoil Counter Monte Carlo Analysis ~- Spectrum of CM Pion Angle with and without Recoil Counter Bremsstrahlung Spectrum and Photon Energy Resolution Curves n fat Ratio and nt Photoproduction from Deuterium - Experimental Results "Ratio" Cross Sections, 1 Photoproduction Cross Sections from Deuterium with and without Recoil Counter Angular Distributions of Final nm Cross Sections . Energy Distributions of Final 1 Cross Sections Total Cross Section - 7 Photoproduction 0° Cross Section - 1 Photoproduction 180° Cross Section - 7 Photoproduction Comparison of Results with Hilpert et al. (38) Comparison of Results with Lodi-Rizzini et al. (37) Comparison of Results with Ito et al. (40) Page 13 15 18 20 21 33 65 79 101 110 127 128 129 132 133 134 19, 20, 21. 22. 23. 26. 27. 28. 29. 30. “31. 32, 33. LIST OF FIGURES (continued) Comparison of Results with Beneventano et al. (39) Comparison of Results with Fujii et ai. (11) Initial Fit of Add-on Helicity Elements for wt Photoproduction Fit of Recoil Proton Polarizations for 1 Photoproduction Fit of Polarized Target Asymmetries for 7. Photoproduction Plot of Components of H, Helicity Amplitude at 0° 2 Plot of Free Neutron Cross Section, Deuterium Cross Section, "Spin~-flip" Cross Section, and "Spin-non-flip" Cross Section at 900 MeV Fitted Free.Neutron Cross Section, Calculated Deuterium Cross Section, and Experimental Deuterium Cross Section for m Photoproduction at 10 Initial Fit of Add-on Helicity Elements for wv Photoproduction + Fit of Recoil Neutron Polarizations for 7 Photoproduction at 60 < + Fit of Recoil Neutron Polarizations for Photoproduction at 90 Fit of Polarized Beam Asymmetries for nt Photoproduction at 90 Fit of Polarized Target Asymmetries for nt Photoproduction at 40 Fitted Free Proton Cross Section, Calculated Deuterium Cross Section, and Experimental Deuterium Cross Section for m Photoproduction at 10 T/P Ratio for Wilson Quantameter Page 135 136 148 162 163 165 167 168 170 183 184 185 186 187 196 34, 38. 39. 40, 41, 42. 43, 44, 45. 46. 47. 48, villi LIST OF FIGURES (continued) Comparison of Average Beam Energies Calculated via Each Secondary Monitor Schematic of HEMA Spectrometer ~ Counter Positions Schematic of LEM Spectrometer - Counter Positions Diagram of Recoil Counter - Counter Dimensions Schematic of HEMA Electronics Schematic of LEM Electronics Schematic of Recoil Electronics Variables in the CM Frame Contributions of Helicity Elements to Helicity Amplitudes Feynman Diagrams for the Born Approximation Typical Behavior of a Resonance Final Fit of Add-on Helicity Elements for 1 Photoproduction Total Helicity Elements from Final Fit of 1 Photoproduction Final Fit of Add-on Helicity Elements for 1 Photoproduction Total Helicity Elements from Final Fit of nt Photoproduction Page 202 204 210 214 216 217 218 222 231 236 239 250 261 272 283 ll. 12. ix LIST OF TABLES Resolution Widths for Selected Pion Angles and ‘Photon Energies n/n Ratio a Cross Section from Deuterium, 7 Cross Section from Deuterium, and "Ratio" Cross Section Recoil Cross Sections Final Cross Sections for the Reaction yn > tT p Total 7 Cross Section, 0° Cross Section, and 180° Cross Section Experiments Used in Partial Wave Analysis Relationship of Helicity Elements to Electric. and Magnetic Multipoles List of Resonances and Changes Made-.by Fit HEMA Acceptance Properties OUTR Acceptance Properties LEM Acceptance Properties Page 43 49 60 95 138 143 161 206 207 212 PART I INTRODUCTION Low energy pion photoproduction data Ky? < 1.5 GeV) have been used to locate and identify some of the more prominent pion-nucleon resonances without extensive partial wave analysis. The total cross-section for single positive pion photoproduction off protons. (Figure 1) clearly shows the presence of the "Ist", "2nd", and "3rd" photoproduction resonances which have been identified as the P,,(1236), D, 301520), and (partially) the Fy, (1688) respectively, From phase shift analyses of pion-nucleon scattering data, several other resonances are known or believed to exist in this energy region, namely the P1470), 8), (1535), DB), (1670), S,, (1700), 8, , (1650), D3, (1670), and perhaps the P,, (1780). Recent quark model schemes have made predictions for the amplitudes of these resonances for the photoproduction of pions off of both proton and neutron targets. (1,2,21) In order for one to be able to confirm or deny such predictions, it would be helpful if the photoproduction data were sufficiently precise in this energy region for partial wave analysis. It is desirable to have precise data for both proton and neutron targets, not only to confirm or deny quark model schemes, but in order to pin down the isospin character of 61 ASS NI“WS.LSAS IO NI ASYSNS WLOL N 8 2 o'1 Sl e ZI Leon Ley ¥ [hk Leoop | aN & e 6 rs) t A® by nani “Send i ~9D° 3b T vl Li v Ly v us v v a qT t v y “sl 21 Tl Ol O68 of Of o98 OS Ov og A39 NI “SV NI ASYSNS NOLOHd LNSGION: ‘8%? y ord OOl 00¢ OO0€ FIGURE 1 the electromagnetic interaction, which has. always been an interesting question, This point is clearly illustrated by writing down the amplitudes for the four single pion photo~ production reactions in terms of the isoscalar and isovector amplitudes Ae and AY as follows: tt ! i ! A(yp > ttn) = at = (/i73ya¥3 ~ (7573) (a¥? — a8) o = (1273)? + (TTS) (AN - a) A(yp > 7°p) = Ao = 4 _ yee v3 vg GD AQyn > 1 p) & A = (V1/3)A~ - (/273) (A + aS) Ayn > 1°n) = APs (7273) AY? + (V773) (AN? + a8) The vector part of the interaction gives possible final . . os : V3 V1 states of isospin 3/2 and 1/2 with amplitudes A’~ and A respectively. The scalar part gives final states of isospin 1/2 with amplitude AS, The above form of the equations, taken .from Walker (3), assumes no isotensor interaction. The isoscalar and isovector amplitudes may be calculated if at least three of the photoproduction amplitudes (including at least one with neutron target) are known. The isoscalar and isovector character of a spin 1/2 resonance may be : te) + - V3 determined if (eg.) A and A are known since A~ = 0 and V1 the difference of A ‘and Ne is taken for proton targets while the sum is taken for neutron targets. Finally, photoproduction data and associated partial wave analyses can be.used in the application of low energy sum rules and in comparison with dispersion relations pre- dictions. A. Previous data ~- or lack thereof, In the past few years, comprehensive differential cross section measurements of both nt and 1° photoproduction off protons in the energy region Ke < 1.5 GeV have been made by Fischer et al. (4), Betourne et al. (5), Ecklund et al. (6), Thiessen(7), Fischer et al. (8), and Wolverton (9}. Further measurements at selected energies and angles have been made by many groups (10,11,12,13,14,15,16,17,49,55). Also, several recent experiments have measured recoil nucleon polarizations and polarized beam asymmetries for the nt and 1° reactions (18, 19, 20,22,23,24,25,26,27). Finally a recent experiment has measured the we cross section at 40° using a polarized target (28). (A compilation of experiments done before 1967 may be found in the report by Beale et al. (29).) | Several groups (3,30,31,32,33) have attempted partial | wave analyses of these data, using various constraints and models to overcome the difficulty of fitting twice as many amplitudes as in pion-nucleon scattering analyses. Of special interest to me is the comprehensive analysis of low energy photoproduction data carried out by RL. Walker (3), A discussion of my work with Walker's model appears in Part V. The data for photoproduction off neutrons have been relatively sparse due to the difficulties associated with neutron targets. Since fixed targets of free neutrons are impossible to maintain, compound (eg. deuterium) targets must be used; or measurements of the inverse reaction might be made, In both cases, the yn cross section must be calculated under certain assumptions, ie. the spectator model for deuterium or time reversal invariance for the inverse reaction. Up until 1968, when our experiment was started, the main body of 1 photoproduction data below Ke = 1.5 GeV had been collected in experiments with deuterium targets by Sands et al. (34), Beneventano et al. (35), and Neugebauer et al. (36), totalling about 100 data points (all below Ke = 1,0 GeV). It was our desire to augment the above by measureing detailed angular distributions (every 10 to 15 degrees) for many lab photon energies between 575 and 1250 MeV and to improve upon the energy resolution and statistics as much as possible. ‘Since the start of this experiment, several other groups have published © data. Among these are two bubble chamber experiments: Lodi-Rizzini et al. (37) .and Hilpert et al. (38). . a) ; A counter experiment at 90°-has been done by Beneventano etal. (39). Also, a counter measurement of at and 1 photoproduction at 180° using bremsstrahlung subtraction to improve the energy resolution has been made by Fujii et al. (11). Finally, a measurement of the c/n* ratio from deuterium at-0° has been made by Ito et al. (40). All of the above experiments were done with a deuterium target. Comparison of these experiments with the results of our experiment is given in Part IV. One further measurement of the 7 cross section has been made via the inverse reaction pi > ny (41). The results lab _ 500 to 1000 MeV of this experiment in the energy region k are not yet available for comparison. Finally, there have been several new measurements of polarized beam asymmetry and recoil proton polarization for _the 1 reaction(20,42,43,53). I have tried to incorporate some of these in a reanalysis of the m1 reaction using Walker's model (see Part V). B. Preparation of the experimental apparatus. For our experiment, it was desired to use the existing experimental setup in the south beam of the Caltech 1.5 GeV electron synchrotron with as little modification as possible. The synchrotron - now defunct - produced an external brems- ‘strahlung photon beam with cutoff energy at the endpoint of the circulating internal electron beam, The bremsstrahlung beam was then collimated, swept of charged particles, and allowed to strike the (3 inch diameter) liquid deuterium or liquid hydrogen target in the experimental aréa. A schematic diagram of the beam line and experimental area is shown in Figure 2. The particle detection apparatus consisted of two magnetic spectrometers:.one for low momentum (< 600 MeV/c) _ and the other for high momentum (600 .- 1650 MeV/c) charged particle detection. The low energy magnet (LEM) had seven momentum channels with a total momentum range AP/P | ~ 10% while the high energy magnet (HEMA) had four channels with the same total momentum spread. The two spectrometers had © been used in a number of previous. experiments, most recently by S.D. Ecklund, H.A. Thiessen, and F.B. Wolverton in measure- ments of at and 1° photoproduction from hydrogen. In addition, Wolverton's 1° experiment made use of a simple coarse scintil- lation counter hodoscope array (with Pb converter), set up and moveable on a track of about 32 inch radius around the target. This was used to detect gamma ray decays from the n°, The above apparatus appeared to be immediately useable for measurement of 1. photoproduction which produces two charged particles in the final state. One of the spectrometers SIdir sl XIGNAddV LA9OMVL WAS 120 | (3NIT Wve - TIWY 40 LNO NMOHS) a YALNNOD. W0dSYy | | YALSWVLNVNO arall la = TOS . IXIA Ve ° IA\ as LIT | ES \ [] § 3 a / \ \ at \y hy =. Y m, | YAEGWVHO NOl NINO [|] SYsadvVyosS st YSHOLVO WV3g YA99I4 LAO [ti | i~ | woLvivY . = WV3g HLNOS SLINOVW ONIGSSMS YOLVAITI00 AYVWIYd VWSH | LS9UVL SYadVYOS - .YALSWOYLOadS Wa Na9080AK V 19 | YBLEWONLORdS FIGURE. 2 could be used to detect the pion while a simple hodoscope set up on the track could be used to detect the recoil proton. The modifications of the existing setup to measure w photoproduction were as follows: 1) The "hydrogen" target was, of course, filled with deuterium. 2) The seven channel momentum hodoscope (produced by four overlapping counters) on the low energy magnet was replaced by a four channel hodoscope (produced by four non-overlapping counters). | 3) The four channel "gamma counter" hadoscope on the track surrounding the target was replaced by.a single channel counter telescope (the “recoil counter"). | 4) Finally, the electronics of the experiment was com- pletely rewired from scratch, using the newer Tollestrup circuit modules to replace the older Marshall circuit modules, The magnetic spectrometers had already been calibrated by Thiessen and Wolverton (see Appendix III) and it was deemed unnecessary to recalibrate them except to translate the acceptance parameters for the seven-channel hodoscope on the LEM to acceptance parameters for the new four-channel momentum counter (44). A more detailed description of the 10 apparatus and electronics is presented in Appendix III. C. Division of work on the experiment. This 1 photoproduction experiment was a joint effort of myself (P.S.) and Patrick L, Walden (P.W.). The division of work on the experiment was as follows: 1) Physical modification of apparatus ~ P.S., P.W., various undergraduates, and the synchrotron crew. 2) Setup of electronics - P.S. and P.W. 3) Initial Monte carlo study of effects of using "recoil counter" - P.S, | 4) Determination of optimum recoil counter size - P.W. 5) Beam energy monitoring analysis - P.S8. 6) Reduction of scaler data to true particle rates - P.W. 7) Calculation of acceptances and direct cross sections _ using spectator model - P.W. 8) Averaging.and interpolation of final data, simple resolution correction ~ P.S. 9) Attempt at partial wave analysis of final cross sections ~ PS. | 10) Investigation of deuterium effects neglected in the cross section calculation - P.S. and P.W. ll PART IT THE DEUTERIUM PROBLEM As mentioned above, the differential cross section for the reaction yn > 7 p must be calculated from particle rates of photoproduction off a compound nucleus (deuterium) ; The actual reaction is then yd> 7 pp. The main considera~ tions with a deuterium target are: 1) The target neutron is bound. 2) The momentum of the bound nucleons in deuterium is not negligible compared with the other particle momenta, 3) In the initial state, the proton in deuterium "shadows" the neutron with consequent effect on the cross section (Glauber effect). 4) In the final state, the outgoing pion and "recoil" proton may interact with the "spectator" proton. A. The spectator model of photoproduction from deuterium The spectator model is used to approximate the behavior of the neutron in deuterium to take care of. problems 1) and. 2). The model is equivalent to the "impulse approximation" for complex nuclei which states that the reaction amplitude is the sum of reaction amplitudes off of each nucleon separately, with no collective effects. The conditions for the validity 12 of the impulse approximation are discussed by Chew and Lewis (45) and are shown to be satisfied by the deuteron, because of its small binding energy and spread out wave function. Since a single 7 can be photoproduced only from neutrons, the spectator model assumes that in deuterium, only the neutron reacts with the incoming gamma ray to produce a single 1 , while the proton acts as a "spectator" whose momentum in the final state equals its momentum in the initial state. Thus in its simplest form, this model ignores initial and final state interactions with the spectator. B. Bound nucleon momentum, A rough derivation of the internal momentum distribution of nucleons in the deuteron can be made assuming a simple nuclear potential and relatively simple form for the deuteron wave function. One such "derivation" (46), using, a Yukawa potential, gives the Hulthen wave function u, (8) and associated Fourier transform momentum space wave function e(k) (see “Appendix IV). The probability density for the magnitude of the nucleon momentum is given by Ark? | eR) |? and is plotted in Figure 3. The most likely momentum for the target neutron in the deuteron is roughly 50 MeV/c, a quantity which cannot be ignored in comparison with the momenta of the other 13 WDW NOS TOON TUNUBLN, i cot FIGURE 3 ALISNSG ALD IPSSeOeld WOLNSKOW NOILINNS SAGM NSHITINH 14 particles.in the reaction, On the other hand, because of the simplified assumptions and the approximations used, we know that these functions are somewhat innacurate}; and specifically, our lack of any knowledge of the true wave function and potential at small radius p is translated into large uncertainty in the momentum distribution at large momenta. In fact, recent measurements of this momentum distribution in 7d production experiments | (bubble chamber) have shown relatively large numbers of events at spectator momenta. greater than 200 MeV/c in disagreement with the Hulthen function prediction. (56) A comparison of the Hulthen momentum function with the _ spectator proton momentum distribution obtained in the 7 photoproduction bubble chamber experiment by Hilpert et al. (38) shows that for photon energies below 1.5 GeV, the Hulthen function is in fair agreement with experiment for momenta below 300 MeV/c (Figure 4). C. Energy resolution of the 1 photoproduction experiment. The target nucleon momentum has an effect on the calcu- lation of the photon energy at each data point. The gamma ray beam incident on the deuterium target is a bremsstrahlung number of events {C00 T 15 : 7 yt d—e pap + ree 10 248 events _ ! 50 . ! 100 1 0 = 20 250. cee) FIGURE 4 16 beam, continuous in energy up to a cutoff equal to the end- point energy of the synchrotron, The specific photon energy for the reaction must be calculated at each data point from kinematics determined by measurement of outgoing particles and our knowledge of the photon beam direction. The finite width of the spectrometer aperture is reflected into.a finite resolution width in our knowledge of the photon energy. Other contributions to the resolution width are finite target size and finite beam width, This resolution width is not too broad in experiments done using a hydrogen target, where the target nucleon (proton) can be considered to be at rest in the lab. The two-body kinematics of the reaction are completely determined by measurement of the vector momentum of one outgoing particle (plus our knowledge of the photon beam direction). The width of the spectrometer aperture, target width, and beam width are reflected into a small resolution width in photon energy, eg. about 25 MeV at forward angles. However, when a deuterium target is used, the target nucleon is in motion; and, at each data point, events corres- ponding to many possible target nucleon momenta are counted. If again, only one outgoing particle is detected (in. the spectrometer), the two-body kinematics can be calculated 17 assuming the validity of the spectator model. But now, there is another major contribution to the photon energy resolution width: the uncertainty in the ‘initial. momentum of the target nucleon. The effect is to increase the energy resolution width by a factor of two or more. D, Reduction of energy resolution width by using a "recoil counter" to detect the second charged particle. It seemed likely that the use of a counter telescope or hodoscope to detect the second charged particle ("recoil proton") in the reaction might help to reduce the resolution width to acceptable levels. I have done a Monte Carlo investigation of the angular distribution of proton recoils as a function of initial target neutron.momentum.for a given spectrometer setting and aperture, Thus I have been able to determine the effect of using a recoil counter to detect this recoil proton. it was found that events with the largest angular deviation from the central recoil angle had high target neutron momenta, a result which is not very surprising. Thus, a recoil counter of appropriate size could be used to discriminate against these high neutron momenta and improve the resolution of the experiment. Figure 5 shows a typical result: of the analysis. The high momentum tail of the Hulthen 18 CO/ASWD LNG BA NBITSNN LsOebl as ose o0e 081 CO? OS 0 OP STS ce So Ao a et Wb Li 7 i | oo i it ~“ = ted i t aa in i i id a i | : if | ! | —_ im 7 milmnil { UL : a WSINNBS. ViDISe HLIM oc a HAINNBO TiOosY INGH LIM of 7 F H : i. H NOINSWDA NOS TSON ABQesi a0 SONLINGSW a8 ANYLOSdS SISATENG Ob SLNOW | Cot FIGURE 5 19 momentum distribution has been cut off by the addition of the recoil counter. As may be seen in Figure 6, the CM total energy resolution has been improved, mainly by cutoff of large tails due to high target neutron momenta. Figure 7 shows a similar improvement in the resolution of the CM pion angle. A study made by Patrick Walden of the tradeoff between percentage of events (corresponding to a pion in the spec- - trometer) detected by the recoil counter and reduction in resolution width was used to determine the optimum counter size. Roughly, the optimum size was determined to be the angular aperture which accepted 50% of the events corresponding to a pion in the spectrometer. For smaller recoil counter size, the energy resolution width fell off slowly, while for larger counter sizes, the resolution width increased rapidly. Based on these results, a recoil counter telescope system was designed by Craig Maxwell to be placed on the existing circular track surrounding the target. Details of the recoil counter system are given in Appendix III, A short summary of the actual resolution widths for this experiment calculated at selected pion CM angles and "free" neutron rest energies (see Appendix I) is given in Table 1, 20 = OoST OShi = j iv 5 ~ 0s a =| OGT a T = 081 — ¥ -_ — Goze co | ¥SLNNO9 T1903" HLIN Z - i+ LOINAOD TIOQOSH LNBHLIM 1 7% i i 1 MOYSNA WO T6LOL 49 WAYLOSdS SISATEND DID SLNOW BOs FIGURE 6 on Oy *) \./ _2i THI. IG o j ; H pS MN if at ONY we L FIGURE 7 22 TABLE 1 RESOLUTION WIDTHS FOR SELECTED PION ANGLES AND PHOTON ENERGIES CM . "Lab" 20 (degrees) 20 (MeV) Pion Photon Angular Resolution Energy Resolution Angle Energy Pion With Pion With (deg) (MeV) Only Recoil Only Recoil 6 612 Lal | 70 6 916 1.2 108 6 1220 1.6 150 45 612 4.1 1.4 64 29 45 916. 3.9 1.4 100 45 45 1220 3.7 1.5 132 68 75 612 6.4. 2.5 60 * 40 75 916 5.8 2.6 90 62 75 1220 5.2 2.8 112 84 120 612 8.0 3.3 72 80 120 916 7.5 3.0 112 106 120 1220 7.6 4.5 146 124 160 672 8.5 1.8 | 108 90 16C 916 8.9 1.7 192 120 160 1220 8.6 1.7 248 148 23 It is obvious that the energy resolution at backward pion angles is very poor and that the recoil counter is of little help. On the other hand, the angular resolution is greatly improved by the use of the recoil counter. E, The Glauber effect. The Glauber effect is the reduction of cross section | per nucleon in a compound nucleus fron the free nucleon cross section due to the "shadowing" effects on a given nucleon by all the rest. In deuterium, the 1 photoproduction cross section off the target neutron should be slightly reduced compared with the free neutron cross section because for a certain fraction of the time, the proton intersects the line of sight between the incoming photon and target neutron. The rough effect, as derived by Glauber (47), can be expressed as a relationship between the total cross section from deuterium and the total yN cross section from the free neutron and proton: | 0, = oF + o,7 G.C. (II.1) “24 Where G.C., the Glauber correction, is given by: o oO, 1 G.C. = a roa 2 ; . (II. 2) where r is the average separation of the nucleons in the deuteron. If we take r= 1.7 fermi, and o, =O, 100 ub, then this correction is equal to 0.028 ub or - 0.028% , which is negligible, However, it has been shown (48) that the photon can materialize as a 0° which interacts strongly in nuclear matter. A rough estimate of the pN cross section is oon = 25 mb. If we replace ° and o, in equation II.2 with this value, the the correction becomes 6.9%, which is significant. An indication of the fraction of time that the photon spends as a 0° while traversing the deuteron may be obtained by application of the uncertainty principle. Consider the materialization of a 1 GeV photon into a e° with the same momentum. The energy of the 0° is then given by: Ey =.v¥ (1)* + (.765)% = 1.26 GeV where ./65 is the rest mass of the 0°. The extra energy needed is AE = 260 MeV. Applying the inequality AEAt > ¥/2, an 24 we obtain At = 1.26 x10” sec., which, even at the speed of light, corresponds to only 0.4 fermi. The mean free 25 path of the 0° in nuclear matter is about 3 fermis, and thus the photon has relatively little time to interact as a 0° for photon energies % 1 GeV. Thus we conclude that the Glauber effect is negligible ( vy 1% or less.) for our experiment. F, Final state interactions. There remains the possibility that in the reaction yd > T PLP, ‘the outgoing pion or the recoil proton PL interacts with the spectator proton Ps: The only-easily separated component of these final state interactions is the effect of the Pauli exclusion principle on the allowable final states of the two-proton system. A calculation of the effect of the Pauli principle on the deuterium photoproduction cross section has been made by Chew and Lewis (45). The deuterium cross section is given in terms of the "spin-flip" and "“spin-non-flip" cross sections off free nucleons and the deuteron form factor assuming the Hulthen wave function for the deuteron (see Appendix V). The calculation of other final state effects (eg. oN scattering) is very difficult. Because of this, and because 26 our experimental results seem to indicate that most of the final state effects seem to be accounted for by the Pauli principle, we have chosen to neglect these other interactions. 