Polarixation of Recoil Protons from the Photoproduction of Neutral Pions in Hydrogen Between 750 and 1450 MeV Citation Bloom, Elliott Daniel (1967) Polarixation of Recoil Protons from the Photoproduction of Neutral Pions in Hydrogen Between 750 and 1450 MeV. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SEXB-B858. https://resolver.caltech.edu/CaltechETD:etd-05032005-103209 Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. In a recent experiment on [...] photoproduction at the Caltech 1.5 BeV Electron Synchrotron, the polarization of the recoil proton was measured. The measurement was performed using a scattering and range spark chamber built out of variable thickness carbon modules. The sample of [...] was pure to better than 98%. Approximately 3500 useful scatters were obtained to yield polarization values, around 60[...] c.m. for the produced pion, for incoming photon energies 750 [...] k [...] 1450 MeV. The polarization values were obtained with a maximum likelihood method. A thorough investigation was made of all analyzing power data available for proton carbon scattering. The results indicate a striking angular dependence, with the polarization changing sign for [...] ~ 60[degrees] to 70[degrees] throughout the energy region covered. These results are interpreted in the framework of an isobar model of [...] photoproduction with Regge-ized [...] exchange amplitude added. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Heusch, Clemens A. (advisor) Walker, Robert Lee (advisor) Thesis Committee: Unknown, Unknown Defense Date: 4 May 1967 Record Number: CaltechETD:etd-05032005-103209 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-05032005-103209 DOI: 10.7907/SEXB-B858 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1592 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 03 May 2005 Last Modified: 15 Mar 2024 18:11 Thesis Files Preview PDF (Bloom_ed_1967.pdf) - Final Version See Usage Policy. 4MB Repository Staff Only: item control page

POLARIZATION OF RECOIL PROTONS FROM THE PHOTO- PRODUCTION OF NEUTRAL PIONS IN HYDROGEN BETWEEN 750 AND 1450 MeV Thesis by Elliott Daniel Bloom In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology | Pasadena, California 1967 (Submitted May 4, 1967) ii ACKNOWLEDGMENTS This thesis work was supervised by C. A. Heusch. He conceived the experiment and was active in all aspects of its operation. The presence of his creativity and experience was a necessary element in the success of our effort. Charles Prescott and Leon Rochester also deserve many thanks for the active part they played. They were present from the inception of this work, and made a uniquely valuable contribution to it, Walter Nilsson deserves special thanks for invaluable contributions to the apparatus of the experiment, His expertise as a craftsman, and attention to detail, made success a good deal easier to obtain. The patience and efficiency of Sherwood Wilner is appreciated. Much time was saved in the data scanning and measurement process due to his participation, Steven Cheng, William McNeely, and Bruce Winstein, were very helpful in the analysis of the experiment, The author appreciates the continual support and advice of R. L. Walker. His recent work in the phenomonology of tm photo- production was essential to the theoretical section of this thesis. S. Frautschi was very helpful in keeping the author on the correct theoretical path. We thank him for many useful and informative discussions. Fred Gilman has also provided useful suggestions concerning the theoretical interpretation of this experiment. Assistance from the synchrotron crew under Larry Loucks, from Earle Emery, and Dick Wileman, who built and maintained the - hydrogen target, and from the synchrotron operators, headed by Al Neubieser, is gratefully acknowledged. For financial support, the author is indebted to International Business Machines Corporation, General Atomic Corporation, the Atomic Energy Commission, and to the California Institute of Technology. iii ABSTRACT In a recent experiment on 7° photoproduction at the Caltech 1.5 BeV Electron Synchrotron, the polarization of the recoil proton was measured. The measurement was performed using a scattering and range spark chamber built out of variable thickness carbon modules. The sample of no's was pure to better than 98%. Approximately 3500 useful scatters were obtained to yield polari- zation values, around 60° c.m. for the produced pion, for incoming photon energies 750 < k < 1450 MeV. The polarization values were obtained with a maximum likelihood method, A thorough investigation was made of all analyzing power data available for proton carbon scattering, The results indicate a striking angular dependence, with the polarization changing sign for e* ~ 60° to 70° throughout the energy region covered. These results are interpreted in the frame- work of an isobar model of T° photoproduction with Regge-ized w exchange amplitude added, iv To my wife, Sue TABLE OF CONTENTS PART © TITLE PAGE | 1 INTRODUCTION 1 2 #EXPERIMENTAL METHOD 6 2.1 General 2.2 Primary Interaction Trigger 2.3 Event Information . 12 2.4 Proton-Carbon Analyzing Scatter 16 3 DATA ANALYSIS 20 3.1 Scanning and Measurement 20 3. 2 Data Reduction — 22 3.3 Calculation of the Polarization 30 4 RESULTS 34 i) DISCUSSION 42 6 . CONCLUSIONS 50 7 APPENDICES 55 7.1 n° Detection 55 .%.2 Proton Telescope and Spark Chamber 58 7.3 Optics and Fiducials | 64 7.4 The Scintillation Counters 66 7.5 Electronics 66 7.6 Method of Surveying 72 7.7 Spark Chamber Characteristics 73 7,8 Hydrogen Target 75 7,9 Scanning Bias and Efficiency - 17 PAR vi TITLE 7.16 Scanning Efficiency Formulae 7.11 Analyzing Power 7,12 n° Cross Section 7.13 Backgrounds 7.14 Beam Monitoring 7.15 Theoretical Analysis REFERENCES _ PAGE él 84 93 102 106 109 117 FIGURE 11 1.2. 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 3.5 4.1- 4,2 4.3 4.4 5.1 5.2 5.3 . Vii LIST OF FIGURES PART Diagrams contributing to n photoproduction Born terms contributing to n° photoproduction Experimental setup idealized Experimental setup schematic Proton telescope pulse-height distributions yp and P-Cy5 interaction kinematics Distribution of events in hydrogen target P-Ci polar scatter angle distribution Distribution in T p Distributions in iT, Typical likelihood functions Distribution in k Data at 6* = 60° + 10° Distribution in or Data at 6* = 55° and 65°25" Added low-lying partial waves Model fits to cross section at k = 800, 1175 and 1400 MeV Model fits to polarization at k = 85°, 925 MeV. , and at 6* = 60° PAGE 11 13 93 24 28 29 32 35 37 38 40 45 46 47 ’ FIGURE 5.4 6.1 es 11-2 7.21 7. 2-2 7. 2-3 7.3 15-1 15-2 17 18— 7. 11-1. 7. 11-2 vili TITLE ‘w coupling as a function of k - weexchange comparison y-systems of n° side of the experiment Lead-lucite shower counter distributions The proton detection apparatus Details of chamber modules Distribution in scatter module Fiducial and lens system Fast logic for pion trigger Readout and calibration systems Spark chamber delay curves The hydrogen target | Double P-Cy5 scatter kinematics Distribution in AT, 7,11-3,6 McNeely fits to analyzing power 7. 12-1 7. 12-2 112-3 7. 12-4 7. 12-5 ‘I, 13-1 k resolution, o,, for k= (850) k resolution, 0,, for k = (1350) AT, with little inelasticity in the P-Cy5 scatter Nuclear corrections re) en gs t cross section | A@_ distribution for (k) = 850 MeV PAGE 48 53 56 57 59 61-b 63 65 69 70 74 76 85 88 89-92 94 95 97 98 101 103 FIGURE 7. 13-2 7.1343 7. 13-4 TITLE ss PAGE The qualitative reasons for multipion background suppression 104-105 20° background . 107 AG. distributions for (k) = 850, 1100, 1350 MeV 108 TABLE VI VOL. vit LIST OF TABLES TITLE PAGE Measured variables 14-15 Derived variables 26 Polarization values for a = 60° + 10°; Ak = + 50 MeV | 36 Polarization values for ¢* = 65°, 65° 5°; Ak = 50 MeV 39 Resonance parameters 49 Setup kinematics 61-a The counters of the experiment 67-8 Systematic effects in the cross section determination 99 1. INTRODUCTION Up to about three years ago, or just past the time of the inception of this experiment, the common view of the nm photo- production mechanism in the photon energy region k < 1.5 BeV was relatively simple. Theoretical models at that time)» (2) usually included only the most prominent resonant states, e.¢., the so-called Ist, 2nd and 3rd 1 N resonances, plus the Born terms, and maybe an elementary we exchange. Detailed information on the photoproduction process (r=, 7°) was limited to cross section measurements of unspectacular precision, and very few polari- zation measurements on the recoil nucleon. (3) The polarization measurements were mainly in the region of the second resonance at 6% ~ 90°. Since that time, experiments of considerably improved statistical accuracy have been performed, exposing the more subtle aspects of the cross section?) . Also, a number of (3) These have vastly extended knowledge of the polarization to polarization experiments’ ’, including this one, have been completed. previously unexplored photon energies and pion CM angles. With this additional information, refined methods of phenomenological (4) multiplicity of direct-channel resonant states, and so achieved a analysis were developed‘”’ which have been able to uncover a much more complete understanding of the photoproduction process in the region k < 1.5 MeV. These investigations also supported (5) It is not surprising, then, that the original theoretical similiar findings‘ obtained from nN elastic scattering data, motivation for this experiment should be somewhat outdated. Never- theless, considerations along the lines then accessible were important in the selection of a kinematical region in which to make measure- T°T omnstg NOILONGOYdOLOHd ,4f OL SONILNGIMLNOOD SAVYOVIC SONVHOX] | — uvgOSl > and N BORN TERMS CONTRIBUTING _ TO w®? PHOTOPRODUCTION Sigure 1.2 ments. Due to the lack of previous polarization experiments the possibilities were broad. The large amount of beam time needed, and the inordinate analyzing time required, restricted our choice to a limited region considered interesting. Polarization experiments previous to this one usually had as their motivation the determination of the relative parity of two resonances. For example, the relatively simple structure of the n° photoproduction process postulated in past times, as mentioned above, led Sakurai ®) to propose a polarization measurement at 6* = 90° and at photon energies around the second TN resonance, N* (1512). This experiment was to determine the relative parities of the Ist and 2nd resonances. If the parities were the same, no . polarization should be seen, since only different parity states can produce a substantial polarization value at oF = 90°, However, even in the simplified view of the past, as one proceeds to higher photon energy, the number of contributing states increases. Hence, arguments like Sakurai's become somewhat (7) just previous to this experiment had raised the possibility of w= ambiguous to apply. Also, some cross section measurements exchange becoming an important feature in the rr photopreduction — amplitude. Some aoess in fitting n° photoproduction had been . established resonances with w°- exchange. This model suggested that the region of ae = 60°, 750 < k < 1200 MeV would exhibit particularly interesting features. It predicted a zero crossing for “the polarization at about 900 to 1100 MeV, at 60°. . The kinematical region suggested by this model aiso turns achieved by Beder*”’ using a model which incorporated the well- out to be rather accessible to experimental techniques. The laboratory angles with respect to the photon beam are large enough so that the flood of low-energy electrons accompanying the beam do not affect the thin-foil spark chambers. Also, the recoil energy of the protons is between 80 and 300 MeV. This is (8) analyzing power is well measured in this region’ ) and its low- convenient for using carbon’ ’ as a polarization analyzer. Carbon's’ lying energy levels are relatively well separated in energy. The latter point is important for the accurate determination of the analyzing power. It also results in a relatively depressed cross section for the excited levels of carbon, the analyzing power for which is less well known. The Kinematical region finaily chosen for the incoming _ photon energy, k, and the center-of-mass Production angle oF was 700 < k < 1480 MeV, and 50° < 6° < 70°, Although phase shift analyses of recent yp and wp), (5), (10) gata strongly suggest that the model employed by Beder is over-simplified, the kinematical region chosen still turns out to be a particularly interesting one. The polarization exhibits striking features in its dependence on both energy and production angle. This is discussed more fully in Section 4. 2,, EXPERIMENTAL METHOD ' 2,1 General The reaction under study in this experiment is the two-body process ytpr>om +p. (2. 1-1) | 7 YY The polarization of the recoil proton was measured for incident photon momentum, k, between 750 MeV and 1450 MeV, at pion CM angles between 50° and 70°, The polarization was (8) the recoil protons. The P-C 45 scatters occurred in a large, thick measured by observing the asymmetry in p-Ci5 scattering of carbon plate, spark chamber. This allowed one to follow the entire proton trajectory. Hence, the efficiency in observing scatters was high, and inelasticities in the PCy scatter could be taken into account, The possibility of artifically introduced asymmetry was also minimized, — Briefly, the entire experimental procedure can be enumerated in the following steps (see Figure 2.1). (i) The bremsstrahlungbeam of the C.LT. Synchrotron was passed through a liquid hydrogen target. (2) A counter system which detected all final-state particles from the target was used to obtain a very clean 7° trigger. TZ oInsly TWLNSNIY3dX4 dNLas SHSLNNOO f MIMOHS € ‘ # SYaLNNOD a NOLOUd | SYSaNVHO — HOI NIHL “hn _- _ ae ~~ ap a] 3 — NOLO __—— SHOUMIN (3) Thin-foil spark chambers were used in conjunction with counter hodoscopes to obtain the complete determination of the n° photoproduction kinematics upon analysis of pictures recording the chamber- hodoscope information. (4) Alarge, carbon-plate, modular spark chamber was used to analyze the recoil proton polarization by means of P-Cy5 interaction (scatter) in the chamber. The scatter information was recorded on film together with (3). One hundred forty-three thousand pictures were taken in tour kinematical settings of the apparatus, Approximately 10°? equivalent quanta of photon beam were used, Data were accumulated at the average rate of one picture (i.e., one pion) per six seconds with the synchrotron pulsing once per second, Of these, 3500 tinally passed all scanning and measuring requirements and were used to obtain the final polarization values, In the next sections the details of what has been outlined above will be discussed more completely. The details of the experimental apparatus can be found in the Appendices. 