Photoproduction of Neutral Pions in Hydrogen from 500 to 950 Mev Citation Vette, James Ira (1958) Photoproduction of Neutral Pions in Hydrogen from 500 to 950 Mev. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KAHJ-0H20. https://resolver.caltech.edu/CaltechETD:etd-04112005-090012 Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The process [...] has been studied by detecting recoil protons from a liquid hydrogen target which was bombarded by the bremsstrahlung beam of the California Institute of Technology electron synchrotron. The angle and momentum of the recoil protons were measured by a magnetic spectrometer-three scintillation counter coincidence system. The process has been studied between photon laboratory energies of 490 and 940 Mev. and between pion center-of-mass angles of [...] and [...]. Protons which arose from meson pair production were significant at forward laboratory angles. A correction for this contamination is discussed. The rapid decrease of the total cross section above 320 Mev. continues out to 600 Mev. and then rises slightly reaching a peak value around 800 Mev. The center-of-mass angular distributions are analyzed in a power series of the cosine of the pion angle and it is found that terms up to the fourth power are necessary to fit the data above 600 Mev. A multipole expansion is made assuming that mesons are produced in only S, P and D states; this expansion is used to show that no single multipole absorption is responsible for the rise in the cross section above 600 Mev. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Mathematics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Walker, Robert Lee Thesis Committee: Unknown, Unknown Defense Date: 1 January 1958 Record Number: CaltechETD:etd-04112005-090012 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-04112005-090012 DOI: 10.7907/KAHJ-0H20 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1341 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 11 Apr 2005 Last Modified: 17 Oct 2023 18:45 Thesis Files Preview PDF (Vette_ji_1958.pdf) - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

PHOTOPRODUCTION OF NEUTRAL PIONS IN HYDROGEN FROM 500 TO 950 MEV. Thesis by James Ira Vette In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology ‘Pasadena, California 1958 ACKNOWLEDGEMENTS Dr. Robert L. Walker supervised this work; his interest and many helpful suggestions have contributed materially to the success of the entire project. The assistance and guidance provided by Dr. Walker during the author's graduate residence, although fully appreciated, can- not be sufficiently acknowledged. The constant advice and encouragement of Dr. Robert F. Bacher have been invaluable. Members of the synchrotron staff, especially Dr. A. V. Tollestrup, Dr. M. L. Sands, Dr. R. Gomez and Dr. J. M. Teem, have provided useful counsel. The author is indebted to Dr. V. Z. Peterson and Mr. Earl B. Emery for their maintenance of the liquid hydrogen target. Many enlightening discussions with Mr. Paul L. Donoho have been the source of helpful suggestions in all phases of this work, The assistance of Mr. Walter W. Wales in all phases of this experiment is gratefully acknowledged. Mr. Howard M. Brody and . Mr. Franklin P. Dixon were very useful in helping to take data. Discussions with Mr. Robert M. Worlock have proved useful. The discussions with Mr. Michel A. Bloch concerning his experimental results have been very instructive. The synchrotron engineering staff and crew designed, constructed and maintained much of the equipment. The author is especially indebted to Mr. Dan Sell, Mr. Larry Loucks, Mr. Bruce Rule and Mr. Larry Sill in this connection. The support of the International Business Machines Corporation through a predoctoral fellowship is appreciated. The financial support of the U. S. Atomic Energy Commission is gratefully acknowledged. ABSTRACT The process y + P—+1r° + P has been studied by detecting recoil protons from a liquid hydrogen target which was bombarded by the bremsstrahlung beam of the California Institute of Technology electron synchrotron, "The angle and momentum of the recoil protons were measured by a magnetic spectrometer-three scintillation counter coincidence system. The process has been studied between photon laboratory energies of 490 and 940 Mev. and between pion center-of- mass angles of 31. 5° and 147°. Protons which arose from meson pair production were significant at forward laboratory angles. A correction for this contamination is discussed. The rapid decrease of the total cross section above 320 Mev. continues out to 600 Mev. and then rises slightly reaching a peak value around 800 Mev. The center-of-mass angular distributions are analyzed in a power series of the cosine of the pion angle and it is found that terms up to the fourth power are necessary to fit the data above 600 Mev. A multipole expansion is made assuming that mesons are produced in only S, P and D states; this expansion is used to show that no single multipole absorption is responsible for the rise in the cross section above 600 Mev. “SECTION II. Il. IV. VI. Vil. Vil. IX. XI. XII. TABLE OF CONTENTS TITLE ACKNOWLEDGEMENTS ABSTRACT INTRODUCTION EXPERIMENTAL APPARATUS EXPERIMENTAL PROCEDURE BACKGROUNDS DATA REDUCTION CORRECTIONS ERRORS AND EXCITATION FUNCTIONS ANGULAR DISTRIBUTIONS THEORY INTERPRETATION EXPERIMENTAL SUGGESTIONS CONCLUSIONS REFERENCES PAGE 20 31 33 48 58 69 93 106 110 113 114 I. INTRODUCTION The pioneering experiments of Steinberger, Panofsky and Steller (1, 2) firmly established the existence of the neutral pion and showed that the total cross section for the reaction y+ P—»+7° +P (1) was comparable to that for charged photomeson production from hydrogen at a laboratory photon energy of 330 Mev. The measurements of Silverman and Stearns (3) and Cocconi and Silverman (4), which covered the photon energy range 200-315 Mev., indicated that the ns are produced predominantly ina P state. The rapid rise of their excitation functions and the large magnitude of the cross section were suggestive of a resonance interaction. Since these early measurements reaction 1 has been studied extensively (5) and this early indication of a resonance behavior has been confirmed. At this laboratory the pion angular distribution for photon lab energies between 260 and 450 Mev. has been measured by Walker, Oakley and Tollestrup (6), Oakley and Walker (7), and McDonald, Peterson and Corson (8). Walker, Oakley and Tollestrup used a photon counter and a proton counter telescope to detect one T decay gamma ray in coincidence with the recoil proton. Measurements were made with polyethylene and graphite targets and a subtraction made to obtain the cross section in hydrogen. Their method, which suffers from a low counting rate and the fact that the efficiency of the photon counter enters into the calculation of the cross section, was necessary to identify the reaction with the targets that were used. -2- If it can be established that the only appreciable production of protons from hydrogen comes from reaction 1, the simplest method is the detection of recoil protons from a hydrogen target. Since reaction 1 is a two body process, the measurement of the momentum and angle of the proton coupled with the knowledge of the direction of the photon beam allows one to solve the dynamical problem completely. Oakley and Walker used a magnetic spectrometer and a two counter coincidence system to measure the recoil protons from a high pressure hydrogen gas target; they were able to show that at least 98 °/o of the protons produced in the hydrogen came from reaction 1 rather than from the competing reactions: ' y + P—-+»y + P (2) + =- Y+ P— wr +7 + P (3) y + P—~» mT +a +P (4) (Reactions 3 and 4 are only possible for photons above 320 Mev. lab energy.) Their measurements covered pion center-of-mass (C.M.) angles between 70° and 150°; this was extended to angles as far forward as 26° by McDonald, Peterson and Corson who detected low energy _ protons by placing nuclear emulsions inside a hydrogen gas target. The combined data of these two experiments will be referred to as the OM data. The results showed that the cross section exhibits a resonance type behavior with the maximum value occurring at a photon lab energy of 320 Mev. If the assumption is made that mesons are produced only ~3- in S and P states in this energy region, the C.M. differential cross 4 section, O (k, 0); can be written Co (k, o) = Aj(k) + A, (k) cosé_ + A,(k) cos“0_ (5) where k is the photon lab energy and Q. is the pion C.M. angle. An equation of this form gives a good least squares fit to the data. The results are consistent with the model first proposed by Brueckner and Case (9) that production occurs mainly by magnetic dipole absorption leading to a state of isotopic spin 3/2 and total angular momentum 3/2 together with some small S wave interference terms. The inclusion of the emulsion data showed that the electric quadrupole absorption is very small. The purpose of the present experiment has been to investigate reaction 1 for k values between 500 and 950 Mev. The process has been studied between oe values of 31.5° and 147° by detecting the recoil protons from a liquid hydrogen target. The momentum and angle of the proton were measured by a magnetic spectrometer and a three scintillation counter coincidence system. It was possible to keep the contribution of protons from reactions 3 and 4 small in most cases and to calculate a correction for this contamination. In the "low" energy region a very good understanding of photo- meson production has been achieved through its relationship to the scattering problem. The dominance of the (3,3) state has made it possible to construct successful models for low energy production. -4. ‘However the region above 450 Mev. photon lab energies is devoid of theoretical predictions. The two main reasons for this are that no detailed scattering measurements other than total cross sections have been made in this region and the fact that the (3,3) state is no longer expected to dominate. Certainly higher partial waves will become important. It is hoped that information of the m° reaction along with the other photomeson reactions in this higher energy region can be used to suggest new models and guides to the theorists. There are several places where the information obtained in this experiment might be useful. The data might contribute to the under- standing of the peak in the I = 1/2 total cross section which has been observed by Cool, Piccioni and Clark (10) in their experiments on pion-proton total cross sections. A comparison with the results of Bloch and Sands (11), who have studied the photoproduction of Ts from hydrogen, can give an indication of the ratio of single to multiple meson production at these energies. Both of these points will be discussed further in Section X. The knowledge of the photomeson cross sections at high energy can also be used to more correctly evaluate dispersion integrals such as those that appear in the calculation of Compton scattering. (12). ~5- Il) EXPERIMENTAL APPARATUS The experimental area of the California Institute of Technology electron synchrotron laboratory is shown in figure 1. The circulating electron beam strikes a .031 inch thick tantalum radiator once each second, this. being the repetition period of the synchrotron. The beam is "dumped" slowly by tailoring the R.F. amplitude so that each beam pulse lasts about 20 milliseconds. During this time the magnetic field of the synchrotron is maintained at constant value to give a fixed bremsstrahlung end point energy. The resultant photon beam passes out of the machine through a primary lead collimator; it then goes through the high pressure gas target, a secondary collimator, the liquid hydrogen target, and finally into the beam monitor. An 8 inch lead scraper wall is used down beam from the primary collimator to block, without further collimation, any beam splatter from the primary collimator. A similar 4 inch wall is used down beam from the second- ary collimator for the same purpose. A series of radar magnets placed after the secondary collimator is used to sweep out charged particles generated by the beam in passing through the gas target and the secondary collimator. A large amount of concrete shielding is used around the machine to reduce the general background. The primary collimator used during this experiment was made of a 12 inch long, tapered, lead cylinder with a tapered