27 PART III. CALCULATION OF THE yn > Tp DIFFERENTIAL CROSS SECTION A. Methods. In order to try to overcome deuterium problems and for comparison purposes, the cross section for yn > a) was calculated in three ways. These were: 1) Ratio method. The spectrometer rates of a from the reaction yd > 7 pp + + | and of t from the reaction yd > 7 nn were measured and used to calculate the cross section for the reaction yn > 7 p according to the formula: o(yn > 5) =: n Rate(yd > 7 nn) where the proton cross sections were taken from the fit made by Ecklund (6) of the nt eross sections from hydrogen measured by Ecklund (6) .and Thiessen(7). This method assumes that the deuterium corrections cancel in the ratio, thus making the ratio equal to that of the free nucleon cross sections. To the extent that deuterium effects, especially final state effects, do not cancel in the ratio, the yn cross sections calculated by this method will be inaccurate. 28 Final state effects, especially that due to the Pauli exclusion principle, are most prominent at small forward pion angles (corresponding to small recoil nucleon momentum) and thus this ratio calculation probably has a moderate systematic error at our small angle settings 6, 10, 20, and 30 degrees CM. An attempt to calculate this correction by using "spin-flip" and "spin-non-flip" cross sections is made ja Part V. Despite the above problems, the ratio method is the simplest way to determine the 7 cross section off neutrons. Until exact corrections can be worked out in detail, this method provides the best estimate of this cross section, especially at small pion angles. One disadvantage of the ratio method as we used it. is that the energy resolution and angular resolution were poor because the recoil counter rates were not used, 2) Recoil (and reverse recoil) cross sections. The recoil counter was used to detect the recoil proton when the pion went through the spectrometer; and at backward pion angles the recoil counter was used to detect the pion when the proton went through the spectrometer (reverse recoil runs), 29 £4. direct calculation of the yn cross section.was made, using the spectator model, Hulthen wave function,.and recoil counter rates. Since both outgoing particles were detected, this method gives improved energy and angular resolution, besides reducing background rates. The calculation of the spectrometer and recoil counter acceptances, and the average CM pion angle and "lab". photon — energy at each setting was done by means of a Monte: Carlo program written by Patrick Walden. The program randomly chooses the following variables for each experimental setup: the pion (or proton for reverse recoil runs) lab momentum across the acceptance of one momentum channel of the spec~ ‘trometer, the position of the reaction in the target, the “spectator nucleon initial momentum weighted by the Hulthen wave function. The program then calculates the photon energy and weights the total event by the bremsstrahlung spectrum at ‘that photon energy. The program then checks whether or not the recoil proton (or pion for reverse recoil run) went: through the recoil counter. By calculating many such events, the program obtains ‘average values of the photon energy, CM pion angle, and spectrometer and recoil counter acceptances for the given experimental setup. Knowledge of the particle rates and system acceptance gives the cross section average 30 over the acceptance, The program makes corrections for momentum loss of the spectrometer particle as it travels from the target, through air and various counter materials, to the last counter in the system. Corrections are also made for energy loss of the recoil proton in escaping through: the aluminum wall of the target assembly and in traversing the material in the recoil _vunter system. The effects of pion decay Cm > w + v) were ‘investigated by a special Monte Carlo program which was run for a selected number of experimental settings. The results of this program were combined with corrections for nuclear | absorption in the spectrometer to produce a final acceptance. This final acceptance was multiplied by the rates to obtain the final recoil cross section. Details on the above corrections and about the.geometrical acceptance calculations may be found in the Ph.D. thesis by.Patrick Walden. Unfortunately, the calculation using the recoil counter Yates could not be done at forward pion angles, because the recoil proton does not have enough energy to escape through the mylar and aluminum walls of the target assembly. Thus, the . : ) "recoil" cross sections were calculated only at angles 2 45° CM. 31 3) Direct cross sections - pion only. The third method is a direct calculation of the 1 cross section using only the spectrometer (pion) rates. The calculation proceeds exactly as in 2) except that the recoil counter is ignored. The corrected system acceptance is multiplied by the particle rates to obtain the final "pion only" cross sections. This method has all the disadvantages of the other two. The. energy and angular resolutions are poor. The Hulthen wave function was used at high values for the internal nucleon momentum, an area where it is known to be inaccurate. Finally, background rates were significant, especially at backward pion angles. Also, while this method could be used to calculate eross sections at pion CM angles < 45°, the results are very likely not equal to the true yn cross section, because of the predominance of final state effects in this region. It should be noted that the average lab photon energies and CM pion angles calculated by the Monte Carlo program for each experimental setting by this method are the same angles and energies which have been assigned to the ratio cross sections (Method 1). 32 B. Elimination of competing reactions. Since photodisintegration of deuterium (yd > pn) is eliminated by either requiring a pion in the spectrometer or by requiring two outgoing charged particles, the main competing reactions are multiple pion photoproduction, especially the following: 1) yd > nt nn / 2) yd > prin 3) yd > pr mp Reactions 1 and 2 may contaminate x photoproduction (from deuterium) and reactions 2 and 3 may contaminate 1 photopro- duction, These reactions were limited by reducing the synchrotron - endpoint below the threshold photon energy required for producing the second pion. This completely eliminated 27 contamination, except perhaps in the lowest of the four momentum channels of the spectrometer. A schematic diagram showing the situation is given in Figure 8. For single pion photoproduction, the four momentum channels of the spectrometer are reflected into resolution curves in the photon energy. Each curve gives the probability that a photon of given energy will produce a single pion in the given momentum channel. The channel of lowest momentum 18 mie > ¢. 63 wel 33 oF eA oS © reat) ey wal C3 t~ o wns a _— = — C va STANNVHO u-—z STHNNVHO 4 HTONIS ADWHNG INTOdONS i H i ! i } hI SAASNS Ne fino Sad SHENG NOLBHd ONG CNX D Wn 13dS ONT THEY LSSWAYE 8 FIGURE 34 “is reflected into the energy resolution curve of lowest energy. A similar set of four energy resolution curves can be.generated for double pion photoproduction. These are shown in the figures ' For our spectrometer, the highest energy resolution. curve for single pion photoproduction is separated from the lowest energy curve for double pion photoproduction by a small gap. Thus if the synchrotron endpoint is set in the gap, only single pions can be produced, However because of the poor resolution due to deuterium smearing, and the fact that the bremsstrahlung endpoint is not sharp, the tail of the bremsstrahlung spectrum and the lower side of the resolution curve for the lowest momentum channel for double pion photo- production overlap as shown. Thus our lowest momentum channel may have significant 27 contamination, This problem, however, becomes insignificant in cases where the resolution is improved by addition of the recoil counter. Also we hope that most of the 21 contamination for our bottom channel will cancel out in the ratio method described above. For a detailed calculation of the 2n effects for this experiment, refer to the Ph.D. thesis by Patrick Walden. 35 PART IV RESULTS -) + ‘ + : — The 7 /t ratio, ™ cross sections from deuterium, m cross sections from deuterium via the ratio method, via the direct method with pion only detected, and via’the direct. method with both pion and recoil proton detected are given in Tables 2, 3, and 4 and in Figures 9 and 10. A. The a fn ratio, (Table 2, Figure 9) The ratio curves show very well the general effect that has been observed in this experiment: the 1 cross section is relatively low compared to the nt cross section in the _third resonance region at about 1000 MeV photon energy (total CM energy = 1650 MeV). These ratio curves have not been corrected for resolution effects, so that the dip should actually be a little deeper, especially at 45 and 60° CM, where the nt cross section shows a pronounced peak at the above energy. The ratio curves are fairly smooth, indicating a good consistancy from setting to setting in the experiment. There are a few anomalously high points at 135° -caused by the tm results. These are as yet unexplained. 36 At the angles 20°, 60°, 90°, 120°, 150°, and 160° are: plotted the ratio data of Neugebauer (36) (dark points). The agreement is excellent, a result which is not too surprising since the two experiments were performed with almost the same experimental apparatus (nine years apart).at the Caltech synchrotron, B The ratio cross sections. (Table 3, Figure 10) The ratio cross sections have been plotted twice, for comparison with the "recoil" cross sections and the "pion only" cross sections, At small angles, where the ratio cross sections and direct. cross sections differ due to final state effects, a few points (half-blacked in) have been artificially generated by interpolation where the nt rates were not available to form the ratio. (These points are identified by a * in Table 3.) This was done because we believe the ratio results to be the best indication of the yn > 7 p cross section at these small angles. The direct cross sections, calculated via the spectator model from the deuterium 1 rates, are expected to be smaller than the yn cross sections due to the above-mentioned final state effects (45). This seems to be born out on our experiment. The difference between our ratio cross sections 37 and ovr direct cross sections approaches zero at about 45° CM, a result which is consistant with some preliminary calcu- lations of "spin-flip" and "spin-non-£1ip" cross sections and the deuterium model used by Chew and Lewis (45), See Part V. | In the ratio cross sections, a simple correction for resolution effects was made at 45° and 60° CM at photon energies around 1000 MeV. (These points are half-blacked in in Figure 10.) Here the (direct) 1 cross section is flat with energy while the 1 cross section has a pronounced hump. Use of the | uncorrected ratio to’ multiply the Ecklund cross sections would have given a hump to the m (ratio) cross section, a result which would be inconsistent with the direct 7 rates. The effect of the correction was, essentially, to set the 1 ratio cross section equal to the direct (pion only) cross section at these few points. A complete unfolding of the cross sections was not done. C. Direct nt cross sections from deuterium. (Table 3, Figure 9) The ne cross sections from deuterium (calculated by method 3 in Section III.A) have been plotted for comparison with the 38 fits made by Ecklund (6) ,.of the ue eross sections from hydrogen measured by Ecklund (6) and: Thiessen(7), The deuterium cross sections are lower in the forward direction, a result which is consistent with the expected drop due to final state effects (45). However, in the backward direction, the deuterium ne results appear anomalously high. This apparent jump in the cross section at 90° seems to be correlated with our switching from the high momentum spectrometer (HEMA) to the low momentum spectrometer (LEM). After much thought and calculation (especially by Pat Walden), we think that this might be due to an electron-positron background at large angles, which we previously thought to be negligible. Since the LEM was not equipped to distinguish pions from electrons (as HEMA was), this background will show up in our direct cross section calculations. Thiessen(50) ‘seemed to observe a similar effect in his 1 experiment (hydrogen target) at wide angles where he used the same spectrometer. He made a small number of measurements of the effect and has made a fit .of the results, Using this fit and normalizing it to the electron rates observed at 75° with the HEMA, Pat Walden has calculated that this effect could completely account for our high results 39 at backward angles. The ratio cross sections are relatively insensitive to this effect since the direct (pion only) 1 cross. sections have a similar high behavior at backward angles. However, since electrons are not expected to completely cancel in the ratio, a small systematic error in the backward ratio eross sections is indicated. The recoil cross sections are believed to be unaffected by the electron problem because a coincidence of two particles is required. D. Direct 1 cross section (pion only detected) from deuterium. (Table 3, Figure 10) The direct 7 cross section calculated via the spectator model from the spectrometer pion rates only is plotted with the ratio cross sections for comparison. The direct cross sections are lower than the ratio cross sections at pion angles less than 45° CM, a result which is again consistent with the Chew and Lewis treatment of final state effects. This gives us hope that the ratio cross section might be a good approxi- mation to the real yn cross section, As in the at case, the direct 1 cross sections (pion only detected) seem to jump at 90°, As I have said above, 40 we believe that this is due to an unsubtracted electron background, E. Direct 7 cross section (both pion and recoil proton detected) from deuterium. (Cable 4, Figure 10) These "recoil" cross sections are plotted with the ratio cross sections for comparison. In general, the two cross sections agree well with each other, There are, however, some specific areas of disagreement. At angles less than 75° at the smallest energies, the recoil results are off, This is due to the problems encountered when trying to correct for protons which do not escape from the target. ‘The details of this correction and the various difficulties involved are discussed by Patrick Walden{44) . At 105° the recoil results deviate wildly from the ratio cross sections at low energies. We have not been able to explain this behavior and I am inclined to blame the problem on the recoil electronics which may have been acting up that day. At 150 and 160°, there are some spots at intermediate energies where the recoil and ratio results disagree. This is a region of poor statistics and large accidentals and perhaps one of these is the cause of the discrepancy. 41 F, Accidentals and dead time at backward pion angles. Because of a mistake in the setup of the HEMA and LEM. electronics, we were not able to distinguish between some accidentals and dead time corrections. This problem was not severe at angles less than 120° as the maximum possible correction was of the order of one percent or less. However, at larger angles and especially at 150 and 160°, the possible corrections grew to as much as 20%, Since we were unsure ‘whether we should add a correction (for dead time) or subtract a correction (for accidentals), we simply increased the error bars in proportion to the possible correction. Thus , at backward angles, the errors listed are not completely statistical but may contain a systematic component due to our uncertainty about this problem. In any case, all runs with an "accidentals" rate of more than about 4% have been thrown out and are not included in the graphs or tables. G. Backgrounds. (Figures 9 and 10) Empty target backgrounds were measured for about two thirds of the 1 settings and for a small number of the . settings. For the 1. settings for which no backgrounds were taken, an interpolated background was used to calculate the 42 the subtracted 1 direct cross sections. (These interpolated points are indicated by vertical bars in Figure 10) “The measured and interpolated backgrounds are plotted along with the direct (subtracted) 1 cross sections to show their general level. The few measured at backgrounds are plotted along with the deuterium x cross sections in Figure 9, An artificial subtraction has been performed on the deuterium nt cross sections using the 1 backgrounds divided ‘by the a fat ratio. This is equivalent to assuming that the at backgrounds were the same percentage of the foregrounds as the 7 backgrounds were of theiz foregrounds. Comparison of the measured 1. backgrounds to the artificially generated ones gives rough agreement, The x fat ratio was calculated from the foregrounds only, which is equivalent to using the above assumption on the back- grounds, The question of whether we should have taken more ne backgrounds is still a moot point; time was a factor, and to reserve more time for ne backgrounds would have cut time from taking foreground data. The effect on the ratio of using the foregrounds only is very small except perhaps at f backward angles, where the background percentages are highest. Finally, the backgrounds for the recoil runs were very small and we have neglected them in the calculation of the final recoil cross sections. 43 TABLE 2 n/t RATIO See Appendix I for explanation of "lab" photon energy. Lab CM Photon Pion _ 4 Energy Angle a /r Stat. (MeV) (deg.) Ratio Error 583.9 6.22 1.169 0,068 601.1 6.23 1.207 0.070 614.1 6.27 1.162 0.069 630.8 6.35 1.231 0.068 641.0 6.21 1.277 0.077 659.1 6.22 1.093 0.068 674.2 6.30 1.164 0.130 695.5 6.29 1.290 0.083 713.4 6.20 1.039 0.059 “730.2 6.25 0.987 0.059 748.0 6.30 0.908 0.056 764.5 6.38 .1.001 0.063 © 874.5 6.28 0.575 0.056 898.8 6.31 0.603 0.060 922.2 6.35 0.553 0.058 947.2 6.43 0.693 0.071 585.4 10.12 1.305 0.108 601.1 10.18 1.200 0.080 616.8 10.23 1.236 0.083 631.6 10.34 1.128 0.073 642.0 10.09 1.080 0.074 659 .6 10.13 1.277 0.090 675.8 10.18 1.100 0.076 694.8 10.29 1.170 0.081 711.4 10.00 1.255 0.089 727.6 10.10 1.169 0.105 747.8 10.18 0.973 0.076 770.8 10.22 1.000 0.075 790.1 10.18 0.715 0.044 808.3 (10.24 0.751 0.046 831.3 10.28 0.662 0.042 850.1 10.42 0.618 0.040 875.3 10.19 0.656 0.046 896.4 10.22 0.602 0.045 923.9 10.29 0.542 0.042 947.4 10.35 0.470 0.039 1073.3 10.07 0.648 0.042 1096.3 10.20 0.763 0.118 1121.7 10.29 0.802 0.058 1156.4 10.36 0.745 0.075 44 Lab CM Photon Pion _ Energy Angle a /t Stat. (MeV) (deg.) Ratio Error 1170.3 10.24 0.738 0.099 1198.2 10.30 0.644 0.090 1216.7 10.46 0.780 0.107 1243.9 10.56 0.786 0.112 583.8 20.20 1,099 0.061 598.7 20.32 1.175 0.065 617.0 20.38 1.246 0.069 632.1 20.57 1.186 0.063 642.5 20.15 1.112 0.062 659.6 20.29 1.214 0.067 677.8 20.41 1.113 0.061 695.3 20.61 1.207 0.068 7411.5 20.09 1.160 0.051 731.3 20.21 1.104 0.050 750.8 20.37..1.016 0.048 768.0 20.53 0.916 0.045 786.7 20.24 0.769 0.076 808.8 20.40 0.745 0.047 829.9 20.53 0.713 0.045 850.8 20.72 0.646 0.042 869.5 20.18 0.634 0.033 896.1 20.23 0.593 0.031 919.7 20.44 0.586 0.030 946.4 20.62 0.600 0.032 967.5 20.28 0.590 0.027 994.2 20.37 0.582 0.026 1026.1 20.45 0.586 0.032 1054.1 20.62 0.625 0,030 1069.8 20.24 0.658 0.037 1096.2 .20.41 0.740 0.044 -1124.9 20.64 0.708 0.042 1158.8 20.75 0.797 0.048 1166.1 20.24 0.838 0.089 1192.1 20.40 0.901 0.102 1220.6. 20.56 0.901 0.100 1249.8 20.70 0.894 0.111 585.3 30.17 1,122 0.070 599.4 30.34 1.081 0.065 616.5 30.49 1.108 0.065 632.8 30.76 1.098 0.065 Lab CM Photon Pion 4 Energy Angle 1/1 Stat. (MeV) (deg.) Ratio Error 644.6 30.05 1.085 0.051 658.1 30.34 1.030 0.076 676.5 30.52 1.067 0.050 693.1 30.84 1.040 0.048 710.8 - 30.13 0.965 0.043 728.4 30.37 0.901 0.040 752.0 30.45 0.969 0.045 771.2 30.79 0.844 0.041 785.7 30.16 0.688 0.053 810.9 30.20 0.810 0.063 830.6 30.53 0.662 0.053 856.3 30.72 0.642 0.051 874.1 30.03 0.682 0.026 899.2 30.19 0.646 0.031 923.9 30.44 0.647 0.023 949.9 30.71 0.590 0.022 968.9 30.03 0.608 0.035 998.1 30.18 0.600 0.027 1025.0 30.41 0.577 0.026 1056.7 30.62 0.688 0.032 1164.2 29.99 0.880 0.053 1195.2 30.15 0.916 0.058 1230.5 30.40 0.876 0.058 1264.6 30.68 0.920 0.063 585.0 45.07 0.959 0.078 602.5 45.13 0.964 0.076 617.7 45.57 0.887 0.070 633.3 45.99 0.929 0.069 640.8 45.15 0.832 0.046 659.6 45.34 0.841 0.047 677.5 45.66 0.843 0.046 696.8 45.98 0.797 0.044 712.5 44.96 0.813 0.040 729.4 45.30 0.803 0.040 750.8 45.54 0.756 0.050 773.3 45.87 0.664 0.035 786.2 44.83 0.703 0.031 807.4 45.20 0.712 0.052 833.1 45.44 0.695 0.040 854.8 45.90 0.629 0.030 45 Lab _ CM Photon Pion oo Energy Angle « /t tat. (MeV) (deg.) Ratio Error 875.0 44.92 0.623 0.040 898.0 45.19 0.566. 0.036 922.0 45.63 0.542 0.035 949.8 45.99 0.527 0.078 971.5 44.78 0.545 0.026 996.8 45.24 0.565 0.029 1027.4 45.57 0.552 0.027 1058.4 45.84 0.568 0.029 1062.3 44.88 0.636 0.030 1098.5 45.02 0.647 0.034 1128.3 45.48 0.768 0.041 1161.6 45.79 0.790 0.045 1161.8 44.77 0.900 0.113 1194.2 45.22 0.933 0.060 1233.7 45.49 0.932 0.064 1270.1 45.83 0.834 0.060 585.5 59.89 0.893 0.058 599.2 60.38 0.920 0.060 619.3 60.54 0.896 0.056 636.2 60.97 0.841 0,052 640.1 59.87 0.832 0.032 659.6 60.14 0.755 0.027 679.2 60.48 0.748 0.033 701.2 60.86 0.714 0.024 707.6 59.89 0.743 0.034 730.6 60.14 0.707 0.057 751.1 60.59 0.691 0.035 776.0 60.99 0.735 0.042 786.1 59.70 0.703 0.044 808.8 60.11 0.618 0.031. 835.3 60.52 0.664 0.034 858.6 61.04 0.554 0.031 872.7 59.74 0.587 0.047 898.9 60.22 0.603 0.048 925.2 60.57 0.520 0.041 957.7 60.96 0.427 0.035 967.3 59.60 0.437 0.030 998.7 60.03 0.472 0.027 1028.8 60.49 0.442 0.026 1064.5 60.82 0.509 0,034 1274.8 0.890 Lab CM Photon Pion _- i" Energy Angle w/t Stat. (MeV) (deg.) Ratio Error 1063.14 59.69 0.481 06.031 1102.7 59.90 0.620 0.043 1131.9 60.47 0.629 0.091 1168.7 60.91 0.820 0.074 1160.3 59.43 0.712 0.058 1196.2 59.89 0.828 0.076 1232.8 60.53 0.837 0.082 1276.9 60.75 0.921 0.104 581.8 74.78 0.852 0.034 599.0 75.32 0,825 0.030 617.4 75.52 0.818 0.050 638.3 75.85 0.790 0.031 639.6 74.67 0.834 0.063 659.1 75.15 0.699 0.071 680.0 75.51 0.818 0.051 699.7 75.97 0.809 0.043 706.1 74.47 0.758 0.043 731.5 74.96 0,802 0.047 752.1 75.59 0,704 0.045 774.4 76.03 0.604 0.044 783.5 74.59 0.660 0.060 809.1 75.03 0.564 0.057 834.9 75.43 0.628 0.070 865,4 75.82 0.577 0.073 866.6 74.56 0.448 0.034 897.8 74.96 0.554 0.044 925.0 75.44 0.391 0.047 959.7 75.84 0.350 0.045 964.9 74.67 0.345 0.028 996.6 74.98 0.399 0.034 1030.7 75.41 0.363 0.035 1064.0 75.95 0.418 0.041 1059.4 74.42 0.379 0.036 1094.1 74.77 0.498 0.049 1132.1 75.44 0.647 0.073 -1169.4 75.76 0.647 0.138 1156.3 74.24 0,656 0.104 1198.2 74.83 0.701. 0.118 1233.7 75.41 0.815 0.151 75.80 0.181 46 Lab CM Photon Pion og Energy Angle a /m Stat. (MeV) (deg.). Ratio Error 579.8 89,70 0.916 . 0.057 598.5 90.06 1.014 0.058 619.2 90.43 0.973 0.060 637.9 90.86 0.919 0.077 636.0 89.54 0.700 0.040 657.6 89.85 0.755 0.043 679.0 90.49 0.773 0.041 700.8 90.78 0.754 0.041 702.6 89.32 0.750 0.025 725.3 89.89 0.757 0.035 750.2 90.33 0.736 0.048 776.1 90.72. 0.702 0.029 780.3 89.16 0.719 0.034 803.3 89.92 0.679 0.035 833.1 90.26 0.591 0.036 860.9 90.71 0.557 0.039 577.3 104.4 1.041 0.068 598.7 104.6 1.096 0.120 617.3 105.2 1.058 0.067 637.0 105.6 1.034 0.064 633.4 104.1 1.056 0.073 655.8 104.8 1.024 0.088 676.9 105.1 0.834 0.092 698.3. 105.7 0.965 0.065 769.6 104.1 0.725 0.039 799.5 104.7 0.738 0.043 829.2 105.1 0.594 0.046 857.9 105.5 0.604 0.085 854.6 103.8 0.591 0.045 886.6 104.6 0.544 0.045— 920.1 105.0 0.553 0.048 949.9 104.9 0.553 0.051 949.5 103.8 0.563 0.069 982.5 104.3 0.590 06.043 1014.8 104.8 0.504 0.040 105i.1 105.3 0.628 0.069 1035.6 108.6 0.672 0.038 1075.1. 109.1. 