The Photoproduction of Positive Pions from Hydrogen at Energies of 1.1 to 1.4 GeV Citation Kilner, Joseph R. (1963) The Photoproduction of Positive Pions from Hydrogen at Energies of 1.1 to 1.4 GeV. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/G211-PZ76. https://resolver.caltech.edu/CaltechTHESIS:04202012-090651904 Abstract A magnetic spectrometer and counter telescope system was used to detect positive pions photoproduced singly in a liquid hydrogen target. Measurements of the differential cross section were made at mean laboratory photon energies, k = 1.1, 1.2, 1.3, and 1.4 GeV and in the angular range from 5° to 165 ° in the center-of-momentum system of the pion. The shape of the angular distribution of the differential cross sections at each value of k is very similar to that of the previously measured distribution at k = 1.0 GeV. The angular distributions were integrated to give the total cross sections. The third pion-nucleon "resonance" peak is seen to be very close to k = 1.0 GeV. A leveling off of the total cross section at k = 1.4 GeV may be due to the fourth "resonance". The accurate small angle data at k = 1.1 and 1.2 GeV permitted a reasonable extrapolation of the differential cross section to the pion-nucleon pole. The value of the pion-nucleon coupling constant, f, was extracted from this extrapolation. The result was f^2 = 0.078 ± 0.011. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Walker, Robert Lee Thesis Committee: Unknown, Unknown Defense Date: 1 January 1963 Record Number: CaltechTHESIS:04202012-090651904 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:04202012-090651904 DOI: 10.7907/G211-PZ76 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 6952 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 20 Apr 2012 16:44 Last Modified: 04 Jan 2024 18:36 Thesis Files Preview PDF - Final Version See Usage Policy. 9MB Repository Staff Only: item control page

THE ~HOTOPRODUCTION OF 0 0S!TIVE !?IONS FROM HYDROGEN AT ENERGIES OF 1. 1 TO 1. 4 GEV Thesis by Joseph R. Kilner In !:lartial Fulfillment of the Requirements For the Degree o! Doctor of Philosophy California Institute of Technology -::>aaadena, California 1963 \. ACKNOWLEDGEMENTS The intere•t and guidance of Dr. R.. L . Walker during the author• a graduate J"esidonce have been invaluable. His supematon during the course of this work ie greatly appreciated. The aseitJta.nce and suggestiao.a of many at&ff members and gr3.duate students of the SynchrotrOD Laboratory have been most helpful. Dr. J. 0. Maloy h.a.s made many valuable contribution• to the multlpole analysie program. The active asstetanee 0'1. Dr. R.. E . Diebold in a.c:cumulating data is deeply appreciated. L . Louc:ka and the Synch.rotl!'on crew gave excellent support in operating and maintaining the macldne and equipment. Special thanks , are due E . B . Emery for hi& maintainance of the liquid hydrogen target. The a.ssistanc:e ol a.U ol the synchrotron operators, and especially A. Neubeiaer, is appreciated. Disc:us&io:ns with C . G . Montgomery have been very helpful. The u.ae ol the c:om~ iacUitiea and. the assillta.nc:e of the staffs of both the Western Data Proc:e&aing Center, Univereity ol California a.t Los Angeles, and the Caltcch Computing Center have been invaluable. The partial financial support of the United States Atomic: Energy Commis"ion is gratcdully acknowledged. ABSTRACT A mapetk •pec:tromotor and counter teleec:ope system was u•ed to detect positive plexus photoPJ'ocluced singly in a liquid hydrogen target. Measurer.nente of the d.ifierential croaa eection wea-e made at mean laboratory photoo energies, k = 1. 1. 1. Z, 1. ~. and 1. 4 GeV and in the anplar range from 5° to 165° in the center-of-momenN!n system o1 the pion. The eha.pe o1 the angula.s- dietribution ol the differential erose eectiGifta at ca.ch value of 1~ ls very aimUar to that ot the pl'cviously meaaurect diatributioo at k • 1. 0 GeV. The angular distribution• were integrated to give the total erose eectiCDc. The third pion· nuclecm "resonance" peak is seen to be very cloae to k A leveling off of the total cross aecttOD at k • The accurate small angle data at k • :as 1. 0 Ge V. 1. 4 GeV may be due 1. 1 and 1. z. GoV per- mitted a l'eaacmable extrapolation of the differential cl'oes sectiOD to the pt.an.. smc:leOD pole. The value of the ptcn-nucleCD couplinc conatant, f, waa extracted fJ'om this extrapolattcn. The result waa ;. • o. 078 + o. 011 • - TABLE OF CONTENTS CHAPTER TITLE PAGE 1 INTRODUCTION 1 U THE EXPERIMENTAL METHOD 3 A. B. C. D. E. F. General The Synchrotron Beam Geometry The Liquid Hydrocen Target The Magnetic Spectrometer The Counter System .?article Selection and Electronics 3 5 5 7 7 12 m THE COUNTING RATES 16 IV DATA REDUCTION 24 A.. B. Croee Section Formulas The Calculation of K 2.4 25 v THE RESULTS 28 VI Ju'iALYSIS 38 A. Genoral Moravcsik Polynomial Fitting and the 38 Coupl~ng Ccms~ 38 42 44 44 B. c. D. E. VD The 0 a.nd 180 Cross Section• The Total Cross Section Multtpole Atlalysls CONCLUSIONS AND SUGGESTIONS 47 1 COlJNTER. EFFECIENCIES 49 n m NUCLEAR ABSORPTION 55 DECAY AND SCATTE~G CORRECTIONS 57 IV EOUIP.MENT CHECKS 77 V BEAM MONITORING AND THE AJ?i?ENDIX BREMSSTRAHLUNG SPECTRUM 82. REFERENCES 86 LIST OF ILLUSTRATIONS FIGURE TITLE PAGE l. The Pion Kinematics 4 Z. The Experimental Area 6 3. The HydJ'ogen Target and Magnetic Spectrometer 8 4. Electronics Block Diagram 13 5. The Background Counting Rates ~3 6. Center o1 Momentum Angular Distributions 33 7. The 0° and 180° Crose Sections 43 8. Tho Total Crose Section 45 A1. Cherenkov Counter and Electron Detector Efficiencies SO A2 . Decay Coordinate System and Parameters 59 A3. Magnetic Spectrometer Momentum Reepoose 63 A4. Mom.entwn Response for Muons from the ?ian Decay 67 AS . Multiple Scattering of i'ions 76 A6 . Measured and Calculated Spectrmneter Reeponse 79 A7. TI1e Beam Monitor Calibration 83 A8. The Bremsstrahlung Spectrum 85 LIST OF TABLES TABLE TITLE PAGE 1. Deac:ription of the Counter& 11 2.. The CCNnting Rates 18 3. The Reeults ~9 4. Leaet Squares Coefficients 39 5. Residues at the Pole and Estimated Points 41 Al. Parameters 1or the Decay Correction Program 61 A2.. Multiple Scattering Calculation Parameter& 74 Al. The Speetr01neter Acceptance 78 -1- I. INTRODUCTION The exietence of the pi meson was !iret proposed by Yukawa (1 ) in 1935. In 1947 Lattee , Occhialini , and Powell (Z) discovered the pion in emulsions . Since then a vast amount of experimental and theoretical investigation of the pion and its role in nuclear forces has been done , the pion-nucleon scattering and the pion photoproduction experiments being the most fruitful . Thus far four "resonancc:u 11 of the pion - nucleon eystem have been observed. The erose section peaks observed may not actually be resonances but will be referred to as such he r e . These are ( 3 ) ; Mass Resonance Width (MeV) laospin Angular Momentum Parity ( MeV) 1 1238 145 3/2 p 3/2 + 2 1512 130 1/2 D 3/2 3 1688 140 1/2 F 5/2. + 4 1922 185 3/Z ? ? The first three have been definitely obeerved in pion photoproduction, and this experhnent may detect an indication of the fourth . At energies in the region of the first resonance and lower , the dispersion theory o! Chew, Goldberger , Low, and Nambu (4) is quite eucceeeful in fitting the photoproduction data . For lack of a succese- ful theory at higher energiee phenomenological methode are ueed in the analysis of such data . The application of the concepts of Regge pole• to the photoproduction analysis problem may prove rewarding at higher energies . -zAn experiment was planned to meaaure the angular distribution• of 1r + meaona produced in a liquid hydrogen taraet at pion center of momentum. anglee from 5° to 165° and at photon energiea of 1. 1 and 1. Z GeV. The improvement of the synchrotron accelerating syatem during the courae of thie experiment made possible an extension to photon energiea of l. 3 and l. 4 OeV although the operation at 1. 4 GeV was marginal and the statistical accuracy of the data obtained i8 not very good. An interval of 1. 71 to 1. 87 CieV in the total c . m . energy ie covered in thh experiment. At the two higher photon energies the momentum of the pions produced at the forward angles was too high to be analyzed with the largest spectrometer available and the angular distributions are not so complete as at the lower two energies. To a large extent thla experiment employed the same apparatus and experimental techniques ae used by Dixon (5) and Boyden (6). Thus it ia expected that the agreement among these experiments should be quite good. The angular dietributlons obtained at all these energies are remarkably similar to the one at k = l. 0 aev. The total cro•• sec- tion decreases markedly to lese than ZO }J- b above a photon energy of 1. Z GeV, compared with a total cross section of 55 }J- b at the third resonance peak (very close to 1. 0 CieV). The value of the square of the pion•nucleon coupling constant (~) measured in thh experiznent i• 0.078 + 0.011. -3- U. A. THE EXPEIUMENT AL METHOD QEN.li:R.AL A Uquld hydrogen tazoeet was irradiated by the photon beam produced by the CnU.f01'1lia Jnetltute ol. Technology aynchrotrcm. mozneotwn. p. and angle, The 8LAB' of Tr+ meeana proch&ced in tbb target wezoo eelected by a magnetic apectrom.eter and counter teleacope ayatem. .A. la well known. p and 8LAB determine the photan enersv, k. (with a width detezomlned by the apparatus) for the reactl011 y + p ~ Tr+ + n. The peak energy of the photon spectrum, E 0 , waa choae:o. eo that the pion• detected by the countea- ayatem were produced ooly by the above reaction. In partlculaJ' thb pw"Oper choice ol. E eliminated the de- o tec:tlcn of plone produced in palra by the procea see Tr + p and all htghel' order pi'OCeaaea. The kinematic • for aingle llmldng clU'Ve lor a Tr + Tr + photoproduction ae well ae the prodll~ed lD the pall' prochu:UCIIl reac:tiooe are giveo ln Flgul"e 1. Jn additlGD to plooa. pl'otona and electroae of momentum p were abo pS"odt&ced in the forward direction. with the electroru cOIIlftned to the very forward anslea ooly. The protem• were di acrimtnated from the pf.ona by their lowel" velocity, while the electron• wel"e :rejected by -4- 1.5 1.4 1.3 1.2 - - y+p --7T++( N+7T) (UPPER 1.1 Ll MIT ) .9 u ........ > w C) ~ .8 .7 ::::> f- z w ~ .6 0 ~ (I) .5 <l _J z .4 0 a... - .3 .2 .I .0~--~----~--~----~----L----L----~--~--~ 0 20 40 60 80 PION LAB ANGLE Figure I. The 0 100 120 DEGREES ion Kinematic s 140 160 180 -5- detecting tho showers they produced in lead absol'bera. B. THE SYNCHROTRON BEAM GEOMETRY The overall view of the experimental area and equipment 1e ahown in Figure ~. The photon beam waa produced at the rac.iator inside the synchrotron vacuum cha!nber. emerged thrcugh the primary collimator whleh fixed the beam size, paaaed thrCK1jh a lead •~raper, then thrCNgh a sweeping magnet to remove the many (mainly pail'produc:ed) electron•, through a aecood scraper. IJtNc:k the liquld hydrogen target, and waa finally stopped in the lead block containing the beam m.ooltor. The gaa hydrogen target used by T. Chang (7) or various thin t&l"gets placed j\ut in front of the sweeping maanet by H . Rudonnan (8) were often in the beam whUe this experiment was in operation. A.. b dlscusaed in Appendix V the effects of these targets em the bremsstrahlung apec:ti'Um may be neglected. C. THE LIQUID HYDROGEN TARGET The target of liquid hydrogen was contained in a three iuc:h diameter Mylar cyllndel' located in a vacuum chamber and aurrounded by a series oi heat shields cooled by liquid nitrogen. aigned by V. Thh target wae de- z. Petersen Dnd improved by R. L. Walker. Jt is a rr.odl- fied veraicm ol the Qlle used by Dlxoo (5) and the same as that ueed by Boyden (6). The asymetrical "fogho1"nn·abaped aluminum shield with Mylar windows shown in ngure :s is designed to reduce the background from the tu-get atructure. When data is taken at emaU angles (lese than 15°) the shield may be rotated 180° uom the position shown in Figu.re 3 (a) to :rechlce the amount of material the picms must pa.se ~_I-- _I_]~--. SCAL£ LJ l I 0 I' 2' 3' -· - ( ' 1 LL. _ l ·1 /.{',~ ~--.:~,;.: ( -{..',:.·.j ' ( -;-,I I . .. L:: •. ) 't 11 \ '' _:. ' j -·- : \ •:;_: .: I ' ' < • ' • ' -,\ I . 'I \ - . . , J ' ~{ • ', \ /,' .r1•f- ·- -1 1 \'. _.>, """~ Figure 2. / The Ex )e rimental Area Tl TARGET -: lt _~_jL l __ ~l.- ~ I ' T HIM 1;-~::-.. ~ -..., t-, C' r-- I["] ' lj I I toft l I ' I ' ..t r J-~ . l ~ ' '" / CHAIII8Ett --- -- : " LIN£ c.<. KAII - - ../ I ~·-::.~:- "~~, 1~~~ ·-'"pP ·)~(;~ -~. r f"·-\olTOI~ ' < • •,'' IIAGNE ) -lr-- \%)./ (. i: ; ( 'l ~ ~Pb '-<._'[;~ ~~~\\ . . ~·~· .. ~·~ IIOM£NTUII TE r-~ . _1.: ' I\ . •\• w .. LOW - - - -,1 I I I 0' -7- throu..gh on emerging from the target. D. THE MAGNETIC SPECTROMETER The magnetic spectrometer and counter telescope are abown 1n both the hlgh and meclium energy conftguraticma in Ftgure 3 . An in- ternal l'eport (9) give a a detailed deecl"iptlon of thh spoctrometel' and the meaaurCJnenta made to determine ita propel'ties. The spectrom- eter can be eaaUy rotated about the target on the steel tracks shown 1n ilgul'e ~ and can be set with an error of lea a than 0. 1 degreea . A proton reaonance .magnotom.eter waa used in a<ij\utlDg the magnetic field. and the magnet current was l'egulated to 0 . 11o. (See Appendix m and Appendix IV I~ some of the spectrometer propertiea. ) E. THE COUNTER SYSTEM The counter ayatem used to detect the particle• conatated ol five sc:1nt1Uatian cOQntere, ooe luclte Cherenkov c::cunter, and a set of pole face veto counters C"lana") to reject particle a scattered .from the pole !aces. Thesca cou.ntere are each described 1n Table 1 and shown ln Figure 3. (See also Appendix m. ) Altogether five dWel'ent cClDfigura- tiCXJ.a ol. cCNntol's and spectrometers were used at the vuicua ansles. The Cllerenkov counter (C ), Cl , C~L, C3, and the 'ffana" were used in all the ccmilguratiooa except as indicated below. The c::c:mfigurattons were; 1. H . E . A25 and H . E . A2L .In the high energy con.figuration (H . E. ) at sm.aU angles (leas than ab<Mt 10° ln the laboratory). the front aperture counter. Al. cO.Ud not be used bec:ause of the very large number ol electrons: thue a. rear -8· Figure 3. (a) The Hydrogen Target and Magnetic Spectrometer The magnet in the high momentum position is •hown at zero degrees. (b) The medium momentum position h 0 ahown at 90 . 0 The bottom portion of the hydrogen target may be rotated 180 from the po•ition shown in (a) to permit operation at laboratory angle• le•• than 15 degree• without a thick portion of the target "horn'' in the path of the pion•. Not •hown ia a four inch thick lead wall placed roughly parallel to the path of the piona in the region between the counter box and the rear aperture of the magnet. This wall •erved to ehield the counters in the counter box from particle& produced in the air along the photon beam. The off center lead shielding ln (a) was needed to reduce the number of shower particle• entering the magnet gap when the •peetrometer was placed at the smalleet angles, since the beam then struck the magnet coils clo•e to this gap. -9- -1 0- .. }} ... Table 1 Deecrtpticn of the Counter• Deeig. Size! lnc:hee Type u•• A1 ecint. lZ. 34x 3 . Z4x O. Z50 apertu~:e deflnttlon and timo ot Jlight aolectlan Fan• acln~. two aete ol fOUl' rode 1/2. x 3/4 (eee Figure 3) l'ejectiGA ot particlee ecattered from pole Upe (AlL ) 11. 84xZ. 99x0. 46 aperture deflnttioo (AZS ) 6. OOxZ. 99 x 0. 46 acint. Cl 5. 75xll.Ox0.787 ecint. dE/ dx partiele selectic:m cz sclnt. c C3 (CZL) (CZS) 4 . 7Sx ll. Olt0. 787 2. OOx 11. Ox 0. 787 dE/ dx panicle eeleetion, time of flight eelectioo. momentum acceptance lntei"Val defl.. nitlc;m.. and ehower detection ChereDkO'l 6. 0 X 11. 0 X 1. 50 velocity selection -.eint. 5 . 75 X 11. 0 X 0 . 394 dE/ dx particle selec:tlan and shower detection -1Zaperture counter, AZL or A2S, was ueed. The amallrear aperture CQQDter, AZS, waa used at the emallest angle• where the la~rger vert- ide atze ol. A2L would cause a deterioration of the angular resolution. ~. H. E . end H . E . C~S Jn the atandard high energy spectrometer configuration u•ed at medium anal••• Al l'eplaeee A2. At the luger angles obtainable with the high onergy apectrometer ( ~50°) CZS replaced C~L to reduce the momentum acceptance of the apectrometer. 3. W.E. Tho Chere:okov counter wae removed lro:m tho countal' b~ when the medium energy spectrometer waa used. Al and C2S were ueecl in thie conftguratton. F. PARTICLE SELECTION AND ELECTRONICS A block diagram of the electranice eyetem h given ln Figure 4. Partielee traversing the apeetrometer ayetem were detected and db- tinguiehed by the fallowing fQU methode 1 1. The adntiUation counte:re, A l, AZ, Cl, CZ , and C3 give pulaoa proportiCDal to the epecWc: ionization, dE/ dx.. ~. The Cherenkov counter which le of the total intei'Il&l :reflection type, pvee a pulae only U the particle velocity exceoda abolat o. 85 c (aee Appendix I). 3. Tho Al . ca eoincidenee ie a tlmo·of-tught eelectioo system giving an ou..tpu.t pulao only U the time the particle take• to go from Al to ca ia cloae to some preaelected value. 4. Electron shower• produced in a 1/2." lead convener placed in front ol. C3 gSve large pu.leee in C3. At tho aznaUeat angle•. where Ftgure 4. ElectronJ.c:a Block Diagram The number• 6655 and 6810 refer to phototube typee . Hewlett-Packard amplifier le designated by H.P. The Except for the oecU· loecope, all oi the other units shown were buUt at the eynchl'otroo lab- oratoaoy. The 6 channel coincidence circuit baa a resolving time of about a quutel" of a micro-eeccmd. The faet coincidence ct.rcuita, which have adJustable cllppt.ng atube, have reeolvlng time11 from about 5 to lS nano- seconds. Whan the medium energy spectl'ometel' was used tho Chel'enkov countel' wae l'emoved and the alow CNtp\U &om Cl wae ueed ln place of the Cl • C fast coincidence . -14V' c POLE FACE VE:. TO A2 COUNTERS AI --- ____j 6 6- 0-2 TRIG Tl i-'-----'-~!___1~- ~-6 CHANN(L SCALAR r C OINCIDENCE DELA'fS FA S ANTI - ~J L , - VERT. 513 0 TfKTRO- COI.NC I OENCE CORCU>T (12 3) ' F'23- 4- 56) PION+ ELECTRON ~~ •• ~ M ON1Tr R Fc•~•• l II t DISCRIMINATOR DELAYS - - MONITOR C3 CHANNEL GATED MONITOR C2 !c•L••] 3 MOD 100 CHANNEL Ol,~fllt.IINATOR AND COI,.C C KT It f"l SCA~~~ II "ELECTRONS" () -15- large number• o! electron• are present, a oecond converter placed in front of CZ serves to increase the efficiency for producing laree shower pube• (eee Appendix I) . The use of these methods and the conversion of the various measured counting rates into the actual pion flux will be diecu•aed in the next chapter . Several experimental tests were made to check the proper functioning of the equipment. Theee are discussed in Appendix IV . -16Ill. THE COUNTINC RA TFS In the general case when pions , protons , an<l electrone were all present three counting ratea C , ?, w ithout hydrogen in the target. C and E were taken simultaneously while P required a separate run. and E were measured with and These counting rates are defined by the following coincidences: C = (Al · C2) · ~ · C2 · C3 · FAN C · C2 · C3 ·FAN or (A2 Cl ) · or (A 1 C2 ) · Cl · C2 · C3 · FAN P .::: the aarne as C with (?-of. F . only) C replaced by C E = (C · C3*) (single converter ) or (C · C3*) + (C · C2*) - (G · C3* · C2*) (double converter) where FAN designates the pole face veto counters, a bar over a counter signifiee an anticoincidence , and an asterisk tneana a higher biae is used . L et C TT , C , and C be respectively the true numbere o£ p e piona , protons , and electrons paesing thr:>ugh the system. C , P , and E may be written in terms of these as follows: ce + C= (1·7]~)C L;p P= ce p -17- where the TJ '• are efficiencies (see Appendix I) of the varbu• coun- ters (designated by the first aubacript) for the three particles {desigThe time of flight system h desig- nated by the second subscript). nated by T and the electron detection system by E . The T and C efficiencies for pions and electrons are taken to be identical since their velocities are both above 0. 