hole of 1.9 cm. maximum diameter. The secondary collimator, which was made ina similar manner, contained a tapered rectangular hole of maximum dimensions 5.1 cm. x 4.1cm. The resultant beam size at the liquid Figure l. Plan View of Experimental Area. mo ( NOLLISOd ~ ~ Y de WNLN3WON HOIH NI NMOHS) OVW WOLN3WOW HOIH ONY WNIC3W L3NOWA WALNZNOW M07 / vA. LaNOVW ONIDSIMS yvove A Buh ty YOLYAIT100 ASWONOOSS nd Le a». L™ 4 ae i \ 30S = ~. i Sigh anal YX YY € zo aq -8- “hydrogen target was 6.6 cm. vertical height and 5.5 cm. horizontal width, The spatial density of the beam at this point was obtained by measuring the density of blackening of 400 micron Ilford G-5 nuclear emulsions which had been exposed to the beam behind a 1/8 inch lead plate. In order to study the T reaction, recoil protons from the liquid hydrogen target were measured in this experiment. The target, which was designed by Dr. V. Z. Peterson, is shown in figure 2. It consists of a 3 inch diameter, 5-1/2 inch long, cylindrical cup made of -003 inch Mylar. This cup is surrounded by a series of cylindrical copper and aluminum radiation shields, the smallest having a diameter of about 8-1/2 inches. The region between the cup and a .024 inch Mylar, 360°, external window is maintained under a high vacuum. A 10 liter liquid hydrogen reservoir, which is surrounded by a 26 liter liquid nitrogen reservoir (both partially shown in figure 2), sits concentrically above the cup. Hydrogen gas which flows through the center of this reservoir is condensed in the cup and remains in this state by heat exchange with the liquid hydrogen reservoir. Particles originating in the target must penetrate .027 inch of Mylar, .003 inch of copper and .0005 inch of aluminum before reaching the outside. The detection system is shown in figure 3. Charged particles which emerged from the target within a specified solid angle were momentum analyzed by a uniform field, wedge shaped magnetic spectrometer and focussed on a three scintillation counter array. Protons were identified by their energy loss in these counters. The Figure 2. Liquid Hydrogen Target. This. figure shows the bottom portion of the target which is suspended below the liquid hydrogen and liquid nitrogen reservoirs. The center line of the target is directly over the pivot point of the magnets. For more details of the target see Drawing 13 M 792A. - 1 a i Bi )j - = RK 1d i~e- \ ND 100° * [ TIN oO . _ | Sa7alIHs fF? S2000 Pa oi igiqua nag “un Laouv _-- 99,200 7H OT MOGNIM O9¢ 1 YW TAN peo ~] \ ¥ t O ~ Figure 3. -ll- Experimental Layout. This figure shows a cross sectional view taken through the median plane of the magnet. This particular arrangement shows the medium momentum magnet. The arrangements with the low and high momentum magnets are very similar, the main difference being the magnet-target and counter-magnet distances. The lead slit was not used with the low momentum magnet. -|2- FWwoOSs L39Y¥vi CH Gino WYIC.© / LS 9d f 4008¢d FONYNOS 34 YVSTONN 7 | WOLLYSA ~WLNOZINOH G3I9YOSeV ONINISSG SYNLYSdY Gd IAG 3d0ud -13- spectrometer solid angle is defined in the vertical direction by a 6 inch thick lead slit mounted on the front aperture of the magnet. The faces of the slit are tapered to point toward the center of the target in order to minimize scattering and slit penetration. The solid angle is defined in the horizontal direction by a system of lead slits which are attached to the magnet pole tips. The position and size of these slits are such that particles scattering off the pole tip faces will either miss the counters or be blocked from them by one of the slits. The magnetic field, which is produced by a current regulated D.C. generator, was measured and monitored by a proton resonance magnetometer during the whole experiment. With this apparatus it is possible to measure and maintain the magnetic field to an accuracy of 0.1 °/o. Three different magnetic spectrometers were used in the course of the experiment. These are referred to as the low, medium and high momentum magnets. The high momentum magnet is made by attaching a pole tip modification to the medium momentum magnet and reposition- ing it with respect to the target. The same set of counters was used with these two magnets. The low momentum magnet is equipped with a stainless steel vacuum chamber that encloses the counters and extends to within 8 inches of the external window of the target in order to measure low energy protons. The medium-high momentum magnet was designed by P. L. Donoho; the low momentum one was designed by J. I. Vette. The characteristics of these spectrometers have been measured very carefully by means of the stretched wire technique. Since these measurements are discussed in detail elsewhere (13, 14), ~14- only some of the results will be listed in Table I for reference. TABLE I. Width of Solid -AP/P Defining Magnet P (Mev/c) Angle AP/P Counter max Low 275 .0194 . 081 3.8 in. Medium 600 . 0075 . 098 4,75 in. High 1200 | . 00243 099 4.75 in. To improve the angular resolution for a given solid angle, the magnets deflect the particles in a vertical plane. Each magnet is mounted on a frame which is supported at one end by a set of wheels which roll on steel tracks. The other end of the frame is supported by a roller bearing pivot which is centered on the axis of the liquid. hydrogen target. The counters for the medium-high momentum magnet are mounted in a 4 inch lead house which is attached to ‘the magnet frame. The low momentum magnet counters are mounted in the vacuum chamber and 4 inches of lead is stacked around this section of the chamber. This arrangement makes it very easy for one person to manually change the angular position of either magnet without removing -any shielding. Angular marks along the tracks have been surveyed in every 10°. An angle measuring device attached to the magnet frame interpolates between these marks. With this arrangement the angular position of the magnet can be set to within + 0. 05°, ~15- All the scintillation counters were made with a polystyrene base plastic scintillator material obtained from the University of California Radiation Laboratory at Livermore, Each counter was viewed on two ends through lucite light pipes by RCA type 6655 photomultipliers. One- half mil bright aluminum wrapped around the scintillator served as a reflector. The outputs of the two phototubes which viewed a single counter were balanced and then connected in parallel. The medium-high momentum magnet counters were 11 inches long; two of these were 2 cm. thick and the other was 1 cm. in thickness. P. L. Donoho has measured the resolution of these counters with 486 Mev./c pions and protons. The results of this measurement were: u H om (2 cm.) = 0.15 Ad (2 cm.) c, (2 cm.) = 0.06 MK, (2 cm.) o (1 cm.) = 0.21 A (1 cm.) oa cm, ) 0.08 4, (1 cm.) where © is the standard deviation and 4 is the mean pulse height. The low momentum magnet counters were 8-1/2 inches long; the front counter (C-1 in figure 3) was .16 cm. thick and the central one was l,l cm. The highest momentum protons that were measured with this spectrometer stopped in the central counter. Since the protons lost ‘at least 5 times as much energy as the mesons for the low momentum runs, there was no problem in distinguishing the two types of particles. The standard deviation of the proton pulses in the 0.16 cm. counter was about 30 °/o of the mean pulse height for protons in the momentum range 200-275 Mew/c. ~16- The electronic circuits utilized in this experiment are shown in figure 4 along with the Synchrotron Lab drawing number of each one. The two paralled outputs of the photomultipliers which viewed a single counter were fed into an integrating preamplifier where the pulses were shaped by a shorted delay line into 0.5 microsecond rectangular pulses. The preamplifier outputs were amplified by 0.07 microsecond rise time pulse amplifiers and fed into both a delay line mixer and a 6 channel gated discriminator. (It is necessary to gate the counting equipment so that it is on only for the short period when the electron beam is striking the radiator; this eliminates the many transients which occur during injection time and reduces cosmic ray background. ) The delay line mixer delayed inputs 1, 2 and 3 by 0.5, 1.5 and 2.5 microseconds, respectively. The single output of this circuit was fed into the vertical amplifier of an oscilloscope. The outputs of the 6 channel discriminator were fed into a 6 channel coincidence-anti- coincidence circuit which had a resolving time of 0.15 microsecond. The pulses from C-1, C-2 and C-3 were placed in coincidence (referred to as 1.2.3) except for those runs where the protons could only penetrate the first two counters; in this case a 1.2 coincidence was used. In normal operation a 1.2.3 (or 1.2) pulse triggered the horizontal sweep of the oscilloscope and the resulting trace, which displayed the pulse heights of all three counters, was photographed. Time exposures containing of the order of 50 traces each were made and used to help set the biases properly to discriminate against pions but not protons. The accidental rate was obtained by delaying the -17- Figure 4, Block Diagram of the Electronic Apparatus. -18- zane Bry znt FO | | SNLVYVddY JINOYLI3S13 =A 40 CHZH l# WVYOVIG MOO1E dWv Worlds EIS 3dAL XINOMLX3L yaxiw a1980 aNI7 Avi130 3d09S0 a Sia VuaNVo Cele l# J any alouviod “ONIOD EZ I { “ONIOD 211 NOW e9l-1-Of “ONI09 NOW b9t- 1-01 9M0 oma € 2 1fONI09 21 v 119419 Py we ZzG GOW —| ZONIGIONIODILNY g91- 1-01 9Ma dV JONAGIONIOD | 2 # yOLVNIWINDSIa | o# asin4g Vv NOW Now 92 Sa0NIS TAaNNVHO 9 [7% | G31V9 TANNVHO 9 [| * # c# z#* 1#* NON NOW JISNIS BATONS 2 (# tOl-1-O01 5MQ suvidvos 374N0a0 GS99 3dAl VOU sesdes; LF} LE] Li 2ig¢-1-01 OMG b2 QOWN Y3idtIdWY Jud ce C# SIg£-L-O1 DMO Ve} Lngisia 1--~— S3dld LHOIT ALISN az BOVLIIOA YAWAWIeL Vd| 3dNLOLOHd gl 8 YIXIN vi SYSMIdILINWOLOHG ad SYOLVITNINIOS -- -19- output of the rear counter one microsecond and putting it in coincidence with a 1.2 coincidence (referred to as 1.2.3%*). The 1.2.3* rate (or 1, 2*) was negligible for all the runs. Protons were selected by raising the discriminator biases to exclude mesons. Scalers were used to record the desired counting rates. The synchrotron beam monitor is a thick walled Cornell type, air ionization chamber. The response of this chamber as a function of the peak energy of the bremsstrahlung has been measured and will be discussed later. ~20- Il EXPERIMENTAL PROCEDURE Since the reaction under investigation is a two body process, the photon lab energy, k, and the meson C.M. angle, a, can be calculated once the lab momentum, P, and the lab angle, ey of the recoil proton are known. To make a run the magnet angle and central momentum were set to correspond to a desired k, Q value. Then the biases on the discriminators were raised until only proton pulses were seen on the photographed oscilloscope traces. Pictures were taken during all the runs to make sure that no mesons were counted and no protons were missed. In general, a series of points corresponding to a constant k and various values of Q were run with hydrogen in the target; then the points were repeated with no hydrogen in the cup to obtain the background counting rate. When another value of k was investigated, the same values of oe were chosen. In this manner the angular distribution functions and the excitation functions for a constant o were measured directly. | When a gamma ray in the energy range 500-1100 Mev. strikes a hydrogen target, protons can arise from the reactions: y + P—»y +P (1) y + P+ +P (2) + - y + P—»nr +7 +P (3a) y + P+» + 7° +P (3b) ~21- y + P——+ 3n's + P (4) 1 y + P——» 4-515 + P (5) Of course there are also protons produced in the Mylar cup which holds the hydrogen; this background from the target will be discussed later. It is possible to eliminate the contamination from reactions 4 and 5 and to reduce that which comes from reaction 3 at most points by running with the maximum energy of the bremsstrahlung, Eo: about 100 Mev. above the k value being investigated for reaction 2. This will be illustrated by the situation depicted in figure 5. Here it is desired to study reaction 2 at k = 800 Mev. The rectangle represents the window in P, 8, space that the magnetic spectrometer-scintillation counter system provides. The value for E, is chosen to be 940 Mev. The curves drawn for reactions 3 and 4 are computed on the assumption that the mesons go off together; consequently these lines represent the maximum momentum that protons from reactions 3 and 4 can have at the given lab angle, oy with the machine running at EG = 940 Mev. If the bremsstrahlung cutoff at E, were very sharp, the optimum situation would be to lower Ey until the curve k = Eo for reaction 2 just begins to intersect the top of the P, o, window. A further reduction of Ey would result in a undesirable loss in counting rate, Because the energy spectrum of the bremsstrahlung beam had not been measured at the time these data were taken, the optimum setting of E, was never realized. In order to make this point clear, Figure 5. -22- Kinematics for the Photoproduction of One, Two and Three Mesons in Hydrogen. The solid curves give the proton laboratory momentum versus laboratory angle for the y + P—»1° +P reaction at the constant photon energies of 800 and 940 Mev. The curves for the other two reactions are calculated on the assumption that the 2 or 3 mesons are emitted together. These curves give the maximum momentum that protons from the reactions y + P— 2's + P and y + P——»3n's + P can have at a given laboratory angle if the machine energy is 940 Mev. The shaded region represents the sensitive region provided by the detection system when the magnet is set at the angle and momentum shown. For a discussion of this figure see page 21. 