0.637 0.041 1115.8 109.6 0.659 0.047 1154.3 109.8 0.577 0.043 Lab CM Photon Pion _ Energy Angle am /m Stat. (MeV) (deg.) Ratio Error 574.1 119.0 1.421 0.088 592.5 119.6 1.449 0.085 617.4 119.9 1.215 0.068 638.6 120.5 1.470 0.081 628.0 118.9 1.445 0,091 652.8 119.5 1.537 0.094 673.2 119.9 1.231 0.075 698.1 120.4 1.121 0.069 692.5 118.9 1.109 0.065 716.6 119.5 0.966 0.059 744.0 119.6 1.000 0.063 769.6 120.0 0.873 0.065 . 762.1 119.0 0.897 0.059 794.0 119.2 0.817 0.057 824.5 119.7 0.702 0.055 850.3 120.2 0.665 0.060 846.0 118.9 0,633 0.058 878.8 119.0 0.642 0.059 909.6 119.7 0.604 0.057 944.6 120.0 0.562 0.058 943.8 118.8 0.576 0.054 984.4 119.5 0.522 0.054 1023.7. 120.0 0.520 0.053 1074.9 120.6 0.572 0.064 1020.2 118.3 0.550 0.034 1071.0 118.7 (0.533 0.036 1105.1 119.3 0.711 0,080 1147.0 119.7 0.558 0.059 1109.4 118.0 0.643 0.054 1159.3 118.7 0.720 0.059 1205.4 119.0 0.696 0.071 1247.3 119.7 0.716 0.110 570.7 134.2 2.195 0.164 587.3 134.1 1.895 0.135 611.6 134.6 . 1.849 0.132 633.7. 135.0 2.009 0.154 622.0 133.8 2.000 0.151 647.1 134.4 1.843 0.135 668.4 134.5 1.650 0.118° 694.1 134.8 1.815 0.141 47 Lab CM Photon Pion . Energy Angle a /7 Stat. (MeV) (dee. Ratio Error 681.3 133.7 1.462 0.102 710.3 134.2 1.285 0.089 737.7 134.7 1.155 0.085 767.3 134.6 1.436 0.118 750.4 133.6 1.526 0.113 787.3 133.9 1.078 0.086 814.9 134.7 1.009 0.088 847.2 134.6 0.906 0.086 831.2 133.5 1.064 0.089 865.3 133.9 0.994 0.085 901.8 134.2 1.045 0.099 926.0 134.8 0.774 0.084 926.8 133.6 0.763 0.072 974.8 134.3 0.777 0.077 1017.6 134.5 0.695 0.073 1063.1 135.0 0.659 0,079 1012.1 133.6 0.599 . 0.072 1058.8 133.7 0.581 0.074 1114.5 134.3 0.568 0.080 1166.4 134.8 0.772 0.117 563.6 149.0 2.098 0.169 584.3 149.1 2.344 0.194 611.5 149.2 2.289 0.185 629.4 149.5 2.762 0.243 617.7 148.8 2.230 0.180 640.9 148.9 2.451 0.202 666.8 149.3 °2.497 0.210 690.5 149.3 2.376 0.207 679.9 148.6 1.861 0.170 706.6 149.2 1.956 0.176 733.8 149.1. 2.126 0.216 755.4 149.3 1.696 0.178 815.0 148.1 1.663 0.158 852.4 148.6 1.273 0.128 898.2 148.8 1.277. 0.135 924.7 149.3 1.266 0.147 912.3 148.4 1.412 0.152 953.4 148.6 1.087 0.117 1006.6 149.2 1.199 0.133 1057.8 149.7 0.912 0.117 Lab CM Photon Pion Energy Angle a /m Stat. (MeV) (dee.) Ratio Error 993.6 148.3 1.107 0.134 1053.9 149.2 0.944 0.115 1104.0 149.5 0.981 0.130 1162.2 149.7 1,171 0.176 1062.9 147.9 0.984 0.123 1114.9 148.4 (0.970 0.137 1155.6 148.5 0.948 0.156 1211.9 148.8 0.633 0.122 610.4 158.5 2.495 0,223 636.6 158.6 2.719 0.234 660.4 158.8 3.240 0.300 688.0 158.9 3.095 0.284 673.4 158.6 2.581 0.266 698.4 158.8 .2.838 0.307 725.8 158.8 2.163 0,227 755.1 159.0 2.167 0.240 821.3 158.5 2.110 0.211 862.4 158.8 1.794 0.182 906.2 159.0 1,657 0.172 945.7 159.3 1.699 0.190 (898.5 158.3 1.923 0.210 949.3 158.7 1.582 0.164 1005.2 159.0 1.740 0.219 1046.4 159.1 1.701 0,228 992.4 158.7 1.482 0.172 1024.7: 158.6 1.562 0.149 1081.5 159.1 1.428 0.160 1137.0 159.0 1.752 0.183 1044.2 158.3 1.474 0.211 1104.4 158.4 1.329 0.206 1146.7 158.4 1.342 0.217 1178.1 158.2. 1.007 0.188 48 49 TABLE 3 + : : . 1) «w Qirect) Cross Section from Deuterium ‘(pion only detected) 2) 1 (Direct) Cross Section from Deuterium (pion only detected) 3) w (Ratio) Cross Section (neutron cross section -~) + calculated from 1 /m ratio and free proton eross section) See Appendix I for explanation of "lab" photon energy. * indicates artificial (interpolated) cross section . 50 Lab CM 1. T Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (yb/sr) Error (ub/sve) Error 583.9 6.22 14.78 0.75 17.20 0.73 20.72 1,21 601.1 6.23 14.75 0.74 17.65 0.74 21.44: 1.24 614.1 6.27 14.96 0.79 17.54 0.71 21.13 1.26 630.8 6.35 14.73 0.72 «| 18.21 0.71 22.00 1.22 641.0 6.21 14.92 0.80 19,23 0.91 23.12 1.39 659.1 6.22 15.01 0.80 16.06 0.85 ‘20,26 1.26 674.2 6.30 14.51 1.66 16.94 0,84 21.29 2.38 695.5 6.29 12,09 0.69 15.73 0.80 22.54 1.45 713.4 6.20 14,29 0.74 14,98 0.68 17.83 1,01 730.2 6.25 13.04 0.69 12.75 0.63 15.30 0.91 748.0 6.30 12.14 0.65 10.84 0.58 13.47 0,84 764.5 6.38 11.13 0.62 11.31 0.57 14.59 0.92 790.9 6.25 10.71 0.55 13.15% 0.48 808.7 6.25 10.25 0.49 12.13% 0.44 828.6 6.33 — 8.64 0.45 10.54% 0.41 848, 8 6,39 7.72 0.41 9.41% 0.38 874.5 6.28 10.23 0.85 5.41 0.54 7.76 0.75 898.8 6.31 9.17 0.78 5.64 0.50 7.59 0.76 - 922.2 6.35 8.61 0.74 4.74 0.46 6.78 0.70 947.2 6.43 7.58 0.68 5.63 0.47 7.40 0.76 1070.8 6.14 3.80 0.36 5.03% 0.33 1097.4 6.18 4.16 0.35 5.48% 0,30 1123.7 6.26 3.41 0.52 4.41% 0.51 1155.6 6.34 3.09 0,30 4.34% 0,26 1170.0 6.41 4.13 0.45 4.92% 0,35 1191.5 6.58 4.03 0.43 4.68% 0.35 1213.7 6.69 3.30 0.44 4,30* 0.33 1250.2 6.70 3.06 0.40 3.86* 0.30 585.4 10.12 12.68 0.72 16.57 1.11 20.32 1,68 601.1 10.18 13.72 0.75 16.45 0.78 18.63 1.24 616.8 10.23 12,55 0.70 15.54 0.73 19,42 1,31 631.6 10,34 13.84 0.73 15.57 0.73 17.38 1.12 642.0 10.09 13.46 0.72 14.66 0.77 17.00 1.16 659.6 10.13 11.73 0.67 14.94 0.79 20.27 1.43 675.8 10.18 12.55 0.69 13.58 0.75 17.17 1.19 694.8 10,29 11.76 0.65 13.88 0.72 17.55 1,21 711.4 10.00 10.86 0.65 13.41 0.66 18.57 1.32 727.6 10.10 10.26 0.63 12.06 0.88 15.90 1.43 747.8 (10.18 11.36 0.66 11.16 0.67 12.30 0.96 770.8 10,22 10.21 0.62 10,26 0.55 12.07 0.90 + 51 Lab cM T T Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat, (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 790.1 10.18 10.28 0.47 7.29 0,39 8.55 0.52 808.3 10.24. 9.78 0.46 7.39 0.38 9.01 0.55 831.3 10.28 9.46 0.44 6.22 0.35 7.62 0.49 850.1 10.42 9.16 0.43 5.81 0.32 6.89 0.45 875.3 10.19 8.85 0.44 5.81 0.38 7.29 0.52 896,4 10.22 8.06 0.41 4,83 0.34 6.31 0.47 923.9 10.29 8.05 0.40 4.29 0.32 5.42 0.42 947.4 10.35 7.60 0.39 3.66 0.28 4.17 0.35 970.5 10.17 3.40 0,27 4,278 0.25 994.8 10.25 3.56 0.28 4.43% 0.26 1025.2 10.31 2.86 0.25 3.78% 0,23 1050.8 10.38 3.42 0,28 4.14% 0,28 1073.3 10.07 5.04 0.28 3.35 0.18 3.83 0.25 1096.3 10.20 4.14 0.25 3.18 0.50 4,11 0.63 1121.7 10,29 3.91 0.24 3.09 0.20 3.86 0.28 1156.4 10.36 3.90 0.24 3.04 0.28 3.17 0.32 1170.3 10.24 3.73 0.34." 2.84 0.31 3.22 0.43 1198,2 10,30 3.91 0.36 2.48 0.31 2.62 0.37 1216.7 10.46 3.54 0.34 2.65 0,32 2.99 0.41 1243.9 10.56 3.11 0.31 2.50 0.29 2.77 0.39 583.8 20.20 11.02 0.49 12.17 0.50 13.02 0.73 598.7 20.32 10.64 0.48 12.46 0.51 13.81 0.76 617.0 20.38 9.87 0.45 12,29 0.50 14,32 0.79 632.1 20.57 10.42 0.45: 12.36 0.49 13.71 0.74 642.5 20.15 10.77 0.48 12.05 0.50 13.15 0.73 659.6 20.29 10.14 0.46 12.22 0.51 14.17 0.78 677.8 20.41 10.23 0.46 11.30 0.48 13.03 0.72 695.3 20.61 9.30 0.43 11.33 0.46 13.98 0.78 711.5 20.09 9.38 0.33 10.96 0.39 13.24 0.58 731.3 20.21 8.82 0.32 9.72 0.36 11.62 °° 0.53 750.8 20.37 8.03 0.30. 8.10 0.33 9.86 0.47 768.0 20.53 7.95 0.30 7.27 0.31 8.30 0.41- 786.7 20.24 7.58 0.69. 5.80 0.33 6.87 0.68 808.8 20.40 7.29 0.28 5.47 0.31 6.62 0.41 829.9 20.53 7.25 0.28° 5.21 0.30 5.90 0.37 850.8 20.72 6.99 0.27 4.47 0,28 5.31 0.35 869.5 20.18 7.53 0.27 4.66 0.22 5.34 0.28 896.1 20.23 7.29 0.26 4.40 0.20 4.96 0.26 919.7 20.44 7.35 0.26 4.28 0.20 4.75 0.24 946.4 20.62 6.91 0.25 4,21 0.19 4.76 0.25 52 Lab CM ne 7 Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 967.5 20.28 6.76 0.25 3.90 (0.12 4.73 0.21 994,2 20.37 6.88 0.26 3.98 0.12 4,57. 0.21 1026.1 20.45 6.43 0.24 3.77 0.11 4.40 0.24 1054.1 20.62 5.60 0.22 3.55 0.11 4.25 0.20 1069.8 20.24 5.80 0.22 3.86 0.19 4,32 0.24 1096.2 20.41 4.79 0.20 3.56 0.18 4.42 0.26 1124.9 20.64 4.95 0.20 3.50 0.18 3.72 0.22 1158.8 20.75 4.31 0.19 3.38 0.18 3.69 0.22 - 1166.1 20.24 3.75 0.23 3.14 0,29 3.80 0.40 1192.1 20.40 3.06 0,20 2.74 0.27 4.00 0.45 1220.6 20,56 3.27 0.21 2.94 0.28 3.81 0.42 1249.8 20.70 2.62 0.19 2.36 0.25 3.62 0.45 585.3 30.17 9.25 0.44 10,49 0.46 12.26 0.76 599.4 30,34 9.87 0.45 10.59 0.47 11,71 0.70 616.5 30.49 9.71 0.44 10.70 0.46 11.86 0.70 632.8 30.76 9.56 0.43 10.52 0.45 11.82 0.70 644.6 30.05 9.67 0.35 10.52 0.38 11,95 0.56 658.1 30.34 9.87 0.68 10.01 0.38 11.40 0.85 676.5 30.52 9.24 0.34 9.91 0.36 12.12 0.57 693.1 30.84 9.37. 0.34 9.82 0.35 11.78 0.55 710.8 30.13 10,05 0.34 9.71 0.33 10.80 0.48 728.4 30.37 10.23 0.35 9.17 0.32 9.30 0.41 752.0 30.45 8.52 0.31 8.29 0.30 9.09 0.42 771.2 30.79 8.25 0.30 6.96 0.27 7.32 0.35 785.7 30.16 7.73 0.46 5.28 0.29 5.76 0.44 810.9 30.20 6.98 0.44 5.70 0.30 6.55 0.51 830.6 30.53 6.98 0.43 4.64 0.26 5.02 0.40 856.3 30.72 7.26 0.44 4.63 0.27 4.87 0.38 874.1 30.03 6.72 0.18 4.61 0.15 5.38 0.20 899.2 30.19 6.91 0.19 4,49 0.16 5.32 0.26. 923.9. 30.44 7.09 0.20 4.54 0.15 5.25 0.19 949.9 30.71 7.06 0.18 4.18 0.15 5.00 0.18 968.9 30.03 7.90 0.29 4.72 0.18 5.41 0,31 998.1 30.18 7.64 0.28 4.44 0.16 5.43 0.24 1025.0 30.41 7.62 0.28 4.33 0.12 5.19 0.23 1056,7 30.62 6.57 0.26 4.50 0,13 5.62 0.26 1064.9 30.02 6.49 0.25 1095.8 30.24 6.06 0.24 1126.8 30.44 5.24 0.22 1160.2 30.70 4.67 0.21 + 53 Lab CM T TT Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat, (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 1065.2 320.04 4.57 0.21 5.08% 0.21 1094.0 30.26 4.28 0.21 4.85% 0.20 1128.3 30.42 4.36 0.20 4,81* 0.20 1160.3 30.68 4.47 0.21 4.90% 0.21 1164.2 29.99 © 4.91 0,22 4.31 0.22 4.44 0.27 1195.2 30.15 4.29 0.20 3.76 0.22 4,32 0.27 1230.5 30.40 3.94 0.19 3.54 0.19 3.85 0.26 1264.6 30.68 3.75 0.19 3.54 0.19 3.94 0.27 585.0 45.07 9.65 0.46 9.28 0.65 10.08 0.82 602.5 45.13 9.99 0.46 9.48 0.65 10,21 0.80 617.7 45.57 10.25 0.46 9.15 0.63 9.53 0.75 633.3 45,99 11.08 0.48 10.36 0.66 9.97 0.74 640.8 45.15 10.56 0.42 8.82 0.37 9.07 0.50 659.6 45.34 9.59 0.39 8.00 0.35 9.57 0.54 677.5 45.66 10.10 G.40 8.47 0.36 9.95 0.54 696.8 45.98 9.80 0.39 7.88 0.34 9,29 0.52 712.5 44.96 10.23 0.49 8.40 0.21 9.39 0.47 729 4 45.30 10.05 0.48 8.12 0.20 8,34 0.41 750.8 45.54 9.04 0.44 6.76 0.35 7.16 0.48 773.3 45.87 8.84 0.44 5.80 0.17 5.65 0.30 786.2 44.83 7.65 0.26 5.30 0.18 5.50 0.24 807.4 45.20 6.65 0.46 4.67 0.17 5.04 0.37 833.1 45.44 6.50 0.33 4.43 0.16 4.57 0.26 854.8 45.90 6.58 0.24 3.96 0.30 4,00 0,19 875.0 44.92 6.49 0.30 4.27 0.20 4.17 0.27 898.0 45.19 7.21 0.32 3.87 0.15 4.08 0.26 922.0 45.63 6.88 0.31 3.82 0.15 4.00 0.26 949.8 45.99 7.77 0.34 4.02 0.31 4.12 0.61 971.5 44.75 7.78 0.21 4.32 0.15 4.33 0.23 997.5 45,21 8,03 0.21 4.42 0.18 4.67 0.26 - 1027.1 45.55 7.52 0.20 4.10 0.15 4,29 0.24 1059.1 45.81 6.58 0.19 3.77 0.14 3.73 0.24 1063.3 44.84 6.80 0.42 1097.9 45.02 6.04 0.23 1128.5 45.46 4.72 0,20 1162.1 45.78 4.39 0.24 1062.3 44.88 4.22 0.13 4,38 0.24 1098.5 45.02 3.89 0.15 4,20 0.22 1128.3 45.48 3.62 0.12 4,02 0.21 1161.6 45.79 3.37 0.12 3.36 0.20 54 Lab cM 7 TT Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 1161.8 44.77 4.02 0.21 3.56 0.44 3.91 0.49 1194.2 45.22 3.62 0,20 3.44 0.15— 3.50. 0.23 1233.7 45.49 3.17 0.18 2.89 0.15 3.05 0.21 1270.1 45.83 3.19 0.19 2.7/2 0.14 2.63 0.19 585.5 59.89 9.41 0.53 8.48 0.32 8.50 0.55 599.2 60.38 8.83 0.51 8.03 0.32 8.96 0.59 619.3 60.54 9.32 0.51 8.35 0.32 8.92 0.56 636.2 60.97 9.79 0.52 8.25 0.32 8.63 0.53 640.1 59.87 9.84 0.46 8.14 0.30 8.69 0,33 659.6 60.14 11.06 0.32 8.42 0.41 8.18 0.30 679.2 60.48 10,24 0.46 7.84 0.30 8.42 0.37 701.2 60.86 . 10.45 0.35 7.61 0.29 8.03 0,27 707.6 59.89 10.05 0.59 7.41 0.23 8.35 0.38 730.6 60.14 9.13 0.55 7.02 0.22 7.26 0.58 751.1 60.59 8.44 0.53 6.11 0.24 6.28 0.32 776.0 60.99 6.69 0.47 5,07 0.25 5.57 0.31 786.1 59.70 6.73. 0.22 4.65 0.21 4,83 0.30 808.8 60.11 6.30 0.24 3.86 0.15 3.50 0.18 835.3 60.52 5.42 0,20 3.35 0.14 3,12 0.17 858.6 61.04 5.36 0.20 2.96 0.13 2.56 0.14 872.7 59.74 5.06 0.28 2.92 0.14 2.81 0.23 898.9 60,22 5.01 0.27 3.01 0.13 3.01 0.24 925.2 60.57 5.50 0,29 2,84 0.13 2.75 0.22 957.7 60.96 5.74 0.30 2.44. 0.120 2.45 0.20 967.3 59.60 5.82 0,26 2.63 0.19 998.7 60.03 5.88 0.26 2.82 0.19 1028.8 60.49 5.80 0.26 2.59 0.17 1064.5 60.82 4.83 0.25 2.88 0.19 967.5 59.60 2./0 0.09 999.1 60.02 2.73 0.08 1028.2 60.52 2.76 0.10 1063.0 60.88 2.66 0.12 1063.1 59.69 5.36 0.25 2.55 0.14 2.84 0.18 1102.7 59.90 3.97 0.21 2.47 0.13 2,74 0.19 1131.9 60.47 3.54 0.20 2.23 0.31 2.17 0,32 1168.7 60.91 2.30 0.16 1.90 0.12 2.04 0.18 1160.3 59.43 2.90 0.19 2.07 0.11 2.03 0.17 1196.2 59.89 2.22 0.17 1.84 0.10 1.84 0.17 1232.8 60.53 1.89 0.15 1.58 0.10 1.47 0.14 1276.9 60.75 1,57 0.15 1,44 0,10 1.46 0.16 55 Lab — cM 1. 1. Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ib/sx) Error (yb/sr) Error (uwb/sr) Error 581.8 74.79 8.54 0.26 7.19 0.24 6.71 0.27 598.8 75.32 8.99 0.26 7.41 0.25 6.62 0.24 617.3 75.51 8.99 0.26 7.24 0.61 6.77 0.42 638.3 75.85 9,17 0.59 7.12: 0.73 6.95 0.27 639.5. . 74.64 8.58 0.26 7.20 0.53 7.47 0.56 659.1 75.23 9.73 0.91 7.14 0.19 6.42 0.65 680.0 75.52 9,01 0.22 7.45 0.37 7.98 0.50 699.7 75.97 8.44 0.22 6.95 0.30 7.97 0.42 706.1 74.47 8.66 0.36 7.62 0.44 731.5 74.96 8.24 0.36 7.69 0.45 752.1 75.59 7.26 0.33 5.67 0.36 774.4 76.03 6.26 0.31 4,03 0.29 706.9 74.55 , 6.59 0.24 730.9 74.98 6.26 0.39 753.3 75.51 5.05 0,20 776.4 75.90 3.85 0.18 783.5 74.59 5.72 0.38 3.71 0.18 3.98 0.36 809.1 75.03 5.22 0.37 3.14 0,16 2.54 0.26 834.9 75.43 © 3.96 0.32 2.52 0.15 2.28 0.25 865.4 75.82 3.37 0.30 1.81 0.13 1.77 0.22 866.6 74.56 3.93 0,22 1.75 0.10 1,42 0.11 897.8 74.96 3.32 0.20 1.85 0.11 1.63 0,13 925.0 75.44 3.64 0.21 1,42 0.16 1,21 0,14 959.7 75.84 3.37 0.37 1.18 0.09 1.12 0.14 964.9 74.67 3.84 0.25 1.34 0.06 1.19 0.10 996.6 74.98 3.31 0.23 1.29 0.06 1.46 0.12 1030.7 75.41 3.31 0.23 1.20 0.05 1,28 0.12 1064.0 75.95 2.89 0.24 1.18 0.06 1.26 0.12 1059.4 74.42 3.05 0.20 1,13 0.09 1.27 0.12 1094.1 74.77 - 2.48 0.18 1.24 0.09 1.30 0.13 1132.1 75.44 1.68 0.15 1.08 0.09 1.25 0.14 1169.4 75.76 1.35 0.14 0.89 0.17 0.83 0.18 1156.3 74.24 1.65 0.15 1.01 0.08 1.09 Q.17 1198.2 74.83 1.28 0.13 0.85 0,07 0.85 0.14 1233.7 75.41 1.01° 0.12 0.81 0.07 0.74 0.14 1274.8 75.80 0.90 0.12 0.74 0.08 0.68 0.14 579.8 89.70 7.18 0.32 6.51 0.33 5.74 0.36 598.5 90.06 7.22 0.33 7.34 0.32 6.19 0.36 619.2 90.43 7.30 0.33. 7.10 0.35 6.34 0.39 637.9 90.86 7.62 0.34 7.06 0.54 6.26 0.52 Lab 56 CM T T Ratio Photon Pion Cross Cross Cross Energy Angle. Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 636.0 89.54 7.56 0.32 5.29 0.26 4,87 0.28 657.6 89.85 7.58 0.33 5.74 0.27 5.48 0.31 679.0 90.49 8.48 0.35 6.60 0.29 6.09 0.32 700.8 90.78 8.60 0.37 6.44 0.31 6.07 0.33 702.6 89.32 . 8.37 0.21 6.30 0.18 6.20 0.21 725.4 89.88 8.10 0.21 6,09 0.31 6.31 0.29 750.3 90,32 6.79 0.36 5.01 0.16 5.16 0.34 776.0 90.72 5.92 0.24 4.20 0.16 3.99 0.17 780.3 89.16 6.43 0.24 4.62 0.19 3.96 0.19 803.3 89.92 5.55 0.22 3.80 0.17 2.90 0.15 833.1 90.26 4.39 0.19 2.61 0.14 1.95 0.12 860.9 90.71 3.72 0.18 2.01 0.14 1.40 0.10 577.3 104.3 5.28 0.29 5.55 0.26 5.08 0.33 598.7 104.6 5.49 0.59 6.02 0.28 5.17 0.57 617.3 105.2 5.66 0.31 5.89 0.28 5.30 0,33 637.0 105.6 6.38 0.35 6.63 0.31 5.36 0.33 633.4 104.1 6.02 0.32 6.38 0.34 5.58 0.38 655.8 104.8 6.41 0.49 ' 6,60 0.35 5.77 0.50 676.9 105.1 6.87 0.71 5.74 0.33 5.12 0.56 698.3 105.7 6.93 0.36 6.64 0.37 6.14 0.41 698.0 104.4 6.52 0.26 723.7 104.8 7.03 0.27 749.1 105.2 6.18 0.26 775.5 105.4 5.10 0.25 696.6 104.0 5.75 0.23 720.5 104.6 5.56 0,23 750.7 105.0 4.09 0.20 775.2 105.5 3.99 0.20 769.6 104.1 5.80 0.24 4.30 0.18 3.84 0,21 799.5 104.7 4.93 0.22 3.59 0.15 3,18 0.18 829.2 105.1 4.27 0.21 2.72 0.22 2.05 0.16 857.9 105.5 3.54 0.20 2.15 0.19 1.64 0.23 854.6 103.8 3.52 0.19 2.06 0.10 1.63 0.12 886.6 104.6 3.21 0.18 1.82 0.10 1.35 0.11 920.1 105.0 3.02 0.18 1.69 0.10 1.36 0.12 949.9 104.9 3.03 0.20 1.48 0.14 1.38 0.13 949.5 103.8 2.99 0.16 1.75 0.20 1.38 0.17 982.5 104.3 3.16 0.17 1.93 0.11 1.43. 0.10 1014.8 104.8 3.10 0.18 1.53 0.11 1,415 0.10 1051.1 105.3 2.43 0.17 1.42 0.16 1.15 0.13 57 Lab CM ne 1 Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (ub/sr) Error (ub/sr) Error 1035.6 108.6 2.26 0.14 1.62 0.10 1.50 0.08 1075.41 109.1 2.04 0.14 1.27 0.11 1.01 0,06 1115.8 109.6 1.71: O.11 0 1.14 0.10 0.62 0.04 1154.3 109.8 1.60 0.12 0.84 0.12 0.35 0.03 574.1 119.0 4.32 0,22 6.14 0.29 5.09 0.32 592.5 119.6 4.37 0.21 6.34 0,29 5.49 0,32 617.4 119.9 4.75 0.21 5.75 0,29 4.75 0.27 638.6 120.5 4.69 0,22 6.92 0.33 6.03 0,33 628.0 118.9 4.43 0.23 6.40 0.30 5.86 0.37 652.8 119.5 4.65 0.24 7.17 0.32 6.86 0.42 673.2 119.9 5.23 0.26 6.43 0.31 5.84 0.36 698.1 120.3 5.88 0.31 6.59 0.34 5.84 0.36 692.5 118.9 5.48 0,26 6.11 0.28 5.76 0.34 ‘716.6 119.5 5.43 0.26 5.25 0.26 5.41 0.33 744.0 119.6 5.25 6.27 5,25 0.28 5.08 0.32 769.6 120.0 4.31 0.25 3,72 0,24 3.91 0.29 762.1 119.0 4,58 0,24 4.15 0.23 4.22 0.28 794.0 119,2 4.63 0.25 3.81 0.23 3.30 0,23 824.5 119.7 4.08 0,24 2.85 0.20 2.31 0.18 850.3 120.2 3.61 0.24 2.36 0.20 1.98 0.18 846.0 118.9 3.73 0.23 2.36 0.19 1.92 0.18 878.8 119.0 4.00 0.25 2.57 0,21 1.83 0.17 909.6 119.7 3.97 0.26 2.40 0.20 1.77 0.17 944.6 120.0 4.05 0.29 2.27 0,22 1.68 0.17 943.8 118.8 3.12 0.23 1.86 0.17 1.71 0.16 984.4 119.5 2.73 0.21 1.51 0.14 1.67 0.17 1023.7 120.0 2.84 0.22 1.44 0.16 1,53 0.16 1074.9 120.6 2.32 0.20 1,21 0.17 1,42 0.13 1020.2 118.3 2.58 0.16 1.50 0.09 1.60 0.10 1071.0 118.7 2.43 0.16 1.26 0.12 1.06 0.07 1105.1° 119.3 1,82 0.21 1,32 0,12 0.93 0.10 1147.0 119.7 1.89 0.16 “0.98 0.15 0.42 0.04 1109.4 118.0 1,61 0.15 1.15 0.07 0.77, 0,06 1159.3 118.7 1.33 0.12 0.79 0.13 0.46 0.04 1205.4 119.0 1.20 0,12 0.91 0.09 0.26 0.03 1247.3 119.7 1.11 0.13 0.78 0.16 0.25 0.04 570.7 134.2 3.29 0,23 7.22 0,37 5.61 0.42 587.3 134.1 3.72 0.24 7.05 0.37 5.70 0.41 611.6 134.6 3.80 0.25 7.02 0.37 6.03 0.43 633.7 135.0 3,52 0.25 7.08 0.40 6.50 0.50 58 Lab CM at 1 Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (ub/sr) Error (pb/sr) Error (ub/sr) Error 622.0 133.8 3.64 0.25 7.28 0.39 6.41 0.49 647.1 134.4 4.00 0.26 7.36 0.39 6.35 0.46 668.4 134.5 4.63 0.30 7.65 0,41 6.19 0.44 694.1 134.8 4.14 0.29 7.51 0.44 7.64 0.59 681.3 133.7 4.35 0.27 6.39 0.35 5,81 0.41 710.3 134.2 4.67 0.28 6.01 0.34 5.69 0.39 737.7 134.7 4.53 0.29 5.20 0.33 4,80. 0.35 767.3 134.6 3.67 0.27 5.24 0.36 5.28 0.44 750.4 133.6 3.73 0.25 5.79 0.32 6.07 0.45 787.3 133.9 3.74 0.25 4.03 0.28— 3.52 0.28 814.9 134.7 3.55 0.26 3.55 0.28 2.78 0.24 847.2 134.6 3.53 0,28 3.14 0.28 2.40 0.23 831.2 133.5 3.39 0.24 3.70 0.25 2,80 0.23 865.3 133.9 3.54 0.26 3.67 0.25 2.75 0.23 901.8 134.2 3.00 0.24 3.07 0.25 2.95 0.28 926.0. 134.8 3.37 0.30 2.44 0.27 2.21 0.24. 926.8 133.6 3.32 0.25 2.56 0.22 2.20 0.21 974.8 134.3 2.98 0.24 2.42 0.20 2.34 0.23 1017.6 134.5 2.95 0.24 2.03 0.20 2.11 0.22 1063.1 135.0 2.51 0.23 1.54 0.20 1.62 0.20 1012.1 133.6 2.74 0.25 1.60 0.20 1,84 0,22 1058.8 133.7 2.48 0.24 1.49 0.18 1.47 0.19 1114.5 134.3 2.13 0.22 1.23 0.17 0.86 0.12 1166.4 134.8 1.71 0.21 1.29 0.20 0.75 0.11 563.6 149.0 3.33 0.24 6.96 0.38 4,99 0.40 584.3 149.1 3.20 0.24 7.49 0.41 6.35 0.53 611.5 149.2 3.44 0.26 7.89 0.42 6.69 0.54 629.4 149.5 2.97 0.25 8.23 0.46 7.88 0.69 617.7 148.8 3.42 0.25 7.63 0.40 6.40 0.52 640.9 148.9 3.25 0.24 7.97 0.41 7.09 0.58 666.8 149.3 3.30 0.25 8.24 0.44 7.74 0.65 690.5 149.3 3.26: 0.26.. 7.75 0.44 8.03 0.70 679.9 148.6 3.98 0.33 7.43 0.40 5.97 0.54 706.6 149.2 4.18 0.34 8.21 0.42 6.84 0.62 733.8 149.1 3.12 0.29 6.63 0.39 6.92 0.70 755.4 149.3 3.52 0.34 5.94 0.41 5.24 0.36 815.0 148.1 3.03 0.25 5.07 0.34 3.81 0.36 852.4 148.6 3.19 0.26 4.05 0.32 2.94 0.30 898.2 148.8 3.11 0.27 3.96. 0.33 3.14 0.33 924.7 149.3 3.20 0.32 4.05 0,37 3.14 0.36 -+ 59 Lab CM T TT Ratio Photon Pion Cross Cross Cross Energy Angle Section Stat. Section Stat. Section Stat. (MeV) (deg.) (wb/sr) Error (ub/sr) Error (ub/sr) Error 912.3 148.4 2.68 0.25 3.81 0.28 3.50 0.38 953.4 148.6 3.08 0.28 3,36 0.27 2.67 0.29 1006.6 149.2 2.74 0.26 3.29 0.27 2.99 0.33 1057.8 149.7 2.69 0.28 2.41 0.25 2,00 0.26 993.6 148.3 2.48 0.24 2.76 0,34 1053.9 149.2 2.70 0.25 2.13 0.26 1104.0 149.5 2.43 0.25 1.62 0,22 1162.2 149.7 2.13 0.26 1,38 0.21 994.8 148.4 2.93 0,23 1054.0 149.1 2.69 0.20 1103.6 149.4 2.44 0.20 1157.1 149.7 2.42 0.21 1062.9 147.9 2.68 0.27 2.55 0,28 2.17 0.27 1114.9 148.4 2.34 0.27 2.37 0.25 1.50 0.21 1155.6 148.5 2.06 0.27 2.02 0.26 1.15 0.19 1211.9 148.8 2.69 0.38 1.62 0,31 0.70 0.14 610.4 158.5 3.01 0.25 7.58 0.41 7.18 0.64 636.6 158.6 3.18 0.25 8.45 0.46 7.63 0.66 660.4 158.8 2.89 0,26 9.51 0.50 9,32 0.86 688.0 158.9 3.35 0.30 - 10.34 0.59 9.08 0.84 673.4 158.6 3.24 0.31 8.37 0.51 7.32 0.75 698.4 158.8 2.93 0.30 8.33 0.53 8.88 0.96 725.8 158.8 3.58 0.34 7.74 0.52 6.04 0.63 755.1 159.0 3.70 0.38 8.01 0.58 5.46 0.60 821.3 158.5 2.64 0.25 5.48 0.38 4.76 0.48 862.4 158.8 2.93 0.27 5.36 0.37 3.94 0.40 906.2 159.0 2.89 0.27 4,81 0.37 3.83 0.40 945.7 159.3 2.70 0.28 4.56 0.39 4.00 0.45 898.5 158.3 2.51 0.25 4.85 0.35 4.41 0.48 949.3 158.8 3.02 0.28 4,80 0.36 3.72 0.39 1005.2 159.0 2.10 0.23 3.60 0.33 3,86 0.49 1046.4 159.1 2.13 0.25 3.64 0.35 3,22 0.43 992.4 158.7 2.50 0.32 3.55 0.46 3.31 0.38 1024.7 158.6 2.13 0.23 3.35 0.37 3.31 0.32 1081.5 159.1 2.00 0.23 2.64 0.42 2.24 0,25 1137.0 159.0 1.68 0.22 3.28 0.27 2.02 0.21 1044.2 158.3 1.81 0.25 2.97 0,29 2.87 0.41 1104.4 158.4 1.81 0.26 2.53 0.31 1.87 0.29 1146.7 158.4 1.87 0.28 2.46 0.36 1.51. 0.24 1178.1 158.2 2.28 0.38 1.92 0.47 1.02 0.19 60 TABLE 4 "Recoil" Cross Sections direct calculation from rates where both pion and nucleon are detected. 1) Forward recoil runs - pion through spectrometer and recoil proton through recoil counter - ° 6° - 110° (also 120° points marked *) 2) Reverse recoil runs ~ recoil proton through spectrometer and pion through recoil counter - 120° - 160° See Appendix. I for explanation of "lab" photon energy. 61 Lab CM Recoil Lab CM Recoil Photon Pion Cross. Photon Pion Cross Energy Angle Section Stat. Energy Angle Section Stat, (MeV) (deg.) (yb/sr) Error (MeV) (deg.) (itb/sr) Error 608.5 44.85 14.21 4.11 714.0 59.47 7.20 0.45 615.6 45.32 17.22 4.09 735.1 59.83 5.86 0.44 632.6 45.42 (8.92. 2.14 757.9 60.18 5.45 0,39 648.7 45.77 17.45 3.31 782.7 = =60.58 4.66 0.31 657.4 44.93 10.80 1.65 791.1 59.49 4,16 0.45 673.1 45.18 11.50 1.52 811.2 59.93 3.37. 0.41 691.9 45,33 9.18 1.16 839.1 60.35 2.84 0.36 708.0 45.74 10.20 1.15 866.0 60.75 2.21 0.31 725.7 44.77 9.44 0.76 876.4 59.53 1.77. 0.49 738.9 45.07 8.89 0.71 906.1 59,86 2.40 0.30 761.6 45.33 5.54 0.41 932.1 60.29 2.27 0.18 783.4 45.62 5.26 0.50 963.3 60.80 2.00 0.16 797.0 44,59 4.94 0.46 971.6 59.35 2.25 O.11 818.7 44.92 4.18 0,36 1004.7. 59.79 2.46 0.12 842.3 45.17 4,23 0.36 1036.0 60.20 2.46 0.12 867.6 45.48 3.54 0,32 1069.1 60.67 2.50 0.14 882.7 44.67 5.18 0.47 1067.2 59.58 2.42 0.19 904.7 44,92 3.62 0.35 1101.8 59.89 2.30 0,21 930.7 45.34 “4.20 0,38 1135.8 60.29 1.94 0.16 960.8 45.61 3.77 0.35 1174.8 60.70 1.70 0.15 976.9 44.60 3.96 0.28 1163.1 59.41 1.73 0.16 1007.5. 44.97 4.05 0.45 1199.2 59.73 1.63 0.14 1038.8 45.26 4,32 0.31 1240.0 60.30 1.30 0.12 1066.3 45.59 3.80 0.27 1281.6 60.70 1.22 0.12 1072.7. 44.57 4.14 0.26 586.2 74.41 4.84 0.93 1102.7 44.94 3.78 0.24 604.1 74.84 5.92 0.62 1138.2 45.17 3.27 0.25 622.6 75.21 5.79 0.39 1168.7 45.61 3.47 0.24 641.5 75.66 5.65 0.64 1166.5 44.61 3.03 0.29 642.7 74.55 5.95 0.27 1204.6 44.92 3.23 0.32 662.9 74.96 5.26 0.41 1239.2 45.33 2.81 0.23 684.3 75.33 6.10 0.27 1276.7 45.64 2.67 0.22 706.3 75.76 5.97 0.27 591.0 59.59 7.72 0.62 711.0 74.37 5.98 0.44 605.7 59.91 7.06 0.56 733.5 74.86 6.53 0.48 624.6 60.22 7.58 0.59 757.6 75.23 4.36 0.35 643.1 60.61 8.02 0.59 782.3 75.68 3.54 0.32- 645.5 59.57 6.65 0.52 787.4 74.43 3.15 0.22 665.1 59.82 7.06 O71 812.5 74.93 2.60 0.20 684.5. 60.21 7.42 0.52 839.2 75.24 1.95 0.19 706.3 60.68 6.66 0.48 869.1 . 75.75 1.32 0.13 62 120.0 Lab CM Recoil Lab cM Recoil Photon Pion Cross Photon Pion Cross Energy Angle Section Stat. Energy Angle Section Stat. (MeV) (deg.) (ub/sr) Error (MeV) (deg.) (ub/sr) Error 871.3 74.41 1.46 0.13 858.2 104.3 1.38 0.10 903.2 74.88 1.30 0.12 892.7 104.8 1.29 0.10 933.1 75.30 1.06 0.11 926.2 105.1 1.21 0.09 964.9 75.82 0.93 0.10 958.0 105.5 1.12 O.11 968.8 74,33 1.05 0.07 953.7 .104.2 0.94 0.13 1001.3 74.88 1.00 0.07 991.2 104.6 1.14 O.11- 1037.2 75.30 0.89 0.08 1022.5 105.2 0.95 0.10 1072.1 75.70 0.95 0.10 1058.9 105.6 0.77 0.20 1064.3 74.32 0.75 0.09 1043.2 109.3: 0.77 0.09 1098.5 74.77 0.90 0.09 1082.1 109.7 0.62 0.09 1138.6 75,32 ° 0.93 0.10 1124.9 110.1 0.46 0.12 1173.5 75.87 0.75 0.09 1165.8 110.5 0.30 0.06 1159.7 74.31 0.78 0.09 594.1 119.8 4.71 0.50 1199.3 74.88 0.72 0.10 605.5 119.7 5.47 0.38 1239.7 75.38 0.70 0.08 626.3 120.0 4,98 0.33 1281.4 75.82 0.67 0.09 648.2 120.1 5.52 0.44 583.0 89.50 5.42 0.58 647.0 119.6 5.58 0.56 601.8 89.87 5.28 0.38 666.7 119.7 6.07 0.49 623.2 90,38 5.40 0.38 688.2 120.0 5.43 0.42 641.5 90.74 5.94 0.46 709.9 120.1 5.96 0.46 639.8 89.53 4.35 0.32 713.6 119.6 5.11 0.35 . 660.4 89.85 4.79 0.34 735.4 119.8 4.95 0.33 * 681.5 90.35 5.49 0.36 758.7 119.9 4,10 0.34 703.9 90.71 5.03 0.34 782.9 120.1 3.42 0.31 705.5 89.31 5.21: 0.24 789.9° 120.1 2.91 0.28 730.2 89.73 4.78 0,22 816.7 120.3 2.34 0.24 754.6 90.23 3.91 0.18 842.0 120.2 2.13 0.23 780.4 90.60 3.08 0.42 864.0 120.2 1.56 0.18 783.1 89.35 3.76 0.23 876.2 119.8 1,64 0.18 810.6 89.79 2.95 0.19 903.9 119.8 1.56 0.17 837.1 90.36 1.85 0.14 929.8 119.8 1.46 0.16 866.2 90.80 1.26 0.12 964.6 119.9 1,22 0.15 636.9 104.4 5.32 0.40 972.5 119.6 1,38 0.16 658.7 104.9 5.81 0.42 1000.0 119.7 1.40 0.16 682.3 105.1 4.87 0.38 1040.7 119.8 0.92 0.13 706.4 105.6 6.42 0.45 1068.4 119.6 - 0.88 0.12 °— 775.5 104.4 3.56 0.23 1119.5 118.9 0.53* 0.05 806.4 104.9 2.21 0.22 1169.6 119.5 0.29% 0.04 834.9 105.3 1.67 0.42 1217.5 119.8 0.21% 0.07 866.7 105.7 1.30 0.22 1262.2 0.23% 0.05 63 Lab CM Recoil Lab CM Recoil Photon Pion Cross Photon Pion Cross Energy. Angle Section Stat. Energy Angle Section Stat. (MeV) (deg.) (ub/sr) Error (4eV) (deg.) (ub/sr) Error 587.6 134.8 5.76 0.48 976.8 149.7 2.29 0.28 613.4 134.8 5.55 0.45 1000.0 149.8 2.35 0.30 628.6 135.0 5.22 0.42 1023.8 149.7 2.53 0.33 646.8 135.1 6.46 0.50 1046.9 149.7 2.08 0.29 645.0 134.7 6.40 0.58 1061.5 149.7 1.26 0.19 665.7 135.0 6.74 0.55 1096.1 149.8 1,79 0.23 694.8 135.0 5.95 0.43 1128.0 149.8 1,66 0,22 703.6 134.8 5.73 0.44 1153.8 149.8 1,20 0.20 716.7 134.8 5.64 0.47 1172.8 149.9 1.12 0.20 726.9 134.6 5.17 0.44 1203.8 149.8 0.68 0.15 756.4 134.7 3.95 0.32 1231.0 149.8 1.06 0.19 786.3 135.1 3.86 0.36 1259.3 149.7 1.05 0.20 790.6 134.7 3.67 0.29 592.4 159.8 7.27 0.68 812.9 134.8 3.24 0.26 609.5 159.8 8.50 0.76 841.3 134.8 2.55 0.21] 623.9 159.7 7.44 0.58 870.1. 