π⁺ Photoproduction at Angles from 50° to 165° CM. and Energies from 500 to 1350 MeV Citation Thiessen, Henry Archer (1967) π⁺ Photoproduction at Angles from 50° to 165° CM. and Energies from 500 to 1350 MeV. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/A91P-5Z84. https://resolver.caltech.edu/CaltechETD:etd-10042002-155413 Abstract The cross section for the reaction γ + p → π⁺ + n was measured at the Caltech synchrotron. The π⁺ was detected in a multichannel magnetic spectrometer, and the data were recorded in the memory of a pulse height analyzer. The results are presented in the form of energy distributions at 12 fixed laboratory angles from 34° to 155°. cross section measurements are reported with photon energies between 500 MeV and 1350 MeV. No detailed fitting of the entire angular range was attempted; however, a narrow bump in the cross section at 180° is explained as the effect of a cusp at the eta meson threshold. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Economics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Economics Thesis Availability: Public (worldwide access) Research Advisor(s): Walker, Robert Lee Thesis Committee: Unknown, Unknown Defense Date: 27 September 1966 Record Number: CaltechETD:etd-10042002-155413 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-10042002-155413 DOI: 10.7907/A91P-5Z84 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 3901 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 07 Oct 2002 Last Modified: 16 Jun 2021 20:46 Thesis Files Preview PDF (Thiessen_ha_1967.pdf) - Final Version See Usage Policy. 5MB Repository Staff Only: item control page

x’ PHOTOPRODUCTION AT ANGLES FROM SO° To 165° c.x. AND ENERGIES FROM 500 TO 12350 MEV thesis by Henry A. Thiessen In Partial Fulfillment of the Requirements for the Degree of Doctor cof Philosophy California institute of Technology Pasadena, California 1867 (Submitted September 27, 1955} ii ACKNOWLEDGMENTS This experiment was supervised by Professor R. L. Walker. His interest, encouragement, and willingness to talk over problems have made a great contribution to the success of the experiment. Iam indebted to Dr. J. Owen Maloy for many helpful discussions during the design and construction of the electronics. Joe Laurinovics and Ray Green did most of the construction of the electronics. Professor A. V. Tollestrup suggested the use of integrated circuits. Mr. Mike Hauser joined the cxperiment at the time when the fast electronics was being set up. Since then, he has played a major role in planning and carrying out the experiment. I gratefully acknowledge the large number of helpful comments aud the many hours of dala laking which Mike bas contributed. The data analysis of this experiment was done in close collaboration with Mr, Stan Ecklund. Since his experiment was very similar to this one, it was possible to use several computer programs for both experiments. Iam indebted to Stan for his contribution to the programming as well as for his many helpful discussions, No synchrotron experiment can succeed without the competent help of the synchrotron technical staff. In particular, I would like to thank Larry Loucks, Al Neubeiser, and Earl Emery for their contributions to the maintenance of the synchrotron and the liquid hydrogen target. For financial support, Iam indebted to the National Science Foundation, the Atomic Energy Commission, the California Institute of Technology, my parents, and my wife's parents. iii ABSTRACT The cross section for the reaction y+ p- 7 +n was measured at the Caltech synchrotron. The mn” was detected in a multi-channel magnetic spectrometer, and the data were recorded in the memory of a pulse height analyzer, The results are presented in the form of energy distributions at 12 fixed laboratory angles from 34° to 155°. 378 cross section measure- ments are reported with photon energies between 500 MeV and 1350 MeV. No detailed fitting of the entire angular range was attempted; however, a narrow bump in the cross section at 180° is explained as the effect of a cusp at the eta meson threshold, iv To Challis TABLE OF CONTENTS PART PAGE L TINTRODUC TION 1 I, EXPERIMENTAL METHOD, GENERAL 3 It, APPARATUS 5 A, The Photon Beam, Liquid Hydrogen Target, and Beam Monitoring Equipment 5 iB Magnetic Spectrometer and Counters 8 C, Electronics 15 Iv. EXPERIMENTAL TECHNIQUE 23 A. Particle Identification 25 B. Empty Target Background 25 C. Negative Field Background 26 D. Excitation Functions as Proof of Particle and Reaction Identification 32 V. DATA AND DATA ANALYSIS 48 A. Cross Section Calculation 48 B. Resolution Unfolding 54 C. Data Point Summary and Internal Consistency of Data 57 D. Tabulation of Data 65 E. Angular Distributions by Interpolation 98 F, Summary of Experimental Errors 104 G. Data Fitting 105 VL CONCLUSIONS AND SUGGESTIONS 113 APPENDICES 115 L Beam Monitoring and Hydrogen Target Details 115 I Nuclear Absorption 122 vi PAGE PART Ii, Multiple Scattering 132 IV. t- Decay Corrections 136 V. Resolution Calculations 147 VI. Plexiglass Target Calibration Runs 152 158 REFERENCES 6a, b. Ta-1,. 8a-d. 10, 11, 12. 13. 14, 15. LIST OF TABLES Characteristics of 600 MeV/c Magnet Counters Properties of 600 MeV/c Magnet Momentum Channels Coding of Address Register Bits Fractional Empty Target Rates Summed Over Seven Channels Summary of Negative Field Runs Kinematic Parameters and Some Intermediate Results of Cross Section Calculation Average and Unfolded Cross Sections Interpolated Angular Distributions Absorption Measurements by Direct Method Absorption Measurements by Improved Method Calculation of Total Absorption Cross Section per Atom for Pions Incident on Plexiglass (C 5H,0.) Material Through Which Pions Pass Calculation of Nuclear Absorption vs. Pion Momentum Resolution Function for Pions Counted by r-y Decay Process Plexiglass Target Calibration Run Summary PAGE 13 14 21 27 29 66 99 123 124 128 130 131i 148 153 13a-q. 14a, b, 15. 16, 17, 18, vili LIST OF FIGURES PAGE Beam Area Layout 7 600 MeV/c Magnet and Counters g 600 MeV/c Magnet Momentum Resolution Functions 10 600 MeV/c Magnet Optics at 10 Kilogauss 12 Momentum Hodoscope Counters pi 16 System Block Diagram, 600 MeV/c Magnet Electronics 17 Trigger Logic System Block Diagram and Pulse Height 18 Analysis System Block Diagram Data Storage System Block Diagram 20 Negative Field Background vs. Lab Angle 31 Excitation Functions 34 Location of Data Points on K-6 Plane 63 Integral 4° Probability Distribution 64 Data 79 Cusp Fitting 110 Total Absorption Cross Section Per Atom 126 r Plexiglass (C..H,O,) m-. Decay Resolution Functions 139 Decay Correction Summary 145 Laboratory Angular Resolution Functions, 600 MeV/c148 Magnet 19. 20, 21, PAGE Total Momentum Resolution Functions, 600 MeV/c 149 Magnet R. M.S. Resolution in Lab Energy (K) vs. Lab 151 Angle Plexiglass Target Calibration Run Data 154 L INTRODUCTION There is presently a considerable theoretical interest in photoproduction data. Several authors have used the data for evaluating sum rules, (1,2, 3) For these purposes, a multipole and isotopic spin decomposition of the photoproduction amplitudes is desired, Similar decompositions are already available for the pion scattering data, (4, 5, 6, 7, 8) This experiment was designed to collect a large number of points of the cross section for y+ p- nr +n with sufficient resolution to extract the energy dependence of the cross section, When the data of this experiment are combined with the data of Ecklund and Walker, (9) a consistent set of cross sections is available for angles between 6° and 165° c.m, and photon energies between 589 MeV and 1269 MeV, with some additional data available between 500 and 1350 MeV. In particular, this experiment covered the angular range from 50° to 165° c. m. for the entire range of energies (see Section V-C for further details), These data are being combined with data from the other single pion photaproduction reactions and an attempt is being made to determine the decomposition of the photoproduction amplitudes. (10) However, it appears likely that much more data will be required on the polarization and the cross section in the other channels before a unique decomposition can be made for energies greater than 800 MeV. A second important consideration in the design of this experi- ment was to set up a spectrometer which can be used simultaneously with the already existing High Energy Magnet. A 600 MeV/c spectro- meter was constructed by modifying the former Low Energy Magnet, then the spectrometer was carefully calibrated and instrumented with several general purpose counters. This spectrometer is available as a laboratory instrument, and an experiment is now in progress which uses both magnets simultaneously. (11) Since this experiment and the experiment of Ecklund and Walker were done at approximately the same time, a considerable amount of work was saved by avoiding a duplication of eifort. Thus the same computer programs were used in the data reduction of both experiments. In general, this author did most oi the programming for magnet resolution, etc., while Stan Ecklund did the evaluation of the cross section integrals and a large amount of data fitting. In practice, a strict division of the work was not always possible, and many parts of this thesis are very similar to his thesis. I EXPERIMENTAL METHOD, GENERAL The reaction y +p- nm? +n was studied at the Caltech 1.5 GeV Electron Synchrotron, The experimental method was very similar to that which was used in several past experiments 2» 13, 14, 15, 16, 17) namely, the photon beam irradiated a liquid hydrogen target and the positive pions produced were detected and momentum analyzed in a magnetic spectrometer. The kinematics of the reaction relate the observed quantities, Pin: Sap? desired quantities, k, ®@_qy, (where k is the photon lab energy) under the assumption that only one pion was produced, If two or more pions are produced, as in the reactions, + 0 y+prm +ntt + - > 7 +p > nm’ + N+ (nn) soe then there will be a minimum photon energy, Ko required to produce a m with the observed angle and momentum. In general, Koo will be greater than k, In the energy region of this experiment, it is possible to choose Eo» the maximum energy of the photon spectrum, to lie between k and Ko so that the multiple pion reaction will not be observed. The background of particles incident on the spectrometer includes protons, electrons, and muons, Protons are eliminated by velocity selection in a lucite Cerenkov counter, crude time-of-flight requirements, and dE/dx selection in two scintillation counters. Electrons and muons are indistinguishable from pions in the electronics. This experiment relies on the fact that previous experiments have shown that electron contamination al large angles from the photon beam is small; several checks with magnet field reversed have been made to look for this kind of contamination. The major source of muons is the decay of the T, T ur +, since typically 20% of the pions decay while passing through the spectrometer. Muon pair production, y+p- ur + LL +p, is usually eliminated by the same kinematical requirement that eliminates pion pair production. In addition, the cross section for muon pair production should be down by a factor 4_ 1 ~ \T37 can be safely ignored. The spectrometer, the 600 MeV/c Magnet, differs from those used in the earlier work in that it collects data in several e 4 from pion pair production. Thus this source of events momentum channels simultancously. Because the kinematic transfor- mation between lab and center-of-mass co-ordinate systems varies rapidly with P. and ae ab? it was not feasible to measure angular distributions at fixed values of k, Instead, the data were taken as energy scans at fixed lab angle. Several spectrometer momentum settings were required for each scan and an appropriate value of By was chosen for each spectrometer setting. Angular distributions were obtained by linear interpolation in the measured data. The data were taken during two separate periods, May - August 1965, and December 1965 - March 1966. Each point was measured at least once during each period, and checks were made for consistency between runs, Mm APPARATUS A, The Photon Beam, Liquid Hydrogen Target, and Bcam Monitoring Equipment The photon beam was generated by bremsstrahlung in a 0.2 radiation length tantalum radiator in the Caltech 1.5 GeV Electron Synchrotron, At energies greater than 0,91 GeV, the synchrotron produced a nearly uniform 100 msec, beam spill once per second. For energies less than 0,91 GeV, it was possible to run the synchrotron twice per second with a beam spill time of 50 msec, At the lowest energy used in this experiment, 0,66 GeV, it was extremely difficult to obtain a uniform beam spill, The cause of this difficulty was not fully understood, but it is believed that the radio frequency control system was sensitive to noise from many sources when operated at the very low power levels required to make a uniform dump at this energy. The result of this difficulty was a large spike superimposed upon the normal spill. This spike, which was of about 200 usec duration, contained on the order of 5% of the total energy of the dump. During the first data-taking period, this problem was eliminated by careful tuning, but during the second period it was not possible to eliminate this effect. Since an accidentals monitoring system was used continuously during the experiment, the 660 MeV points were repeated with this poor spill. The liquid hydrogen target is the same one that has been used by the magnet group for all experiments since that of J. Boyden. (18) The liquid hydrogen is contained in a long 3 inch diameter cylinder ("appendix") with 0,005 inch mylar walls. The axis of this cylinder is perpendicular to the beam line and is coincident with the axis of rotation of the spectrometer. The beam line was adjusted to intersect the axis of the cylinder and the beam was collimated to a rectangular cross section 1 1/2 inch horizontal by 1 3/4 inch vertical, Because it has been observed that after long use "ice" builds up on the walls of the appendix) the target was disassembled and cleaned at approximately monthly intervals. In addition, empty target runs were usually taken within a week of full target runs, so that a gradual accumulation of "ice" would be corrected by the empty target subtraction. The beam area layout during the first data-taking period is shown in Figure 1. For the second data-taking period, the quantameter was relocated on the scraping wall immediately up- stream of the hydrogen target. Otherwise, the setup was unchanged between the two data-taking periods. Figure 1 shows the High Energy Magnet at an angle for which the beam line intercepted the magnet yoke. During the running period of this experiment, Mr. F. Wolverton was setting up another experiment to detect protons at small angles from the photon beam with the High Energy Magnet. Occasionally, Mr. Wolverton needed to make a test with the High Energy Magnet in the beam line. Under these circumstances, a careful check of the consistency of data taken with the Iligh Energy Magnct in the beam linc and data taken under normal circumstances showed no significant difference. The beam moniloring equipment consisted of several different instruments which were used at various times during the run, ‘The primary standard was a Wilson type quantameter, (20) An absolute calibration of this instrument against a Faraday Cup was made at the Stanford Mark Ill Linear Accelerator on 2 May, 1966. YASNVH) NO! Y3HILVI Nv3d ! mokvey]T vary weeg °[ sINsTyZ (aN wyae dO _NO NMOHS} XIONSdd¥ LIOYVL N3SONOAK Y3L3WVLNYNO 1BOVP_ WANDA [7 Vi L39NYL N3SONQAH / ( 4 _s ) fan YyOLMdvYa SS 2°N M3EWVHD NO! NIHL ) WV38 HLNOS ANOVA ASYSNF- HOI L39NVL NSDONGAH “WTON / \\weiwwimos AMV JGNOVW ADYSN3 wor” SIENOVA ONIdCZSMS SY3IdVHDS {ON Y38WVHD NOI NIHL This calibration differed from the previous absolute calibrations and the theoretical value by less than 1.5%. (21) The secondary monitors consisted of two very thin ion chambers located upstream of the hydrogen target, a thick ion chamber located in the beam catcher, a 2-counter telescope which monitored particles produced at 90° from the hydrogen target, and a radio frequency monitor of the circulating beam which is commonly called the "40 mc. probe'’, The uses of these secondary monitors are described in Appendix I, B. Magnetic Spectrometer and Counters The magnetic spectrometer used for this experiment, designated the 600 MeV/c Magnet, was constructed by modifying the former Low Energy Magnet. The magnet is of the wedge-shaped, uniform field type and is very similar in design to the magnets which have been used by Professor R, L. Walker and his students for many years, An elevation view of the spectrometer is shown in Figure 2, The calibration of the spectrometer is the subject of a separate report (2). and only a few important results will be summarized here. The solid angle of the spectrometer is 3.3 x 10° sr. and the total momentum acceptance is 10.3%. The momentum interval is divided into seven smaller channels. With the beam size typically used in this experiment (1.5 inch horizontal by 1,8 inch vertical) the r.m.s. momentum resolution obtained is 1.10%, when no scattering or other similar resolution degrading effects are included. (Note that the full width at half maximum is 2, 2 times the r.m.s. width for a Gaussian resolution function), A graph of these basic resolution functions is presented as Figure 3, RGET oO ul ely ua ox ea ZO Sa =a LIQUID HYDROGEN TA PHOTON BEAM AREA 24" . 12" SCALE SHIELDING ry NC MAGNETIC LEAD SHIELDING SHIELDING MAGNETIC 300 MeV/c Magnet and Counters a Jer LE Figure 2. 10 € omnsty OVo- "4 /(°%d-d) Olc+ 0 1 1 ' J T 9 J | qd 8) g Vv J TANNVHS WLOL SNOILONN4 NOLL IOS3Y WALNSWON LINSVW 2/A2W 009 i 1 i Jj l i it (SLIND AYVeLIGNV) STONY aiT0s 11 A graphic display of the results of the magnet calibration measurements is presented in Figure 4. In this drawing, a contour map of the magnetic field is superimposed on a drawing of the pole tip structure. Three particle trajectories calculated by the ray tracing program 29) are shown. In addition, the effective edges (for a model with uniform field and zero fringe fields) computed by the same ray tracing program are shown. The accuracy of 40 AP/P calculated from ray traces is expected to be + 1% when a small correction for the variation with central field is included, (22) The uniform field of the spectrometer is monitored with a nuclear resonance magnetometer, The central momentum of the spectrometer has been calibrated against the magnetometer by floating wire techniques, (22) This calibration has an absolute accuracy of + 0, 2% for a fixed location of the beam centroid. Because the beam centroid seems to wander slowly for fixed synchrotron energy, and because there is a systematic movement of the beam centroid with the synchrotron energy, the total error in the momentum cali- bration is taken to be + 0.5%, The counters used with the 600 MeV/c Magnet are very similar in design and function to those which are in use on the High Encrgy Magnet, (9) The location of the counters is shown on Figure 3. The physical characteristics and use of each counter are given in Table 1. The fan counters were designed so that no charged particle originating in the hydrogen target can undergo a single scattering from the pole tips and be counted in $2 without also being counted by one of the arms of the fan counters. In retrospect, it might have been useful to strengthen the specifications to include provision for vetoing neutrals which convert in the pole tips. The fan counters of the present design veto all events generated in the USN 12 3903 JAILIS453 LIXa ¥3INNOD SYNLYAdY SSNVDOM> O1 IV SO1LdO LANOVW O/APW 009 ‘P BINS (d¥9 7) dil 31d (SNV1d AMLAWAAS NO ) °a/@ ANVLSNOD 40 SYNOLN 4 OD —-—— (dv9 8) 3ddld 310d | L39YVL 1 \ N390H0AH WO fanaa fenenne 3903 AALLOI4dS SAONVYLNS ' ' ae ‘ ‘ I 4 4 i i t ! i ' i I ‘ a 1 ' SHIMOLOSr VEL JVWILYV “Vv jo adid yustt ysnory} Sutssed ajotyred YIM STUBAS 019A "SOOR] aod WIcA BULIOWVOS OJOA *suojoid Jo uotpefar xp/qp pue (@S ‘V) JUSITJ-Jo-IuTLL 2 8'O ~ UeYy SSa_ AWOOTAA YPM Saparyred spafar YoryM 1eyuN0d AoyUaTED ‘(g onST J aes) UnjJuawoW souTjeag 13 ‘xp /qp Aq suojord jo uonoalor pue UOTHUTJep aToTpTed oj peasy "odid WYSIT O}IONT uTYy] ‘SuoT UG paynoy, *Tajeworjads Jo a[suye prjos SOULE “oSP ye yo spuy "poh 3 ysno1y sstd soporszeg SyUOUWIULO LS) SIOPUNOD JOUSLT, 2/ASW OOO JO SOTISTISJOVALYD V9S99 VOT89~-% VGG99-¢ VOT89-¢ VS5S99 VSG99-G VOT89-T oqnjojoyd LOYETIUTOS ZOL HN TOVETINTIG Z0l AN LOJETIEUTOG ZOl AN eqony LAN LoyeTIHUTOS ZOT AN royeTTHUTOS ZOl AN TOPETTEJULIS GOT AN od AJ, yyed Tet r10Uu ut 10U yyed yeurrou ul jou vL 0 $8 °S 082 "0 X 00 “@1 * 00°8 A *? QINS1lY UT UMOUS Se quoq Spor Z/T X @/T-8 sued > 096 “0 * 00°ST * OS°L és 00‘°T * 00ST X 0G °L OT Jeuuey) d 80 °T .GLE OX 00ST X GL‘. o8eIBAY PL°O «(992 °0 * 00°ST X OSL Ts PG ‘0 Gel ‘0% 0S 6 X GL °@ V gum? /ws (Soyaut) azoyunoy (Sutddeim LOTSUSUTE (Surpnyour) ssveyl "T DIGVL 14 TABLE 2. Properties of Momentum Channels of 600 MeV/c Magnet Width (P- Py) /P, AQ AP/P, Channel (inches) x 102 x 10° Logical Definition A 0,759 -4,29 4.314 ppl p2.p3 B 0.734 -2, 96 4.324 Pp. pl. pe. p? C 0. 