2 3- 1200 ~-= y+p— 27 +p — Y+tp—+mTr°+p —— Y+Pp—~3rt+p 100 1000 oO [e) (e) Magnetic (Spectrometer ‘, Window PROTON MOMENTUM (Mev/c) 800 700 4. 1 fe) 20 30 PROTON LAB ANGLE (DEGREES) -24- a discussion of the energy spectrum and its measurement will now be. made. The number of photons within the energy interval k to k + dk, N(k)dk, is given by N(k)dk = 2 B (k/E,, E,)dk (6) where Q is a quantity that is independent of k and will be discussed later. The function B(k/E,, Ea) which is used to describe the spectrum, is normalized so that 1 Bit, E)dt = 1 (7) Yo where t = k/E,. The tantalum radiator of the synchrotron is 0.2 radiation length thick and so constitutes a "thick" target. D. D. Elliott (15) has made a calculation of the spectrum to be expected from this target; his B(t, Eo = 1000 Mev.) is shown in figure 6. Recently the spectrum has been measured by Dr. R. L. Walker, P. L. Donoho and E. Emery (16) with a pair spectrometer, Although the results have not been fully analyzed yet, the preliminary calculations indicate a spectrum similar to that of a "thin" target. At the high energy end, k OE, the | measured spectrum falls off rapidly; the step is almost as steep as possible for the known energy resolution of the spectrometer. Until this upper end is better analyzed, it is approximated by a sharp step in figure 6 which gives the preliminary measured B(t, Ey = 1000) used in analyzing the w° data. _ The fact that the cutoff is shown as a Figure 6. -25- Bremsstrahlung Spectrum Function B(k/E_, Eo = 1000 Mev.) The dotted curve is the function calculated by Elliott (15) for the 0.2 radiation length tantalum target used in the synchrotron. The solid curve, which was abstracted from the pair spectrometer measurements of Walker, Donoho and Emery (16), was used in the data reduction of this experiment. For a further discussion see page 24. | I ~-- CALCULATED ——"“MEASURED —- 0.6F 1 \ \ 04+ 7 \ \ \ 0.2 A | J i i 1 0 0.2 0.4 0.6 0.8 |.0 k/E 9 -27- discontinuous step will have no effect on any experiment which has a poorer photon energy resolution than the 2 °/o resolution of the pair spectrometer system. Since the spectrum was previously believed to be roughly that calculated by Elliott, it was decided to make the runs with a slightly higher value of E, than the optimum case for a sharp cutoff. In order to be compatible with other experiments that were being done at the same time, Ey was generally a compromise value determined by the various experiments. The five k values investigated by this experiment were centered around 500, 600, 700, 800 and 950 Mev. and the corresponding Ey values were 720, 720, 820, 920-940 and 1080 Mev. for most of the runs. A correction for the contamination of reaction 3 has been calculated and will be discussed later. The smallness of the contribution of protons from reaction 1 will also be discussed at that time. For momenta above 850 Mev. /c the ratio of the energy lost by protons to that lost by mesons in the counters becomes less than 1.5 and the two peaks can no longer be clearly resolved. Below this value a proper setting of all three discriminator biases allows one to reject mesons without cutting into the proton peak. (One set of runs witha thick lucite target in the beam revealed a deuteron peak clearly “separated from the proton peak.) Fortunately a more elaborate pulse height analysis was not necessary in this experiment to measure protons above 850 Mev./c. The highest momentum mesons produced in hydrogen at a given lab angle are made by the peak energy photons in the reaction ~28- y + P—+w'tn (8) The kinematics of this reaction are plotted in figure 7 for photon energies corresponding to the Eo values that were used in this experiment. The kinematics for reaction 2 are plotted for the photon energies which were investigated. The size of the spectrometer- scintillation counter window was such that no mesons produced in hydrogen could get into the counters through the magnet in this experiment when protons above 850 Mev. /c were measured. The temperature of the beam monitor, atmospheric pressure and Eo? which was obtained by measuring the magnetic field of the synchrotron during beam dump, were recorded periodically. Different runs for the same point taken a week apart checked very well in most cases. Sufficient background runs were taken at each point to minimize the relative counting error for a given integrated beam intensity. A lead slit, 3-3/4 inches wide placed 11 inches from the center of the target (see figure 3), was used for all the runs taken with the medium momentum magnet and most of those taken with the high momentum magnet. The slit was used to reduce the background which came from the region of the external window of the target that was ‘bombarded by the photon beam. Runs with and without the slit were made to check that no additional protons from the hydrogen were scattered into the magnet by this slit. Figure 7. -29- Kinematics for Photoproduction of a Single Meson in Hydrogen. The dotted curves give the + laboratory momentum versus laboratory angle at constant photon energies for the y + P—»nt +N reaction. The solid curves give the proton laboratory momentum versus laboratory angle for the y + P—»7n° + P reaction. The peculiar selection of k values is explained on page 27. CHARGED PARTICLE MOMENTUM (Mev/c ) 1200 100 1000 900 800 700 600 500 400 300 200 100 -36- — Y+P+T*’ +p —-- y+p—+mt+Nn it j 1 i i 1 10 20 30 40 50 60 CHARGED PARTICLE LAB ANGLE (DEGREES ) 70 -31- IV. BACKGROUNDS The main background counting rate came from photoprotons produced in the 3 mil Mylar cup. Measurements were made witha carbon target and a hollow Mylar cylinder the same size as the cup to check that the magnitude and the energy dependence of the background were consistent with protons produced in Mylar. Most of the back- ground from the radiation shields and the external window was eliminated by the slits described in the previous section. Unfortunately this latter source was not realized during the low momentum magnet runs, which were made at the beginning of the experiment. The fact that these runs were made without a slit and that the cross section for the photoproduction of low energy protons in Mylar is large resulted in an empty target rate that amounted to 50 - 60 °/o of the full target rate. The background rate for the medium momentum magnet runs was 10 - 30 °/o of the hydrogen runs. There were two additional sources of background for many of the points taken with the high momentum magnet. Cosmic rays represented about 20 °/o of the counts. This was taken into account by recording the time of each run and the length of the pulse used to gate the discriminator circuit. The cosmic ray rate was measured under the same conditions as the full target runs. Several of the runs taken at °, = 15° and 20° had background counts which arose from the production of electrons in the hydrogen which were scattered by the air into the counters. Since the protons coming through the magnet were nearly minimum ionizing, it was not possible to distinguish the -32- electrons from the protons by pulse height analysis. Although the lead shielding around the counters eliminated most of this source of back- ground, more shielding could have reduced it even further. This fact was not discovered until after the full target runs had been made. This additional background was measured by blocking up the magnet aperture with 10 inches of lead and making both full and empty target runs under the same conditions as the regular runs. The counting rate difference between these two types of runs was added to the normal empty target rate to obtain the complete background. This additional rate amounted to 20 °/o of the total background rate. The total background rate was 10 - 30 °/o of the full target runs. ~33- 'V.. DATA REDUCTION The output of the 1 inch copper air ionization chamber is fed into an ion current integrator; the unit of integrated beam intensity is called a BIP, the abbreviation for beam integrator pulse. The total amount of beam energy in Mev., U, which must pass through the ion chamber to give one BIP depends on the ion chamber temperature, the atmospheric pressure, the maximum energy of the bremsstrahlung, and the constant of the integrator circuit. Using the ideal gas law to correct for temperature and pressure, one can write Tp \M U(E_, T, P) = K(E) fe] fe} Oo (1) TOP where K (EQ) is the response of the ion chamber in Mev./coulomb at standard temperature and pressure, M is the integrator calibration in caulomb/BIP, T is the temperature in degrees Kelvin and p is the pressure inmm. of Hg. It is convenient to denote U(E., To P,) = Us = Kj(EQIM, (2) where M, is the calibration for the standard integrator. Dr. R. Gomez (17) has measured Kj(E,) using the energy _independent multiple plate chamber designed by Wilson (18) and has calibrated the ion current integrator. The values of K, obtained were 4,45, 5.05, 5.41 x 10'° Mev./coulomb at E, = 497, 789, 1080 7 Mev., respectively.. The value for M, was 2.22 x 10> + 0.5 °/o coulomb/BIP. -34- Li In many cases several runs taken at the same k, 6 - point had slightly different values of T,p and Ey indicated by primes. Instead of using the number of BIPs, N, for a run taken with an integrator whose calibration constant was M, the quantity ' 1 NTp MU(E)E * re) fe) fe) N* = ° (3) To P M, UE) Ey was used to divide into the total number of counts that remained after cosmic rays were subtracted to obtain the counting rate, om The counting rate obtained by subtracting the background and contamination rates from CG will be denoted by C. It is possible to convert C into an average C.M. differential cross section. Consider an element of volume dxdydz in the hydrogen target where x and y are coordinates transverse to the direction defined by the photon beam and z is along the beam. The number of photons in the energy interval k to k + dk striking this element of volume per standard BIP is B(k/E,, E,) N(k)dk n(x, y)dxdy = U, —————— dk n(x, y) dxdy (4) E_k fe) where n(x, y) is the spatial density of the beam at the target. The area over which n(x, y) is non-zero is determined by the beam collimators. This function is normalized so that n(x, y)dxdy = 1 (5) ~35- where the integral is taken over the region in which n(x, y) is non- zero. The counting rate of the recoil protons from the wv reaction that-emerge from this volume at the angle ®, within the solid angle , ad, and with momentum P is given by dc = dz ! pN do /90 B(k/E_,E_) 2 ; dQQ O° dk n(x, y) dxdy (6) A” aa \aQ}, k where: p is the density of the hydrogen A is the atomic weight of hydrogen Q= Ui/E, is the number of equivalent photons per standard BIP Ny is Avogadro's number do ay is the C.M. differential section for the n° reaction oR) u (35) is the ratio of C.M. differential solid angle to k laboratory differential solid angle at a constant photon: energy. * * The relationship between k, °,, and P is given by the formula 4 (m* - 2M”) + va Pp *4 M2 k = (7) * * *2 2 M+ P cos ©, - P™+M where m and M are the mass of the m° meson and the proton, -36- respectively. The solid angle ratio is given by the equation CA 2 2, *,2 2 21-8 ae) _ 67-2) [=p p, cos ony? - = pV C- BEI]? o sal, 0.0 (B - B. cos oe) where 3 B = (9) p’ + M2 and k = — (10) Pe k+M In order to take account of the loss of counts due to effects such as nuclear absorption and coulomb scattering in the scintillation counters, equation 6 must be multiplied by a correction factor R. The total counting rate observed by the detection system is then N ax (XQ B(k/E_,E_) / c-' 2 R — (——] aQa O09 dk n(x, y)dxdydz (11) A dL \SQ/, k The limits of x and y have already been discussed. The limits of z depend on x and y and the dimensions of the target. The limits on k and fare determined by the magnetic spectrometer- scintillation counter system and in general depend on x, y and z. do Since the only unknown quantity in the integrand is —— _, equation 11] is written as -37- N Q B(kK/E_,E ) C= +2 ROS) 92) 4 -$—°_ dk n(x, y)dxdydz (12) where ' B(k/E_,E_) <a (22) ~ o.