135.0 1.97 0.19 642.1 159.9 7.60 0.73 874.9 134.7 1.94 0.17 640.5 159.7 9.35 0.76 898.3 134.8 2.12 0.18 657.9 159.7 8.56 0.62 933.0 134.9 2.02 0.18 673.9 159.6 8.67 0,66 970.3 135.0 1.68 0.16 702.5 159.7 9,17 0.78 590.0 149.7 7.20 0.57 705.6 159.6 8.72 0.73 604.4 149.7 6.95 0.53 733.2 159.7 9.32 0.80 629.8 149.9 8.36 0.67 756.5 159.6 7.32 0.59 646.3 149.9 8.28 0.81 782.9 159.8 6.78 0.58 644.0 ° 149.8 7.81 0.61 779.6 159.5 6.01 0.53 659.1 149.8 8.83° 0.69 817.4 159.6 6.24 0.58 683.0 149.9 9.48 0.74 834.8 159.7 5.39 0.49 707.1 150.0 7.48 0.75 853.4 159.6 5.09 0.46 713.0 149.7 7.84 0.68 875.0 159.8 3.80 0.40 732.1 149.7 6.27 0.52 893.9 159.8 4,94 0.57 756.1 149.7 5.85 0.50 925.0 159.8 4,53 0.47 781.1 149.8 5.20 0.47 938.1 159.7 4,02 0.47 786.9 149.8 5.49 0.50 981.3 159.8 3.63 0.41 816.1 149.7 4.48 0.41 1002.5 159.7 3.92 0.46 837.6 149.8 4.42 0.40 1028.8 159.8 3.61 0.45 866.7 149.8 3.48 0.32 1056.8 159.8. 2.72 0.34 870.8 149.8 3.26 0.31 1071.0 159.7 2.66 0.33 906.4 149.8 3.59 0.35 1098.8 159.7 * 3.12 0.38 923.2 149.6 3.30 0.31 1124.4 159.7 1.91 0.27 957.6 149.8 0.27 1145.2 159.7 1.86 0.28 2.78 64 Lab cM Recoil ’ Photon Pion Cross Energy Angle Section Stat. (MeV) (deg.) (ub/sr) Error 1171.7 159.9 1.36 0.24 1205.2 159.8 1.68 0.28 1219.3 159.8 °41.82 0.30 1253.0 159.6 1.06 0.24 65 FIGURE 9 1) TOP - a fue Ratio | Dark points at 20, 60, 90, 120, 150, and | 160° are from Neugebauer et al. (36). Dark points in Fig. 9.9 are for 110°. 2) BOTTOM - ne Cross Section from Deuterium (background subtracted) and 1’ backgrounds. Ecklund's fit to a photoproduction from hydrogen has been plotted for comparison ("X"). PI MINUS TO PI PLUS RATIO 66 — PY MINUS TO PI PLUS RATIO - DEUTERIUM 3 i i T T T . t T CM PION ANGLE 6 2+ . T 4 aig 1 + p 4 bf pia? O50 660 700 800 300 1000 1100 1200 1300 LAB PHOTON ENERGY CMEV) PI PLUS PHOTOPRODUCTION FROM DEUTERIUM au T T T qT q T T ~ 2b CM PION ANGLE 6 J oe x xX ECKLUND FIT - HYDROGEN X ye x% ee ™% % PION ONLY - oO xx & BACKGROUND - PION GNLY v IE weil 5” / Zz iitinay | Xx ; rs io b } iF xx | wn ti © 8 } : om © . O 9665 B00 700 800 300 {000 i100 1200 1300 LAB PHOTON ENERGY CMEV> FIGURE 9.1. 67 PY MINUS T@ PI PLUS RATIO - DEUTERIUM -PI MINUS T@ PI PLUS RATIG 3 T t ul T T T T CM PIGN ANGLE 10 2r 4 Lak, ors 1} PY at 4 pa fat le 5 O00 600 700 800 800 100011001200 1300 LAB PHOTON ENERGY (MEV) PI PLUS PHOTOPRODUCTION FROM DEUTERIUM 24 U T T T T T T ~ 2b CM PION ANGLE 10 7 5} X ECKLUND FIT - HYDROGEN N * PION ONLY = A BACKGROUND ~ PION ONLY ~ 16 t- XK XyX * 4 = x S i! ih, x © 12 - i I XXX, 4 ud i k *x x ep) k tix x y B EY k x & BF k ; F3 a om ad x . EX y te uF RE RF Hy y o 0 me pee 1 i \ 4 ha ® 500 600 700 800 g00«1000,s«110G-s« 1200S: 300 LAB PHOTON ENERGY CMEYV) . FIGURE 9,2... PI MINUS TO PI PLUS RATIO -2u 20 12 DIFF. CROSS SECTION CUB/SR> 68 PY MINUS TORI PLUS RATIG - DEUTERIUM CM PIGN ANGLE 20 ey pg Es : "aE fp te i 2 @ z oy * SD Bp ooo 9 08 500 600 700 800 300 1000 1100 1200 1300 LAB PHOTON ENERGY (MEV) PI PLUS PHOTOPRODUCTIGN FROM DEUTERIUM L CM PIGN ANGLE 20 J x ECKLUND FIT ~ HYOROGGEN * 2 PIGN ONLY A BACKGROUND - PION GNLY - RX yy XK XK i FEL” x & x - FET x xe * x x 7 FERS EES KE Xx KE * L. . wx x -| Hog ° 500 600 700 800 “300 *T000 : i100 1200 1300 LAB PHOTON ENERGY (MEV) FIGURE :9.3.. . 69 PI MINUS TG P] PLUS RATIO ~ DEUTERIUM 3 U T UJ T t LJ U CM PION ANGLE 30 co) i c& 2 . w ae) _J a. 0 i) BS Lah ; wo ar ® $ a 3! iu] = PEP DP op yy a 0 1 ! 1 4 L i 1 ‘ 900 600 700 800 - 800 1060 1100 1200 1300 LAB PHGTGN ENERGY CMEV) PI PLUS PHOTOPRODUCTIGN FROM DEUTERIUM 2u T v T T ¥ T T A 909 b CM PION ANGLE 30 ~~ . oS X ECKLUND FIT ~ HYDROGEN ~N 3% = =PION GNLY Ss 4 ~~ BACKGROUND - PIGN GNLY ~w 16 - 4 z 2 — 127 4 7 2 He ye RK EX . tiqet ys? m glint ye?” x — eo SF KL yx XX “EB gy OK 4 6 git pure ne K . i uy f By x 4 OseG 600 700 800. “300 “"y000. “T1060 1200 1300 LAB PHOTON ENERGY (MEV) - FIGURE 9,4 70 PI MINUS TO PI PLUS RATIG ~ DEUTERIUM PI MINUS TO PI PLUS RATIO T T t t T : T t CM PIGN ANGLE Us hea ses 5 : ee Q go 2 B a ae 5 5 f® hop P 300 ay 600 706 800 ago 10001100100 ~—~«T300 LAB PHOTON ENERGY ¢MEV) PI PLUS PHOTOPRODUCTION FROM DEUTERIUM 12 ub DIFF. CROSS SECTION CUB/SR) i I y T T T 1 CM PION ANGLE U5 a X ECKLUND FIT - HYDROGEN ~ % PION ONLY 4 BACKGROUND - PIGN GNLY ) i] i yan: SOOT 900 600 700 800 600 1000 Tigd “1200-1300 LAB PHOTON ENERGY CMEV) FIGURE .9.5. PI MINUS TO PI PLUS RATIO . CROSS SECTION CUB/SR) DIFF 12 10 71. PI MINUS TG PI PLUS RATIG - DEUTERIUM CM PION ANGLE GO F 7 pO } re ee phi Ry ® a 5 & 8 m @& om A soo 600.~-700~~~«800.~«SG0 1001100 ~—~«1200 1300 LAB PHOTON ENERGY CMEV > PI PLUS PHOTOPRODUCTION FROM DEUTERIUM i x XK | i [i CM PIGN ANGLE 60 1 at X ECKLUND FIT - HYDROGEN {1 *% PION ONLY A BACKGROUND - PIGN ONLY : ; A Hy x : * L i x / ~ay, g BRE i x EK ; ‘ L X Re i 4 1 1 a GF 4 4 4 L sd0. 600. 700. 4600. 900 1000 1100 1200 1300 LAB PHOTON ENERGY (MEV) . FIGURE 9.6 DIFF. CROSS SECTION (UB/SR Pi MINUS TQ PI PLUS RATIO 12 10 72 P] MINUS TO PI PLUS RATIO - DEUTERIUM CM PION ANGLE 75 Babes 5 Zz a Se 5 5 a 500 600 700 a00 8601000 ~~Ti00~—~«1200 F300 LAB PHOTON ENERGY (MEV) PI] PLUS PHOTOPRODUCTION FROM DEUTERIUM : x CM PION ANGLE 75 4 *" x x ECKLUND FIT - HYDROGEN Te % PION ONLY ryt Ok i 4 BACKGROUND - PION ONLY } “% x 7 4 4 | — k : | i EE ty X L Ye 4 BR i k x S00 600 700 goo -800~-1000~-i100~~*1200~*1300 LAB PHOTON ENERGY (MEV) FIGURE 9.7 PI MINUS T@ PI PLUS RATIG DIFF. CROSS SECTION ¢UB/SR> —.73 PI MINUS 10 PI PLUS RATIG - DEUTERIUM 3 1 T : T 1 T 1 T CM PION ANGLE 90 2h - fy : ! Be. . pea Bg 3 0 Ze L t \ L L. ‘ 500 600 700 800 800 1000 1100 1200 1300 LAB PHOTON ENERGY CMEV) PI PLUS PHGTGPRODUCTIGN FROM DEUTERIUM 12 T T 1 T T 1 T val CM PION ANGLE 90 ; xX ECKLUND FIT - HYOROGEN % PION ONLY . ‘ : ‘ A = BACKGROUND - PION ONLY I ty x i eb Xx” , i 1 ri x ¥ Ye "i a x ' x 2k = 2609 600 700 800 300 1000 1 160 1200 {300 LAB PHOTON ENERGY (MEV? - FIGURE 9.8 PI MINUS T@ PI PLUS RATIO CROSS SECTION (UB/SR> DIFF. 12 10 74 PI MINUS TO PI PLUS RATIG - DEUTERIUM 7 T T T t T t CM PIGN ANGLE 105 4 500 | ! i t i 4 I 600 700 800 900 1000 1100 1200 1300 LAB PHGTON ENERGY (MEV) PI PLUS PHOTGPRODUCTIGN FROM DEUTERIUM CM PION ANGLE 105 4 X ECKLUND FIT - HYDROGEN % PION ONLY A BACKGROUND - PION ONLY ae: x KR X x BH i Me g Rog 7 x ! 1 a Ar 4 «4 600 700 goo. 900 100011001200 ~~-4300 LAB PHOTON ENERGY (MEV) : FIGURE 9.9 75 PY MINUS T@ PI PLUS RATIO - DEUTERIUM 3 T T J Li T . T T CM PIGN ANGLE 120 ©) a c 2b 4 St = a Va be aon te BS . Z my Bay = Ph ep 5 2 ~ & O. sco 600—~—~C~SD~C«D SCG 1G T0200 1300 LAB PHOTGN ENERGY (MEV) PI PLUS PHOTOPRODUCTIGN FROM DEUTERIUM 12 J T qT T T UJ T A 19 b CM PION ANGLE 120 : Cc X ECKLUND FIT - HYDROGEN X % PION ONLY | 0 A BACKGROUND - PION ONLY ww Br + = 18] > 6H } J G cybn sf xX ~ k ih <I Sup HEE Ay pit i 2 P z : i 4 i Oo , Hoos § x J J { { { i c x “soo 600 60.~—~SCG SOG GO «12007300 LAB PHOTON ENERGY (MEV) FIGURE..9,10. PI MINUS TQ.PI PLUS RATIO DIFF. CROSS SECTION ¢UB/SR> 76 P] MINUS TG PI PLUS RATIG ~- DEUTERIUM 3. t T T T T T ¥ CM PIGN ANGLE 135 big, } Fey 569 600 700 B00 900 1000 1100 1200 1360 LAB PHGTGN ENERGY ¢ MEV) PI PLUS PHOTGPRODUCTIGN FROM DEUTERIUM 12 T T T T T T LJ io b CM PION ANGLE 135 | x ECKLUND FIT - HYDROGEN x PION ONLY A BACKGROUND - PIGN ONLY a : 6 7 big uF iy ii i 4 pipe HEHE gy x Xxx X ii ik ei i 2+ i 4 x # x 0 pa BE a Bia n [hey a 3 at : 500 600 700 800 300 1000 1100 1200 1300 LAB PHOTON ENERGY (MEV) ». FIGURE 9,11 PI MINUS TG PI PLUS RATIG DIFF. CROSS SECTION ¢UB/SR) 77 PI MINUS TO PI PLUS RATIO — DEUTERIUM 3 t T T T T T T 4 CM PIGN ANGLE 150 rl | HH i te f : i i / S60 600 700 800 360 7000 1 100 1200 1300 LAB PHOTON ENERGY (MEV) PI PLUS PHOTGPRODUCTIGN FROM DEUTERIUM 12 qT T T qT T qT T to | CM PIGN ANGLE 150 : X €CKLUND FIT - HYDROGEN % PION ONLY A BACKGROUND ~ PIGN ONLY 8+ a 6 F -| YE 1 f } ' 4 ee BR & T x x x XAK x i Sr i rt 2+ oats if - 0 L lt pe 4 Fak gn te ; 1. . ab 500 600 700 goo. = s00—«—«éatD—~Cié‘iDS:SC“‘édLDO~SS«1300 LAB PHOTON ENERGY CMEV ) _ FIGURE 9.12°°° | PI MINUS TG PI PLUS RATIO DIFF. CROSS SECTION ¢UB/SR> 12 10 78 PI MINUS TG PI PLUS RATIC ~ DEUTERIUM | CM PIGN ANGLE 160 Hil HH H 5600 . 600 700 B00 300 1000 Tio 1300 1300 LAB PHGTGON ENERGY ¢MEV) PI PLUS PHOTOPRODUCTIGN FROM DEUTERIUM | CM PIG@N ANGLE 160 / x ECKLUND FIT. - HYDROGEN K PION ONLY A BACKGROUND - PIGN ONLY x i x : x i. I I t r , ite di g : x x oe x if , a 2 @ a ! | Box 7 ES i S00 606 700 800 3909 © 1000 1100 1200 1300 LAB PHOTON ENERGY ¢MEV) FIGURE 9.13 79 FIGURE 10 1) TOP - Ratio Cross sections and Recoil Cross Sections Half-dark points are artificial (interpolated) cross sections. Dark points in Fig. 10.9 are for 110° 2) BOTTOM - Ratio Cross Sections and 1 (pion only detected) Cross Sections from Deuterium (background subtracted) and 7 Backgrounds. Half-dark points are artificial (interpolated) “eross sections. Dark points in Fig. 10.9 are for 110°, Artificial (interpolated) background points - are identified by a vertical bar. 80 © Pl MINUS PHOTGPRODUCTIGN FROM DEUTERIUM 2u N oO i if i CM PIGN ANGLE 6 : ad) FROM RATIG ; A WITH RECOIL PROTON oc wm ™ am) co 16 + () 12 + é uJ Me o é ® Bey a7 " B° ag L yok bp 2g 6 + OGG 00 0~S~COSC«SC«O S000 LAB PHOTON ENERGY CMEV> PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM 2u I ; q q J t J ~ 09 | iH CM PION ANGLE 6 | CS | | (FROM RATIO : < it! } % PION ONLY a AtE’ SE I. : 4 BACKGROUND - PION ONLY C16 + Phy 4 = ie] - uh O12 5 ag i 4 e DO ob i | : hy] , z ' f p®. 8; = ae x5, gt Fenes, Reagan, Ae anh og “soo 6G0.~—~CSGDS~S~CS~“C*«SSC“‘iOSC«*dCOD:~S=«i0~SC300 LAB PHOTON ENERGY CMEV) . FIGURE 10.1 au 7 oN oO ms op) DIFF. CROSS SECTION CUB/SR> S) DIFF. 81 | PI-MINUS PHOTOPRODUCTIGN FROM DEUTERIUM T T U t v U ? : CM PIGN ANGLE 10 ° J | [° FROM RATIO lt — & WITH RECOIL PROTON g | . fy 7 ® : WF pe pp Boe 4 — [sca 0SBODSCSGSCSCLO~«DOD 300 | LAB PHOTON ENERGY ¢MEV) PI MINUS PHOTOPRGDUCTION FROM DEUTERIUM au T T t T q t I A oo | CM PION ANGLE 10 : cc [ FROM RATIO ~ . % PION ONLY 3 r H A BACKGROUND ~ PION ONLY S16 f i 7 ; z it 2 iy G 12 F : ti 4 ~ k i p gL p 4 ra gifs § . . Ho EGE a Spee : KBs ES gw 0 i aS CA LS SS SS soo. 0 600~Sfs—i‘<(OO~””sS800-—'—=s—«<C‘0”'é=i‘ 0~S*é«d:'00'”s=‘i0~—=«d8000 LAB PHOTON ENERGY (MEV) FIGURE 10,2 - Qu DIFF. CROSS SECTION (UB/SR) DIFF. CROSS SECTION CUB/SR) 82 Pl MINUS PHOTGPRODUCTIGN FROM DEUTFRIUM 20 + CM PION ANCLE 20 _ O FRGM RATIG A WITH RECOIL PROTON ig F- - qT. 1 j | # au : | | p . gb @ 4 ae Yop " Pond. moe be 4 0555 . 600 700 800 360 1000 1100 i300 {300 LAB PHOTON ENERGY (MEV) PI MINUS PHOTOPRGDUCT ION FROM DEUTERIUM au | T T t | 7 T T 20 CM PION ANGLE 20 4 O FROM RATIC K PION ONLY 4 BACKGROUND - PION ONLY 16 + - 4 fiat dy 12 + : mea fig! Eo 8 + xf Z ik re FEEL pp one D om Yoh Pek woe ep g Pe RE F Bg de 0 44 A AL ak ES A A doa [A A AS a Ap A AL a AAA ad 500 600 ~=— 700 800 900 {000 {100 1200 1300 “LAB PHOTON ENERGY (MEV) FIGURE 10.3 a3 - — PI MINUS PHOTGPRODUCTION FROM DEUTERIUM - au C 1 T T T T ’ ~ 20 b CM PION ANGLE 30 : Oe © FROM RATIO > A&A WITH RECOIL PROTON = 18 - = cae fe - G2 - SYEFE Ey 3 peg 2 fe s : ue ee ee ae ui 4 . OB 4 Oo 0 500 600 700 800 300 100011001200 1300 LAB PHOTON ENERGY (MEV) Pl MINUS PHOTOPRODUCT IGN FROM DEUTERIUM au i 1 i r T 1 7 ~ oF CM PIGN ANGLE 30 2 OS M FROM RATIO NN K PION ONLY a : A BACKGROUND - PIGN CNLY & tee | k . grt Hane | ” Sete wn *8 a Oo ¢ a 8F 7 f . g Bx x an Hf 5 ¥ t ro ub Kou R y Le ns Y tS R 5 i + —" Q 0 rtrssdapdd | bata n An Aa aan da as tt a ad 4 of 300 600 700 800 800 1000 1100 1200. 1300 LAB PHOTON ENERGY ¢CMEV> FIGURE 10.4... Bu Nm oO — op) co DIFF. CROSS SECTION CUB/SR) o£ S eu 20 12 DIFF. CROSS SECTION CUB/SR D BA PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM T T i t T t T i] CM PION ANGLE US — ‘ © FROM RATIO T 4S WITH RECOIL PROTON 2 Pay i q to fi Bi ad de RRS TA Oh - fs th ds Oo J 1 : ] J i ] 600 700 .800 300 1000 1100 1200 1300 500 ” LAB PHOTON ENERGY CMEV) PJ MINUS PHOTOPRODUCTIGN FROM DEUTERIUM L CM PION ANGLE US a { FROM RATIO % PION ONLY 4 BACKGROUND - PION ONLY Lt Hye | gE pha : - g by . . - 7 ee ee ee 4 Hoy AfassSadan 4 ania gad h | din a am AA ol fn S00 6U0 700 800 900 1000 1160 1200 1300 LAB PHOTON ENERGY (MEV) FIGURE 10.5 -. DIFF. CROSS SECTION (UB/SR) DIFF. CROSS SECTION (UB/SR) “42 10 12 10 85. PI MINUS PHOTOPRODUCTION FROM DEUTERIUM . CM PIGN ANGLE 60 a M FROM RATIO Li A WITH RECOIL PROTON 4 4 sha. 8 | i mo, a ! & & sod 600.~~«700~SC*SDS~“CS*~S SCG 1200-1300 LAB PHOTON ENERGY CMEV> PI MINUS PHOYGPRODUCTION FROM DEUTERIUM i CM PION ANGLE 60 - ( FROM RATIO 1 % PION ONLY : Hy : H : A BACKGROUND - PION ONLY L Odo a b 7 2 aes fi 4 Bb sfac dd ban aa nad bd de an ah ado be JJ 500. 600 700 6800. 900 1000. 1100 1200 1300 LAB PHOTGN ENERGY (MEV) FIGURE - 10.6. 42 LFF. CROSS SECTION CUB/SR > > d D DIFF. CROSS SECTION CUB/SR > “86 PI. MINUS PHOTOPRGDUCTIGN FROM DEUTERIUM 10 F T q T T i F T CM PION ANGLE 75 ({ FROM RATIO A WITH RECOIL PROTON 6 + Z | i i —¢§ 2k = u EB A “opm Dp os ‘oe 4 2 5 535 OB ffs "560 600 700 860 800. i000 1100 1200-1300 LAB PHOTON ENERGY (MEV) PI MINUS PHOTOGPRODUCTIGON FROM DEUTERIUM 12 T T T li T T J 10 CM PION ANGLE 75 J i; [ FROM RATIO % PION ONLY A BACKGROUND - PIGN GNLY er re fy | il ae ant] 1 6 - ' _ k ub e 7 Fi b & . > ® 7) | : ob “pe H hh aa ru, a gp ga mw A om ata jt, fh i SOO 600 700 800 goo. 1000 1100 1200 #1300 LAB PHOTON ENERGY CMEV> » FIGURE 10.7 12 DIFF. CROSS SECTION CUB/SR) DIFF. CROSS SECTION CUB/SR 10 4 12 10 PI MINUS PHOTOPRODUCTION FROM DEUTERIUM _ CM PION ANGLE 90 a [ FROM RATIO & WITH RECOIL PROTON . Tf: a % _ Es S00 600 700 800 800 1000 1100 1300 1300 LAB PHOTON ENERGY (MEV) PI MINUS PHOTGPRODUCTION FROM DEUTERIUM T i T T 1 t q L_ CM PION ANGLE 930 a M FROM RATIO * PION ONLY A BACKGROUND - PIGN ONLY i } oF : ii Ail J : d - & I tb y 4 i] | & ~ iu] ae ee ee |! ; Soo 600 700 800 300 1000 1100 1200 1300 LAB PHOTON ENERGY (MEV) - FIGURE 10.8. _DIFF. CROSS SECTION (UB/SR) . CROSS SECTIGN (UB/SR) FF DI 12 10 F 12 °88 . PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM T T tT qv T if T CM PIGN ANGLE 105 = © FROM RATIO A WITH RECOIL PROTON ppt | 4 8 L § ; a vee bn. & o 5 f ba Oy 8 # rete ., SOG 600 760 800 800 1000 1 100 (300 1300 LAB PHOTON ENERGY CMEV) PI] MINUS PHOTOPRODUCTION FROM DEUTERIUM Li T T T ¥ T T | L CM PION ANGLE 105 | [ FROM RATIO * PION ONLY L & BACKGROUND - PIGN ONLY | | | HH ' L tS 4 fy i) t- ao x ze | B 5 : ; ° KE zy atheeeka ana p tora bh pibah eye g i 509 600 . 700 800 300 1000 1100 1200 1300 LAB PHOTON ENERGY (MEV) FIGURE .10.9. ;. CROSS SECTION ¢UB/SR) DIFF. DIFF. CROSS SECTION (LB/SR) ‘ 89 PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM q J v T i t F io b CM PION ANGLE 120 : © > FROM RATIO | A WHITH RECOIL PROTGN eb J 6 fF i} i His vg) wi qu ae b | 2+ BE : zs 2 th 0 ! L t ! fl i ave pa Oa 500 600 700 . 800 g00. 1060 1100 1200 1300 LAB PHOTON ENERGY ¢MEV3> PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM 12 T T 1 T , T 1 io CM PION ANGLE 120 2 FROM RATIG K PION ONLY A BACKGROUND - PION ONLY 8 fF _ i I op Lat ay et { pay | , peta er 2 go : Be 7 0 keh ddkE AHA Ok LM Lk db gg aw £! po 500 600 §©6700 800 900 1000 1100 120 1300 LAB PHOTON ENERGY (MEV) - FIGURE 10:10. - 90 PI. MINUS PHOTGPRODUCTIGN FROM DEUTERIUM 12 1 1 r T T T T ~ 104 CM PION ANGLE 135. oe FROM RATIG ~ A WITH RECOIL PROTON cS ek | FS WY . yb I i . = : a) } . . $258 5 OQ Q 5 sco 860.~—~CSOD~—SBODS~CS~SOSC‘GD~«LO 200-1300 LAB PHOTON ENERGY CMEV) PI MINUS PHGOTOPREDUCTION FROM DEUTERIUM 12 T T t T T J q A a b CM PIGN ANGLE 135 : Oe ™ FROM RATIO \ % PION ONLY cl A BACKGROUND - PIGN ONLY al I71 it | Zz ai Bo) HELL, : ep) in cg) ; OQ yl J ia FEE O _, ; e258 hog ‘om ; | x : 0 Ae thd eke ‘EAR AGE, x f L (Zi E La ay . soo g00—'—‘zzS~S*«iKSC“‘<«é‘ SCLC 1100. 1200 ~—«1300 LAB PHOTON ENERGY CMEV) FIGURE-.10,11.... 42 DIFF. CROSS SECTION (UB/SR) CROSS SECTION (UB/SR) DIFF. 91 PI. MINUS PHOTGPRGDUCTION FROM DEUTERIUM to L CM PION ANGLE 150 _ © FROM RATIO A WITH RECOIL PROTON 8 = . + 6 + . ob atl pe . 7 ey | | | x r °sag60o~S~C~SSC<C~RSC“«‘NSCOCO «200 ~~—«100 LAB PHOTGN ENERGY (MEV) PI MINUS PHOTOPRODUCTIGN FROM DEUTERIUM 12 T T T U T T y io L CM PION ANGLE 150 / © FROM RATIO *% PION ONLY. 4 ~~ BACKGROUND - PIGN ONLY 8 Fr 4 6 F 4 YT 43 iH 4 | “Te gy 2r +4 ist t 4 o 6 Ff * 5 500 600 700 800 800 1000 1100 120 1300 LAB PHOTON ENERGY CMEV) _. FIGURE .10.12.. 12 fon} reo} CROSS SECTION (UB/SR) co rr. N DI 12 10 DIFF. CROSS SECTION CUB/SR) PI MINUS PHOTGPRODUCTIGN FROM DEUTERIUM i: | CM PION ANGLE 160 | M FROM RATIG I i A WITH RECOIL PROTON hey : i I . : Pa ed py | i un _ OR 500 600 700 800 300 1000 i100 1300 1300 LAB PHOTON ENERGY (MEV) PI MINUS PHOTOPRODUCTION FROM DEUTERIUM CM PIGN ANGLE 160 | P . | 1 FROM RATIO ; 3K PIGN ONLY Lo | A BACKGROUND. - PIGN ONLY o 4 | | = : f | hy ¥ : if : i | ig | | 500 600 700 800 900° }§=61000 1100 1200 {300 LAB PHOTGN ENERGY ¢CMEV> - FIGURE. 10.13 93 H, Final + cross sections (yn > 7 p)_ To obtain a final set of data points for publication and fitting purposes, the following procedure was used.. The ratio cross sections and recoil cross sections were separately interpolated to standard energies at each rough angular setting. ‘The interpolated ratio cross sections and interpolated recoil cross sections were then averaged to obtain the final cross section for the reaction yn> ap. These final cross sections are listed in Table 5 and plotted in Figures 11 and 12. Details of the interpolation and averaging were as follows. A straight line interpolation between data points was used. While this type of interpolation tended to smooth out large deviations, the later averaging of the two types of cross section would do the same thing. Therefore, I considered a linear interpolation to be adequate. The final cross section was a weighted average according to the formula: 2 2 ce C,/E, + CA/E, (IV.1) 2 2 L/Ey + VE, where Cy and Cy are respectively the ratio and recoil cross 94 sections and Ey and Ey are their statistical errors. The final errors of the averaged cross sections were set equal to the larger of the following: ‘ 1) The standard deviation of the data points from their average! ~ ¥CC)-C)/B,)? -* CC ~C)/B,)7 Vifey + 17a S.D.. (IV.2) 2) The standard error in the average of the two data points: o = i (IV.3) are 3 ¥ 1/EF 4 1/ES I. Total cross section, 0° cross section, 180° cross section. By means of Moravcesik fits, Pat Walden (44) has obtained values for the 0° cross section, 180° cross section, and total integrated cross section at each energy. These are given in Table 6 and plotted in Figures 13, 14, and 15. The errors given are due to the possible error of the fit. A notable characteristic of all three curves is the sharp dropoff. occuring between 700 and 800 MeV lab photon energy. A discussion of this behavior is given in Part V. 95 TABLE 5 FINAL CROSS SECTIONS FOR THE REACTION yn > 1 p Average of Ratio and Recoil Cross Sections (only . . fe) Ratio cross sections at angles less than 45° CM) Lab K 8h o(8) Ao(@) 600 6.2 21.39 1.24 600 10,2 18.75 1.27 600 20.3 13.85 0.76 600 30.3 11.72 +0.70 600 45.1 10.19 0.81 600 60.4 8.95 0.58 600 75.3 6.63 0.25 600 90.1 6.21 0.36 600 104.6 5.18 0.55 600 119.7 5.22 0.25 600 134.6 5.78 0.31 600 149.4 6.78 0.38 600 159.8 7.82 0.71 620 6.3 21.44 1.24 620 10.3 18.98 1.27 620 20.4 14.20 0.78 620 30.5 11.86 0.70 620 45.6 9.59 0.75 620 60.6 8.91 0.56 620 75.6 6.79 0.40 620 90.4 6.34 0.39 620 105.2 5.31 0.33 620 119.9 4,99 0.22. 620 134.8 5.79 0.40 620 149.3 7.09 0.40 620 159.2 7.54 0.45 640 6.2 23.01 1.38 640 10.1 17.07 1.15 640 20.3 13.29 0.73 640 30.3 11.90 0.62 640 45.2 9.17 0.52 640 59.9 8.68 0.34 640 74.7 7.45 0.56 640 89.6 4.99 0.29 640 104.3 5.63 0.42 640 119.6 5.84 0.51 640 134.6 6.18 0.33 640 149.3 7.46 0.64 640 7.73 0.50 96 lab 660 © 660 660 660 660 660 660 660 660 660 660 660 660 680 680 680 680 680 680 680 680 680 680 680 680 680 700 700 700 700 700 700 700 700 700 700 700 700 45.8 60.8 75.9 90.8 119.4 134.4 149.4 159.3 o (8) 20.33 20.19 14.15 11.48 9.58 8.18 > 6.49 5.55 5.64 6.27 6.41 8.14 8.82 21.63 17.25 13,15 12.05 9.86 8.41 7.98 6.09 5.27 5.77 6.59 7.40 8.56 21.35 17.87 13.77 11.40 9.31 8.05 7.96 6.07 5.67 5.77 7.19 8.96 Ao (6) 1.32 1.42 0.78 0.82 0.54 0.30 0.65 0.31 0.51 0.310 0.35 . 0.65 0.51 2.13 1.20 0.72 0.57 0.54 0.37 0.50 0.32 0.54 0.28 0.35 1.00 0.44 1.34 1.25 0.72 0.52 0.51 0.29 0.42 0.33 . 0.27 0.29 0.70 0.60 lab k a o(68) Aa(6) 720 6.2 16.83 0.97 720 10.0 17.15 1.38 720 20.1 12.55 0.56 720 30.3 10.01 0.44 720 45.1 8.92 0.44 720 60.0 7.76 0.44 720 74.7 7.66 0.44 720 89.8 6.28 0.27 720 119.6 5.22 0.24 720 134.5 5.42 0.29 720 149.4 7.09 0.45 720 159.2 7.73 1.19 740 6.3 14.30 0.87 740 10.1 13,69 1.14 740 20.3 10.83 0.50 740 30.4 9.20 0.42 740 45,4 7.76 0.44 740 60.3 6.81 0.46 740 75.2 6.86 0.41 740 90.1 5.63 0.32 740 119.7 4.96 0.23 740 134.6 4.74 0.26 740 149,7 6.13 0.51 740 159.2 6.99 1.46 760 6.4 14.28 0.90 760 10.2 12.18 0.93 760 20.5 9.03 0.44 760 30.6 8.35 0.39 760 45.5 6.18 0.38 760 60.5 5.76 0.32 760 75.5 4.69 0.41 760 90.4 4.14 0.48 760 119.9 4.22 0.23 760 134.4 4.68 0.48 760 149.7 5.75 0.49 760 159.6 7.25 0.59 97 780 780 780 780 780 780 780 780 780° 780 780 780 780 800 800 800 800 800 800 800 800 800 800 800 800 800 825 825 825 825 825 825 825 825 825 825 825 825 825 0.66 0.72 0.59 0.41 0,23 0,26 0.23 0.32 0.15 0.20 0.23 0.47 0.41 0.46 0.54 0.52 0.48 0.26 0.20 0.17 0.12 0.33 0.20 0.19 0.46 0.56 0.41 0.50 0.38 0.43 0.25 0.16 0.16 0.10 0.15 0.14 0.17 0.43 0.59 lab cM im 6 a(6) Ac(6) 850 6.4 9.33 0.39 850 10.4 6.90 0.45 850 20.7 5.33 0.35 850 30.7 4.91 0.39 850 45.7 4.10 0.18 850 60.8 2.74 0.14 850 75.5 1.83 0.14 850 90.5 1.60 0.08 850 105.4 1.68 0.18 850 119.7 1.94 0.11 850 134.4 2.54 0.19 850 149.1 . 3.40 0.50 850 159.1] 4,62 0.48 875 6.3 7.76 0.75 875 10,2 7.29 Q.51 875 20.2 5.27. 0.27 875 30.0 5.38 0.20 875 45.0 4.23 0.22 875 59.8 2.64 0.39 875 74.6 1.46 0.08 875 104.4 1.38 0.07 875 119.4 1.74 0.12 875 134.5 2.21 0.40 875 149.3 3.17. 0.22 875 159.3 3.85 0.28 900 6.3 7.55 0.75 900 10.2 6.19 0.47 900 20.3 4.93 0.26 900 30.2 5.32 0.25 900 45.1 4.04 0.21 900 60.1 2.76 0.34 900 74.9 1.45 0.14 900 104.8 1.31 0.07 900 119.6 1.68 0.12 900 §=134.6 2.36 0.38 900 §=149.3 3.33 0.24 900 159.0 4.25 0.29 98 lab 1 925 925 925 925 925 925 925 925 925 925 925 925 950 950 950 950 950 950 950 950 950 950 950 975 975 975 975 975 975 975 975 975 975 975 o (6) 6.85 5.36 4.75 5.24 4.03 2.52 1.16 1.27 1.60 2.11 3.26 4,14 4,18 4.75 5.00 3.97 2.28 1.04 1.21 1.51 2.02 2.82 3,80 4.30 4.68 5.42 4,21 2.38 1.11 1.23 1,53 2.34 2.55 3.73 Aa (8) 0.71 0.41 0.25 0.19 0.23 0.23 0.09 0.07 0.13 0.14 0.23 0.25 0.34 0.24 0.19 0.31 0.20 0.08° 0.10 0.19 0.19 0.20 0,29 0.25 0.21 0.30 0.22 0.18 0.41 0.18 0.15 0.23 0.23 0.30 lab 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1025 1025 1025 1025 1025 1025 1025 1025 1025 1025 1025 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 10.3 20.4 30.2 45.2 59.8 74.9 104.7 119.7 134.4 149.1 - 159.0 10.3 20.4 30.4 45.4 60.2 75.2 105.1 119.1 134.1 149.3 159.0 10.4 20.6 30.6 45.6 60.5 75.5 105.3 109.0 119.2 134.3 149.5 159.0 o(0) Ac(é@) 4,32 0.25 4.54 0.21 5.41 0.24 4.46 0.27 2.54 0.17 1.10 0.18 1.19 0.10 1.50 0.12 2.20 0.23 2.64 0.18 3.62 0.24 3.78 0.23 4.41 0.24 5.19 0.23 4.29 0.20 2.51 0.10 1.63 0.17 1.05 O.11 1.43 0.13 1.88 0.15 2.52 0.18 3.45 0.22 4.13 0.28 4.27 0.21 5.53 -0.25 3.97 0.19 2.57 0.13 1.03 0.17 1.04 0.16 1.08 0.28 1.20 0.12 1.65 0.14 2.08 0.15 2.85 0.20 lab CM ke o o(6) Ao(6) 1075 6.1 5.10 0.33 1075 10.1 .3.85 0.28 1075 20.3 4.34 0.25 1075 30.1] 5.00 0,21 1075 44.8 4.22 0.17 1075 59.7 2.61 0.21 1075 74.5 0.96 0.23 1075 109.3 0.88 0.17 1075 118.8 1.04 0.08 1075 133.9 1,29 0.17 1075 149.1 1.75 0.18 1075 159.0 2.46 0.18 1100 6.2 5.37 0,32 1100 10.2 4.07 0.58 1100 20.4 4.33 0.25 1100 30.3 4,84 0.20 1100 45,0 4.02 0.19 1100 59.9 2.54 0,22 1100 74.8 1,04 0.18 1100 109.5 0.72 0.09 1100 119.2 .0.95 0.10 1100 134.1 1.02 0.14 1100 149.2 1.71 0.13 1100 159.0 2.27 0.29 1125 6.3 4.41 0.50 1125 10.3 3,79 0,28 1125 20.6 3.72 0.22 1125 30.4 4,82 06.20 1125 45.3 3.79 0.28 1125 60,2 2.13 O.15 1125 75.2 1.03 0.16 1125 109.7 0.54 0.04 1125 118.8 0.60 0.06 1125 134.4 0.84 0.12 1125 149.2. 