98 c in the foreward direction where eluctrona are present. "'l c rr ie ve ry cloae to one, P n'lay be Since approximated by p = (1 - Solving the above equations for c - E ) - <1 - < c7T gives .,.., ·t Fe > -1 c- ..,,. , {.,;p \£ < l - n., vp ~ ) <n·1I:'e - n·1E: p ) P e rr = V:hen no electrons are present ti1i8 ie c - TJ cp <I - TJ ~P> - t P e rr = "'lT rr TJ ~ 7T When the medium energy configuration h used (and the Cherenkov counter re mo ved) this becomes c 7T = All of the measured quantities and the calculated pion fluxes are given in Table z. The erro1·a on all of the quantities appearing in the equation for C 1T are uaeu in calculating the error of c .,. . Some of the data were taken with the fan counters turned off. To -18- TABLE Z The Counting Rates All ol the experimentally meaaured quantities used in calculating the cCIIWlting rate• &l'e givcm in this tabl e . These quantities are as follows: PT The paint nwnber--the number used throughout the data reduction process is kept here fol' convenience. The missing nwnbers were elthel' unused Ol' the data were dbcarded. E The breme atra.hlung end point energy tn Ge V. 0 The spectrometer central momentum 1n Go VIc. The spectrometer angle in degrees . The spectrometer conilguration as follows: M .E . 1'he medlwn energy spectrometer using the front aperture counter, Al , and the small momentum deilning C:OQ:uter CZS. H. E . The high energy spectrometer uaing the front aperture counter, Al , and the large momentum defining counter CZL. The single converter is used unlea e the (\Oid.ble converter, 0 , 1a indicated. The remaining configurations all refer to change c. ln the high energy spectrometer coniiguratioo. AZS and AlL refer respectively to the small and large rear aperture counters used instead of Al. C , E , and P These are the counting rate• as defined in the text. ( •.1\n asterisk here indicates an estimated or inter- polated counting rate• - the background• belnn given as the fraction of the full target counting rate. ) BIPS The integrated amount of beam intensity ""sed. (Se0 Ulapter IV. B ,Z.) -19- The 77'• ~eler to the varlGUe e.Ulctenclea (eee Appendix Al). The errcwe on theeo leur ue o. ooa, o. oos. o. oos, and o. OO! reepecttvely. In addltico 7Jc.:rr • 0.9960 + .OOlZ (H.E. CJDly) and 7J T TT • -v. 9964 .:t •OOl4 were used. The elec:tran cCIUDting rate ln electrons per DIP. The p!Gn counting rate in plClWI per BIP when eloc:troo au.btractlon le included. The plOD cOQDdag ~ate in plaa.a per .BlP when lt b aaeumed that no electrc:me are pzoeaent. An aeteriek alter C TT tndlcatee that the tan counter• were not uaed when the data waa takeu and a suitable eurectloo baa been made. In put (b) of the table the columna from 7JE TT to Cf' lndualve have been omitted eince the entr1e s are not neceeaai'Y. '>.4 A2S OC 756 ll .l A2L 3328 d.l H.E. 202 10 . 9 H.(. 3'>59 10 .'1 A2l 132 H.E. 1.2 1.078 1.2 1. 072 1. 2 1. 0 72 L. l 1. 062 t. 2 1. 062 1. 2 1. 036 1. 2 • '175 1.2 .8~5 L. 2 • 8l'3 1. 2 • 716 .71 1> 54 .6 • 603 70.0 • 509 85. 7 .427 lt·4.4 .427 1(4 . 4 .3d6 117. ? .361 126.5 . 323 152.1 1. 2 1.2 1. 2 1. 2 1. 3 t. ? t. 3 1.1 L. 3 t. 183 1.3 t.LB3 l. J 1. 179 l. 3 l.l/ 9 t. 3 1.160 \. 3 I. lbiJ 7 12 13 14 15 16 17 18 l'l 20 21 22 23 24 25 26 30 31 12 3j )4 2'~ 2H l7 9 l(J ll ~ b E ll iPS P/BIPS Rl2 l9bl 84 u 241R 1 24 2u 77 14 4'12 b'i 73bC 3.1 A2S OC 1265 3 .1 A2S DC 128 7 A2l 769 5. 2 A2S !> . 2 7L A2l 651 10 . 6 A2l II> · l' 24 . 5 l. 3 l. 1 l C L. l I . IJ62 DC H. E. H. E. ~ 2L 10 .6 10.6 l6.l) l. 3 l. 161) L. 3 1. LJC A2~ "·E• Lu4 438 887 140 '>6 1 4llb 4979 43<.0 ~ . ...M.£. 13 lll7 bt 16(:0 82 l '-J.jb 2\J 4 b3 t77 J 35~"/ 2669 318 6382 4854 1'1<:'1 5 446 462'1 24 1 298 175 4096 2820 1462 936 3'13 3'169 373b 40U8 M.E. M. E. M.l. M.E. C2S H.E. H.E. H. E. H.E. 98 286 32 7 323 3 17 16 . 2 25.0 34.3 44 . 6 54 . 6 9 ll 62/24'1 l4l/4'>l 2 1 }/4'1'1 85/ 152 lll/5b 1 24 19 l Ob 196 . . .. .,. 4 1J ~~ 27 0 168 / 53 4 166/46 7 180 / 282 18 /1'1 735/l254 . . .. . 11 5 40 14 lll 55 11 8 l3 0 0 0 . . RACKGROUNO E OIP S 2 P/Bl PS 0 0 0 0 0 0 0 (a) .1 ut. L2 3 1177 lb/34 (; . u5> t. 0 2 556 3/l B~ .l (l t. ~2 ! 56 77 2 62/3 l7 . 2/ t. u3 27 124? 12 1/ 500 • 1St . (•3 1 R2 1 78/261> 20311 l446 2130 . 045 t. 01 3t•50 H58 2633 t ess b l 1b 1 4 1/70 1 131 8 3/ 5 78 915 0 . 04 Lot. Gl . 045* . 0 1 20 1278 69/560 10 ~5 69 188 / 961 • t2i. u2 13 151'1 65/565 .L Ot . u2 482'1 4394 4 0~5 280 /1 06 7 .30 t. 0 3 346 25 1 2 1'>1 80/55'1 . 2a. o 3 71 2436 245/ 68 1 238 c 0 0 0 0 485/1819 126 /1ll2 26 / 935 l/618 l/654 tbl 3203 340/772 32j 8 4'1 3 1648/2069 2t 337 94/183 283 ~544 '>47 /136 5 u 333 136 / 231 2. 711 2SOC 868 1 7141> 5276 760 /1437 2 .1 112S OC 2~8 22~ 24S •.45i.05 4 .1 A2S DC 1889 R36 5193 154 11 662 4.1 ' A2S 34.4 1 3'1 175 141/295 5. 4 A2l 32 11 65o 6512 1 338 /1459 L. O!i4 t.Od4 L. OlliJ l. 01!0 1. 078 c 1. 2 1.2 1. 2 L. 2 1. 2 CONF I G 2 3 4 5 eLA8 P• Eo PT TABLE ~£11 ~Ep c.,. . . . .. s .14~ .!44 .1 02 .1 02 .1 0 1 . G78 . 0 78 . u>2 . C52 . u57 . 053 . LD L . 05 7 . 053 . !46 . 062 . G5l . ll'JH . 065 . 05 1 . \·98 . 065 . 045 . 055 . U55 . os5 . 0'>5 . 051 . 0£9 . 02d .o.n . 5~vt . O L3 . C•'i'I ±. CLS . l.v t. u t ; . 42j± . ul'l . 23lt . O,b . 054 ±. U26 .11 3±. 0 13 .t 3 !±. 0 12 . Ol 2 t. u24 . 25l t. O l ~ . U·Ib i. Ol 4 . 004 ±. 0 1'1 .2 21 ±. 0 14 . oo5 ~o. u t 8 . '134 . '177 . 932 -.OOl t. 075 •. 432 . ~34 .93 5 .'/35 . '171 . '1 77 . 041 .08 8 . u'IO . 92 7 .o l9 .~'15t. u ll .L 03 t. l•l3 . t2 lt. Ol4 .4 2u t. Olt . 248 t. U25 .2'17±.ul4 . <2~ t. O l 2 . u5 lt. 'J04 . 05 7±. 00 4 • u36t. I)U3 . ~ 7h. •)U~ . Lli2 :t . L'Ll~ . U35 L (•U4 .v7e t. ?u'> . c 76 t. IJ05 . 55l! t. Ol 2 .35'-H. Oll .1b£, t. t)Ub . C82 t .f,v4 3U 31 jl 3J j4 2 '1 ·"'' 25 • 26 27 24 £3 22 l 'l <l' 21 LO l7 l& ~~ 14 l3 12 " b 2 3 4 I' I . 04 7 .1 32 . 0'19 . ~ 7 6 . Ol 2 t. 0 l 5 .L bvt . Oll 7 .o4t- . c<u . oao . 929 . 003i. Ol3 .302t.OLC .305 t. 00t • 8 .4 9~ 1. 049 .)091. 04 4 . 046 . C92 . Cilu . 929 . 045 .~9 1 .003 . '128 -. Ollt. 02 1 . 511 t. Ul5 .>6L~. V l 3 Lu . 045 . 09 1 . (Jt! 3 . 928 . U04 i. 055 .3l'>±. 0 4Z . 320t.0Jt • ll . 040~o.o t7 .02lto. Ol6 .l b li. 0 l 0 .1 95 +. 024 .3L 5t . u t 2 .L 6H.03~ 'IT c•• Ce "'.976 re . 234t. 02R .l e3 t. Ol 2 .047 .13 3 . ~9 7 .047 .133 . 097 . '176 . 04 7 .1 32 . 0 ~~ .976 . ll47 . 093 . () 7~ .~ 29 .047 . C.93 ~ 0 7 8 . 929 ?zp I N 0 1.4 1• 5 1. 1 1.165 1. 5 1.1 27 l.) l. Ou2 1. 5 o 86fo 1. 5 . 601 61 62 63 (,') 71 7 () 66 67 61i 64 1. 5 1. 'l 1. 4 1.4 1. 4 1.4 1. 4 57 58 5';1 f>O 1.149 1. 050 1 . O::>G . ':IJ4 M. E. li • C o H, [ . 1-1 . [ . 1·1 . E • t, I • A 'J l o 7 '"' C' • ., • 4•J3 '1 '-1 , 7 .43 2 1 I 4 . 4 ~. E . H. f: . H. t: . ~2 . •) e <0 . l vt e L = M. t.: . 47 2<; l <J3 1H l 78 3d 54 129 13 C2S M. C. 33 57 62 16 8 140 CiS H . t: . 2273 I 35 42 74/2'l 2 1 'J5 / 51>6 '•8 / / C2 2 1/23 6 6 / 6 49 \) l) ( b) 0 u l 5v4 0 14 ~ 1 I 5 t,; ~ 25/392 D/41!1 4/2 l6 0 74 L 14 dZ L 4 J6 ltl'J 7 14 11 0 (J 39 73 161 0 •. 00 4±. 002 1'-J'-13 0 /5 43 3'1U6 0 451& 0 l) 3864 17 tl5 1R5 7 34H ?8413 74 8 'l40 463 I 33:..>4 ')4 J j 4Cv7 1 1a 1% !12 ') 2 2 'I 7 l!J 11 !3 5 5 u 4<~ 1.}1) 171 (, 9 II fj u 50'-IJ 4'-J'it> "l 8 30 UACI\ u -:flUNG II I J> S t P/BIPS tl 6 . OfJ:t. u3 . U'J.t. G3 • • . Ol-'i .t. U2 .u4L:t. 0 1 . Gt.6:t. r 1 '•C!.J c; ~ ,, .1 2 ±. 0 4 113 0 2 0'-JZ . ()42 ±. 0 1 . CI 46:t:. 0 1 . •J46:t . 0 1 . l!6 :t:.U2 L249 . u 4U. v 1 . u4t t. U1 ( , I.J9 1 . 065 .t.. G2 "1\; 3 1 7 H. 1 5 13 1 b66 .1 2±. u 4 • • • • • • • • • • • • l/1 5•) 2 /1 6'-1 0 0 ':i /1 63 2/l 67 2/141 l) u (J I) -- - - -- - · 1/ ':iil2 f7'i 6 • .U4 2.t. 0 1 • . v42 .t. tH • • G'•o :t.. C1 0 'I J73l c 16 7 221 1'-I U ,.., t--J . :. : . H. E. C2S h. t . H. C . ' . 416 11 5 . d .341 1 ~0 . 5 . 936 42 . 6 . 8 12 53 . '1 • RP 5 l. '1 . 6 1C 7(, . 9 . 472 1 Ll. 2 42.6 (').6 23 . 'l 32 . i' 32 . R l. l-:11 1 • 11 1.4 1. 4 1.4 1. 4 50 51 53 54 55 11. r . M. t . " . E. . ~. E• ,.,, • E . M. E. l4 . r, • 4 50 1<•2 . 7 • 4'.>C 1i.' 2 . 7 . 4v0 117. 2 • 36C 113 · '' .33 2 15 1. 3 • ? 't l I •3 1. 3 1.4 1. 3 1.4 1. 4 41 42 43 44 45 46 l" . c. /1) . ? 7G. ~ • (;) 2 ~:> . 2 • 7 ;A I•J 1 • "j 4:! . H :H 38 4C 1• 3 1. J 3 L7 . '-173 • HtO , H ( (: 1. 1 36 c P/b!PS E tl I t-> e> --- --· ---- - -·---- - --·- - - - 224 1319 ts/2 13 H. L. 16 ·u 0 / J(d H. c. . '1 7 (j H. [ . 4 4fl 71) 11.J1t H. E. 'J Bu. a CONF ! G 35 p. Eo l' f . 0:) 1 . 04 1 . 0~'· .03 6 • (l:>6 .0 52 . 0 45 . 045 . 036 • L' ~9 'lcp c7f 55 57 5e 59 6lJ 61 62 . l20.t. GC4 , (,21:1 ±. 1)0 4 . v 15 .t, Ju2 • ,, 15~ . 'J (J 3 , ._, 3.?!:. \lv3 . u 31±. 0 ·J3 . v l 6 :t. (JU5 29±.1)0 ~ . (, 1 R± · 'IU'• , l; .1 23.t. 0l(; • 1 l 1 .t • i) 1-4) • v 44:t. CO t. . l26.t. Ov4 . vJZ :t. OUS 5(, 51 53 . £:27 t. Gl3 . 2':i'J:t:. v l4 .1 2 7;t. (J0 7 . l'':i3 ±. vus • (; 4 'H. 00 5 70 71 6'J 65 66 67 68 63 ~4. 41 4L 43 44 45 46 4L J t. 35 36 J7 PT • C 3 1 :t: • L' '"' 3 . C: 4G±.003 . l.J':i .t. \) 0 4 . C32.t.0u4 o L• )2 ±. ( '()"i . d 8 t. L0 2 -.1 td .t. 0 12 . C'J "Tt. •)u6 . v 76 .t. d 13• . l 3'J :t. ·lv4 • v49 t. (·04 I - N correct for this the fraction of counted particlee (the unecattered ones as well as those scattered from the pole face e) pae sing through the fane wae meaeured (at the spectrometer central mornentw·n, p GeV/c, OLAB 0 = l . 036 = 16. 0, and E 0 .:: 1. 2 GeV) and found to be 0 . 043! . 008 . It is aeeumed that this fraction may be subtracted from all the counting ratee taken with the fane off to correct for thie condition. The background (empty target) counting rates were not alwaye measured but could be estimated uaing the curve given in Figure 5 obtained from the n"\eaeured points. (/) ~I A? I T II II 1.3 1.4 X II 1.2 0 0 GEV k = 1.1 0 .... ~ II A" T I 0 20 80 DEGREES 100 120 The Background Counting Rates Bcm • 60 Figure 5 . 40 140 160 180 0~~---L--~--~--~~--~~-L--~--~--~~--~---L--~--~--~~ 4 cr <( 0 I- a.. 6 .J 14 oo ll..Z a.. ::> ~0 wU 1-Z >-I- - ~~ u..cr _jl::><l ..JW I- cr~ <(~ (!)