° n(x, y) d Vdkdxdydz afk 8) = W\dQ/, (13) 8.0 B(k/Eo, Eo) n (x, y) dQdkdxdydz aa) Here k and 3 represent central values of the k and o resolution functions which will be discussed later. The bar over the variables will be dropped in later sections for convenience of writing. Because the protons experience energy loss in penetrating the hydrogen, the Mylar cup, the radiation shields, the external target window and the air path, they enter the magnet with a lower momentum P. Let all this material expressed in terms of its equivalent hydrogen range be denoted by Ar. This quantity depends on the point in the target where the protons are produced. If p* is expressed in terms of its hydrogen range by the equation P* = f(r) (14) then P is given by P = f(r - Ar) (15) To see more clearly the effect of energy loss, a transformation of variables from:.k to P will be made by substituting into the integral -38- of equation 12 the relation ok ap* dk = 5 dP (16) oP o* oP Pp where dk -M+k(1- 1/B cos 0”) a ) x = 6 * x * = (17) oP 9 M+P cos@ - pre 4 yi" Pp Pp and ap" f (x) = eo (18) aP f£ (x - Ar) Equation 12 is then written PN, fpa\ (ek) — BIKE,,E,) — \aa./ k \3 Py 9” k P . R QO(k, a) A £ (r) : dPdQ dxdydz (19) f (rv - Ar) If the energy loss is very small in comparison to the energy of the protons, Ar/r is very small and the f ratio in the integrand can be set equal to unity. If the dependence of the limits of . and P on the target variables can be neglected, the integration over target variables can be performed easily to obtain the factor -39- n(x, y) dxdydz = Q (20) which is generally referred to as the effective length of the target. With the collimators used during this experiment ] was 7 cm. For many of the runs made in this experiment Ar/r was large enough so that the integrand of equation 19 became a function of the target variables which had too large a variation over the target to neglect. Since the integral in equation 12 is quite complex, it was calculated numerically on the Cal Tech Electrodata digital computer. The computer program for the medium-high momentum magnet was coded by P. L. Donoho and the details are given elsewhere (14). In . order to see what the k resolution function for a given angle and momentum setting of the magnetic spectrometer-scintillation counter system is, the computer is made to print out the function 1 K(k) = (22. B(K/Eq:Eo) n(x, y) dQ. axdydz (21) 9.2 Ac K The quantity K(k)/K, ox is plotted in figure 8 for some typical medium and high momentum magnet runs. The central value of k for most of the runs was 490, 585, 690, 785 and 940 Mev. For any one of these energies the resolution function, whether the point was taken with the medium or high momentum magnet, is practically identical to the one shown in figure 8. For the low momentum magnet runs it was necessary to take into account the effects of scattering in the hydrogen target. When Figure 8, -40- Energy Resolution for Medium and High Momentum Magnets. The figure shows the photon energy resolution provided by the magnets when the ® reaction is studied. The value of k which divides each resolution function into equal areas is referred to as the central value of k. Both magnets provide essentially the same resolution and this resolution is practically independent of the angle setting of the magnet provided the central k value remains the same. The curves have central values of k = 490, 585, 690, 785, 940 Mev. Most of the data have k values very close to these (see Table II). RESOLUTION FUNCTION (DIMENSIONLESS UNITS) 0.8}- O4r O ] ] | | MED. AND HIGH MOMENTUM MAGNET RESOLUTION FUNCTIONS | | i | 400 500 600 700 800 900 1000 k (PHOTON LAB ENERGY IN MEV.) HOO -42- scattering is considered, there is a distinction between the angle of . * production, 85° and the angle, oy with which the proton leaves the target. Equation 11 must be changed to the following formula N do B(k/E_,E_) C= eo R _ Qo. d&q ——2 2 ax A dXt \aa ke k n(x, y) dxdydz P(O.AO,) dL, | (22) where P( 1+0,,) is the probability that a proton is scattered from the solid angle d.2 at <% into the solid angle d OL, at |: In this case the detection system determines the limits of LL 1 rather than £1. Two types of scattering were considered; small angle multiple Coulomb scattering and single wide angle nuclear scattering events. The rms Coulomb scattering angle was only the order of 1°, but the quantity 3 x was approximately 70 Mev./degree in the region where the low P momentum magnet was used. Consequently this small scattering angle was enough to spread the photon resolution function over the top of the bremsstrahlung resulting in a lower value for the integral than would be obtained if it were evaluated without scattering. Essentially the angular distribution of protons in the ‘target at these lab angles (63° - 70°) is so sharply cut off by the brems strahlung limit that scattering in the target results in more particles being scattered out of the detection system than are scattered into it. -43_ The probability that a proton, in passing out of the target, would undergo nuclear scattering was 1-2 °/o in the momentum range 200 - 275 Mev./c. It was not apparent that scattering in would be compensated by scattering out for this type of scattering. The . cross section in the region above 600 Mev. is down from the value around the resonance by a factor of about 10. Protons produced by photons around the resonance energy at more forward angles could undergo a wide angle ‘scattering event which would result in a proton having the proper momentum and direction to be counted by the detection system. For these reasons it was necessary to consider quantitatively the effect of nuclear scattering. The complete scattering problem was treated in the following manner. The function P( 2-2.) was broken into two parts P(Q-D,) &% P(PY, Ar) P(. QA) + PUR) — (23) where PP’, Ar) is the probability that no nuclear scattering occurs, Po Q-Q,) is the probability that protons scatter from LL to LL by small angle multiple Coulomb scattering (19) and P (-0,) is the probability that protons scatter from OL to L 1 by nuclear scattering (20,21). This method neglects the interference between Coulomb and nuclear scattering plus the effects of multiple scattering after a nuclear scattering event has occurred. However these will introduce very little error. A substitution of equation 23 into equation 22 gives ~44- ' B(k/E.,E.) dkdxdydz P,P. (Q—-0,) do. 1 bol bo Y B(k/E_,E_) do a ao oo’ oa n(x, y) a \aa/, k dkdxdydz P_(Qe>,)4. (24) Both of these integrals were done on the Electrodata computer with ‘programs coded by J. I. Vette. The specific details of the programs do dd was evaluated by the data of Oakley and Walker (4) for photon energies are given elsewhere (13). In the second integral of equation 24, below 450 Mev.; the contributions above 450 Mev. were negligible. This second term was treated as a contamination rate since it arises from protons produced in hydrogen which were not desired. This contamin-. ation rate was 1- 2 lo of the true counting rate. The computer program to do the first integral makes the computer print out 5d B(k/E,, E,) K(k) = Cae) dL ——-—=- nlx, y) P, P(Q1->01,,) dxdydzd, (25) aL A k Two plots of K(k)/K ox for the low momentum magnet are given in figure 9; a comparison with figure 8 shows that the resolution for the low momentum points is much poorer than the rest. Figure 9. -45- Energy Resolution for Low Momentum Magnet. The figure shows the photon energy resolution for two of points studied with the low momentum magnet. The curve with an 880 Mev. central value corres- ponds to a magnet angle of 70° and a 261 Mev. /c central momentum. The curve with the central value of 584 Mev. corresponds to a magnet setting of 63.5° and 250 Mev./c. The effects of scattering in the target have been included in the calculation. The fact that Es and 3s are large in this region resultsin much wider resolution functions than those shown in figure 8. RESOLUTION FUNCTION (DIMENSIONLESS UNITS) O0.8F- 0.4 >- 0 | { | I I I LOW MOMENTUM MAGNET RESCLUTION FUNCTIONS 1 i i } 400 500 600 k (PHOTON 700 800 900 1000 LAB ENERGY IN MEV.) HOO -47- The values m = 135.1 Mev. and M = 938.2 Mev. were used in all the calculations discussed in this section. The material in the target plus any air path was converted to its equivalent hydrogen range by the tables of Rich and Madey (22) and the relation between momentum and its range in hydrogen was also obtained from these tables. The density of the hydrogen in the target was 0.0726 gm/cc. (23). The correction factor R will be discussed in the next section. Once all these calculations are made, the average C.M. differential cross section can be obtained by —_! o(k6) = Ac (26) where pN, ~ Q | K(k) dk (27) al -~48- VI. CORRECTIONS There were a number of corrections applied to the data before the cross sections were computed. These corrections can be divided into two groups; one constitutes the multiplicative factor R mentioned in the previous section. The other arises from protons produced in hydrogen by reactions other than the one under investiga- tion. The counting rate from these undesired reactions is referred to as a contamination rate. The factor R will be discussed first. The rear counter that was used with the medium momentum magnet was not quite large enough to catch all particles passing through the central counter. This reduced the momentum acceptance interval to 96.5 °/o of the value obtained by the stretched wire measurements. This same rear counter caused a reduction in the solid angle of 2.8 °/o when it was used with the high momentum magnet. A calculation of the Coulomb scattering in the counters gave a negligible correction, Nuclear absorption in the counters was measured by narrowing down the central counter with a lead slit to be certain that all particles passing through this counter from the magnet would strike the rear counter. Then the ratio of 1.2 to 1.2.3 coincidences was measured, The absorption cross section obtained in this manner was slightly less than the geometric cross section. The correction for this effect varied from 0 for the low momentum magnet runs up to 4.4 °/o. Most of the high momentum magnet runs were made with a 1/2 inch piece of lead between the first and second counter to reduce -49- the background counts which did not come through the magnet. The absorption for this lead was measured by placing it directly in front of the rear counter and comparing the 1.2 and 1.2.3 coincidences. After taking account of the absorption in the central counter, this correction was found to be 8 °/o. Both the absorption cross section for the lead and the counter were shown to be independent of the momentum of the protons in the region of interest. The loss of counts due to the scattering of protons in the lead was calculated by Dr. R. L. Walker and was measured. The calculated correction was a little smaller than the measured one; an average of these two was used as the correction since both methods were susceptible to error. This momentum dependent correction varied from 0 - 3 °/o. All of the above factors were combined to make the total correction factor R. The small source of undesired protons for the low momentum runs coming from the m reaction has been discussed in the previous section. These protons are not desired because they come from photons of lower energy than the region under investigation. The second reaction that can contribute to the contamination rate is Compton scattering. Measurements of this process up to photon energies of 270 Mev. (24) show that this cross section is about l °/o of the