756 ~1.58 4.612 B°. pl. pp? D 0.753 -0.13 4,800 Bp. pl, p2. 5° E 0.758 1.38 4,976 6°. pip. p? F 0,734 2,92 5.000 Pp’. pl. p2. ps G 0.759 4.59 5.359 Do. pl. pe p? H= TOTAL 5,253 0.19 33. 65 Sum of events satis- fying logic for each of above channels. (Note that this definition is not the same as p?, php? p?, ) = mean momentum of particles accepted by a given channel Pp P, = central momentum of magnet 15 pole tips by charged particles, but approximately 1/3 of the area of the pole tips is not shielded against events generated by neuirals. The momentum-defining counter consisted of four scintillators which were mounted in the form of a seven channel hodoscope. A drawing of this counter is shown in Figure 5. The important parameters defined by the seven channels of this hodoscope are presented in Table 2, The decoding of the output of this hodoscope was done by the IBM 7094 computer, The logical definition used for this decoding is also given in Table 2. C, Electronics The electronics system for this experiment was broken down into three independent subblocks: a fast logic system containing the coincidence circuits; a pulse-height analysis system containing linear gates and discriminators; and a data storage system making use of a Nuclear Data 1024 channel pulse-height analyzer. The relationship between these three subsystems is shown in Figure 6. The block diagrams of the fast logic system and the pulse- height analysis system are given in Figure 7. The modules from which these two systems were constructed have been described in the literature. (24, 25) Some of these modules were upgraded by installing more modern transistors on already existing circuit boards; otherwise these modules were the same ones which were used in the Groom- Marshall Kr telescope experiment, (28) The particle signature in this experiment consisted of a fast (10 nanosecond) triple coincidence, A-S1-52, with coincidence circuit input biases of approximately 1/4 minimum ionizing. The basic trigger generated by the fast logic was 7d siajun0) edossopoy wnJUSWOW “Gg BINSTA Vv “TaNNVHO ——— od YB.NNOO @ 3NNVHO ——— 9. TSNNVHO ——= || = ,d YSLNNOD Q “3NNVHO ——- 3 3NNVHO —— zd YaLNNOO 4 73aNNVHO —~— 9 NNVHO —- | ed HALNTOO ea od YALNNCOD id WALNNOD tn ee ee ee ee ee i nee | zd Y3LNI00 e¢ YALNNOOD | ad 5 | AdVL YadVd QIHONNd VIA p6OL NEI OL SOINOULOATS LANOVW 9/A®W O09 WYNOVId yOO18 NALSAS 9 9nd1q NOLLVWHOSNI WAISAS NOLLVWYOSNI LHOIBH -3S Nd SISATVNV ee ————- | HOISH- 3S Nd TWLISIG LHOISH - Astin SOIWNV 319 /\ WALSAS Yya99IML <—_ S9VNOLS k= viva Yvd NOILLVNYOSNI WALSAS NOLLVWYOSNI ONIALL << ____. ONIAIL WL9I0 919071 LSV4 SOWNV 18 L 8in3tJ WVHOVIO HOOTE WALSAS SISATWNY LHOISH 3S1Nd (4) Oo 2-31 + ie a osia va IS OL «—i » oo ° ra ‘ ze . ec iyo yS99N1L YALdVOV ONITWOS OL yFTVOS B¥d 0449079 |wi- oA] VI-OL VIA WL y31vIS osid Bv9 Kd it - GL su OS ASN +98 Ve-3L NOLVNINGAL INA di 1S WOHS NOULYNINN3SL LndNd ONIOD Mii tb -WGL eel] cov 4v730 SU OO} v1 SR 3LVS IS OL oe | BV 2S OL VI-WL act | Lt xai¢ Wy -AW 19 PAR = A: 81-52 + Ay Si- $2 where A, indicates that the A signal was delayed by 100 nanoseconds from the correct timing. The signal PAR was usedta operate the linear gates of the pulse-height analysis system and to trigger the data storage system. Several scalers were used in the fast logic system. These scalers were extremely useful for diagnostic purposes, but they did not record numbers which could be used directly in cross section calculations, The final data were recorded only by the data storage system. The data storage system was a new feature of this experi- ment. This system operated on the principle that each event could be represented by a 9 bit binary number, Each bit of this binary number was controlled by a digital output from either the fast logic system or the pulse-height analysis system. For each event, a count was added to the channel whose address was the same as this binary number. After a data-taking run, the contents of the memory were punched on paper tape. The IBM 7094 computer was then used to sort the 512 possible types of events into physically useful classes. (27) A block diagram of the data storage system is presented in Figure 8, For further details of the electronics, the reader should refer to the SCALING ADAPTER instruction manual, (28) The correspondence between digital signals and the various bits of the binary number which defines the address is explained more fuily in Table 3, Note thal lhe 2° bit is always set to 1 so that the result will be stored in the second half of the memory. As an example of how the address for each event is generated, consider the event 20 WVYOVIAO AHO01G WALSAS A9VYOLS VLVG H+<=—— 30d0ud IW Ob <<——— Wd g ens i t M3073 WALSAS TOYLNOD yaSoIdL SLINIOd LSAL WV\ yS99INL VHd HOLINOW A LHOI3H- 3S Nd WOus STYNEIS AYOWSAW YIWIS MBLIYMIGAL YO TANNVHO +20! Bd VL Uadvd OL Viva LINDYID OLAA -vs7 \evs YVIDNN “ONIOD GALOA TAS HOLIMS LIdNi Ol binvidih y_\ SLANI SLNdNi z SOWNY ONIOD SS S.LYIANOD SYaLSINAN 82 WHSI OL uO < 4ass"a 2 Q103-Ol [= LI8 | ve SOIWNY Twn OK 8 « Vivd Y¥va1onN “WOILNAI O} 2 ———— O3ASNNN a IOV << —— NY 2S <——— 15 <——_—— <—— <d <———— od <——__- id <— od al TABLE 3. Coding of Address Register Bits Address Bit Signal Source 2° p? 2 pi 2” p? 2° p? of LC 2° Sl 2° 82 a! (FV): PAR=FAN 2° A, Sl: 82 = ACC 2° unused Requirement 1/2 x minimum ionizing 1/2 x minimum ionizing 1/2 x minimum ionizing 1/2 x minimum ionizing ~ 1 photoelectron or * > 0,8 ~ 2.5 x minimum ionizing ~ 2.9 % minimum ionizing F or V count within - 8 ns of PAR PAR generated by accidental event in A always ''i'' so that all events are stored in second haif of memory 22 3 52 pl . p*, pl. p? ACC: FAN. S2- SI- LC- P -P where S1 and S2 represent the high biases ( 2.5 x minimum ionizing) on these two counters, This event is a typical pion in the central momentum channel. The address corresponding to this event is 1000010110 binary, or 534 decimal, Because only 512 of the 1024 available channels of memory were needed for storage of the data, provision was built into the control system to allow the pulse-height analyzer to go through a normal pulse-height analysis cycle before storing the digital data for each event. The result of the pulse-height analysis was always recorded in the first half of the memory. Since the pulse-heighi analysis cycle did not interfere with the normal data storage cycle, the pulse- height analyzer was free for use as a diagnostic tool during data taking. Using this feature, the pulse-height distribution in each counter was checked on a daily basis. An additional provision built into the control system permitted the use of the normal clock channel of the memory, channel zero, for recording beam monitoring information. This feature proved to be of only marginal value, however, fur nu single beam moniior was considered to be stable enough for use in cross section computations. This subject is discussed further in Appendix L 23 IV, EXPERIMENTAL TECHNIQUE A. Particle Identification The major problems lo be solved by the particle identification scheme were elimination of proton contamination and correction for accidentals. The proton contamination problem was most serious at small angles and high momenta where the time-of-flight requirements did not completely eliminate protons and the ratio of 7 to protons incident on the spectrometer was 1:3. The efficiencies of the various devices which eliminated protons are given in the following table: Typical Pion and Proton Efficiency at 570 MeV/c Technique e Ep Time-of-flight 1, 00 0.1 S1 (high bias) 0,05 0. 98 S2 (high bias) 0.05 0. 98 LC 0, 98 0, 03 The time-of-flight requirement in conjunction with any two of the other counters was more than sufficient to eliminate protons under the worst conditions. The redundancy provided by LC permitted a continuous monitoring of the efficiencies of each counter for pions and protons, The definition of nm’ used in this experiment was n’ = PAR- (81-52) 24 where Sli and S2 indicate the high biases on counters $1 and 82. The IBM 7094 computer automatically corrected each run for the inefficiency of the pion definition and any residual proton contami- nation, Both of these corrections were less than 1.0% in the worst case, The counter system of the 600 MeV/c Magnet was designed for minimum mass in the particle trajectories in order to minimize the effects of multiple scattering on the resolution of the spectro- meter. Since only one aperture counter was used, this system was particularly sensitive to events produced by an accidental in counter A and a real event in the rear counter system. Since the data recording system was triggered by A-S1-52+A a’ S1-S2, the IBM 7094 automatically corrected the observed number of pions for this type of accidental by subtracting the events with an A q* ACC pulse from those events with no ACC pulse. A correction for accidentals in the mamentum defining counters was also made. This correction was based on the observed number of cvents with counts in the momentum hodoscope which could be generated only by accidentals or two particles passing through the hodoscope within the 50 ns. gate, An example of such an event is p?, pl. p’. p3, Eight of the sixteen possible kinds of event in the momentum hoduscupe fell ilo this calegory, and these events were used to compute the corrections for each channel on the assumption that there was no correlation between the location of the true event and the second particle. The magnitude of this correction to the sum channel (H) was typically 0.5%, while the correction to individual channels was less than 2%. It is important to note that events in which a second particle passes through the channel adjacent to the true particle cannot be distinguished from single particle 29 events, However, such events were counted only once and were counted in either the correct channel or the channel adjacent to the correct channel, Several checks were made of the efficiency of the fast electronics. For counters A, 81, 52, and V a separate small counter was used to define a beam and test the efficiency of the coincidence circuit. In each case the efficiency was greater than 99%. The 1% of inefficient events were observed on an oscilloscope and most of these were found to have no pulse at all in the counter being tested, These events were assumed to be events due to nuclear absorption or photon conversion in the counters and the electronic efficiency was taken to be 1.00 in each case. The A:S1+S2 and A q’ S1-S2 systems were checked by installing an extra 100 ns, length of cable in the A input. The result was that the two systems gave the same number of counts to within 5%. The fan counter efficiency was tested and found to be greater than 95% for minimum ionizing particles passing through the tip of the longest arm of each counter (see Figure 2). Fan accidentals in the F + V system were found to be less than 1% under normal operating conditions, On the basis of these measurements, it was believed that the overall efficiency of the electronic system was 1.00+ 0, 01. B. Empty Target Background The empty target background was measured on two or more occasions for each data point. In general, empty target runs were taken within a few days of full target runs to correct for any possible buildup of solid substances on the mylar cup. For those cases in which the high energy magnet yoke was in the beam line for a full 26 target run, an empty target run was taken under the same condilions. Typically, one-fifth of the total running time was spent measuring the emply target background, For illustrative purposes, the observed ratios of empty target to full target rates are presented in Table 4. ‘The data have been summed over the seven channels and averaged over the several runs taken at each point. However, the cross section computing program did not average the empty target runs; instead, it associated each full target run with a particular empty target run and calculated the cross sections independently. Only in this way would a varying empty target rate be correctly treated. C. Negative Field Background Since nv electron detector was used in this experiment, a series of tests was made to look for possible e” contamination in the n* events. These tests were made with the normal magnet and synchrotron settings, but with the magnet field reversed. Under these conditions, the only single pion photoproduction process which can contribute is the reaction Ytrn- 1 +p Since neutrons are found only in the target structure, these events should be removed by an empty target subtraction. If we assume that e” and e” are produced in equal numbers, as in pair production, then the e yield in the field reversed run should be equal to the e* contamination in the normal runs, 27 TABLE 4, Fractional Empty Target Rates Summed Over 7 Channels (See Table 6 for Point No. Definition) Point No. Empty/ Full Point No, Empty/ Full 34-1 5.22 0.3% 84-1 7.84+ 1.1% 34-2 4.%7+0.4% 84-2 6,04 0.8% 34-3 6.1+0,4% 84-3 3,9+ 0.6% 84-4 2.94 0.5% 40-J 3.9+ 0.3% 85-5 5.4 = 0.5% 40-2 3.8 + 0.3% 84-6 4,9 4+ 0,5% 40-3 4.64 0,6% 94-1 7.84 1.0% 48-1 3.6 + 0.4% 94-2 5.2-0.7% 48-2 3.4 4.0,3% 94-3 4,5 +0. 7% 48-3 4,6 + 0.5% 94-4 2.8 + 0.5% 48-4 4,9+0,5% 94-5 §,0+ 0.7% 53-1 4.8+0,5% 108-1 8,0 + 0. 8% 56-2 4,6 + 0,5% 106-2 5.8 + 0.7% 56-3 4.5 + 0.5% 106-3 4,9+ 0.7% 56-4 3.6 + 0,5% 106-4 4,9+ 0.7% 106-5 5.6 + 0.7% 64-1 4.7 + 0.5% 64-3 3.6 + 0.5% 129-2 4,720.9% 64-4 4.640.5% 120-3 5.94 0.7% 64-5 6.44 0.5% 120-4 5.34 0.7% 120-5 6.8 + 0.8% 7A-1 5.6 + 0, 8% 74-2 4.74 0.7% 134-1 6.2 + 0.6%, 74-3 4.3 +40.5% 134-2 6.0 + 0. 9%, 74-4 4.62 0.5% 134-3 4,9 + 0.6% 74-5 4,.540,7% 134-4 5.6 40.7% 74-6 3.74 0.5% 156-1 10.7 + 1. 2% 156-2 5.7 + 0. 8% 156-3 7,4+ 1.0% 156-4 10.5 4 1.1% 28 The field reversed runs were taken at several points which scanned the entire range of angles and energies used in this experi- ment, In order to improve the statistics, the resulis were summed over the seven momentum channels. The total amount of synchrotron time used for each of these points was approximately equal to half the amount of time used at each of the normal points. The results of these negative field tests are presented in Table 5, These results indicate that approximately two thirds of the observed events are produced in the target structure, but that the remainder of the events are produced in the hydrogen. Except for the points taken at the highest energies and most backwards angles, neglecting these events would result in errors which were small compared with the statistical errors of this experiment, Several possibilities for the source of the negative field events have been considered. n° photoproduction with conversion of the decay photons in the target structure could result in a source of high energy electrons. However, this process can be calculated from known 3° cross sections and gives an upper limit of 0. 2% of the =" rate. If photons were converted in the aperture counter at the rear of the magnet, then low energy electrons could be counted, To check this effect, a 1/8" copper radiator was placed on the hydrogen target side of the aperture counter, This radiator hada thickness in radiation lengths of 29 times that of the aperture counter, For point number 134-4, the full target negative field yield was 0.17 + 0.02 counts/QBIP, while with the radiator in place this rate increased to 0,55 + 0,07 counts/QBIP, If we assume that half the full target events are due to 1 produced in the target walls, we would have expected an increase of a factor of 15 if all the remaining events were due to photons converting in the radiator, whereas a Point 34-1 48-2 64-3 84-1 84-4 106-1 106-4 134-1 134-3 * summed over momentum channels so that AQ AP/P = 3.4 x 10° #* 41 QBIP = 1,2 x10! 29 TABLE 5, Summary of Negative Field Runs Fuil Target. 7” /QBIP 0,950 + 0, 07 0. 400 + 0, 04 0, 330 4. 0, 03 0,110 + 0, 013 0, 205 + 0, 017 0,113 + 0, 014 0.187 + 0.017 0.111 + 0.015 0,119 + 0. 011 *" Empty Target - 4k nm /QBIP 0, 620 + 0,06 0, 340 + 0.04 0, 200 + 0,02 0,049 + 0,009 0.110 + 0,015 0,064 + 0,010 0, 125 + 0, 016 0, 052 + 0,009 0,100 + 0,012 3 Mev Difference - AK tr /QBIP 0. 330 + 0. 09 0, 060 + 0. 06 0,180 + 0,04 0, 061 + 0, 015 oOo .095 + 0, 023 0, 049 + 0,017 0, 062 + 0, 023 0.059 + 0,017 0, 019 + 0.019 [= . 012 + 0, 003 =) . 003 + 0. 003 0. 008 + 0, 002 0. 007 + 0. 002 0, 012 + 0, 003 0, 049 + 0, 017 0. 015 + 0, 005 0,055 + 0.017 0, 007 + 0. 007 4 30 factor of 3.2 + 0.4 was observed. Thus. this process can only account for a small fraction of the observed events. The contri- bution of multiple pion photoproduction was also checked, Using the known shape of the tails of the resolution functions due to decay and multiple scattering and data on 1 photoproduction at 84° lap 14) , we find that at most 10% of the observed events can be due to this process. The negative field events can also be due to low energy pions or electrons which have the wrong momentum but can be counted because of wide-angle scattering processes, or the events may be due to conversion of photons in portions of the magnet iron which are not guarded by veto counters. Neither of these possi- bilities was investigated in any detail. The conclusion drawn from the negative field runs was that an unexplained background exists and must be subtracted from the 7’ data. To make this subtraction, it was necessary to extra- polate to angles and energies at which no negative field runs were taken. For the purposes of this extrapolation, the negative field yield was assumed to be a function only of lab angle. The empirical formula oO 1” /QBIP = 0,03 + 0,05 (2-48 )? 