1.53 0.12 1125 1.91 0.14 159.0 100 lab Cif lab cM KY 6 o{6) Ao(é) ae oe o (6) Ao (0) 1150 6.3 4,35 0.31 1225 6.7 4.17 0.32 1150 10.3 3.30 0.31 1225 10.5 2,92 0.40 1150 20.7 3.69 0,22 1225 20.6 3.78 0.42 1150 30.6 4.87 0.21 1225 30.4 3.92 0.26 1150 45.5 3.50 0.15 1225 45.3 3.09 0.17 1150 60.5 1.93 0.13 1225 60.2 1.48 0.10 1150 75.5 0.92 0.08 1225 75.2 0.72 0.07 1150 109.9 | 0.38 0.03 1225 119.4 0.24 0.03 1150 118.9 0.45 0.07 1225 149.8 0.97 0.18 1150 134.7. 0.78 0.12 1225 159.7 1.69 0.29 1150 149.3 1.29 0,12 — 1150 159.0 1.59 0.18 ® 1250 6.7 3.86 0.30 1250 30.6 3.90 0.26 1175 6.4 4.86 0.35 1250 45.5 2.82 0.15 1175 .10.3 3.11 0.42 1250 60.5 1.35 0.09 1175 20.3 3.87 0.42 1250 75.5 0.70 0.07 1175 30.0 4.40 0.27 1250 120.0 0.23 0.05 1175 44.8 3.32 0.32 1250 149.7 1.05 0.20 1175 59.6 1.81 0.13 1250 159.6 1.13 0.24 1175 74.5 0.81 0.10 1175 ° 119.1 0.35 0.05 1175 149.2 1.04 0.13 1175 =158.9 1.19 0.16 1200 6.6 4.53. 0.34 1200 10.3 2.66 0.37 1200 20.4 3.94 0.44 1200 30.2 4.25 0.27 1200 45,1 3.36 0.18 _ 1200 59.8 1.70 Q.11 1200 74.9 0.76 0.08 1200 119.1 0.27 0.02 1200 =149.3 0.77 O.11 1200 159.8 1.63 0.27 101 FIGURE 11 ANGULAR DISTRIBUTIONS OF FINAL 1 CROSS SECTIONS . 0 ‘ Points at 180° are from the experiment by Fujii et al. (11) DIFF. CROSS SECTION - (UB/SR) DIFF. CROSS SECTION - CUB/SR et nN oO ro ep) — nN fos) = \ PI MINUS PHOTOPREDUCT IGN \ T T LAB K = 600 0 80 120 180 C.M. PION ANGLE (DEGREES) PI MINUS PHOTOPRODUCT ION 2u yt LAB K = 640 0 60 120 180 C.M. PION ANGLE (DEGREES) 102 | DIFF. CROSS SECTIGN - (UB/SR) DIFF. CROSS SECTION - (UB/SR) au nN OQ — a _ nN © = au MINUS PHOTGPRGDUCT IGN LAB K = 620 \ PI 0 60 120 180 C.M. PION ANGLE (DEGREES) MINUS PHOTOPRODUCT ION LAB K = 660 0 60 120 180 C.M. PION ANGLE (DEGREES) FIGURE- 11.1... CROSS SE DIFF. DIFF. CROSS SECTION - (UB/SR) CTIGN - CUB/SR) au 20 16 12 au 20 \ PI MINUS PHOTOPRODUCT IGN F t \ LAB K = 680 0 60 120 C.M. PION ANGLE (DEGREES) PI MINUS PHOTOPRODUCTION 180 LAB K = 720 i 120 G 60 C.M. PION ANGLE (DEGREES) FIGURE.11.2. 00.0: 180 103 DIFF. CROSS SECTION - CUB/SR) DIFF. CROSS SECTIGN - (UB/SR) att MINUS PHOTOPRGDUCT ION T T LAB K = 700 0 ! i 60 120 180 C.M. PIGN ANGLE CDEGREES >) PI MINUS PHOTOPRODUCT IGN au LAB K = 740 0 L 1 60 120 180 C.M. PION ANGLE CDEGREES ) DIFF. CROSS SECTION - (UB/SR) DIFF. CROSS SECTION - CUB/SR) au — rod ie) eo) N 2) QO t H ££ au 20 16 PI MINUS PHOTOPRODUCTION LAB K = 760 y i 0 60 120 180 C.M. PIGN ANGLE (DEGREES) PI MINUS PHOTOGPRODUCT IGN T LAB K = 800 0 60 120 180 C.M. PIGN ANGLE (DEGREES) 104 DIFF. CROSS SECTION - (UB/SR) DIFF. CROSS SECTION - (UB/SR) 24 NM Co i _ a nN ©. — 24 20 16 PI MINUS PHOTOPRODUCT IGN T LAB K = 780 ) n 60 i 120 180 C.M. PION ANGLE (DEGREES) PI] MINUS PHOTOPRODUCTICN T LAB K = 825 0 . 60 120 180 C.M. PION ANGLE (DEGREES) FIGURE. 11.3 DIFF. CRGSS SECTIGN - (UB/SR) DIFF nN CROSS SECTION - CUB/SR? DIFF. .105 PI MINUS PHOTGPRODUCTIGN — PI MINUS PHOTOPRODUCT IGN 2u i ‘ 12 t T LAB K = 859 LAB K = 875 ron OQ t it 20 + 4 . @ 12 + +o . CRESS SECTIGN - €UB/SR) i ! 1 t 0 60 126 180 0 60 120 180 C.M. PION ANGLE CDEGREES ) C.M. PION ANGLE (DEGREES ) PI MINUS PHOTOPRODUCTIGN PI MINUS PHOTGPRODUCTIGN 12 T T 12 T T LAB K = g00 | | LAB K = 925 10 + + DIFF. CROSS SECTIGN - CUB/SR) m a) 60 120 180 0 : 60 1 20 180 C.M. PION ANGLE. (DEGREES) C.M. PION ANGLE (DEGREES) FIGURE 11.4 DIFF. CROSS SECTION - CUB/SR) DIFF. CROSS SECTIGN - (UB/SR) 12 10 12 10 PI] MINUS PHOTOPRODUCTIGN LAB K = 9350 os 0 60 120 C.M. PION ANGLE (DEGREES) PI MINUS PHOTOPRODUCTIGN LAB K = 1000 i t. 2 - 0 60 120 180 C.M. PION ANGLE (DEGREES) .. FIGURE 11.5 180 106 FF. CROSS SECTIGN - (UB/SR> t 4 D DIFF. CROSS SECTION - (UB/SR) 12 10 i2 10 PI MINUS PHOTOPRODUCT IGN LAB K = 975 to] 0 60 120 180 C.M. PIGN ANGLE (DEGREES) PI MINUS PHOTGPRODUCT ION LAB K = 1025 120 C.M. PION ANGLE (DEGREES) | 0 . 60 180 DIFF. CROSS SECTION — CUB/SR? SECTION - CUB/SR) o S v DIFF. CROS 12 10 i2 10 PI MINUS PHOTOPRODUCTION LAB K = 1050 DIFF. CROSS SECTION - CUB/SR) 0 60 120 C.M. PION ANGLE (DEGREES) PI MINUS PHOTOPRODUCTION 180 LAB K = 1100 120 (DEGREES 0 60 C.M. PION ANGLE 180 107 F. CROSS SECTIGN - CUB/SR) DIF 12 10 }- 12 10 PT MINUS PHOTOPRODUCTION LAB K = 1075 L Q 60 120 180 C.M. PION ANGLE (DEGREES >) PI] MINUS PHOTOPR@DUCTION LAB K = li2s i) i 120 180 0 ~ 60 C.M. PION ANGLE (DEGREES) FIGURE 11.6... DIFF. CROSS SECTIGN - (UB/SR) DIFF. CROSS SECTION - ¢UB/SR) 12 10 uk 12 10 108 PI MINUS PHOTGPRODUCT ION PI MINUS PHOTGPRODUCT ION 7 T LAB K = 1175 1 T 12 LAB K = 1150 7 Cc { 4 M 10 F- ~N jam) a L - 1 ek Zz 2 Oo 6 Lis ice) ica) SB oy x . oO i 0 60 120 180 0 0 C.M. PION ANGLE C DEGREES > C.M. PI MINUS PHOTOPRODUCTION 7 T - 12 LAB K = 60 120 180 PION ANGLE (DEGREES) PI MINUS PHOTGPRODUCTIGN 1200 DIFF. CROSS SECTION - (UB/SR) 102) 1 8) 60 C.M. PIGN ANGLE (DEGREES) C.M. 120 t T LAB K = 1225 180 0 | PIGURE 11.7 0. . 60 120 180 | PION ANGLE (DEGREES) DIFF. CRESS SECTIGN -— (UB/SR) 12 107} - 109 PI MINUS PHOTOPROBUCT ICN LAB K = 1250 i 0 60 120 180 C.M. PIGN ANGLE (DEGREES) . FIGURE 11.8 110 FIGURE 12 ENERGY DISTRIBUTIONS OF FINAL 1 CROSS SECTIONS (at rough angular settings) lll one o~ oO rad H — Li ole 54 CO sgroored Hi oa iT: 5 wed | 5 2 i j : i VV 0) puss Cc MS god | Se bi i M i Y i RN aA 5 RODUCT IGN i 7 £3 a i 30i i. et | . sored cr an teh . — tH gf OW. coe Perea dS Poms wot (3 —E}—-} C2 a ae 5 meee , | CD — [orm Bmoned ery CG j \ _t € perl O 9 a CO may c3 at ray = ed CYS/SA) NOILIAS SSAYO * 41d FIGURE 12.1. - ©) ome 112. 4 > m™ Cds co /‘ ™ vend cM) NOLL ELGURE 12. 2. CO AS f = SSM ‘asl 4 ORM i3ca 1200 1100 a) C5 A 3 113 ary i i | i a a hESH “ oe | LEH ™ - Ea i) _ a i 4 ae) ea a - — we em wou, i “ ED Teron Ec Qn. Pa] a C2 aH (EH ane ber es PEt Ped aves i here) van L. | j L.: =i Cp ce) iN co = oo OM a | wend word US/arl) NOTLOIS rev 12.3 sso * J41¢ (2 Rd ead ED C3 cad i i i 1 | oy spree tc) Ol 2 fen wt cm . CS wet ‘a o 4 pom roa | - {3 Zz RH io bEH 2 be cp AN me : _ a { | | , H a) (2 ate) ran oe) =f! cD ON} ; wet md cusyarly NG QLLI3S ssoyo "ATL FIGURE 12.4 * panne nae reve | icy El E] hEH EH a FS] a) HEH 1a (EH =" ™ a ™] (9 aS | word speed CuS/arl) NOLO . FIGURE 12,5 oO ~y C AS SS ae J °: itep 05 (Ye Lid whee Lat = cS — — seve 116 cae CO <8) Lal -E- Es fd ' sped t ssameane Lo rcrmeercens| i tas J iz i | > 2 oO tO xis CYS/or) ) NOTIIIS FICURE 12.6. 2 apex | weed sen ae ae) bd even C2 ae (i (i. ae —_ a) W) Pana LL7. ae oe oO 3 “it arly NOTLOAS Sse FIGURE 12.7 is ee iN} Bias Bs areas, © (2 ond aged) 8) i) s i ae 3 ae ae) AAT MEV? é i H many one CF} a, homens foot ne oo 118: iad belt ta beat ° Ee ERI Jonditan} poof | i t i. Od word ae OO ee] = rend CYS/SP) NOTLOSS FIGURE 12.8 ; ™] C> SSH * aald OOTY Ldwis c os) anew oe) c) 05) RY Lob ik 3 8 j L119: ae 4 3 CY ; good uu | Q | vod 5 aod cc “ > . Q = ga snd “> es | te a fo - Sm bmn &) . MH ti , ‘ i A | | lo AL wb | Ria “) era ee : pa nomen foves {towed femetipemed rat i ! \ ! | 4¢c9 Cul cy. ae) wo aru aN ae) 7AND NOTIIAS SSOMQ * Aid FIGURE 12.9. 120 7) . goo ol ea on) C5 hoy wa — C Ss eo my Nd” ee . a near ra foro ve & fermen Cc e ie ON ec Oo tO ai m™ 3 . FIGURE 12.10. pete Keer eens Fy 121 ford MEH | El—I bon Ed | ! in] Ba ~~ 2 nd coud om spo] CO O HS/SM) NOTLOSS § .. FIGURE 12.11... . a) Cc spun good AW ei iw ca ja ae = ae 300 7UG —) | ED oe) ™ ae QYo “44d 122 on word agreenh AAA) M ASRS) Wn] is) 1s got and —_ am SF = a pm i?) = ois E32 in being i MILE MOT POLIS ING NOTE WD eral oe | eI bb} Snes £ enw E z ahs as rT i i fH 3 3 on 234 t wid D a) ans om x3 ron pod JAC ce shel ce SS ¢ i Jal pa sree FIGURE 12,12 2, aaa Awe femal QL 123 Det ace CS ne) yond ™I eon wnt Tp) CHS/EM) NOT 19a . FIGURE: 12,13. } wre di Cc Ow vod quer am cry aes a, 8 me) ay, and msm gy ove 2 tm 124 ™ yond i i a) geod Pehl ene = wet ke 7 | Vee Al @ | tH = . tH : en) . LJ | bet nf © wns Pan | Bon _ ea i) > S hel =| 3 pone) cd vt podbot n pom ned ot fo bE : boiled |. sveeaef fone wd oe ee “3 | '.) a i a) te > 8) ce a m™ co NBT Ss 125 TABLE 6. 1) Total + Cross Section _ 2) 0° + Cross Section > oO ~~ 3) 180° wt Cross Section. from Moravesik fits of final m angular distributions. See Ph.D. Thesis by Patrick Walden. 126 lab cat) Coe eee o(0°) Ao(0°) (180°) Ao(180°) 600.0 93.63 1.63 23.49 1.00 . 7.62 0.37 620.0 94.48 1.77 23.74 1.02 7.72 0.34 640.0 93.28 1.65 23.49 1,02 8.30 0.38. 660.0 96.15 1.64 +24.33 1.09 9.15 0.40 680.0 97.98 1,64 22.67 1,23 8.67 0.39 700.0 96.64 1.60 23.91 1.25 9.98 0.75 720.0 91.15 1.58 | 20.22 1.04 9.43. 0.86 740.0 81.65 1.63 16.87 0.94 7.98 0.95 760.0 68.72 1.68 16.63 0.92 7.91 0.67 780.0 58.43 1,01 16.04 0.69 6.96 0.51 800.0 49.96 0.93 14.30 0.52 6.84 0.59 825.0 41.46 0.83 13.12 0.51 6.55 0.78 850.0 35.31 0.74 11.61 0.48 5.65 0.67 875.0 32.05 0.65 10.50 0.72 4.72 O44 900.0 31.73 0.74 9.66 0.72. 5.21 0.46 925.0 30.15 0.60 8.71 0.66 5.39 0.39 950.0 28.18 0.68 6.60 0.76 4.71 0.46 975.0 28.56 0.76 6.56 0.63 4.35 0.48 1000.0 28.84 0.72 7.03 0.65 4,56 0.41 1025.0 27.49 0.64 6.26 0.61 4.29 0.37 1050.0 26.16 0.70 6.85 0.71 3.53 0.34 1075.0 24.06 0.91 6.82 0.41 3.20 0.34 1100.0 23.03 0.76 7.32 0.45 3.01 0.40 1125.0 20.88 0.57 6.21 0.46 1.89 0.13 1150.0 18.71 0.42 5.82 0.37 1.53 0.13 1175.0 16.11 0.56 6.50 0.44 1.30 0.15 1200.0 15.17 0.44 6.00 0.43 lll 0.16 1225.0 14.41 0.44 6.13 0.42 1.49 0.23 1250.0 13.54 0.49 6.01 0.44 - 1,26 0.22 127 yevirst (KGW). LOWINZ NOLOHd SHI cools CS to to eos rel to! tol bot | A 4 I NOTLONGOYdDLOKd -Id NOILOGS-x “1D! On 09 iD ™ SSB x mM NOL LO (eh) FIGURE 13 128 18 21A37 . 1900 BQ0 NERGY (MEY) E 600 AB PHOTON i> a ke} 4 tt bel bol 4 WY) rol Li} rot CO}; bet ; Hs be ho CO bot © bot . > -o-| & tH -~ — ke Cor KH 4 a) bo-| Ss to ro fr bot ea f poo a t—- to &) t-o--| I to~-! Oo bof 17 f-o—| + 1 J. L } I a) LM LA a) LN op) aN Ol — aan ("HSLS/EN) NOTLOIS SSB FIGURE 14 I on 129 . FIGURE 15 ( 1 i v t = bot 7 bo-! lam) et bl Ud + b-o—| LJ om bed | iJ ‘b-ot lan , set CS 0O b> © + bo Lid © p—o-—-f — a > ~ oa ayes or bot 7O oc a) t—s-—| Oi om) bea omn| a ra }——o-—---| Lid i bg] = a5 + }—-o-—- S b— boi — a) b=} a) J bom ae 7 nal of . Lome (2 | cm) o -~t L J. } 1} { O MO QD’ CO =f aN yl soot . (“HALS/EN) NOTLOSAS SSOYD 130 Jd. Comparison with other experiments. Since the present experiment was started, the results of several other 1 photoproduction experiments have been published. Comparison of the results of our experiment with these new data are given in Figures 16, 17, 18, 19, and 20. The total cross section for the bubble chamber experiment of Hilpert et al. (38) (Figure 16) is in good agreement with the total cross section obtained from the Moravesik fit of our ‘data. Hovever, some of the differential cross sections from the bubble chamber experiment disagree with ours; these occur mostly where very few events were observed in a given energy- angle bin for Hilpert et al. and thus where their statistics were very poor, | The bubble chamber experiment done by Lodi-Rizzini et al. (37) is in poor agreement with ours in the region just above the second resonance. The total cross sections are compared in Figure 17. The drop in the cross section above the second resonance has been displaced downward about 50 MeV in the bubble chamber experiment. This disagreement, as yet unexplained, may cast some doubt on the partial wave analysis of 1 photo- production in this energy region, especially on the values of the Sll, Pll, and D13 resonances (see Part V). 131 Comparison of the results of Ito et al. (40) at zero degrees with the results of the Moravesik fit of our experiment at this angle is given in Figure 18. The agreement is very good except perhaps at 1100 MeV where the discrepancy is about three standard deviations. fa) at 90 oO The counter experiment of Beneventano et al. (39) is compared with our fit in Figure 19. There is a slight disagreement at about 620 MeV. Since we had a couple of anomalously low points near this energy, I am inclined to believe the data of Beneventano here. Finally, the results of Fujii et al. (11) at 180° are compared with our fit in Figure 20. In general Fujii's results are higher than ours while also showing more structure. The resolution of our experiment was very poor at 180° and this explains our lack of. structure. However there is still probably a slight normalization disagreement between the two experiments. The results of Fujii et al. have been used in the partial wave analysis of 1 photoproduction described in Part V.- 132 9tvirsi 0021 (A —“H ah L9WIN3 NOLOH 008 J i me IL L NOTLONGOYADLO Hd ~Id NOTLO5S-X “LOL On 03 O8 00? ‘Oct NOTLOSS SSOYD (S11) 16 FIGURE 133 stviret (ASW) 008 LOYSNI NOLOHd Sd 00g T NOTLOINGBYcaLORd “Ig NOTLSS-x “181 09 08 O01 Oe 4S SSOYI Jz ~ New NOI! (af) 17 _ FIGURE 134. sevirsl MI sored (ABW) AQH3NZ NOLOHd 887 008 009 is Ly GO © NOILINGGUdDLOHd -Id C3 De 2) We S cp) NOT LO: (HS1S/e8M) 18 FIGURE 135. wort (ABW) ASY3N3 NOLOHd 887 Wlareal 0001 008 OOS P ic - vi AT faa y 7 oli L | ~~ [ +Q Ol : ra £ ~S33H930 06 8 NOILINGGEYdOLOHd -Id FIGURE 19 136 (“H3IS/8M) NOTLOIS SSOuD H ¥ ¥ T 7 n 7) r C Al ved 1 , fa LJ. 7 1 nw > > } = a) (> xo} CO wed _— > @r Lid = ww ) ht a bt MC! (or 10) om a) COL ‘am wl > ti On. OW | = bk te 0) gm a ia x Oo. S) OW. | me aa mH cr o dt OU we 137 PART V PARTIAL WAVE ANALYSIS The large amount of new data for single pion: photoproduction from this experiment and others will help in the determination of partial wave amplitudes. An analysis of the three reactions yp > nn, Yp > rp, and yn > ™ p has been made by Walker (3) based on data taken before 1967, r will present here a refine- ment of Walker's analysis for the first and third reactions which uses some selected data taken up to 1971. A list of the experiments included in the analysis is given in Table 7. An attempt has also been made to analyse the second reaction Cyp > rp) but the results have not been clear cut due to disagreements of different T° experiments. Work on the analysis of these single pion photoproduction reactions is being continued by William J. Metcalf and Robert L. Walker. In my analysis, the new polarization and asymmetry data have a large effect on the partial wave amplitudes, especially bringing into question the amplitudes for the S$, (1535) and P1470) resonances, In the 1 reaction, new amplitudes will be given for the S,, (1535), D,,(1520) (helicity 1/2 part), and the F 5 (1688) + . . . . resonances. In the 7 reaction, new amplitudes will be given 138 TABLE 7 EXPERIMENTS USED IN PARTIAL WAVE ANALYSES 1) w photoproduction a) Scheffler and Walden (52) - cross sections 600 - 1250 MeV. b) Fujii et al. (11) ~ 180° cross sections. c) Neugebauer (36) with Thiessen (7) ~- cross. sections at 510 MeV. d) Beneventano et al. (42) - 90° recoil proton polari- zations. Interpolated, e) Metcalé (43) - 90° recoil proton polarizations. Interpolated. . f) Kondo et al. (53) ~ 90° polarized beam asymmetries. Interpolated. g) Alspector et al. (20) - 90° polarized beam asymmetries. Interpolated. + . 2) w photoproduction a) Betourne et al. (5) - cross sections 400 ~- 750 MeV. b) Ecklund and Walker (6) ~- cross sections 600 ~ 1270 MeV. c) Thiessen(7) - cross sections 500 ~ 1250 MeV. d) Fujii et al. (11) ~ 180° cross sections. e) Hahn et al. (19) -- 60° and 90° recoil neutron polari- zation. Interpolated. iter. ‘f£) Grilli et al. (18) - 90° polarized beam asymmetry near 400 MeV. Interpolated, 139 TABLE 7 (continued) g) Liu et al. (54) - 90° polarized beam asymmetry. Interpolated. h) Alspector et al. (20) - 90° polarized beam asymmetry. Interpolated. i) Althoff et al. (28) - 40° polarized target asymmetry. Interpolated. 140 for the P,, (1470), Fy. (1688) (helicity 3/2 part) and perhaps the S,, (1535) resonances, A. Model for the partial wave analysis. The model used is the same as that given by Walker (3). The relatively poor precision of photoproduction data, combined with the small excitation of higher partial waves in the energy lab region of interest (ky = 500 to 1300 MeV), precludes any ‘reasonably precise determination of partial waves for > 5/2, Jtot Instead of setting these equal to zero, Walker sets them equal to the partial wave decomposition of the electric Born approxima~ tion (see Appendix VII) which is (perhaps) closer to reality. In any case, these amplitudes are small for Jeot > 5/2, Also, the electric Born approximation is known to have roughly the same qualitative behavior as the photoproduction cross section (eg. the forward peak for 1 photoproduction and ‘the forward and backward peaks for 1 photoproduction) so that the Born terms are also added to the lower partial waves to try to reduce the background. The parameters of the fit are then the extra lowest partial waves Geot = 1/2, 3/2, 5/2) which are added to the Born terms to give the best fit to the experimental 141, data, . Walker divides these extra lowest partial waves into two parts, resonant and non-resonant. Using the N and A resonance widths and energies obtained from 1N scattering analyses, and Breit-Wigner forms for the resonances (Appendix VII), he then determines the resonance amplitudes which make the non-resonant (background) part of the fit as small and as smooth as possible with energy. Explicitly, the parameters of the fit are the resonance ° amplitudes (helicity 1/2 and helicity 3/2 parts) and the extra | add-on helicity elements A, and By which are added to. the Qt t electric Born terms and the resonances, The total helicity elements Ans and Bos are then obtained by summing the Born contribution, the resonance contribution, and the add-on helicity element contribution. The definition of the helicity amplitudes and helicity elements are given in Appendices V and VI. The helicity element Ags is the amplitude for an initial state of total cM helicity 1/2 (in the photon direction), total angular momentum Jtot = 2+ 1/2, to go into. a final state of orbital angular momentum & .(parity -(-1)*9, and total angular momentum Jtot = Rt 1/2. The element Bos is similarly the ainplitude for an initial state of total helicity 3/2, total angular momentum 142 Soe = 2% + 1/2, to go into a final state as above. Note that the amplitude is not given for a final state of definite helicity, but rather of definite parity (or equivalently of definite orbital angular momentum). These amplitudes can then be used to describe resonant behavior, since the resonances have definite parity. The (initial) helicity 3/2 (Bo 4 and helicity 1/2 (Ay) components of the (resonance) amplitudes are linear combina- tions of the (perhaps more familiar) electric (Ey) and magnetic (M44) multipole components which were introduced by | CGLN (51). Expressing the E M,, in terms of the Anas B RE? Rt Qt? we have: -@+iy tc Boe gy + 7% Bed Moy = (e+ 17 (Ay, - (2 + 2) By) . (v.12) Eger THAD © Acar 7 2G + 2) Begyy_ -1 1 Moyer FD Acer + 7% Bengt) For further orientation, Table 8 gives the properties of the lowest order helicity elements and their relationship to electric and magnetic multipoles. etTodnjz [9 *3eK on W € € + ejTodnapend *osTy Za te 4o YA T+ Z/S € eg ety eTodnqo9 ‘*oeTY oF +o € € eTodnapend °Sey rant ant 2 z T- Z/S Zz Fg ety eTodnapend °*3ey ZH: ~t Z Z eTodtg ‘oeTg 1a “ey I I- Z/€ Z eg «by etodnapend ‘ery ZH Teg z _ etodrq *SeK IK thy ul T T+ Z/€ ( Te ctly “ etodra "SPH Tx wh +! T T+ Z/t KO vty eTodta *2eTH 1a Ong i I- Z/t 0 oy eweN eTodyItnN “F780 Ac ge FOF e Ae (I-)-= @ 704 $s RUSS TT eTodtaqTan NIOO d : epodTaran % AQTAeg unjUeUOX wnyuewoY AQPOTTOH (wo ,0Ug) aepTnsuy ae[Tnsuy JO wnjzUSMO;{ Ter0L TeAFato repTnsuy Teura SeTodTaTnR Of_@eusey] pue WrAVoOeTY oF 8 Alavi Sjueuety AIpoOT[eq go drysuopzepey 144 B, Fitting procedure. | Walker's fit was done essentially "by hand", That is, a set of parameters was chosen and the calculated. cross sections, polarizations, and asymmetries were plotted for visual comparison with the data. A table of first derivatives was — printed to determine the first order effects on the cross sections, etc. of small changes in the parameters. Then the parameters were adjusted according to the effects of their derivatives to improve the agreement between the fit and experiment. This procedure wes done at many energies (roughly 50 to 100 MeViapart) and an attempt was made to smooth the energy dependence of the add-on helicity elements and still keep a fairly good fit at each energy. The smoothing is part of the model and is justified by the belief that the true amplitudes are smooth. The smoothing was necessary because there are not enough data to determine all the parameters very well at each energy. A free energy by energy fit would in some cases cause large variations in the parameters because of statistical fluctuations of the data. ‘The above procedure was very tedious and time-consuming, but nevertheless has given a set of helicity elements and resonance parameters which fit the available data very well. I have written a computer program which will adjust all 145 the parameters automatically by minimizing " at each energy. The procedure for minimizing 2 is described in Appendix VIII, The main problem in fitting the photoproduction data was to find a way to automatically smooth the data with energy. I have tried two methods: 1) In a grand design to fit all energies at once, the add-on helicity element parameters were approximated as polynimials with respect to photon energy. For example, A,, (k) i$ was given by; _ La 2 A, 4.(k) = C0 b Ck + Cok (V.2) a second order polinomial in k described by the three parameters c,c 6 and C,. While this method may yet work for small 1? 2 energy regions or larger order polynomials, I had much more success with a second method which I now describe. 2) The initial set of add-on helicity elements (the initial parameters of an energy by energy fit) were treated as experimental data points and were assigned "errors". These artificial data points were included in the calculation of vor and thus the fitted add-on helicity elements were prevented from departing too far from their initial values. As an initial set of parameters (add-on heleicity elements), I used the final results of Walker's analysis, Assuming that the initial set. of (smooth) parameters is close to the true parameters, (his method seems to be a good way to constrain the fitted parameters to be relatively 146 smooth with energy and is also a good method to observe any resonant behavior which we have not yet removed from the add-on elements. Any large deviation of the fitted parameters from the initial set probably represents a real behavior of the helicity elements, since they are straining to increase the artificial part of 2 while the total 2 was reduced, Any observed resonant behavior in the fitted add-on. elements should be removed and added to the resonance amplitudes. s C. Results of partial wave analysis. 1) « Photoproduction, , Some striking behavior was observed in the initial fit of 1 photoproduction using the second method described above. The initial values for the add-on elements were set equal to the final values of Walker's analysis. The resonance parameters were set equal to Walker's with some small changes in the energies and widths. - The data used in the fit were taken from . the experiments listed in Table 7. The results of the initial fit are shown in the ten “are the initial set graphs of Figure 21. The plotted points. of add-on helicity. elements (Walker's /final values). The jagged lines are the program's fitted set of add-on elements. 147 Also plotted for comparison are the resonance amplitudes and (in some cases) the decompositior. of the electric Born approximation for the particular helicity element (see page 148 for key). . A striking resonant behavior is observed for the Ag. add-on element (Figure 21.1), which seems to want to cancel the given resonance amplitude due to the 8, (1535). (For a list of the resonances and the helicity elements they affect, refer to Table 9.) The resonant behavior of the add- on element is shifted down by about 40 MeV, which indicates that perhaps the central energy used for the S 1535 MeV, 11? is slightly off. This new behavior disagrees with the quark model prediction(2), which supports a large negative amplitude, in agreement with Walker's value. Another fitted add-on element with a possible resonant behavior is the Ay_ (Figure 21.5). The resonance corresponding to this element is the helicity 1/2 component of the D3 (1520) which is located at a photon energy of about 760 MeV. The real part of the fitted add-on amplitude has a strange behavior between 600 and 700 MeV, but it does decrease rapidly at the resonance energy, a behavior which is characteristic of a positive resonance (see Appendix VII). Walker's analysis was unable to determine any definite finite value for the helicity 1/2 component of the D, (1520) and so it was set to zero. The present fit, perhaps, wants to give the A, resonant element a definite positive value. 2. 