m° cross section at the same energies. Mathews (12) has calculated the Compton cross section up to 270 Mev. by the use of dispersion theory. This type of calculation shows there is a relation- ship between these two processes. It is doubtful that the Compton : . fe) cross section is ever more than several percent of the wm cross ~50- section ‘at the same photon energy (25). Figure 10 shows the sim- ilarity of the dynamics of these reactions in the region in which this experiment is concerned. Because of these considerations, no correction for this process was made. The contamination of protons coming from the production of meson pairs was briefly discussed in Section IV. Since this reaction contributes an appreciable fraction of the protons that are detected at the forward lab angles, the correction for this effect will be discussed in some detail. In the region where this correction is necessary, protons have a large enough momentum that energy loss in the target can be neglected. The proton counting rate per standard BIP due to the pair production of mesons is 2 - do B(k/E_,E_) = R 0’ ‘o Cy = pn 2 xX Q t { dE dk df (1) lam adi k ! Where E is the total C.M. energy of the proton. The quantity 2 do ' 1 OB) (k) = —— dEdty (2) dE du is the total cross section for pair production at photon energy k. Here the integration extends over the full range of the variables. Since the detection system provides limits for the laboratory solid angle, it is convenient to make the solid angle transformation from C.M. to lab system. Then Figure 10. -51- Kinematics for Compton Scattering and a Photo- production. The solid curves give the proton laboratory momentum versus laboratory angle at constant photon energies for the y + P—»7w° + P reaction. The dotted curves give the same kinematics for the y + P—»y' + P reaction. PROTON MOMENTUM (Mev/c) 1200 100 1OOOF 900 800 700 600 500 400 300 200 100 — ytp—Tr°tp \ --- ytp—y'tp j } 1 i | i 10 20 30 40 50 60 PROTON LAB ANGLE (DEGREES) 70 -53- 2 a" oo. B(k/E_,E_) Cc, =D —— oo dE dk dQ (3) dEdQL' \aAlQi J, 2 k where D = PN, = Q . The quantity ERY) , is given by equation VI-8, but there is now no unique relation between k, a. and te P since pair production involves three particles in the final state. 1 After the change of variables from E to P is made, equation 3 becomes . 2 ! ' a“ o OE B(k/E_,E_) Cc, =D ——— 0a — °° aP dk df (4) dE AQ, \AQ x. E \OP /o* k a p! where OE _ B - B. cos 8, 6) OP / gx k 1 - Be 6, Pp In order to proceed further it is necessary to obtain some expression do dE'a.' Protons arise from photomeson pair production in hydrogen for by the two reactions: y + P——»w + 7° +P (6) y + Poway + + iP (7) At energies well above threshold (k = 320), it might be expected -5 4. that the two reactions would be comparable since the production of single neutral and charged mesons is similar for energies well above threshold. Bloch and Sands (11) have obtained 2 Oc for i 7 dE dO, reaction 7 by subtracting the yields of m measured from hydrogen at different values of E, , the maximum energy of the bremsstrahlung. Their measurements indicate that this quantity is roughly isotropic in the C.M. system and the energy dependence on E , the C.M. total energy of the mw, is not inconsistent with a density of states factor obtained by integrating out the proton and positive meson variables from a three particle final state density. With these facts in mind, the cross section is divided into the contributions from reaction 6 and 7; then it is assumed that the cross section for reaction 6 is proportional to that of 7. Thus ao, ao dE di dE dit where a_ is the proportionality factor mentioned above. In analogy with the information obtained by Bloch and Sands, it is assumed that the cross section can be written 2 do, 2 —<— = |i(x)| gtk, ) (9) dE ath t where g(k,E ) is obtained by integrating out the meson variables from a three particle density of states. Berman (26) has obtained the -55- formula ! t Hi ‘ g(k,E) =7E jw-z) (Ee -E*) - 4 @?-5} | (10) where W=M \ 1 + 2k/M (11) and 2,'2 . 2 1 ' i] (w-E) + \|(w-E )*-(w*4+M*-2E w)+ 42 e. -M ) (W°4M°-2E Ww) E, = (12) It is possible to evaluate LG)” by the data of Bloch and Sands. An integration of equation 9 yields — 2 do roo ——- dE dL = OF (k) = 4 [1-0] *G(ik) (13) dE df where Gik) = | g(k,E)dE (14) A smilar integration of the quantity measured by Bloch and Sands gives 2 ao ' ' c ded = 61 (k) = (4m) 4.5107 cm + 30%0 (15) dE dQ. T T essentially independent of k in the region between 600 and 980 Mev. Using all this information equation 1 can be written -56- (14 a) Dio g(k, E ) 3.0 aE B({k/E_,E_) C,= | — - o_o aPdka (16) 4a G(k) aM% ap k The evaluation of the integral in equation 16 was made numerically by J. I. Vette and Dr. R. L. Walker using the Electrodata computer. The dependence of the integrand on oe was neglected and the trivial integration over the solid angle performed before the numerical work was done. In order to check the assumptions of this calculation and to evaluate the constant a, runs were made with different values of E, while holding the magnet angle and momentum constant. This procedure changed the fraction of observed protons that came from meson pair production. Surprisingly these measurements, although they were very rough, indicated that a = 0 is not inconsistent. This will be shown in a moment. The results of these calculations are presented ‘in the following manner. The answer obtained from equation 16 with a =0 was multiplied by VU (see equation V-27) to give a pseudo-1 cross section which will be denoted by the symbol oe This quantity is given in Table II in the next section. The evidence that a = 0 and that the correction seems reason- able can be seen in figures 12 and 15 (see next section). The points denoted by the triangles were taken at a higher value of Ey than those denoted by the circles. It can be seen that after the pair correction is made, the two cross sections are within statistical errors. -57- Since the difference of the correction for a given point is large, the agreement of the final answer is a good indication that assumptions about oe are reasonable. If the data of Oakley and Walker (4) dE dtd are extrapolated from 450 Mev. to 490 and 500 Mev., and compared with those two points in figures 12 and 15 which have just been discussed, the agreement is very good. Since these cross sections were computed on the basis of a pair correction with a = 0, and since these corrections were large, this value for a was used for all the corrections. It is possible that the method of calculation over- estimated the contribution from reaction 7; however with the data available reaction 6 seems small compared to 7. In general the pair correction is smaller than at these points where the calculation was checked. =58- VII. ERRORS AND EXCITATION FUNCTIONS After the contamination and background rates were subtracted t from C to obtain C, the average C.M. differential cross sections were computed by the method discussed in Section V. The final results of the data reduction are given in Table I. The errors have been classified into three types. The quoted errors are estimated standard errors. A. Cc, Errors in the absolute cross section which are independent of the proton momentum and angle. 1. Beam calibration = + 3 °/o. 2. Errors in K arising from errors in stretched wire measurements and in the dimensions of the target cup =+2 °lo. Random statistical errors which vary from point to point. 1. Standard counting errors. 2. Small variations not accounted for by periodic monitoring. a. Ion chamber temperature =+ 1/2 °/0 b. Peak energy of the synchrotron = + 1/2 °/o. 3. lon current integrator stability = + 1.5 °/o. Systematic errors which depend on the momentum, angle and E_. fe) 1. Error in nuclear absorption correction = +5 °/o of the correction. 2. Error in lead scattering correction = + 20 "lo of the correction. 3.. Error in the pair correction oc, = + 30 °/o of the correction. -59- TABLE II. This table presents all the data obtained in this experiment. The magnet that was used to take the data is given in the first column. The central value of the pion C.M. angular resolution in degrees is given next. The third column lists the central value of the photon resolution in Mev. The average C.M. differential cross sections for the reaction y + P——»1° + P are in the fourth column. The B and C type errors are given in columns six and seven. The combination of these two statistical errors are given in the fifth column. The last column gives the calculated correction for the contamination of protons coming from meson pair production. This correction is expressed in terms of a pseudo-m®° cross section (see page 50). Without this correction the data would yield cross sections equal to the sum of the fourth and eighth columns. -60- Table Il. 30 C.M. Differential Cross Sections in Units of 10° cm“/ster. 1 ' B+c Type B Type G Magnet a k o(k, 0.) Error Error Error co, High 147 954 3.09 0. 40 0.29 0.28 0.94 High 147 799 1.94 0. 45 0.28 0.35 1.18 High 147 702 2.00 0.47 0.35 0.31 1.05 High 147 593 9.32 0.56 0. 34 0. 44 1.47 High 147 496 2.51 2.21 0.80 2.06 6.85 High 147 495 1.33 1.26 0. 43 1.19 3.99 High 135 945 3.64 0.38 0.30 6. 23 0.76 High 135 793 2.34 0.41 0.24 0. 33 1.09 High 135 693 2.77 0.41 0.29 0. 30 1.01 High 120 936 2.59 0.33 0. 26 0.20 0. 65 High 120 788 3.12 0.34 0.23 0.25 0. 82 High 120 692 2.90 0. 36 0.29 0.21 0.71 High 120 593 2.90 0.57 0.47 0. 32 1.08 ‘High 120 ~ 495 4.65 1.07 0.58 0.90 3.00 High 113 790 3.32 0.30 0. 26 0.15 0.50 High 105 943 2.22 0.19 0.16 0.11 0.38 High 105 793 3.62 0. 24 0.19 0.14 0.24 High 105 689 3.39 0.30 0.27 0.15 0. 40 High 90 936 2.27 0.21 0.19 0.09 0.20 High 90 788 4.07 0.21 0.16 0.14 0.27 High 90 690 3.88 0.41 0.39 . 0.13 0.00 Med. 90 579 3.27 0. 26 0.23 0.11 0.14 Med. 90 484 5.43 0. 41 0.29 0.29 0.98 High 75 937 1.32 0.19 0.18 0.06 0.12 High 75 784 3.54 0. 42 0.41 0.10 o.1l Med. 75 784 3,11 0.15 0.12 0.09 0.04 Med. 75 660 2.70 0.29 0.28 0.07 O.11 Med. 75 593 2.56 0.22 Q. 21 0. 08 0.05 Med. 75 495 5.06 0.35 0.32 0.14 0. 46 Med. 67.5 931 1,36 0.08 0.06 0. 04 0.02 Med. 67.5 879 1.96 0.23 0.22 0. 06 0.08 Med. 67.5 807 2.41 0.13 QO.11 0.07 0.00 Med. 67.5 688 2.27 0.38 0.24 0. 30 1.02 Med. 67.5 582 2.75 0.24 0.23 0.08 0.00 Med. 67.5 486 4.93 0.33 0.32 0.07 0. 24 Med. . 67.5 486 5.16 0.50 0.38 0.33 I.11 Med. 60 938 1.72 0.12 0.11 0.05 0.00 Med. 60 884 1.49 0.12 QO.11 0.05 0.02 Med. 60 786 2.53 0.15 0.12 0.08 0.00 -61- Table II. (Continued) 7 ' 1 B+G Type B TypecC Magnet Q k Oo (k, @.) Error Error Error TC T p Med. 60 587 2.54 0.25 0.24 0.08 0.00 Med. 60 479 3.94 0. 36 0.34 0.12 0.05 Med. 52.5 950 2.01 0.11 0.19 0. 06 0.00 Med. 52.5 784 2.61 0.16 0.14 0.08 0.00 Med. 52.5 583 2.10 0.29 0.28 0. 06 0.00 Med. 45 910 1.98 0.16 0.15 0. 06 0.00 Med. 45 772 1.96 0.17 0.15 0.06 0.00 Low 45 640 1,69 0.27 0.26 0.07 0.10 Low 45 584 2.68 0. 40 0. 40 0.08 0.12 Low 45 524 3.96 0.35 0. 34 0.11 0.12 Low 37 762 2.55 0.26 0. 25 0. 08 0.00 Low 37 734 2.37 0.26 0.26 0.07 0.00 Low 37 710 2.44 0.52 0.52 0. 07 0,00 Low 37 680 2.12 0. 43 0. 42 0.06 0.00 Low 37 652 2.13 0.60 0.59 0.06 0.00 . Low 37 620 2.42 0.31 0.30 0.07 0.00 Low 31.5 912 2.42 0.43 0. 43 0.07 0.00 Low 31.5 880 3.21 0.28 0.26 0.10 0.00 Low 31.5 853 2.40 0.34 0.34 0.07 0.00 Low 31.5 825 2.46 0.35 0.35 0.07 0.00 Low 31.5 790 2.59 0. 60 0. 60 0.08 0.00 Low 31.5 760 2.52 0.64 0. 64 0. 08 0.00 Low 31.5 744 2.08 0.29 0.28 0. 06 0.00 -62- 4. Error due to neglect of Compton scattering < - 3 °/o. 5. Error due to aperture penetration = + 0-1/2 °lo. 6.. Errog due to + .05° error in magnet angle and .1 “/o error in magnet momentum <i 1/2 °/o. The excitation functions for various pion C.M. angles are plotted in figures 11-15. Figures 11-15. Figure ll. Figure 12. Figure 13. Figure 14, Figure 15. , o(0_ = 147°) = 1.910 ~63- Excitation Functions for Reaction y + P—» Tr +P The corrected C.M. differential cross sections (open circles) for a constant pion C.M. angle are plotted as a function of k. The errors are the combined B and C type errors defined on page 58. The solid points represent the correction calculated for the contribution of protons coming from meson pair production expressed in terms of a pseudo-n° C.M. differential cross section. This correction does not necessarily show a smooth variation because it depends critically on the value of E, which varied from point to point (see page 50). The values of o7 for each figure are given below. 