2.2 Primary Interaction Trigger Figure 2.2 shows the general layout of the experimental | apparatus relative to the C.I.T. Synchrotron, The bremsstrahlung beam from the machine was collimated, scraped, and purified in a sweeping magnet. It then passed through a liquid hydrogen target containing 1.427 gm/ cm” of liquid hydrogen. The duty cycle of the Suze, Nno3 3L9ny Qv3ay . Novy cae ONId IIMs aH | AM aSI1g : f. m SN3T W314 ee: } ation Ag “oO \ Te2wy5 ie — \ : _— \- | \ \ CF . \ \ ONO 434 2N93 10 synchrotron was 15%, allowing coincidence work to be done with ease at the rate of beam accumulation used (see Table Vil for typical counting rates), __ Since the results of this experiment are sensitive to back- grounds, care was taken to insure that contamination was minimal. The major source of background was due to protons assumed to originate from processes (2. 1-1) but which did not. The final back- ground contamination of less than 2% (see Appendix 7.13) was achieved by employing a detection scheme which required all final- state particles (i.e., y, Y, p) inthe trigger. Basically, two systems were used to obtain the trigger. 1. The r detection apparatus consisted of two y-detecting . systems, Each y-system contained scintillation counters and a lead-lucite Cerenkov counter arranged to insure a clean separation of y's from charged r's. The two systems were placed in the laboratory at the symmetrical decay angle of the central no's. By central, one means those a's which originated from photons with median k of the kinematical setting being considered, and which had 6° = 60°. (See Table VI.) The two systems were also placed so that their line of centers were vertical in the laboratory, i.e., approximately perpendicular to the production plane. This last detail yielded maximal angular resolution in the pion laboratory production angle, and allowed one to maintain roughly equal counting rates in both systems. (See Appendix 7.1 for details of the y- “systems; Appendix 7.13 indicates further why the y-systems were placed as they were in the laboratory. ) Bx! CHARGED PARTICLE PEAK, ~ MAINLY ar 'S PROTON PEAK frre mlelst A - Raw distribution SINGLE PROTON COUNTER RAW DISTRIBUTION SHOWING BIAS CUTOFF AT LOW PULSE HEIGHTS | DISTRIBUTION FROM SINGLE i i | PROTON COUNTER TRIGGERED | a WITH 7° EVENTS jh 1 ul ho Dh te in 0 | Lond fo “ATYPICAL BIAS ON COUNTERS IN PROTON TELESCOPE see ; wiz, _O B - Protons associated with w's Figure 2.3 Proton telescoce pulse height distributions 12 2. The proton telescope consisted of two or three scintillation counters (two or three depending on kinematical setting) placed as in Figure 2.1. The protons were slow enough to yield counter pulse heights well above those of minimum- ionizing particles. The electronic bias on these counters was adjusted so as to exclude particles which had ionizing power Significantly below the protons produced at the kinematical setting being considered, However, the bias was carefully set not to exclude the protons desired, For all the settings the proton energy was low enough (< 290 MeV, 8 < .65) that the proton telescope obtained a reasonably clean pulse height separation between protons and 8 1 charged particles, mainly m's (see Figure 2.3A). A typical pulse height distribution for protons obtained by the full 7 trigger is shown in Figure 2.3B; this further demonstrates the purity of trigger. (See Appendix 7. 2 for details of the proton side of the experiment. ) For clarity, then, a n° signature was a two-fold coincidence between the y-systems in coincidence with the proton telescope, 2.3 Event Information When a w° Signature was indicated by the fast logic, the spark chambers were fired and a picture was taken (see Appendix 7.5). The picture contained all the information needed to completely reconstruct the event kinematically: (i) The proton trajectory and range information were contained in thin-foil and range-scattering spark chambers. 13 SOTJLUISULY UOT]OV.A19 UT aT, pue dA yz oanStq SNVId NOILONGONd NOILONGOYdOLOHd oN oft ORONDO 6 om % yaa eee re a A LNGGIONI ATX | “ / aed do ~ Yo pean 18s NOLOYd Woosy Sed ny, Py (9x4) 3NWId ONINALIVIS OL TWAYON *AJUTEIIIOUN s8uer LIBIeT Yoru 14 dABY SPWOAS OYSVTouT “ssou -3OTY} oyeTd uogarvo OIUTT 01 ATLrewtad anp si o1ey I0OTIg uotjovrequt ST 4-d onsete WIM SjueAO TOF ATUO Sploy peyeIs OIG su, “OIL ~~ J08.1e4 ULSTIO JUDAS Jo AyUTeLIIO -UN oTL" ~ edoasopoy JO PTAA ULC OPLUT YT dy SB oultg *IOLIO SULINSVOU > UOTLIOISTP ‘990° ~ Io1ze JUOUIEINSveUt G8" BUTL9}}eOS aTdynyy IOIIG Jo 90anog coleyy %& > ° ri +] ot’ F SerqULELIO0uQ SO[QVLIVA JO SenjVA Teolzeunyy Teor J, THTavia 2 "UOGIBD UT VsuUeT TLIO, °jaS.1V] UT ULSTIO JUIAD TOT popsou AxoyooelBrzy uoload snjd uol}eULZOsUL edoasopoy-A d °'9 SB sures *STOquIeYyo TLOJ-UTYy UL SyoV1} Jo JUOWOANSvoyy SUIUTEIGO JOT o1npo00ag SOTQLLIVA poinsvoyy “UuoqIvd jo wo /ws ¢g° * Ajyeotds, ‘sayetd 6 _ §OTY} UL oSueI Jo puo ye uojor1d Jo uotyeooT, Sutddois ul Ayutey.190uN YIM pepfoy UOTIVULUTLIOJOp XOMOA UL 1OLIG ‘,w0/w3 g* F > eyed UCqred YOTY} UT XopTEA oF 4-4 oururzezep 04 ANTICY 10 998° > Ajurejreoun oats mi 6 GequVeYyoO SUTLLOI}VOS SBsueBI Jo Sorjdo TeyIO pus SEeSUST PTET] WO} UOTLIOISTp yey} Jou pTnoys suo dg se oweg *soretd UCGIVD SPISUL X979A oTsue Sutzojiwos ST 5-d jo vorzes0T ur AyUTe.LE0UN YIM peurq -Ul0D JOTI JUOUIOINSBSYY OILY JO soarnog zolfeyy SoTJUTe}.IE0UQ (uoqieo ATuTeU) “soe Fy uojord jo puso | 0} seyyeos ¢F5-d jo ur8i20 moss [°T F> WOT} Telreyeul Jo zu {us *ronvos SI5-d jo u8t10 0} jos.1e] UesoIpAY JO Lo}Ueo Wody [elzeyew jo _wo/wus wo/us 6° F > z d d , 8 SOO UL [T° > ,9 Se@ ouleg "STSquUIvyd [LOZ ULY} pue Isquivyo BUL1E}}e0S -o8ueA of 2 Ul SyoVa} Jo JUoMOAINnsvoyy SoTqelivaA JO SonyTeA [eotroumMy peordA J, SULULEIAQ JOT sinpssoig (°y009) T ATaAVAL Ce SOTGVLIVA DOANSBITAL 16 (2) The nr trajectory was obtained from the two y-systems as hodoscope information, assuming - ' an origin in the hydrogen target determined from the proton trajectory. (The y-shower pulse heights were also recorded. See Appendix 7.5.) (3) The complete p-Cy5 scattering kinematics were contained in the range-scattering chamber. The measured variables describing the event kinematics, information about the errors in these variables, and the manner in which they were obtained are given in Table i, Complementary to this table is Figure 2.4 which defines the variables. 2,4 Proton-Carbon Analyzing Scatter Consider a P-Cy5 scatter in the context of general spin 1/2-spin 0 scattering. The most general amplitude one can write which conserves all quantities conserved by the strong interactions (e.g., parity, J... etc.) is > Feft+o. 9 8 . (2.4~1) > . D...72 : : “a A A the o being the usual Fauli spin mairices, Ny = p x p'. (where « indicates a unit vector ), fand g are Fermi's invariant amplitudes, One can easily show that a spin 1/2 beam with initial polarization (1 0, Pp gives 17 o( 8,0) =C|f] “+ |g] “+ 2ReG* ¢)R,- P] =o (s)(1+Aa,- P) ae | — (2,4-2) 0,(8) = {f| 2. le 2 is the unpolarized cross section, A = 2Re(f*g)/o,.(9); A is the analyzing power, a property of the scattering material, i.e., carbon, which has been measured in other experiments (see Appendix 7.11.) . In the case of n° pnotoproduction with the initial state unpolarized, parity conservation requires that the final state proton pe polarized ina direction perpendicular to the production plane. Hence, take P = ny P, ay =k x D; equation (2.4-2) then gives o(8) o)* 0 (8) (1+ AP cos 1) . (2.4-3) See Figure 2.4. Equation (2.4-3) is the key to a proton polarization measurement in our energy range. One can proceed in two ways from here: _- (1) Scintillation counters can be set up behind a carbon block such that cos Py = +1 for one counter, a, and cos Oh = -~1 for the other, 8. Then, assuming the two counter detection efficiencies equal, N = ¢(i + AP), N, = c(i - AP), -N being the number of counts and c a constant; and N -N - 4 8 _ ma kG - €f THN AP, where A is the average R Kes) 18 analyzing power over the kinematical region of acceptance (usually quite limited for this method). By looking at the counting asymmetry ¢, and knowing the analyzing power, A, one can obtain the polarization, P. . (2) A soark chamber containing carbon plates can be used to see the scatters. in this case the greater part of the proton trajectory can be seen, and so apparatus-induced asymmetries are avoided. Also, a rather precise measurement of 8 » cos Pry can be made over relatively large ranges of these variables compared with method 1. Here statistical methods are used to determine the polarization, briefly as follows. The expected distribution for p-C,5 scattering is given by (2.4-3). For each (k, e* ) bin one measures a large number, n, of such scatters each with an associated cos by and i Ay We then form n L(P)= mn G+ A, P cos ys for each (k, en) bin, (2.4-4) i= As described in more detail later (Section 3.3), L(P) is the so-called likelihood function. The value of P which maximizes L(P), P* data. This method also assumes, of course, that no artificial , is the best value of the polarization obtainable from the asyrameiries have been introduced into the observed scatter asymmetry. One also must be sure that the detection efficiency 19 for scatters is independent of polarization. (These considerations are treated in Appendix 7.9.) This experiment used the latter method for the polarization determination, The chambers used are described in Appendix 7.2. The parameters measured were eo? Ro and Ry , which were used to determine the relevant value of analyzing power associated with each event (Section 6.2) cos Py was measured also; however, this number was used in a purely geometrical way - i.e., in (2.4-4) directly. Table I together with Figure 2.4 completely defines these variables; in addition, the table mentions the way they were obtained, and the approximate errors involved, 20 3. DATA ANALYSIS 3.1 Scanning and Measurement ° The data analysis was broken into two distinct parts in order to reduce the data in a reasonable time. | First, all 143, 000 pictures were pre-scanned for P-Ci5 scatters according to the following rules. To be included for further analysis (scatter refers to p-Cy5 scaiters): (1) (2) (3) (6) Each event must have a scatter of 3° or greater in the top view of the chamber. (The top view displays the horizontal plane in the laboratory. The horizontal plane was approximately the plane in which the photo- production process occurred, ) Each event must have a track length after scatter long enough to measure well (usually three sparking moduies). Each event must not have a significant double scatter. (This would badly smear the scatter kinematics. ) Each event must not have a nuclear reaction with more than two prongs (proton in, proton out), Each event must be correlated in all chambers. Each event must be completely contained in the spark chambers. Each scatter used in the experiment was scanned twice, veritied once and réverifie d, (See. Appendix 7.9 for details.) | al Even though the scanning process was rather involved, the time taken to process all the data was only about three months. Much of the work was done while the experimenters were collecting data. The subject of artifically introduced asymmetries arises here. Of prime importance in a polarization measurement is the certainty that no left/right bias is introduced in the experimental method, or in the handling of the data. Appendix 7.9 treats this topic completely; as this appendix shows, there was no such bias in this experiment, Of the initial 143, 000 pictures, about 5,500 satisfied the criteria of the pre-scan, and were passed to the next step in the _ analysis. The second step in the analysis was considerably more time-consuming than the first, taking about six months. For each accepted picture the proton trajectory was measured from the spark chamber information. (See Table L) Also, pion angular information was obtained from the hodoscopes. This information together with necessary event identification was encoded and placed on IBM cards. Each event was measured at least twice for comparison purposes, indeed, each event was measured over and compared with previous measurements until satisfactory agreement between at least two measures were obtained, or until a fifth measure was required, An event of the latter type was discarded, 95% of the admitted events remained after the completion of the measurement process, i.e., about 5, 200 events. 