90 was found to give a good fit to the data, This function and the data of Table 5 are plotted in Figure 9, In order to indicate the expected errors in this correction, an rms error of 1/2 the correction has been included in the error bars of all the cross sections measured in this experiment, 0.50 0.40 0.30 w~ YIELD (COUNTS/QBIP ) ro) & 0.10 31 T ' u i r ' NEGATIVE FIELD BACKGROUND VS. LAB ANGLE t | 0 30 60 90 120 150 @.ag (DEGREES) iso Figure 9 32 Experimental evidence for a smali positron contamination at large angles is lacking in previous experiments, For experi- ments at small angles, the positron detection system usually showed a large ratio en /n* which decreased rapidly to zero near 15° lab, For angles between 15 and 45°, et /n was found to be small and (12) nor Kilner!) used electron detection systems neither Dixon for lab angles greater than 55°. One bit of evidence is available from the present experiment. The excitation curve taken at Bab = 64° near K = 880 showed a background of events in the below threshold region. This background was 0, 15 + 0,02 counts/QBIP in seven channels before correction for negative field contamination, The correction used in this experiment gives 0. 10+ 0. 05 counts/ QBIP. By comparison, the 1 yield was 5.0 counts/QBIP for the normal point. Thus it appears that the correction used gives a reasonable but crude approximation to the true background, D. Excitation Functions as Proof of Particle and Reaction Identification Two excitation functions were measured during this experiment, The first was taken near Som = 95° and K = 900 MeV, and the second near eam = 150° and K = 750 MeV. For each measurement, the magnet was set at constant momentum and lab angle while the synchrotron cnergy was varied. The counting rate in each channel was measured as a function of the synchrotron beam energy meter reading. The expected values of these rates were computed from the cross sections measured in this experiment and the resolution function used in reducing all the data. This resolution function includes the effects of multiple scattering, pion 33 decay, and angular resolution. The data and the expected yields are plotted in Figures 10a - 10n. The plotted data were corrected for empty target and negative field background. Several important conclusions can be obtained from these data. The first conclusion is that in the off kinematics region (where the expected yields were less than 3% of the peak yields), there is a background of 1.0+ 1.0%, and most of the uncertainty comes from the negative field correction. The second conclusion is that the resolution function calculation gives a reasonable approximation to the true resolution of this experiment, Finally, the best fit to the data gives a value for the energy meter calibration constant, Ey true’ Ey meter 1.025 + 0.005. This caro) agrees satis- factorily with the measurements of Stan Ecklund*”’ and the new (29) calibration of the beam energy meter electronics, 34 ‘Gey (P9 ye UoTjOUNY uoTFeWOXY “eT eanstgy CAJW) Y3L3W AONING OOTT ooot 006 008 002 ee meee a ; YALAW ASYSNS SA ALVY LNNOD V TANNVHO 0 — Zz s (0201-7 At ae en oe AMaLaW-O x? q Sz0'1 - _ NUL O35 ( q tf 4 L 0F0' W dI1@ YALAWVANVNO A3d SINNOD 35 ‘Qe (po Ye Uotoung UoTyeYoxy “qoT ernsty (ASW) YSL3W ADNAN] OOTT 0001 006 008 004 0 — Vas [ ae / ~~ MBLB-O “ano SZo'l-] | og01- ] f : 9° = 8 e o°t d3LSN ASYSN3S SA 31lVe LNNOD @ TANNVHD dIG 4ALSWVINVNDO Yad SLINNOS 36 "GBT (b9 Fe UoTjOUNY UOT}EHTOXY ‘OOT exnsty CA3W) Y3L3W ADMINS OO1T oo0t 006 008 004 y, — Z e Cohe 33-0 ay I e — v° Logo — _. Y — 3: o'r MSLIN ADNAN] SA 3LVa INNOD 2 TSNNVHO dI@ YSLSWVINVNO Yad SINNOOD 37 ‘Q2T (bo 7e uorpUNg uoTETOX™ ‘poy eansrg (ASW) M3L3W ADNAN] ooTl CO0T 006 008 002 L = 0 of a ¢ 0201-4 af val o, SZ0'1- Hy SNUIL ae ( - _ OFO' . a — : Yl 3° 8° O'T YalaW ASYSN]S SA ALYY LNAOD Gd TSNNVHI dIG YSLAWVINVNO Yad SINNOI 38 "qeT (9 We UOTOUNY UOTIeWOXE ‘ogy oansry (ASW) YSILIW AXDYINSG OO1t 0001 006 008 004 “~ 0 Zz s ‘ o201-7 : YALIAWN O al ~——— 4. —=|0 goit | —t P * | | Of01 Yy 7 9° 8° O°! YAlAN ASYSNS SA 3LVe LNNOD 3 TANNVH3 JIG ¥aL3WVINVNO Yad SINNOD 39 OOTT ‘Qe (pg ye UoTOUNy uCTFeWOXA “jo omn3py CAAW) YSLSAW ADNAN OOOT 006 008 002 ~ 020'I 3LAW-0 y oa E| ff | S201 > | shai 05 - + YW, r O£04 J as YalaW ASYAN]S SA ALVY LNNOD 3 TSNNVH3 dIG@ YZLAEWVINVND Y3d SLNNOD 40 "qey 79 ye UOTOUNY UOT}eYOX™ “Soy ainsLyz O''CABH) NALIN ADIN] COTT 0001 006 008 004 area a | Fat 0 Val . [-——~_ i ~ OzO'l ) in| = \ YSL N-O5 y° fy ~~ a ~ ee / + 0201 | 3° 8° O°t Y5LaW ASYSNA SA 3LVY LNNOD 9 TANNVHD dI8 YSLIWVINVNAD wad SINNOD 41 BAIND YOOWS LO} GZO'T = 000% Ja}OU O_ ANI} oO CASW) Y3SL3IW ADYSIN]A 006 008 002 a/ A “eT (pet ye uoHouny uoryeyox” ‘YOT eansrg 009 00° or’ 02° oe° Or° Y5LAW ASYSANSA SA 3LVe LNAOD VY TSNNYFO os° dIG@ YSLAWVINVNAO Yad SINNOS 42 aang moourg toy Gzg "y= OPM Og -qeT Sper ye uoHOUNy UOTTEOXA “TOT omBrg (ASW) Y3LaW A9N3Na 000T 006 008s 002 009 00° L O [ : z — ol’ a » m / 2 / 02° c > z / 5 + / of’ in tiene - w I Or’ 5 | | 1c YSalaW ASYANA SA SlVe LNNOD € TANNVHI 43 SAIND YOOUTY LOJ GZO’L = O00t I9}8Ul 0_ ena o a/ CASW) YS3LIW ADYINS 006 008 002 00g 00° 01° 0c” O€° dalAW AQYSN3S SA ALVY LNNOD 2D TSNNVH9 os or A ‘QV (pet ye uorjoung uoreyoxy [oy aims JIG Y3SL3AWVINVNO Yad SINNOD 44 BSAIND YlOoulg IO GZO ‘Tt oooT _ dajour O_ ant} o a/ CA3W) Y3L3IW ADYINS 006 008 002 009 00° ot” 02° oe” Or’ YALAW ADYSNS SA 3lVYe LNNOD Q TANNVHO os” A “GRY (pet ye uorjoung uoyyesyoxy ‘yo, onary dI8 YSLSWVINVND Yad SLINNOI 45 SAIND YOOUIS JOF GZO’L = Coot I3jaw O_ ano a/ CA3W) Y3L3W AOYIN| 006 008 004 2 “GVL pel ye uoroung uoreyOXY "107 oanspy 009 00° oT° 02° oe° 0v° YSLaW ASYANS SA ALVY LNOOD 3 TANNVHO os* d1@ YRLBWVINVND Yad SLNNOD 46 aAIND YJOOW I0f GZO'T = QoOoT I9jaUt O_ ant} o a/ (ASW) YSLIW ADVAN] 006 008 002 009g 00° o1° 02° oe” Ov" YALAW AQYSNS SA ALVY LNNOD 3 TANNVHI 0s” A “AVL pel ye UOT OUN, UoLyeyOX| “WoT emnsLy dI8 YSLAIWVINVNO Usd SINNOI 47 aaang yjooug roy ggg"t = a / A “AVL Per Je voHOUNY voryePOxY “ugyT oanByy CASW) YSLSW ADYANI Qoot 006 008 004 0093 ena} 0 00° 7 or° 0c° oE° 0r° os° YALAW AIYANS SA ALVa LNNOI 9 TANNVHO d18 YSLEWVANVWND Yad SLINNOI 48 V. DATA AND DATA ANALYSIS A. Cross Section Calculation The observed pion counting rate in the th spectrometer channel, C;, may be written as a multiple integral over geometrical and kinematical quantities and the cross section o(k, 6*) co= [IP LPT os, 0) Go, p) Nis, x, y) pls, y, 2) x A(p, 9) E, (x, Y,Z, p, 9) dQ dp dx dy dz where C = number of events/quantameter BIP satisfying the pion definition after subtraction of backgrounds, o(k, @*) = differential cross section for single nm photo- production from hydrogen by a photon of lab energy k producing a nm’ in do* at 6* (* refers to c.m, system), the Jacobian of the transformation between the u G(A, p) independent variables (k, @*) and (p, 9), N(k, x, y) = number of photons per BIP per em” with energy between k and k + dk striking a plane perpen- dicular to the beam line at the hydrogen target at the point (x, y), 49 nyy(X, y;4) - number of prutonus/ em? at lhe point x, y, 2 where the origin is at the center of the hydrogen target and the z-axis is along the beam line, A(p,9) = a correction for nuclear absorption in the material in the path of particles passing through the spectrometer, E,(, y,Z,p,Q) = efficiency of the th spectrometer channel for accepting an event originating at the point X, y, Z with momentum p and at lab solid angle Q. As this integral is defined here, the limits on the effective hydrogen target volume are contained in the functions Ty Cs, y,z) and N(k, x, y) while the limits for the spectrometer acceptance are contained in the function E(x, y,Z, p, 9). In order to simplify the evaluation of this multiple integral, several approximations were made. The first approximation involved averaging the bremsstrahlung spectrum over the target and collimator geometry. The spectrometer acceptance was taken outside of this integral and replaced with an average acceptance, This approximation may be schematically represented as follows: ' Bik, E.) [fax dy dx ~ Ey (0,0) [f fax dy de ~ B, (, 0) & where E,(p, ) = the spectrometer efficiency averaged over the origin of events, 50 W = total energy in the photon beam per quantameter BIP, E_ = synchrotron end point energy, bremsstrahlung spectrum averaged over target and bol a bi ul collimator geometry (defined below), N.. = number of protons per square centimeter in a planar target of thickness equal to the diameter of the hydrogen target appendix, This approximation allows the separation of the calculation of the spectrometer acceptance and the bremsstrahlung spectrum into two separate computer programs, The effect of averaging the spectro- meter acceptance is a broadening of the momentum resolution, while the total volume of p, phase space accepted remains constant, There is also a correlation between z and 2 which has been neglected. Since the bremsstrahlung distribution in z (along the beam line) is uniform, neglecting this correlation will have no effect on B(k, EO): The average bremsstrahlung spectrum, B (k, EQ) was computed from the differential spectrum, BR(k, E or Ox? 6 3 given by the program BPAII written by Mr, Frank Wolverton, Bis defined by the average of BR over the target and collimator geomeiry, namely 9 . B =f B(k, E,) = | t k,E,, 2%y) Pp d3,de, ay min ey min 51 where the angic between the photon and the nominal Co) I x’ “y beam line, D = the diameter of the hydrogen target appendix, d(3,,, 6) = the thickness of the hydrogen target at an angle oe b to the nominal beam line, a. 8 xXmMmin’ xX max limits on the photon beam angles defined by ey min’ ey max the primary collimator. Mr. Mike Hauser coded a program to tabulate the value of B(k, E o for several values of k and Eo: (31) A second short subroutine, also coded by Mr. Hauser, was hie to compute Bik, E o by inter- polation on the tabular values, (31) This subroutine was used for all the data analysis of this experiment, Using this first approximation, the counting rate integral was reduced from a six fold integral to a three fold integral over da dp. This integral contains the effects of the finite resolution of the spectrometer in the quantities k and 6*, Since the unfolding of two dimentional resolution is a difficult numerical analysis problem, an approximation was made to reduce the integral to an integral over a single variable, k, This approximation consisted of replacing 6, y, and 6* by the mean values 6, 9, and 6*, and may be schematically represented as follows [ [4a - Rp,7,,9 Glp, 6) ok, 6) 52 wherc Rte > Po? 8) = the effective momentum resolution function for the ra spectrometer channel, the spectrometer central momentum. u Po The effective resolution function defined here is normalized so that the integral over p gives AQ Ap, ie. . fe) fo) ) where AQ AP, _ ( 7 ). = the volume of AQ Ap/P, phase space accepted Oo by spectrometer chamel i, The details of the calculation of the effective resolution function are described in Appendix V. This second approximation results in ignoring any effects of finite resolution in 9*. Because the observed angular distributions were smooth and the resolution in angle was good (less than 1,5 degrees r.m.s.), these effects were expected to be small. After changing the variable of integration from p to k, the counting rate integral may be written CE, = folk, k, 0) R, (p(k, 6), p 98) (5,2) Alolk, 8), 8) N HEE 0] B(k, E,) X po dk 53 where C(k, 6*) « the pion counting rate per quaiulameter BIP explicitly labelled with k and 6*, and k = the photon lab energy calculated from 6 and the mean momentum of particles accepted by the rho spectrometer channel. The equation was solved in two steps. First, o was assumed to be slowly varying in the region for which R is non-zero and was taken outside the integral. This approximation to o, which will be called G, is related to C by an easily calculable factor, namely AEF C(k, 6* o(k, 6*) = — aoF & e) w BG EQ) — rr @\ J 406, 29) Ger (8) A PB) Ny BE a 0 or -—,—-— k. 9x a, 3) = SU. 8") The average cross section, o, was calculated for each point by evaluating » numerically. The computer program which computed Oo was called CRGS, and was a joint effort of the author and Mr. Stan Ecklund, (9) 54 The second step in the process of calculating o was to start with the measured values of o and correct for the effects of the finite resolution of the spectrometer, The details of this process, which is called unfolding, are the subject of Section V-B. B. Resolution Unfolding The equation for o may be rewritten in the form of a Fredholm equation of the first kind, namely (Ke) = | o(k, 8) K(k,k, 8) dk ) where the kernel is given by the normalized resolution function, i.e. , _ B&, ot rs 0) K(k, k, 6) = Fam, — a ts, 8) = where k is the photon energy corresponding to the mean momentum and angle accepted by the lh spectrometer channel. The limits of the integrals are not actually infinite as shown, for there were no photons of energy greater than the maximum possible energy of the synchrotron, namely, 1.5 GeV. This integral equation may be converted into a sum if an appropriate numerical quadrature method is used. The method chosen was to assume that o could be sufficiently accurately represented by straight line segments connecting the D9 experimental points and then to use Simpson's rule to calculate the integrals. For regions in which no experimental data existed, namely, for energies below the lowest energy measured or energies above the highest energy measured, o was assumed to be constant and have the same value as o at the nearest measured point, We may then write a matrix equation in which o and 3 represent vectors whose components are the values of o and o at the measured points. This equation may be written as follows 9, (8) =} K5 (8) 05 (8) j or in simplified notation (8) = K(@) o(8) The solution to this equation is -1,—.—,= _ K “ (8) (6) = 0(6) A computer program was written to compute K and mh The matrix inversion was computed in double precision and elements of the matrix E, where 14 E=KK were typically of order 10° 12 Then the vector o was computed from the vector o. The resulting solution for o was violently oscillatory. Ina typical example, o was nearly constant at about 56 3 microbarns/steradian while o would vary between + 2000 micro- barns/steradian, There are three possible sources for errors which can build up into the observed violent oscillations. These sources include statistical errors in o, inaccuracy of the numerical integration method, and the near singularity inherent in the solution of the Fredholm equation. The statistical errors are much greater than the errors of the quadrature method, so that we may safely neglect this source of oscillations, Goa?) has made extensive studies of a method which has shown some success in eliminating the singularities of the Fredholm equation. This method was tried, but it was found that the statistical errors in o were greatly magnified in computing ¢. Twomey 33) has invented a method which attempts to filter out the oscillations and obtain a smooth unfolded result. This method was also coded for the computer, However, the smoothing function required to eliminate the oscillations was as broad as the resolution functions of the spectrometer, Intuitively, no gain may be obtained by this method, Some success was obtained when the response matrix, K, was wvrillen as the sum of a diagonal matrix and another "small" matrix, The diagonal matrix was associated with the normal part of the resolution functions and the "small" matrix was associaied with the tails of the resolution functions which result from the 1 -U+ decay process (see Appendix 1V). In the integral equation, this approximation is equivalent to assuming that the normal part of the resolution function is a delta function. Using this approximation, the inverted response matrix gave reasonable results, and the error bars for o came out about 10% greater than the error bars for co. Since the effects of the resolution function tails on the peaks and O7 valleys was about 2%, it was felt that this correction would be worthwhile. Because there may be objections to the details of the unfolding method used, both the values of o and o were tabulated, One may wonder why the method previously used by R, Diebotd 24) was not tried. Diebold fit the data with a theory which was folded with the resolution. The parameters of the theory determined in this fit were used to compuie the unfolded cross sections, Since any reasonable theory must also work for regions not measured in this experiment, all available data must be fit simultaneously, and the program which does this job must be more complicated than the phenomenological analysis programs presently used by 8. Ecklund” and C, Clinesmith 1°) . Since the other data which are available at the present time have similar or worse resolution, it is unreasonable to attempt this task now. If it is necessary to completely unfold the resolution at some later date, one may start with the unfolded data (in which the effects of the tails have been correctcd) and approximate the resolution functions by Gaussians with standard deviations given by the values of ak m. Ss. from Table 7, A sample calculation has shown that a Gaussian will be within + 10% of the exact resolution functions (without decay tails) for values of (k - k) less Lhan 2 Ak... ms." C. Data Point Summary and Internal Consistency of Data The data were obtained from 12 momentum scans at 12 lab angles. At each lab angle, from three to six spectrometer central momentum settings were required to cover the range of 58 TABLE 6-a and 6-b Kinematic Parameters and Some Intermediate Results of the Cross Section Calculation is the mean spectrometer lab angle in degrees. lab f is the nuclear resonance magnetometer frequency in mc, PB, is the mean momentum of the seven momentum channels (taken as one channel) referred to pion momentum at the center of the hydrogen target, Q* is the mean pion C. M. angle in degrees. k ain is the mean photon lab energy in MeV accepted by Channel A, ke ax is the mean photon lab cnergy in MeV accepted by Channel G, ko, is the photon energy threshold in MeV for double pion photoproduction in Channel A. Ey is the synchrotron end point energy in MeV, 1 is the observed number of pions summed over the seven channels in a pair of full and empty target runs. QAVG is the number of Quantameter BIPS in each run determined by the average of the other monitors (see Appendix J). CCORR rer deg f 59 is the constant relating cross sections in microbarns per Steradian and pion yield in counts per Quantameter BIP (pions summed over all seven channels), The total energy/BIP was 1. 214 x 1018 MeV/BIP and the number of hydrogen atoms/ cm” in one diameter of the hydrogen target was 3.138 x 107° for all the runs shown in this table. is the correction for the field reversed background in units of microbarns/steradian. is the cross section in microbarns/steradian calculated from the run shown (averaged over the seven channels) with no correction for resolution effects. is the cross section in microbarns/steradian computed for all data available at the given point. is the statistical error associated with o (see Section V-F). is the value of x- Squared obtained for the several runs at the given point. is the number of degrees of freedom (number of runs ~-1) associated with y-squared at the given point. 