~ w I- 201 22 t- T w I N IV . A. DATA REDUCTION CROSS SECTION FORMULAS The observed pion counting rate. C 7r, may be expressed in tenna of geometrical and kinematical quantities and the cross section, CT (k , 8 ). C7r c ffffff o- (k. 8 ) a A 7r NH N(k) n(x, y ) where .a • A 7r for the pion absorption (aee = correction Appendix D) NH z: the effective number of hydrogen nuclei per unit volume N (k)dk • the number of photons per E IP with energy k in the interval elk n(x, y) = the relative beam intensity at the target an anL d .UL correction for the pion deca.y lnc:luding the muon background (aee Appendix W ) tranaformati on from c . m . to l ab . solid = the angl e • laborato ry solid angle incre1nent • The limite on theae integrations are functions of the variables in the intearand snaking the detaUed integration quite cornpUeated. o-(k. Q) h the unknown quantity that is to be meaaured in this experiment, but only the average value over tl'le limit• of theae integro.tion6 may be obtained. Actually many of the quantities in the integrand are nearly -2.S· constant and can be replaced by their avera1e value• . The following simplified equations containing average and intearated quantities may be used. where w a normaUzation factor (see section B ) = the average value of the photon epecti"UD'l (see •ection B) the mean photon energy = the aver~gt) value of G B. the mean path length lor the photon beam through the target anL ap • the average aolid angle of the epectrometer • the mOinentum dispersion of the spectl"orneter = the • pectrometer central momentwn THE CALCULATION 1. an ok o~:- K Hydre~gen Density The liquid hydrogen target b operated at 1/2. 9•i above atmoapheric preseure at its boiling point, which corJPesponds to a denaity of 0 . 0707 g/cc. The background rune were taken with hydrogen gas at the same temperature and pres aure inatead of Uquid in the target . The gas density h 0. 0015 g / cc . The effective hydrogen density (lor the full target minus bac:kgrOWld rune ) ia thu• Pa = o. 0707 - o. 0015 :a o. 0692. g / cc . Using 1 . 008 for the atomic weight, M., and 6 . 02.4 x 10Z 3 for Avogodro' e number, N , the density of hydrogen nuclei 0 23 0. 4 1 36 x 1 o NH aa nucl ei/cc is obtained. z. The l?hoton P opulation In the equation £or K, the lnteeral ol N(k) over the accept- ance region of the spectrozneter has been expree sed in terms of where W ia a normalization factor such that The measurements of Vi and B(k. E ) aFe diecuaeed in Appendix V . 0 D (k. E 0 } and k were calculated using a simple computel' program which averaged the photon spectrum, B(k. E lutian function of the magnet . 0 ), over the momentum reao- The resolution functions used wel'e taken from the results of the decay correction calculation (see Appendix m) except t11e one for the high energy configuration using Al and CZL which wa& taken irom the magnet report (9). 3. The Effective Target Length, T A computer program written by J. Boyden (6) was uaed to average the target thickness weighted by the beam density. Thia pro- gram contained within it the spatial dbtribution of the beam. n(x, y), (meaaured by J. Boyden) which haa a aUght energy dependence, and evaluated the integral T c f ff *' y) dx dy ds where tho limlta are determined by the target size and posttian. The remaining non-kinematical quandtiea are diacusaed 1n the appendices: R in III. A .,. in D. and the spectrometer acceptance, ~ ~r. p ,u, in IV. 0 The values of K and each of. its separate factors are given in Table 3 in the next chapter. V. THE RESULTS The differential cross-section and all the quantities used in ca.lculating it are given in Table 3. Also given ie the differential cross sec- tion averaged over all the configurations used at a particular 8 and k. This averaged value has also been interpolated to k values of 1. 1, l. 2, 1. 3, and I. 39 GeV for convenience in handling the data. The differential cross section for each of these k values is plotted in Figure 6, along with a curve which will be discussed in the next chapter. In Table 3 aud Figure 6 only thoee statistical errors which ariee from the counting rate and efficiency measurements are given. M ost of the systeunatic errors are estimated to be only a few per cent (see Appendix IV). cation of the effects of an error in E 0 , the change in the calculated dif- ferential cross section, due to a Zo/o increase in E and is given in Table 3. As an indi- 0 has been com.puted TABLE 3 The Results AU the ~ties uaed In calculating the eros • •ec:tlGDa from the cOQDtmg rate• are given here. The hydrogen dell•ity NH • o. 4136 x 1013 nuclei/cc was u•ed for aU pointe. The point number aa in Table~. The •peetrom.eter angle in degree•. The plan center-af..mcane!JDtW'n angle Ia degrees. The brem••tra.bluna ODd point energy tn aev. The spectrometer eenbral momentum ln GeV/e. The pi011 momentum at t:be aource corroapcwUng to p 0 in OeV/c. The mean photao enel"gy In Ge V. R The decay correetlco. The ahaozoption correction. ACC The •pectro:metez ac:ceptance, ( ~ n ) ( ~ p/ p 0 ). The effective length of the hydrogen target in em. The mean value of the phctOD apectrwn, B Ck. E ). in 0 the J'ange used. a w c ak/ ap) c an 1 an LAB) K a- • C 7r The plco cOWlttag rate in plona/BIP taken from Table l. ~ The .fractional ebaD.ge ln the calculated value of a- when using a value ol. E ~larger than the ane ahown in thb 0 table. Tho eneqy per BIP in GeV/ BIP. c 71" /K (See text) -30- (j (j The dUfercmtial croaa aection in fL b/SR.. Tbe d.Uferenttal erose sectlGD ln fL b/SR averaged over the vadOGa canftguratiau uaod and interpolated (o:r eztrapolated) to the values ol. k shown. 10. 0 15.0 !5. 0 20.0 20.0 29.5 44.5 ,<;.5 74.4 ~ 7.5 8 7.5 1.2 5.4 8.1 8.1 10.9 10.9 I 6 ._2. 25 . 0 34.3 44.6 54.6 54.6 us . 7 1<:0 .0 1.2 104.4 135.1 1.2 194.4 135.1 1.3 117.2 144.1 1.2 126.5 15 0. 1 1.3 152.1 165. 0 1.3 7 B 9 1::> ll 12 13 14 15 16 17 1a 19 20 21 22 23 2'4 3.1 3.1 5.2 5.2 10.6 10.6 10 . 6 16. 0 16. (' 24.5 30 31 32 33 34 1.3 1• 3 1.3 1.3 1.3 1.3 1.1 1.3 1.3 1.3 6.0 6. 0 10.0 10.0 20 . 0 20 . 0 20 . 0 30.0 30 . 0 4'>.0 1o.o · 10 5.1 1.2 25 26 27 28 29 1.078 1. 0 72 1. 0 72 1.062 1.062 1.084 1.084 1.080 1.080 1.078 p. 1.082 1. 0 76 1.076 1. 066 1.066 1.088 1.088 1.084 1.084 1.082 Jt 1.099 !.099 1.096 1.096 1.099 1.100 1.1 00 1.098 1.098 1.098 k ACC .,o-• .54 1.08 1.95 1.95 1.08 .820 .54 .820 .54 .820 .54 .861 .54 .861 1.08 A .974 .820 .~52 .861 .946 .861 .946 .661 .952 .861 .948 .948 .948 .948 .952 R 1.160 1.160 1.130 1.110 1. 062 1.183 1 • 18 3 1.179 1.179 1.160 .386 .363 .323 .716 .60 3 .509 .427 .427 1. 090 1. 090 1.0 87 1.088 1.090 .906 .938 .928 .911 .'127 .861 .90 7 .90 7 .90 7 .907 .87 2.75 2.75 2.75 2.75 7.26 2 7.262 7.262 7.262 7.266 7.262 7.262 7.26 2 7.262 7.2 62 7.262 7.262 7.262 7.262 7.262 7.262 7.262 7.262 7.262 7.262 1 .865 .862 .d62 . 854 .886 .852 .850 .847 .841 .830 .851 .851 .853 . 853 .850 .850 .8 50 .852 .852 .852 B 3 3.32 3.29 3.23 3.16 3.16 3.38 3.37 3.36 3.34 3.32 3.38 3.38 3.38 3.38 3.38 3.38 3.38 3 .38 3.38 3.38 G .891 .893 .894 .895 .891 .867 .877 .876 .876 .876 .871 .864 .867 .866 .864 .870 . 8 74 .871 .872 .867 w •10., .284 .821 .675 .539 .523 .938 .884 .BOO .702 .606 .258 .537 .974 .964 .532 .259 .260 .259 .272 .543 K •to-2' A .03 5:t.004 .078±. 005 .076±.005 .082±.005 . 0 73±.005 .Ou63 .00 62 . 0059 . 0008 .0179 .595±. 0 11 . 0004 .550±. 0 12 -.0007 .359±.011 -.0027 .166±.C06 -.0074 . 082 ±. 00 4 -. 0 154 .160 ±.011 .0000 .305±. 008 .ooo 1 .5 09±.044 . 00 11 .560:t.013 .0009 .j20t.036 -. 0003 .183:t. 012 -.0004 ~161±.038 -.0004 .161±. 0 10 .0006 .195±.024 .0006 .3-t5:t. C•12 . 0005 c7r 1.164 1.164 1.114 1.134 1. 06 7 .955 • 9 55 .949 .955 .949 1.1'19 .953 1.1~ 8 . '149 1.196 . 946 1. 2 vt• .949 1.1 97 .~4 2 1.187 1.1'19 1. 1 B 7 1. 1 9~ 1.183 1.199 1.183 1.1'1'1 1.164 1.19R .861 .820 . 861 . fl6 1 . 861 .54 1.0u 1.95 1.u& 1.95 (a) 7.266 7. 266 7. 266 7. 266 7.2h6 3 .59 3.59 3.60 3 .60 3.59 . 839 3.59 . 840 3 .5 9 . 8 19 1.60 . H36 3.60 . 833 3 . 59 .820 .54 7.266 . 8 40 .82 0 .54 7. 266 . 8 4 0 .861 1.08 7.2 66 . 84 1 .861 .54 7.266 .B40 .861 1. 08 7.266 . 840 .262 .499 .9 2 1 .5 07 . 8~ 7 . 8~1 .256 .256 .534 .268 .525 .880 . 871 . 8 7'1 . 878 .880 .bBu .880 .sa o .88 0 .1 03±. C1 3 - .OC7 2 . 22 1±. u 14 -.0067 .4 ?C :t. C16 -. 00 72 . 248 ±. 025 -. Ou~3 . 297 t. 0 14 -.012 0 .113±.013 -.0 061 .131t. u l2 -.0063 .25 2 t. 0 1 8 -.0062 . 098 ±. 019 -.oo66 . 225 t. 0 12 -.Ou67 • 391 1.087 .899 .9 0 7 2.75 7.262 .850 3.10 .896 .471 .051±. 00 4 -.0022 .368 1.089 .~02 .907 2.75 7.266 .886 3.06 .892 .420 .057t. OG4 .o 177 .327 1.0'10 . aao .907 2.75 7.266 .885 2 .98 .892 .352 .C36:t. u03 . 0 174 .721 .608 .513 .432 .432 1.2 1.036 1.040 1.096 .945 .861 1.95 1.2 .975 .979 1.095 .939 .861 1.95 1.2 .895 .900 1.0':14 .'131 .861 1.95 1.2 .803 .807 1.092 .'J21 .861 !.95 1.2 .716 • 721 1.090 .908 .861 1.95 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 5.0 5.0 7.5 7.5 !0.0 2.7 2.7 4.1 4.1 5.4 2 3 4 5 6 Eo e 8LA6 PT TABLE 1.93 ±.) \) 4.23±.26 4.56:t.17 4.8'1t.4'1 3 .4 5 ±.1b 4.42t.51 5.12t.47 4.72±.34 3.66t.71 4.29±.23 1. 0'1 ±.09 1.3H. 09 1.02±.1 0 1.24±.13 .94±.06 1.12±.07 1.5 2 :t.09 1.4 0 ±.09 6 .35±.1 2 6.22±.14 4.49±.14 2.36±.09 1.J5±.07 6.21±.43 5.68±.15 5.23±.4) 5 .81*.13 6.02±.68 7.08:t.46 6.2 ±1.5 6.23±. 39 7.18:t.88 5.8G±.22 cr 4.56±.17 3.41±.16 4.21±.17 4.5Gt.31 4.76±.32 k = 1. 2(;() l. 0 4t. 09 1.33:t. O'I • 9H. 10 1. 39±. (,6 1.27±.06 .t12:t. 06 1. 0 4±. 07 6.28:t.l2 6.09±.14 4.3 5 ±.14 2 .24±. 09 5.7H.l3 5.62±.14 5.67±.20 6.35±.36 7. 00±.44 k: 1.100 (F I UJ .41 6 .34 3 1 15 . & 14 5 . 0 1.4 15U . 5 165 . 0 1. 5 62 63 9 '~ . 7 114.4 7() 71 66 67 btl 69 1 35 .1 1. ') 1. 5 14 ~ .1 .4 93 .4 32 . ~29 1. 294 d 30 1. 2~7 . '1 15 1.2'14 . '1 15 1. 28 4 .~ 3 4 1. 28 1 . 9 15 1.298 . 94 7 1. 29 ~ . Y4 5 1. 293 . 940 1. 295 . 939 1.2 8 7 . •13 0 1 . 1 86 . 9 1 3 1. 1 88 .~ 2 8 1.1 8 3 .900 1.1 ~3 . b 98 1.1 79 . 88 3 1.1 ~ 7 .~3 5 R A.,. ACC 1. 95 1. 95 1. 95 2 .7 5 1. 9~ xto-'f 7. 266 7. 2 70 7. 266 7. 270 7. 270 7. ?~6 7. 