22 3.2 Data Reduction . The reduction of the information on the encoded IBM cards to usable information was an involved problem requiring the use of a computer. A Fortran IV computer program was composed to do the following for each event (see Table J): (1) Fiducials, punched for each event, were fitted to a master grid, (2) Geometrical reduction of chamber spark information ielded 6, and . y p? Px (3) The approximate event origin was found using the proton trajectory. Note: The accuracy of the encoding table, and the reduction procedure (1)-(3) is well illustrated by Figure 3.1 which displays origin of events versus target position. | (4) 8 was obtained geometrically. (5) Second-scatter parameters, Bh. cos OPCyo , scatter vertex position, were reconstructed geometrically. (see Figure 3.2), (6) Ro Ro and Ro were reconstructed from ey? position “of P-Cy5 scatter vertex, and a number which indicated in which carbon module the proton stopped. Steps (1) through (6) gave all measured quantities of the experiment usec in the complete reduction. The rest of the computer program COUNTS COUNTS 700 600 500 400 _ 300 200 100 350 300 250 200 150 100 +O 23 i T q T 1 q q T T . a° POLARIZATION EXPERIMENT DISTRIBUTION IN TARGET - X DIRECTION . COMPLETE SCATTER DATA 4 CUP DIAMETER 5 -4 -3 -2 7 ie} | 2] 3 4 5 X, (cm.) (perpendicular to beam direction) i if T T | qT in mt i] 7? POLARIZATION EXPERIMENT P DISTRIBUTION IN TARGET -Z DIRECTION | _ ~ COMPLETE SCATTER DATA 4 CUP LENGTH as LJ i l t L { iT i i if 12.5 -10.0 “7.5 -5.0 -2.5 16) 2.5 5.0 7.5 10,0 12.5 Z, (cm.) (in beam direction) Figure 3.1 COUNTS 400 5 350 300 250 200 150 100 50 24 | i] { | i J | _ SCANNING CUTOFF PL : | | <k) = 850 | P-C,. SCATTER - | POLAR ANGLE DISTRIBUTION 4 | | — — i | | | | i | = | 4 {i | | i l l 5 iO 15 20 25 30 65, (DEG) igure 3.2 Distribution in p-C,, polar scatiering angie, ° 1@ Smooth curve is calciifeted using the known p-C.. astic and inelastic cross sections, without foicing in the scanning cutofi, or efficiency. The curve is normalizec to the data to obtain a best fit; however, its shape is ly determined by the cross sections, 2 3) ts ao obtained quantities derived through kinematical relations. To specify vtpo> n° + o Kinematically, one needs to optain the 16 four-momentum components of the reaction. Conservation of momentum-energy plus knowledge of the particie masses leaves 8 to be determined. In this experiment, we have 2 momentum components from the incident y-beam direction, 3 from the proton at rest in the hydrogen, 3 from the range and trajectory of the proton, and finally, 1 from the direction of the 7° (coplanarity not measured), Altogether one measures 9 momentum components; hence, the photoprocuction reaction is singly over- determined (assuming a 1° was produced), There is one quantity however, which is rather poorly Known. Due to inelastic P-Ci5 scatters, the total range of the recoil proton may be unrelated to the proton energy. In making a polari- zation measurement, only ne events in which a P-Cyo scatter occurs are used; hence, the range measurement is unreliable. fh order to reconstruct the kinematics with confidence, we must show that only no's make up the event sample, i.e., that the trigger is very clean. in that case, the 1 mass can be assumed; and even without the range measurement, e and 85 completely determine the production kinematics. | One can show that the n° trigger is pure to > 98% by selecting recoil protons with no p-C, inelasticity and using their over-determined kinematics, as described in Appendices 7.12 and 7,13, Since the p-C. 5 interaction has nothing to do with the primary interaction, the clean trigger results obviously must hold for the events used in the determination of the polarization vaiues, After geometrically reducing the raw data in steps (1) through (6) to obtain the measured variables of Table I, the computer program began to calculate the derived variables of Table [. 26 "T-SL"°L Oansty 99g .a.d (uu) L sev oweg "Z-TT'L ANSty oag ASW VT ~ %3 F BLO oO wri + 4 "Z- ‘T-8T°L, SOanstg oeg A®W Gp ¥ Aqreotdéy, uoTNjposery d, uu dy Q@ = 8 u dda * wi Surumsse ‘Cu) 1% 6 6 Sursn soryeut ~ouly woTjonpoud o- WoL dd dq (uu) L+Tfo0e2) - 5, *1011808 rove Uoqred UL oduey "XOLIOA ones lg 0} [elszoyeur {le ysnoiy] uoTyejer AS1ous -adued SoyerssyUL reyrduroo out ‘oare} uesoxrpAy Jo sixe Je J, UPA surqreig d “TL pue xy se oureg *y sv ouresg u u gq & SsuULWUINSse pue * 9 ‘ @ Sursn soryeur -9UTY UoTIONPOId of WoL poATIOd MOP TY WiTayib *SOTIwUL -oury Ur We Suruinsse JO SSOU{D9IIOD SISAL Lt *ATOATIOSdSaA SoTsuv UOT} -onpoud ot qeT pue FD ol 5-0 *1eyyeos Clg roye uojord jo ABieu_q "AWOTSOUL 10}VoOs "reyVeoS ola ig arojeq isn uojoid Tfodea jo ASTOUA "ott jo eptsue uotjonpoid FD °u0}04d Trooea Jo Asrouq “-uojoyd wiveq jo As.rouy Ssquoserderxy y SOTIRIABA, poanrod (7) k, To. 9% are computed using 8» eo and assuming the 7° mass as described above. (8) T.. » “ae energy of the recoil proton just before p- i scatter,is calculated (see Figure 3.3). Cre 9) aT_=T @) at,=T, m f PR) is the energy of the proton after the scatter - (Recoil + Ty Ro )) is determined, where (see Figure 3.4). aT, is the inelasticity of the p-Cy5 scatter, (10) TAR)» the proton energy as determined from its range, is obtained, (11) , are calculated from Pe T, R,) (see k ) R.? or R P p Appendix 7.12). (12) ag = (6 - @ ) is formed (see Appendix 7.13). Tt T p _Note: The quantities of (11) and (12) were used in the context of Appendices 7.12 and 7,13 only. Their usefulness was severely limited when they were calculated for the events used in the polarization determination, This was because of the inelasticity in many of the p-C, 9 interactions of those events. (13) All the above information (i)-(12) was punched by the computer, in code, on a single IBM card, XOLIOA SULIOWeOS ae eu} arojed isnf suoioszd J jo ASxeue opeuTy ouq ‘ qd. UE UOTIRGLLISIG e°s aansLT AOW 'YBLIVOS “O-d SYOITA LSNP NOLOYd JO AONANA G12 OSS GOS 002 GL OSI Sdl OO! . GL OG 85 ~ + OOl a - 002 a J OO€ Eo | -+| 00% VIVO YSLLVOS SALA 1dAOO az dl 4 OOS HILLVOS ~9-d adosad isnr . NOLOUd JO ASYSNA NI NOLLNGIYLSIO a + 009 INSWIYSdXxS NOLLYZINV10d of | | { I L { I ! | J OOL INOD SL 29 140 rT T T T —T T — T aw? POLARIZATION EXPERIMENT 120 + ; 4 DISTRIBUTION IN ATp 100 + - CROSS SECTION DATA WITH 5° 4 . CUTOFF IN P-C,, SCATTER ; <k) #1350 no 80 + , . a ke = 3 os) 60 + t a : ij 4 i 20+ | 4 | 1 fe) [— ee eee a 1 L i L L L L -50 ~40 -30 ~20 -10 re) ite) 20 30 40 50 70 T T T T T t T T T w® POLARIZATION EXPERIMENT 60 + 4 DISTRIBUTION IN ATp 50 F CROSS SECTION DATA WITH 5° 4 CUTOFF IN P-C,, SCATTER <k) = HOO nn 40+ 4 kK Zz an) 8 30 | J 20 F 4 10'r 4 fe) 1 1 lL -50 10 20 30 40 50 140 T : T T T T T T i T m° POLARIZATION EXPERIMENT 120 & 5 : DISTRIBUTION IN ATp 100 - I CROSS SECTION DATA WITH 5° 4 \ CUTOFF IN P-C, SCATTER 1 <k) = 850 no BoF 4 5 5 .o) I oO 60 7 i 1 . [ 40 + | ! i 20 + ' i ob eens eee eT L i vl 4 -50 -40 -30 -20 -i0 re) . 10 20 30 40 50 igure 3.4 AD, curves for Gata selected to minimize inelasticity, Note fhe inale dtisndiy tn 2 3 y : ; ae NOve NOW IMeiasticity increases as (k) increases. This is due hig finition see text). 3G We have, in Tables Iand 1, and in the above steps one through thirteen, enumerated briefly the reduction of 7 IBM cards per event to one card per event. This card contained all the necessary information for the final determination of the polarization. 3.3 Calculation of the Polarization A second computer program was written to compute the polarization from the information supplied on the cards mentioned above (one card per event). This program had two major sections: 1. This part of the program assembled all the relevant | information, calculated the polarization values for specified bins of k and o* using the maximum likelihood method. It then calculated errors on the polarization from the same maximum - likelihood method, and wrote out all necessary information, The maximum likelihood theorem can be stated as follows. (42)(43) Let f[ (x, » Xqp eee, Xi) 93 a] be a normalized probability distribution of known analytical form for random events that can be described by m random variables and an unknown parameter a, Let successive samples 5. (k = 1, 2, 3...) be taken, each sample containing n events described by (X,, X5, e+e, X_), where j=1, n. Then if there exists any as a / mj estimate a* of the parameter a from the data sample 8, such k ~ no. that the likelihood function, defined as L{n, k, a) = TfL (,, Xo, cee Ky) al, satisfies the maximum condition | (= in L@, k, a], 24x 79, ($.3-1) Si then the estimate a* is unique and is the most probable value that can be obtained from a measured sample, (x;; Xo, ++ .) Ky) 9p j= 1; n, | _ For n=, the likelihood function approaches a gaussian, as can be shown using the central limit theorem. In that case, its variance is estimated using pe (3,3-2) 2 da ={-[y ML, & al, _ ae 8a in this experiment, the gaussian approximation was always a good one (see Figure 3.5). | _ Cramer, in proving the maximum likelihood theorem, (14) shows that in the limit of large n, a* approaches the true physical value of the parameter a, with no other method of estimation more accurate, In this experiment, the likelihood function is, n LP) = Ilo fT, 94, aT JECT, ; ; \P cos «.)] int, ° Ps P 1 Bs ae ! {4 ' 6 ” aT» 3) UA» 6 o AT. for the n events of a particular (k, a*) bin. ms is the unpolarized cross section; E is the detection eiZiciency. Both are not functions of P (£ is an even function of p,)e Hence, equations 3.3-1 and 3.3-2 imply that an equivalent likelihood function is L®)= 7 C04 AC, ' T )Pcoso.)]. 3.3-3 oy ¢ By A ») 4) J ( ) aan i a T T qT 45} 40+ LIKELIHOOD FUNCTION L(P) vs. P FOR K= 750 MeV 8,* = 60° CMS 35 =I [1+A(6, 7) cos $P] = L(P) t ~-- = GAUSSIAN WITH MEAN 3.0 + AND SIGMA BELOW MEAN = +.66 255 SIGMA = 38 liO EVENTS 2.0 + ; LS 4 LO + 05+ 4 4. it =1,0 -0.5 0 0.5 0 P T q t 2.0 - — LIKELIHOOD FUNCTION L(P) vs. P 4 FOR K= 1050 MeV 8,* = 60° CMS “ ——~=T/l+A(@.,T.)c iP) =L(P 1 [I+ A(6;,T;) cos @;P] = LCP) “——~ = GAUSSIAN WITH MEAN 1S b AND SIGMA BELOW 4 MEAN = +,07 SIGMA = IO 960 EVENTS LO F 4 0.5 + ; @} i 4 i" “1.0 -0.5 0 0.5 1.0 ‘ P igure.3.5 Typical likelihood functions 33 Reference 18 gives some valuable hints for using 3.3-3. They reduce the computer time used to calculate the polarization and its error, 2, The second part of the program supplies the analyzing power, A(T. , 8 ; aT), for each event. Appendix 7.11-2 indicates how the anal¥zing power was constructed for each event. 4. RESULTS This experiment was originally proposed to investigate the kinematic region of k = 750 to 1250 MeV, oe = 60°, Since the time of the proposal, additional experiments (3) have been completed. These experiments have covered the region below 850 MeV rather well, Hence, a shift toward higher energy has been made, Measurements with reasonable errors were made for k between 850 MeV and 1350 MeV and oe = 60°, In addition, a check point at 756 MeV was taken, with a somewhat larger error; it wag taken for consistency only. (Figure 4.1 shows _ the k distribution of the events used in the polarization determination.) An additional point was also obtained at, 1450 MeV. Here again the error is larger; this point is thus presented in the spirit that some information is better than none. The data are presented in Figure 4,2 and Table TL, Even though the statistics are not good, it turned out that dividing our wide angular acceptance of 60° = 10° (see Figure 4.3) into two bins at ox = 55°, and 65°+5°, revealed a striking angular variation of the polarization, for the angles covered. This variation is caused by the presence of a large number of resonant states in the region 756 < k < 1450 MeV. Figure 4.4 and Tabie IV display the more finely binned data, Some vis) resulting from oO} comparison. In the smali region of overlap, the agreement between an experiment at the Stanford Mark DT linac are shown ior this experiment and the Stanford data is good. The strong angular gradient of the polarization (indications of which had been seen at lower energies in reference 15) appear to be present over the entire energy region of this experiment. *UOLS9I STU] UL poUTe}qo e190 Sieq TOLIe AaTfews sous = “arey] pojoedxe a4oA SOnNj[VA UOTIEZTIeIod [LUIS osnvdsd UOTSII Y [exjUsO olf] UL Uoye] SVM eTEp jo JuNOWe aSsiey Y “*SyuoAe poqdooor Ayreury jo ‘y “umyuotour uoJoUd Surulosut UL UCTINqIAISTq ASW *Y Glbl OSE! SzZ2l Oo} GLE oss GZZ 009 GLY OSE S22, + 001 -| 002 9 -+ 00¢ | + 00% VIVE MILIVIS JLIIdNOD pS . ~+ 00S | 4 NI NOLLN@IMLSIC L | + 009 LINSWINSdX3S NOLLVZINV 10d oA | { 1 ! it i i J i OO2 SLNAOD 36 “gqU9AD IOAO O8VIOAG poTYSIAM WOT] poupUizojop Sv UG JO TOUS = {> ‘UIG JO LeyUNO TwoTajowuIcay = ¢ >) acme v8 °- 09 G*6S OSrT GSErl 8t° i aa 09 0°6S OSéT evel st’ g*- 09 G°6S OGert OVE - T°’ g0° «69 1°64 oOSTT GYIT i g0° 09 8 °6S OSOT TSOT vt’ 20° 09 $09 0&6 GS6 Ze" er" 09 G°Z9 ogg 598 8g" 6h" 09 G89 OSh GOL ave d Cee) 8) Gt) (a) ASI OGE= 4V ‘OTF 409 IOS San{VA UOTTeZLIelOg MW Wiavi 37 OSPl WO UE (OT + 929 ye eyep UoTyeZzliejog ¢°h eInstq (AS) ¥ ose! oszl OSII oso! OS6 OS8 OSL t I L 7 bo b—o-H O9~e NOLO 4 xy vv NOLLOSYIG NI NOLLWZINV10d JAILISOd NOLVZI8NV10d NOLOYd WO93Y d tot =— d +A b——S —— Ol- Od Ol 38 ep ean3tEy ZL (94d) ‘x @ G22 ooL $79 oS9 G29 O09 GZS O6G G2S OOS Sub { 1 { | I { | po ] O - -| 002 . 4 oop. : ~ +1 009 ob + 008 VIVO YALIVOS JLATdWOO - | | -| 0001 | | <"@ NI NOILLNEIMLSIG - -+ OOd! | LNAWINSdXa NOLLVZINV 10d o% wd. ] ! } Leese cal ! 4 | | oleh} SLINA AMVELIGYY 39 Hi “"N ng "SUDAN IOAO OSVAIBAV POJYSTOM WOT] poulWMss}ep SB UTq Jo To}JUID ‘UG JO FoJUSO [eoTAjoWICNyH = ¢ ) LG" 80 °- G9 S‘T9 OSST Lpet gt ° 10 °- 99 ATO na! GPZT qt’ v1" G9 0°z9 OSTT — SéIt i Ze" Go G°Z9 OSOT ZSOT gt" GT" ey 0°E9 096 ZG6 gz" Lg" gg 1°89 098 68 ep’ Oht- gg °LG OShT Pept 03" OL*- Gg ZG osst CPST LT* gg *- fe €°LS eas LYST gq° 70 '-: GG ss LG ost Crit v1" 9% gg Lag gol osor Ta" Li '- gg. of 29 096 =—ti(<“‘ié‘;é‘«s SG ave a (48) (48) CH) (4) i ; ; A®W 09 F=3V me F=y46V OF SONTVA UoTEZLAIVoOg Al HAGVL 40 WO UL 0G F (G9 pue (Gg ye vIEp UOTeZTAKJog Pp omNST A VLVd GYOINVLS G9~0' GSwe LNFWIYNSdxXS SIHL o6G9 ~0'.GG ex NOLOUd 4 x y - NOWOSAYIG NI NOILVZIdv 710d AILISOd NOILVZINV10d NOLOYd HO33SY d+ ol -2— d+ A (AS) ¥ OSGI OGEI OGdI OGII _ OSOl OS6 0S8 OGL | i q 1 T t i i K a L = - T i af. a _ + 1 = 4 i x % \ 7 = = A + ® _ L LL é “+ a L 1 Of Ol- 0 Ol The errors which are shown are purely statistical. Systematic errors originating from obvious sources such as - analyzing power inaccuracies (see Appendix 7.11-2) or shifts in relevant Kinematic quantities, e.¢., sty » have been investigated. The polarization values were shifted only slightly in each case. In all cases except the analyzing power test,the amount of the polari- zation shift was less than 15% of the quoted error bar. The analyzing power test yielded polarization shifts of less than 30% of the quoted error bar, These tests of the sensitivity of the polari- zation to a systematic high or low shift in the above-mentioned quantities gives an upper limit of the possible deviation in the polarization. The probability that the measurements of any one of these quantities are ali off in one direction is negligible. 