1 45° oOo i] @ = 67.5° The k = 490 Mev. data denoted by the triangle were taken with E_ = 1072 Mev. and the circle was taken with Eo = 722 Mev. Without the pair correction these two points would differ by more than the errors. An extrapolation of the Walker-Oakley data (7) from 450 to 490 Mev. gives o(e! = 67.5°) = 5 x 107? °cm*/ster. _ fo) o. = 90 ' Oo 8 = 120 T ! fe) ) = 147 T The k = 500 Mev. point denoted by the triangle was taken with Eg = 946 Mev. and the circle was taken with Eg = 725 Mev. An extrapolation of the Walker-Oakley data from 450 to 500 Mev. gives ~30.m*/ster. Without the pair correction these two points would be very different and both would be too large. 8 | T 1 o(k,@_ = 45°) aL : x10 °°CM*/STER 6F 4 5E _ OL | @ ® °¢@ n | | 400 500 600 700 800 900 1000 k (PHOTON LAB ENERGY IN MEV.) 8r— T T T T T o(k,@_ = 67 !/2°) aL ; x10 °°CM*/STER 6h _ o) os 4 i ae 2 | Ll 1 i _@ 400 500 600 700 800 900 1000 k (PHOTON LAB ENERGY IN MEV.) 8 | o(k,@_ = 90°) x10 °°CM*/STER b-O- e l e| N | ,° 0 400 500 600 700 800 900 1000 k (PHOTON LAB ENERGY IN MEV) T T q T | o(k,@_= 120°) x10 °°CM*/STER F-O— ! | | i | 400 500 600 700 800 900 1000 k(PHOTON LAB ENERGY IN MEV) o(k,9_ = 147°) 7h a xlo°°ocmM*/STER 4 6 _ 5r _] . 4+ e 4 400 500 600 700. 800 900 1000 k (PHOTON LAB ENERGY IN MEV) -69- VIII. ANGULAR DISTRIBUTIONS The angular distributions for the five energies investigated are _plotted in figures 16-20. The C.M. angular resolutions are indicated ' * at the bottom of each figure. The relationship between o. and e is given by the formula Py ' \ 1 - Bo sin @ tan Q. =- P (1) - B,/B + cos oe ' * Figure 21 shows that the lines of constant o. ona graph of P versus oF are nearly vertical in the region of investigation. In this case the angular resolution in the lab system is converted into one in the C.M. system by multiplying by a scale factor. Several of the values represented on the angular distributions were obtained by interpolating © the excitation functions to the correct energy. However most of the points represent a direct measurement. For convenience the data plotted in figures 16-20arelisted in Table III. Before beginning an analysis of the angular distribution it is desirable to make a few comments. The primary purpose of this experiment was to investigate the w° reaction in the 700-950 Mev. region. However enough data were obtained at the lower energies to include in this report. The pair corrections for the 490 Mev. data were excessive because the data were taken with Ey = 720 Mev. It was not convenient to run with a lower value of Ey during the course of this t experiment. There are not enough data backward of o.. = 90° at the ‘Figures 16-20. Figure Figure Figure Figure Figure a 16. 17. 18. 19. 20. Solid curve is m -70- Angular Distributions for Reaction y + Pi+1° +P Each figure shows the C.M. differential cross sections for a constant photon laboratory energy plotted versus the pion C.-M. angle. Most of the points represent a direct measurement; others are interpolations from the excitation functions. The errors are the combined B and C type errors defined on page 58. The angular resolutions are shown at the bottom of each figure. The solid and dotted curves are maximum likelihood (least squares) fits of the form m oe. k) = \ A (k)cos™ 0. The value of m will be used to characterize each curve. The values of the photon energy and the identification of the fits are given below. k = 490 Mev. Solid curve is m= 2. Dotted curve is m = 3; this fit goes negative at 165° and as such is not acceptable. k = 585 Mev. Solid curve is m= 2. Dotted curve is m = 4; this fit goes negative at 150° and as such is not acceptable. k = 690 Mev. 2. Dotted curve is m = 4. k = 785 Mev. It * 2. Dotted curve is m Solid curve is m k = 940 Mev. Hl - Solid curve is m =2. Dotted curve is m 7 J T T o(@,,k=490) 6+ x10 2°cM?/STER 4 \ \ an O 1 I\ I\ | La O° 30° 60° 90° I20° I50° 180° @_.(MESON C.M. ANGLE) of I T T T 1 o(@1,k = 585) BF yx 10 °°CM*/STER + O° 30° 60° 90° I2ZO° J {I50° 180° 61. (MESON C.M. ANGLE) ~73- T T | qT | o(@7.,k = 690) | x10 °°CM*/STER 4 “SAL. ir ‘SS | / ~s ON “4 [\ hh deh 30° 60° 90° I20° 150° Q1,(MESON C.M. ANGLE) ¢ — T 1 T o(@..,k= 785) 6 x10 °°CM*/STER - L_i\ [| ft | Q° 30° 60° 90° 120° 150° {80° 9, (MESON C.M. ANGLE) -75~ ft: TT T T o(8.,k =940) 6E x10 2°CM*/STER Nn T NB eo _/\ ft | |_ oe = =6©30° =660® 902 120°—s«:150° I80° 6,, (MESON C.M. ANGLE) Figure 21. -76- Kinematics for the Reaction y + P—»n° +P The solid curves give the proton laboratory momentum versus laboratory angle at constant photon laboratory energies. The dotted curves gives the same relation at constant pion C.M. angles. -77- {9/49W) WNLNAWOW NOLOUd ! | I 1 1 1 L L ! ! 1 Ke) () QO. oO oO Q fe} OQ O° fo) fs} Q fe) re) ° ° ° oO fe) fo) g oO fo) O = ° o © S o oO r N . = 30 40 50 60 70 PROTON LAB ANGLE (DEGREES) 20 10 -78- TABLE III. This table lists the values of the cross section used in the angular distributions. The central k values are given in Mev. Most of the points are direct measurements but a few are interpolations of the excitation functions. The errors are the combined B and C type errors defined on page 58. -79- Or’ + 60°E 8E° +F9'E 66° + 6S°2 61° + 22 '2 12° + l2°2 80° + 9€°T 06 °*19 Wo (° 2298/76 GI'+T1'€ EL’ + 1h '2 GI° + €G°2 91° + 19° LI’ + 96°T 09° +29°2 09° + GF'z S8L Lb* + 00°2 9g°+7€° Ip’ + L1L°2 - 9¢° + 06°2 LS* + 06°2 og’ ¥ bee - Ip" + 88°€ 9z° + L2°€ gz‘ + 48 °2 72° +99°2 ge° + L2°2 $7° + GL'2 Gz7° + G99 °2 GZ°+#S'2 06° +09°2 62° + 01'2 GZ° + SL'1 OF* +99°2 0¢° +0€°Z - 09° +0I'Z - 069 8S EL°T + 26°1 LO°T + S9°% Ip + €h's se°+90°S: 8z° + 00'S +I 9¢° + F6°E 9° +GG'F 06% = 4 olhl ffl 021 Ell SOT 06 GL oS 29 G°2g Sb Le of TE _OT S}fUf UI) SUOTINGIZ3SsIq Ie[NBUY UT pesM suUOTIIeg ssOID TeTUeTETIG “W'D “TTT eTge -80- two lower energies to get a good angular distribution. It is certainly reasonable to expect partial waves with Q>1 to be important at the energies under investigation (see following section). Consequently the angular distributions were fit to an expression of the form m o(k,@_) = > A 0s) cos"@. (2) n=0 by the principle of maximum likelihood (frequently called least squares). The maximum value of m that was tried was m = 4 for k = 490 and 585 Mev. and m = 6 for the other values of k. This was done on the Electrodata computer with a program coded by W. Wales. In an attempt to decide what value of m gives the most reason- able fit to the data a number of factors were considered. Some of the fits give a negative cross section outside of the measured regions. No attempt was made to refit the data with the constraint that the cross section not be negative for those values of m. The chi-squared good- ness of fit test (27) was applied to the fits and the results are summa- rized in Table IV. There are not enough data at the two lower energies for this test to be very good. However a value of m = 2 is certainly consistent with the data on the basis of this test. The m = 4 fit for the 490 Mev. data has a very strong forward peak mainly due to the 60° point, which seems very low. The m = 3 fit goes negative at 165° while the m = 3 and 4 fits for the 585 Mev. data go negative around 150°. On the basis of n° the fit of the 690 Mev. data is not improved -8l- TABLE IV. This table summarizes the chi-squared goodness of fit test. The photon energy in Mev. is listed in the first column. The second column gives ‘the highest power of cosQ, used in the fit; an asterisk indicates that particular fit gives a negative cross section outside the region of measurement. The third column gives the quantity 2 COD where 0 (0_) is the measured cross section and o (Ox) is the value calculated by the fit at On = 6;. The quantity s is the number of measured points in the angular distribution and e; is the combined B and C type errors for the measurement at each angle. The next column gives the expected value for 4 and the last column lists the probability that 24% could have a larger value than that listed in the third column if it has a chi-squared distribution. A small value of this quantity means the fit is very unlikely. The quantities in the parentheses are the results of the goodness of fit test with several suspicious points suppressed. See the text for a discussion of these points. 2 490 490 490 585 585 585 690 690 690 690 690 785 785 785 785 785 940 940 940 940 940 -82- Table IV. Chi-Squared Goodness of Fit Test m He 2 6.5 3* 3.4 4 3.3 2 9.1 3" 3.2 4" 2.8 2 9.2 3 8.1 4 6.6 5 6.6 6 6.6 2 35.7(19. 3) 37 26. 8(12. 6) 4 17. 9(6.5) 5 15.5(7.5) 6 13. 8(7.5) 2 26. 1(16.9 3 17. 2(11. 8) 4 16. 1(9. 3) 5 14, 3(9. 3) 6" 10. 5(8. 8) Z. 3. 2. 2 5 4 4 .3(7. .3(6. .3(5. .3(4. .3(3. .3(6. .3(5. .3(4. .4(3. ~ 4(2. 3) /3) 3) 4) 4) 3) 3) 4) 4) 4) . 20 11 53 . 36 42 42 47 . 36 . 26 0. <0. . 02(. Ol(. O1(. .03(. .04(, 01. . 02(. .01(. 01. . 03(. 01) 08) 37) 19) 11) 02) 07) 11) 05) 03) -83- by taking values of m larger than 4. It was surprising to see that the higher energy data have such large values for X 2 . The two 785 Mev. points at 52.5° and 67,5° give a very large contribution to X 2 ; if the v4 2 contribution of these two points is suppressed then the test (shown in parentheses in Table V1) indicates that m = 4 gives a good fit and larger values of m do not improve the fit. If the data were fit without these two points, 2 “X_. would be even smaller than that indicated in the parentheses. The 52.5°, 60° and 67.5° points were run very close together. Individual runs at each point were very consistent and the backgrounds were very small. The one point that gives a large contribution to 12 for the 940 Mev. data is the 90° point. The individual runs at this point also showed fairly good consistency. The U. 2 test without this point is also given in Table VI. Here again values of m larger than 4 do not improve the fit. Although the evidence is by no means conclusive, it seems that m values no larger than 4 are necessary to fit the data. The fits for m = 2 and 4 are shown in figures 16-20 with one exception. The m = 4 30 fit for 490 Mev. reaches a value of 7 x 10° cm*/ster. at 0°; for convenience of plotting the m = 3 curve is shown instead. McDonald (28) obtained a good fit to the 450 Mev. OM datawith m = 2 that showed a slight tendency toward a rise in the forward o direction. To further examine the fits to the angular distributions, the coefficients A, (k) for the curves drawn in figures 16-20 are plotted in figures 22 and 23 along with the values obtained by McDonald for Figures 22-23. Figure 22. Figure 23. -84- Angular Distribution Coefficients The coefficients A,(k) obtained by fitting the data with the formula m ! n t fox (0_,k) = Atk) cos o. n=0 are plotted versus photon energy. The open circles are the values obtained from the OM data by McDonald (28). The solid circles are the values obtained in this experiment using an m = 3 fit at 490 Mev. and m = 4 fit for all the other energies investigated. The triangles are the values obtained by using an m = 2 fit for all the data. The solid curves are best eye fits assuming m = 2 fits below 600 Mev. and m = 4 fits above this energy. A_ and A, Versus k ° 2 Where no errors are shown, they are smaller than the points. A): A, and A, Versus k -~35- — 30 TH l l - T T x1075° CM*/STER 25L | 20 : -20P 4 ~25 | _ i | | L L I 200 300 400 500 600 700 800 900 k (PHOTON LAB ENERGY IN MEV.) q al i i T . T q 200 300 400 500 600 700 800 900 k(PHOTON LAB ENERGY IN MEV.) -87- ‘the OM data. If one ‘assumes that only m = 2 is necessary for energies below 600 Mev. and m = 4 for higher energies, both A, and A, have reasonable shapes. It is believed that this is the best interpretation of the angular distributions. Once the fit to the angular distribution has been obtained, the total cross section can be calculated from the formula 1 1 The values of the coefficients selected and the total cross sections obtained by substituting these values in equation 3 are given in Table V. The total cross sections obtained by all the fits including the m = 6 fits are all within the statistical error of the values given in Table V. The total cross section is plotted in figure 24 along with that obtained from the OM data. ‘It is apparent that the 'resonance tail' is contributing to the total cross section above 600 Mev. In order to see if the rise above 600 Mev. is a broad peak riding on top of the 'resonance tail', it is necessary to subtract out the effects of the (3,3) resonance. This has been done by using the one level dispersion formula given by Gell-Mann and Watson (29). It is realized that the justification of this type of formula is difficult to establish in a relativistic region and it has been used only to provide a definite way of making the subtraction. The solid curve of figure 24 has been obtained from the formula = 20 x2 Py (4) (t-T,)° + rey4 -88- TABLE V. This table gives the angular distribution coefficients obtained for the data by assuming only terms up to cos2Q' are necessary below k = 600 Mev. and terms up to cos*o7 are necessary above this energy. The total cross sections obtained from an integration of these angular distributions are given in the last column. -89- é EL +162 S'L+1°9€ B°L +2 °KE 1'2 + 6°92 wo T'G + 8°EG 0¢ o1x to ae) urd ( S/o lI +2°2 ZL + Lb L'L + €°€- 9°0 +%°2- €e't + L'2- ly O¢- €€°+88'I- bE’ + OET- 1S¢° +00°I- I€° + 1F°0 OI FO $3tun) EL’ +2L‘1 PI’ +OL‘E Ez’ + &h'€ 81° + G6'2 Lz° + 02'S Oy SUOT}JIEG SSOID [e}JO], pue syUSToTJye04y uolnaqtajysiq rze~suy “A PT9U2L 0F6 Sel 069 S8S 06% Figure 24, -90- Total Cross Section for the Reaction y + P+n° +P The total cross sections obtained by integrating the angular distributions are plotted versus k. The open circles are those given by McDonald for the OM data. The solid circles are the results of this experiment. The solid curve is calculated from a one level dispersion formula of the type given by Watson and Gell-Mann (29). The dotted curve is the difference between the total cross section and the solid curve and is taken to represent the contribution not due to the (3, 3) resonance. 