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In addition, the region scanned by 8. Eckluna™) is also shown, The basic experimental parameters for each data point are given in Table 6. The momentum was calculated from the magnetometer calibration and includes a 2.7 MeV/c correction for momentum lost in the hydrogen target structure. Several useful kinematic quantities derived from the basic parameters are also given. The observed mn’ rates and a few intermediate results of the cross section calculation are also presented in Table 6. These quantities may be used to check the cross section computation or to estimate count rates for similar experiments using the 600 MeV/c Magnet. The nm’ rates shown are for a typical pair of full and empty target runs only. At least twice this much data was used for the final results which are presented in Section V-D. The internal consistency of the data was investigated by comparing the yields for the sum of the seven momentum channels at each point. This method should show up normalization inconsistencies more clearly than investigating the channels separately because of the better statistics of the sum. The observed valuc of x -squared and the number of degrees of freedom at each point are presented in Table 6. The integral y-squared probability distribution is presented in Figure 12, This figure indicates that the quoted errors are approximately correct, but that there is an excess of runs in the low probability tail. This effect is probably a result of the fact that the normalization errors do not have a Gaussian distribution. Three runs deserve special comment, The cross section for point 48-2 was computed from 63 Os! SURI x) ‘3 UO SJUTOg Vyeg Jo UOT}WOOT ‘TT aun3tyq (SIAY9AG) 4 O09] Ot) Od! 00] 08 09 Ov \OrA O I a Oe T - : fo ot tt Wii r f ff “| | | | : i 7p ot 4 1 y | til a | | | | by Wi — yo toi oq 4d bo Hill bob of tb ot to bine en ee ee a Pry rd rege g by ty eet Php by dy by by by bate Pi ydy by ty tatd dann g Pet pd by ly allay fide lbapade Pp ya dl | — \ 1 { ttt a WH 7 aqs ———-- 1 vi o1 NUMBER OF COUNTS 64 93 = IT T T T T T T T T T T T SO F SY NUMBER OF POINTS WITH 7 \Y PROBABILITY LESS THAN P . FOR x® DISTRIBUTION WITH \ STATISTICAL ERROR AND x 1.65% NORMALIZATION ERROR 40 - \ FOR EACH POINT. 4 AN N ----— EXPECTED \ \ OBSERVED ZO b \ _ \ \ \ \ N 20+ \ 4 N\ \ \ \ \\ lO b NL 4 N N\ NZ saw, 0 i t ! | i Nl Ls | I ! ' C= 99 98 95 390 80 70 60 50 40 .30 .20 P Figure 12 10 .05 02 .0l 65 one run because the second run at this point had inconsistencies in beam monitoring which could not be resolved. Point 84-6, which isone ofthe two points with y-squared probability less than 1%, is « point at which the high energy magnet was in the beam line for uus of the two runs, and the two runs disagreed by 10%. Since this effect was not observed for other points, it was assumed that each of the two runs was equally likely to be wrong and thus neither run was thrown away. Point 120-5, which was the other point with probability less than 1%, consisted of three runs. After the first two runs were taken, it was observed that there was a 15% discrepancy for 3% statistics, A third run was taken and the results of this run fell almost exactly at the mean of the two preceeding runs, Thus,there was no way of distinguishing the observed discrepancy at this point from a large statistical fluctuation, D. Tabulation of Data The data are presented in Tables 7A - 7L, in which the spectrometer lab angle is a constant for each table. The (unfolded) data are also plotted in Figures 13a - 131, and the spectrometer lab angle is also a constant for each figure. A smooth curve has been drawn through the data on five of these figures, The same smooth curves are also shown on Figures 13m - 13q, along with a representative set of data from other experiments. (9, 12, 13, 15, 16, 37) Since all of the data from this experiment have been plotted in Stan Ecklund's thesis (9) only a small part of the data available from his experiment is shown here. 66 TABLES 7A - 7L Average and Unfolded Cross Sections POINT NO, THETA LAB K W THETA C, M, SIGMA AVERAGE DSIGMA AVERAGE SIGMA UNFOLDED corresponds to the designation of the kine- matical parameters given in Tables 6-a and 6-b, is the mean laboratory angle of the spectrometer in degrees. is the mean photon lab energy in MeV, is the total c.m, energy in MeV. is the pion laboratory angle in degrees. is the measured C.m. cross section in micro- barns/steradian without resolution corrections. is the statistical error associated with Sigma Average (see Section V-F). is the measured c.m. cross section in micro- barns/steradian including a correction for the "tails’’ of the resolution functions (see Section V-B). DSIGMA UNFOLDED is the statistical error associated with Sigma 4K ns Untolded (see Section V- Ff). is the r.m.s, resolution in photon energy in MeV after correction for the tails of the resolution functions. 67 AVERAGE AND UNFOLDED CROSS SECTIONS POINT THETA K NOe Lan 34-3 34.9 93 34=3 34.0 615. 34-3 34.9 527. 34-3 3465 53a6 34-3 34.0 53%. + 94a 3-34 O- - Sa be + 34-3 34.9 555. 34-2 34.0 504. 34~2 3460 5726 34~2 a4“.o 589. ES 2 a aa 34eG—-— — SRF 34-2 34.9 53h. 34-2 34.0 60K. 34-2 34.0 617. 34-1 34.9 629.4 34-1 34.0 648.6 34-1 34.0 O98 « 34-1 34.0 66R6 34-1 3460 6796 34-1 34.0 O96 TABLE 7a Ww THETA STIGMA DSIGMA STIGMA DSIGMA AK Gothe AVERAGE UNFOLOLD RMS 1354. 48.6 9.791 0.254 9.787 0.2289 6.8 1359. GR. 9.3469 0.253 9-290 0.281 6.4 1364. 4829. 9.607 0.4253 9.581 9.280 6.9 1369. 49e1 Ge32L 04246 9-254 0.273 7.0 1374. 4942 9.661 02248 e631 04275 Te2 1 BBD ee 49 eH ——-10 0 028-0 245--—10 6033 — 06271 ----- 704. 13866 49.6 9e8UD Useds% Del f3S 80255 728 1392. 4947 10.463 0.266 10.500 04293 76 1397. 49.9 9-810 C262 9-764 0.288 726 1433. BALL 10.517 G.244 10.542 0.2791 7.7 14096 ~~ —50~ 2-106 689. ---0. 263 ——10 e712 _0 +287... 7-9 —_ 1415-6 50.4 9.776 0.250 9.712 0.271 Bel 1421. 50-6 10.913 0.266 10.955 0.287 8.4 1428. 59.8 10.422 0.248 10-411 9.266 8.8 1435. 51.0 10.995 0.353 1L.017 0.2382 826 1441 -——_ 5S ee 2-1 9.6536 0. 35.1 _- 106 509.0379. 8 & ____ 1447. 51.3 10.470 0.341 10.435 0.367 8.8 14346 BLS 102069 Oe341 104063 06365 609 1461. 5le? 11.094 0.343 11.095 0.365 92 1468. 51-9 11-931... 0.349. 11.981 . 0.370 -9e5S 1475.6 52el 11-634 02337 11.650 04362 10.0 68 ee oe... _ TABLE Tb a AVERAGE AND UNFOLOED CROSS SECTIONS POINT THETA K W THETA SIGMA OSIGMA SIGMA OSIGMA 4K 0. LAB CeMe AVERAGE UNFOLDED RMS 40-3 4000. 52501366. 5700947290392 «94 TSL 00445 OT” 46-3 G09 5336 1371le 5Tel 9.2650 O.38T 9.072 0e%Z2Z8 Tad 40-3 40.0 5406 1376.4 57.3 9.085 0.361 9.046 0.398 Te5 40-3. 40.0 549.2. 1382... 5765. Ba984. 06370 64942 00408 Ta 40-3 40.0 s55%e 3B Be 5707 86662 00346 8583 043822749 AO-A7 40.6 SAA 13494 579 8.9900 0.354 8.950 0.3492 ARAL 40-3. 40.0. ST6e 1400. 58.1 9.384 06340 96380 0.374 865 40-2 4000 58561407 58.3 90146 02399 94106 064360 Bah 40-2. 40.0 . 594s. 1412. $8.5. 92693 0.462 . 9.707 02438 Bah 40<2 46024 6036 1418. 5Be7? 10.406 9407 166476 0.4442 8.5 40-2 We 192-1425 58.9 0615 0.386. 92600. 0.415... Bal 40-2 4000 6236143 es 59.1 90347 00382-90301 06411920 40-2 4060 «633. 143K... $943... 10.215..02400 .. 106241 02427 9a 40-2 40-0 644. 1445, 69.58 9.684 0.384 9.658 Ou407 9.68 40-1 40.0 6566 1453. 59.8 10.667 66346 10.681 0.374 9.6 -#0r1——_40..0__.6666--1459 60.0 11.124 0.363 11.163 0.391906 __- 40-1 * 40.0 677. 146656 6062 116392 06356 1146435 0.382 928 40-1 40.0 BRA GTB... 6004.--.116269...00351... 11.289 0.374 10.0 40-1 4060 699% 1480. = 6006 140324 06346 116341 0.367 1063 40-1 - 4046 Tile 1488. 6009... 126807. .02357....112855.. 0.377.. 10a7 46-1 40.0 72341496. lel 106389 06326 106336 0.3468 lel POINT FHETA NO. LAK 48-4 4000 48-4 48.0 48-4 48.0 48-4 48.0 48-4 48.0 — 48-4... 48-00 —__... 48-4 48.0 48-3 48.0 48-3 4600 48-3 43.9 48-3 48.0. __... 48-3 48.0 4R-4 48.0 48-3 48.0 48-2 48.9 ~hB a2 4B GO -- 48-2 48.0 48-2 468.0 48-2 49.0 48-2 48.0 48-2 48.0 48-1 48.0 48-1 48.0 48-1 48.0 48-1 48.0 48-1 46.0 4821. 480. 48-1 46.0 69 TABLE 7c AVERAGE AND UNFOLDED CROSS SECTIONS. THETA SIGMA 73.0 6.196° 02197 SIGMA DSIGMA &éK Came AVERAGE UNFOLOED RMS C605 64940 Ge999 DerZ1 Teo 66.7 8.036 72969 04395 7.5 66.9 8.716 8.747 0.395 7466 67.1 8.207 8el7S5 0.382 7.7 67.3 8.239 8.211 0.389 7.9 1373.—...--6725......86240 04336 .. 86214 0.376 8.2 67.7 8.031 7.978 0.357 8.5 67.9 7.969 7-904 02406 8.5 OGel 64569 G@e35Q0 Getll Ged 68.3 8.503 826494 0.396 B.7 2404468 06... 431 0.0 366 82404 . 00404... BoB 68.8 ~ 8.4256 8.202 04388 9.1 49.0 9.201 9.2346 6.412 9.4 69.3 8.427 8.367 0.381 9.8 69-5 9.228 92213 02482 9.8 » L4BT en 69 e F--— 10 066166470 .102770 _ 0.517 9.8 70.0 9.831 9.847 0.496 10.0 1962 94549 9.529 0.482 10.2 70.5 9.596 04427 92572 02464 10.5 70.7 10.587 0.452 10.651 0.489 10.9 71-0 1O.36r 10.397 O.4%69 11.4% 71.3 10.853 0.285 10.972 0.308 11.4 71.6 10.095 10.151 0.300 11.5 7128 194164 10.242 0.291 11.7 72.1 9.418 9.457 0.271 12.0 1204 74686 04229 72625 0.2244 12.4 Lent 24329 42286. 02235 12.8 6-096 O-2i11 13.5 70 TABLE 7d AVERAGE ANDO UNFOLDED CROSS SECTIONS POINT THETA K W THETA SIGMA DSIGMA SIGMA DSIGMA AK NO. LAB Cade AVERAGE UNFOLDED RMS 54-4 56.0 525. 13666 77.0 7.815 04312 72843 0.357 8.0 56-4 56.0 533. 1371. 77.2 7.455 0.310 76435 0.345 8.6 56-4 5620 542. 1377, T7064 72693 0.305 7e7T06 0.339 8.8 56-4 56.0 551. 1383. 77.6 74143 0.4295 7.091 0.328 8.9 56-4 56.0 5606 1390. 7729 7e293 06291 70262 06323 9.2 ——. 5694-960 U--—___ 3 Fe -—_1 3 98 FH FoZ3T— 04292 70h 99..00324 . .. 925------ 56-4 56.0 S406 1403. 780% 72-480 04287 70467 0.317 9.9 56-3 56.9 592.6 1411. 78.6 7.396 0.246 72341 0.275 9.9 56-2 56.0 60L.- 1417. 7Ta.9 7.517 0.248 7-469 0.277 10.0 56-3 54.0 6li.e 1424. 7961 72844 02246 To827 0.2274 10.2 5693-94 0 -—-- 62 2 eo —--- 1431 Tole 8308 0.255 6. 334..-0.283.. 10.4 _--— 56-3 56.0 633. 1436 79.6 7.742 0-238 70687 02263 10.7 56-3 56.0 645. 14466 7969 8.155 0.250 - 8.137 0.275 Viel 56-3 56.0 657. 1454. 80.2 BoB UeZ51 Be90Z e275 11-7 56-2 56.0 6710.6 1462. 80.5 8.434 04348 86477 0.385 11.7 he Dea 5G O = O82 1469 ¢-——-B0 ¥ 8-9 040. —0 0 35.8 -__9.6 1 54-06 395..... 1128 —— 50-2 54.9 0946 L477 81.0 @.976 0.352 8.965 0.387 12.0 56-2 56.0 T0866. 14852 ©. A@le3.- 94829 04363. ..10.029 0.398 12-3. 56-2 56.0 7206 1494, 81.6 8.525 02335 8591 0.366 12.7 56-2 56.0 734. 1502. 81.9 .--. 96397 -06350...-.92580 0.380 13.2 56-2 56.0 748. 1511. 82.3 7.385 0.299 72396 0.323 13.9 56-1 56.0 T7656 1522. 82.6 6.976 04238 7.040 0.258 14.0 56-1 56.0 719. 1530. |. 6269 ...--.5 0576... 06216.......-50557 . 02233 14.1 56-1 56.0 7936 1539. 83.3 4.918 0.194 4.893 0.209 1464 56-1 56.0 BOR. 1Lb4B. - 8346 4.006...O0172 —_32955 .02184 14.6 56-1 56.0 825. 1558. 83.9 3.343 0.157 3.286 0.167 1564 Séan1 565 B41 1542 Bod. A103 9.1469 40965) 0.4158 16.0... 56-1 56.0 859. 1576. 8426 26432 02133 22366 04143 16.8 V1 TABLE Te AVERAGE AND UNFOLDED CROSS SECTIONS POINT THETA K W THETA SIGMA DSIGMA SIGMA DSIGMA 4K NO. LAB CoM. AVERAGE UNFOLDED RMS bbe5 4a <490e—«1:346e ~~ B5e4 e517 00247 6.513 06287 86 64-5 640 504. 1351. 85.7 6.938 02251 6.996 04284 8.7 64-5 64.0 513. 1357. 85.9 6.537 04239 60534 04269 Ad 64-5 646.0 S2le . 1363. 86.1 6.299 0.233 6.265 0.263 9.0 64-5 6420 531. 13706 86.3 6.388 0.227 6.370 0.256 9.2 6405 64.0 540.6 13 76. Bb.6 An5A4- 0023162594... 00260... M5 64-5 64.0 550. 13836 86.8 60344 06219 6.319 02246 9.9 64-4 64.0 562. 1391. 87.1 6.572 00181 6.561 0.205 10.0 64-4 6420 571. 13976 87.4 6.246 06173 6.184 02196 10.1 64-4 64.0 SBle 1404. 8726 5.971 06169 5.865 O-19L 1023 64-4 64.0 §91 14114 £79. re AN? LT 62933. 0.198..._10.5 —__. 64-4 64.0 602. 1418. 8Ba2 6334 06170 6.262 0.191 10.9 64-4. 6460 614. 14256 88.4.._ 62599 . 0.168 66554 0.188 11.2 64-4 64.0 6264 1433.6 88.7 6.993 02169 6.986 0.188 11.8 64-3 64.0 639. 14426 89.0 Te459 UeZ1¥ T0490 062431109 — 64% 2 bili 650 1449 ;: Ke oeee.4 7 0) O75 6 969...06237.-12.0._. 64-3 64.0 662. 1457. 89.6 7.254 0.216 7.240 02238 | 1202 6493 64.0. 6756. 14650. 8909. T6831 04222 70864 0.243 . 1225 6473 64-0 OBbe L474. 9042 8.035 0.221 8.074 0.240 13.0 64-3 64.0 702... 1482. 9065 86292... 02233... 86344 04252. 1324 64-3 64.0 Tlbe 14916 90.9 8e273 00222 8.315 04239 14.0 64~2 64.0 732. 1501. 91.2 72963 06245 8.083 0.268 14.3 64-2 6460 The 15106-91465 —.70081...00230 70135 02251. 1445 64-2 64.0 766. 15196 91.8 60383 04219 6.399 0.237 14.8 64-2 64.0 Tos. 1528-9202. 50466 02199 50441 02.215 15.2 . 64-2 64.0 792. 15386 92.5 40605 06179 40549 06192 1568 hin? bith BOD 1542 Lo eT re LA i 174 5 oa 64-2 64.0 B26. 15596 93.3 3.631 0.159 3.580 0.169 16.6 64-1640 B47%e. ~«15T2e. 9307 20765 Oslil 20716 0.120 176 | —_64—1__-. 640 0 --____ 864 » —_15 82.-—__94.-1 __ 2.641 0.106 2.412 O.114 17.9. 64-1 64.0 882. 1592. 94.4 22328 0.099 22296 0.106 1664 Lin) £46) feta 1602 94.2 2149 9. O85 2ai17 O10) 19.6 64-1 64.0 921. 1615. 95.2 2.034 04090 2.011 0.096 19.8 bbe) .__ 64.0 9426 1627 956 20427 0,094. 24333 0.100. .20.6- 64-1 64.0 964. 1640. 96.0 20075 0.088 20064 0.094 2lef 72 __ TABLE 7£ AVERAGE AND UNFOLDED CROSS SECTIONS POINT THETA K w THETA SIGMA OSIGMA SIGMA DSIGMA AK NO. LAR CoM. AVERAGE UNFOLDED RMS 14-6 THe «Te 13336) 950R 6076 06315 0 14S -04371 89 14-6 7420 485. 133A. 96.0 5-672 04317 5-671 0.363 9.0 T4~6 74.0 4936 1344. 96.2 5.595 0.6296 50588 04337 Sel T4~6 14.4 5026 1350. 96.4 §.758 0.303 5-781 0.346 923 74~& 74.9 Dll. 1356. 96.7 5.812 0.290 5949 0.331 926 om FG T4000... GZbe -- 1L36360...... 9609 2 50349... 00290... e320 O43B3T... Gad T4~6 1469 S31. 1370. 972 5.445 02272 5-440 0.309 10.3 74-5 74.0 S41. 1377. 9764 52146 0.238 5-097 0.2790 1064 T4~5 74.0 55). 1383. 97.7 §.309 0.242 §.2AQ 6.263 10.5 T4995 74.9 5606 1390. 97.9 §.368 0.232 5-361 0.261 10.7 wa Fn 5 1600 BT LOGI ..-- 98 2 5232800225 | 5.313 ...0.4253 111.0 T4~5 7409 5SAR26 1404. 98.5 56294 04221 5.280 0.246 11.3 74-5 74.9 594. 1412. 98.7 5219 06225 5.190 0.250 11.7 T4~5 14.0 606. 1420. 99-0 - 54322 Oe221 30302 0.4244 12.3 T4~4 74.0 6206 1429. 99.4 5.587 0.198 52556 0.222 12.5 ——T4eh4.—__74.0 —.... 63 Le —- 14376 9927. - 5690. 02203 _ 52662 .. 04227 .....12 67 744 74.0 644. 1445. 100.9 6.848 0.203 5-827 0.226 12-9 T4~4 74.0 6576 1453. 100.3 ..5.999 0.197 5.981 0.218 13.3 T4~4 74.0 670. 1462. 109.6 6.756 02206 6-807 0.4227 13.7 T4454 7420 Gh5e 1471. 100.9 6.898 O.2Z11 64934 04231 14.3 T4-4 7429 709. 1481. 101.2 G.745 0.207 6.759 0.225 15.0 74~3 74.0 Tle. 1491. 101.6 7.536 0.201 7710 04222 15.3 74-3 74.0 730. 15090. 102.9 . 6.834 046192 .. 6.910 0.211 15.5 714-3 74.9 T4660 1510. 102.3 6.256 04181 6-297 0.198 15.9 F4-3 7400 F7o2e 15206 L0208 50690 Gell ...50692 OsalAG - Loar 74-3 74.0 TT9 1530, 103.0 5.101 0.157 5.083 0.170 17.0 ~—_74-3—_14 0-797 «—_1541.-__-103.4_..__4..696.__0.152 4.670. 0.16417.7 . 74-3 74.0 816. 1553. 163.8 3.825 0.137 3.758 0.146 18.3 74-2 74.9 8366 1565. 164.2 3.298 0.151 32264 04166 19.2 -— T4-2 74.0 854. ...1576.... 104.5. 2.849... 02150... 2.800 Oa165....1926. 14-2 74.0 873.6 1587. 104.9 2.487 0.4133 26429) 02145 2001 L422 74.20. 894.— 1599. 105.3. 22639 0.2134 22618 04146 20.8 T4r2 T4He9 FLD. Lol2. LUSef 22622 Uel2zy 20612 Usl4O 2lef ~.. 7482)... 74.9 938... 1625. -. 10602. 2.586_0.131_.... 2.583... 0.141... 22.7 | 74-2 74.0 9626 1639. 10606 2.515 Ool2? 2-511 04136 24el T4-)} 74.0 9o1. LASS... 107.1 2.829 O.157 2.875 0.169 24.9 hha] 14.0101 4s—_1 668, _107.6._ 2,388 0.148 —_2.404 0.159 25.5 74-1 T4609 1039. 1682. 108.0 20126 04133 20131 0.142 26.3 ee Thad on T4008. 10656 1697. 108.5 - 26701...00123.-... 16688 . 00831... 2722 74-) 7460 1693. 1712. 108.9 2.332 O4l12 1.309 0.6118 280i ~~ 74-1 74.0. .1123..-...1728. 109.4 -04763.. 0.101. ....00720 04106... 271 74-1 7420 1155. 1746. 109.9 0.696 02114 02656 042122 28.3 73 TABLE 7g AVERAGE AND UNFOLDED CROSS SECTIONS POINT THETA K W THETA SIGMA OSIGMA SIGMA DSIGMA 4k NO. LAB CMe AVERAGE UNFOLDED RMS 84-6 84,9 487, 1339. 10662 4.749 0.2218 4.792 0.258 969 84-6 84.0 4966 1345. 106.4 4.279 0.204 40243 02234 10.0 84-6 84.0 50%. 1352. 106.6 4.662 0.208 4.693 0.237 10.2 84-6 84290 3L4e 1358. 106.8 4.268 02196 4#e29%G 02223 10.4% 84-6 84.9 524.6 1365. 107.1 4.254 0.187 4227 0.213 10.7 ~—_ 84-6 84.0 535... L3726-—- 167.3.-_.. 4.323... 04186 --4.e309 0.2212....11.0 ..... 84-6 84.0 545-6 1380. 107.6 4.039 O.177 3.980 0.202 11.5 B4-5 84.0 556. 1387. 107.9 4.719 0.4174 4.744 0.200 11.8 84-5 84.0 567s 1394. 106.1 4.464 0.173 40441 0.199 11.9 84-5 84.0 578. 1402. 108.4 32902 0.4162 3-786 O.185 12.1 —- 84-5... 84.0... S89... 1609... 108.7. _4.362..0.142.__--4.313._ 02185... ..12.4.___ 84-5 84.0 6%? « 1418. 109.0 4e436 04161 4.389 O.183 12.9 84-5 84.0 6156 1426. 109.3 -4.735 QO.171 4.718 0.194 13.3 84-5 84.0 628. 1435. 109.6 4.537 0.163 4.479 0.183 14.0 84-4 6400 6456 1446. 169.9 $2279 0.222 5.324 0.2252 L404 84-4 8460 -..-- 658 o--. 14546-—---110.2-____ 5241 8. 06230..-_ 52468 _.0.261 —..14.6 — 84-4 84.0 672. 1463. 110.5 5.214 0.218 $2223 0.246 15.0 84-4 84.0 6876 1473. 110.9 -52928 04228 ....6.025 0.4256 15.4 B4-4 84.0 T0026 1483. 111.2 5-776 02223 5.842 0.250 16.0 84-4 84.0 719.4 1493. 111.6 62.329 0.2233 -60458 0.2259 16.7 B4=4 B4.9 1366 1504. 111.9 5.728 0.219 5.783 0.242 17.6 84-3 84.9 T56.6 1516. 112.3 5.595 0.216 5.697 0.241 18.1 84-3 84.0 T7323. 1526-6 112.7 52032... 00204.......52084 04227 18.4 84-3 84.0 791. 1537. 113.0 4.276 0.181 4.261 9.200 19.0 84~3 84.9 810. 1549. 113.4 3.739 . 0.173 .....34696 0.4191 19.6 84-3 84.0 P30 e 1561-6 113.8 3-499 06.160 36463 O6175 20.5 84-3 R40 ROL LS74. 114.2 2.980 0.157_._ 2.919. 0.171 21.4... 84-3 84.0 874. L587. 114.6 2.909 0.143 22868 0.4155 22.7 84-2 B4.C 896.6 1601. 115.6 22823 0.150 2-803 2166 2364 84-2 84.0 91R&. -. lol3e 115.4 ...2.942...0.156 __ 2.952. 0.172 ...24.0 84-2 84.0 941. 1627. 115.8 2-903 0.147 20914 O.161 24.8 — 84n2- 84. G0-___966.—_1641.._--1 16..3—.__ 3-048 _0.150 __ 3.083 0.1646 _.25.8 B4-2 84.0 993. 1656. 116.7 3.2028 04146 3.066 0.158 27.1 84-2 84.90 1621. 1672. 117.2.-——2-973_0.150......3.018.. 0.162 28.5 84-2 B4.0 1O5le LOBGe Life? 22416 Uel33 22425 Cel 3043 84-1 B4.0 1C¢85. L707. 118.2 1.636 0.087 1.624 0.094 31.6 ——84".1—___ 84.4.0 11 46-724, —_1 1 8.7 __1.0546 0.076 —_1.016-_0.082 32.6 94-1 84.9 RUA. L741. 119.2 0.960 0.063 C.765 0.073 34.0 84-1 84.0 1186. 1759. 119.7.......0.481.. 0.061 .....G2442 . 0.065 35.5 84-1 84.0 1216. L778. 120.2 0-432 0.058 0.407 9.062 37.5 84=-) 64.0. 1255. 1799. 120.8 ....0¢391 . 0.056 -06375 0.059 39.3 84-1 64.0 1297. 1820. 121.3 0.377 06.058 06366 0.962 39.4 74 TABLE Th AVERAGE AND UNFOLDED CROSS SECTIONS = ©). paint TuETA K ta THETA ~ SIGMA OSIGMA : SIGMA BDSTCMA Ak NOs LAB CoMe. AVERAGE -.. UNFOLDED RMS 94-5 94.0 5326 1371. 116.7 4.151 06215 4.162 0.254 11.9 34~-5 34.0 D426 1378. 116.9 3.952 0.216 3.931 9.2248 12.1 94-5 94.0 5536 1385. 1172 3.7290 0.204 32666 0.233 12.3 -94-5 .. .94.0 5656 1393. 117e4......3.535 .0.200 ....34452 0.228 1266... 94-5 94.0 577. [401. 117.7 30435 0.189 3.333 04216 13.1 ——O4+5 .. 94.9 S890. —1410-—.118.0___4.202__0.207 —__A.214._0.236 _13.5__ 94~5 94.0 6036 1419. 118.3 4.109 0.195 4.093 0.222 14.2 94~4 94.0 617. 1427. 118.6 4.166 02202 4.156 0.232 14.6 94~4 -94.0 ... 630-6... 1436. 118.8... 4.057... 0.200 —%e021 0.229 14.8 __. 94~4 94.0 643-6 1445. 119¢1 42226 04203 GeZ11 04232 1542 —-Gh4=4-—_- Fhe D658 1 454. 11924 4.629. 00206 4.664... 04234 1526. " 94-4 94.0 674. 1464. 119.7 4.617 04203 4#0640 0.230 16.2 —--94~4..—__ 944.0....-- 690. 6-14 V5.0 120.1 52416. 0.217... §.539._ 0.245... 16.9 94-4 9420 70K. 14866 12064 4288S 0.2203 40927 O6228 17-9 94~3 94.0 729. 1499. 120.8 §.610 0.233 52793 0.263 18.5 oon Gh $9 feo O..-__2464—— 1510. 121.2 _ 4.504 0,215. 4.533 0.242. 18.9 94~3 94.0 TO4e 1521. 121.5 4.232 0.204 $0243 00229 § 1965 —-94~+3.. 94.0... 783 « —... 1533 121.9 4.087.0.197 4.099 04220... 20.2. 94~3 94.0 RO4. 1545.6 1222 3.648 0.183 3e627 04203 2161 wn BOB = 9G OW B25 o---.. 1558.—_ 122.6 ___3..244_0.174 30199 020194 _.2241 __ 94-3 94.0 848. 1572. 123.0 2.929 04162 2-873 06178 23-5 94~2 94.0 8756 1588. 