42 5, DISCUSSION As one moves to higher energies in 7 photoproduction, a) dQ “c.m,.’? which becomes more and more difficult to explain in terms of the differential cross section, ( develops a characteristic isobars alone. This characteristic is the peaking of the differential cross section at small angles, the peak moving to smaller angles as energy increases, Even at photon energies as low as 1175 MeV, a peak exists at 6° ~ 40° which requires major non-isobaric contributions to the amplitude if one also includes the polarization data from this experiment in the fit. This fact has been noted in the (7) vector exchange in the yp data fitting process. This exchange past’ “, and so various attempts have been made to include i-channel possesses the desired forward peaking to a greater or lesser degree depending on the particular way it is introduced,i.e., as an ele- mentary or Regge-ized exchange. (This distinction is discussed in Section 6.) in recent times some success has been obtained in fitting nN scattering with Regge-ized vector meson exchange plus isobars (i was made here to include a Regge wo exchange (the 0° and 0° at total CM. energies as low as 1900 MeV. 8) Hence, the attempt mesons have the correct quantum numbers to be exchanged; however, smali couplings suppress their contribution as explained in Section 6 ) in the analysis of data with CM energies around 1900 MeV, and even lower. The following approach was used. | Below k ~ 1500 MeV, the isobaric states are the major Oo - : part of the 1m production amplitude. Hence we started froma (1), (2), (4) primarily the form developed by R. L. Walker“), Though probably basically isobaric model of photoproduction , using 43 in a non-unique way, this model is very successful in fitting all existing . data below k = 900 MeV, including recoil proton polarization data, and ' polarized photon data. Since it fits all yN reactions except yn ~ nn (where no data exist), a Separation of isotopic spin amplitudes is obtained. Hence a particularly good idea of the various isobaric conditions can be gained. Even at lower energies, the isobars do not make up the entire photoproduction amplitude. In i photoproduction, the t-channel n= exchange is rather important in the forward direction. Also, the Born terms and other small additions in the low-lying partial waves are necessary to describe the non-resonant background; these must be included to obtain good fits. I refer the reader to Reference 4 for information on the details of this procedure. One point must be - mentioned however: the small amounts of low-lying partial waves, i.¢., &4=0, 1, 2, which are added, should have a smooth energy dependence for credibility. This procedure also introduces a certain ambiguity in the result. For our fitting program, we use Walker's model 4) in the following way: 1. The isobars are put in as Breit-Wigner forms in the s-channel, exactly as in Reference 4. (See also Appendix 7. 15-2.) 2. We include the electric Born approximation, i.e., the s and u channel nucleon poles, without anomalous magnetic coupling. In addition we extend this model as follows to obtain the fits above 850 MeV incident photon energy: 3. We include the fourth resonance wre (1924) in a way con- sistent with results from t + ohotoproduction 4 8) . (See Section 6. ) 44 4, We add the exchange of the w°- trajectory in the t-channel, however, with a modified energy . dependence as explained in Section 6. (Also see Appendix 7.15-3. ) 5... Ina way which produced good fits to the data at these higher energies, we smoothly extend the low- lying partial wave additions to 1500 MeV. (See Figure 5.1.) The results of our fitting procedure according to this model are displayed in Figures 5.2 through 5.4, and Table V. (ub) 0.5 T T T T T T T 7 ic AO+ HELICITY ELEMENTS T T T T T T T T Ait, Blt HELICITY ELEMENTS 4 o---—----— = — 4 — Bl+ (iM) \ 4 01 Bi+ (RE) 4 4 -0.2 4 LL | “0.3 + — Alt (RE) 4 pam 4 “0.4 - 4 Te me ne ~iM j “I (ub)2 ost "I Ale HELICITY ELEMENTS A2-, B2- HELICITY L. 4 0.4 ELEMENTS “———B2- (RE) L 4 03 4 4 Oat 4 4 Out . ; A2~ (RE) , J 7 oF we a 7 ms . et Ba IM) J. i lL rn 1. A. L L -O. 1 L L ~ _— L L. 4 1 800 1000 1200 1400 1600 800 1000 1200 1400 k, (MeV) k, (MeV) U 1 i} qT q Y qT t O3F B2+, A3- HELICITY ELEMENTS 1 0.24 4 B2+ (RE) Ol- i * 4 0 na 82+ (IM) 4 A3~ (RE) -O1 - | -0.2- ; 4 l (ub)? O35 F 7 B3-, B3+ HELICITY ELEMENTS 02+ a Ol F 4 83+ (RE) of Te ee en B= (IMI -O1- B= (REM -0.2 bm | -0.3 i i \ \ 1 L L 800 1 1000 1200 k, (MeV) i400 1600 Figure 5.1 Low-lying partial waves in helicity notation (cf reference 4), Smoothness in energy of these fitted helicity elements is demanded by the model, 1600 5.0 + — ; _ | i a! i a 4.0 - r mm [ef er fh ¢ mY an B30 | 7 \ a > \ 1 By 7 1 * 7 TT 5 Aeteeee HN Ss * %~ 2.0 af | | PTT] \ [~9 = WARD '66 UCLA | © = WORLOCK ‘60 CALTECHTC] Ke) 7 o = DE STAEBLER '65 STANFORD] i a = STEIN '58 CORNELL TT 7 6 = VETTE 'S8 CALTECH TO 4 = BELLETTINI '66 FRASCATI7 Y > = BERKELMAN '6O CORNELL. {J re) i ae 1. \ j 1 1 4. L i (6) 30 60 90 120 150 CROSS SECTION 7r°k = 800 CM ANGLE @ in DEGREES 180 46 CROSS SECTION a°k = 1175 x = HATCH '66 CALTECH + » = TALMAN '63 CALTECH + «= DIEBOLD '63 CALTECH + 2.0 nee & STATIN wy S i \ 2 i ; & yA / \ foe] | = 10 f it 8 RLY | / i ft f ik L 5 10) o 30 60 90 120° 150 CM ANGLE @ in DEGREES CROSS SECTION 7°k = 1400 “ AA o= HAMBURG ‘66 (9) 7] + | x= HATCH '66 CALTECH | 20h-—+-+-4 ix /+\ I & 1.5 i 7 iv S oar + | i = / \ 2 1.0 | \ | / \ / \ 5 ~ fe) _ i . 0 30 60 90 120 150 180 CM ANGLE @ in DEGREES Figure 5.2 Cross section fits at various energies. 180 47 P(@) POLARIZATION 7° k= 850 4 POLARIZATION 2° k= 925 1.0 . = 0.5 Wa tT e lA N\ 1 1 x Z x ea x 5 Qa L ma Lt |. | 4 | i ry 0.5 : ' ¢ = LUNDQUIST '66 STANFORD | °* vencuccin "ee ER ASCATI ] ma EXPERIMENT 4 a = LUNDQUIST ‘66 STANFORD (950 MeV) 4 os eo = LUNDQUIST '66 STANFORD (900 MeV) 4 LEE PTTL tT Ey -1,0 PS CU CS CE US HY VON 30 60 90 120 150 180 fe} 30 60 90 120 150 {80 CM ANGLE @ in DEGREES CM ANGLE @ in DEGREES (a) (b) 1.0 - T qT , qT LU Uj UJ ' y* P= 779+ P 1 i RECOIL PROTON POLARIZATION 7 j POSITIVE POLARIZATION IN DIRECTION L. AA 4 BE kx Pproron | @~ 60° CMS H KH “1.0 Nl 1 n i . L 1 | | 750 - 850 950 1050 1150 1250 1350 1450 k (Mev) (c) Figure 5.3 Polarization fits as a function of (a), (b) angle, (c) energy. oolz OO6I "0% PU’ EL SeodUerTOJoa Jo vyep Bursn ACG gf 7e SHI} UOTJIES Sso1o Aq pSUlTUIAejop ST [wulymy °yY Jo uCTIOUNT ve Se yUR}SUOD BuT{Anoo m b°g OINSt (ASI) * 0021 OOSI O0O¢! OOll 4 AO. I | qT I I I J J ‘SLIad NOILOSS SSOYD HONOY AG GSENINYSLAG ‘(S0NLIIdNVY © OL SAILISNSSNI YSHLVY) SNO1V 09 iv SLld NOILVZINV 10d AG GSANINWYSALAG ‘SLI4 NOILOSS SSOYD GNV NOILVZIYV 10d HLOG AG GANINYSL3G NOILONAA SV FNL o” 042139934 I { J | ! J | | s‘0 Ss‘! 49 0S¢°0 ose°o 098°0 0S€"O ogs"0 ogs"0 0S§"0 0GE°0 -O9T"O 09T"O. ‘g 09T'0- "g GeP'o Z 00T‘0- ‘0 09%°0 Z 798°0 % Gg6°0 % LLT'O T LLT'O T Sh'e- T pIP'T % | Cay (@-GI°L XIpuoddy 90s) s1ojouvieg soueuosey Ah WTaVL OLT°O POT’O VEto Ost’o ost’o cOt’o c0T*O 00¢°0 OZT°0 OZT°0 be6°T oL9°T 6G9'T T9S°T 61ST 6IG°T 61g°T The TE 966°T 9E0'T +8a -¢d +ed +0V “TV Ta TV queWAaT AVLOITEH 50 6. CONCLUSIONS In trying to arrive at a unified picture of n° photoproduction, we rely on the information presently available. This consists of cross section, recoil proton polarization, and polarized photon data, which we can roughly divide into three regions: (a) Data originating from k <1 BeV. These data, which we will cail low energy data, can be found conveniently catalogued, in Reference 3. In this region the isobars are completely dominant. (b) Data from 1<k< 2 BeV. Some of the data which give information on this intermediate region can also be found in (19) _. Reference 3. The rest of the existing data are from Hamburg’ ’, and cra?) and this experiment. In this region, the forward peaking of the cross section is seen to emerge at the lower energies, finally becoming the dominant feature of the cross section at ~ 2 BeV. Both isobars and t-channel exchange seem to be needed in this energy region, (c) Data from k> 2 BeV. This high energy region has only been lightly explored to date. The extant data are cross section measurements from Hamburg and CEA, These data seem to indicate that Regge poles in the t-channel may dominate the cross sectioat®, From the above information, our data fits as described in the previous section, and Appendix 7.15, we arrive at the following conclusions, which appeay, as of this date, to yield the most consistent explanation of the r photoproduction mechanism, 51 1. The low energy region is essentially understood on the _ basis of a modified isobaric model as in Reference 4. 2. Including the "fourth resonance", we(1924) 0) improves the low energy polarization fits and explains the strong angular and energy dependence of the polarization of the recoil proton up to 1500 MeV, The amount of the N*(1924) required was found, after the completion of our fitting, to be consistent with the mn data N* (1924) . requirements, Ecklund, (18) in making a Moravcsik type fit to. r data at k = 1264 MeV found the coefficient involving the fourth resonance (his C (8)) to have the value, C (8) = -.474 + 1132. Using isospin conservation on the fourth resonance decay (see Appendix 7,15-2), we find that our n° fit implies a 7 coefficient . c! (g) = -.311 . The errors on c? (2) are difficult to estimate; however, they are probably on the order of the C (8) error, or worse, considering the relative precision of the data used in the two fits. 3. An isobaric type model alone, including a non-resonant background, cannot give good fits for energies above 1200 MeV. Hence, we must look to t-channel vector meson exchange. The only exchanges of known particles vossible in 1 photoproduction are w? and 0° and 0° vector meson exchanges. However, the ratio fe) . . Of p TTY coupling to wry coupling is 52 while that of »NN electric coupling to wNN electric coupling ig?) given by (see Appendix 7.15-2) Fy ONN Fw NN 0D Hence the overall ratio is ~ i/? making the w exchange dominant. The » meson exchange contributes even less,than the 0. 4, An elementary w-exchange, even including some ' attempt at absorptive corrections, gives the wrong angular dependence as compared to the data. The peaking due to elementary exchange occurs at too large an angle (see Figure 6.1), _5.. Good fits can be obtained through the inclusion of Regge- ized w° exchange (see Appendix 7.15-3) with a modified energy dependence below k ~ 2 BeV (see Figure 5.4). The energy dependence associated with the single Regge pole approximation,i. e., ee (t) ~ 520 (t) - 1) (where s is the square of the total CM energy, SsS- @ t- the four-momentum transfer) should not be expected to hold in the intermediate region. This is caused by the relatively small value of s, and by the possible presence of further trajectories associated with presently unidentified particles able to contribute to n° photo- production, These trajectories would probably intersect the Re a (t) axis at a(0) <= 0. As an example, consider such a trajectory with a, (0) ~w-.5. We see with s=.9+ 1.8 Kap? at kx 1500 MeV, and ta 0, . o(@) ARBITRARY UNITS w°-EXCHANGE COMPARISON k=1350 125 T ene ee eee r es — TT a a REGGEIZED w°- EXCHANGE — p~ =---- ELEMENTARY w°-EXCHANGE WITH s AND p ~ = PARTIAL WAVES ABSORBED OUT COMPLETELY — pee ELEMENTARY w°-EXCHANGE (NO ABSORPTION) — fii K “\ / \ 74 \ aN ; i ‘\ \N | / / \ _h N {il \ | aT AV Pe 50 i$ \ Lt i/ \ \ | | / \ n ! / \ \ \ \. / os I OCP EE 7 Li f \ iN A iI / \ \ Va iy \ J+ ~ = we L \ L 0 Li NY O [5 30 45 60 75 50 53 CM ANGLE @ in DEGREES Figure 6.1 54 . X Amplitude . ‘wy Amplitude ~ 30% . More than one such trajectory may exist; we can easily imagine, then, a 30% to 60% modification of the w-pole energy dependence around 1500 MeV. As one moves to higher energies, these complications disappear. The trajectory with the largest intercept on the Re «a (0) axis, associated with the w-meson, will assert its predominance. However, notwithstanding the necessity of modifying the w-exchange energy dependence, its inclusion at all energies above ~ 1200 MeV appears to be necessary to obtain good fits to the angular distributions, 6. In the high energy region, where w exchange is expected to dominate, good fits can be made to the somewhat incomplete data on the basis of w dominance. The firmest inference to be drawn from the above, however, seems to be the following: Our fit, yielding the features described in (1) through (6), affords a somewhat unified view of the -° photo- production process. However, careful investigations of both the cross section and the polarization of the recoil proton for 1 photo-. production will be needed before a quantitatively reliable model can be worked out. 55 7. APPENDIX | 71 ne Detection The apparatus used in this experiment was similar to that used in a recent experiment on the photoproduction of n mesons. (21) The only important differences were in the range and scattering chamber, and in the associated optics. Here, we will concentrate on the features which are new to this experiment. In order to obtain a clean n° trigger, both photons of the nm were detected. The detection devices (see Figure 7.1-1) were arranged in two symmetrically placed arms for reasons touched _ upon in Section 2,2 and Appendix 7.13, Each arm had essentially three elements: 1, Two veto scintillation counters in coincidence which disallowed charged particles with an efficiency of 99%. The efficiency was found rate-dependent; however, the rates in these counters remained low enough so that the high efficiency was maintained. (See Appendix 7.4 for details of counter construction. ) 2. Five overlapping scintillation counters giving nine angular bins. A sheet of lead, two radiation lengths thick, was placed in front of this hodoscope, converting the incoming decay photons with about 80% efficiency. These counters located the photon shower to about + 1° in the laboratory. 