250 200k 4 I5O0r f d I lOOF 4 ~ SOF O _1 L yi i Nl l _t 200 8 300 400 500 600 700 800 900 k (PHOTON LAB ENERGY IN MEV) -92- where 2m X is the C. M. photon wave length, T is the sum of the C.M. photon energy and the nucleon C.M. kinetic energy, 2a/x)° = b (5) 1 + (a/X \2 and ia me 2 Pp: = ¢ (6) 2 1 + (a/x) To a, b and c’ are parameters whose values in this calculation are (170 + mc*) Mev., .88h/mc, 150 Mev. and .27 Mev., respectively. The dotted curve in figure 24 is obtained by subtracting the solid curve from the total cross section. It is seen that a broad peak starting at 600 Mev. accounts for the rise in the total cross section above this energy. Before discussing the possible significance at this point or attempting to interpret the angular distributions, some theoretical relationships will be described in the next section. _-93- IX. THEORY In order to see what theoretical relationships might be valid for photoproduction at high energies, it will be useful to discuss the basis of our understanding of these processes below 450 Mev. Much of this understanding has been achieved through the development of general relationships between photoproduction and meson-nucleon scattering. The scattering of the different types of pions is most easily discussed in terms of the isotopic spin formalism which was first applied to mesons by Kemmer (30). A system comprised of one pion and one nucleon can have six possible charge configurations which are given in Table V1 in terms of pure isotopic spin states. Table VI. I = 3/2 I= 1/2 L = + 3/2 Prt re) + fe) + I =+ 1/2 N2/3PqH - N1/3N7 N1/3Pr° + N2/3Ner L=- 1/2 N1/3Pa” + N2/3Nn° N2/3Pa - V1/3Nqn° I =- 3/2 Na a - Here N and P refer to the two charge states of the nucleon and me? ° refer to the three meson charge states. The hypothesis of charge independence means that I, the total isotopic spin, is a good quantum number for the meson-nucleon interaction and that the scattering amplitudes depend on I but are independent of 1: This principle -94- reduces to two the number of independent scattering amplitudes for a given orbital (Q) and total (j) angular momentum. For laboratory pion energies below 300 Mev. only S and P waves are important (31), and the data can be characterized by the two S wave phase shifts, 5) and 5.3, and the four P wave phase shifts, Say 513: 53, and 533: The subscript for an S wave phase shift refers to twice the value of the isotopic spin as does the first subscript of a P wave phase shift; the second subscript refers to twice the value of the total angular mementum. Although meson photoproduction occurs by the absorption of a photon, the meson-nucleon interaction is involved in a very direct way. Even though the total isotopic spin is not conserved in electromagnetic interactions (I, is conserved), Watson (32) applied the isotopic spin formalism to meson photoproduction and showed that the four basic reactions: IL y+P—+r' +N II. y + N——+r +P Il. yt P__+1 +P IV. y+ N- 7 +N are related by three independent amplitudes if charge independence is valid. The Roman numerals will be used to denote the reactions. The amplitudes, T, are given by: T(L) = N2t(3) + YN 2t(1) - N26t(1) (1) T(II) = N2t(3) + VN 2t(1) +N 26t(1) (2) -95- i T(IL) = 2t(3) - 1/2t(1) + &t(1) (3) T(IV) = 2t(3) - 1/2t(1) - &t(1) (4) where 6t(l1) is an amplitude which arises from nucleon recoil and leads to final states of isotopic spin I = 1/2; t(1) and t(3) are amplitudes which give rise to final states of I= 1/2 and I = 3/2, respectively. Equations 1-4 can be written in a more concise form by the use of 2x 2 matrices in nucleon isotopic spin space. For example Chew, Goldberger, Low and Nambu (33) write a general single meson photo- production amplitude as AzAtAt + af + ao? (5) where af +,0 are the isotopic spin matrices whose elements are given in Table VII. The A*’° are just three linearly independent combinations of t(3), t(1) and 6t(1). Table VII. Reaction I II III IV Matrix f* 1 1 0 0 - - 9 0 N2 -N2 f° 1 -1 N2 N 2 The experimental results of photomeson production have been analyzed by phenomenological theories and specific meson theories. Both of these approaches show that photoproduction is related to -~96- mieson-nucleon scattering through the phase shifts. Using the facts that the pion is pseudoscalar (34, 35) and has zero spin (36), Feld (37) has made an analysis on the basis of angular momentum considerations. The results are summarized in Table VIII where the total angular momentum and parity of the intermediate state are given in the second column and the angular distribution, wie), is given in the fourth column. The first subscript on the amplitude gives the order of the multipole and the second subscript gives twice the total angular momentum. The isotopic spin index, when shown, will be the value 2I enclosed in parentheses. When a mixture of states occurs, the angular distribution is complicated by interference terms. Table VIII. y-Ray. Intermediate Q of ' Absorbed State meson w(@_) Amplitude Mag. dipole 1/2 + 1 constant MM) . 2 ' Mag. dipole 3/2 + 1 5- 3cos 0. M)3 Elect. dipole 1/2 - 0 constant Ey 7 2 ! Elect. dipole 3/2 - 2 5- 3cos a. E13 WA ! Elect. quad. 3/24 1 1+ cos o. E43 Elect. quad. 5/2+ 3 1+ 6cos“0. E55 - 5cos*0' w If meson production occurs only in S and P states, Gell-Mann and Watson (29) have shown that the angular distribution is given by -97- 2 2 | ? 2! = 1 - w(0 ) l=, + [my | + 1/2|M,,|° (5 - 3cos“0_) 2 2,' 1/8|£,,| (1 + cos 0) * t - 2Re E |, (M,3 - M 1/2E,3) cosQ ll . * a - 1/2Re E,, (M,, - M,,) (cos e- * 2.! - Re M 3M), (3cos 0. - 1) (6) Watson (38) has shown that the phase of each multipole amplitude is given by the scattering phase shift of the corresponding final state. For example M,3(3) is the magnetic dipole amplitude which produces a meson-nucleon state with j = 3/2, & = 1, 1 = 3/2 and it can be written as i6 2 33 (7) M,3(3) = |, 3(3) Watson, Keck, Tollestrup and Walker (39) have analyzed the photomeson data below 400 Mev. from hydrogen and deuterium with a model that considers the pion-nucleon state with R= 1, j= 3/2, I = 3/2 to be one of strong, attractive interaction. This state is generally referred to as the (3, 3) state. By expanding the cross sections in terms of the multipole amplitudes and phase shifts and using the measured values for the phase shifts, they were able to find the various multipoles from the data. The results, which were obtained before the data of McDonald, Peterson and Corson were available, -98- indicated that both M, 3(3) and E,3(3) were important. Chew and Low (40,41) developed a cutoff Yukawa type meson theory of pseudoscalar mesons with pseudovector coupling. The theory achieves some simplicity by eliminating nucleon-antinucleon pairs and nucleon recoil. Instead of the many (multipole) parameters of the phenomenological theory of Watson et al, their theory contains only two, the renormalized coupling constant and the pion cutoff momentum. In this static theory the dependence of the photomeson cross sections on the scattering phase shifts is explicit. This theory has had some success (42) in correlating meson scattering and photoproduction. Recently Chew, Goldberger, Low and Nambu (33) have applied the dispersion relations to both scattering and photoproduction. By assum- _ing that the (3, 3) resonance not only dominates but exhausts the disper- sion integrals, they have been able to obtain the equations which in the limit of infinite nucleon mass are those derived by the static theory. One advantage of this new method is that the nucleon recoil effects can be included in an unambigious way. McDonald (28) has used this theory and the measured phase shifts to calculate the angular distribu- tion for + production up to 450 Mev. and has found that the agreement with the OM data is very good. Since the electric quadrupole term has not been explicitly calculated by this theory, it has not been included in McDonald's work. Unfortunately the successful techniques just discussed fail in higher energy regions. The (3, 3) resonance is falling off rapidly and cannot be expected to dominate as it does around 300 Mev. Scattering -99- phase shifts become complex when an additional meson can be formed in the scattering process further complicating the picture. Experiments on w -P scattering at 1.0 Bev. pion lab kinetic energy show that ratio of scattering with production of an additional meson to scattering which results in only one meson in the final state is about 0.6 (43). Consequently phase shifts are known to be complex in this region. However one can proceed to develop formulas similar to equation 6 which include higher partial waves. This will prove to be useful in the event that at most one or two multipole amplitudes are non-zero in this higher energy region; if this is the case it will be possible to identify them by means of the angular distributions. Moravcsik (44) has pointed out that a partial wave analysis for charged ' photomeson production is complicated by a retardation term which arises from the interaction of the photon with the meson current. Since no such term appears in neutral production, a normal partial wave analysis can be made. Because the range of the interaction between mesons and nucleons is not expected to be much greater than the meson Compton wavelength, angular momentum greater than h Q = a (8) (where 21 is the meson deBroglie wavelength) are not expected to be important. The above expression gives =2, 3, 4 at photon lab energies of 390, 650, 960 Mev., respectively. It was seen in the last section that the data could be fit by considering 2 < 2. Consequently, -100- a multipole expansion including only S, P and D waves will suffice. A very general expression for the photoproduction amplitude of a single meson can be written down without recourse to a specific meson theory. The general arguments are given in detail by Chew et al (33) and will be briefly summarized here. In this section all the quantities will be written in the C.M. system. The most general S-~matrix elements must be comprised of Lorentz invariant quantities. The available four-vector variables in the photoproduction of a spin zero meson are: 1. Incident photon momentum, k 2. Photon polarization, e 3. Initial nucleon momentum, Py 4, Final nucleon momentum, Po 5. Outgoing pion momentum, q 6. Nucleon Dirac operator, y The possible number of independent scalars which can be formed from these variables is restricted by the Dirac equation, momentum-energy conservation and the equations: 2 2 2 P) =P,=-M (9) q” =- m* (10) 2 k” = 0 (11) where m and M are the meson and nucleon mass, respectively. Using the fact that the matrix element must be linear and homogeneous in € _-101- and invoking the requirement of gauge invariance, Chew et al write down the four allowed forms as: M(1) =iygy -¢ y-k | (12) M(2) = 2iy,(P-¢ q:k - P-k qe ) (13) M(3) = yely-€ a-k - y-k qe ) (14) M(4) = 2y,(y-¢ P+k - y-k P.e - iMy-e y-k) (15) where P = 1/2(p, + p,) (16) and the appears because the mesons are pseudoscalar. Ys5 2PP The complete invariant