266 7. 266 7. 266 7. 266 7. 266 1 . 8 20 . 8 19 . tlOA . 84 8 . gc2 . 85 1 . 8 41 . 88 4 . 8 35 . ti8 4 . 88 4 . 824 . b08 . 808 .7 80 . 856 8 . 8 61 . 8 7 7. 2 70 . tl 4 8 . 86 1 1. 95 7. 2 70 .755 . 8 61 . 8 7 7. 27 0 . 8 45 . 90 7 2 .7 5 7. 2 7 G . 8 4 5 .9 ~ 7 2 .f 5 7. 27 0 . 929 . 6 55 1.-1 s 1. 2 10 • 661 1. 9~ 7. 2 7 0 • 861 1.9~ 7. 2 7 0 . 861 . 8 7 7. 2 {0 . 8 61 1.95 1. 2 10 . 90 7 2 .7 5 . 90 7 2 .7 5 . 907 2 .75 . 90 7 2 .7 5 .9 0 7 2 .7 5 . 90 7 2 .75 . 06 1 . '12 4 . 86 1 1 .1 95 . 92 4 . 86 1 1.1 '1 1 .41 0 . 86 1 1.1 !18 .Y3 R .90 7 1.1'1 ~ 1.1 9 6 k w •to'I 3 .7 b 3 .7 6 3 .7 6 3 .70 3 . 60 3 . b2 3. 81 3 . 80 3 . 80 1.11 . 87 1 . 6 71 . &7 5 . 8 77 . 8 79 . 8 73 . 8 74 . 872 . 875 . 8 71 3 .4 6 . 88 7 ~ . 38 . 8 8 8 3. 38 - ~ 8 5 3 .31 . 888 3 . 2 4 . 886 1 .17 . 88~ 3 . 58 .879 3 . ~ 7 .87 '1 3 . 5 7 .~79 3.5 S . 8 7 8 3 . 5 1 .88 6 G .1 62 t. 0 12 . 05 7t. 006 . 076 t. OI 3 . 0 35 ±. 00 4 . 0 4 9 ±. 00 4 c1T -. 0 190 - . 03 15 - . 0 31 5 - . 0 621 . 002 4 .A . 30 1 .516 . 256 . 65 1 .471 . 652 . 825 .f Jb .343 . 64 2 -. Gl u 7 -. 022 4 -. 0 306 -. 0020 - . 0 434 . 020 t. I)0 4 -. 00 18 . 02R t. 00 4 -. 065 1 . 0 15t. 003 -. 00 4 0 . 0 3 5 t. 003 -. Oe 4 2 . 032 t. 0U 3 - . 0 16 5 . 22 7t. v l3 . 259 :1:. 0 14 . 12 7t. C0 7 . 053 ±. 005 . 0 49±. 005 . 63 7 . 03 1t. V03 - . Cv06 . 50 ~ . 0 4 0 ±. 003 -. 0082 .498 . 039 t. 0(• 4 . 0 17 4 . 43 1 . 03? t. lJli 4 -. 0 12b . 3 7 2 . 032 t. 00 3 . o 171 . 330 . 0 18 ±. 002 . o 170 .7 68 .66 3 .66 3 . 5 47 .764 K xto-l'f . ~4 5 . 44 7 1. 3 ff . 431 1. 37:. • 'J( ~ . ~ 10 1. 390 . 9 4 2 1. 38 7 . '13 4 1. 3 ~2 . ~?0 1. 3~ 1 • ~ 12 1. 3~3 1. 95 7. 274 1. 95 7. 274 1. '1 ~ 7. 2 74 1. 95 7 . t. (4 2 . 75 7. 2 7 4 . ~32 • 798 .{ 8 9 .7 6 7 • f 28 4. 02 4. 0 1 4 . 00 3 .'18 1 .'1•) . 8 3 6 . 5 43 . 12 3t. ~ 1 0 - .033 4 . R36 . 68 1 . 1 Jlt. v 1G - . 0 4 ':> 7 . u36 . 5R 4 . 0 4 4 t. OU 4 -. Ob02 . il 3 & . 471 . 026 ±. 00 4 - . voVO . w. s . 5~8 . 032 t. 005 - . v 1 38 (b) . 90 7 2 .7 5 7. 7 f4 . 8 13 3 . 82 . R4 S .4 3 1 . ( i''H . OC5 - . 026') • 40 7 2 . 7 5 7. 2 74 .7 9 3 I . 7'; • 8 4 5 . 3:.B . ~ 1 R ~. 00 4 -. 0 3 f 5 . 6 55 . A6 1 . 86 1 .86 1 . 90 7 .4 2 1 1. 2b0 .'10 4 .40 7 2 .7 5 7. 2 70 . ~ 14 3 . 5 3 . 8 8 0 . 399 . U3 1i. uU3 - . v255 .347 1. 286 . 884 . 90 7 2 .7 5 7. 2 74 . 8 79 3 . 40 . 8 49 . 2 99 . 0 16 .t.. G05 . 0 147 . 940 . 8 17 . 8 17 . 6 14 .47 5 26 . I 'JO . O 1. 5 1.16 5 1. 20 7 32. 0 60 . 0 1. 5 1.1 2 7 1.132 4 1. 6 7 4 . '1 1. 5 1. 002 1. 006 . 866 . 8 71 52 . 7 '<O . (J 1. 5 . 60 7 R0 . 9 l.c.O . O 1. 5 . 60 1 . 936 . 8 12 . e 12 .61 0 .4 72 1.4 1. 4 1. 4 1.4 1.4 6~ .54 6 .454 .4 5 4 .40 4 . 365 .337 . 9 78 . 8 74 . 8 74 .763 .636 p~ 3C . I) 1.4 1. 191 1. 2 31 4 ~ . 0 1.4 1.149 1.1 5 4 60 . 0 1.4 1. 050 1. 0 5 5 60 . 0 1.4 1. C~O 1. 0 5 5 74. 8 1. 4 • 9 34 .938 • 541 .4 50 .4 50 .4 00 .360 . 332 .973 . 8 70 . 8 7l) .7 58 .6 32 p. 4 2 . 6 74. 9 5 3. 9 90 . 2 5 3. 9 90 . 2 76. 9 1 15. 0 1CI. ? 135 . 0 15. 6 2 3. 6 32 . 8 32 . 8 42. 6 50 51 ')3 54 55 1.3 1.3 1.4 1. 3 1 ~5 . 0 1.4 165 . U 1.4 120 . 0 135 .1 1 35 .1 14 5 . 0 1.3 1.3 1.3 1. 3 1. 3 Eo 57 58 59 60 61 tl 4. C 102 .7 10 ?.7 117. 2 13 3.4 15 1. 3 41 42 43 44 45 4b 33 .7 60 . 1) 4 3. e 75 . 0 4 3. 8 7 ~ . 0 55 . 2 90 . 0 70 . 3 10 7. 0 35 36 37 30 40 e 6JL A8 PT ';1:. 08 . 6 fi.11 . 5 •. t.1 0 2 . 27 ±. 21 1. 6 3:1:.1 4 . n t. o6 . 5'J t. O'i . <; Bt. C'J - ~ lt.1 3 •7 . 6 '>t.l 2 . 5 lt. 0 7 . 5 ·H. I)8 . '> <tt. O'> . 68 t. 0 7 . 6 7t.11 . :.>C t.1 L • :)t\.t • I 'I 2 . 27 .t.. 2 1 1. 6 .H. l 4 .7 6 t . .... 6 • S:> t. •.• 9 k = 1. 3'>0 .7 4 t. Ob . 52 t.I H . 6 7~. r:r . 5 4t. (i~ .5 6 t. (J~ • 7 H. o.. / 1. 66 t. C: f 1. 5~ t.1 5 • 77t. Vd 3 .47.t.. 2 4 3 .1 2 t.l7 k = 1. 3v(J • 76 i · ' ~ • 7 2 t. I"•IJ . 8 4t. Oil . 52 .t.. C· 7 .4!!J: . ( 4 3 .48 t.2 4 3 .1 4 t.17 1. 7 .H. O'-J .7 8 t. v 7 .74t. 08 . 1:!6 ±. 08 • 54 t. 0 7 • 7'1 ±. 0 1 .4 6 t. 0 4 . &lt . Ob . 6 H. t~ .64t. O~ . 88 t. 0 8 2 . v 7t.1 5 cr 1.1 :>t. 2v . 6 4t. Otl . AS t. O ~ 2 .11:1:.1 ~ cr I I (.)J 1\) -33- Flg\U'e 6. Center of MCIDlentum Angular Dlatributiona of Plona from the !leacUc:m. y + p ~ 1r + + o at the Following Laboratory ?bocon ~ergiee , k: !!l (;, k D 1.1 GeV k a:: 1.~ GeV k • l. 3 OeV (d ) k • 1. 39 GeV The eolld curves are least equaree fits of the Moloavcelk type a- (Q) • (1 - f3 coa 9) -2 with N • 6. P alynomlal ilta are poor in comparia(ID with those of the MoravcaUt type. Not shown are some artificial data polntiJ uaed 1n the fitting proceae to keep the flt "aenatble" in a regi<m of few data points. The pim nudeOD coupling ccmatant as it enters the formula for the rcuddue at the piGl pole waa alao used aa input data in the fittf.nJ procedure. (See Table 5.) The errOI'a shown &l'e those ol a atat:Ut.ical nature cmly. -34- 0 co (J) 0 0 w w 0: (.!) w 0 0 0 co E u Cb 0 (.!) 0 N '(8 I 1'1='>1).0 0 -35- 0 CX) 0 0 I.D 0 ~ 0 C\J 0 0 0 (/) w w ct: (!) w 0 ..0 0 CX) E u CD 0 I.D 0 ~ 0 C\J 0 0 ' (8 ' 2 "1 ='>I ) .£) -36- 0 co 0 0 (f) w w a: (!) w 0 u 0 co E u Q) 0 <D '(8 '£'1='>1).D -37- 0 co 0 <D 0 ¢ 0 N 0 0 (f) w w cr <::> w 0 0 "0 co E u Q) 0 <.D .. 38VI. A. ANALYSIS GENEllAL At energies much above the fb•t resODance no satidaetory theo- ry of piCIIl pbotoproduetion as yet exieta. It b thus necessary to use a phenomenalogieal analyde to extract what informa.tioc aoe can fro:m tho data. Several methods that have been u.eed previc:,.uly (e. g. .Boyden (6) or Dl.xon (5)) wiU be dbcueeed tn ~is chapter. eee They are polynomial fitting, multlpole fitting, extrapolation of the erose section to 0 0 0 B. MORAVCSIK POLYNOMIAL FITTING AND THE COUPLING and 180 , and integration to obtain the total erose section. CONSTANT A polynomial of the form cr (G) • (l - {3 coa G) -Z has been ahown by Moravesik (10) to be "uperior to a polynomial with· 2 out the retarda.Uc:m denominator, (1 - {3 cos Gf , when fitting charged pion pbotoprodQctton data. Here {3 and Q are the c:cmter ol. momentum veloc:Uy and angle of the pion. respectively. A computer }Wogram written and described by Boyden (6) wae used to perform a least equaree fit to the data lor varicus orders, N. Table 4 eCJDtaine the results of thb fitting program. and the curve• for N c 6 are plotted with the data ln Figure 6. The values of the reeidue at the pion pole and some estbnated points given In Table 5 were also used in the leaat aqu&roe fitting. When the residue at the pion polo waa not uaed ae a ·39TABLE <6 Lea•t Squares Coeffletente The l'eault. Ott tbe least •f!U&ros fits to the data al'e lieted here. The data includes the reeiwea at the pole• and the estimated point• given In Table 5. The fittina fu.ncdcc ta ol. the torm (j (8) • (l ... /3 coe erZ as euggeeted by Moravc•ik (1 0)• .il addldCD the number ol. degree• of freedom. D, tbe value ol 2 2 X , the ps"ciDabWty, P , ol larger X • and the taal croe• aectlcm.. (jT' are given.. The square ol. the plOD•n\1CleGD COQpliDg COUtant, r, was calculated uotq an ...uapalatiac of the fitting CtU"Ve Cobtained without lnc:l'GdiDg the l'cetW.. at the pale) to the ploa pole. - 40 - TABLE 4 k= L. 1 ~ 5 6 6~ 1.27~0.04 1.11~0.04 BJ 6z 63 6¥ 6,- -0.22*0.12 1.25±0.26 0.80t0.17 2.21:t0. 29 -10.11:t0.68 1.43:1:0.40 7 .9l.tO. 70 -3.39t0.40 -4.~3~0.17 -0.04:1:0.36 2.28.t0.20 ~ s.,. 6€ 0 Pz 11 93.91 <0.01 <r,- 31.16t0.34 x• f 0.136~0.011 k= "\ 10 22.70 0.013 0.080:t0.013 31.90t0.35 7 1.09:t0.05 0.59:t0.20 3.11:t0. 54 -9.70~0.11 -1.65tl.61 a~ 8.93~0.1l7 6.04~4.28 -0.9H1. 31 -1.49:1:0.75 -0.6H1.99 -0.90t2.85 -0.35±1.63 8 18.75 0.017 9 16.60 O.C3 0.053±0.017 32.10±0. 36 1 8 0.53:t.0.04 -0.10t0.09 2.05±0.24 -3.41:1:0.17 -1.47t0.28 2.4H0.18 0.56:t0.05 -0. 3L.t:0.16 1.92±0.25 -2.42:t0.66 -1.83:1:0.37 1.49:1:0.62 0.59:1:0.38 0. 59.t:O. 05 -0.25±0.16 1. 32:1:0.54 -2.42:t0.66 0.05±1.53 0.60±0.94 -0.83:1:1.19 0.95:!:0.75 9 34.48 < 0.01 0.061:1:0.016 18.34:1:0.37 8 32.08 <0. 0 1 0.074:t 0 .020 18.24:1:0.38 7 30.47 <0. 0 1 O.l Ol:t0.028 18.76:1:0.38 0 .69:1:0.06 -1. 0 L.t:0.25 0 .26.t:0.60 4.39.t:l.81 0 .03tl.5J -15.05t3.9a 6.04:1:2.07 u . o 1±2.60 - 6.36:1:1.57 6 14.10 0 . 0 25 5 6 7 0.480c0.04 -o. 37to.n 2.12:t0.29 -2. 82i:O. 2 3 -1.6U0.46 2.2lt0.28 0.50*0.04 -0.49:1:0.17 1. 97:1:0.33 - 2.05t0.79 - 1.81.t:0.50 1.32t0.91 0 .56t0.55 6 10.99 0.09 15.58t0.44 5 9.95 0.08 15.65t0.44 0.50•0.04 -0.53t0.21 2 .12t0. 56 -1.93t0.86 -2.44t1.92 1.49:1:1.04 1.13±1.78 -0. 3 5tl.01 4 9.84 0.05 15.67:t0.45 5 6 1 0.49t0.06 -0.59:1:0.25 2.26:1:0.49 -2.18:1:0.40 - 2.44t0.88 2.4H0.51 0.50t0.06 -0.67:1:0.36 2.17:1:0.57 - 1.68tl. 74 - 2.57t0.98 1.87:1:2.11 o.38t1.30 0.50:1:0.08 -0.70t0.51 2.25tl.12 - 1.57:1:2.20 -2.98t5.15 1.93±2.26 0.8 2 t5.60 - 0.25:1:3.14 2 1.47 0.48 15. (;5±1.13 tl - aa 0 X;. ~L r;. k = 1. 3 N llo a, a, a) a¥ as a, 87 0 xz p c:. k = 1. 39 N ---- 6~ 87 0 xz p c:; 32.09:1:0.36 6 a. tl, 3.09t 0 .67 -9.33.t1.88 -1.57tl.65 5 N s, Bo 6, a, a3 a" 1.09:1:0 .05 0.56~0.26 1.2 ao a, a, a: '\, 6 4 1.56 0.81 14.85t0.90 3 1.48 0.69 1~.05.t1.13 16.43±0.38 -41- TABLE 5 R.eal clues at the Pole and .Eetimuad Pointe A. 1\.eal dueo at the P ole . k c oaQ • (Uaing 1//3 0 . 081 ! 6 . 7~ ) (1 - /3 c oa8)z cr (8 ) j coaQ • (fLb / SR) (GeV) B. r• 1.1 1. OZ76 • 00998 -+ • 00067 l. Z l. OZ46 • 007Sl 1. 3 l. OZZ2 -+ • 00050 • 00581 1. 39 1. OZOl • 00457 -++ • OOO.i9 . 00031 E.Umated Polnts . k ~ (GeV) (d egrees ) { fLb / SR) 1. 3 10 3 . 35 + 0 . 8 1. 3 zo 3. z + 0. 5 1. 39 10 3. 35 + 1. 5 1. 39 30 3. 5 -+ 0. 8 cr (G ) 1//3 -42- data poiD.t, the differential cJ.•os s section wae extrapolated to the pole as wae done by Boyden (6). The pion-nuclecn coupling COQatant, f, to related to the extl'apolated value at the pole (ace equation 1. S in refer- ence 11 ). The value of its a quare (~) obtained from the extrapol.atian i• given in Table 4 . The low XZ. probabWty at k • 1. 1 and 1. Z Oe V can be at- tributed to the large 11 aca.tte.-" of the data points at backward angles. For N 2: 6 the qualitative agreement with the data ia quite good. while for smaller N it h noticeably poorer. than N • The need to go no higher 6 ie coneietent with previous l'eeulte, (S), (6). be pointed out, however, that this is less certain at k • a •hould 1. 