38. A lead-lucite Cerenkov counter® 1) which induced the decay photons, typically of energies 200-400 MeV, to shower sizably. This - supplied an additional bias in the trigger favoring photons over 56 FIVE OVERLAPPING SCINTILLATOR HODOSCOPE LEAD-LUCITE TARGET SHOWER COUNTERS PRODUCTION A PLANE A PION CALIBRATION COUNTERS VETO COUNTERS SIDE VIEW 6-FINGER LEAD-LUCITE 2X9 LEAD SHOWER COUNTER CONVERTER Re Pe se] Se Say $ Re ceashes ny Se es ee — siatateteies 5 S ss free COUNTERS PION CALIBRATION COUNTERS FIVE OVERLAPPING SCINTILLATOR HODOSCOPE (9 ANGULAR BINS) | TOP VIEW Figure 7,1-1 y-systems of m° side of the experiment. 57 *keoop WU oi UlOTy SABI-A Ot " jo UOTIV[9LAIOI ASUS 9G} 0} onp St STU Z, °(q) pue (ev) poppe . Rimopues ysnf{ suo yr *o't ‘Spuno73 yeorystyeys Ajpoand Uo payoedxe Uey} SSeT ST (0) WOTFNGTAASTp JO YIPIA 94} yey} dJON “Saseaoys peppe (9) ‘Saemoys Tenpratpur (q) ‘(e) SuOTINGTxSTp 1eUNCA “AaMOCYsS oon -peoy- Z-L eh omer (2) 2+! LHOISH 3S1Nd Osi ovl o¢l Oz! ol ool 06 os OL og os ov o¢ 02 ol fe) <a y T T T T T T T T T T T T i) L + 02 7 4 OF - 40 Q co) E 4 - + 08 a ose = «> yaLivos 79-4 NI 4401N0 r . eS HLIM WIV NOILISS SSOYD 4] 001 2+1 LHOISH 3SiNd Ni NOILNEIYLSId ot INSWINSdX3S NOWULVZINV10d o% i 4 1 i k 1 4 L 3 i i L i Ovi (q) | (2) 2 LHOISH 3S Nd | LHOIGH 39 7Nd oor 06 og OL fo) os O¢ of 02 al ° fore] ° fo) =o i T T 7 7 a . | 79 3 5 4 og co 2 4 . r jo - +4 08 ose =m) ose = <4) usiivos "9-4 Nb 440LN9 : y3Ltvos )-d NI 45OLND r 2G HIM VEO NOILO3S SSO 7 Oot r oS HLIM Vivd NOILOaS SSOND 4 001 i @ LHOISH 3SWNd NI NOILNGIYLSIG 02! | LHOISH 3SWNd Ni NOLLAGIYLSIO oz! INSWINSdXS NOLLVZIEV 10d of . : INSWIYSdX3 NOLLVZINV10d o# i a 1 i L L 4 a Ov! L L n 4 4 1 n t 4 O¢t 4 SLNNOD 58 charged particles. The pulse heights from the Cerenkov counters were proportional to the energy of the initiating y, and were much larger on the average than charged-particle pulse heights. (A bias was set on the shower counters to exclude .5 minimum pulse heights. ) _ However, the fast logic ne trigger was so pure that the additional information these pulse heights offered was not needed. (See Figure 7,1-2 for typical pulse height distribution. ) The noe side signature consisted of no pulse from the vetoes, a pulse from the hodoscopes and lead-lucite counters, in coincidence from both arms. All necessary information such as pulse heights from the Cerenkov counters and signals from the relevant hodoscope counters . was, digitally displayed, together with the track in the spark chamber, on the picture frame (see Figure 7.2-1). Of course, for the present polarization experiment precise efficiencies were not needed, only certainty of a pure trigger. How- ever, a n° cross section was calculated for check purposes. Also, more ambitious designs were made for the future use of the exposures Oem Te Gey er tie tae oct Fe ween pt, senor, a Dy thr alee Sy paws, eC ety te ee RP my 58 VERTICAL MIRRORS ee TO CAMERA —— PROTON TELESCOPE + Hel HODOSCOPE TOP VIEW H-i, Hp2, R CHAMBERS — TOP VIEW a as TOP MIRRORS FOR H-2 + RANGE FOR H-I Ss tft —. eter} + > i ao + | aaa == 7 PbL-1, PpL-2 HODOSCOPE ting DATE at LiL beL | CHAMBERS BEAN coal PARAMETERS INSIDE HOUSE =| i ——----.-| al LL NS ‘ . olspLay ~ s F2.R — SIDE VIEW SPARK GAPS, p~ PANEL ~ HV, ate, ee SHIELDED RANGE CHAMBER R BACK VIEW AS SEEN FROM CAMERA Figure 7.2-1 The proton detection apparatus, 60 enough, and hence the ionizing power great enough, that a clean proton trigger could be obtained using a bias which did not exclude protons desired. | For the higher energy settings centered around (ap) = 1100 and 1350 MeV, three counters were needed to achieve this goal, (See Table VI ; also see Figure 2.3 for typical pulse height distribution from proton telescope. ) | The system was designed such that the last scintillator, SP-3, defined the solid angle of the proton side of the experiment. The size and placement of SP-3 also insured that no more thana ~ negligible number of useful scatters would leave the sides of the range scattering chamber (see Appendix 7.9). That is, the solid angle defined by SP-3 was safely enclosed by the range and , scattering chamber. The first two chambers were thin-foil chambers used to determine the trajectory of the proton while introducing minimum multiple scattering (see Reference 21). In order not to flood the first chamber with tracks due to low energy particles, a 1/16" piece of lucite was placed at the target to absorb low energy particles. (See Figure 7.2-1 for layout of proton side of experiment. ) The range- scattering, chamber was new to this experiment, and so will be described in some detail. The main elements of this chamber were the sparking modules, and the carbon scattering modules, The sparking modules were independent units each having three thin foils glued to lucite frames as in Figure 7,2-2. The high voltage was applied to the central foil, while the outer foils were (8) enclosed in its perimeter by a lucite frame. The size of this frame | grounded, The carbon modules were made of a carbon slab was identical to that of the sparking module. The faces of the carbon were covered with thin aluminum foil. The foil acted both as a Setup Number (6 55.08° 55.08° 55,08 55,08° (@) 37.52° 34,7° 32.43 41,1 (oyvy/2) 10,85° 8.53 7,00° 11.15° (k) 850 MeV 1100 . MeV 1350 MeV 850 MeV TABLE VI (er) 60° 60 60 65 E° 1171 MeV 1372 MeV 1476 MeV 1171 MeV T_ Bite p i 83 MeV to 173 MeV 130 MeV to 237 MeV 157 MeV to 290 MeV 100 MeV to 224 MeV Number of Counters - in Proton Number Telescope Pictures 2 30 x 10° 3 60 x 10° 3 30 x 10° 3 23 x 10° Final Events — 250. 1470 980 800 Total Cio in Range Scattering Chambers 20 ems/em” . 2 37 gms/cem 2 51 gms/cm 32 ems/em” eB - T9 61-b {ONNOUD OL 03193NNO0) CHHL 100°) 103 WANINT TY wE UW] wf U Solnpour Jequreyo jo STrVjed %-Z"L SANSA aInNdOW NoOsYvd Von fui J wh wh ¥ COHL 100°) hod WANINNTY SSN SYS JINGOW ONINYVdS v4 NOLLISNNOD ‘A'H J sv e——- MBIA FS AIA DOL \ $3903 GSHSIN0d 62 ground plate anda protection for the cover foils of the sparking modules. The outer dimensions of all the modules were the same, ~ only the thicknesses of the carbon modules varied. Since the range- scattering chamber had to have different thickness carbon modules for each kinematical setting, the chamber was designed to be easily changed, The operation was somewhat like stacking cards, with a change-over taking a few hours. There were four kinematical settings altogether. Each setting had a proton energy bite of about 120 MeV. One could have chosen to make the carbon modules of equal thickness for each setting. However, since the proton energy range was 80 to 290 MeV for all settings, and the total number of modules was limited, _ the resolution would have become intolerable, and the efficiency for obtaining useful scatters would have decreased. The solution was to place most of the carbon in front of the first sparking module, except the amount needed to obtain the proton energy bite consistent with the overall acceptance of the apparatus, | This amount of carbon was placed through the range-scattering chamber in modules of varying thickness... We used enough modules to split the bite into the desired small bins of proton energy (24 was always enough). The one pitfall was the possibility that the first carbon piece would become so thick as to badly obscure the scatter vertex position needed for the analysis (see Section 3.2). This was not a problem however, since the vertex was uncertain to at worst + .5 cm through track reconstruction, This was consistent with the average carbon module thickness. . ‘The setting with the lowest mean energy had only i cm of carbon in front while the highest energy setting had 6 cm,in front 63 O02 91 E-Z°}, QANST AT JINGOW YALLVOS vl A Ol 8 9 v cA AINGOW YALLVOS NI NOILNINLSIG LNSWIYadxX4 NOILVZIYV 10d ot i J ij I { j f i j j i j | 00S OOO! OOSG| SLNAOD 64 (see Table VI for chamber configurations), The thicknesses of the rest of the modules were chosen to obtain about 3% resolution in aT, / Ty for elastically scattered protons, Most scatters occurred in the first module (see Figure 7,2-3), 7.3 Optics and Fiducials Since the range-scattering chamber was quite large, it was necessary to use field lenses to allow the camera to see directly into the chamber, These were two plane-convex plastic lenses, each with a focal length of 19 feet. The distortion in the lenses was quite small, being 1/3 mm in 5 cm or 0.6%, The distortion was determined by photographing a grid in the optical system and then measuring the grid points from this picture on our encoding table. A computer program compared the measured grid points and produced the quoted number, Since the lenses were made of machined plastic, the distortions were due mainly to machining irregularities, with a smaller amount of the common aberrations present, (2 2) The distortions were certainly small compared with other measurement errors in the range-scattering chamber. Hence,no corrections were applied, | . Care was taken to align the two lenses so that the camera was at their common focal point, and such that the flat sides of the lenses were opticaliy parallel to the walls of the spark chamber. This was done to insure a direct view into the chamber as mentioned above. One also notes (see Figure 7.3) that the flat sides of the lenses are toward the camera rather than toward the chambers. Theoretically, this configuration greatly reduced the common aberrations, (22) BE. g., spherical aberrations were decreased by almost a factor of four. 65 g7), dant aq M3iA Vay SNA Q7ais ee [ —~— YSEWVHO ONIMSLIVOS - SONVY SN31 OTals ONIAZAUNS Ni G3sn . SOOQSLHOIVULS NOISIOSYd . —— = sn y ¥ es \ Sd tLS WIAA ONIQIOH SWVYSs YSEWVHO LNOY4 SWSLSAS SN31 GNV WIONdI4 oT ; HSV14 ne te ee ne ee re ee ee eee SdIYLS WIDNdIS ONIGIOH SWVYd WANINATY GIdld SLYeVdss 66 In total, including mirrors and lenses, the optical system looked as in Figures 7.1-3 and 7.3. Two 90° stereo views were photographed of each event. A reference fiducial system for the rear two chambers was obiained by mounting a rigid aluminum frame independently of these chambers, On this frame were mounted lucite strips on which crosses were accurately machined; the strips were straddling the chambers, The independent mounting enabled the range-scattering chamber to be moved for change-over without disturbing the fiducials in the slightest (see Appendix 7.6). The front chamber had similar strips straddling it; but here, the mounting was to the chamber itself since this chamber was never moved (see Figure 7.3). | 7.4 The Scintillation Counters The scintillator material used in all counters was Ne 102, All phototubes were RCA 7850's except those on the shower counters, which were RCA 7046's, and those on the 7 counters, which were RCA 6810's, The lead-lucite shower counters are described in detail in References 21 and 31. - | Table Vif gives all relevant information about the counters used in the experiment. As noted in the table,two systems, SP-4, and the 7 counters were used for calibration purposes only. These counters were not in the trigger logic, 7.5 Electronics Figures 75-1 and 7.5-2 show the general layout of the fast logic and readout systems. The fast logic consisted of a two-fold “OT XL'T = 9782 aouepto -UTOO [-A: “gOT X SL°T = OTH-9H jo wing “g0T x Go°l = SH ,-"TH Jo ums JUBADTOY ON X e gol x & xX bd gol g aT Xx oe 9?! eT puooeg 139d oyey suryunog reords y, cOT ON cOT ON cOTF ON ZOT ON ZOT ON ZOT ON ZOL ON [eT royey] “Wd FE9" “UD FE9* "Wd FEO" "Ud HG °S "Wd FE9° "UD Eg" "WD FE9° SSouyoTy L “UD O°GT “utd @°GT "wD E°GT "WD OF "UL Q°ES "WD B°ES "WD FCS epts [eoTVI9 A _*gopotyred posareyo So}OA *T-A 9OUApTO "Wd 7°GZ -UI09 UL apts ot vo pesn UOLTBULULI91Op O[SUB gt OF APTS 4 1 UO pesn *OL-9 pue g-T edoos “WO 79°C -opoy jo S1o}UNOD opts}no *UOT]VULULIO}Ep QTSUe gl IOJ OPIS g 4 UO pesn “oT-9 pue “g-T edoos "UID OFS -Opoy jo SzoeyUNOD ¢g [eajUID ‘sdooseaje} UojOId oyeAqI[Vd 0} "UID OZ pesQ °OLSOT 10sS11} UT ION "ud 9'bZ «=—s-s A ayuNOD odoosojaj, uoJoIg *uld Q°6Z ~~ «=—«- L9uNOD edoosoToJ, uo}OIg "WD Q°TZ tayunoy edoodseTay, uojorg aprg qUOUITIsdxY UL osg Teuo Zl 1oH TA ATaViL y-dS ¢-ds Z-ds I-ds reyunoy *queARTOY JON 68 x p01 I gO XLT = ayer aouapta “Ul0D Z-A puoosg Idg o7ey — Burquno04 yeordé y, _ GOT ON “WD FE9" (L-T°L o4nsty 90s) yoTyy Oy T pot jo sjooys G UIIM podeds.zequr YOTY} WO 7G ° SLAsUTy OONT LAN 9 *r190]UNO0d O JO JUOAF UL P¥ol XZ ZOL ON Terroyeypy “WD $§9° SSoUpory "UID "ud ZI “WD B°PT “UD "GS "ID B°GT «= "UID H"GZ . Opts opts TeoljrsaA =: TeJUOZLAOY (4009) TTA WIAVL *g.10]UNO0D Tdd oyeaqifeo 0} pesn *OLSOT TOSSL1} UL JON *suoqoUud JOd}ep 04 Spts 4 UO pesn szoyuNod IaMOYS son] peo] *sopotyred pasazeyo S30}9A °Z-A QOUapTo -UJOO UT opts Oo” uo pos yUOWTLIOdxY UE Osa nN @ i EEEE rt NI oD St 1 *2-"1dd tidd | "Ze-A IZ-A arezyunoe 9 69 T-S°L Oanst 7 ySa99INL NO!ld 4O4 DIDO1 LSV4 SOINOULIITI LNOGv3y oy SH3SWVHD YYuVdS 7 on (988 @"} HOLvY3N39 (92s ¢7) ° 3WiL Gv3G ya99IeL OL3A ZJINIGIONIOD YILSVA 31Lv9 WV38 zi.4% 5 4 TA-H:2-14d OLA Su31VvOS o8 )-SUaTVIS 4 [uo] [een-ren | [x0 | zin-ViA ponna nanan i | osia | [ asia | | ‘osia | ‘S10 [ osia | [asia | [ -2sia | “9S10 ‘asia | ot’ ' win wo wit ‘wo “wn . wo “wit | wit | WH YaZATYNY Hd oO ree 2-14d. OI-9H 22A {ZA add tds £38 e@d$ tds 2 VAWNVS ; t VAAVS : . 