photomeson transition matrix element is written as 4 (a, | |u,) =) (a, [Mta) |u,) A(i) (17) i=l where uy and u, are the initial and final nucleon spinors, respectively. The A(i)'s are functions of P-k, q-k and the nucleon isotopic spin. The isotopic spin can be made explicit by writing each A in the form given by equation 5, The differential cross section is written as do. <2 [| 1)| 2 (18) aly where F can be expressed Feio.er + Oa: (kxe)F2 (19) -102- Here the vector quantities are the regular three-vector equivalents of the terms defined earlier and © is the Pauli spin matrix. The quantities Fi F,; F,; Fy are given in terms of the derivatives of the Legendre polynomials by the formulas: co Fi = y- (RM yy + E ge) Pyar (4 Q=o0 + R41 My + Ey | Py) () it [a + 1)My, + My | Pye) (Eg, - My) By) + (Eg +My ) B(x) »©O F,= > (Mo, - Egy - Mg - E9_) Pp (x) where x is the cosine of the angle that the pion makes with the direction defined by the incident photon. The energy dependent amplitudes M n and E n refer to the transitions caused by the absorption of magnetic and electric radiation leading to states of orbital angular momentum Q and total angular momentum Q + 1/2, (20) (21) (22) (23) Each of the M's and E's can be written in the isotopic spin notation by + £ means of equation IX-5. After evaluating equations 20-23 for 2 4 2 and substituting in equation 19, an average over initial spins and polarizations and a sum over final spins yields -103- dg _ ' __2,' 3! ia = A, + A,cos@ + A,cos o. + A,cos Qo. ‘ 4 . + A,cos e. (24) t where a is the pion C.M. angle and: oO 2 Ay ~ le, 2 2 2 2 +9/2|E,,| +|M, | +5/2|M, | +5/2|E, | + 45/ale, P E 2- 2 2 * + g/2lm, | + 9/2|M, + 3Re Eo (M,_ -M,, 2+) * * - 3Re E 14 (Mi, - M,_) + 3/2 Re E,,(3M,, - 3M, _ + 5E,_) * FS * +3ReE, (M, -M,,)+ReMj,M,_ -9Re My, My (25) A, = 2ReE" (M M 3E ) = @Re EQ (M), - M,_ + 3E),) 6Re E* (3E 3M 3M. - 2E + ORe FE), (3E,, + 3M)_- 3M, - 2E,) 2Re EX (M. -M 18Re E~ (M M + ¢4Re E,_ (M,,- M,_) + eE,, (M,_-M),) * * + 6Re My, (3M,, + 2M,_)+ 9ReM,_(M,, + 2M, ) (26) -104- 2 “12 2 2 2 A, = o/2{, || - 3/2(M,, | - 3/2|E, | + 27/2 \E,,| + 27|M,,| 4 9/2|M P 3Re E* (6E E 3M 3 {Mz_] + 3Re Eo, (OE, + E,_ + 3M;, - 3M) _) +9Re E* (M,.-M 3Re M* e Fi, (M),-M,_)- 3ReM),M,_ * * -9Re E,, (9M,,- 9M, +7E,)+9ReE, (M,,-M, ) En + 81Re M 4M 2 (27) 2- * A, = 18Re E (Eo, + 2M), - 2M 3 1+ _tE 2 2.) * * + 30Re E5, (M), - M,_)- 6Re Mj, (2M,, + 3M,_) * - 15Re M,_M (28) a+ ok + 225/2 Re E 24 (M 2 A, = 45/4 Ee aa | 247 Mz_+ FE ,_) 4 - 45/2|M ? 2+ * -~ 90Re M, , Mp. (29) These results can be compared with those of Gell-Mann and Watson - given in equation 6 by making the substitutions: -105- E ot - Ei 3E,, = 1/2E,, M,_ = - Mj) M), = - M3 and equating all the other terms to zero. The results are consistent t with the fact that the highest power of cos a. that can appear in the angular distribution is 2j] - 1 when j is half-integer. The expressions will be used to see if any multipoles can be identified by the angular distributions. -106- X. INTERPRETATION As pointed out in section VIII there is a rise in the total cross section above k = 600 Mev. If the interpretation that this is a broad peak which starts at 600 Mev. is correct, the dotted curve in figure 24 shows that its value is about 10 °/0 of the value of the (3, 3) resonance peak. The peak in the I = 1/2 total pion-nucleon scattering cross section obtained by Cool, Piccioni and Clark (22) occurs at 800 Mev. pion laboratory energy and has a full width at half maximum of approximately 600 Mev. They have concluded that their data are consistent with scattering in a state of j = 5/2. The corresponding peak in photoproduction should occur at k = 950 Mev.; this is certainly consistent with the data of this experiment, and it will be interesting to investigate further the possible connection between these two phenomena. The fact that A, and Ay: the angular distribution coefficients, become non-zero around 600 Mev. suggests the possibility that a higher value multipole might be associated with the rise in total cross section. A non-zero A, term can only occur if the meson is produced ina j > 5/2 state. By the use of equations IX 24-29 it is possible to obtain relations between the various coefficients AL if only one or two multipoles are important. Judging from the behavior of the total cross section, the multipole responsible for the (3, 3) resonance, M,,,is large enough above 600 Mev. that it should not be neglected. If one assumes the only other non-zero multipole is one leading to a j = 5/2 state, the only choice is ES since A4 is positive (at least below + -107- 900 Mev.). With this choice one obtains the relations /A, =- 0.6 (1) Although equation 1 is consistent with the data, equation 2 is definitely not consistent. Since A, tends to go further negative between 600 and 800 Mev., an examination of equation IX-27 shows that the only non- interference term besides Mi, which will do this is BE, - If one takes M,,; Eo, and Ey as the only multipoles of any consequence, then by evaluating the contribution of the Mi, by means of the resonance tail contribution, the values of the other multipoles can be obtained from the value of the A,'s: Within the errors, which are large, this model gives results which are reasonable. The effects of Es. are dominant below 800 Mev. and then the effects of E 24 become dominant. However until there is some good theoretical guide, not much significance can be attached to an interpretation of this kind. Certainly the change in the angular distribution between 785 and 940 Mev. is indicative of some effect. The only conclusion that seems reasonable is that there is no one dominant multipole responsible for the rise in the cross section. The fact that A, is non-zero suggests that D wave mesons ina j = 5/2 state are produced. On the basis of this experiment alone, one cannot make any isotopic spin assignment. When the results of the charged photomeson production from hydrogen are available, it is possible that an isotopic -108- spin assignment can be made. A reference to equations IX-1 and 2 showsgthat the charged meson production contains a larger contribution of the I = 1/2 state than the m° reaction. Thus it will be interesting to | combine the present data with data on nt photoproduction to see if the rise above 600 Mev. can be attributed to the state of I = 1/2. Since this experiment became involved with meson pair pro- duction, it is probably appropriate to list the experimental evidence obtained at this laboratory about the ratio of double to single meson production. The only experiments available are this one and that of Bloch and Sands (11) which has been discussed in connection with the pair correction. They have obtained a total cross section of 56+ 17x 107 >° om? which is roughly constant in the energy region between 600 and 1000 Mev. The discussion in section VII gave the evidence that the reaction y + P—+r° + wo + P (3) was much less than y+ Pen +0 +P (4) A reasonable number for the total cross section of the two reactions is 70x 107 3% em". If one assumes that the cross section for the reaction y + P——»+3r' +N (5) is roughly the same as the reaction studied in this experiment, then -109- the minimum ratio of double to single production in hydrogen is about 1 in the energy region 600-1000 Mev. There is no experimental evidence about the reaction y + Pet +r +N (6) which might make the ratio even higher. The ratio of double to single meson production in P-P collisions at a comparable available C.M. energy is only 0.25 (45). Certainly more information is needed for the photoproduction processes before a study of multiple meson production can be made, -110- XI. EXPERIMENTAL SUGGESTIONS When this experiment was first begun, it was not clear that the detection of the recoil proton alone would yield good results for the single neutral meson production because of the unknown contribution of protons from meson pair production. After considering all factors, it is concluded that the method is a good one with a high enough counting rate to measure good angular distributions in a reasonable amount of machine time. The results, with the exception of a few points, are consistent and it is believed that they represent single production. There were a number of places for improvement and a discussion of these should prove valuable for the planning of future experiments on this reaction. It would be desirable to reduce the background and the pair correction and to extend the angular range of measurements. The pulse height analysis used in this experiment was very direct and worked exceedingly well up to a momentum of 850 Mev. /c. Above this value a different method would be preferable because the background from mesons produced in the Mylar walls of the target would be eliminated. A more careful shielding of the high momentum magnet counters by the use of a lead bridge from the counter house to the magnet would prevent electrons which are scattered by the air from getting into the counters. If this had been done, the use of the 1/2 inch piece of lead between the counters would not have been necessary. A great deal of time was spent measuring all the effects of this lead. If it is possible to shield the region of the external window of the target struck by the beam from the field of view of the magnet, the runs made -ill- forward of 30° will have much less background. The slit used in this experiment did a good job backward of 30°. The cosmic ray back- ground was a factor for the high momentum runs mainly because the machine was running poorly at that time; however the use of a counter in front of the magnet for high momentum runs might be useful. The meson pair correction is only important for angles forward of 35° in the lab. Since the energy spectrum of the beam is now known to have a sharp cutoff, it is possible to make the runs with lower values of Ey than were used in this experiment. Although a reduction in counting rate is not desirable, a smaller momentum window would reduce the correction even further. One extreme possibility is to allow the peak of the bremsstrahlung to define the upper limit of the APA® window. In this manner the pair correction can be completely eliminated for all the points run in this experiment. Unfortunately this method reduces the signal by a factor of two in the worst case but does not reduce the background. The background for the low momentum magnet runs could have -been reduced about a factor of two by the use of a lead slit. A smaller hydrogen target with a thinner Mylar cup would have reduced the scattering correction, improved the energy resolution and allowed the detection of lower energy protons with the low momentum magnet. Thus more forward n° C.M. angles could be studied. The equipment exists to measure 10 Mev. protons. The detection of the recoil proton by a magnetic spectrometer is the only means of studying the T : ' reaction at a laboratory angle of 0° (0. = 180°). The dynamics of the -ll2- reaction are such that electrons produced by the peak energy photons - have a lower momentum than recoil protons which are produced in the r reaction by photons whose energy is somewhat below the peak energy. This very interesting region of investigation must wait until the back- ground can be reduced to a reasonable value by the removal of much of the air path along the beam. The limitation of forward laboratory angle investigation was due to’ excessive background. -113- XII. CONCLUSIONS It is possible to study the photoproduction of single neutral mesons from hydrogen up ‘to photon energies of 1 Bev. by the detection of the recoil proton. A reasonable correction for the con- tribution of protons arising from meson pair production at forward laboratory angles can be made. Minor improvements of this method of study will reduce this correction for meson pair production and extend the angular range of measurement. It is necessary to use terms up to cos “9. to fit the angular distributions above laboratory photon energies of 600 Mev. This indicates the production of D wave mesons in a total angular momentum 5/2 state. The rise in the total cross section above 600 Mev. can be interpreted as a small broad peak which occurs in the proper energy region to be associated with the peak detected in pion-nucleon scatter- ing measurements. This peak can not be characterized by the dominance of any single multipole absorption as is the case for the (3,3) resonance near 300 Mev. 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