148 FIGURE 21 INITIAL FIT OF ADD-ON HELICITY ELEMENTS FOR 1 PHOTOPRODUCTION The Figure, consisting of ten graphs, is a little confusing on first glance; so a short explanation is given here. There are ten graphs for the ten lowest order heleicity elements: Ang. and A Grot = 1/2); Aya> Buys Ay_s By_ Geot = 3/2); Anis Boys Ags Ba Cirot = 5/2). Refer to Table 8 (page 143) for the characteristics of these helicity elements. As described in Section V.A on Walker's model, the total helicity element is composed of three parts: the Born part, the resonance part, and the add-on or background part. In my fit, the Born part and the resonance part are initially set and are not varied during the fit. The add-on part is initially set to ' ‘ : tae i eto ae 2 Walker's values and is varied during the fit to minimize y™. Figure 21 is a plot of four distinct quantities: 1) A continuous plot of the Born part of the particular helicity element (line identified by #.). The Born amplitude is completely real. 2) <A continuous plot of the resonance part of the particular helicity element (curves are identified by © for real part and & for imaginary part). Typical behavior of a resonant amplitude is given on page 239. 3) A set of points showing the initial add-on elements of the fit. These are taken from Walker's analysis. The real part is given by kf and the imaginary part by + 4) <A jagged plot of the final fitted add-on elements. The fit was done at energies 510, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 825, 850, 875, 900, 925, 950, 975, 1000, 1025, 1050, 1075, 1100, 1125, 1150, 1175, 1200, 1225, and 1250 MeV. A continuous (jagged) curve was drawn through the points’ at these energies. The curve for the real part is identified by 4 and the imaginary curve is identified by Y 148a The interesting point is to compare the curves 4) with Walker's points 3), to see how much the fit wanted to change the add-on elements from their initial values. Remember that the fitted add-on elements were constrained not to depart too far from their initial (Walker) values by the artificial errors assigned to the Walker values (see page 145). The artificial exrors used in this fit were +.2 for the Jeot = 1/2 elements, +,1 for the j “tot elements. For convenience, the artificial error is shown on the left = 3/2 elements, and +.05 for the Jeot = 5/2 of each graph. Note: for a list of the resonances and the helicity elements which they affect, see Table 9, page 161. © C |p JY in L ld 4 memes y NGI 149 Tesy on oe , TE HLITNI PY LT OLit Li] CASA ASYSNS NOLGHd Yo) nt 00c1 OCOT C08 008 0Ch . O0¢ OA. t i \ 5 i { ono (@ATIeSeU) oTeos Jyo st qaed uzog iqzed BouSuoSey . or eu su roaren on L TEOe ~~, peustsse FT a 1OA1y i 5 i 4 a a ae See i 2. 4. a wee DK AreUTZEUT ; l oe | omens re \ ane eatery se 4 Axeureenl neem T ne UX = c" ‘a | to-ppe poastd | : A eK st Fam “ Nana A [3 no) Jd aa NO FIGURE 21.1 i saa e a. Se O"¢ ae © ) C4 on +f -) ‘an OL. b—~} Ob 150 | oe) (AAW) ASYSNS NOLOHd Ont O01 O0C} 008 O09 Con 00¢ i j i] } i i (OLYI)ITd ~ roo i i ‘ TTS j x x i 4 x on x x x K x ‘x x JuUd AUUNTOURT ot ittd WEY ° i { } i i a 4 Qo L ! s/arh) LNSW313 ALTOL ISH na) © ol! i {\Ce cot ~~ C FIGURE .21.2-- - 151 CASW) ADdaNa NOLQHd dol OO! 00} 0001 003 O03 007 _ 0 a I - , (9¢z1) © | | Ls + ud AUUNTSUNI idud “Way EETTIVM XC ++ i 7 NO-Q0S =t+le d-lId JINSH ¢ ao Wa Js ALL 3 © vd aa oti “LIN FIGURE 21.3. . LL VW ASS =F w © Nex C CASW > ADdaNa NOLOHG Gut Al OOdT COT O08 009 oon 00d oO ., a —— f S"T- (9ez1) **a = O'T- 152 NSW _ FIGURE 21.4 tt 32 re - dibd AUNTS d “ ited WWay x RRNIVA i i NO-Gd8 = +18—Ss did a ALTOID TSH ‘ ? ™ 2/ TCS = od Ooh — O0¢ CARN ADGANS NOLOHd 8b] ~~ 0 i 4 coz9t)®*a cozst) © Fa | | 153 K Hy x a 3 R x x pth NF iutd ASENISENT + SOUT iubd Wau i : j i. a . ( C3 an | ™N Cr 0... | by OW. C2 JI 14H o Ne J AL Jarl INSWIL -.. FIGURE 21.5 ™ ane) H C/ IC — a) © 154 CASW) 0021 O01 oc i 1 j vv (ozot) *£a (WHS AMBNTSSKT aa 300G ACUNiVOIS i - WaT ant such es idd Wad { i NO-O08 O° i- S*0- ome ALTOI SH : ~ Z/ICYS/ENY LNSWST _ FIGURE. 21.6:.. ™ a wont -) CASW) ADGSNS NOB dbl C3 © © 00d! O00} 008 O09 COOH 00d © i H | (oz9t) *ta | i | =~ WVO- _, | J N 1 ALI | | ‘ | < <4 Po X 155. bof © © eel 3 oe —heirieink * Jah) LN: CN Oo » C/1Cd - FIGURE 21.7. 156 NOLGHd do | OonT 00d) eeien COn 00¢ 0 T T T —~F ARCH OE (0291) 2! a ikud AYENISENT = + lutd Tse HIV j i i H NO-O03 +¢ q hi’ O- c'0- cme i 6°70 = © 3° 0 AH Ata ALIOI | | Nee | pa : . FIGURE 21,8 C7 D/ a LACS C 157 © a vel CASW) AQdSNS NOLOHd Go N\ C01 O00 t O08 OOS OOh 00 j [ i j i (ego) 2h a Iuud AUUNIOUNT = + iusd We - METIVM A i L mj NO-Cgu EB d-Id © ALIOUTSH ° Az Jari) LNW —™~ S | J C/1Ce FIGURE 21.9. - 158 0OnT O00T 4 NOIGHd OOn au | 00¢ 0 © 1! (8891) Vs 359 i 7 pt : EAA we aS we KX JUUd ABUNISEME + yayayn ikud TWsu x j 1 J i i | IO —CO i— 7 IB-GG cd d-id 9° O- tl rm mn O- ov) — < gc O- m7 — Pil a — 00 = i “oN we) aa wed OO Nw? —s Ze ™ AO NO FIGURE 21,10 159 Finally, this + fit seems to want to reduce the amplitude of the Be resonant element (Figure 21.10). which corresponds to the F (1688) resonance, helicity 3/2 component. The quark model (1) predicts that this resonant element is zero, and it is interesting to note that the fit is pushing the Ba amplitude in the right direction to agree with the model. However, the amplitude apparently does not go completely to zero. The smallness of the B 5 (1688) in this analysis appears to be directly related to the smallness of the w cross section compared to the ne eross section at Ke = 1000 MeV. The Ay add-on element (Figure 21.2) wants to add a sig- nificant imaginary part in the region of the Py, (4470) resonance. However, the real part of the add-on amplitude does not have the correct behavior for a negative resonance amplitude, and thus a resonance interpretation of the add-on amplitude is dubious. T have set the initial value of the Pid resonance to ~0.250 instead of zero as in Walker's paper. Walker had the same problem with the P and he noted that the A 1 resonant amplitude was j- poorly determined for 1 photoproduction. In any case, despite -my insertion of the resonance and along with an already negative add-on amplitude, this fit wants to add even more negative imaginary part. There seems to be very little resonant behavior for the and B yhelicity elements (Figures 21.7 and 21.8). Thus, f Ags 2 leave the amplitudes for the Dy 5 (1670) resonance at Walker's values. 160 Furthermore, the data are too poor to determine any definite amplitudes for the 84, (1650), Dy (1670), and 8, , (1700) all of which were left out of Walker's analysis. I have done a final fit with changes to the resonances as given in Table 9. Plots of the add-on and of the total helicity elements which resulted from the fit are given in Appendix IX. The cross sections produced by this fit are the curves plotted through the final angular distributions (Figure 11) of this T experiment. The fitted proton polarizations are plotted at 90° for comparison with the data in Figure 22 while the fitted beam asymmetries and experimental beam asymmetry data at 90° are plotted in Figure 23, The fit to the asymmetries is very good while the fit to the polarizations is as good as can be expected with the poor consistency of the data. It should be noted that the smoothness of the polarization and asymmetry fits is due to the fact that interpolated smooth values of data were used at each energy of the fit. OSé=l “9 “0 “0 Oy The <4 (COLT) N Q0Z*0- 00S'O- Sz¥°0 ~—-00S"0=: 009"0- ae corel “9 “0 “0 “ty sts Zs (9991) 8 . . . -Z * ° me ° 2. €€ ZZ seem "0 "0 "0 V a ee COL9T)V TyT°O —-OOT'O- 1YT°0 ree a . un. +2 ST Zz O7t=d 0 @) a) Vv a CT COL9T)N ~ OSt=d - “0 “0 - + 10.5 Te, ££ — vogat)y Z Te oi j= (nem ; , , . ; +0 i zz aay VOW OZST) OSZ°0+ O008°0- 097°0 é 0S9°0- V S i (SEST)N OST*I- 0%6°0 Oze"T- “Cg octet ooo fo ont . ~Z EI Zz ) 7T°O 007°0- V qd CT (OZSTDN . - yg: o€z=l i ‘0s LLT"0.-~—s-0070~ 0SZ"0- Ly tT, ge (OZ¥71) N a OS7*t- Oe E- ogy z- te ovtez O00°l = viv"T 000°T thy ees ££ (eztv ee 312 aexTem aexTeM Jia aeoxpTem JUolieTy UWoTqaeustsegq TL soueuosey STUL sTuUL $a TOT 18H d v oY iy 6 GTaVi 162 QO WING NOLONd eT ont COG t OOoT 088 O08 Och 002... I i 7 Ort- r oe 7 eo } it U a A oe rc pot F : =| 8°0- i L - Loy 4 ee Gof tn | aL 7 906 = eT8uy uota KO: = ho ~ —“ 3°90 (€7} FTBIIOW .- szutog uedo = (z7} "T@ Je. ouequeAsueg - sjZutog y7eq — 2°09 i { i H | etd | VWO0s" ldo ld NOLO: Se NOT LY 22 7 a FIGURE 163 uh? COST GOCT 08S OOS OOT Oe i \ [ i i _ - | b a: i i | j i. 906 = eT8ty uota WO 4 i i (027) "Te 29 xoqoedsTy -. sRUuTOoOg usedo oot a i i - (es) ‘Te Je.opuoy - squtog y2e¢ “ 4 i i i i i IOT LOMO EO COAITEY To NOTLOACGYdBLOHd SANIW Ta ort IZIdv bd AYLAWNWASH L. dbl Q Bh 23 t FIGUR 164 a) The zero degree cross section. The zero degree cross section obtained from this fit and the one obtained from a Moravesik fit (Figure 13) are almost identical, The main characteristic of the zero degree cross section for 1 photoproduction is the sharp dropoff at am = 700 MeV. A possible explanation fon this sharp dropoff is the interference of a positive resonance (real part) with a positive background (real part) or of a negative resonance with a negative background, While this may be partially the case, my final fit seems to indicate that most of the dropoff is due to the add-on (background) elements. This clouds the physical interpretation of the 0° behavior of the cross section. Figure 24 is a plot of the total helicity amplitude Hy (see Appendix V for the definition of the helicity amplitudes H,) at 0 and of its various components. The total real and imaginary parts (square and "x") both have the above behavior at 700 MeV, although the behavior is not so striking in the amplitude as it is in the cross section. The interference (sum) of all the resonant components of the helicity 1/2 elements (Ay) produces the resonant component (real and imaginary parts) of Hy (octogon and "cradle" curves) which has a slight dropoff effect. The interference of all the add-on components of the helicity elements produces the greatest dropoff, especially in the real part ("diamond" curve). 165 C (j2ed AavuTsewy) Jueuodwoo uo-—ppy (qaed [eey) QuouodwoD uo-ppy (qaed AzeuTsewul) Jueuodwoo soueuosey (,4ed Teoy) JQueuoduos soueUOsey (aed Teey ATuo) jJuUseuodu0D uz0Og (32eqg AzeupTsewy) Teio, (qaed [eoy) TeRIOL TTL AH fear Qo» nx dO ca tO JONLT Ade AL] anom Md C3 CO 2/1CYS/ END C3 on wel FIGURE 24 166 It should not be surprising that the main component of the real part of H, at 0° is that due to the Born approxima~ 2 tion (triangles) which is characterized by a forward peak. fo. b) The deuterium cross section, After fitting what we hope are the true neutron cross sections, we can calculate what the deuterium cross section should be from the final state model of Chew and Lewis (45). The relationship between the deuterium cross section, neutron cross section, "spin-flip" cross section, and "spin-non-flip" cross section (see Appendix V) ts illustrated in Figure 25. The spin-non~flip cross section goes to zero at forward and backward angles while the spin-flip cross section approaches the neutron cross section at these angles. The deuterium cross section is reduced at forward angles and gradually merges with the neutron cross section at about 60°. A comparison of the deuterium cross section calculated from the fit and the deuterium experimental cross section data at 10° is given in’ Figure 26. The agreement is excellent except at the lowest energies. This leads to the conclusion that (at least above 650 MeV) the "ratio" cross sections are probably a good approximation to the true neutron cross sections, Also, most of the final state effects seem to be accounted for by the Pauli exclusion principle. _ 167 PI MINUS PHOTSPRODUCT ICON 12 LAB K = 900 W= 1604 —-~ Free Neutron Cross Section & Deuterium Cross Section & "Spin-flip" Cross Section GO "Spin-non-flip Cross Sectiow 0 60 130 180 C.M. PION ANGLE (DEGREES) FIGURE 25 168 KTH PAYLITIAUT ATM EOELE 2 GT CASWD ADEANS NEL So | mot FT OTT ate: ane MD Os Rate on are Web O02 Wish + Boot WS C8 Lue. UUs BOS ILI a ~ quowTpaedxg stu worzy (peqoorep [Tuo wotd) suoTq#oeg ssoig 4 - sjutOg e7eq _ ~ j REX WOAZ UOTIVVg ssOAQ WNTAaQNEe - sAAINg azanoy ‘ ATTY Worf woOTWoOeg ssoig UOAGNSyN vezZ - eaArng azsddp Ol FDISNH NOTA °W°D | one 3 ONG Nulled N Oo | | I H ! i i i i i a we bn — Co) 2 | CG) om ‘om gv) |— CO - QW. gy) 4 a I 2 ne] QW. “4 cl CO wort CYS/arl) - NOTIO an ™ J4TO SOUD S AS FIGURE 26 169 2. nt Photoproduction, I have also done a preliminary fit of cr photoproduction from 425 MeV to 1269 MeV using the data listed in Table 7. Since the data for this reaction had been fairly comprehensive at the time of Walker's analysis, I did not expect much change in the resonance parameters. . However, as with the 1 analysis, there were some striking effects (Fig. 27) mainly due to the addition of new polarization and target asymmetry data, The most. interesting effect was in the A, amplitude j- at the energy corresponding to the Py, 01470) resonance. The add-on imaginary part had a large hump of amplitude equal to the initial resonance amplitude (-0.250). The real part of the add-on element had the correct behavior for a negative resonance but with a much smaller amplitude. I have thus increased the Pi, amplitude to -0.400 which is enough to cancel the behavior of the real add-on amplitude. The only other definite resonant behavior was in’ the Ba element, corresponding to. the F 5 (1688) resonance, helicity 3/2 component. A small decrease in this amplitude was indicated; I have changed the value from ~.600 to ~.500, There are two other possible cases of resonant behavior in the add-on elements. One is the significant deviation 170 ' FIGURE 27 INITIAL FIT OF ADD-ON HELICITY ELEMENTS (BACKGROUND) FOR ne PHOTOPRODUCTION There are ten graphs for the ten lowest order partial A B A B A a4? Boys 8 waves A A 3-2 Ba. o-? Aye Apps Baye Apne Bows Refer to Table 8 (page 143) for the properties of these helicity elements. Refer to Table 9 (page 161) for a list of resonances and their associated helicity elements. Refer to page 148 for key to symbols on graphs. Artificial errors assigned to the Walker helicity elements are shown on the left of each graph. They are +.1 for the j = 1/2 elements, and +.05 for the j = 3/2 and j = 5/2 elements. The energies used in the fit were as follows: 425, 450, 475, 500, 525, 550, 603, 635, 663, 698, 733, 772, 813, 857, 902, 977, 1002, 1028, 1056, 1102, 1131, 1174, 1204, 1235, and 1269 MeV. The experiments used in this fit are listed in Table 7. 5 ©) Ca on) = 171 Lied AYUNTOUNT igvsd Wy Pt ia NO-OCb Ntld J ALTOLD SH 4] wens JIN FIGURE 27,1 Z/1CHS/EN) IN 172 — OOn1 a . ABN) ASYSNS NOLOHd G01 COci_ 001 COs O09 oon 002 0. —_— 1 i i t t Coca) ta a | i i iid AWUNTSUN K+ xR \x KERR XK ied WI". VE MTV { i NO-COs —1b { Nt+Id 9° q Oo - o- “O- ¢ O- ane) z i (Oo ALTOTVSH W414 ~ Z2/1Cus/arl) IN FIGURE 27.2 © 2) fH | | CASW) ADXSNS NOLDHD Go) | eoztooot = 08s oof 002 O i Tt i | 3° 0- I coezt) © a 4 ho 173 0°O | on itd AYONTOUNT +. ittd Wy CATV ) INSWA1S ALIDITSH- FIGURE 27.3 C/1CdS/EF C = CASH) AOYINS NOLOHd By 9° 0- mi O01 O001 008 009 j; OOh — 002 0 “4 q t i T J = © I (9ez1) **a 174 O° 0 , 4 ro] usd AMONTOUNE = + lugd WEY Ga TIVM j i ; 9°0 NQ-Q06b =WN8 N+ld | JH - FIGURE 27.4 Z/1CYS/S) LNSWIVS ALIOIN =? a, OF melera i v >» ) cm Lit ZZ lit a a) b~ a OW CAS O01 O01 008 O09 id i mi (oz91) **a cozst) *ta 175 ob + istd AWONTOSWE oo ied Way og MeTIvi j 4 _| { i } font NO-ddv 9-2 N+Id @ hi FIGURE 27.5 fy INSWAT3 ALISIVSH va Ci / ) C C/1\Cu 176 OonT O0é1 0001 rT CASW) ADSM goog 00 ! OO i 3 NOLCHKd ddl g i fq (OL9T) | --(ozst)*!a — O0¢ — iddd AUSNISUNT idvd Ws ak 4 + GprIva 54 NO-GG¥ = ~zg ae {. 4 QO 8° 0- 0°O jie ca) om ct Z/1CUS/EN) LNGNITS ALIQITSH FIGURE 27.6 OQ jon comet CAaW) ASYSNS NBIDHs ob! o00t 008 009 ooh «002 i i 4 (oz91) ta | | 177 ited AUONTSUNT + ited Iie CHATVA _t NO-ddd +2b N+Id 9° O- “TC cm) n° O- O = —< Z°0- mm <a i ‘0°O0 S ~ gO ™“ C4 =e N7 . NN ThO A 9°0 FIGURE 27.7 178 oOont C0cT i ~~ CAAW) ASYSNS NOLOHD Gb i of g & Sian (oz91) Sta dued AWuNTOUNE = + ied Wey oo va a __t —_— t frosemoh smsconal NO-G0U «= +29—ié«WNT 9° Q- ISH } r Meee CO _ @ co ™ CY ee / > en 9°0 © dWald All FIGURE 27.8 CASW) ADPYSNS NOLOHd ab) 179 0021 elsien! 008 =-« gas coh §=©=6 oo 0 . 7 { + ; | 9° O- (ge9t) *ta | | J atp- wl, 2° O- ome “ 2°0 = AO iid IveNTouNT = + ivdd Way ATT i! l i i j 9°O NO-OCb eb N+Id [13H } a ALI FIGURE 27.9 Z2/1C4S/8f) INSIWIT 180 00 ibs CAsW) ASYSNS ot 008 009 ant 0021 0} «| NBLDHd SU | 00 i 00¢ 0 ——- i t t (got) ha ivtvd W3Y jet 9° 0- ¢° QO- 0°O 90 H 3 Z/1CYS/Ef) INSWI19 ALIOIN FIGURE 27.10 181 of the imaginary part of the Ao. element at an energy somie- what below that of the S, 1535) resonance. The presence of the jagged real part in Walker's solution, which was inserted to reproduce the cusp effect seen in the 0° and 180° data at the n threshold, makes the search for resonant behavior very difficult. Even so, it seems that a slight resonant behavior of the real add-on part is indicated, since the fitted solution is greater than Walker's solution below the center of the imaginary (add-on) hump, and the fitted solution is leas than Walker's above the center of the hump. However, the differences are very small and probably do not justify changing the value of the resonance. There may also be a slight resonant behavior in the Boy element, corresponding to the D1 51670) resonance, helicity 3/2 component. There appears to be an imaginary background, with a slight resonant hump beneath the Dis: The "inverse" behavior of the imaginary part is not reassuring, however, Unfortunately, there are several places where humps seem to be needed to fit the data but where no resonances are known to occur. At about 600 MeV photon energy, many of the elements have a hump in the real or imaginary parts. I have not had time to investigate this phenomenon fully and cannot make a statement as to its cause. I can only say that in 182 my final fit, where the humps are included, the fit and the data agree very well. I have obtained a final fit of the . reaction where I have used the altered values of the Pai and Fis given above. Plots of this fit (add-on and total helicity elements) may be found in Appendix IX. The final fit to the available polarizations and asymmetries ‘is shown in Figures 28 - 31. The agreement is not as good as in the 1 case, but is within the error bars. | Again, as in the 7 case, we can calculate the expected . cross section from deuterium using the model of Chew and Lewis. <A comparison of this calculation with the deuterium ne data at 10° (Figure 32) shows fair agreement. Thus it seems that most of the final state effects are due to the Pauli exclusion principle. [—E—4 bE“ 183 ye uueyq jo e7eG “= eT3uy uotd KO 17. Jad NOTIGZTYU Od NOYINAN TIO FIGURE 28 184 ON rt VY oO . lo) rt _ on icv] {i 4 to) g ‘oo q © <t ri Gq a fe) oO “d : an pu is) 4 iy jaan) L | i | | { | L | 2° 8 @ # vy Q@ YH Q we Loe] Loe} oe 3 © md © G NOILUZILY Od NOWLNSN WOTaY FIGURE 29 oo? ved (ame) CASW) ADYSNS NOLOHA GOT o0ZT 0o0t 008 008 ooh Q0e.. 7 i zojo00dsTy - squtod. uedg ‘Te 18 NTI - squpod yzeqg 4 Paw id Lmaaeenes | pH 185 30 FIGURE 186 CAS WD A QYSNa NOLOHd gy) Ochs 0023 c00% 008 009 00h i 1 i 1 t Jed L ¢ he z ! I (ez) "Te 38. F30uaTY JO. BARC — Oy = eTBuy uotd WO ASB LaNdbl Uaztd dy Vv NS 4 FIGURE 31 L tl a A} AIT ID ALL EM EGLE Av 1 rs NOT LONG dOLDHd Silia id C 187 T. oy IST on SAAT rac Nn oO ans me fom 00c1 OOTT DOO} 008 O08 002 O03 005 OU) i i 4 i i i i j | { i i i \ ; LL queupaedxg sty3 > /\ i wory wnytAeynegd wWoAry suoTRVeS ssotn 4 = SqUtTOg Ble 3TH WOAg UoT}IOSeS Sssoig wWhTAejned - sarang azaemoy ATG WOAF UOTFADVS ssozp uojJoOAg oeag_ - eaany asddg ent “PISA EE yp Up Fie Ub a UNO Neid WoO j i i i i i i i a CO bem} }-~ C) _ f) f ‘a ae j---- C FIGURE 32 187a D. Discussion of results for the $1, 01535) resonance, As shown above (page 149), the amplitude for the S|, (1535) resonance in 1 photoproduction seems to want to go t6 zero or perhaps even to positive values. In a "final" fit, I have set the resonance amplitude to +0.25 and the energy to 1520 (page 251) to remove most of the resonant behavior in the real ’ part of the fitted add-on element. The imaginary part of the fitted add-on element still wants to go positive at energies below the resonance energy. This behavior may be due to wrong values for energy, width, or amplitude of the resonance, or may be unrelated to resonance behavior. Obviously, more work needs to be done on this problem. In any case, whatever the final values of the resonance parameters for the § 1? TY initial analysis (Figure 21.1, page 149) 1 shows that a large negative amplitude is unlikely. Now the final results of Walker's analysis give amplitudes of -0.65 and -0.80 for the S,, in nt and 1 photoproduction respectively. ll (Table 9) These amplitudes are roughly in agreement with the “quark model and imply that the S,, is excited mainly by isovector ll photons (see eqn. I.1, page 3). However, if the 7 amplitude is wrong and should be changed to zero or positive value, this would imply a significant amount of isoscalar excitation. It is interesting to note that the S11 has been: predicted to be mainly isoscalar from the results of n photoproduction experiments. (57) 188 PART VI CONCLUSIONS 1) The reaction yn > 1 p has a much smaller cross section than yp > ven in the third resonance region (1000 MeV photon energy). A partial wave analysis of the m veaction indicates that this is mainly due to weaker excitation of the Fy, (1688) , helicity 3/2 resonance. This resonance appears to have a finite amplitude, however,in disagreement with a quark model prediction of zero. 2) The above partial wave analysis favors a positive amplitude for the S,, (1535) resonance in m photoproduction, 11 in disagreement with previous analyses and with a quark model prediction. The positive amplitude seems to be required to fit the new polarization and asymmetry data. The present analysis may indicate the S,, resonance is excited by isoscalar 11 photons, in agreement with the results of Anderson and Prepost (57) in n photoproduction, 3) The status of the P, (1470) resonance in pion photo- production is still indefinite although there appear to be large humps in the imaginary parts of the corresponding helicity elements. 4) Final state effects in the deuterium cross section seem to be mostly accounted for by the Pauli exclusion principle. 189 5) Partial wave analysis of photoproduction in the low energy region ra < 1.5 GeV) is still presenting difficulties due to lack of data. Especially needed are polarization . and asymmetry data at many angles and energies. In the analysis of 1 photoproduction presented in this paper, the effects of a few new asyinmetry and polarization data. points were very large. 