43d09S43721 NOLOUd © 70 MASTER "TRIGGER ; PoL-i PbL-2 [ DELAY | | DELAY fo I ‘ |} Linear Gare | —uinear cate | v Mi [wTesRaToR [iwTecrator | TWO CHANNEL ANALOG - DIGITAL CONVERTER yt MEMORY AND READOUT TRIGGER ERASE LIGHTING AND LIGHTING CAMERA CONTROLS| CONTROL | owe to CAMERA ADVANCE PULSE HEIGHT ELECTRONICS LAMP DRIVERS TERMINATED PATCH PANEL TRIGGER ALL PHOTOTUBE . SIGNALS AVAILABLE ! \ | \ | | | | (USED ONLY DURING COUNTER CALIBRATIONS) LINEAR GATE INTEGRATOR PULSE HEIGHT ANALYZER 256 CHANNELS SYSTEM_FOR. COUNTER CALIBRATION wil wi2 w2) w22 to MASTER to MASTER coinc, COINC. PION CALIBRATION FOR SHOWER COUNTERS HODOSCOPES MEMORY AND LAMP DRIVER CIRCUITS PT HODOSCOPE ELECTRONICS Figure 7,5-2 Readout and calibration systems 71 master coincidence between the 1” side of the experiment and the proton telescope, | '. The pulses coming from all counters used for the logic were brought inio limiters, The outputs of the limiters were clipped and fed into the discriminators. The signals from the discriminators were used in the various coincidence circuits determining the trigger. The coincidence circuits had delay curves with typical widths of about 20 ns. The counting rates combined with such typical delay curve widths gave negligible accidental rates at all levels of the logic, and kept dead time corrections down to a minimum, (See Appendix 7.4 for typical rates. ) ‘The fast logic master coincidence generated a number of slower logic operations: 1. The spark chambers were triggered. 2. The angular information of the hodoscopes was digitized and displayed by means of coded lights, 3. The pulse-height information of the shower counter was digitized and displayed by means of coded lights. also, 4, The fiducials were flashed and general frame illumination was produced. 5. Other pertinent event information was recorded on the film, e.g., event number, ... etc. The picture frame was then advanced, The entire operation took 300 milliseconds, so that we were limited to one frame per synchrotron 72 pulse (one per second). To insure that a second n° signature did not trigger the system in a single synchrotron dump, a veto circuit stopped the master coincidence circuit from triggering again, Corrections due to dead time are presented in Appendix 7.12, 7.6 Method of Surveying The accuracy with which the apparatus was placed in the laboratory was of course critical, Much time was spent in creating a surveying system which placed the spark chamber house to better thanil mm. This was accomplished using a precision straight-edge lined up through the center of the house. Angular measurements could then be made to .5 min, of arc using the precision edge. Distance measurements were made by placing a rider on this straight edge (see Figure 7.3). The laboratory coordinate system was defined by scribed pieces of aluminum. Some were epoxied under the beam line, and others epoxied at known angular increments relative to the beam line, Beam height was defined by similar metal pieces epoxied onto the walls of the laboratory. A transit was used for angular measure- ments; it was kept calibrated using these reference marks, Less care was taken in placing and surveying the n° side of the experiment, Since the kinematics were less sensitive to this information, The transit was placed at the origin of the lab coordinate system as for the proton measurements. Here, however, instead of ‘making measurements good to .5 min. of arc, we restricted our accuracy to + 1°, using the center of the shower counter faces as references. Care was taken that the counters in the two arms of the 3° side were perpendicular to the line of sight of the transit when it _ was placed at the proper angle. 73 The 7 side was moved and reset four times during the experiment, The proton side was untouched except for the range- scattering chamber module changes. ‘Three checks on the proton side during the experiment indicated no movement of the spark chambers and scintillators consistent with measurement precision. 7.7 Spark Chamber Characteristics The knowledge of two characteristics of a spark chamber system is essential: the time needed for the chambers to spark after a proton passes through the chamber, and the efficiency with which such a proton is seen. ‘The delay time of our chambers was measured to be 500 ns when operating in the system, That is, the time from particle detection in the proton telescope to the time of track appearance was 500 ns. This delay time, together with the proton telescope counting rate determines the number of tracks one will see in the chambers per trigger. In this experiment, both were low enough that, almost always, only one track was seen. The one exception was in the highest energy setting where the external y beam was relatively dirty. (Collimation was not as good as in other settings _due to high energy orbit blowup in the synchrotron.) Here, the front chamber showed multiple tracks in some of the pictures, but the selection of the real trigger protons was usually obvious. In Figure 7.7 curves of chamber efficiency versus trigger delay are shown for various sweeping voltages. Since, as stated before, the intrinsic delay of the spark chamber as used in the experiment was 500 ns , we chose a sweeping voltage just below the voltages at which the curve in Figure 7.7 breaks away from 100% efficiency; at 500ns delay, or at about 50 volts, At this "Tt SUTTeqey e8eyjoA ZuIdeeMs OU] UIA PoOAINnSvoUl SPM OAIND yOeY “*saaano ABTep roqureyo yaedg = =L°), DINSTT (9esu NI AV 130) V OOO! . O06 008 OoL 009 00S OOV OO0€ O07 OO] O 74 | T i ] i i I O mele) (%) AONALIS34 dv SAIONIS SOVESAV 75 point, a minimum amount of background tracks, consistent with maximum efficiency, was obtained. One should note that the | range-scattering chamber had two sparks per module, and so the inefficiency governing range information was negligibly small. . One way of shortening the 'memory" of the chambers is to add a quenching agent, such as ethanol, to the gas flowing through the system. Hence, the gas flowing through the chambers consisted of one part helium bubbled through ethanol, and five parts argon. Adding helium to the mixture supposedly increases the efficiency of the chambers, But, in tests we conducted, the efficiency was found to be relatively insensitive to the ratio of helium to argon. In summary, the efficiency of the chambers per gap was > 99%, with one track per picture being the general rule. 7,8 Hydrogen Target A thin-walled hydrogen target (see Figure 7.8) was located, with its cylindrical cup containing the liquid hydrogen, centered at the origin of the laboratory coordinate system. The cup was made of 5 mil mylar. Its dimensions were 20.93 cm long by 3.81 cm in diameter, and it placed 1.47 grams per om” of liquid hydrogen | in the bremsstrahlung beam's path. Care was taken that little material was in the way of both the incoming photon beam and the recoil protons. This was accomplished by means of thin, .005'' mylar windows located appropriately. The decay y-rays from the 7 passed through .035"" aluminum. For the determination of cross ‘sections, a correction had to be applied for photon conversion (see Appendix 7.12). yosre} UasompsY oY, Q°y atNST yvmzo 2H ojus L q 7 - S3HONI 7 TO er 4 Sbpez1-0 tne WS , en dwnd Noisnssid ~ han a . | CO . ww s¢co"o ~ - EF | NN E 1] mi il it 4. es ~ L avan/f lw s 2Nn Li WA A i “av fd YVIAW Hag SSVdA@ LI aaang {| ASQVHX3 @N 9 LSNWHX3 7H V7 One should note that the consumption of liquid hydrogen by the target was about 1 liter per 4 hours. This resulted in a negligible amount of gaseous hydrogen in the target at any time. 7.9 Scanning Bias and Efficiency When making a polarization measurement, one must be certain that no left/right bias is present in the experimental method, or in the handling of the data. Several tests were made to be certain such a bias was not present in this experiment. The first consideration is the purity of events, and, as Appendix 7.13 demonstrates, one is certain that backgrounds in the experiment are negligibly small, being on the order of 2%: we therefore assume that we start with a pure sample of protons from ne photoproduction. The efficiency for seeing a proton scatter to the left or right could be a function of particle position in the spark chamber. The main possible source of trouble here consists of tracks leaving the sides of the chamber. We scanned 6, 600 frames in order to determine the extent of this effect. No events were seen leaving the chamber; this is clearly not an important source of bias. Other possible problems, such as the dependence of sparking efficiency or optical distortion on position were found to be negligible. If the scanning method is not completely efficient, a bias may be introduced by a preferential selection of left or right scattered events due to unbalanced scanners. Hence, a scanning method was designed to achieve as great an efficiency as possible for events which contributed the heaviest weight in the final polarization values, . 78 To achieve the above-stated end of maximal efficiency, the following procedure was used: 1. One of the criteria for event selection was the value of the projected angle of each event, i.e., 6 D projected on the horizontal plane in the laboratory. The limits taken in the scanning process on the projected angle were 3° to 40°, In order to be included in the final polarization determination an event had to be measured on the measuring table to have 85 between 3.5° and 30°, Unless cos Py was appreciably less than 1, the projected angle limits safely included all events desired. The only loss of events comes from scanner inefficiency and small cos Pp (6 projected = tan 1 tan ) b cos p ] ). As we will see in the next section the only region of scanner ” snetficiency was for 6 projected < 5°. But events with 85 < 5° or cos Py << 1 have small effective analyzing | power, A cos Pp . Hence all events in the region of appreciable scanner inefficiency tended to have small effective analyzing power relative to events with 6 projected > 5°. Since the weight of each event in determining the final polarization value is proportional to the square of the effective analyzing power associated with it, the events with 6 projected < 5° had a disproportionately small weight in the analysis. 2. Each event was scanned twice, once each by two different scanners. To be accepted, the event had to satisfy the criteria previously mentioned in Section 3.1, but repeated here for convenience, 79 (1) Each’event must have scatter of 3° or greater in top _ view of chamber. (Horizontal plane which was approximately the photoproduction production plane. ) (2) Event must have track length after scatter long enough - to measure well. (Usually three sparking modules, ) (3) Event must not have significant double scatter. (Smears scatter kinematics badly. ) (4) Event must not leave a nuclear interaction with more than two prongs. (Proton in, proton out.) (5) Event must be correlated in all chambers. (6) Event must be completely contained in the spark chambers. The run number, event number and other pertinent, but brief, information about each good event were marked on supplied forms. These forms were then transferred to punched cards and processed by an IBM 7094 Computer. The computer made a pre-selection of events based on the energy in the second scatter as roughly determined by number of carbon modules in the track after the scatter. The cutoff was placed at 90 MeV. The computer also indicated events agreed upon by two scanners and those thought to be events by only one scanner, These events were checked by a selected group of experienced scanners and the points of contention resolved in each case; the result was a single list of supposedly good events. However, to be sure the criteria were being consistently applied, all the good events were looked at a third _ 80 time by one scanner who was considered the most qualified. Using the above method the following scanning efficiencies were obtained - as calculated from a limited but random subset of the data, Scanning Efficiency For 0 O 6 6 . Projected Angle 3° to 5 5 to 40 Group lof Four Scanners 84,1%+1.7% 98.0%+ 1% Group 2 of Four Scanners 70% + 2.2% 98.6% + .8% The angular bins denoted above are rough in that only a scanning table measurement was used; however, the clear result is that the | only important inefficiency is in spotting events with projected angle ' of less than 5°, and these events add a disproportionately small contribution in the final analysis, as mentioned above. Since the question of bias is such an important consideration, a further test was made. The events missed were split into missed left and right. The efficiency for detecting left and right scatters, el and er, respectively, were found for each group. We then define for each angular bin | el - er a = (asymmetry) = sla or (see next Appendix) for each group of scanners. The results of this test displayed below indicate no asymmetry in scanning. Asymmetry as Function } ° 0 0 of Projected Angle a (3° to 5°) a (5 to 40 ) Group 1 | .054 + .032 .012 + .012 Group 2 038+ .039 .007+ .007 81 To test the projection apparatus, a reversed scan (the film was placed in the projector such that left scatters appeared right and vice-versa) was made for part of the film. Comparison of the events obtained in the reverse scan with those found in the original scan yielded results compatible with the scanning efficiency. Since we have shown above that no scanner asymmetry is present, the null result of the reverse scan test indicated that no bias was caused by the projection equipment. To summarize, the bias introduced in this experiment by scanning procedure seems to be consistent with zero, and certainly is much smaller than the purely statistical errors of the measure- ment. (12) 7.10 Scanning Efficiency and Asymmetry Formulae Consider two independent scans of the data in which Ny events were found in the first scan and No events were found in the second scan. Ny and No should be samples of roughly equiva- lent events, That is, the difficulty of finding any subset of Ny or No in the scan should be about the same; e.g., in our case it is easier by far to pick out 15° scatters than 3° scatters in both sets. In this experiment 3° - 5° scatters and 5° - 30° were considered separately. The efficiencies obtained are quite different, as demonstrated in the previous Appendix, The formulae used in the efficiency determination are as follows. Let ny = the number of events found by scan 1 that were not found by scan 2. Ny = the number of events found by scan 2 that were not found by scan 1, 82 N, = (N, = ny) = (Ny - Ny) is the number of events found by both scans, then, -1 -1 4% (1 + n,/N,) » 69% (1 + n/N.) ; (7.10-1) where e 1 and e 9 are scanning efficiencies of scans 1 and 2 respectively. The rms statistical uncertainty for ¢ 1 is, Ae, = e,( - e,) (1/ny - 1/nyi/? , and similarly for e¢ 9° Considering left and right scattering events separately, we obtain ¢ Ly? é Ly? °RY é Ry’ the scan 1 and 2 efficiencies for detecting left and right scatters. We now define, ST ERO a,= —————. , with i= 1,2. (7.10-2) li. €, +€ L. R, i i a. provides a measure of bias in the scanning procedure of scan 1 and 2, . The error of a, is given by Le ae Sep 2 SL 2 1/2 Aa, = —— [( ) + )] ,ist,2. 