123.5 2.938 042156 2-914 0.4174 2404 ——-94~2..—__.94,.0._...- 898-—_ 1 601 123.9. 3.022...0.160.___ 3.023 0.178 —__25.21___ 94~2 94.0 S226 1616. 124.3 3.009 ‘0.156 32015 0.4173 26.0 we DR OO D4 NG. 16310-12427 2.9 42_ 0-183 2-936 ..0.169 27-1... 94~2 94.0 976. 1647. 12561 32456 0.159 32523 046174 28.5 4 12526. 3.279. 0.155 34334 0.169 30.2 94~2 94.0 1038. 1682. 126.1 2.809 0.143 26827 0.155 3202 gael 9460 «1070s :16996 1266620207 06110 20220 06120 33-5 | 94~ 19440-1102 1717%.—_127.0___1.678_0.098 _1.661__0.107___ 34.7 94~1 94.0. 1135-0 1735s) 12725) = 10006 0.085 «= 06951 0.092 3643 94~1 9400 LZize L776. 126.5 06630 04070 02592 046075 400% ——94~ 1 —___94..0___1254-—__1798. 129.0 0.592. 0.070 _0.547 0.074 4203 __ 94-1 94.0 1300. 1822. 12926 0.533 0.072 0e513 O.077 4168 75 TABLE Ti AVERAGE AND UNFOLDED CROSS SECTIONS POINT TULTA K Wt THETA StGMA DSIGMA SIGMA DSIGMA AK NO. LAB CoM. AVERAGE UNFOLDED RMS 106-5 106.0 512. 1357. 126.7 3.773 0.190 3.791 9.228 12.3 106-5 106.0 922-6 1364. 126.9 3.948 Q.192 3.999 0.223 1244 106-5 106.0 5336 i371. 127.1 3.639 0.178 32637 0.4206 12.7 106-5 106.0 544. 1379. 127.4 3.399 O.178 3.361 0.206 13.0 106-5 106.9 5566 1387.6 127.6 3.006 0.164 2.904 Q.190 13.4 —106=5 105.0. SOD 2.396 £27493 0 $910 0 LOD. 50 G TF9 A L941 5D. 106-5 106.0 562. 1405. 128.1 3.450 0.167 32426 0.19% 14.5 106-4 106.0 597. 1415. 128.4 3.441 0.180 3.410 0.209 15.1 106-4 106.0 611. 1423. 128.7 3-636 9.189 32-635 9.219 18.3 106-4 106.0 624, 1432. 129.0 3.284 0.171 3.218 0.198 15.7 —106=4—-106.0-._.639 4-__1442..-__.129..2___._3.606__Q.171..-__ 3.591 0.197._16.2.._. 106-4 106.9 655. 1453. 129.5 3.873 0.178 3.895 0.204 16.9 -- 1Q6-4& 106.0 6720. 14636... 12968..-—..3.798 0.177... 3.795 0.202 17.6 2 106-4 106.0 6906 1475.4 130.1 4.118 0.183 4.157 0.208 18.6 106-3 196.9 TO. 1486. 130.5 4-931 0.234 5.115 0.268 19.2 —l06=3 106.0-. 725. 1497 4130.8 42479 0.230 4.584 0.262 19.6 100-3 166.0 Tae 1506-6 L31lel #et8G Ge2ld 440596 Oe249 2063 —— 106-3 .106.0.—.. 76346--...1521.-..—131.4 36489...0.195 3.463 ..04220 —. 21.0 ._ 106-3 106.0 785.6 1534. 131.7 3.839 0.199 3.884 0.223 22.0 106-3 106.0 B07... 1547... 13262 ...-.3.033.0.187..._.2.987.. 02208 23.61 106-3 106.0 831. 1562. 132.5 2.567 0.159 22487 0.176 24.6 106-2 106.0 8ble 1580. ‘132.9 2.759 0.168 2.737 Q.189 25.8 ~~ 106-2 ..-.106.0.-.. BBSes—.. 1594....--133.3.. 2.679_.0.169......2.657 0.190 26.5 ...- 106-2 106.0 910. 1609.6 133.7 2-648 0.159 2-627 0.177 27.6 106-2 106.0 G3be 16256 134601... SeF3L- Yello —..- 20956 0 Vel lt 2Bed 106-2 106.0 968. 1662. 134.5 2-846 0.158 26862 04174 30.5 —106=2—1.06.0— 1000... 1 661.___134.9___2.828 0.1463. 2.852. 0.179 __ 32.4. 106-2 106.0 1035, 1680. 13524 3.031 0.166 3.079 0.180 34.8 106-1 106.0 1075. 1702. 135.9 2.341 O12) 22368 0.133 3666 wee AGG 2.20600 —. L11Ge D721 6. --13663.._. 12563... 06103 ..1.524...06113 38.1... 106-1 106.0 1147. 1742. 13668 1.104 0.090 1.042 0.09% 40.0 ~ EI... 176 oh 48_ 0.084 1,004 0.093... 42.2... 106-1 106.0 1234. L787. 137.7 12053 0.084 1.028 06.090 44.7 eh O6~ 1. 10660... 1282 « — 1813 e138. O.797__0.082._..0.764_. 0.088 ...4449 ..... 1334.6 138.8 0.764 0.097 0.734 9.106 44.9 106-1 106.0 1840. 76 TABLE 7j AVERAGE AND UNFOLDED CROSS SECTIONS POINT THETA K Ww THETA SIGMA OSIGMA STIGMA OSIGMA 4k NGe Las Come AVERAGE UNFOLDED RMS 120-5 120.9 492. 1343. 137.7 36467 04180 36510 02216 1206 1270=5 120.0 Sol. 1349. 147.9 Aa.14623 4.145 3-148 9.192 12.7 120-5 120.0 5126 1357. 13861] 32505 0.173 3-554 0.260 13.0 120-5 120.0 523. 1365. 138.3 3.292 0.4166 3.307 0.191 13.3 120-5 120.0 5356 1373. 138.5 3-257 0.160 3+270 04184 13.7 —20=5--— 120.0 _ $48... 1381._138.7_.._. 2.838... 0.155... 24788. OeL7B.. 14.2 - 120-5 12060 61s 1390. 138-9 30168 Qeidds 3el82Z OelT4 14-9 120-4 120.0 S77. 1401. 139.1 20805 O4161 2-741 0.187 15.5 120-4 126.0 $90. 1410. 139.4 2-679 0.166 22597 0.192 15.8 126-4 120.8 C4. 1419. 139.6 3-304 0.174 3-327 6.201 16.2 120-4 120.0 619» 1429._139.B8____2.984 0.163. 22949... O.LA7_.. 1647... 120-4 120.0 6356 14396 14061 34195 0.2165 32189 0.188 17.4 120-4 120.0 651. 1450. 140.3 .... 3.021 0.146 2-973 0.188 18.1 120-4 120.0 669.6 1462. 140.6 3.482 0.2170 3-504 0.191 19.1 120-3 120.0 6904 1475. 140.9 3.577 04185 34620 0.210 20.0 —120-3-_120.0 70 %e——1486 141.2 — 3-882 _0.191 __ 3975 0.217 ._.20.5.._. 120-3 120.90 7266 1498. 141.4 32718 0.182 3774 04205 21lei - 120-3 ..12049 To7e LSlle |. L41.7 -~ 30539. Gel?Z. ~-3e575 02193 Ziad. 120-3 120.0 769. 1524. 142.0 34384 0.164 3405 0.182 23.0 120-3 120.0 7926 1539. 142.3 2-550. Q.157 .. 26483 0.173 2349 120-3 120.0 818. 1554. 142.6 20625 0.147 2-583 Q.162 23.8 120-2 1206.6 B43. 1569.6 143.0 20424 04174 2.377 0.198 27-0 120-2 120.0 Bos. 1584... 143.3 22656 . 0.173 22654 02196 27.9 120-2 120.0 8956 1600. 143.6 26557 0.165 2-543 04186 29.0 120-2 120.6 924.6 L6i7s.. 143.9 -20576.. 06159 .. 20574 O4178 30.5 120-2 12020 9966 L635-6 144.3 20598 OelGs 2-60L Uslds 3203 —-120=2 120.0 990. 1655 1464.7 _2.686 02172 _-_ 2.708 02190 —_34.44._._ 120-2 120.0 1027. 1675. 145.3 2-795 02167 2-834 0.183 37.1 120-1 120.90 1073~ 1701- 145-6 2-212 O4140 2-229 O.155 39.4% ~- L26-1-— 129.0 —.. LLL be— 17226-14529. _ 1 o TTL - 06 1392--- 1 0 754... 06146... 4442 - 120-1 120.9 1152. 1744. 14643 16547 04121 1.524 0.133 43.44 120m} 2 20,9 LIUOF 17-68.—$_1466+8.—_1 +165. 105. 1.122. 0.114 46.1 120-1 120.0 1247. 1795-6 147.2 ~~ 12Q-1---_120.9.-—13914--—-1A23e— --.147-7. 120.0 1361. 1853. 120-1 148.2. 0.794 0.747 0.094 OeRT4 02109 0.129 G.735 0.102 0-838.0-117 02698 04143 -. 46.8 .... 54.5 77 TABLE TK AVERAGE AND UNFOLDED CROSS SECTIONS =~ oe POINT THETA K “oy THETA = SIGMA DSIGMA SIGMA DSIGMA AK _ NO. LAB CoM. ... AVERAGE UNFOLDED RMS 134-4 134.0 S41. 1377. 14920 32046 06139 3.059 0.167 15.2 134-4 134.0 554. 1385. - 149.1 2-701 0.138 2-652 02160 15.5 134-4 134.9 567. 1394. 149.3 20837 04135 22815 0.156 15.8 134-4 134.9 .. S81. 1403, 149.5. 2-876 O5137 . 2.860 0.158 16.3 134-4 134.0 896. 1413. 149.7 2.995 0.134 20997 04154 16.9 —t34- & 1.34.6. Lo 1424 14949. 32520—04«i32. 3eS23...00151--_.. 1706 134-3 134.0 646, 1448, 150.3 20990 Oel5l 3.003 O«175 19.5 134-3 134.6 6654 1459. 150.5 32200. 0.153 3.246 0.2178 19.9 134-3 134.0 683, 1479. 150.7 30238 04158 30285 Oel82 2046 134-3._134.0. 7L2 1482 150.9... 3.570 02154 _._3.673._0.177.__ 21.4... 134-3 134.0 7236 1496. 151.2 30289 G0i47 32333 0.168 2264 --. 134-3 134.0 T45e..-.. 1509, —- 151.4... 20838 001461... 2.831 .0.160 . 23.5. 134-3 134.0 T6968 1524. 151-7 2.785 0.132 2-783 04148 2501 134-2 134.0 7966 1541. 151.9 20413 0.2136 20377 0.156 26.3 —134=2-—134.0._. 82041555. 152.2 2.131 O.127 2.064. 0.145... 27,2. 1a4—2 3324.0 ROAw LST71. 1592.4 2.204 4.129 221460 0.164 78.4% —- 134-2... 134.0 B74... 1688... —15267..-—_ 26503. —06130.—__242509 .. 02146....29.7... 134-2 134.60 905. 1606. 153.0 22503 0.127 20511 046142 31.5 134-2. .134.0... GBM... 16254.-...15363..... 20492 .06128._20500 02142... 33.5 134-2 134.0 974. 1646. 15326 2-195 0.124 20174 0.136 35.3 134-1 134.0 1010. 1666. 153.9 2.358 0.093 "20407 006105 38.2 134-1... 134.0 LOST. LOBT 6 15402 -—_ 16992... 00086 —_. 22002. 0.096 39.9 134-1 134.0 1087. 1709. 154.5 1.703 0.080 1.692 0.089 4201 134-2 13420... LLBL 6... U73 26-184 8-1 255 0.2070 .__1-208 0.-077....44.8 134-1 134.0 1179.6 1759. 155.2 1.057 0.067 1.008 0.073 48.2 a L3H d__ 134.0. 1232, 1787, 155.5. dL LB GTB. 0.073 51,2 134-1 134.0 1290.6 1817. 155.9 0.877 0.066 0.829 0.073 50.5 78 TABLE 71 AVERAGE AND UNFOLDED CROSS SECTIONS | POINT THETA K« wW THETA STIGMA QSIGMA SIGMA DSIGHA aK NO. LAB CoM. AVERAGE UNFOLDED RMS 156-4 159.4 510. 1355. 163.6 3.057 0.160 3.088 0.196 1541 156-4 155.4 5226 1363. 163.7 3.225 0.161 3.4288 04190 15.3 156-4 1595.44 534.6 1372. 163.8 22742 02152 2.709 0.4178 15.6 156-4 15564 54?e 1361. 16369 26662 02144. 2.621 04169 16.1 156-4 155.4 561. 1390, 164.0 22855 0.147 2.855 0.172 1606 154-4 155.4 S76 14000... 1640e1 30104. Ge A475 0 1S2]2... Ooh 72. LP e Dd. 156-4 155.4 592. 1411. 164.2 20841 06139 26835 O4«l6l 18.2 156-3 15564 609, 1422, 164.3 22782 06158 2.782 0.185 19.1 156-3 15544 625. 1433. 164.4 3.077 6.156 3.137 02183 19.6 156-3 155.4 642. 1444, 164.5 207G0 00146 22692 0-170 20.2 —t5o~3..155.4-___ 660... 1456.__.164.6___ 2.816 00151 2.845. 0.176. 20.9. 156-3 155.44 bBL. 1468. 164.7 26541 0414) 24517 04163 21.9 156~3 155.4 Tle 1482. 164.9... 2.929...0.154. ...2.978 . O.177 23.0 356-3 165.2% P26 1496. 165.0 20455 0-135 2et*3l OelSé& 2404 156-2 15544 T5C6 1513. 165-1 “20410 04149 22398 04173 25.8 —_156~-2 155.44 773 1527 165.3 2017302137... 22129._.0.159_.. 26.7. 156~2 155.4 798. 1542. 16564 20544 Oel45 2.570 04167 27.8 156-2... 155.4 .. 825. 1558. 165.6. .....20370...0.137 2.373 0.157 29.1 156-2 15564 B54. 1576. 16567 20164 04131 Z2el40 06149 30.9 156-2 155.4 846. 1594. 165.9... 26069. 00136 .....2.040.. 0.2153 32.9 156-2 155.4 920. 1615. 166.0 22348 94131 2362 02146 3525 156-1 155.4 9650 1637. 16662 24298 0.129 26353 04147 37.7 156~1 155.4 9956 165A. 16604. 2018S 06130. ... 24233 04147 39.4 156-1 155.4 1034. 1679. 166.5 1.834 0.119 1.845 0.134 41.7 154-1 155.46 1077. 1703. 144.7 1.329 9.104 1.293 0.115 44.4 156~1 15504 11256 1729, 16609 1.075 6.091 1,030 0.100 48.0 —156=1] 1554-1177. 1752._167.1---_0..848 ~02082..0.796 0.090... 51.9... 156-1 155.4 1234. 1788. 167.3 0.452 0.072 02364 02080 5502 CROSS SECTION CMICROBARNS/STERADIAN) 79 LAB ANGLE 34. DEGREES is r 10 q 5 0 ptt 400 600 g00 =: 1000 1200 ©1400 LAB PHOTON ENERGY (MEV, Figure 13a CROSS SECTION CMICROBARNS/STERADIAN) 80 LAB ANGLE 40. DEGREES 15 if : 10 Fat. , =a 5 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY CMEV) Figure 13b. CROSS SECTION CMICROBARNS/STERADIAN) LAB ANGLE "56. DEGREES 1S ~~ o as peg | e u 400 600 800 1000 1200 LAB PHOTON ENERGY CMEV) Figure 13c 1400 CMICROBARNS/STERADIAN) CROSS SECTION LAB ANGLE 64. DEGREES 15 10 er | i 4 i) = 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 13d CMICROBARNS/STERADIAN) CROSS SECTION LAB ANGLE °°48. DEGREES iS Taf 1 My o | i§& 5 . / 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 13e CMICROBARNS/STERADIAN) CROSS SECTION 8 LAB ANGLE "74. DEGREES iS 10 i tT pt qi cy 2 3 ps a 4. cy ry g ~ + apes i o z fF 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY CMEV) Figure 13f CMICROBARNS/STERADIAN} CROSS SECTION 15. LAB ANGLE °84. DEGREES —-+- _ fee] By Fim: ¥ fo RY = x= Pe ae ae 400 600 800 1000 Figure 13g 1200 LAB PHOTON ENERGY CMEV) CMICROBARNS/STERADIAN) CROSS SECTION 15 LAB ANGLE °°94. DEGREES -_ [=] ii re z ro a zx 0 C~t 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 13h CMICROBARNS/STERADIAN) CROSS SECTION 87 LAB ANGLE 106. DEGREES 15 10 if — = Bs a + cz ry Te +4 cm Eusr Zr 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 13i CROSS SECTION CMICROBARNS/STERADIAN) 15 88 LAB ANGLE 120. DEGREES 10 400 600 800 1000 1200 LAB PHOTON ENERGY CMEV) Figure 13j 1400 CMICROBARNS/STERADIAN) CROSS SECTION 89 LAB ANGLE 134. DEGREES iS 10 i) 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (CMEV) Figure 13k CROSS SECTION CMICROBARNS/STERADIAN) 15 90 LAB ANGLE 155. DEGREES 10 a s rE b 2a¢ ey Lo} KH x= 400 600 800 1000 1200 LAB PHOTON ENERGY CMEV) Figure 13 1 1400 CROSS SECTION CMICROBARNS/STERADIAN) 91 DATA COMPARISON NEAR 34 DEGREES LAB 15 ~~ © i ! ECKLUND HEINBERG THIS EXPERIMENT wn : t pee fe i | : | eee te a 2 ' . i ! : 4 othe _ ¢ l t i . i : i | : ‘ 1 ~ H j t i : : ab t i ns ans } | : i 7 si if { | t : i : 1 . : i | } ' H H i ! i | : i —_ i } { 400 600 800 1060 1200 LAB PHOTON ENERGY CMEV) Figure 13m 1400 CROSS SECTION (CMICROBARNS/STERADIAN) 92 DATA COMPARISON NEAR 56 DEGREES LAB 15 HEINBERG WALKER t t t TOLLESTRUP i ECKLUND 10 THIS EXPERIMENT wu rH b= rt 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (CMEV3) Figure 13n CROSS SECTION CMICROBARNS/STERADIAN) DATA COMPARISON NEAR 64 DEGREES LAB 15 a b DIXON : | - me i ECKLUND : ew THIS EXPERIMENT 10 ! on a MN =z iy x a 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 130 CROSS SECTION C(CMICROBARNS/STERAOIAN) 94 DATA COMPARISON NEAR 120 DEGREES LAB is 10 ! } DIXON i k WALKER HEINBERG KILNER THIS EXPERIMENT ji : q : 3 == — \ : > — ce $ t_ | x z 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY (MEV) Figure 13p (MICROBARNS/STERADIAN) CROSS SECTION 95 DATA COMPARISON NEAR 134 DEGREES LAB 15. a —_ 4 WALKER ae i TOLLESTRUP 3 HAND AND SCHAERF ! | - b DIXON 10 i KILNER ew THIS EXPERIMENT | 5 i L i c T x PN l x = ~ ~~ | 0 400 600 800 1000 1200 1400 LAB PHOTON ENERGY CMEV) Figure 13q 96 In general, this experiment agrees with other experiments as well as can be expected. There is excellent agreement with the data of Ecklund and Walker. (9) A detailed comparison of the results in the region of overlap of the two experiments gives a difference of 2.54 2.0%, where the cross sections of this experiment are smaller than those of Ecklund and Walker. This experiment also agrees very well with Dixon and Walker ‘!2) after a small correction is made to interpolate their results to constant lab angle. This experiment is in good agreement with the results of Kiiner'!*) at 1300 and 1390 MeV, but his data seem to be systematically smaller than the data of this experiment at 1100 MeV and 1200 MeV, especialiy at 120 degrees in the lab. Sincc this cxperiment agrces with Dixon and Walker at 1000 MeV at the same angle and varies smoothly through the region of 1000 to 1350 MeV, it is hard to explain the 30-50% disagreement with Kilner. An important experimental problem is the matching of this experiment with lower energy experiments near the first resonance. Only two experiments provide any data which overlap both the first and second resonance, namely, the experiments of Heinberg et al. (15) and Bizot et al. (37) The Heinberg data is in agreement with this experiment at 3° and 58° in the lab, but the 118° data are signifi- cantly larger near 500 MeV, The data of Bizot et al. at 35° are approximately 10% larger than the data of this experiment. On the other hand, the two previous experiments at 470 MeV, namely Walker et al. (35) and Tollestrup et al., (36) systematically 20% to 50% smaller than those of this experiment at ~ 500 MeV. Both of those experiments agree to the order of 10% with other data at 400 MeV and lower. It is possible that their results at 470 MeV were in error because the synchrotron end point gave cross sections 97 energy was very near the photon energy (the synchrotron end point energy was 500 + 5 MeV for all data taken in both experiments). If the data of Walker and Tollestrup at 470 MeV are ignored, it is possible to draw a smooth curve which passes through the low energy data and the data of this experiment. There is a serious disagreement between this experiment and the experiment of Hand and Schaerf. (16) This experiment reproduced the energy dependence of the cross section measured by Hand and Schaerf at 135° lab, but their data are systematically 30% smaller. Since these authors assumed that no muons were counted in their apparatus, a correct treatment of the decay cor- rection is likely to make the discrepancy as large as 40% - 50%. Hand and Schaerf estimate their systematic errors to be less than 25%. A portion of the experiment was repeated by Schaerf. (17) The new results agreed with the old to the order of 5%, and again Schaerf estimated his systematic errors to be on the order of 20%. Because the results of this experiment are larger than those of Hand and Schaerf, the possibility exists that an undetected background is included in our data. However, the excitation curve measured at 134° indicates that the background is 1.0 + 1.0% (see Section IV-D). Thus, we conclude that Hand and Schaerf made a beam monitoring or magnet calibration crror, and that their data should he multiplied by the factor 1.5 to get an absolute cross section which agrees with this experiment, 98 E, Angular Distributions by Interpolation For some purposes, angular distributions of the cross section are more useful than data in the form of energy distributions at constant angle. A set of angular distributions was obtained by linear interpolation in the data of Table 7a - Te. The energies chosen were the nominal energies of Stan Ecklund's angular distri- butions (9) , with a few additional energies below 589 MeV. For the lowest and highest energies, the interpolated data may represent an extrapolation of the measured data. However, no data were used which came from an extrapolation of more than 20 MeV. The error bars on the interpolated data were arbitrarily taken to be equal to the error bars on the nearest measured point. The interpolated angular distributions are presented in Tables 8a - 8d. THETA SIGMA DSIGMA 99 TABLE 8a - 8d Interpolated Angular Distributions is the c.m. pion angle in degrees is the c.m. differential cross section in microbarns per steradian is the statistical error associated with SIGMA in microbarns per steradian is the laboratory photon energy in MeV is the total center of mass energy in MeV TABLE 8a 100 INTERPULATED ANGULAR DISTRIBUTIONS THETA*® SIGMA OSIEGMA THETA* SIGMA DSIGMA THETA* SIGMA OSIGMA Ka 490. K= 570. Ke 635. WS 1342. w= 1396. W= 1439. 48.3 11.029 0.289 49.9 9.920 0.293 51lel 10.671 0.382 0664 9eTTS O0442Z1 3Be0 YolZ6 Used? 2903 106125 0.427 85.3 6.128 0.287 68.3 8.471 04411 69.8 10.508 0.517 S6el 56620 06363 78.1 7.2200 0.324 79.7 72753 6274 106.2 4.605 0.258 87.4 6.224 0.205 89.0 7.347 0.243 137.7 3-569 O.216 90<2 $2316 O-26i 99208 Be7l2 C6227 163.5 2.4740 0.196 108-2 4.244 0.4199 109.7 4.819 0.252 117.5 3.401 0.228 118.9 4.095 0.232 127.9 34475 0.194 12962 34482 0.198 139.0 27.930 Q.1Aa7 140.1 3.184 O.18a8 149.4 2.826 0.158 150.2 2-761 0.179 164.0 3.034 0.172 164.5 2.874 0.183 Ks 510. K= 589. K= 647. We 1355. W= 1409. W= 1447. 48.7 9.609 0.289 50.2 10.690 0.287 51.3 10.439 0.379 56.7 9.935 0.445 58.4 9.354 0.438 59.6 9.944 0.407 66.9 8.706 0.395 6867 82233 0.404 7O.l 96710 0.496 Th06 Ge584% 02357 TOeG Fe3GF Oo3i17 8000 Ge270 O6275 85.8 6.6673 0.284 87.8 6.4689 0.198 89-2 FellT 0.243 96.6 5.641 02346 98.6 56225 0.250 100.0 5.868 0.226 106.7 4.431 0.237 108.7 42295 0.185 110.0 5.2348 0.261 126.7 4.756 O.227A 118.0 4.159 0.236 119.2 4.322 0.234 138.0 3.477 0.200 28.3 3.4419 0.209 129.4 32736 0.204 163.6 3.088 0.196 139464 2.605 0.192 140.3 3.030 0.184 149.6 2.938 0.158 150.3 24986 0.175 164.2 2.888 0.172 164.5 2.732 Q.176 Ks 530. K= 603. K= 663. We 1369. W= 1418. W= 1456. 4961 9.273 0.275 50-5 10.366 0.287 51.6 10.885 0.365 STel 94701 046445 3GeT 106408 04442 S969 LEOULE 06391 67.3 8.212 0.389 69-1 9.028 0.412 T0e4 92566 044682 T7ek 72589 02357 78.9 7.533 0.277 80.3 8.707 0.385 86.3 6.364 0.263 88.2 6.277 0.191 B9.6 7.285 0.243 97.2 §.432 0.337 99.90 5.278 0.250 100.4% 66370 O.227 10762 4.274 0.213 109.0 4.4419 0.194 110.4 5.380 0.261 116.6 4,209.0.254 Li8.3 4.096 0.236 119.5 4.657 0.234 127.l 34722 04223 128.5 3.506 0.219 129.7 3.849 0.204 138.4 3.286 0.191 139.6 3.295 0.201 140.5 3.315 0.191 148.9 3.437 0.167 149.8 3.009 0.154 150.5 3.223 0.178 163.7 2.881 0.190 164-2 2.801 0.185 164.6 2.790 0.176 Kz 550. K= 618. K= 680. we 13b36 w= L42be W= 1468. 49.5 9.909 0.271 50-8 10.448 0.382 5220 11-948 0.370 57.5 8.884 0.408 59.0 9.439 0.415 60.3 11.389 0.382 67.8 7.935 02406 6944 8.896 0.482 7068 10.572 0.489 77.6 7.139 0.339 T9234 Bel44 02283 800% 9e065 046395 B6.8 6.319 0.260 68.5 6.705 0.188 90.0 76947 046243 97-7 5.285 06270 9943 5.525 0.244 100.8 6.894 0.231 107. 4.305 0.202 109.3 4.662 0.194 110.7 54662 0.256 117.1 34745 0.248 118.6 4.142 0.232 119.9 4.98? 0.2745 127.5 3.136 0.206 128.8 3.4410 0.219 130.0 3.958 0.208 138.7 2.853 0.178 139.8 2.962 0.201 140.8 3.565 0.210 149.1 2.768 0.167 150.0 2.872 0.151 150.7 3.279 0.182 163.9 2.674 0.172 164.3 2.980 0.185 164.7 2.517 0.176 TABLE 8b INTERPOLATED ANGULAR DISTRIBUTIONS THETA* SIGMA DSTGMA Ka 696. Ws 1480. 