190 APPENDICES 191 APPENDIX I NOTES ON KINEMATICS A brief explanation of some kinematical quantities is necessary for the interpretation of tables and graphs. The measured reaction is yd +1 pp , which has a three- body final state. From this, we extract cross section infor- mation about the reaction yn > 1 p and express our results in terms of kinematical quantities defined for the two-body final state. Define as four-momenta k, Pg> d> Pps and Py for the incoming photon, the target deuteron, the outgoing pion, the "recoil" proton, and the "spectator" proton respectively. Then the equation of four-momentum conservation is: k+p,=a+P, +P, (1.1) To express the kinematics in terms of the two-body reaction of interest, we define the CM total energy W of the (1 , recoil p) system by: ; Ww = (q + P)” (1.2) Now, if the target neutron in deuterium were on the mass shell, there would be no ambiguity in the definition of the photon energy k' in the neutron rest system for the two-body reaction. That is, for a free neutron: _k' (free neutron rest system) = — (1.3) 192 where MO is the rest mass of the neutron; | and k' and W are uniquely related. This is the relation between the lab photon energy and the CM total energy in single pion photo- production reactions with a hydrogen target, where MO is replaced by MM However, because the neutron is bound, this relation is no longer true for a deuterium target with W defined as above. In order to compare our a photoproduction results with experiments using hydrogen targets (since the results of these experiments are usually given in terms of lab photon energy and CM pion angle measured from the photon beam line), we define an artificial photon energy k' given by equation 1.3. It is this photon energy which is given in the tables and graphs and which is (perhaps confusingly) called the "lab photon energy". However, only the CM total energy W of the two-body final state has definite physical meaning, and the value of k' should be considered mainly as a means of defining W by equation 1.3. It should be noted, however, that in the partial wave analysis of m photoproduction, the values of k' given in the tables and graphs have been treated as photon energies in the free micleon rest frame, 193. APPENDIX ITI BEAM ENERGY MONITORING The total energy in the bremsstrahlung beam passing through the deuterium target for each data run was measured indirectly with a Wilson type quantameter[58,59) . The quantameter could not be placed in the beam line during data runs where the particle detected in the spectrometer came off at a-smali lab angle (<15°), due to the interference of the spectrometer with the beam line. To make for efficiency, at the sacrifice of some accuracy, the quantameter was not used at all during data runs. Rather the relative beam energy was measured by several secondary monitors during data runs, and these were then intercalibrated with the quantameter during special "monitor" runs taken inbetween the data runs. The quantameter, which could be pushed in and out of the beam line, was located just upstream of the deuterium target (Figure 2 yA description of the monitors and the specific monitoring procedure follows. A. Wilson quantameter ~- primary monitor. The Wilson quantameter is a closed chamber consisting of 12 plates of copper, each 1 cm. thick, and separated by gaps alternating between 1 and 2 ecm. in length. The chamber was (initially) filled with a gas mixture of 95% argon, 5% carbon dioxide at a total pressure ~800 im. Hg. at a temperature 194 f) =20° C. The amount of material is enough to almost completely absorb the beam, The beam enexgy is calculated by measuring the ionization of the gas caused by the electron-photon shower generated mainly in the copper plates. ‘The plates are alternately held at ground potential ‘and a negative high voltage. The electrons from ionization are collected at the grounded plates and the total charge collected is measured by an electronic integrator. If we know the amount of energy loss per ion pair formed in the gas and the ratio of energy loss in Cu to energy loss in the gas, we can theoretically calculate the total energy contained in the beam, given the fionization of the gas. (58) \ 1. Calibration constant of the (south) quantameter. The theoretical calculation described above gives for this quantameter: 18 = (4,80 + 0.15) X 10°” MeV/coulomb U Q of ionization electrons collected. This number has been : re) given for a pressure of 800 mm. Hg. and temperature 20° C. This constant has been measured twice for our quantameter in an electron beam at Stanford by comparing the quantameter to a Faraday cup. The results were: 18 " In 1960 U MeV/coulomb Q In 1966 U " Q where both numbers have been corrected to 800 mm. Hg. and (4.73 £ 0.07) X 10 (4.78 + 0.14) x 10°8 + MeV/coulomb 20° c. (60) Gomez et al. (59) suggest that the accuracy of the 195 experimental numbers is not good enough to justify using them and that the theoretical value should be used instead. Thus the calibration constant used in this experiment was Uo = (4,80 + 0.15) X 10!8 and T = 20° Cc. MeV/coulomb at P = 800 mm. He. 2, Leakage of gas, Tf the ratio T (°K) /P were constant for the quantameter, the above calibration constant would be valid for the experiment, A change in this ratio indicates a leakage of gas (PV=nRT). A slow leakage has been observed, and the ratio TOK) /P was seen to change at a rate of +1.53% per year over the course of this experiment (one year). (Figure 33 ) If the mixture of gasses remained the same, it might be expected that the ionization of the gas per unit input beam energy would be simply proportional to the gas density, or equivalently, to P/T. Indeed, we have made this assumption, in the calculation of beam energy for this experiment. — The above calibration constant then becomes: 18 = (13.10 + 0.41) X 10°" MeV/coulomb per T/P “Q or Ug = Co X T/P where the units of T are °x and the units of P.are mm. Hg. It is unfortunate. that .the calibration of the: quantameter has not been checked since 1966, However, this quantameter has been known to leak gas in the past while the two calibration measurements mentioned above, separated by 6 years,were consistent 196 ond mH) SOC] LOR T OS 4 - Bool its) a) ee) Lan 4 MN cy =H o © SOOO" =NGIISIAZG SHY ae 0) i dd ¢ a wy co G9 ay = Onno = bea = ve fence Lanes = Ln ™N ‘y zh © R ‘i PIGU 197 with theory within experimental error. Therefore I believe that it is safe to continue to use the theoretical constant. 3. Temperature and pressure. The pressure (in mm. Hg.) of the gas inside the quantameter is read off a gauge which is part of the quantameter unit. The temperature of the gas is assumed to be the same as the temperature of a Centigrade thermometer which is put in good thermal contact with the metal case. Even if there is a long adjustment time between gas and case (room) temperature, the statistical scattering caused by possibly erroneous temperature readings causes an error in T/P of the order of only 0.22, because the absolute temperature is used in the ratio. The pressure gauge on the quantameter is assumed to be operating correctly. B. Secondary monitors. > Five secondary monitors were used in this experiment to determine the relative beam total energy during data runs. Three of these were also active during monitor runs when the Wilson quantameter was in the beam line for intercalibration. 1. 40 MHz probe. The 40 MHz probe is a device to monitor the relative circulating electron current in the synchrotron. It was gated to sense the current at a time immediately before. the electron beam was dumped (converted to an external bremsstrahlung beam 198 by the internal tantalum target ("‘radiator")). It operated during both data runs and monitor runs. Assuming that the full beam is "dumped", this monitor should give a good indication of the relative beam energy. | 2. TC1 (thin chamber). TCl was a thin (mylar) walled ionization chamber filled with an inert gas which was placed in the path of the photon beam, whose energy it monitored by the small ionization of the gas. It was located immediately downstream of the primary Pb collimator ‘through which the photon beam exited from the synchrotron, Ionized electrons were collected and fed to a current integrator whose output (counter and meter) was proportional to the charge collected, and ‘thus to the amount of ionization. TCl was active during both monitor and data runs. 3. TC2 (thin chamber). TC2 was another thin walled ionization chamber similar to TC1 and was located downstream of the UCLA hydrogen target and just upstream of the last sweeping magnet. This monitor was active during both monitor and data runs. 4, MT (monitor telescope). The monitor telescope consisted of two scintillation counters located below the deuterium target and surrounded by lead brick shielding. The counters were physically set in a telescopic arrangement (one below the other) and electronically connected in coincidence in order to detect reaction products 199 moving straight down from the target, thus providing another relative monitor of the beam total energy. Since the deuterium target was located downstream of the Wilson quantameter, this monitor was inactive during monitor runs. 5. BC (beam catcher). The beam catcher is another ionization chamber where an electron-photon shower is generated in a few copper plates. Directly behind this chamber is the termination of the beam line. This monitor, being downstream of the quantameter, was not active during monitor runs. Also it could not be used during data runs in which the high momentum magnetic spectrometer (HEMA or OUTR) blocked the beam line. As with TC1l and TC2, the current output of this monitor was integrated and the relative charge read off on a counter and meter. A brief description of the current integrators and integrator calibrator follows. C. Current integrators, integrator calibrator. The current pulses collected by the various ionization chambers were fed into current integrators whose outputs gave the relative charge collected in units of BIP's (beam integrator pulses). Whole BIP's were read off a counter (scaler) and fractions of a BIP were read off a meter. One BIP is the charge collected in the integrator by a fixed capacitance which has been charged to a fixed voltage (Q=CV). 200 The integrator used by the Wilson quantameter was calibrated in coulombs/BIP by the integrator calibrator, which was a circuit rack containing an extremely precise capacitance which is pulse discharged from a fixed voltage value which has been precisely measured with a null voltmeter with standard reference cell. The coulombs/pulse delivered by this calibrator during our experiment was 10 + 0.25% (on the 50 volt setting) C/Pulse = 503.75 X 10° The combination of quantameter calibration constant, integrator calibrator constant, and integrator calibration constant gives the useful constant: MeV _ MeV Coulombs Calibrator pulses BIP Coulomb Calibrator pulse Integrator BIP (3.1) which for our experiment was roughly 11 X 10°? MeV/BIP for the integrator used with the quantameter. D. Specific program for calculation of total beam energy The total beam energy passing through the deuterium target for a given data run was calculated using the following formula: MeV (data run) = carp (QBIP's),, . (3.2) where MeV/QBIP is the energy per BIP of the quantameter integrator as calculated in equation 3.1, and (QBIP'S) aug is as given in equation 3.3. The MeV/QBIP was calculated once a day or after a synchrotron endpoint change. 201 (QBIP's) 5 is defined by: (QBIP's) 9 = 3% eae X (iCi-BiP's), + leascpapls X (TO2-BIP's), QBIP's . + ga X (40 MHz scaler), (3.3) where the subscript S means that an. average is taken over the two monitor runs surrounding the data run, and D refers to quantities measured during the data run. An estimate of the standard deviation in the quantity (QBIP'S) oe due to variations of the three secondary monitors from the average was. obtained by plotting the differences (CQBIP's) 5. goi ~ QBIP'S) Vg) > (CQBIP'S) i ag2 7 (QBIP'S) ag) > Tp ~ vr . Vo : and ( (QBIP 8) ia 40 Miz (QBIP 8) ave » where (QBIP 8) ta : is the appropriate term in equation 3.3, An example of this is given in Figure 34 . The standard deviation varies from slightly less than 1% to about 2%. This error is a statistical error which, however, is not included in the statistical error given for the final data. In several cases, one of the monitors TC1, TC2, or 40 MHz gave wild results and was not included in the average. 202 | i a a) jt aoe Gl nae = | Ed © wi de or} a Col ewer OLE ES : C3 Lat wn zit oe) ck. Lit | pny COL ed “ I ~ ened ce been C3 Neo? E ome, yeoal bend eo fh. a) a | ot ran o 7 | ADWING SOWWSAY WOHA NOTLYTARO FIGURE 34 py 203 APPENDIX ITI EXPERIMENTAL APPARATUS A. Spectrometers and counters At each data point, .a magnetic spectrometer was used to identify one of the outgoing charged particles and to measure its vector momentum. Two magnetic spectrometers with a total of three possible configurations were available for this task. A low momentum spectrometer, or low energy magnet (LEM) was used to measure particle momenta up to 600 MeV/c. A high energy magnet (HEMA) could measure momenta up to 1200 MeV/c; and by means of extensions to the HEMA frame, another configuration (OUTR for ' ‘outrigger") was possible which extended the maximum allowable momentum to 1650 MeV/c. Both spectrometers were set in frames which could be rotated around the deuterium target assembly. The maximum allowable lab angles for the various configurations were 148° for the LEM, 55° for the HEMA and 39° for the OUTR. Figure 2. shows one possible position for the spectrometers in the experimental area. 1) HEMA and OUTR A schematic diagram of the counters in the high momentum - spectrometer (side view) is given in Figure 35. A central particle trajectory is shown which originates at the deuterium “ewe YsAgyOSEV GV37 HONI et gS YALNNOd 7 MOMNSYSD SLIONT] (G°OdOL'L) 2s IS YALNNOD AOMNSY8SQ SV9 NOSYS — 204 r—N NV4 DY — La9uvL 2 gino FIGURE 35 205 target, passes between the pole faces of the magnet, and is there bent downward to pass through the various scintil- lation counters and Cerenkov counters. A set of three FAN counters (scintillation counters) were set against the inner sides of the pole faces of the magnet to veto particles which scattered off the pole faces and went through the. rest of the system. A particle event was defined by a five-fold coincidence between the counters Al, A2, Sl, $2, and S83 along with a veto from the FAN's. The four-channel hodoscope $2 defined the momentum channels of the spectrometer. ‘The horizontal aperture (perpendicular to the plane of the diagram) of the spectrometer was defined by the counter Al whose angular width was 0.0158 radians or about 0.9° at the deuterium target. The vertical aperture was roughly 0.1 radians or about 6° at the target. The momentum calibration and aperture measurements were made by F. Wolverton(61). A summary of the acceptance properties of the HEMA and OUTR configurations for each momentum channel is given in Table 10 and Table ll. For each channel, the momentum spread (AP/P ) was about 2.5%. Particle identification was accomplished by means of the two Cerenkov counters FC and LC. A suitable combination of triggers of FC and LC was used to distinguish between e 206 soueqdoooe aeTnsue [eI0q = BV eanqaede TeqRUozTzoy = eV vanjasde TeoTIAeA = gV fe) (o) fe) Zeqsuorjzoeds syj JO wUNJUSUIOU TeaquUeED ey ST g szSyn d/( d-4a =0 cHOlx EL°E c-Olx €€9°T — 8ST0"0 9€Z00°0 8ZZ0°0 E€OT"O O8€0*0- a cuO1x 68°€ c-O1x 8z9°T — 8STO*O 97700°0 6€7Z0°0 O€OT"O 6Z10°O- Od c-0lx 80°7 g-0ix 0%9"T —-8S10"0 8SZ00°0 ZS70°0 9ZOT°O = SE TOO OL c-Olx 0°97 g-Olx 7I9"T — 8STO"O ZLZ00°0 99z0°0 ZZ0T*O €770°0 L SsueTpPere4sS suerTpeie4s sueTpea sueTtper SUBT DEL Oo uee,_ TeuueyD BVOV . BV ov . oVvEeV ov gV un USO SIoRZUNOD WNAUSWIOM YOUT gT’I aZequUNed singaede YOUT ¢/°Z x ZT setqaedorzg ooueqdeso0y VKH Ol #1GVL 207 OTx L£9°% OTx 7L°C OIx 78°? cu0lX 86°2 suBTpereys Byov OIx €0S'T OIx 10S"T OIx 667°T g-O1x L67°T suetpezejs OV 7910°0O €9100°0 8ZT0°O 9T60°O 9TE0"0- a 7910°O £9100°0 Z8t0°O ST60°0 ZctO°O- = od 79T0°O €ZT00°0 68T0°O. 7160°0 0g00°0 Ou —4¥9T0"0 Z8100°0 6610°0 - €1T60°0 Z6Z0°O L sueTpEZ suetTper SuUeT PEL O ursyl Teuueuyg eV oVSV OV dV unqUuEWo, Si9jUNOD WNZUSWOU YOUT gI°T gzequnoo oanqaede your ¢/°Z x ZT setqaedorg soueqgdso0y YLAO TT aleve 208 electrons, pions, and protons. Muons and pions gave the same set of triggers and no attempt was made to distinguish between them, since it was assumed that all muons came from pion decays. . The Freon Cerenkov counter (FC) consisted of a large gas-filled box with phototube to collect Cerenkov light from particles moving at a speed greater than 0.999c. Since no pion or proton detected by the spectrometer ever reached this speed, FC was triggered only on electrons (or positrons). For electrons causing a particle trigger (A1l*A2+S1+S2+S3*FAN), the detection efficiency of FC was very high, averaging around 99.7%. Measurements of this efficiency were made (periodically during the experiment) in a pure electron beam generated by placing a pinhole Pb collimeter in the photon beam while the magnet was placed at 0°, Low energy electrons which might not trigger FC, were absorbed bya 1/2 inch slab. of lead placed downstream of LC. The Lucite Cerenkov counter (LC) consisted of a Lucite slab with a phototube attached at each end. A combination of the effects of the index of refraction of Lucite and of the optical path to the phototubes gave the counter a threshold 209 of 0.9c. Since all pions and electrons measured by HEMA and OUTR were above this threshold, LC was triggered on these particles. However, due to losses (the optical system was not perfect) the pion (and electron) efficiency of LC averaged only about 98.5%. This number was measured by setting the magnetic field of the spectrometer so as to detect only negatively charged particles, thus eliminating protons. Unfortunately, LC had a non-zero proton efficiency which was probably due to "knock-on" electrons and perhaps some scintillation due to low energy protons. The efficiency ranged from 0.7% to 4%, . To measure this efficiency, an almost pure proton beam was generated by setting the synchrotron endpoint below the energy necessary to produce pions of a given momentum in the spectrometer while still allowing protons of this momentum. Also, time of flight restrictions were imposed to reduce pion contamination. Nevertheless, due to smearing, all pions could not be eliminated. A comparison was made between a pulse height spectrum produced by this beam and that of a pion beam in order to subtract out any remaining pion contamination. 2) LEM A schematic of the low energy magnet counter system is given in Figure 36, A particle trigger was defined by the 210 vIGiPst LAOYVL?G GINDIT = fb, suainnoa nva” | Ih / Vn Gog ‘OL *L wn IS as \ FIGURE 36 211 four-fold concidence of A, SI, P, and $2, along with a veto from the FAN counters. The P counter was a four~channel hodoscope which defined the momentum channels of the spectrometer. The horizontal aperture was defined by A whose angular width was 0.0289 radians or about 1.7° at the deuterium target. The vertical aperture of the magnet system was about 0.11 radians or about 6° ‘at the target. The LEM was calibrated by H. Thiessen (62) for a 7-momentun channel hodoscope P. We have replaced Thiessen's 7-channel counter with a 4-channel counter. A recalculation of the acceptance parameters for the new momentum channels, using the field map measurements of Thiessen, was done by P, Walden (44 and a summary of the new LEM acceptances is given in Table 12. For each channel, the momentum spread (AP/P.) was about 2.6% In the LEM, particle identification was accomplished by means of pulse height discrimination in counters $1 and $3 along with time of flight restrictions. Proton energies in the LEM were much lower than the energy for minimum ioniza- tion, and the larger proton pulse heights were easily distinguished from pion pulse heights. The separation, however, was not perfect; and at best settings of pulse height discriminators, the pion efficiency averaged 99.6% while the proton efficiency hovered near 1 s Hi eanjaede TequUozTAoy AV souejzdsooe zeTngue Tejoq = BY eangasde TBOTRAeA gv iH ° oe) cuOlx E9°L cAOIX 72°E 6870°0 £S700°G 6ZZ0°0 OZTI“O 7EEO"O- gq cHOlX PL°L cAOTx 72°E 687Z0°0 89Z00°0 6€Z0°O OZIT'O LyTO°O- og c-Olx O1'8 c-OlX 972°€ 6870°0 08Z00°0 0¢Z0°0 OZT1"O ZT10°O OL ~ cuOlX 67°8 — ¢_OTX 92°E 68720°O 76Z00°0 Z9Z0°0 OZTI*O 78E0°O L SUBTPEA9IS suetpere4s SUPT PEA SUB TDRA sue Tpe.l O uve, Tsuueug BOY BV eV oVEV OV gv unjuewo} SAORUNOD WNAUSUIOM YOUT CZ] AequnNod eanjasde your ¢/°*Z x C°6 setqaedosg ooueqdoooy WET él d1gvL 213 The LEM was unable to distinguish pions from electrons, At the start of the experiment, we were not worried about this defect, since we assumed that the electron rates were negligible at the large lab angles at which the LEM was used. However, during the experiment, we observed a discontinuous jump between the HEMA cross sections and the LEM cross sections which we now believe to be due to electron~positron contami-~ nation in the LEM results. A further discussion of this problem is given in Section IV.C. B. The recoil counter The recoil counter was used to detect the recoil proton P,. (from the reaction yd > 7 ppp.) while the spectrometer was used to detect the pion. At backward pion angles, however, the arrangement was reversed with the proton being detected by the spectrometer (HEMA or OUTR) while the pion was detected in the "recoil" counter. The recoil counter was designed to accept about 50% of the recoil particles associated with a particle in the spectrometer, Figure 37 shows the structure arid dimensions of this counter. The actual aperture is defined by the smali counter RC. The three counters RB, RL, and RR were used to define a coincidence with RC and to crudely indicate any left-right iG aa rf XSt XS Te pue wy 4 4 + we < u78 xX uS Ou SNOISNEKIG YEINACO 214 woe THOUVL OL WHINGOD ILOOTY AHL Te Od wa SURE 37 G FI 215 asymmetry in the distribution of recoils. The recoil counter systel was set up and moveable in angle on a circular track of 32 inch radius surrounding the deuterium target. C. Electronics Schematics of the HEMA, LEM, and recoil electronics are given in Figures 38, 39, and 40 respectively. In general, for the spectrometers, a fast coincidence of about 5 nanoseconds was required between the counters defining a particle trigger. This fast coincidence is produced n the coincidence circuit module labelled "S" in the HEM ik i ~ HE AS fle and LEM diagrams. Actually, due to the fact that this module could physically take only four inputs, the final particle trigger was obtained in the module PAR*FAN whose inputs were a fast (5ns) pulse from S and slower. (longer) pulses (10 ns) from FAN (veto) and from A2 (HEMA). Particle identification was then made by the slower electronics (50 ns pulse lengths). In the HEMA electronics, the various combinations of LC and FC and their vetos were fed into the coincidence circuits 7, p, e, and X. The X coincidence circuit identified a normally impossible situation where FC was triggered and LC was not. Counts in this circuit were due purely to the inefficiencies of the Cerenkov counters. 216 sopuasy QO iene Qs Oe fu. C3 ©) t, ioe anes. tr} bod fu O too t C3 (3 bh. 9 | 4 FUGURE 38 fT Lume § io) Ore CC es & Lil 217 G> 9) qs & ora ov es & mes Q rm) £3 Gs e % 6 ) f fh. fi & % mt 8. 7 to é of wad | G 7) 1S) Y 1 w «3 | ra) £2) a ra fu. ke ri ra e os oe C. f. cL th. . of GL} Ge oe f. orn Or YG, [. Ss >» | =D Cu os G wed C3 e wet oo ce =3 3 ® ra vt ° m os} a 4h, hu | | meserereeeles i bescneenaeant i on a. . = ete a NNN xc Oy uv) FIGURE 39 — Co Pee ae wry Sse oe) 218 @ Gs ie) a ta 3 Ce cowed oe a o es fond bet toot Con weg 0. Bhoee Ch. &) tnt De Ce Ce ea am) o e oo & frog bang bed G. to Brus [ | wot wud | ] bP © ®) 219 In the LEM electronics, the coincidence signal and veto signal frem the circuit S10*S2U were fec into the p and -1 coincidence circuits. As electrons were not distinguished from pions, there was no separate electron circuit. Finally, the t signal (or the p signal for the reverse recoil setup) was put in coincidence with the 4 momentum channels to obtain the 7 (or p) counts in each channel. If the recoil counter was used, the signals S (fast), - wm (or p), and the 4 momentum channels were put in coincidence with the final recoil signal B-C toe obtain the number of events in each momentum channel for which a recoil particle was observed. To monitor FAN triggers and various accidentals rates, appropriate coincidences were defined. A problem with the definition of Al and Al*A2 accidentals is mentioned in Section IV.F. The reduction of scaler counts to true particle rates using counter efficiencies and accidentals corrections was done by P. Walden and is completely described in Appendix 10 of his Ph.D. thesis (44). 220 APPENDIX IV THE HULTHEN WAVE FUNCTION A useful representation of the deuteron ground state is given by the Hulthen wave function: 5, Op Bp | 0, (e - e@ ) - h u, () tae - =| 0 (4.1) where a = 45,69 MeV : 6B = 275.74 MeV p, = 0.0088177 Mev} = 1.74 fermi Py is the neutron-proton effective range and is related to a and 8 by the normalization condition: -~_ 4 1 Pi (a +B) B (4,2) The corresponding momentum-space wave function is: _ o “ (g2 - 0%) c(k) = eae - =] (a* + k*) (B* + k*) (4.3) The momentum (magnitude) probability density is then = hak | oC) |?. This last function is plotted in Figure 3 . The curve peaks at about 50 MeV/c which is then the most likely internal nucleon momentum. The deuteron form factor then is given by: F(k) = fexp (kB) uf (p) a? (4.4) - (| [tan e/20) ~ tan”) (k/28) - 2een” ces (ot8))] 221 APPENDIX V NOTATION AND HELICITY FORMALISM FOR PARTIAL WAVE ANALYSTS All variables are in the center of momentum (CM) system. Particle four-momenta: see Figure 41. k = (kk) incident photon ~ > > P= (H)»P,) initial (target) nucleon (note Py = ~k) > s . g = (w,q) outgoing pion > . . > > Py = (Ey »Py) final (recoil) nucleon (note Py q) My = mass of initial nucleon m= mass of outgoing pion My = mass of final nucleon CM total energy § = en = angle between q and k W HH} Units used in theoretical formulas: K=1 c= ] Unit of energy = 1 GeV 2 Unit of cross section = 1 GeV Units used in graphs and numerical tables: > ~ 30 2 Unit of cross section = 1 microbarn (ub) = 10 em 1 Unit of helicity amplitudes = (1 tb)? -2 Conversion of GeV to ub: 1 Gev"* = 389.5 ub 222 Variables in CM Frame vis FIGURE 41 E > 1? Pye 1 223 Mo Particle helicities: (in the CM system) (Helicity is defined as the particle spin component in the direction of motion.) Ae = t+] = photon helicity Ay = ih = helicity of initial nucleon ra = 0 = helicity of pion ho = tly = helicity of final nucleon A= he - ry = 43/2, 41/2 = total initial helicity (along i) WEA 7 Ay = 41/2 = total final helicity (along @) Definition of helicity amplitude A (059) : Walker ( 3) HI 3/2, 1/2, -1/2, -3/2 0, ¢=0 initial states labeled by A 8 i final states labeled by yp = 1/2, -1/2 ; 8 » > A is defined in terms of the S matrix by: | + 5 (2n)4 se, ~ P,) (80tIN) A (5.1) mn HI nom 1 me) (2k 2E i where N 2u 2E,) and P, and Ps are the 1 f£ total final and initial four-momenta. ! The cross-section formula is (M = 87WNA) 3 dp 4 4 2 Voi 1 = Im]? (2094 6 (P, - P,) 4. 