1 ER. ey. 1 1 83 Care must be exercised in applying equation (7,16-2), Let us construct a simple example: consider a proton beam with polarization 8, The energy of the beam is such that p-C,5 scatters with eh between 3° and 5°, (angular range J) have average analyzing power Ay = .125, while P-Ci5 scatters from 5° to 30°, (angular range 1) have analyzing power A, =.5 . If a hundred scatters were measured in each angular range, we would find on the average; _NL-NR. 1 P=NDGNR * A or 50-40, 1 _ 3_p _ 70-30 P = i I 100 * 7125 ~° ti 100. *.5 ? assuming 100% detection efficiency. However, let us say that the scatters between 3° and 5° are detected with 50% efficiency, while those in the 5° to 30° bin are detected with 100% efficiency. Grouping the two bins together we obtain (on the average) NA = 25+ 70, NY. = 20+.30 CL CR ny = 25 Dy = 20 so that, using equations (7.10-1, 2), —- _ 4. -1_ = -1_ ez, = (1+ 25/95)" = .79, E, = (1+ 20/50)" = .71 or 84 a non-zero value of a indicating a bias in scanning. Obviously, an error has been made in the above procedure. The problem arises when one considers, as one set, two subsets of events with very different average efficiencies and analyzing powers. If we consider the two angular bins I, and I, separately in the above example, we obtain cy, = (1+ 25/25)" = .5 = ep = (1+ 20/20)" 1 1 = (140/70) 42126, = (1+ 0/30) 1. € Ly 0 or ay = ay = 0, as expected, In the n° polarization experiment, the prime reason for the angular separation of scatters, described in Appendix 7.9, was the above- stated pitfall. 7.11 Analyzing Power 1. As stated in section 2.4, the "analyzing power", A, of equation 2.4-2, is a property of the analyzer, in this case carbon, (9) A brief description will be given here of the general methodology obtained from experiments in double proton-carbon scattering, of these measurements, (see Figure 7.11-1). The first P-Cy5 protons, We assume spin 1/2 spin 0 kinematics even though higher scatter involved monoenergetic, unpolarized 85 ‘IOMOd SuLZATBUS OU} SUTUTIOJap SyusuITLedKa asoT J, *SyUOTULLEdKxa SUILIYVOS UWOdIVd UCjOAd O[qnOp TOF posh SUOTHUTJep TeoTjVUIOUTY [~T][*y eanstq SATII LYVd TIV SNINIVLNOD SNV 1d ONINSLIVOS oe ) SUALNNOD PA NOILWTWLNIOS x NOLOUd: —-_ d . SN319NN y ™. NOgyvo Ja =.4g ON 'V \.NOLOYd WO95Y Y3LIVIS GNOD3ES <O. | NOLOYd WODSY YALIVIS LSYIS SNATIDNAN NOSYV9 NOLOYd LNSGION! Ngee = U v g Uu ANV 1d ONIYSLLIVIS OL IWWYON 86 (11) spin states of carbon can be excited in the p-C... interaction. However, we also assume that the analyzing ower of only one level of carbon is being measured ata time. This is true of most experiments using protons below 300 MeV kinetic energy. As in Section 2.4 the amplitude describing the P-Ci5 interaction can be written as F=f+6 ng, = ° x p, where the o are the Pauli spin matrices. (7.11-1) (11) from the first scatter is. As one can easily show , the polarization of the recoil proton (o ) 7 SA(T,, 8 [f| +g] TT). 7,11-2 » ST) (1.112) Recoil protons from the first scatter, emanating at 6 v’ are then rescattered from carbon and observed at 85 = 9 my With he hy ~il, ny =p x —'. Using equation 2,4-3 we then obtain Tat _ - t op) 8 Bp) A (7.11-3) m5 (84) + on (8s) where + and - refers to sign of f- hy ‘This way, A can be determined except for its sign: A=iVJe. The sign of A is obtained in a different experiment, (23) After the first scatter, ‘high energy protons are slowed by passage 87 through an absorber to kinetic energies of less than 10 MeV. A second scatter is then made from helium. The phase shift analysis of p- He, scattering is known well enough to calculate Ape? and hence obtain the sign Ao: Using the above kinematical definitions, Ag=+ /e. 2. An independent survey of the analyzing power of carbon was made for this experiment by W. McNeely. It was done for incident proton energies of 90 to 300 MeV, scatter angles of 3° to 30°, and for inelasticities up to 50 MeV. The complete account of this investigation can be found in Caltech Internal Report 30, (9) and so only a brief summary will be presented in this thesis. | Since the resolution this experiment obtained for AT» the inelasticity of the P-Ci5 scatter, was about 14 MeV (see Figure 7,11-2) it was decided not to integrate over the entire inelasticity interval accepted, as had been done in the past. (12) (13) Instead, the resolution was folded in, and the analyzing power was defined as follows for each event: 89 at )*/20." [ dE[e pS @ o/AndE)A(T, , 81, E)] f fo] fo) 22 ) dE[e S (d“o/dQdE) J -_ (7.11-4) A(T. ,6', aT_)=- Pp PP -(E-AT p)*/20 . where TD is the proton energy just before scatter, ey is the polar f angle of scatter, aT is the measured inelasticity, and Oo. is the experimental resolution in AT p which varied from 12 MeV in setting 1, (k) = 850 MeV, to 15 MeV in setting 3, (k) = 1350 MeV. COUNTS 88 260 a T : T T 1 ! ! m° POLARIZATION EXPERIMENT 240 4 DISTRIBUTION IN AT, 220 + CENTER———~— 4 COMPLETE SCATTER DATA 200 F- ~_——— SMOOTH CURVE OBTAINED 7 USING KNOW P-C,, CROSS SECTIONS AND RESOLUTION 180 IN AT,, 0, * 14 MeV 7 160 4 Igo F 4 A20 + -35 MeV 30 MeV | CUTOFF CUTOFF 100 + | 7 80 + | 4 60 b 4 40+ | | 4 20 + . | 4 fe) L | L it i L l l I l l -50 -40 -30 -20 -10 re) 10 20 30 40 50 AT», (MeV) Figure 7,11-2 Distribution in AT. For all scatters used in the experiment, the cutoffs at 30 and -35 MeV indicate the points past which events were not accepted. Note that curve skewness is due to the excitation of the inelastic levels of carbon, ANALYZING POWER ANALYZING POWER ANALYZING POWER a | # T 89 = 95 Mev T BD. 6 & & o4 2 2 7 its 0 10 20 30 SCATTERING ANGLE (DEGREES) = 155 MeV 0 10 SCATTERING ANGLE T BD. f - 20 30 COEGREES) = 220 MeV rH Q : - 10 SCATTERING ANGLE 20 30 COEGREES) '. Figure 7,11-3 McNeely\®) fits to analyzing power for elastic scattering, 90 $9°G PUS ASIN SPP) ($3349350) 379NY¥ ONTY31L1V9S oe az or 6 C) z \, a 3 Mtoe 8° J ovr ASW 0¢e = ($334930) BIONY ONITYILIVOS oe oz ot C) 0 V4 o a Sa orl A®W GST = L *STAADT OTJS¥ToUT Jo zaMmod SurzAjeue 0} syy ATIeNOW B3aA0d ONIZAIVNY Y3AO0d INI ZATVNY *(STEAST AST (€$334930} oe oz P-IT'L SINS J1ONV ONT YRILIVIS at tq A®W ELT = €$334930) o€ oz L ZI9ONV ONTYRLLVIS | | At] A | J] —_ 9° ASW S&T = J L BIROd SGNIZATVNV B3AROd SNIZATYNY 91 "g sdUOTOJOI_ Ul peqrrosep weis01d J Iaynduod oy} Sutsn poyepodazezut ‘9 = diy ye qs *SA JomMOd SurzATeuy G-TT°y, oansty CAIW) ADYINZ NOLOUd . CARR) ADYUZN2 NOLOUd ooe O42 Orz Ole ast ost ozt 06 ooe 0L2 Ore O12 ost Ost ra | 06 XC] ° ° Zz z° z > a : < . N\ v ~ y a v - s 2 3° m 4 | 2 8° 8° d ort ~aq ort O€ = 18 ct = 9 Oo Oo CARR? AQYINZI NOLOYS CA3BW) AQYINZ NO1OYNd oo€ 022 Oh 24 O12 0st ost oz 06 ooe 02z Ove ore ost ost O21 06 t) 1) : |__ i ee : - - . : . a . . | > - > cr i a s id z a 2 3° 2 19° nm ” - — a ~ - a 3° 8° 4 - - d ori d orl BaaOd ONIZAIVNY BaaGd SNIZAIVNY ‘J[OS]L OUTJNOI OU} UT posn jou evyep ore Sjutod Vyep 94 I, °G sDuEdeyor jo ouTjNOI uOTYeTOdoyUT oy Aq paynduioo seMod SupZATeue ONSET 9-TL"L oInsty 92 ASW 8&T = L AW EET = Sq L €$334¥930) 39NV ONIYZLIVIS ($334930) 3T9NV ONTYILLYIS oe az al a oe oz ot f z z . > a \ ; \ > c oS o © okt if : z . ° e o = ry va ry ss 2 ‘= 3 m _ ° za wr a ° \_1 — } orl ; a ASW SPT = L APN OFT = iL ($334930) 379N¥ ONTYILIVIS ($33N93G). JIONV ONTYRLLVIS ve oz at a oe oz ot 9 a a z 42. a ee > , . z N 2 Lars vw Ox pre ¥° e a 3 Lo 4 Va . m A e Zz _- eo a ° 3° A a- ot ort HIAQd ONIZATYNY H3A0d ONIZAIVNY 93 The variation of o Ss. within a setting caused negligible differences in the analyzing power. d°o/dQdE is the double differential cross ' section for inelastically scattered protons from carbon. (30 MeV was taken as the upper limit in the numerator integral of equation 7,.11-4, since the analyzing power goes to zero for AT, = 30 MeV.) _ Some typical curves of analyzing power versus relevant variables are presented in figures 7.11-3 through 7.11-6. One should note the difference in analyzing power for 3. 5° scatters, 5° scatters, and greater than 5° scatters. The justification for some of the arguments of Appendix 7.9 rests on the values of these numbers, The uncertainties in the analyzing power depend primarily on the uncertainties in the source data, These uncertainties are | discussed in the internal report) Roughly they are + .02 for elastic data and + .1 for inelastic data (where it exists!) The uncertainties in the polarization values due to this effect are small as explained in Section 4. 7.12 T Cross Section In order to insure that the apparatus was working correctly in all details, a small number of events from one kinematical setting centered at {k) = 850 MeV were used to perform a determination of the n° production cross section, The measurement was in a kinematic region which has been well (3) namely the region of the second and third resonance (750 < k<1075 MeV), with the center-of-mass angle of the pion centered at 60°, _ reported, Two measurements of k, the photon energy, are possible, as explained in Section 3.2. One method used the range and angle o, (MeV ) | 35 Fr " ne a 94 50 — T 1 <k) = 850, SET 4 k RESOLUTION, o,, RLO PROGRAM. 40 b CARLO PROG 25 20 F §,, T,) CALCULATED WITH MONTE O ! i a 700 © 800 | 900 1000 k (MeV) Figure 7.12-1 1100 95 60 55 “ (MeV) i i . i ‘ i (k)= 1350, SET 3 k RESOLUTION, o,, CALCULATED WITH MONTE CARLO PROGRAM p» |) ! J 7 | a lO 100 1200 1300 1400 1500 k (MeV) | Figure 7,12-2 96 of the proton in the lab, the other method used the lab angles of the proton and the pion. The former k determination yields a better - value than the latter if the proton trajectory is free of inelastic nuclear interactions. Indeed, for setting 4 with (k) = 850 MeV, the k resolution is about 15 MeV with the former method as compared to 35 MeV for the latter, (See Figures 7.12-1,2.) To insure that few inelasticities were present, a section of the data with (k) = 850 MeV was scanned, excluding events where the P-Cy5 scatter polar angle, e5 » exceeded 5°, The probability of an inelastic interaction for 94 D < 5 is small for protons from | (k) = 850 MeV events, as Figure 7,12-3 demonstrates, Of course, in calculating a cross section one must account for all events. The events with @ p > 5° were corrected for in two ways. These events were separately processed, anda k determination was made from the proton and pion lab angles. A calculation was also made using the experimental cross sections for P-Cr5 scattering, The results of both these approaches are displayed in Figure 7.12-4, ‘The consistency shown gives confidence in the result. _ Other systematic corrections were also necessary, as listed in Table VI. Even though each is rather small, the combined effect is considerable. The general method used in calculating the cross section once all systematic corrections were completed, was essentially that of section V-A of Reference 21. The same computer programs were used to calculate geometrical efficiencies and resolution | functions, The photon conversion data were also obtained from ‘Reference 21. For completeness, the relevant formulae are repeated here. _ 97 d ‘uorjoexoquy &F5-d oy} ut AJTOTISVTOUT OTP WIEN Byep Jo JoTd LV $-ZT*L OmNSTA (A®W) ‘FLV oS Op o¢ oz Ol fe) Ol- O2Z- o¢- Ob- OS- . T T aor ~O . / + 02 SLN3AS OLLSV TANI a + Ov a SII LIOILSVTSNI + o9 ON ONINNASSY NOLL ~VINDW O1NV ALNOW i + 08 a OG8 = (4) YALIVOS “O-d NI 44SOLNO | - oG HLIM VLVG NOILO3S SSONd + OO div NI NOILNGIYISIG F . oo | 4 od! LNSAWIYSdxXS NOLLVZIYV 10d ot 1 _ | j i 1 \ \ \ ! Obl SLNNOO 98 Pret) oanst 7 (A2IN)" 002! Oo! foreye)| ~ 006 008 002 1 q ! q | T ! J i if px pu ds = x f ft. x x x x p-| ; 7 =NO1LOSYYOO i OG8 =(4) HaLLVOS “O-d NI 44OLNO oS HLIM WLVG NOILOSS SSOND 5 — SNOLLOZYYOD YWATONN o# (ANIVA SLNIOSaV) AYOSHL x - QSNINYSLIG ATIWLNSWINadXx3 ; J i } i j 1 ! l I | 20 om 6) 170) G0. 3°0 20 80 99 TABLE Vit Systematic Effects Effect % Loss Remarks I, Electronic Inefficiencies Spark Chamber Dead Time 4.8 SP-1 . SP-2 . SP-3 | . Ppl-1 == Negligible Pb1-2 -- Negligible Vi 024 v2 624 OW. Counter Inefficiencies Photon Pre-conversion* 7.2 Each 3.6% Shower Counter Inefficiencies** 2.0 Each 1% Proton Counter Inefficiencies » -- Negligible Hodoscope Inefficiencies -- Negligible Ti. Scanning Inefficiencies Event Oversight -- Small Multitrack Confusion 1.7 Miscellaneous 2.1 Total Corrections 17.6 * Photons converting in the hydrogen target, air, or other material before reaching veto counters are lost. ** The electronic bias was set to exclude particles which were less than half minimum ionizing. photon showers, This low bias also excluded some where: — 100 MeV/bip), dQ c(i): de a+ D+ N+ We be ake 62. Blk) = Number of events experimentally generated in interval k + ak/2, = Efficiency for detection of event initiated from photon of energy k as modified by the finite k resolution, __ . = Synchrotron endpoint in MeV, = Systematic corrections, i.e., all those of Table VU plus nuclear interaction corrections, = Branching ratio for n° ~ 2y (=,988), = Number of protons in target per em? ‘(= 891 x 1074 protons/em?), = Quantameter constant (= 1.432 x 1013 = Number of bip's, = Energy bin © 25 MeV), = Photon conversion factor (variable between .56 and .62), = The bremsstrahlung function, 101 G-CL°L AINST ( AON y ) OOll - OOO! 006 008 OOL 009 T 1 i T “I ” T NOILNIOSSY ( SISSHL HOSL 1VO) lig) ggaqqos4nn S,qqogziaq “7V © LNAWINSdXx3 SIHL } (SWO 009) ot+d —— d+ -NOILOSS SSOYD WILNSYSSSIG j J J 1 i i O01 +o0¢ 102 and k . = Energy of center of photon bin in MeV. Agreement of the cross section with previous data is good, as shown in Figure 7,12-5, ' 7.13 Backgrounds Figure 7.13-1 shows the Ag. distribution ( = e (T,,, 8) - Q ; see Section 3,2) as obtained from "non-scattering" ° events used in the cross section determination of the previous section. The smooth curve-fit to the data is the expected Ag. ' distribution, as calculated using a Monte-Carlo method, including the known 1° differential cross section. This curve is completely determined except for absolute magnitude... The fit is quite good except for a small number of inelastic P-Cy5 scattering events present at A@ >> 0, (See Figure 7,13-1.) 