3 and l. 39 GeV due to the eomewbat incomplete angular diatributione at these energies. 0. 011. The weighted average of ~ for N • 6 is 0. 07 8 .± This agreea well with the value of 0. 087 + 0. 017 measured by Boyden (6). C. THE 0° Al'JD 180° CROSS SECTIONS The efteet of the pion pole vanhhes at 0° and 180°, making the analy•h at theae point a eimpler. Boyden ( 6) baa carried out auch an analy•is for k up to 1. 0 Cie V without reaching any deiinlte can- cl\&alcna In the regi011 of the third reaonance. from the N c by Boyden. C roaa aec:tiaoa taken 6 Moravcelk lite a re uaed to extend the curve• given This ie ehown ln Figure 7. The data ol Hand and Sc:haerf (l Z ) have been added bec:auae ol. the interesting peak ehown at tlle aec- ond reaonance. The daehed region is very poorly known. The large eta.tietical errore on the data al'ound k = 1. 0 GeV malc.e it dilficult to -43- 20 /- • THIS EXP. 0 DIXON 8 1.5 1.6 1.7 ENERGY, W (GEV) II " I 18 BOYDEN I I I 16 I 14 12 10 a: (f) '.D ::i.. - 8 b 6 4 2 LAB PHOTON 01 I. I 1.2 1.3 TOTAL Figure 7. CM 1.4 The 0° and 180° Cross Sections 1.8 -44see effects at the third resao.ance even a good deal lJUger than thoae aeen by Hand and Scbaerf at the second reacoan.c:e. Thus it le still not poaalble to obtain any de.finlte ccmcluslona abCQt the third reaonance from this analyab; a multipole analyst. muat be attempted. D. THE TOTAL CROSS SECTION The total cross aection, crT' is obtained by integrating the least squares fitting curve•. .,. 1 = cr(Q) •in Q dQ 0 This is included in Table 4. The values from the sixth order curve• are plotted in .Figure 8, together with the results at lower energies (5 ), (6). The peak of the third resonance ie oeen to be very close to k 1. 0 Ge V. The leveling- off of cr , above k 1 • =- 1. 3 Ge V may be an indication of. the fourth reaona.nce. which is obaerved in scattering ex- periinenta (3) at a total c. m. enea-gy of l. 9ZZ GeV. E. MULTIPOLE ANALYSIS An attempt was made to perform a multipole analyaia uelng all of the pion photoprodu.ction data currently available. A high apeed com- puter (the IBM 7090) was \ltUbed in the calculation. fitting pl'O{JI'8m are described elaewhere (13). The detail• of the The specific type• of + data uaed ln thie analysts were angular distributions ol. 7r , the l'atio of .,.- to .,.+ recoil protem in 0 7r photoproductioo. at 90°. 7r 0 • and pbotoprocluc:tion, and the polarization o£ the The Born approximation• for the s-cba.nnel, t-channel (pian pole), and u-channel (nucleon pole) 110 100 0 DIXON e BOYDEN I THIS EXP. ..0 ::l 60 z 0 f- u w 50 (/) (/) (/) 0 a:: u .....J <l f- 0 30 f- 20 10 LAB 0.5 1.3 PHOTON 0.7 ENERGY, (GEV) 0.9 1.1 1.7 1.4 1.5 1.6 TOTAL CM ENERGY Figure 8. k W (GEV) The Tntal Cross Section 1.3 1.8 c.H.asa-ama were employed tuing both the chazoge and a.noma!Otla mag• netic mcm1ent cwplinge. Although it was poealble to pezotcwm thta anal- ysis in the region af the first !'eaonance. great diflicllltiea were en- cou:ntu-ed at higher energiea. They were mainly due to the ~ge eiee of the creaa eectlon produee4 by the nueleoo. pole at hack'WCU"d. angle• (e. g. eee a. H&ler ~ _!! (14). Jt waa predominantly the magnetic: momeDt cOQpUng porttoa of the nucleon pole amplitude that waa large. Thel'e b an i:Ddicatioo. that tile uae of llegge pelea ln tbla analysis may improve the eituatl~ but no definite result• have yet beeD obtained. The effon wm be continued. VII. CONCLUSIONS AND SUGGESTIONS This experiment has shown the third resonance peak in photoproduction to lie very close to k = 1. 0 GeV. 7r + The leveling of! of the total cross section at t."'le higheat energiea investigated here may be due to the fourth pion-nucleon reaonance. The general shape of the angular distributions changes remarkably little from k = 1. 0 to 1. 39 GeV. = 1.3 and 1.39 GeV However , the angular dietributiona at k reported here are incomplete ( mainly in th~ forward direction) making it difficult to draw any conclusions about the fourth resonance. Fxten- sion of thh experiment to higher energies might provide information of value in identifying the fourth resonance. It would be very uaeful to have a theory of pion photoproduction at high energiea. Since thia aeems hard to come by, data on other typea of reactlona at theae energie1 would at least aid in the phenomenological analysia. Useful measurements would include thoae of the angular dia- tributiona of 0 7r and 1r.. - to 1r+ ratio) and the polariza• + and 7r photoproduction. (from the tiona of the recoil nucleon• in 0 1r 1r 2 The square of the pion-nucleon coupling constant, f , baa been found to be 0. 078 + 0. 011 from extrapolation• of the sixth order Moravcslk fitting curvea. The result• obtained from the preatmt data are rather aenaitive to the fitting order chosen. However, an expori- ment might be designed which could circumvent the problema cauaed by 0 the very larae number of electrons near 0 . A more accurate determl- nation of the pion-nucleon coupling conatant should then be possible. The application of the concepts of Regge poles to the analysis of -48pion photoproduction is a moat promising lead and should certainly be investigated . Replacing the Born approximations by Regge pole ampli- tudes will tend to reduce the cross sections, which is exactly what the multipole analysis attempted here has indicated is necessary. lt would be most interesting to investigate whether or not the Regge poles can have an appreciable effect at "medium" energies such as those involved in this experiment. -49A :;,PENDI:X 1 COUNTER EFFICIENCIES Tht calculati.·.>n .:>f the ,:>i.Jn Hu.x from the counting .cate.1 ie based on the kne>wledge of the efiic1encie- of ·everal counter .,;ysterr.s. The efficiency of each counter aysten-:t in detecting various particles vtas measured independently using we ll kn13wn Inethode. Figure A l gives the efficiencies which vary with momentum. The difficulty of selecting a really pure beam o£ pions at the high momenta made it necessary to 111easure. n~ 'I(.; 7T' at lower momenta and extend it to the range used, where it is not expected to decrease . used in :measuring The electrons TJ Ee were .'hotoproduced in a 0. 02 inch lead target. To prevent flooding of the counters the photon beam had been gnul.tly reduced in inten11ity by i>assing it througb. two to three inchee o! lead placed abead of the sweeping n1agnet. Tne curves for TJ Ee have been corrected for a background contamination amounting to 0. 0018 + 0. 001 4 for the double converter and 0.0033 _!. 0.0013 for the single converter. Thia; contamination consisted of electron• }>roduced in the air, 2robably in or after the spectron1eter n1ar;net, which was at zero degreee. These I electrons would h'-ve momenta lower than those produced in the target. The fan counter efficiencies were measured by r>lacing a specially built long, narrow counter behind each of the back fan c:>unterl.J in turn. The average efficiency was "7F ANS 7r = 0. 970 !_. 003. In measuring the efficiency o£ the time of flight system (A l to C2) a lead wall was built around A 1 to prevent particles not p asing thr3ugh -50· Flgul'e Al . CherenJuw COUDter and Electron DetectOI' Efftcieoclee vo Speettrc:rnete!' Centzoal Momentum (value used: 0. 9960 + • 0012) EI'J'OI's (b) "7 cp (c) "7ze (d) "7E -rr (e) '" .,Ep -+ . 002 -+ .. 002 005 -+ . oos -+ The ranges in which theae efficlenclea &l'e ueed In the data l'eductlon are ehown in each FiguJ"e. For the eleeb"Cil deteetozo• 5. C . and D. C . lndlcate amgle ccmvea-te. and d«lblc cawertea- eyatem• reapecttvely. -511.00 .99 RANGE USED ~ >U !==""" . 98 0 .3 0.5 0 .7 Po , 0 .9 GEV / c (a l .06 .04 a. >U !==""" .02 RANGE USED 0.6 0.8 1.0 po , ( b) GE V / c 1.2 -SZ- D.C. RANGE USED 1. 1 Po (c) , GE V/c I. 2 . 12 . 10 .08 .06 0.. w f:" . 04 RAN GE USED . 02 .oo 0.9 1.0 1.1 Po (el , GEV/ c 1. 2 -54Al from being counted. At a momentum of 0. 45 GeV/c, where all pro- tone stop in the lead absorber in front of C3 , the value '7T rr = 0. 9964 .±. . 0014 wae obtained. The efficiency of one counter, Cl, was found to be 0. 993 .±.. 002. However , the nine out of 1Z89 particles that did not give a count above the bias gave no count at all, and it is assumed that theee misae~ Cl completely. Therefore the efficiency of a single dE/d.x counter is taken to be 1 OOo/o. The procedure used by Boyden (6) to insure that the various efficiencies would be stable throughout the course of the experiment was also followed here . Using the large number of electrons found at zero degrees (thle is the eame aet up used for measuring 7JEe) with the absorber• removed to eliminate electron showers and thus large pulses, each bias in turn waa set to a preselected value and the corresponding amplifier gain was adjusted to give an efficiency of 50% !or each. counter. All biases were returned to their normal operating values after thie calibration. During the approximately eight monthe of data taking, no noticeable drift in the efficiencies could be detected. .APPENDIX D NUCLEAR. ABSORPTION The same methoc:l that ~r.l.a uaed by Boyden (6) for meaeurtng the absorption oi piooa by material within the counter box waa followed here. The l'eeulte were in vei'Y good agreement with thoee of Boyden aAd the atathtkal errors have been reduced appreciably. Abaorbera were placed between CZ and C3 and the number not giving cc:unta in C3 were considered to be absorbed. The counting rate with no absorber ln place was aubtracted to obtain the net absorption from the absorber beini meaeured. The results were: .Ahaorber 1/2." Load Fraction Absorbed Mom.entum. Po o. 02.7 + • 004 o.sz O. OZ9 + • 001 0 .90 average 1" Lead o. 028 + • 004 o. 073 + • 012 1 1/2." Lucite o. 025 + • 005 (GeV) o. 9 0. 