52.3 11.417 60.6 11.336 T1.2 10.772 Gle2 92334 90.4 68.268 LOL.2 6.778 lll.l 5.893 120.2 5.261 130.3 4.601 141.0 3.788 150.9 3.593 164.9 2.912 Ka 715. w= 1691. 61.0 11.353 Tle LOeldd 81.5 9.095 90.8 8.318 101.6 7.652 111.25 6.2315 120.6 5.235 130.6 4.885 141.3 3.894 151.1 3.4463 165.0 2.4641 Kz 733. We 1502. 61.3 9.148 72.0 9.843 B19 9.2544 91-2 8.007 102.0 6.405 L11.9 9.907 120.9 5.467 130.9 4.589 141.5 3.709 151.3 3.107 165.1 2.419 K= 752. Ws 1514. 72.4 7.721 B264 72312 91.7 6-813 102.4 6.057 Lk2.2 5.714 121.3 4.430 131.2 4.101 141.8 3.536 151.5 2.817 165.2 26376 0.370 0.374 0.469 02398 0.252 0.231 02256 0.245 O.268 0.217 0.182 O.L?7 0.377 024300 0.398 0.252 0.225 0.259 0.263 02268 0.217 0.177 0.177 0.377 0.291 0.380 0.268 0.211 © Q.259 0.263 0.262 0.205 0.168 OoL73 0.271 0-323 0.251 0.198 02242 0.242 0.249 0.193 0-160 Co173 101 THETA® SIGMA OSIGMA K= Tle. We 1320.6 72.8 6.831 8268 64282 92e1 54659 102.8 6.325 112.7 5.110 121.7 4.180 131.5 34636 142.0 3.6287 151.7? 2.741 165.3 26141 K= T9360 W= 1539. 7323 5.096 8323 %2898 92.66 4.513 103.3 4.755 113.1 4.187 122.0 3.869 131.9 3.549 142.3 2.485 151.9 246425 165.4 2.486 K= 813. w= 1551. 83.7 3.764 9320 32956 103.7 3.879 113.6 3.4657 12264 3.4442 132.2 2.865 142-6 24565 15201 20158 165.5 2.458 Ke B34. W= 1564. 84.1 3.4160 93.4 3.262 104.1 3.308 113.9 3.2356 122.8 3.076 132.5 2511 142.9 2.2449 152.3 20115 165.6 2.300 0.235 0.258 0.237 Q.186 0.241 0.229 0.223 0.182 0.156 Oi 73 0.235 0-233 0.192 0.170 0.200 0.220 04223 0.173 0.167 0.184 6.185 0.164 0.191 0.203 0.208 0.173 0.156 0.167 0.167 0.169 0-166 0.175 0.194 0.189 0.198 00157 THETA® SIGMA DSIGMA K= We 1 84.6 93.9 104.6 114.13 123.2 132.9 143.1 192.5 165.7 K= w= 1 9444 105.1 114.7 123.6 133.2 143.4 15268 165.8 K= We 1 94.8 105.5 Li5el 124.0 13326 143.7 153.0 165.9 K= W= 1 9543 105.9 115.6 124.3 133.9 153-2 166.61 8576 STT. 2-430 22656 2.740 2.906 2.586 2.706 22534 24294 2-131 B80. 2-330 2.493 2.850 2.938 22673 2.604 22509 2.058 902. 604. 2-106 2-616 22843 3.022 2.637 20551 22511 2-191 926. 618. 2.598 22939 22988 2-811 20578 2-504 2-361 0.158 0.120 0.165 O.b?d 0.178 0.189 04198 0.146 0.153 0.114 0.1446 0.166 0.178 0.190 0.196 0.153 0.101 0.146 0.172 OL78 0.190 0.186 0.146 0.153 04100 0.141 0.172 0.173 Q.178 0.187 02142 0.147 _ TABLE 8¢ 1 02 INTERPOLATED ANGULAR OISTRIBUTIONS THETA® SIGMA DSIGMA THETA® SIGMA DSIGMA THETA*® SIGMA DSIGMA Kz 951. K= 1056. Ke 1162. Wa i632. w= 1692. W= 1749. 95.8 2.2222 0.100 108.3 12840 0.142 110.1 0.641 0.122 10644 24544 0.4141 237.8 2.306 0.143 219.6 0.4610 0.073 11600 2698006164 == 2604 24485 00155-12728 «06775 0.092 124.7 24904 0.174 13546 2.705 0.180 13609 1.2029 0.098 L3490el CeFlO Gells 1430% 20449 Gel BS 19664 1643% Gel3S 144.3 2.597 0.187 154.3 1.931 0.096 155.1 1.079 0.077 153.4 26383 00142. 166.6 1.565 0.134 167.1 0.863 0.100 16662 24355 0.147 Ks 977. K= 1074, K= 1174. __ WS L647 ee ee WE LTO2. oo WE 175 . 96.3 1.904 0.100 108.6 1.569 0.131 110.3 0.617 0.122 106.9 2.703 0.169 116.2 16877 06143 11966 802496 0.073 116.5 3.076 0.164 12666 2.149 06120 12600 Us«f02 OA0T9 125.2 3.619 0.174 13569 2.386 0.180 _137.1 1.017 0.098 134.6 2.859 0.179 145.6 2.4213 06155 146.6 1.327 0.133 144.6 22668 0.190. 15404 16791 06096 15501. 16029 00077 15366 ZelF3 Oel36 166.7 16334 046134 167el 026809 02100 16663 26295. 00147... — Ks 1002. ss k* «1102. KE 1204 We 1661. Ws 1717. W= 1772. 10763 2664306169 _ _—«109e1 =10138 00118 > =s«i120.0 04419 0.065 116.9 3.050 0.162 118.5 1.265 0.094 128.4 0.615 0.079 12565 36359 06174. 127.0. 14650 0.107 13704 10012 0.093. 134.9 2.863 0.180 136.2 1.713 0.133 146.8 1.069 0.114 144.8 22730 0.2190 14509 124862 ULI9D5 155e¢3 146046 04073 153.8 2.353 0.136 154.66 12524 0.089 16702 02592 0-090 166.4 2.165 0.6147 16668 1.156 0.115 Kx 1628. K= 1i31. K= 1235. _ W= 1676. . ee . W= 1733. . w= 1788. 107.8 2.248 0.159 109.6 0.704 0.122 120-5 0.392 0.062 117.3 2.880 0.162 119.0 0.881 0.082 12868 06578 0.075 125.9 2.984 0.169 12764 1.041 O.107 13768 16020 0.090 135.3 3.034 0.180 136.6 1.4252 G.113 147ei 04829 02114 145i 26817 O«ld3 146.1 14640 046146 15506 1-074 0.073 . _ 25420 20212 0.105 154-8 1.207 0.077 167.3 0.359 0-090 16G05 16906 Gel4+? LGGe9 10002 04100 TABLE 8d 103 INTERPOLATED ANGULAR DISTRIBUTIONS THETA® SIGHRA USIGMA THETA® SIGMA DSIGMA THETA® SIGMA OSIGMA Ka 1269.4 wa 1806. h26.9 G.372 0.062 129.2 0.550 0.077 138.1 0.434 0.090 147.6 O.777 O.L1T 155.8 0.923 0.073 104 F, Summary of Experimental Errors The random and rapidly fluctuating errors which have been included in the error bars of all cross sections are as follows: Counting Statistics 3-5% Irrcproducibility of Runs 1, 65% (see Appendix VI) Negative Field Background 0-5% Unfolding Process 1% The systematic errors are estimated in the table below (errors of less than + 0.5% have been ignored). These errors are to be inter- preted in the sense of standard deviations. Quantameter Calibration? 1) 3% Nuclear Absorption 1. 5-3% Bremsstrahlung spectrum 29) 2% Pi-Mu Decay Correction 1% Liquid Hydrogen Target 1% Flectronic Efficiency 1% Total Energy Per BIP 0.6% Total . 4-5% 105 G. Data Fitting The most important problem to be solved in data fitting is the multipole and isotopic spin decomposition of the photoproduction amplitudes. Stan Ecklund and Carl Clinesmith are presently working on this problem and are using independent methods. Stan Ecklund is using only nm’ cross section data and has fit the angular distributions with a Moravcsik type formula. Then he is attempting to explain the coefficients of the Moravesik fits with simple functions of energy. (9) Carl Clinesmith is attempting to fit all the data available for all the isotopic spin channels by assuming that the multipole coefficients are ie) Breit- Wigner forms or slowly varying funclivus of energy. Since both of these projects are near completion, it is difficult to make a direct contribution to the fitting without also duplicating a large part of the effort. Rather than work directly on the overall fitting project, an effort was made to explain a striking feature of the 7 cross section at 180° which was observed by Hand and Schaerf™®) repeated by Schaerf, (17) The important characteristic of this cross and later section is that there is a very narrow bump at a photon energy of approximately 710 MeV (W = 1490 MeV). On the basis of evidence from the forward n° photoproduction cross section, D. Beder 8) concluded that the ratio Eo. / My_ - 8 in the vicinity of the second resonance (N**(1512), K = 750 MeV) which causes the contribution of the second resonance to the photoproduction amplitudes to be small at 0° and 180°. An extrapolation of the a’ data of Ecklund and Walker to 0° gives the same conclusion. (9) Theoretically Bietti\)) has used saturated sum rules to derive the same result, Thus we expect that the second resonance does not contribute to the bump at 180° in the a cross section. 106 sakurai®) suggested that the bump might be a cusp effect at the threshold for production of the eta meson (W = 1487 MeV, k = 708 MeV). Since the differential cross section for single n photoproduction is smallest at 180° for energies near 700 MeV, it is possible that a small cusp in the 844 or Pit (first index = 2T, second index = 2J} part of the photoproduction amplitude would show up most at 180°, The most extensive measurements of the eta production reaction come from the experiments of Bulos et al. (40) and Richards et al. (41) These experiments show that the eta production angular distribution is isotropic near threshold, which indicates that either the S44 or the Pay states dominate. When the total cross section is plotted as a function of energy, the first three points fall on a straight line which also passes through the threshold, From this fact, Richards et al. conclude that the Si state is dominant, An examination of the results of several recent partial wave analyses” 6, 7, 8) of m-N elastic scattering shows that the 844 absorption parameter, n,,, is consistent with 1.0 (no absorption) below the eta threshold, but that it drops rapidly to approximately 0.5 shortly above threshold. The reaction cross section computed from the Si4 absorption areal is consistent with the total cross section for eta production, In addition, at least two authors show a cusp behavior in the Sa4 phase shift. (4, 8) On the basis of this evidence, we may conclude that a cusp at the eta threshold has been observed in S-wave r-N scattering and that the photoproduction data should be analyzed in terms of the same phenomenon. The R matrix formalism of Wigner *2) has been applied to the production of strange particles in n-N and y-N interactions by Adair, (43) With only negligible changes, this formalism may be 107 used for the production of eta mesons in the same interactions. If we assume that the absorption in the Say m-N state is due to eta production. (and a small contribution from inverse photoproduction), we may use a three channel S matrix for total angular momentum 1/2, I spin 1/2, odd parity scattering where the three channels are m-N, n-N, and y-N, Since a nucleon appears in each channel, we may simplify the notation by labelling the three channels, nm, n, and y. Near the eta threshold the S matrix may be written in the form +i ka, +i kya | Sip =e (5,57 N,,/D) e where Nye = -2i dK, Py Ry; Rep Py D x=i-ik R -ik R -ik R T TTT M1 nN Y YY k. = center of mass momentum of jth channel with the convention that k is positive imaginary below threshold a, = the channel radius for channel i P. = 1 above threshold in channel i ‘ 0 below threshold in channel i and we may take the elements of the R matrix to be independent of energy. The total cross section may be written in the form . 7 2 o,=— 168 ~ nf a | nt | , TT 108 and The parameters of this formalism may be adjusted to fit the S;, phase shift and absorption parameter, and the eta photo- production reaction cross section, Because of the inconsistencies of the phase shifts and absorption parameters determined by different authors, the high accuracy of a computer fit to the data is not worthwhile at the present time. However, a hand fit was made, For the purposes of this fit, the absorption parameter was assumed to be 0.5 at a pion kinetic energy (lab) of 660 MeV. The parameters were adjusted to satisfy this condition and to give a reasonable fit to the S44 phase shift data of Cence™) and the eta photoproduction data from Stanford. (44) The resulting parameters were (#= c = 1) . R= 2.096 ~- Gey} Tit R_ = 3.699 Gev * nn R= 0,019 ~cev-l YY a = 0.200 Gev! WT a= 0,000 Gev"} V In order to fit the 1* photoproduction data at 180°, it was necessary to make some assumption about the other contributions to the photo- production amplitude. The simplest assumption was that this back- 109 ground was pure imaginary (pure real in the usual convention of perturbation theory). A constant background of + 0.66 u barn) (17) in the region of 1/2 gives the best fit to the corrected Schaerf data the cusp (see Section V-D for the correction to the Schaerf data). The fit and the data for the several reactions are presented in Figures 14a and 14b, The branching ratio for n- 2y was assumed to be 0, 35 in drawing these figures. The fit to the eta production and eta photoproduction data has the difficulty that it rises too rapidly near threshold. This problem appears to be common to several theories which neglect other open channels, (45, 46, 47) Moorhouse and Hendry“) have shown that it is possible to correct this problem by including approximately the multiple pion production channels. However, the fit to the 180 degree T photoproduction differential cross section has the property that it gives a good fit to the shape of the cusp for photon energies within + 50 MeV of the eta threshold. The conclusion derived from this fit is that it is possible to explain the a photoproduction differential cross section at 180 degrees in terms of a cusp at the eta threshold, and that this interpretation is consistent with present data on pion scattering, eta production, and eta photoproduction. This interpretation removes a possible difficulty with the assumption that E,_/ M,_ = 3 in the vicinity of the second resonance, On the basis of pion scattering and eta production data, several authors have made conclusions about the source of the cusp. (46, 47, 48) These authors conclude that there is an eta-nucleon state at approximately the eta nucleon threshold (1487 MeV). This state should be called a resonance if the mass of the "particle" is greater than the threshold, or a virtual bound state if the mass is PHASE SHIFT (deqrees) ABSORPTION PARAMETER f o (millibarns) 110 80 I 1 T FS, PHASE SHIFT 4 60+ $ CENCE _ a } } t AUVIL et al. 40 4 oat 20h z- 3 j = 300 400 500 600 700 800 1.0 $ Fi i ’ - §,, ABSORPTION } 4 | PARAMETER ; ¢ CENCE 0.5 { AUVIL et al. ] | 300 400 500 1.0 7 i o (rr +p ntn, nw 2y) $ RICHARDS e} al. 0.5 > e BULOS et ai. j | l | 300 400 500 600 700 BOO Ty (MeV) Figure l4a, Cusp Fit to n-N Channel do/dQ (pB/Sr) o (2B/Sr) Lil 4.0 T T I t DIFFERENTIAL CROSS SECTION } ac 180° y+p-> 1t+n aly ab J’ ath sili 2.0 fp ¢ SCHAERF X1.5 Lok t THIESSEN (165°) — RESOLUTION THIESSEN SCHAERF | i | l 300 650 TOO 750 800 850 ( | er Fr =s« TOTAL CROSS SECTION E ytp-- n+p 10- L } PREPOST et al. 5b ~J ] | i I 600 650 700 750 800 850 LAB PHOTON ENERGY (MeV) Figure 14b, Cusp Fit to Photoproduction 112 less than threshold. This particle has been speculatively identitied'*®) with the N particle of the n-baryon octet B= (N, A, £, =) postulated by Gyuk and Tuan. (49) purthor data on n-N scattering and eta production are required before ihe mass of this state can be determined accurately. 113 VIL CONCLUSIONS AND SUGGESTIONS A large number of puints of the differential cross scction for nm photoproduction at backward angles were measured in this experiment, When combined with the data of Ecklund and walker), reasonably complete angular distributions are available for all energies between 589 MeV and 1269 MeV. These data can be used to make a considerable improvement in the precision of the phenome- nological analysis of pion photoproduction in the region of the second and third 1-N resonances. Because of operational difficulties with the synchrotron, it was not possible to continue the experiment into the region of the first resonance which has been measured carefully, Thus a similar experiment should be performed covering the energy region from approximately 350 MeV to 650 MeV. It may be necessary to do this experiment at a different accelerator: the Mark II Linac at Stanford University is a logical choice. In order to obtain a unique multipole and isotopic spin decomposition of the photoproduction amplitudes, it will be necessary to take cross section and polarization data on the other pion photo- production reactions. The most direct way to start on this program would be to measure the differential cross section for the reaction y+n-m +! p using a deuterium target. A synchrotron subtraction might be used to separate the events coming from free neutrons, With careful planning, it would be possible to take data with both magnets simultaneously. It should be emphasized that absolutely no apparatus changes are required to perform this experiment! Later, a carbon plate spark chamber might be added to measure the recoil proton polarization as an extension of the same experiment, 114 if a polarized proton target with the order of 20% polarized, free protons can be developed, it would be possible to measure the polarized target asymmetry in the reaction y+ p-~7 ren A synchrotron subtraction would be required to separate the events due to free protons. Another interesting experiment would be to extend the n differential cross section measurements to exactly 180°, However, this experiment would require significant changes in the magnet and beam line geometry. Since some data are already available, this experiment should be assigned a lower priority than the previously suggested experiments, Two improvements in the apparatus would prove to be useful. First, an electron counter could be installed, Sucha counter might reduce the field reversed background which was as much as 10% at high energies. Second, the paper tape punch might be replaced with an on-line link to the campus IBM 360 series computers, Including the price of a remote console (with typewriter input-output), the design and construction cost of the required hard- ware would be on the order of $4000. Such a data link would reduce the turn around time for data processing from several days to a few minutes, and experimental errors would be more easily detected. In addition, the reliability of the system would be significantly improved by eliminating the mechanical tape punch and the paper tape to magnetic tape conversion system. 115 APPENDIX I, BEAM MONITORING AND HYDROGEN TARGET DETAILS The several beam monitors used during this experiment include the quantameter, the beam catcher thick ion chamber, two thin ion chambers, a counter telescope mounted at 90° from the beam line under the hydrogen target, and the "40 mc. probe" which monitored the intensity of the circulating beam. The locations of these monitors are shown in Figure 1. The charge produced by each ion chamber was measured with the standard electronic integrators used in this laboratory for many years. Each time a specified amount of charge has been collected, these integrators put out a pulse called a BIP (beam integrator pulse) and this pulse is usually used to operate a Sodeco’ mechanical counter. Unfortunately, the generation of the output pulse and the determination of the amount of charge per BIP depend on two relays. HE either of these relays chatter or the contacts get dirty, il is possible to get a wrong charge/BIP ratio. Tor this reason, it is important to use several beam monitors even if the beam monitors themselves are stable. The output of the 40 mc, probe is monitored bya voliage-to-frequency converter and the result is counted on an electronic scaler, The counter telescope output is also counted on an electronic scaler. No difficulties with the readout mechanism for either of these beam monitors was observed. The normalization of this experiment depends on the quanta- meter charge output, However, the quantameter cannot be left in the beam line during a data taking run as it absorbs all the energy in the beam. It is not possible to place the quantameter in the beam catcher since the beam spot is too large at that location. Thus this experi- 116 ment also depends onan intercalibration with secondary monitors. The beam monitors which can be directly intercalibrated with the quantameter are the 40 mc. probe and the two thin ion chambers, Unfortunately, the charge collected by thin chamber No. 2 was strongly dependent on the status of the UCLA hydrogen target. In addition, the integrator used with this ion chamber - was found to be very unstable. After a short trial period, the use of this ion chamber was discontinued, The two remaining monitors, TC-1 and the 40 mc. probe, were intercalibrated against the quanta- meter in a short run before and after each data taking run. The monitors which are available only during a data taking run are the monitor telescope and the beam catcher ion chamber. -The beam catcher ion chamber should be as good as the quantameter, except that its calibration depends on the energy of the synchrotron, In addition, the beam catcher ion chamber is not available when the yoke of the High Energy Magnet is in the beam line. Since the beam catcher ion chamber and the quantameter are never available simultaneously, the same integrator was used for both. Thus the ratio Q/RC is independent of slow drifts in the integrator. The monitor telescope has also been demonstrated to be stable. Unfortunately, the monitor telescope was operated from the High Energy Magnet Electronics. Since Mr. F, Wolverton was constantly testing and changing the electronics and turning the power supplies on and off, keeping the monitor telescope calibrated proved to be a tedious chore and its use was eventually discontinued. The monitor telescope probably should be set up as a lab instrument and made to be independent of the transistor power supplies for either magnet. 