2, (5.2) re + (2n)” (27) This reduces to: cM do. -4 sy 12 Ea (6,9) = 7 1A, 6) | (5-3) PA 224 There are 8 amplitudes A , corresponding to the HA 4 possible values of 4 and the 2 possible values of yw. However, by parity symmetry, only 4 of these amplitudes are independent (63). That is: gk Amu) (26) Ay (009) = A 4) (5.4) Definition of the helicity amplitudes H, (06) Let Hs Ha » He, H, be the 4 independent helicity amplitudes for photon helicity Me = +1 defined by the matrix: AQ =tl) = "72,3/2 ®ifajisa | _ | Ba Hy | go (5.5) 4 72,3/2 8-1/2,1/2 My My Note that Hy and H, have initial helicity 3/2 while Hy and Hy have initial helicity 1/2. Formulas for differential cross section, polarization, beam Setting ¢ = 0, we have: cM 1 o(0) = | =z DD Agg 1? por (aay 4 i=l] P » ta ed “ . _ 1 gq J tT olarization P*(k x q) = Tk oey Tra oA) 225 where °y is the y. Pauli spin matrix. The above results hold for both ry = +l and -l. Polarized photon asymmetry OO) = Sr ie otey ROGUE, ~ HyMs) (5.8) where o, is the cross section for linearly polarized photons with electric vector perpendicular to the reaction plane and o, for photons with electric vector parallel to the reaction plane. Polarized target asymmetry T(6) = Pe Oe gly (H w- 4H HW) (5.9) oO, Fo k o(8) meee 7 B3hy . where Go, and o_ are the differential cross sections for target nucleons polarized + and ~ along the direction k xq. CGLN amplitudes - relationship to helicity amplitudes The ceLn (51) amplitudes Pus Pos Fas Fy determine the photoproduction amplitude A by the formula: -) ~y na “a “ -) . “ “a > -) iA(e) = ioe Ft oq a+ (kxe) Fo ta ak qe FP, +i (5.10) where 6 are the Pauli spin matrices and @ is the photon polarization vector. For photon spin defined along the direction of motion k (=z) , (helicity = +1) we have: > > € Chew and Lewis amplitudes - "spin-flip" and 226 The helicity amplitudes may be written in terms of the CGLN amplitudes: H, (8,4) = ~(1//2) et? sin€ cosd (Fy 4 Fy) H, (0,6) = 72 costs (CP, ~ Fj) + 4s(1 - cos) (Fz - F,)) H, (0,0) = (1/72) 73? ino sin'0 (F, ~ F,) (5.12) H, (0,9) = Vz ei? sin’s6 (fF, + ¥,) + s(1 + cos8) (+ F,)) "spin-non-flip"™ cross sections The Chew and Lewis (45) amplitudes K and L may be given by: iA(e) = i (-1/¥2) (6K) + L@) ) (5.13) > where K is the spin-flip amplitude and L is the spin-non > > flip amplitude. For photon polarization ce = E, we have: os a { _ if 2 ag ig K, = Fy cosé By sin’@ cos¢ e Fy . : 2 . id Coos Poe sé F si sind KY 1 By i cosé Py + gsin’6 sind a Fy . : (5.14) K = sind er? F, + sind et? F, + cos8 sind et? EF z 2 3 4 L = - sing et? F 2 The "spin-non-flip" cross section is proportional to 12 : tea “= . . (|x| ) awe" Specifically, at ¢ = 0, we have: ~ i Ah af 2 4 2 o(8) oe = Fe sin’s [P| (5.15) 227 In terms of helicity amplitudes, this is: + H,(0) cos'so|? - (5.16) 0(8) 6 = 6(0) - 0(8) 5 (5.17) Deuterium cross section The deuterium cross section, obtained by assuming a simple 2-nucleon wave function for the deuteron and using the impulse approximation (45) is: o (6) = (1- (1/3) F@) ) o(@). + (1 - FO) ) 0), deut (5.18) where D is the lab nuclear recoil momentum and F(D) is the deuteron form factor given by F(D) = f exp (1D°p) uf @) do (5,19) > where u, Cp) is the Hulthen wave function for the deuteron (see Appendix IV). 228 APPENDTX VI PARTIAL WAVE AMPLITUDES The helicity amplitudes may be decomposed into states‘ of definite total angular momentum, definite initial and final total helicity. The following equation defines the 2 helicity coefficients A : = j fo iJ LO) 6 A (8,4) = ; AN, (3 +1) 4) (0) e (6.1) where the functions (24 + 1) a 0) er Owe are orthogonal and normalized to 4m when integrated over all solid angles. The d functions are described in Jacob and Wick (63). I use the definition given in Equation 18 of Walker ( 3). The total cross section may be expressed very simply in terms of the helicity coefficients: |? wha Oy = 2m 2) (Qj + 1) Jas, (6-2) where the sum goes over only positive values of A. Helicity elements are defined as the linear combinations of the helicity coefficients which have definite initial corresponding to a definite final state orbital angular momentum. These elements are formed by taking sums and differences of coefficients with final total helicity u = +45 and -k. Define the helicity elements Aas and Boy 229 - j aad Ay = 7/2) i /2,1/2 FAN 4/2,1/2 - 3. j Moprye = GlY2) Od yo ayo > Mlaye,1/y - 2 j j Ba aay (45 72,3/2 + AW 1/2,3/2 (nt+1)- n(n+2) 1/2,3/2 ~1/2,3/2 Ans refers to initial helicity 1/2, orbital angular momentum 2, and total angular momentum j = 2 + Boy. refers to tnitial helicity 3/2, orbital angular momentum 2, and total angular momentum j = 2 + 1 The orbital angular momentum 2 refers to the final pion-nucleon system. The parity of this system is ~(-1)" where the initial minus sign is due to the negative parity of the pion. Finally, the helicity amplitudes may be expressed in terms of the helicity elements as follows: H, (8,4) = (1//2) et? sine cosé BiB nd) (2 -P Hos n=] 2 1 1 = le _ _ H (854) v2 costsd ty int Mott) P, Purp (6.4) H.(6,6) = (1/72) e7** sino sinke 5 (BL (+B ) (PaP..) 30? " ; nay Bt (nt+1)- n ntl mt fy i eins A A a H,(0,¢) = ¥2 e°" sinks } ery) Oxted 230 where the d functions have been expressed in terms of sums and differences of derivatives of Legendre polynomials. The contributions of each helicity element to the four helicity amplitudes Hy are shown in Figure 42. Note that at 0°, the only non-zero helicity amplitude is H, and that at 2 180°, the only non-zero helicity amplitude is Hye Only the Any helicity elements contribute at 0° and 180° because of the conservation of angular momentum. HELICITY AMPLITUDE Hi Wok | | 0 60 120 180 CoM. PIGN ANGLE CDEGREES)D 232 1 0 0 60 120 180 C.M. PION ANGLE (DEGREES) 233 HELICIVY AMPLITUDE HS G ( 7 J NO aa fa . | | as 60 120 j C.M. PIGN ANGLE CDEGREES ) 0 oe) FIGURE 42.3 234 HELICITY AMPLITUDE HY | i | 0 60 120 180 C.M. PIGN ANGLE CDEGREES 2 | FIGURE 42.4 235 APPENDIX VII BORN TERMS AND RESONANCES A. Born terms. The Feynman diagrams for the Born approximation are shown in Figure 43. G.. is the pion-nucleon coupling constant for the particular reaction. The couplings are: G,=-G =-726 =+V¥2¢ «26 (7.1) + - fe) ° T T wv p TU 2 2 tas . ' where G°/4r = 14.7. e“/4n is the electromagnetic coupling constant and is equal to 1/137.036 . e, = -1, 0, or +1 for coupling toam, T°, or 1 respectively. ey and Ey each equal 0 or 1 for coupling to a neutron or a proton respectively. Ky and Hy each separately equal -1.913 or +1.793 for magnetic coupling to a neutron or proton respectively. For convenience in the following formulas, define ks Ll 2) = (Ey + M,)° and Z, = (Ey + My)”. The Born approximation 2 for electric coupling e is given in terms of the CGLN amplitudes (see Appendix V) by: ee ee re 1 4n WAM 2W 2 1 u- M 2 — eG gqZ, ay ke, ar 1h t 2 an Z, WM, ) 2W u- Me (7.2) — eG qkZ., ce. - E5 30 4m WZ en 8 a? T 2? 236 T N aN aN ‘\ \ N \ \ Ce ee ee ud 1 Va ¥ . N T N ; Feynman Diagrams for the Born Approximation y N FIGURE 43 a eG gq 2, e. ; Ey Z y 4 1 TT W25 t - me u- Me T 2 2 : where W = s, ands, t, and u «re the Mandelstam variables given by: iss} t (k + Pp)? = (q +p,)? 2 t= ke ~ 4)” = (p, - Py) (7.3) = (k - Po)” = (q - py)” a ! The Born approximation for the anomalous magnetic moment terms is: 2 —_ eG ey My boey - Zu, MW + M,) aw. \M. ke 1 An WZ My kM, u- Mw eG 2" 2u,(W + M,) F = t qk "Vd ~ 24 a eet oe Z 2 At W252, Mk M, ve Me a eC Hodk oA Wo+ My Z 3 TT 2WMo Zy u- Me 2 — eG Hoak q Wt+ M, 4 Av QWM, 252, 2 238 B. Resonances, The resonant amplitude in Walker's model ( 3} is given by: Kodo "4 wre’ AQ) = AM) |Z sf (7.5) S)s -s-iwr fo) where qd 2ht1 ( 4” + x7)" o \q + XY ; (7.6) k 244 (x2 + XV MEPS aw) ¥ oO [ko XY) where Wo is the central energy, and ko doe and Ss, are the values of k, q, and s at W = Woe The resonance parameters are: a) the central energy Wo b) the width tS ec) the amplitude AW) (of the imaginary part at the central energy) d) the angular momentum & e) the photon angular momentum jy (not really a definite quantity for helicity elements) f£) the parameter X which gives a'cutoff for large k or q Typical behavior of the real and imaginary parts of a resonance is shown in Figure 44, 2 239 Typical Behavior of a Resonance The parameters here are: Wo = 1520 MeV (photon energy = 760 MeV) T= 120 Mev A) = +1.00 f= 2, j= 1, and X = 0.350 } i i 0) Real Part I | 609 600 1600 LAB PHOTON ENERGY (MEV) FIGURE 44 120 Q 240 APPENDIX VIII FITTING PROCEDURE We are trying to fit cross sections, polarizations, B., the add-on and asymmetries with the parameters Anas at helicity elements. Or in the case of the "all energy" fits, we use as parameters the resonance amplitudes, widths, energies, and the polynomial coefficients which specify the smooth energy dependence of the add-on elements. The cross sections etc. are quadratic in the A and B helicity elements and are also non~linear in the resonance parameters. Thus a simple least squares fit, which requires the fitting functions to be linear in the parameters, will not work. I will describe two methods for obtaining a fit when the fitting functions are non-linear. I will then write down the actual algorithm used in my analysis, which is a combination of the two fitting methods, A. Possible fitting methods. 1) Linearization of fitting functions It is possible to linearize the fitting functions by expanding them in a Taylor's series in the parameters. However, neglecting the non-linear terms should be expected to work only when the zero-order parameters are already close to the final solution. After the fitting function is linearized, we then go through the procedure of minimizing x’, which is the weighted sum of squares of the deviations of the data points 241 from the fitting function. Let us go through this procedure. First, define: = i'th experimental data value (cross section, etc.) ba i where i = 1,2,...,n {tt fe 4 error of the i'th experimental data point £ (aj sgre++a,) = E. = value of the fitting function at the i'th data point where i = 1,2,...,n and @ysAooee+9a are the m parameters (eg. helicity elements or resonance parameters) being determined by the fit. oOo oO, _ - e+ ag t ' £ (ay s8po00+98)) = £, (0) = value of the fitting function D aor owes wdaw tute t nt) anatr Af maxeans oats for the zero-order (initial) set of parameters. Now expand f. around the point (ay say e+e sac). 3 e of oO 1 om m 976 £. = £,(0) + ay (0) (a, - ate yo 7 i i 46 ) yo ia,‘ de 4 7 2 ) ) vi ye) jel ka °°4°%x o o 1 eee oe x (a, ~ as) (a, - ay) ! (8.1) where (0) after the derivatives means that these derivatives . oo fe) are evaluated at the point (ap sayeeeeaa)- Define 6a, = (a, - a?) J J 242 Now form x2 n : 2 1 2 =e) Ae, 4)? i=l o7 i n 1 ™m of. ~ » 2 fx, ~ £,@) - 2 Ja, (0) *8a, (8.2) i=] o5 jel ij 1 of, 2 ~ +a (0) 6a, 8a = © 9 oe j=l k=] 2 ba,ea jk To minimize, take the derivative with respect to each parameter and set equal to zero: ay n 1 m of, ga Te 2 ly HO - D 3a, 00) 885 &£ i=l io, j=l i , , 1 af, of - aires (0)°Sa,6a, - ss [- 400) (8.3) j=l kel 2 Pa 2a j ok 08 o m af, J. gege Orsay =o] J= ae where use has been made of the fact that ayy ©) is symmetric “4 “2 in j and &. : 2 Now gather terms in 1, éa, 6a’, 243 ed aa,” ° & i 2 . of, = —z (x, - £,(0))* © (0) i=l] o 7 * ; Bay i m n 9 of, of +) fk spr) ge) - G, - £,(0)) jel {i=l ooo. j. R i at, 82,08) 4 This can be written: O=-A + B 6a, + C_,,6a,6a, + «ee (8.5) g jel 2405 421 k=l Lik jk Approximation: assume that we are close to the final solution and that we can neglect the bae (and all higher order) terms in comparison with the 6a terms. Then we have: Tm AD = ay By 468, for 2 = 1,2,...,m (8.6) where : 8 ; af, A, =) 5 x, - £,(0)) +00) R451 of tt 289 (8.7) of, df 97 ¢. ] n s Boy ) 2 =(0) 55 (0) ~ (x, - £,(0)) Sy (0) = 7 4g Pay | 244 In matrix notation, the equation is: K=B oa (8.8) The solution is: which can be obtained by inverting the symmetric matrix B. The é6a's obtained in this solution do not necessarily give a minimum in xy” as we did not solve the exact equation 8.5. However, we hope that .we have moved closer to the minimum and that we might reach it in a few more iterations. For each iteration we start with the a,'s obtained as a solution to the previous iteration. 2) Gradient method In the case that the solution to the above linearization method does not converge, we have probably started with parameters which are too far away from the true final values, and thus the approximations (linearization) will not work. Another kind of fitting procedure which requires x to decrease and is good when we are far from the minimum (but not so good when we approach the minimum) is called A the "gradient search", Instead of trying to move directly to the minimum (as the linearization procedure tries), 245 the gradient search tries to move towards the minimum along 44 . 2, the direction of steepest descent of x”, ie. along the negative of the gradient of an The changes of the parameters along the negative gradient 2 . 3 . are proportional to - oo . It is only necessary to choose a small enough proportionality factor A to insure that the 2 = \(- oxy will cause changing of the parameters by 6a a 2 x to decrease, B. Actual fitting procedure used. My fitting procedure is a combination of methods 1) and 2) described above. To do this, I relate the solution via the gradient method to the solution via the linearization method, The gradient solution is: _ aX ba, = (- ae) (8.10) Now for A very small, ba, is also very small. Then from equations 8.4, 8.5, and 8.7, we have: OX LA (8.11) and equation 8.10 reduces to: 6a, =A, (8.12) j j 246 Now the solution to the linearization method may be written: where j = 1,2,...,m. We can almost resurre equation 8.12 by inserting 4. This gives: -j 43 Sa, = (B a A, J J It turns out that using equation 8.14 to find . . . 2 parameters which cause a decrease in y” works well as using equation 8.12 (8.10) directly. factors @),, have little effect. This fac (equation 8.9) (8.13) ct the form of taking only the diagonal terms of 8.13 and 1 4 (8. a set of almost as The scale t makes it very easy to write an algorithm which will combine the gradient search and the linearization method. I solve the matrix equation > > A= C éa for the é6a's where the matrix C is defined: Bo Boy * (i + y) for Ce, = for where A and B are given by equations 8.7. and In the algorithn, (8.15) (8.16) & # j “y is a parameter 247 whose value determines whether the fitting method is closer to a gradient search or to the lanearization procedure. If y is very small compared to one, C = B and the solution is the same as for the linearization method. If y is large compared to one, the diagonal elements of B predominate and the solution is the same as for equation 8.14 (the modified gradient search) with A= I1/y. I use the following algorithm which is described by Bevington (64). Algorithm for fit: 1) 2) 3) 4) 5) 6) 7) Compute 2 due to the initial set of parameters. Start initially with y = 1/9 Compute Sa using equation 8.15 with the present choice of y. Compute Ye from the latest parameters (a, “F ba) and latest choice of y. Tf yi (a + 6a) > (a), increase y by a factor of 3 and go to step 3, If ae + 8a) < x a), decrease y by a factor of 3, consider Bl-= a+ 6a to be the new starting point, and go to step 3. Tf in step 6, the change in parameters becomes smaller than the error of the fit, the iteration procedure has converged and take a as the final solution. 248 Finally, in the linearization formulas, I have found it practical to drop the second derivatives in the Bay (equation 8.7). 1) 2) 3) 4) 249 APPENDIX IX FINAL HELICITY ELEMENT FITS Add-on Elements - 1 Photoproduction Total Elements - 1 Photoproduction + : Add-on Elements - 1 Photoproduction + Total Elements ~ 1 Photoproduction i Figure 45 Figure 46 Figure 47 Figure 48 250 FIGURE 45 FINAL FIT OF ADD-ON HELICITY ELEMENTS FOR 1 PHOTOPRODUCTION See page 148 for key to symbols. In this fit, the resonances have been changed as follows: $5, 01535) ,; amplitude -0.800 ——— > S, (1520) , amplitude +0.25 (page 251) D, (1520) , amplitude 0.000 -——> +0.300 (page 255) helicity 1/2 Fy, (1688) » amplitude -0.500 -—--* ~0.200 (page 260) helicity 3/2 See Table 9, page 161, for complete summary of resonance changes. } f NI MeN ONY eS LIL ET } i i++ cm bt OW. | ™ 251 fon cc G.., Yo cc cr + WALKER ray cS x S, (1520) new energy and amplitud a + * Foveenvemanerctinvoromnconaiourll LO CO LN Cc — te on) m) C/ittsds/éelid iNowea Ia FIGURE 45,1 C C> an i aye 1200 252 C wot A) sors @ CD — am La rt Co _ a LO “ee Ll as t ) Ce C2 | ved x Sy (coe x y sebaees OW b. om wh Ord | | | | CD Ly C3 LA o) Ln cD ae 4 wt an) a) on) <—t CS ICUS SHLD LNW ts AL{LOT lax ‘a bem QW 253 | ae sod cD oe wd TD ™ speed 7) on syne => LI] c 2 3 = ere j1¢3*” oO . = i ne C5 Lous a Lad eo ig [- owe 7 op g 48% x 4 — OW x + 09 ~ a T a Cy) bet x - ey CL = x wh. 13 2d w OL ™ ' Prremnmanspnennnnen C3 > LNSWa - FIGURE 45.3 13 254 a) Le . wt C3 : oN fom cr o.. vie & | C3 fr M+ CO rt WALKER i. od aa) $ P, ee oy 5 Ln on) Ln or LO © Ln } | Oy gegen be een FIGURE 45.4 ‘ce SN on ae enaset 255 aeons C3 a) C2 ‘on | \! am ‘co bt = ny i \ | | O t(! werd Co a eo be an a A. ‘2 Qtr NI (9 © =i ™ a) NI ae CO C3 OO C C? no pe tie pried. C/LCYS/EID LI FIGURE 45.5 ae a © 256 3 i pe Frorerfamaacedd \ (1) Qo 4 wed LF oe LP © FIGURE 45.6 257 C3 | i I i “| some fms o~ CC C ce ‘Oo - a. d a C3 nd mrs rd Cod won A xemeed Zz o A WALKER xt a & { Ae Xe U C. i H Meteo oer) r i ONS! { OC | } mea fy © O™! = (3 ° Co FIGURE 45.7 258 oe) I | , ~T “| “Ls sgesced \ O ‘ an sent \ ot ( : A 1d fj aN A v spond ~ a XR | Lat cs rl = Ce) v wy | ” wo erty C3 - RTE SS CO aanrmmaodl jaa] mtr C) iu \\)) (5 Ce zi ie (Cc 24 &y Me, se Caer ‘a a nce er rie et bl senee sie, i 6 7 x tempol O | L. to =i at la! CM =p O oO 2 a) O Q O o , mae] Ce | eysyicussary LENIN ' Vogt yep PY ChO/7 oil NIN ia ALL OL ian FIGURE 45.8 259 ALY NO NO}TOUA Quin \an 2 isn NBGBHa db | alats OPT ANAT mo rata ANF ave ny OCA) UG | Cision: OSS “908 WUT OO? Go naa i j 2G UT yt (8891 —_ ale + eee ees ABS KS Govern icone C ran \ een sein, oe) | Co (J en | MO) ‘en Qh | bf QL f. 1 45,9- fh » ay FIGU! a) q ra) apngttdme meu (9g9oT)7 a | on es | 260 Qo L. bem O) FIGURE: 45.10 261 FIGURE 46 TOTAL HELICITY ELEMENTS FROM FINAL FIT OF + PHOTOPRODUCTION The final total (Born part + resonance part + add-on part) helicity elements (plotted curves) are compared with Walker's total helicity elements (plotted points). The curves are identified by {} for the real part and by os for the imaginary part of the total helicity element. Note that there has been a very large change in the imaginary parts of the Au and Ay helicity amplitudes (pages 262 and 263). © 262 coA PEN POUL ETURETE RETR Ems CLIT wias + ~ RG rad = oon | LADIAN? ALOINS Neb uac rae me 7 OAT AONT AAG AQ AOS Ay . L 00d} UU hOS HS UOT] O02 Wo i i nm ‘s— (ozst) Fs 7 ( eed +. +. ww «=UstTVM Cl —_ eS _— - C2) CI. Ch. | boot ‘an -FIGURE 46.1. onl ‘an bd Qu. P, (1470) C/ICHS/ EI] FIGURE 46.2... Lo C3 CO 7) 4 ol | ant ¥ Nz bn : C3 i" Y ALTODH N@ivra Go.) WUT E O02 s C3 C3 aN ccurwl ey Cc? C9 goed ie) wf CO (> C3 CD Cy Cc on Ne} ery oN a od I | Ln ran { a *. + ae ney + nn > é en ae hoe 3 7 UaaTVM Lf aot ai }-~ mS }~- +. ‘an a l bol ane . FIGURE 46,3... tH sero 7) CASA) ADEANS NEED wey CD 265 ‘alata AQT ata fatate vata OO} wien’ UU ier) COOh i H H i t x PULL] PLMGTAYIT 0 UL dibe AXES Tosh] : VENIVM Myf MELATELS Se Liked “HES = 5 L— x. [— a am) . | (1) od CO. ™ ON vot . FICURE 46.4 C> f ATES PHIL TIALS er'iOu Ge CASN) ADHSNS NULBHE Gb | TOF T NANT O aie YS c 9 OO } O00} CCS gOS UUTI 00d Uo a i nd me T —~ Lk cozot)®*a = Coz) ® Fa | Lm 266 CO (3 rar ™ Uy — WHTVM -~ un sewed >... FIGURE 46.5 267 a Ci J ce | ™ OO ant FART REAL a. * “ WALKER (1670) — Hx eal ie faa) ft a EH 1301520) | | x C ee N a me, wa LP ered C LM © ol © © FIGURE 46.6... ap) © LA 268 C) Cc + \ ce WALKER te) Mei Meo eon (3 a C3 RG ran i — Dwar) 1 | ra PT, Oe oy es, Preise ie i wu, 00d ct Su sd Set of om ‘sf a ~*~ “ee 269 x i i bye pole ! , ; i Pi na ot I i | i “Lm a7 io OL POS d7id a c Ca C (© _ FIGURE 46.8 C © 3 Co SoA PANEL ETRAET OREM POMEL E Obm BoP mila! 5 pm pa Abid i ak i aoe NX AATEN 7 eaten! fo Net emc ot | MAP T MMT ainte SON MO ree o wie b WSF OOS UUs Wiusd} UUG UU ae wert boi i ; j i i i ow { _ 270 x x x » x ; GEATVK co C Cl KF ~ i |- evn | ob an l b waar ab .. FIGURE 46.9 274 aerni OFT areal An Ang alek ear WUTIE UU | Siviens Uo UUs WUT UUG j j E i i i i w\ SL, (g89T) 7a | | | | + ood “” XE oe x x _ a4 ~/ ) | | | ) heal iste 7bsy x i “TLE E OI —~Co (7 | IO LiL te did CS oO nO- 1, ™ co © 210. . FIGURE. 46 272 FIGURE 47 FINAL FET OF ADD-ON HELICITY ELEMENTS FOR 1? PHOTOPRODUCTION See page 148 for key to symbols-and explanation of curves, In this fit the resonances have been changed as follows: P,, (1470) , amplitude -0.250 ———~» ~0.400 F 5 (1688) ; amplitude ~0.600 -—--» -0.500 helicity 3/2 See Table 9, page 161, for complete summary of resonance changes. my Lt. - Nn ‘a bs (y- Jan» OO “| ‘an aa Cr _l C3 C3 C33 C3 - C2 CO of CO al 7) «| C2 ™ C3 = UUTEE ed 3 on a iC) N | = C3 273 | Ov 3 l =i O C iued AWENISCHI + vyautym a Tfot ‘ot detid These S C = ‘en 1. =) cr im bmomt en (2 O . FIGURE 47.1 274 e ag z 4 Sweoens — ( pa Y JUIN AIO PD Gu A z i i bm i a 2% * a | | C2 iM © Py oy ee ot, Lvs id bf GOs WS ieee rw) (5 © + — L pesueyo epnartdue Cryty big 2 y a) whe | J ™! CO / af { x ©) 2 Sf Sf Sy’ ter od PRR I ~*~ an ae) | Cl | ‘en < bemod ‘an 47.2 FIGURE 275 of GEES PE XLETIAET CHET VADA SY ASVOGUAD ao | Mok t OST ATT POM IP ata, Pap gy G Pi | pop Gh GE bag tae Pap TALE H wa WAS LEE BG. | Wh b WUG WS Wu ‘ i i i CS Co “t © ee ~XKEK 4 i. be -. FIGURE .47,3 ™ C Ln. a | () (2 en |. cr ae “4 | OW L. wf CD ef Ld x P.,, (1236) freemen ran C2 | ce = ™] C ) =P CO © © © © i ’ Pod odd tot od | wh Cf Lh dD thong da ALLJI lak FIGURE 47,4 277 f A “SP EN Psy} PTA ET rar i Al pm Ne jae | CLAZANY AUUOON. co | SN ONT OP LN TS OF we PT oN OT oo, *, an Sittcn, rie Pagid HTS PSOE ON? } wlenne: WUG |} UU YL OS VOL UG 0 arn i ; i T j wo UT sot sot nie tae / ar, aol, ic — PI a i f H fat T SVL. z Lote ALGNIQSXD + caNt reg mus wy MGT Led feiemtee) ~~ (Oo in (—) (2 i: | ™ CO. b—| Qu. |. on) 4 270-, FIGURE 47.5 278 © H i | aia, i i Xk MMR K x ao , Coy CO © A’ O- ome = © OB © (Ni sed -.PIGURE 47.6-- 279 Rf — NOG LNCS ku i OORT AT AT Tar: , a ii y Rhee & RASS o Kes id Ra Vw s (0291) 24a é lal } § i & A PN ey oe f ; j “f OS en =r a = 3 H 7) oy i vA | j oN a 2 7 7 ie FIGURE: 4 ad C3 fase - CT aed oa Seco } PRE aad E sf a | FIGURE 47.8: mR ; Koweene a) (_) ) en Or) 281 end Ce tat fen pan Pad PPE Ports > ER uke WALK \ 4 688 P15 & foment | | | I (® 7) oy =F ON OQ I ~F (O C3 ae) co ‘ont C ¢ { FIGURE 47.9 282 Cf ASI ty LINE AG AT ata OPT arate mate pyry : od: Fi ; a EE GALS ARS dS RAR & RAL OF on ee a eo 10. oe fm 2 ~ _ Saxrva i i i i Lou. FIGURE: 47 C (0 283 FIGURE 48 TOTAL HELICITY ELEMENTS FROM FINAL FIT OF a PHOTOPRODUCTION are compared with Walker's total helicity elements (plotted points). The curves are identified by \! for the real part and by or /»« for the imaginary part. fA thE) fLVLPTIAETE A cuit CLAZAS ADVaGoN2o | oo | PYIN DP T ES T Oa ar Tv, on OO? 1 een oce IOS O02 Oo. 284 i ; i i it | ~ CH t Te pe a > cosoi)®s (gest) bts i | x - | | ; teh ye a a te k L w : i a > X\ /\¢ 7 ms ™ OND “+ awe Save ‘ef i i j F ' _, qj 48.1. aan iw aa FIGURE ‘cn Ce wad C2 CS a C oe . * | =H C | d | —™ © co ory ~ i ~ : Pm CO © FIGURE 48,2 ble or OOF rt UUG Uo. at ¢ g (sezi) Fa ~ O° * yeni Se _ cpr md . Cc e oO _w = aaa Oem 286 wow He “f+ 3 4 Lo ot PO ie ee iN LS FIGURE 48.3 LADA? AUVs APT MOAT AAG favar rn at HE oge t : ae U aes + Wu: WIG WU 287 + | Ln wel 4 = C C C LO © - FIGURE 48.4 288 COL9T) | f€G “ALETHET hoo " 00¢ G i i i x K # = C3 C2 C3 oe) FIGURE: 48.5... 265. ” fo LILES Pit) whi JON) Aor, a TORT NOP T aeani Tare alate = 4 WUT WUC | WoL Gre: UBS US e { i Hi j j ® x oie “of i ~*~ 4 es i ' Gj v { Ls € €T Z (OL9T) (OZST) ~ toe ate pte Let Sh e . : we CaNIVA a4 i j } LP? sad C3 Lp un LP ot aed ! 6 co + FIGURE 4 290 Ce ~~ id os ™! C2 oe) A q i | CO 28 ye a bed OW L. NV © .. FIGURE 48.7 Oy T CHA? 7 Wie ' Wehdhe & 2 -) j CO { { NM ~ ie oh Tr 4 Ca TVK CD © . FIGURE: 48.8.5. © I “ c “I oC. CD st, : (8g91) 7" = oo 292 C3 , be: x faba. (2 “td & oy (© £ — SOUT 3 & in) C © “ FIGURE 48.9--. 7 ik “HE 3 ca N FA SRN oe { C of an 293 Ww) rd ow C 17 om co © XO ee we fry . WaVIVA ee) C3 a) — | va ) > -|. Femon ‘a FIGURE 48,10 10. ll. 12. 13, 294 L. A. Copley, G. Karl, and FE, Obryk, Nuc. Phys. B13, 303 (1969) R. P. Feynman, M. Kislinger, and F. Ravndal, Phys. Rev. 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