52 Jt was aaauz:ned that the material of C2 and luclte have simllar absorp- tive properties.. The absorption of lucite was measured with the 1/2." Pb absorber in place to prevent any low energy secondarlee from count- ins. Tbh 1/2." absorber waa alwa.yo in front of C3 during the course of the experiment. BO'tden pre,'iously found tho ab~torption to be independ- ent of the pion momentum; this h verified by the l'eawts given above. -56- For material other than the lea.d absorbers and CZ the geometrical absorption length vms ueed. Dixon (5) hae shown this ie rcughly con- ahtent with measured values for material in front of Ule counter box. Accurate direct measurement ol the abaorpttoa in materlal in front of CZ would have been prohibitively time consuming. The ~culated value• ol. the fractional geometrical absorption length for all material tn front ol CZ are: H. E . 0.102 M.E. 0.054 The abaorptic::m correctiona. A ., • for the variwa configuratlone are: H . E. S . C . o. 861 + o. oos H.E. 0. 8ZO + 0 . 013 D.C . o. 907 + o. 005 M.E. The errore liated are thoae from the measured abaorptiona ODly . The points at k • 1. 3. Q • S0° and k • 1. 39. Q = 50° were measured with a one inch thick piece of lead in front of the magnet to reduce the pion momentum to a value which the magnet could accept. (The momentum waa reduced by abou.t 40 MeV/c). There- duction of pion flux tn this lead was asaumed to be the aame as that at a eUahtly lowel' momentum. waa measured cUrectly. The abaorption at the lattcl' momentum (It waa neceaaary to change the magnetic field and to correct for the change in 6 p/p .) It waa found that o. 76 .± 0 0 . 03 of the tnciclent pions were counted alter paaslng thrCJU.3h the lead. Thla fractiOD appears aa part oi A ., in the table of J'eaulte in chapter V. -57APPE~DIX ill DECAY AND SCATTERING CORRECTIONS Typically ten to twenty per cent of the pions decay while traveling from the hydrogen target to the counter telescope via the reaction 7r + ~ p. + + v which has a mean lifetime of (2. 56 !_ • 05) x 10 -8 seconds in the rest system of the pion. Son"le of the muons will give counts indietinguiahable from those produced by the pions . Thh number can be calculated from the kinematic& of the pion decay, and the geometry of the magnetic spectrometer and counter syetem. About the only practi · cal way to carry out such a calculation is to use a Monte Carlo technique on a very fast computer . A procedure somewhat similar to that used by Boyden (6) ia employed. The present results agree very well with hh in regions where they are comparable. A computer program was written to simulate the magnetic epeetrometcr and counter system. "Pione" were then sent through the ays- tem with initial position in the target anJ. initial angles picked randomly. Typically a aeries of about twenty evenly spaced values of the pion momentum. was used at each spectrometer setting, with several hundred "pions" used at each momentum. successfully reaching C2 . The computer counted all ''piona" Fach "pion" was then restarted with the same initial values and allowed to decay at a preselected distance and counted as a "muon" if it reached C2. The decay distances formed a series of about fifteen evenly spaced valuee along the 660 em flight path in the high energy configuration or the 416 em flight path in the medium energy configuration. Figu1·e A2 shows •chematica.lly the magnetic -58- spectrometer and counter syetem with the input parameters as they appear in the computer program. Table Al gives the values of all input parameters to the decay correction program . Let the effective solid angle (in SR ) of the epectrometer be defined as 4 1r times the fraction of particles (all of the same rno.mentum and iaotropically emitted from the target) which would pass properly through the counter system. The effective solid angles for pions and muona are obtained from the program and are plotted aa functions of momentum in .lo"'iguree A3 and A4 respectively. (Table A3 in Appendix IV givee a comparison of the calculated magnet acceptance, 6 f2 6 p/p , with 0 meaeured valuee.) The quotient of the integral (over the obtainable pion momenta) of the muon 1nomentum response function by the integral of the pion momentum response function is th.e fraction of muons which will give counte in the ayatem. It should be noted that errors in the magnet simulation will tend to cancel when this division ia made . Be- cause of the large amount of co1nputer time involved only the points shown in Figure A4 were calculated, the others being obtained by interpolation. The decay CQrrection, which consists of the frac~ion of pions decaying in the syatern times one minua the fraction of n1uona counted, is given in Table 3 in chapter V . The sa1ne magnet silnulation computer program that was used for the decay correction calculations was modified tQ inveatigate the multiple scattering of pions along their flight path. The Monte Carlo technique waa again used and the number o! " pion" counts loat or gained due to multiple acattering was tallied by the computer . In order to aimpllfy the calcula- tion, the air along the flight path was lumped into five planea . Table A2 Figure .A2. Decay C~ection CoOl"dinate System and Parameters The magnetic: spectrometer is shown ochematically in the top and aide view a . Each parameter which c:ontalns an X or a Y refere respectively to an x - or y - eoordinate of the designated point. Angles are eonsidered po•itlve in the sense lndieated. The values of the pa.ra- metez e are given in Table Al. -60- r--- SDIAM ------.AW ---. BW ~_L _l e @) 1cw X _l cz z MAGNETIC - - - - EFFECTIVE y FIELD EDGE w \ _r:lT (.~SH (SX O, SY: \ \ \ \ CXI AXI BXI Gv_,A '(/eve -61- TABLE A1 ~amete~• RHOC • for the Decay Col'rection Program radius ot CUI"YatuJ'e c4 the trajectories in the magnetic: field. FFF (and J"FR) are the fl'inse Aeld correction parameters. The angular deflectlm. upcm entel'ing (o.- leavma) the ma.guetie field. meaaureci in the plane nonnal to the n-y plaAe and c:an.tabdng the trajeetory is gtven by G 20 • (FFF) z I tan e I where g is the angle between the pion paCh and the perpendicular to the field edge. s la the beam shape pal'&meter. The beam intensity distribution is approximated by e -r 2 1s where r ia the distance from the bea:rn center In centimettara • .All other parameters are shown in Figure A2 . given in centimeter s and the angles in radian• . The lengths are -62- TABLE A1 DECAY CORRECTION PARAMETERS s ;{[' SYU SO l A,_1 sw ~H s RHUC AL .~w AYC H.E. A1 H. E.. H.E. A1 C2S A2L - ?Y5. 4 - zqs·'' - 2 ') :i . 4 5l1 . 5 1 7.6 0 4.1 3.8 266 .7 31.34 8.23 59.36 -2 3.0 2o6.7 66.0 7.62 56.33 13.5 2'-JL:- .7 66.0 7.62 56.33 13.5 1J 9 .4 31.34 8.23 S4.02 5.6 7.62 69.0 -13.5 12.06 'J9.0 7.62 69.0 -13.5 5. 0 8 30.07 7.59 93.44 15.24 7.':>9 93.44 12.06 12.06 '-J9.0 7.6 2 89 . 0 -4 0 .6 5.0 8 27.94 -92.41 H8.13 .0037 .0 0 37 27.94 -92.41 378.13 .0037 .0037 21.94 -92.41 .0037 .0037 27. 9 4 -92.41 378.13 .0037 .0037 .05236 .48 00 1. 094 61 2 • ~ r· 9Ll 4 .4 508 77 • U52 36 .4800 1.094612 .30 92 14 .4'>0877 .o .o 7. 6u 4.1 4.9 3.8 2 66 .7 31.34 8.23 5~.36 -23.0 8L tiW ·~9. 0 ~XI CL cw eve C XI FFF FFR T TT u v w M.t.. A1 C2S -£.-,:J.4 '59.') 1 7. 6C 4. 1 4 . '-J 3. 8 ~9.51 AXI BXC H.E. A2S 5tJ .51 7.6 0 4. 1 4.4 3.8 4.'::i o.o 37tl.1~ .309214 l. 0 94o12 .3 0 ~214 .4508 77 o.o .3 0~2 14 1. 0 94~12 .3 0 9214 .45(; 8 77 -14?.1 -;4 . .. -. 7. 6(· 4.1 4.4 3. 8 27.94 -111.~1 334.87 . 003 7 . Ot.:3 7 • (( ( 85 4 .1'> 2 .l.d 55 l4 . 04(j 4J4 . (J3t) 252 F1gu.re A3 . Magnetic Spectl"ometer Momentum Response The abacisaa is the fractional difference ol tho pion momentum born the central momentwn, p • 0 (a) ( /:,p = P - P0 ) HSgh Energy Magnet \Ising the front aperture defining eaunter, Al . (A) This curve waa obtained from the Magnet Report (9) by a rOU&h interpolatic:a betwer.m the curves ior a point 80QJ'Ce and a 3" ~ target. All the .foUowing curve& were obtained from the Mcmte Carlo decay eof:'recti.o.n ealculattcm.. (B) Standard momentwn defining counter, CZ.L. (C) Small mon'lentum defining counter, CZ.S, (approximately half the siz~ ot CZL). (b) High .Energy Magnet using the rear aperture eountel', .A2, and Standard CZ. . (c) (D) Large Aa . CE ) Small Al. . MeGlwn Energy Magnet \l&ing A1 and arnall CZ (curve F). The numbers of potn.ta calculated to obtain these curves are a.e iallows: B , 106 points; C, 31 points; D, 33 pointe; E. 31 points' F, 55 points. The errore CD these point., which result from the etatiatkal errors on the number of "auccesees " counted. are typically between 5 and 1 ~ at the. peak ol. the eu.rve and decrease to absolute size as the •quue root ol the value aloog the curve. -640 (]) 0 <D 0 ~ 0 / / C\J q ( I I I I I I l. 0 C\J ,. 0 - ~ ~ ~ 0 I ....... ' ~ C\J 0 a. ....... a. C\J C\J 0 C\J ~ to -Ol x ~s C\J 0 3l8N'i1 <D 0 ........ <!.' (]) I ' ' <D OllOS '' ~ (]) 0 '' I 0 3/\1.1::>3.:1.:13 0 --: I <J 0 -6S0 co 0 <.D 0 v 0 C\J 0 0 0 a. ........ a. .D <J C\J ,. 0 <.D 0 0 C\J 0 co t;.-Oix~S C\J 3l9N't OllOS 01 3t\llJ3.:l.:l3 -66<;t 0 C\J 0 0 0 0 a. t" ........ a. -(.) 0 <JC\J ,. 0 If) 0 <;t 0 U1 0 <D 0 C\J ' 3l9NV 0 I lOS 01 3/\11J3.:l.:l3 -67- Figure M . MomenCUm R.eapcnae for Mien• From the Pion Dec~y The abecleea ls the fractional differences of the piao momentum from the central momentum. P0 • (a) ( b. p • p - p ) 0 High energy magnet with the tr<Xlt aperture COWlter, Al, and the •tandard momentum dcliDicg counter, C2L. (b) High energy magnet with A2 and the emall momentum defining (c) High energy magnet with the large rear aperture counter, AZL, and C~L . (d) High energy magnet with the emall rear aperture counter, A2.S, and CZL. (e) ldedium eneraY magnet withAl and C2S. There are typically about twenty to forty pointa (not ehown) for each curve with er~:ora ae in Figure A3. -680 <X> 0 <.D 0 ~ 0 C\J 0 0 C\J 0 0 a. '- - <] a. ~ 0 <.D 0 <X> 0 0 C\J 0 <X> b _ol x ~s C\J 3l9N\1 OllOS 3 fl ll. ::>3 .:L:l 3 o, 0 -69- N 0 0 a. ........ a. <J <:t 0 N 01 17 _0ix~S 3l9N't OllOS 31\ 11..::)3 .:L:l3 .0 -700 CX) 0 (.) U) -....... 0 > <I> (.!) CX) ,.._ 0 ~ 0 II _; C\J 0 0 0 a. -....... a. <J C\J 0 U) 0 CX) 0 p _QI X HS 3l~N'.7 OllOS 3AI1:::>3 .:L:l 3 (.) -710 ~ u ........ >cv C) <X) 0 0 <X) 0 ~ 0 v 0 N 0 0 0 a. ........ a. <1 N q I v 0 <X) 0 I (f) WN I<l 0 0 ' 3l8NV OllOS 3t\11J3.:L:I3 "'0 -72.w 0 C\J 0 0 C\J 0 <:t 0 I 0 a. 'a. w <J 0 co 0 Q) l9 11) C\J C\J -0 ~ 0 II 0 a. C\J <:t C\J C\J C\J 0 co C\J 0 co C\J C\J 3l8NV OllOS 3t\l.lJ3.::l.::l3 o, Q) -13lists the properties of the "scatterere" used in the calculation. Figure A5 gives the fractions of pions lost and gained due to scattering. For both. the high energy and medium energy spectrometers the results were quite consietent with zero multiple scattering and thuB no correction to the cross section was made. It should be noted that multiple ecatter- ing will tend to smear out the epectrotneter resolution (in angle and 1nomentu1n). However, this experiment is not very sensitive to this effect becauee of the well-behaved pion kinematics. TABLE .A2. Multiple Scattering Calc:ula.tion PaS'ametesoa The lUst part of the table gives the radiatiOD lellgtlut in em and clenatties in g/ ec o! the materials through wbi~h the pione pas•. (Seattcriag ln the target or iti!S walls is not conaldored. ) The second part givea the position• and effec:tlve thicknesaes of. the "acattereJ's " used in the c::alculatic:m. X-lNT and Q ue respect• ively the x-lntes-cept ln c:m and the angle ta l'adiana of the plane of the 11 ec:atterer" in the coordinate system ahown in Figure A.Z . .EFF. L . is the effective thickness of the "scatterer" in e m , and RAD . L . is the tluclmess expreese4 a.s a .fraction o£ a radiation length . -75 - TARLE A2 MULTIPLE SCATTERING PARAMETERS MATERIAL RAD. L. DE.NSITY AIR SCI1HILLATOR (CH) 37.7 46.4 43.6 o.Gull4<J 1. 052 1. 18 llJCITE !C5 f-ieOz) H. E. SCATTERERS 1 2 3 4 5 6 -, b 9 MAfERIAL )(-lf'.IT. AIK AIR -212.7 -84.2 -22.5 SCI ''H. (A 1 ) AIR SCINT. !A2l AIR AIR SCINT. ( Cl) (~) LUCITE o.o o.o 147.0 208.0 356.4 36 7 .R a EFF. L. RAO. L. 128.5 12B·. 5 0 .635 118. 1.6'>1 1?5. 125. 3.81 0.00392 O.J0392 0.0144 0.00360 0.0281 0.003t11 0.00381 0.0455 0.1030 e EFF. L. RAO. L. 0.07854 1.02102 0.873?4 0.87324 0.87324 68. 6A. 0.635 110. 65. 65. 2.00 0.00207 0.00207 0 .0144 0.00335 0.00198 0.00198 O.<J455 o.o o.u 0.05236 0.61959 1.259 0.47619 0.47619 0.47619 0.47619 ~.oo M. E. SCATTERERS 1 2 3 4 5 6 7 MATERIAL X-1 NT. AIR -87 .. 0 -24.5 5.6 AI~ SCINT. ( Al) AIR AIR AI~ SCINT. ( c 1) o.o 15 2. 2'>4. 304.7 o.o o.o - .02 v .04 .10 .12 .14 .16 .20 . Fi gure A I:> GAINED • TO 1.1 SCATTERING SCATTERING 1.0 DUE TO DUE Multiple Scattering of Pions LOST 0 1.2 I I "' -.J -77- A PPENDIX lV EQUIPMENT CHECKS Throughout the course ol thh expel"iment a. number of measurements were made to teat the satialactory operation ol the equipment. The results ol these measurements are reported ln this appendix. 1. A number of the point• were measured uains different mag- cOillftguratlona. net From theae and a apeclal measurem.ent made when cb.anglng hom the hiah to medium energy conllguration the ratioa of the spectrometer acceptances. ( t::..fL 6.p/p ) , for aeveral configura0 tiona wete obtained. In table A3 the spectrometer acceptances are Uated al0111g with the experimental and calculated ratioe . The agree- ment i• quite cOIUiatont with the statistical e r rore of the measuremente . Z. p 0 • 'I'he medium energy magnet was eet at GLAB ::a 104. l 0 and = 1. 1 GeV. The end point 0. 4Z73 GeV/c corresponding to k 0 energy of the bremmatrahlung beazn, Eo' was varied and the ccu:nting ra.tee shown in Figure A6 were measured. The cui'Ve shown was calcu- lated using the momentum response function calculated by the decay correctian program (see Figure A3). E 0 The agl'eement between p 0 and b consistent to within the sensitivity of the measurement. aa znay be recognized &om the fact •bat the measured pointe are not ahifted consletently to either aide oi the curve. about 1~ in p 3. 0 The conehtency b within and about 3Gft in E 0 • The counting rates (full tazoget m.inua bac:kgr om1d) were meaaua-ed for three pointe p:revf.ou.sly mea.ured by Dlxon (S ). C orrecting TABLE A3 The Spec trometer Aecepta.nce A. SpecltJ'OII'neter Ju:c eptan.eea. 6ft 6 p/ p C~ation X 0 Souzce 1 0• 4 6ft 6 p / p 0 from Tr•fL Decay Program X 10• 4 -+ O.0. OJ03 H. E . Al C2L 1. 954 Dixon 2 .14 H. E . Al cas 0. 865 Dixon 0. 91 + H. E . .UL 1. 08 Boyden 1.14 + 0 . 03 H. E . A2.S 0 . 54 Boyden 0. 59 + 0. 03 czs 2.. 7S Dixan M. E. B. - Z.60 + 0. 04 - Acc eptanc,e Ratioe. Cakulated Ratio Experimental o. so 0. 48 I (H. E . A1 C2L) 0 . 552. o. S9 + 0 . 04 (H. E . Al CZ.S) I (H . E . A1 CZ.L) 0 . 442 0 . 43 (M . E . C2.S) I (H. E . 1. 4 1 1. 45 {H . E . A2S) I (H . E . {H . E . AZ.L) AZ.L) A1 Cl.L) -+ 0 . 03 -+ -+ 0.03 - 0 . 04 -79- w 1<t c:r 1.0 .a (.!) z z 1- :::> 0 u 0 .6 .4 .2 w N _J <t :iE c:r .o - .04 - .02 0 1.0 1.05 1.1 .02 .04 0 6p/po z Figure A6. 1.15 1.2 Eo Measured and Calculated Spectrometer Response -sofor the different beam monitors used, the following c:om.partson may be made: 'I'hla E::tp. 1. 08 2.6.1 O. 96 + • OS 1. 08 35.7 1.00 17.6 o. 61 + • 04 o. 84 + • 06 o. 90 ±. 05 o. 62. + • 04 O. 89 ,:t • OS To within the a.cc:urac:y ol theae m.eaeure:ments (abCNt 6%) the two seta of meawrernents are consistent. Two teats were made with the field of the magnetic spec- 4. trometer reversed ao that cmly negatively charged particles could be counted. The 8rst was a aeuoc:h for electrons prodllced in the liquid hydrogen at a lab angle o:f 16.2° and at a momentum of 1. 036 GeV/c: (the k a 1.1 GeV, i ra 30° point). The value of C-,r obtained with the iu11 hydrogen target was 0. 0200.! 0. 0015 cOWlt•/BlP, wbile 0. 02.01 ± . 0019 cOWlta/BlP were obtained with the hydrogen removed. giving a net value of -0. 0001 .:!: • OOZ4 COWlta/BIP. C7r was calculated using the formula which does not take a.cc:ount ol the presence of electrons, so it may be concluded that there ie not an appreciable nwnber oi. electrons at thie angle and momentum originating in the hydrogen. .By comparlaon the po•ltive-field 7r+ counting rate l8 0. 60 counts/BIP. The observed counting rate ie very likely due to negative pions produced ln the tarcet walla. S. The second negative field teat was made at a lab angle of a. 68° and a momentum of 1. 084 GeV/c (the k .: 1.1 GeV. 0 c S 0 point), where there are many electrons produ.c:ed. If the electron detection sy11te1n -81- operates cortcctly tho net counting rates ahoald be zero. cOWlting ratee, C.,. • are -0.006 .± The net • 010 for the double converter and 0 . 017 .±. 02~ for the single converter, both c011sistent with ~o. The total cOlmtlng rate, C, was appro:dmately 1. 7 counta/BIP while the poaitlve·field .,.+ counting rate. G.,r , was approxh nately 0. 17 counts/BIP. APPENDIX V BEAM MONITORING AND THE BREMSSTRAHLUNG SPECTRUM The photon bearn was monitored by a thick-walled sealed copper ionization chamber filled with a mixture of argon and COz. This was periodically calibrated against a Cornell type qua.ntometer ( 15), which served as the basic reference . With the spectrometer set at angles smaller than 15° the magnet yoke intercepted the beam, and it was necessary to use the thin-walled air ionization chamber located near the primary collimator. Thie chamber was sensitive to atmospheric changes, and so it was calibrated against the thick-walled chamber on the order of once an hour when data was being taken at small anglee. The charge on the ion chamber collector plates was integrated and recorded in unite called BIPS (Beam Integrator Pulses) by integrator number 0249, whic!"l has an integration constant of 0 . 21 10 1nicrocoulombe per BIP. From a knowledge of the photon spectrum shape and the ion chamber calibration the number of BIPS could be converted into the number of photons in the energy range being used . The ion chamber calibration was found to vary slowly with time . It ie given for the data accumulation period of this experiment in Figure A7. The curves at the higher energies have been extrapolated frorn lower energy, with resulting larger errore. However, this error is still small compared to the statistical errors of the data. With the synchrotron operating at E: 0 :. l. 5 GeV the R. F. accel- erating system wae not capable of accelerating all of the electrons to the peak. energy. Therefore 1nany struck the radiator at lower energies .89' T L f - ~ ~ ~ 'i.o ~ f ~t. \j ~ \ ooo ~ J 1960 Fi gur e A 7 . 1961 The Bea m Monitor Calib r ation DATE . 85~~------~------~------~----~~----~------~------~------~~ SEP. AUG. DEC. JAN . OCT. NOV. FEB . JUL. MAR. .86 : 8J- ~ X 0 m~ .sal~ > ....... CD ~ I . 901 .91 .92 lJ,.) I I co -84- thereby altering the apectrum shape. Moreover the number of elec- trons reaching 1. 5 GeV varied frozn pulse to pulse with about one third reaching this energy on the best pulses. To maintain a conata.nt spectrum, the counting electronics and the beam monitor output were gated so as to accept only those photon!!l ;,:>roduced by l. 5 OeV electrons. To correct for the alight inaccuracy introduced by this pro - cedure, W wa& rnulti;llied by 0 .97.!. 0.01. The bremsstrahlung a.,.1ectrum, Boyden (6). B(k, E 0 ), haa been given by It 1e plotted in Figure A8. Running concurrently with this experiment (and using the same photon beam) were the experiments of Ruderman (8) and Chang (7). Often the targets .for these experiments were in the bean• while data for this experiment was being taken. A simple calculation using the curve on p. 84 of High Energy 0 articles by Rossi (16), shows that for a 0. 1 radiation length lead absorber the shape of the photon spectrum is virtually unchanged. ial in the bearn was 1nade . Therefore no correction for mater - B(K,Eo) 0.0 0 .1 0.2 0.3 • L_ 0 .4 ~ - 0.5 0.6 0.7 L._ t L tI 0.8 ~ - 0.9 1.0 1. 1 0.5 Figure A8. 0.6 I ·- L - 0.8 0.9 1.0 T he Brem s :;; trahlung S Jectrum 0 .7 I KfE. \;1 I w -86REFERENCES Proc. Phya. - Math. Soc. Japan .!1.• 48 ( 1935). 1. H. 2. Lattea, Occhia.lini , and Powell , Nature 160, 453 ( 1947) . 3. B . Gregory, CERN Conference ( 1962). 4. Chew, Goldberger , Low, and Nambu, Phya . Rev. 106, 1345 (1957). 5. F . P . 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