11% The procedure used to calculate the number of quantameter BIPs was to calibrate the 40 mc. probe and TC-1 against the quanta- meter in a short run before and after each data taking run. The average ratios (Q/40 mc.) and (Q/TC-1) were calculated from these short calibration runs. The number of quantameter BIPs based on each of these intermediate monitors was calculated from these average ratios and the number of TC-1 and 40 mc. BIPs obtained in the data run, ive. 40 mc. x (Q/40 me. > TC-1 x (Q/TC-1) . Q40 QTC The beam catcher ion chamber could be intercalibrated against the quantameter only by comparing BC with Q40 and QTC. This inter- calibration was done for each night's running by comparing the total BC for a night with the average of Q40 and QTC, The formula used was (@/Bc) = B@M+ QTC) where the sum represents the normal data runs taken during one night. Then the number of quantameter BIPs for each run was computed using BC and the average ratio given above, namely QEC = BC x (Q/BC) Finally, the number of quantameter BIPs for a given run was calcu- lated from the average of Q40, QTC, and QBC. This final value, QAVG, was used for all cross section calculations. 118 _ This complicated averaging procedure had the advantage that a gross error in one of the monitors was easily detected, When an error of more than ~ 2% was detected, the suspected number was ignored and QAVG was recomputed using all the remaining information. Similarly, QBC was ignored when the High Energy Magnet was in the beam line. By using this technique, the r.m.s. deviations of the individual monitors from QAVG were + 0.5%, except at E, = 1350 MeV where + 1. 0% was observed. These errors are presumably already included in the random error deduced from a series of plexiglass target runs (see Appendix VI), and this error was included in the error bars on all cross sections measured in this experiment. The ratio of Q/BC observed at several energies in this experiment may be of use to future experiments. These ratios are given in the following table: E, (meter) Q/BC 660 11, 32 + 0.07 750 11, 18 + 0,07 850 11.35 + 0.07 950 11. 67 + 0,07 1050 11. 64 + 0,07 1150 11.79 + 0.07 1350 12. 07 + 0,12 The quantameter calibration constant, Vo is given by the relation 119 2.730 18 Ug = (4. 80.4 0.14)x 7am x 10 (21) MeV/coulomb where P and T are the absolute pressure and absolute temperature of the quaniameter gas in mm. Hg. and °K respectively. The P/T ratio appears to fluctuate by + 0.5% r.m.s. and, in addition, a gradual drop was observed. The random fluctuation may be due to : (50) The typical quantameter gas pressure was 715 mm. Hg. which was well below atmospheric pressure, Thus the gradual drop must be due to an absorption or selective leakage process which has never been understood, In any case, the P/T value for the first period of data taking (run no. < 700) was 2,445 + 0,010, while during the second period of data taking (run no. > 701) the ratio of P/T was 2.413 + 0.010. Integrator No, 0628 was always used with the quantameter. For some early data (run no. < 407), the integrator was used on scale 3 with a charge/BIP ratio of 2, 225 + 0,005 x 1077 coulomb/BiP, For all later data, the integrator was operated on scale 4 with a charge/BIP ratio of 2.235 + 0,005 x 10°° coulomb/BIP. The resulting values for the total energy per QBIP are given in the following table. non-equilibrium thermal effects (see separate report) Run Number Total Energy/QBIP 000-407 (0. 1192 + 0, 0007) x 10'? mev/@BrP 408-700 (1.198 + 0.007) x 107° MeV/QBIP 13 701-1348 — (1. 214 + 0. 007) x 10°“ MeV/QBIP 120 The liquid hydrogen is contained within an 0, 005" wall Mylar cylinder approximately 3" in diameter. On September 24, 1965, this cup was accidentally broken during the normal cleaning process (no liquid hydrogen was in the target at the time), The Mylar cup was replaced by a new one which was approximately the same diameter, The cup diameter was measured by Mr. Earl Emery at room temperature with a 15 psi pressure on the inside of the cup. The results for the two cups are: run number < 700 3, 003 + 0,005" diameter run number > 700 2. 980 + 0, 005'' diameter The diameter of the cup must be reduced by 0. 4% to correct for the contraction of the Mylar at liquid hydrogen temperature. (1) The liquid hydrogen in the cup is operated at the boiling point and a pressure of 0,5 psi is maintained by a safety check valve. Under these conditions, the hydrogen temperature is 20. 30°K") and its density is 0.0711 gm/cm®, ©) gince the "empty" target runs were taken with hydrogen gas at the same temperature and pressure, the gas density of 0.0014 em/em® (52) must be subtracted from the liquid hydrogen density to give an effective density of 0.0697 gm/ om’, The number which is used in the cross section calculation is Nu» the number of protons per em” in one diameter of the 93 hydrogen target. Taking Avogadro's number to be 6, 025 x 10 the atomic weight of hydrogen to be 1. 008 (which assumes that the deuterium contamination in the liquid hydrogen is small), and the target parameters discussed above, we find that Ne is 121 3. 162 + 0.030 x 102° for run number < 700 Nut 23 3, 138 + 0.030 x 10°° for run number > 700 The error associated with Ny is arbitrarily taken to be + 1% which includes the errors in geometry and the hydrogen density. 122 APPENDIX I, NUCLEAR ABSORPTION All of the pions detected in this experiment had to pass through matter including the hydrogen target vacuum jacket, air, and several counters. Some of the pions incident upon the system interacted with this matter and were lost. For the purposes of this experiment, any interaction other than multiple scattering was defined as nuclear absorption. The nuclear absorption for several locations of absorbers was measured, The technique consisted of placing an additional piece of matter in the path of the pions and noting the difference in counting rate with the additional absorber in or out of the path. In order to get sufficient statistics, a plexiglass target was used, and several runs were taken with absorber in and out. The normal reproducibility of runs over short times precludes any measurement to an accuracy better than + 1% of the no absorber rate. The data taken by this direct technique appear in Table 9. An improved method of measuring the nuclear absorption was used for measuring the effects of nuclear absorption in the counter telescope at the rear of the magnet. For these measure- ments, a pion was defined by all the counters but the last. A certain fraction of the pions defincd in this way did not count in the last counter. This fraction increased when an additional absorber was placed just ahead of the last counter. The difference between the fractional miss rate with and without the additional absorber was defined as the absorption in the additional absorber. In order to measure the effect of an absorber placed a long distance from the last counter, it was necessary to move the last counter further from counter p than the normal configuration. Thus some data were 123 TABLE 9, Absorption Measurements by Direct Method Location Absorber Momentum Absorption At counter §1 ' 26 1/2" ahead of S2 At counter A 87'' ahead of S2 At hydrogen target 1" plexiglass 1/2" plexiglass 3/8" aluminum 300 400 570 570 570 0.073 + 0,010 0, 044 + 0,010 0. 038 + 0.010 0.032 + 0.010 0. 039 + 0,010 124 TABLE 16, Absorption Measurements by Improved Method Distance Absorber to 82 18" 12" 8 1/2" 8 1/2" gr 21/2" 18" 14" 9 1/4" 6” 21/2" Configuration long long long normal normal normal long long normal normal normal Absorber 1" plexiglass 1" plexiglass 1" plexiglass 1" plexiglass 1" plexiglass 2" plexiglass 1" plexiglass 1" plexiglass 1" plexiglass 1" plexiglass i" plexiglass Momentum 500 MeV/c 500 MeV/c 500 MeV/c 500 MeV/c 500 MeV/c 500 MeV/c 300 MeV/c 300 MeV/c 300 MeV/c 300 MeV/c 300 MeV/e Absorption 0, 0350 + 0. 0048 0, 0227 + 0, 0044 0, 0133 + 0, 0042 0.0217 + 0, 0024 0, 0167 + 0, 0024 0, 0359 + 0. 0026 0.0590 + 0, 0050 0. 0519 + 0. 0032 0, 0494 + 0. 0034 0.0390 + 0, 0041 0.0250 + 0. 0044 125 taken with two different geometries: one with the last counter in its normal position 12"' behind $1, and one with the last counter mounled 24" behind counter ph The statistical accuracy of the data taken with this technique is greater than for the data taken by the direct method, however unknown systematic errors may have entered because of the different geometry and the different event definition. The data taken by this method in both configurations is presented in Table 10. Some data on the interaction of pions with light nuclei exist in the literature. (54, 55, 56, 57, 58) The main data for pion momenta comparable to those used in this experiment comes from bubble chamber studies. These studies indicate that the o « A2/ 3 law is verified, but that the constant of proportionality varies with the incident pion momentum. In addition, the majority of the events are inelastic, This is to be contrasted with the n” p interaction which is almost entirely elastic at low momenta, The number obtained from the bubble chamber experiments is called the total absorption cross section, This cross section includes all events with a scattering angle greater than a specified cutoff, but it does not include diffraction scattering. The dependence of the nuclear absorption on the distance from the last counter is explained hy the fact that the solid angle for detecting a secondary from an absorption event depends on this distanee, For an absorber at counter S1, the counter system will accept only those events which scatter less than about 30°, This cutoff is approximately the same as the one used for the total absorption cross section in the bubble chamber measurements. Thus the nuclear absorption measurement for absorber placed 26" from counter S2 can be used to calculate a number for the total 126 00L ST aansTy are 009 OOS OO” OO& 002 OO! ! | 1 t 90H) SSVTDIX31d - +4 OLY Yad NOILO3S SSOND NOILdYOSEY TWLOL 4 001 | 00¢ + 00¢ 0O0v (SusDq}|||W) © 127 absorption cross section for pions on plexiglass. The cross section must be divided by f, the fraction of events due to pions, for the muons in the beam defined at the rear of the magnet have a much smaller total cross section, The details of calculation are presented in Table 11. In order to calculate the total absorption cross section per atom for pions on plexiglass (C, He Oy); the cross section trom each of the three constituent elements was calculated. The total cross section for hydrogen was taken from the well known rT p total cross section, (59) The carbon and oxygen cross sections were computed from the Aa2/ 3 law and the bubble chamber measurement of o/ Pe The measured and expected values of this total absorption cross section are presented in Figure 15. The data and the calculation (55) eom’ agree very well. The absorption correction which was used for the cross sections of this experiment was calculated in a similar manner. First, each piece of matter through which the pions must pass was reduced to a mass of hydrogen and an equivalent mass of carbon using the aa/ 3 law. In order to correct for the fact that some of the secondaries from an absorption event may be counted, an empirical factor, n, was defined as the ratio of the measured absorption (fram Tables 9 and 10)to the ahsorption calculated from the total cross section, Then the effective mass of each absorber was defined as the product of » and the equivalent mass of each absorber, and the absorption resulting from the total effective mass of carbon and hydrogen was computed from the total cross sections. Finally, the absorption was multiplied by the fraction of the events which are due to pions, assuming that the muons have negligible total cross section. 128 TABLE 11. Calculation of Total Absorption Cross Section per Atom for Pions Incident on Plexiglass Measured Absorption P in i” (MeV/c) Plexiglass 300 0,070 + 0.010 300 0, 059 + 0. 005 400 0, 044 + 0.010 500 0, 035 + 0. 005 570 0. 038 + 0, 010 (CHO09) Corrected on Fraction of Srp per atom Pions in per atom (mb. } Beam (mb. ) 259 + 37 0, 84 310 + 45 209 + 17 0, 84 250 + 20 162 + 35 0, 87 187 + 40 129 + 18 0. 89 146 + 20 140 + 36 0, 90 156 + 40 129 In Table 12 is presented a list of the various absorbers in the system, the mass of each absorber, the factor n for each absorber, and the effective mass of each absorber, The fact that n is statistically consistent with 1.0 for most of the matter of the system is evidence that the calculation is correct. Some inter- mediate results and the final numerical values for the absorption as a function of momentum are presented in Table 13, The absorption correction used for the cross section calculation was obtained by linear interpolation in this table. Some additional absorption was added because the pions must pass through a thicker part of the hydrogen target structure at certain angles. This additional absorption was 3.0 + 0. 8% at 34° lab and 0, 9 + 0. 2% at 40° lab. Since only three momenta near 500 MeV/c were used at these angles, the momentum dependence of the additional absorption was ignored. The error of the absorption correction depends directly on the statistical errors of the absorption measurements. Con- sidering the fact that measurements were made at a very limited number of momenta, it is expected that the error in the absorption correction is + 25% of the correction. This results ina 1,5 - 3.0% normalization error in the cross sections. pewmnssy » BSr'0. 91h IROL 0. 00°0 0 200 400 Vv tto'0 «to «sovo Fce’o §=—zo0-Ss seo a0 TPH 0 20°0 0 soo 10°0 IV 980°0 90°. soo Foro peo}6099% = 6% S0®aS 0 £00 0 Soo. 10°0 Iv epo'o «#90 goo F9°0 «49070 «000't)~S 0 TPH 0 ©0°0 0 G00 20°0 Iv zpo'o ~=g90- Soo Fg6°0 ~FHO'o «6090S 90 FH 3 9 €2'0 oT 0070 20 sz0 ©6*o'n seo’o «= es'o0—s—i( sk Fe't) 6co‘o = e0S bb '0 Py" 0 &2°0 «0'T 0 evo seo %on 0 0g°0 0 80 &'0 IV 0 00 ¥OFS'T 0 200 0°0 a9 0 §©0°0 0 20°0 20°0 HO ogz ‘0 0 x0 €§8°0 00°0 &'0 H H ‘arnba u H queTeA _uid/us uoTits 7 w/w 5 mo /w3 -tnba 9 4 -odwoy td /Ws Y uo /uid SSE DATION SSE SUOTG YORUM YSnosyy, weeyW “el WIAVL Surdder A LOJVTTIULIS ZOT PN =@S TE}FUMOH SuUTIdBI A SSRBIXIId Of zeyunep surddermy LOYETTIULOS GOT ON ra T9yUNO Y} SuTdderm LOFETTULIG ZOT PN = TS t9qUNOH Zs rayunoD 0} Y raqyunoy ITV TOJCTPIUTNS BOL PN = Vs AO FUNOD Y JeyUNOD 0} jesrIVY, ITy Ploryg 198NO PIetys yeoH IeTAIN uesoipéy prnbry JoRsIRL | TeTLoyeyl 131 TABLE 13. Calculation of Nuclear Absorption Vs. Pion Momentum T-p+ fraction o Absorp- Absorp- 1-C of Total geom tion a tion Absorp- events Absorp- PE carbon m-C tion dueto tion (MeV/c) (mb. ) of %seom (%) (mb.)4 (%) (%) pions (%) 1 198 330 0,86 5.92 70 1.93 7.85 0,79 6,2 233 330 1.08 7,43 110 3.02 10.45 0.80 8.3 1 259 8330 861.17 8.13 162 4.45 12.58 0,82 10,3 982 330 «1.17 9.13 205 5.63 13.76 0,88 11.4 1 305 330 1.18 8.20 190 5.25 13.45 0,84 11.3 1 332 330 1, 04 7.17 158 4.35 11.52 0.85 9.8 354 330 -0,96¢ 6.61 135 3.71 10.32 0,85 8.8 376 330 0.95 6.55 105 2,88 9.43 0.86 8.1 $98 330 oO. 91) 6,21 90 2.47 8, 68 0,87 7.7 522 330 0.82% 5.66 25 0,69 6.35 0.89 57 625 330 0.74% 5.10 20 0.50 5,60 0,90 5,0 3 03 0, 91 4,5 q1 T27 330 0. 66 4, 56 17 0.47 computed for 0,458 grams hydrogen 4,16 grams carbon equivalent Meshkovskii et al. (55) Interpolated Cronin et al. Jacob and Chew * (58) (59) 132 APPENDIX I. MULTIPLE SCATTERING Multiple scattering in the matter through which pions pass affects the results of the experiment in two ways. First, some events may be scattered out of the apertures and lost, in addition, multiple scattering causes a degrading of the momentum resolution and angular resolution of the spectrometer. The loss of events due to scattering out of the apertures was investigated under the assumption that the spectrum of pions incident on the spectrometer is independent of angle and momentum, An analytic calculation verified that these losses are less than 0, 5% for pion momenta greater than 200 MeV/c. A similar, but less accurate, result was obtained in a Monte Carlo calculation of multiple scattering losses in the High Energy Magnet by J. Kilner. In the 600 MeV/c spectrometer, the momentum of a particle (13) is defined by the intercept of the particle trajectory and the momentum counter, Multiple scattering ahead of the plane of the momentum counter causes a smearing of this intercept and results in a wider momentum resolution function. The effects of multiple scattering in an optical system can be calculated analytically if first-order optics and Gaussian multiple scattering are assumed, Under these assumptions, we may calculate the contribution of a scatterer of thickness ds at the point s along the central ray of the spectrometer momento Laan counter 133 to the uncertainty, dx, in the intercept of the ray with the momentum counter, The mean square projected scattering angle resulting from multiple scattering in thickness ds is given by the relation 2 Fos ds where x, (s) is the radiation length of the scatterer at point s, p and 8 are the momentum and velocity of the particle, respectively, and E ps is the multiple scattering constant for the projected distribution, Eos is related to the constant, E; defined by Rossi ©) by the relation Eas = E//2 = 14.9 MeV Since, in the first order approximation, dx and ds are linearly related, we may write (dx@y = L? (9) (a 02) where L(s) is given by the first order magnet theory. Since the scattering at each point along the trajectory is independent of the scattering at any other point, we may write the relation for the total mean square displacement as momentum counter E 2 2, _ ‘ps L*(s) hydrogen target 134 The contributions of the various scatterers to this integral are given in the table below Scatterer | eyes liquid hydrogen 0. 05 hydrogen target structure 4,05 air front 6. 25 center 10. 92 rear 9.60 counter A 54. 40 counter Sl 2. 28 Total 87, 57 in? To relate the root mean square displacement, ( ax” ) 1/ 2. to a root d mean square uncertainty in momentum, -¢ (= 2 1/ 2 divide by the dispersion of the spectrometer, D = 51.7 inches, , we must 1/2 2.1/2 E dp 2 _ (dx) _ ps () ) = SE 0. 8 When the multiple scattering is folded into the natural resolution of the spectrometer, the momentum resolution becomes a function of the central momentum of the spectrometer. The r.m.s. width of the momentum resolution at several momenta is given in the table below 135 d ($2)? 7? (2)? 7? ( (£8)? 3/2 Pp multiple (MeV/c) natural scattering total 200 1,10 x 1072 1.63 x 1072 1.94 x 1072 300 1, 10 0,94 1. 45 400 1.10 0.71 1. 