7° kinematics imply that inelastic P-Cy5 seatters shiit AG to positive values; hence, one can use the negative side of the Ag curve to indicate the presence of non-1°? background events. Clearly, this background is not very large; however, one would like to make a more quantitative statement. 1 background is excluded both by the veto counters and the lead-lucite shower counters. We thus expect production of multiple n°'s mainly 2 n'S, to be the main source of background, Figures 7.13-2 A,BandC indicate schematically why the detection of n neutral pions with n> 2, is greatly suppressed with respect to nm and 20° detection by our apparatus. Hence, a Monte-Carlo calculation was made using the method of Reference 21 (Appendix ]) COUNTS 103 200 T T 180 F 4 MEAN = +.19 ~ 160 | : +t | <k)= 850 MeV 140 F AL CROSS SECTION DATA * | WITH 5° CUTOFF IN 120 + | P-C,, SCATTER 4 | 100 F | 4 _ | 80 F | a 60 F 7 L | INELASTIC _] 40 : j EVENTS 20 + | ~ re) __ —l] L i ] | l i py -4.5 -3.5 -25 -15 -5 0 5 15 25 35 45 A@m (DEG) Figure 7,13-1 Ao. plot for data with little inelasticity in the p-C, 5. interaction. The smooth curve is obtained by a Monte Carlo calculation assuming no inelasticity, P (m*) (A), 104 Figure 7, 13-2 The qualitative reasons for multipion background suppression TYPICAL MULTI -PION «i PHASE SPACE Mar n (mz) m* fe atfant fe) m* is eifective mass of nt system n= 2.3... if one detects the proton alone, the range uncertainty due to p-C49 inelasticity induces the acceptance of many m*'s from phase space as well as Single pions, But placing the y-systems as described in Sections 2 and 7,1 cuts out most of the background. This is due to a separation of kinematics; i.e., very few m* > m can get their protons and y-rays into the correct counters no matter what the proton energy. This is shown by B (next page). 105 Figure 7,13-2 (Continued) | CROSSHATCHED REGION INDICATES | PROTON ENERGY TOO SMALL TO | GET PROTON INTO RANGE CHAMBER | 60 — ee . BOX INDICATES APPROXIMATE LOCATION OF COUNTERS IN @ LABORATORY CO-ORDINATES, p G4 Oy, 55 (8) 50 45 0 Of course in most cases photons from the decay of n 7 'S can go anywhere in the laboratory; but as shown by C, symmetrical placement of the y-systems so favors 2y-719 » SY Y : ; decays that relatively few backgrounds y-rays make it, (indeed < 2%). _-—— 7° _- DISTRIBUTION P(Byy) n7® DISTRIBUTION — i—) — ele ee ee | | | | i | | | | | | | | | | Dd Ss ~ aw? MIN OPENING ANGLE seen by symmetri- cally placed y counters, ~ - 106 to obtain the 2 *° contamination for data used in the cross section determination of the previous section, The results are shown in ' Figure 7,13-3. The background for every k is less than 2%, with the average contamination being more like 1%. Of course, the experiment covers a large k region compared with (k) = 850 MeV setting alone, since there were four settings altogether. Figure 7,13-4 however indicates consistency with the above arguments. The conclusion is: backgrounds are < 2% for all k considered in this experiment. Hence, one need not consider back- ground corrections in calculating the polarization. 7.14 Beam Monitoring For the purposes of a polarization experiment, all that was necessary was a clean y-beam. Absolute calibration was not necessary. However, the cross section determination necessitated (24) ed in the an absolute calibration. A Wilson type quantameter experiment was found by L, Rochester to be damaged after the completion of the last run, A small leak was found which had decreased the sensitivity of the instrument by 28% over a period of 2 years. The slope of the decay was small. (21) Since this experiment had been performed in the 2 months preceeding the happy discovery, a correction was easily made to obtain the quantameter constant to the required accuracy, The number obtained was, 13 1.432 + .02 x 10°“ MeV/Bip . COUNTS, 7° COUNTS, 27° BACKGROUND (CALCULATED ) i q i ] 240 + a a {k) = 850 / 200 b 7°? EVENTS OBSERVED | CORRECTED FOR NUCLEAR i INTERACTIONS 160 - 4 80 / en | 40 - — i O 5 L 27° BACKGROUND CALCULATED _ WITH MONTE CARLO PROGRAM 44 4 3+ _ 2-{ | | 4 i _ re ee eee O if } l a 700 800 900 1000 tele) | k (MeV). 107 Figure 7, 13-3 i40 T T T t 108 mw? POLARIZATION EXPERIMENT 420+ 4 DISTRIBUTION IN Aw i00 + ; CROSS SECTION DATA WITH 5° ° | CUTOFF IN P-C, SCATTER n 80k (= 1350 | 5 ° Oo 60F + 40+ 4 i?) i a i “125 -100 -75 10.0 125 i40 T T T T T T T T T aw® POLARIZATION EXPERIMENT 20 4 DISTRIBUTION IN A@ar 100 + . 4 CROSS SECTION DATA WITH 5° CUTOFF IN P-C,, SCATTER “(k) #100 80F 4 z > 8 col , 4 40} 4 20+ 4 ° L L rm ial n 1 [l—1, = b 1 “125 -100 -75 ~50 -25 ° 25 5.0 75 10.0 125 350, T 7 T T T T T T T aw°® POLARIZATION EXPERIMENT 3004 4 DISTRIBUTION IN A@z 250 CROSS SECTION DATA WITH 5° CUTOFF IN P-C,, SCATTER 200} <k) = 850 J z 5 ; ° Oo 1504 4 100 + 4 fo) - 4. i Lb wtiti. i i so de i “125 -100 --75 -50 -25 ° 25 5.0 75 10.0 125 A@z7, (DEG) Figure 7,13-4 ae plots for data with little inelasticity in the P~Cy5 interaction, 109 The beam calibration is dependent on the beam integrator as well as the quantameter. A periodic check was made on the beam integrater circuit during the experiment, and its response was found constant to 1.5% during this time. 7.15 Theoretical Analysis (4) 1. Kinematical Definitions: Four-momenta of the incident photon, outgoing pion, the initial nucleon, and the final nucleon, are denoted in the center of mass by ~ _ M= Proton Mass, m_ = Pion Mass. — The total energy in the CM is W. Using the metric, p =-M, | the well known Mandelstam variables, s, t, u are given by s = -(k+ p,)” = Ww t = -(k- q)?=m 2 | okw (1- 8 cos 6*) T wT T u = -(k- py) = M" - 2kE, (1 °b cos °B We use 1 BeV as the unit of energy, and other units such that a =c=l1. The unit of cross section is then 1(Bev)"? = 389.5 ub = (1.972 x 107!* em)”. 110 These units pertain to the w-exchange formulae only. All numerical values quoted for amplitudes, helicity coefficients, etc. are in units (ub) V2) 2. Addition of the fourth resonance. The fourth resonance state Ny /2(1 /a+) 1924), (17) was included using the formalism described in Reference 4. For details © the reader is referred to that paper. However, for completeness we present a brief description here. The following modified Breit-Wigner form has been used for the resonant amplitudes: Kod). 1/2 W rer? A(W) = A(W,) qd S57 S87 iW ° where we define f and ry by. 2 2 Xx : 24¢1.% * L r= Ti a/a) "6 -y—y )” s q +X as, Ko + x? Jy T= To (k/k) [ + J . ¥ Ko + x? Wy is the mass of the resonance, and dy Ky and s o are the values of q, k, and s at the resonant energy W = Wo Py is the half-width at half-maximum of the resonance. 42 represents the final state nN orbital angular momentum, while J y is the orbital angular momentum of the Ny in the initial state. The meaning of 1il AWW ) is obvious. The particular choice of phase space modification of the simple Breit-Wigner form introduces the parameter X. This number is usually taken as ~ 350 MeV and represents the typical interaction distances occurring in a resonant state. A resonance is thus described by the parameters Wo To AW); Ly Js X, These values for the various resonances included can be found in Table V. . | In order to relate n and n° photoproduction the photon interaction can be written in terms of an isovector and isoscalar part. The vector part gives final states of isospin 3/2 and 1/2 with 3 amplitudes AY? and av! respectively. The scalar part gives final states of isospin 1/2 with amplitude AS, Amplitudes for n* and 1° photoproduction may be written in terms of these in a form first given by K, M. Watson: nt: At = 71/3 AY? -~ 73/2 (Av - AS) n°: A° = 72/3 AY? 4 1/3 (Av - AS) . 3. The Regge-ized w °~ exchange. This section is heavily dependent on the work of G, Kramer and P, Stichel (29) (from now on referred to as K-S), The well known paper of coin) contains the definitions of the ‘s and A-D used below. Using equations (7.8) ~ (7.11) of that paper we obtain, in terms of our kinematical variables, the following equations “¥ 1 (w= “12 [A+ (W-M)D + te =u Tt) C-)}, OY . (wea Z So ([-A+ (W+M)D + (a — on c-Dy, oF ww “12 a [(W-M)B + (C-D)], ee Y.-S z gf-(weMB + (C-D)) , 1/2 1/2 » Zo = (E, + M) ° We now use a somewhat modified version of equations (72) - (76) of K-S to obtain the A, B, C, D of (7.15-1) above. The t-region of interest to us is greater than |t| ~ (m_)*; hence, the in which we have, Z,= (E, + M) complications which arise due to the unequal masses of the photo- ) of K-S on the principle that only physically expected t variations production process will be neglected, (30 We simplify the equations Should be included. E.g,, the nonsense zero in the spin-flip amplitude at a, = 0 should be present; the additional kinematical zero in the total amplitude at a = 0 is present; ... etc. We also require that the explicit t-dependence of the elementary w-exchange should be reproduced by the Regge~ized exchange near the w pole. We thus obtain for A-D the following forms; 113 As sth 1 oY) (ese 4 1), B=-A/t , C=0, (7,15-2) D= ety (1 oA) (os yah y i The major simplifications in the K-S formula come in our expressions for ¥,) and y g(t). volt) F (alt) + 1) ( The residues By and Bo are assumed to be constant along the trajectory a(t), Here we are speaking about the w-trajectory and so we take aft) =a (t) = .9t+ 45 . a & is made to pass close to Rea AC) =1 for t= mi. Its slope is chosen roughly parallel to that of the. p trajectory. (26) However, direct information on a (t) is also considered, “4 9) We choose the - parameter S, = 1 (BeV)*. . The calculation of elementary w exchange was performed using the normal Feynman rules with the following interaction vertices: -- The wNN vertex used was 114 (ey) {Fy nw Vy +3 Fownn | By - Py ¥, Jtu(py). (7.15-3) Fy NN? FE QwNN 2Fe the electric and anomalous moment couplings respectively. u(p) is the usual Dirac spinor, and the YY are the 29) - .The wry vertex used was usual Dirac operators. ; (Photon) tomy a B78 “a Byu , (7.15-4) IE oy \2 is proportional to the decay rate of w > my. c, (Photon) is the photon polarization vector. In the t-channel we obtain, using (7.15-3, -4), the following AE BE cB p™ for elementary exchange, corresponding to the A, B, C, D of (7,15-2) for Regge-ized exchange: AE - t E ny FowNN (t- m 2, +il m w ww BE = -a®h (7,15-5) cE =0 p= - tomy F LoNN ({-m 4) ar m w ww Pj» m, are the w full-width at half-maximum and mass, respectively. 2 Near the w-pole in the a(t) plane, i.e., near t = mi at, (t) can be represented as 115 | — _ da(t) 0. (t) w 1+ om (t m )+ il, c= ; (7.15-6) W Comparing (7.15-2) and (7,15-5) near the pole and using (7.15-6), we obtain with é, ~ 1, that Tr m TseeY #209 <1, W € : Ww This is consistent with the representation of Oy (t) near the pole, i,e., (7.15-6). We also obtain for the fixed residues By and By * By = 1/5 (MF 2wNN 7 Fiwnw fumy wo? . (7,15-7) By = 1/5 (1/2 Poonn * Fipnn/m f ny ene Reference 27 gives the following values for the relevant elementary particle couplings.: f (F -1 TT 1 (7,15-8) 2M -.16 r/m_) ~ ~.25(BeV) ", t my Fo NN//4r? < e,” = 4/137. Hence we can neglect the anomalous magnetic coupling. This approximation gives equations (7.15-7) the following form: 116 f ~~9,2 (Bev)"®, By a - 1/5 Fa oNN wiry ew | (7.15-9) ~4 By = (1/5M) Fy nny fury &y © 98 (Bev) These couplings are known to about a factor of two (28). The values actually used for 8,, Bo which obtained the best "fit'' to the cross section data‘), 20) at 3 BeV were 1,25 times the value of those in equation (7.17-9). However, as explained in Section 6, the full value of the coupling gave good "fits" only at the highest energies, iie., 2and3 BeV. To obtain good fits every- where, the coupling had to be gradually turned on, as demonstrated in Figure 5.4, The model used at the higher energies was essentially w= exchange alone; hence, only the forward peak was fit weil t®), These fits are not shown since they are very preliminary. 10, 11, 117 8. REFERENCES P, Salin, Nuovo Cimento, 28, 1294 (1963). D. S. Beder, Nuovo Cimento, 33, 94 (1964), _d. T. Beale, S, D. Ecklund and R, L. Walker, CTSL Report 42, This is a rather complete catalogue of photo- production data from threshold to 1.4 Bev, R. L. Walker, to be published. A. Donnachie, R. Kirsopp, A. Lea, and C. Lovelace, Proc. XI International Conference on High-Energy Physics, (1966) Page 176. J. J. Sakurai, PRL, 1, 258 (1958). R. M, Talman, Ph.D. Thesis, California Institute of Technology (1963). | By carbon I mean normal carbon which is not isotopically pure. In this experiment we use grade ATJ graphite of mean density 1.73 gm/ em’. Throughout the thesis, however, we - speak of P-Cy5 interactions, This is done in the spirit that carbon is predominantly Cio and a negligible error in the nuclear interaction characteristics result in assuming carbon to be all Cro Wm. McNeely, CTSL Internal Report 30. P, Bareyre, C. Brickman, A, V. Stirling, G. Villet, PL., 18, 342 (1965), L, Wolfenstein, Annual Review of Nuclear Science, 6, 43 7 (1956). 12, 13. 14, 15. 16, 17. 18. 19. 20, 21. 22. 23, 118 R, D. Eandi, Ph.D, Thesis, UCRL - 10629 (1963). J. O. Maloy, Ph.D. Thesis, California Institute of Technology (1961) Page 46. H, Cramer, Mathematical Methods of Statistics (Princeton University Press, Princeton, New Jersey, 1958) Page 498. D. E, Lundquist, J. V. Allaby, R. 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Farzam Arbab and Charles B, Chiu, PR 147, 11045 (1966). _ H, Abarbanel,-C, Callan, Jr., and D, Sharpe, PR 143, 1225 (1966). H. Abarbanel. Private communication, G. Kramer and P, Stichel, Z.S. Phys, 178, 519 (1964). S. Frautschi and L. Jones, private communication, C. A, Heusch, C. Prescott, CTSL, 41 (1964); C. A, Heusch C. Prescott, Nuclear Inst. and Methods 29, 205 (1964). 3