31 500 1, 10 0, 56 1,23 600 1.10 0, 46 1,19 A similar method has been used to calculate the r.m. s, angular resolution due to multiple scattering, The result is: 1/2 (a6?) = 0.194 PS = 0, 194 —BS 136 APPENDIX IV. m-~p DECAY CORRECTIONS The decay of the nr, namely, nm +p4+v is a problem in any experiment with a long flight path. In this experiment, as many as 30% of the pions decay in the 421 cm. distance from the hydrogen target to counter pt, If the counter system of the spectrometer were able to distinguish pions from muons, then the decay would simply reduce the number of events observed. However, since pions and muons were indistinguishable, some of the muons from the decay of pions were counted, In general, the muons counted did not come from pions which had the same momentum that the spectrometer was set for. Thus the momentum resolution functions of the spectrometer had long tails due to pions counted indirectly by the decay process. The analytic calculation of the number of muons accepted by the spectrometer is a formidable pro blem involving multiple integrals with variable Hanis io) calculation of this type was per- formed by Dixon and Walker. The same calculation can be casily coded for a digital computer if the Monte Carlo method is used, Such programs have been coded by Boyden 48) and Kilner. (13) The Monte Carlo method was very inefficient and used large amounts of computer time. In order to obtain accurate resolution functions, it was necessary to run the Monte Carlo program for a few points and parameterize the output in such a way that the decay corrections could be used under a widevariety of kinematic conditions. In order to make this parameterization, it was assumed that a resolution function for the central momentum channel could be written as a function of P and P, only. This resolution function gives the solid angle for accepting the decay muon from a pion with 137 momentum between P and P+ dP and with the magnet set at momentum Po A table of values of the solid angle for several p-P values of P, and >= was computed by the Monte Carlo program. Then at fixed (P-P By, P, the solid angle was fit with a quadratic in Po The coefficients of this fit are presented in Table 14. The raw data were computed for P 0” 200, 300, 400, 500 and 600 MeV. These data, and the value of 42 computed from the fit, are presented in Figures 16-a - 16-e, The points computed from the fit are connected by straight lines in these figures, since the trapezoid rule has been used for doing integrals with these functions. The Monte Carlo program which was used to calculate the results of Table 14 was originally written by J. Kilner in FORTRAN IL (13) This program is described in his thesis. The program was converted to FORTRAN IV by the program SIFT, then it was modified to be able to compute results for a nearly vertical rear aperture counter, Finally, a modification was made to correctly compute the off-symmetry plane magnet optics in the first order model, (61) Three approximations are involved in the use of the resolution functions presented in Table 14, The first is that the effect of the lab angle of the spectrometer is negligible. The only place that this angle enters is in the projection of the length of the illuminated region of the hydrogen target on a plane perpendicular to the central ray. All the computations were done for oT ab = 45°, The second approximation is that the resolution function for the je channel can be simply computed from the Monte Carla results for the central channel. Under the assumption that the fraction of the observed events due to muons in the im channel with momentum PB; is the same as the fraction of events due to muons 138 TABLE 14. Resolution Function for Pions Counted by 7-4 Decay Process* P-P. P-P P-P o PP, ant Dp ) = AC 7) )+P Bip) + Py C(-p—) o Qa . Oo (9) P-P, ae Po) of P, ; Po. Po Po Py Po -0, 210 0.3789 x 107° -0.1696 x 10°" —-0, 1804 x 10°29 -0,180 0, 3684 x 107° -0, 1649 x 107” 0, 1754 x 10°19 -0, 150 0,2177 x 1074 -0,8289 x 107" —0, 7780 x 10°10 -0,120. 0,2709 x 1074 -0,9321 x 107" 0.8075 x 10720 -0, 090 0, 3332 x 1074 -0,9218 x10" ~—o, 7159 x 1071 -0, 060 0.1761 x 107* 0, 3500 x tov? -0, 8357 x 107 10 ~0, 045 0.1279 x 107 0.8415 x 1077 = -0, 1355 x 10°” ~0, 030 0. 5264 x 1074 -0.4960x 107" 0, 3000 x 10°13 ~0, 015 0, 9100 x 1074 -0, 1454 x 107° 0, 1335 x 107? 0, 000 0, 4559 x 107° 0.5426 x 10°? = -0, 1024 x 10° 0. 015 0, 3506 x 10°* 0,1964x 107’ -0. 4764 x 10°7° 0. 030 0, 4990 x 1077 -0,3524x 107" ~ -0,3221 x 1077? 0.045 -0,1481 x 107 0,.2197x 10° -0,2860x 10” 0, 060 0, 3823 x 1074 0.5499 x10" 0, 2571 x 1072 0, 090 0, 5439 x 10°4 -0, 1595 x 107° vu, 1382 x 107? 0,120 -0,5887x 10° 0.1173x10°° — -0, 1611 x 107° 0, 150 0, 2993 x 1074 -0, 7438 x 107! 0.5571 x 10° 0, 180 0.1329 x 1074 -0, 2618 x 107! 0, 2187 x 10°10 0, 210 0. 2091 x 10°4 -0,'7228 x 107" 0. 7999 x 10710 0, 240 0, 9166 x 107° 0.5345 x 10°" -0, 8128 x 107 2° 0, 270 0, 3046 x 1074 0.1173. 107° ~—. -o, apas x 107? * computed for 3, 0" x 9,50" aperture counter SOLID ANGLE C(MILLISTERADIANS) -100 ~ 050 139 PI-MU ACCEPTANCE PO= 200 MEV/C if -00 CP-PO1/PO Figure 16a 20 30 SOLID ANGLE (MILLISTERADIANS) PI-MU ACCEPTANCE **°po= 300 MEV/C 100 - 050 f T fL ”~ 00 eed -.390 -»120 ~.10 90 10 -20 390 C€P-P0)/PO Figure 16b SOLID ANGLE C(MILLISTERADIANS) -100 - 050 PI-MU ACCEPTANCE *"po= 400 MEV/C re te eo CP-P0)/PO. Figure 16c 10 20 30 SOLID ANGLE CMELLISTERADIANS) 142 PI-MU ACCEPTANCE PO= ~100 300 MEV/C 2050 va “e 30 “ee 20 ~.10 - 00 210 CP-POJ/PO Figure 16d +20 » 30 SOLID ANGLE CMILLISTERADIANS) - 100 2050 200 143 PI-MU ACCEPTANCE PO= 600 MEV/C ». a ee | ? £ | i | i HH 30 20 ~.10 - 00 10 CP-~PO)/PO0. Figure 16e 020 - 30 144 in the central channel if the central momentum were set to Bi; we find that the decay part of the resolution function for the jth channel may be written as (Andp/p,)i A P-D, ai Gc B-P, ~ WOOP Joona MB) TPG) OP Ao p- p. ba > )] oO where P; is the mean momentum of the jth channel, Py is the central momentum of the spectrometer, the coefficients PP; D-D; PoP; A( ae , >? , and C( >? are defined in Table 14, and the 0) f) 9) values of (AQ Ap/ Po) for the various channels are given in Table 2. The final approximation is that the resolution functions are proportion- al to the area of the aperture counter, This approximation is necessary because the resolution functions were computed for a 3.0" x 9.50" aperture counter in the early days of the experiment. The size of this counter was changed to 2.75" x 9, 50" before any final data was taken, The correction factor a = 0,9167 has been used to correct the coefficients of Table 14 for all the cross sections computed in this experiment. To compute total resolution functions from the resolution functions caiculated for particles which do not decay, we first multiply the no decay resolution functions by a factor which gives the fraction of the pions which do not decay in the magnet. Then we add the resolution function calculated from the coefficients of Table 14, Some summarized results of this calculation are presented in Figure 17, The fraction of pions counted by the process m-uU+ v is computed from the trapezoid rule area of the resolution functions of Table 15. A constant cutoff at (P- Po/P, = +0.27 has been used 145 DECAY CORRECTION SUMMARY 1.2 1.0 Stable Parti¢les aa Total 4 aoa .8 | Pions a Lu / | ra z < A — a. WT oOo & oO «< a lu N = .4 = food o = _ 2 re Muons pe pnb am fw ep a ee a | 0 | 0 200 400 600 800 MOMENTUM (MEV/C3) Acceptance for events originating as pions in hydrogen target which reach momentum counter in state indicated. Top curve is acceptance for stable particles originating in hydrogen target. Figure 17 146 as well as the correction for the smaller aperture counter, The statistical error in the area of the resolution function is + 0.3% of the total resolution function. Including the various approximations used, the decay calculation introduces a + 1% error into the area of the total resolution functions. The decay resolution function also adds a "long tail” to the total resolution function which causes Significant errors when the effects of finite resolution are considered, These effects are discussed separately in Section V-B, 147 APPENDIX V. RESOLUTION CALCULATIONS The angular resolution of the 600 MeV/c spectrometer depends on the size of the hydrogen target cup, the size of the beam spot, the size of the aperture counter, the lab angle of the spectrometer, the central momentum of the spectrometer, and the spectrometer optical properties, The angular resolution functions were computed assuming a uniform beam spot and ignoring effects of pion decay and nuclear scattering. The results of this computation for two typical cases are shown in Figure 18. The effects of multiple scattering discussed in Appendix III have been included. The momentum resolution functions were calculated for the parameters of each data point. For this calculation the resolution functions of Figure 3 were used as input data and the effects of pion decay and multiple scattering were included. Since, in the cross section computation, the angular resolution in 6* was assumed to be a delta function, whereas the k resolution was treated correcily, a correction was made to the momentum resolution functions to include the effect of finite angular resolution on the photon energy resolution, This correction was made by converting the angular resolution functions discussed above into effective momentum resolution functions by the relation P-P - 1 ak/ee (g_ 4 ) Py BP, ok/eP 6) Then these effective momentum resolution functions were folded into the momentum resolution functions for the spectrometer after ACCEPTANCE CARBITRARY UNETS) ACCEPTANCE CARBITRARY UNITS) 1.06 148 PO = S70. MEV/C, THETAO = 34. OFGREES | \ 2 XY -.100 209 2100 THETA-THETAQ (RADIANS) Figure 18. Laboratory Angular Resolution Functions, 600 MeV/c Magnet. — PO = 230. MEV/C, THETAO = 155. DEGREES -100 200 2100 THETA-THETAQ (CRADIANS) SOLID ANGLE CMILLISTERADIANS) SOLID ANGLE CMILLISTERADIANS) 149 PO = 570. MEV/C, THETALAB= 90. DEGREES 5.00 1 _ 4.00 _|- softy os | biG 3.06 4 jana 7 rT; id oe ee = —-4. ; “fen te- —o tee : ij iy 1,001]. - . a Sfendecb ube d i } | i | ae ay ie - —p op | 0 -.150 -.160 -.050 -00 050 100 150 (P-PO)/PO Figure 19, Total Momentum Resolution Functions, 600 MeV/c Magnet PO = 230. MEV/C, THETALAB= 90. DEGREES 3.00 : = _ | 3 ‘- i f fog. ; Page fb fey dy 3.00} 4- i. 4 ee prerareee Py pba 00 CP -P03/P0 150 the multiple scattering and decay effects were calculated. Two examples of the total resolution functions are given in Figure 19. Typically, the angular resolution correction increased the width of the total resolution functions by 10 - 20%. The r.m.s. resolution in photon energy, Ak was ’ computed from the total momentum resolution funetions for ‘each point, Since the effects of the long tails which result from pion decay were corrected by the unfolding process (see Section V-B), the pion decay part of the momentum resolution functions was ignored for the calculation of the photon energy resolution, The values of the r.m,s. resolution obtained are presented in Figure 20. For comparison purposes, the valucs of the resolution obtained by S. Eckluna®) are also shown. The reasons for calculating the momentum resolution function in great detail while ignoring effects of resolution in 6* were threefold. First, the momenium resolution function is weighted by B(k, EW) in the cross section calculation and for a few measurements where k was very close to E go 2 delta function approximation to the momentum resolution function was not accurate enough, Second, the excitation curves of Section IV-D would not be expected to fit the data unless the photon energy resolution was accurately computed. Finally, at the start of the experiment, it was hoped that a successful method for unfolding the photon energy resolution could be found and it was assumed that accurate resolution functions would be required for this purpose. This final reason did not work out in practice (see Section V-B). 151 0g ernst 7 (S335yu9Sa0) ATIONV aVv7t os! os| 02! O06 09 o¢ I u U J i | O09=y 008 = | OO0!=™ LANDVW 9/AS O02! ---— LANOVW 9/A8W COQ —— i oozl=y JIONV AVI ‘SA : (4) ASYSNA SV1 NI NOLLMOSSY SWY | i l i] | OV OS 09 (A®N) NOILATOSSY > SWY 152 APPENDIX VI PLEXIGLASS TARGET CALIBRATION RUNS During the second period of data taking, a series of tests was made to determine the reproducibility of results obtained by this experiment. For these tests, the hydrogen target was replaced by a piece of Plexiglass G" of the same dimensions as the hydrogen target appendix, The kinematic conditions were set up as follows: Ey 850. MeV (meter) Pp 573. MeV/c (magnetometer frequency 68. 26 me.) Oo Sab 51. 0 These settings would yield the results for single pion photo- production at a photon energy of 775 MeV and a center-of-mass pion angle of 16° if the target were free protons. Except for the plexiglass target, the kinematic conditions were thus typical of those used during the experiment. A plexiglass target calibration run was taken every few days during the second period of data taking. The runs were made with the same synchrotron operating conditions as any normal run. The quantameter calibration procedure used for the normal runs was also followed with one exception, namely, the beam catcher ion chamber was assumed to be stable for the entire period of the experiment and a value of Q/BC of 12, 68 was used for all runs. The data obtained in 18 plexiglass target runs are presented in Table 15, These dataare also plotted versus run number in Figure 21, 153 ,_DAVO. JUEISUOD aq PINOYS eB OJOA A+A OYT TY) UOFduNSse oY] JopUN HAVO /,» UT voHErTBA payoodxa au} ST“ # S30" Oh "29 OL *S9 NBD EL BG URSIN ~ peI+ 1290°O bL’@9 00°89 G9°%9 €S°29 PLOT O°LOT 2°LOT = L°LOT §=6TPL9 = O02. “PIN 02 Te"O+ TL0°O GB°09 06°09 «6L°09 «= (609 SLOT «= PLOT «= LOT = PLOT «= oTHSO GGT “SEW GT f.°0+ pL0'O Ges 10'%9 Leo 16°29 LOOT O'LOT 3°90T 9°90T 2h99 SEIT “ENGI 00°0 S80°O 80°19 PITS 0S 919 T'LOE O°LOT ESOT T°COT 2hS2 eBLTT “JBN ST 090+ 910°0 82°89 8'E9 =e “ED ae) 9°90 9°90T 4°90T «=F '90T-«OFLD. SHIT “SUNS co'O- 980°O 90°29 10°%D E8°T9 SE°S9 [SOT 2°SOT F°SOT Q°POT £269 SeIt “aaa rz OF0- 160°O EPS €8°E9 90°S9 {IT'D SPOT S°SOT EOL 8'FOT 1249 LEOT “dea ST Ly‘O- 2600 «SED = HLED = CB ED «= 0B "ED_=— GS 9OT «= BBOT «= ES0T «=o LOT «= 692s GOT “49 UT Oc"O+ = 8300) OB PS = OSH LBD) 80'SD9_ TOOT «=O 90T-— ss 90T «= 6 SOT 2689 = LLOE = “4. OT 00°O «= «800s SLES = GLED «GL“ED)«GL'ED «= SOT) SGOT) = SOT) SOT )= 889 S90T G8 00°0 = S300 BSD TLS) ST 'BD SBD Z9OT «= 'SOT)S BB S0T «= 8 SOT) 6890s PSOT = “'49 B Lo‘O- =6630°0 8609) PEO STD) «4809: Lk SOT) LEOT «= LEOT, «= 8 @OT)=—LSZ@9—ssTSOT «= “G8 82'0- 630°0 8F°29 PTS FO'EO h'29 «SEIT «OB HTT «BUTTS ETT «= ELOL) «= (OSOT 4 L9°0- 9500 GS 0D BSTS «= EBGS «= BOD Ss LOT «=F SOT) BT POT «= OEOE «= GL29) BOT 4 TT 88°0- 650°0 LS'T2 LS'TS FES GhL°TS 2°FOL «63°FOT «6 POT) «= G6 EOT «= OT#D GZOT URE TE et"O- 050°0 «= ED «CTT GS «cB "ED «AT "89 = SOT BSOTL*TOT «=A “20T)S 8869) FAG URE LE Te"O- 030°0 BSED «ATES «HED «DES «= TOL «= S'ZOT)= STOTT, «= SIOT «= SPD LG Ue Og Te'o- = 05600 ShS9 BO"ED «EG TS «1 "ZD_ GS VOT «SCO TOT «Sob HOT «=f SOT «= b2FDsCiGHCié‘“C OQ ie con DAVO/4 OdO/2 OFO/EOLB/4 DAVD =OdO OPO DLO at ung ayeq (Ata)=u AIVUIUNG UNY UOTTICITVD JOSIVL SSvpsixstg “ST SIAVL 154 eyed Uni UOTIRICITED PSAILL SSBISIX9Td “TZ INIT YASWNN NAY MW = == 2 =z Oqoaepe He G6 a emo oO o) Oo vA a On yn NN Oo © a @ & Sef og TSR ASGBSEAaAKR A GS T T T T T T T T T T T T T T T T T A = LP = ‘ / : \ | * / \ i 2 i - \ ip | \ f; a \, / mN a a” 4 ~~ | ys ‘ ~ “Nee —— ee ee \ \ Wi 4 Ye ‘ 7 \ om a W777 ~~ \% 71LN . / . 4 Vv J - og0/# —--— O10 /# ; Sivd OLSA A+4 OL / / 3nd 4} NOLLWINWA ---—- Opo/# ----- oAVO/# | | i i | ! i ! ! ! ! ! ! ! i ! ct Pt (diG/SLNNOD) GIZA NVSW - OT3IA 155 It is immediately obvious that these runs are not consistent with the hypothesis that the only errors result from the counting statistics. Deviations of this magnitude should occur approximately one time in 104, Thus we must assume that there is some other effect which caused the inconsistencies. In the table below are presented the values of the variance of n/Q obtained using the various beam monitors as well as the "additional r.m.s. error" which is due to errors other than counting statistics. counting additional variance statistics rms error 1/QTC 1. 98% 1.23% © 1.55% 71/Q40 2. 36% 1. 23% 2. 07% 1/QBC 2. 07% 1. 23% 1. 66% n/QAVG — 2.06% 1. 23% 1.65% Figure 20 leads us to look for a slow variation which could take place with a period of several days. Because lhe singles rates from a lucite target are much higher than those obtained with hydrogen target, it is possible that accidentals or dead time effects | could cause the observed discrepancies. However, a study showed that the variation in 7'/Q is not correlated with the average beam intensity. The efficiency of the fan counters might also have fluctuated since these were checked at only infrequent intervals. However, if we assume that the fraction of events which are vetoed by F +V should be a constant, we can compute the variations expected from the fact that the fractional F + V veto rate was not constant. The fractional F + V veto rate is given in Table 15, as well as the expected variation in 7’ /QAVG due to this effect. 156 However, the plot of the expected variation vs. run number shown in Figure 20 clearly shows that this effect is not correlated with the observed fluctuations in nr / QAVG,. The pion and proton separation logic in the spectrometer was also shown to be constant to the order of 0. 2%. The beam monitoring was not completely consistent. How- ever, the fact that the values at n/QTC and 1/QBC are consistent to better than 0.5% r,m.s. indicates that the beam monitoring system was not responsible for the major part of the inconsistencies. There remains the possibility that the plexiglass target was dimensionally unstable or absorbed water from the atmosphere. However, data from the manufacturer's catalog indicate that both these effects could contribute less than 0. 3% variations in the n rate. The most likely reason for the discrepancy is that the cross section for 1 photoproduction from free protons is changing rapidly with energy near the kinematic point chosen for the plexi-~ glass runs. The slope of the yield vs. momentum curve can be obtained by looking at the observed yield in the various momentum channels. From this effect, we ohserve that an 0.25% r.m.s. momentum variation can cause the observed 1.65% r.m.s, variation in yicld. The variation of momentum calibration is due to the motion of the beam centroid. An 0,11 inch r.m.s. motion of the beam centroid could cause the observed effect. Since the vertical position of the beam centroid is not under the control of the experi- menter, this motion can exist. However, this much molion seems to be inconsistent with polaroid beam pictures taken each day. 157 Another possibility arising from the rapid variation of the cross section with kinematics is that the momentum of the spectrometer was constant but the synchrotron energy changed, A test run was made with Ey = 890 MeV, or 40 MeV higher than the normal runs. This test yielded the result of 88.0+ 1.4 pions/QBIP. This amounts to an 8.5 + 2.0% increase in the yield for a 40 MeV change in E of If the end point energy is responsible for all the fluctuations observed, then E, must be drifting by 0.9% r.m.s.. This much drift is also unreasonable. The conclusion drawn from the plexiglass target cali- bration runs is that there is a random error in the yields in addition to the counting statistics. 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