ABSTRACT ELASTIC NEUTRON-PROTON CHARGE EXCHANGE SCATTERING BETWEEN 1.75 GeV/c AND 7.20 GeV/c by Smith Thompson Powell,III Chairman: Michael J. Longo The differential cross sections for neutron-proton elastic scattering in the charge exchange region have been measured for incident neutron momenta between 1.75 GeV/c and 7.20 GeV/c. A neutron beam with a broad energy spectrum was produced by steering the external proton beam from the Bevatron onto a beryllium target. After collimation the neutrons were scattered off the protons in a liquid hydrogen target. The momenta of the forward-going protons were measured in a magnet and spark chamber system, while the much less energetic neutrons were detected by an array of thick scintillation counters. The detection efficiencies of the thick plastic scintillators were calculated. Several possible contaminating processes were investigated by-Monte Carlo techniques, and were shown to be effectively eliminated by the cuts made on the data. The data indicate the existence of an energy dependent structure in the differential cross sections.

ELASTIC NEUTRON-PROTON CHARGE EXCHANGE SCATTERING BETWEEN 1.75 GeV/c AND 7.20 GeV/c by Smith Thompson Powell,III A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1970 Doctoral Committee: Professor Michael J. Longo, Chairman Professor Byron P. Roe Professor Robert S. Tickle Associate Professor Gordon L. Kane Assistant Professor Henry C. Griffin

ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Michael Longo, for his guidance throughout the various stages of this experiment. I would also like to thank Dr. Martin Perl of the Stanford Linear Accelerator Center and Dr. Michael Kreisler of Princeton University for their collaboration. The Bevatron staff was most cooperative and helpful during the data acquisition phase. I thank Mr. Orman Haas who contributed his special skills with great zeal. Mrs. Jan Currier and Mr. James Walker did an excellent job of digitizing the spark chamber film. I especially thank Mr. Robert Lang, who not only very carefully measured all of the timing data, but also punched cards, drew graphs-in short, most ably handled many chores for me. I would also like to thank Dr. Gordon Kane and Dr. Marc Ross for many he lpfull discussions. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS..................................... ii LIST OF TABLES...................... v LIST OF FIGURES..................................... vi I. INTRODUCTION................ 1 A. General Comments............ 1 B. Kinematical Preliminaries.......... 5 II. SURVEY OF EXPERIMENTAL DATA AND THEORY..... 10 A. Experimental Data..................... 10 B. Theory................................ 13 III. EXPERIMENTAL APPARATUS AND PROCEDURES....18 A. Neutron Beam....................... 18 B. Liquid Hydrogen Target............... 23 C. Proton Spectrometer.................. 27 D. Optics................................ 31 E. Neutron Detector...................... 33 F. Electronics.37 G. Data Collection............. 41 IV. ANALYSIS.................................. 43 A. Spark Chamber Film..................... 43 B. Timing Film......................... 55 C. Proton Momentum Determination.......... 59 D. Kinematic:s.................... 65 E. Data Cuts and Subtractions............. 68 F. Geometric Detection Efficiency. 73 G. Neutron Detection Efficiency........... 78 iii

Page H. Data Contaminants..................... 82 I. Target Empty Corrections............... 85 Vo RESULTS AND CONCLUSIONS.........**...oooo... 86 A. Differential Cross Section Formula...... 86 Bo Normalizationo.......................... 87 C. Results and Conclusions.............. 89 LIST OF REFERENCESo.....o........................... 110 iv

LIST OF TABLES Table Page I Processes and Exchanges....................... 17 II The Differential Cross Sections for 1.75 GeV/c < p < 2.00 GeV/c.......................... 92 III The Differential Cross Sections for 2.00 GeV/c < p < 2.25 GeV/c.............................. IV The Differential Cross Sections for 2.25 GeV/c < p < 2.50 GeV/c................... 94 V The Differential Cross Sections for 2.50 GeV/c < p < 2.75 GeV/c...................... 96 VI The Differential Cross Sections for 2.75 GeV/c < p < 3.00 GeV/c...................a.......... 98 VII The Differential Cross Sections for 3.00 GeV/c < p < 3.25 GeV/c.................... 100 VIII The Differential Cross Sections for 3.25 Ge'V/c < p < 4.25 GeV/c......1_....................... ]02 IX The Differential Cross Sections for 4.25 GeV/c < p < 5.25 GeV/c.............................. 104 X The Differential Cross Sections for 5.25 GeV/c p < 6.25 GeV/c.............................. 106 X! The Differential Cross Sections for 6.25 GeV/c < p < 7.20 GeV/c................ 108 V

LIST OF FIGURES Figure Page 1 Kinematics of Elastic and Inelastic Processes 4 2 The Variables s, t, u........................ 7 3 The n-p Charge Exchange Data of Friedes et al. and of Manning et al.................. 12 4 The Neutron Beam Production Area............. 19 5 The Beryllium Target Scintillator Mask....... 20 6 Beam Exposures of Polaroids.................. 24 7 A Plan View of the Experiment................ 25 8 The Liquid Hydrogen Target Assembly.......... 26 9 The Hinge Construction of the Spark Chambers. 29 10 The Mirror Foldings....................... 32 11 A Diagram of a Neutron Counter............... 35 12 A Block Diagram of the Electronic Logic...... 38 13 A Frame of the Spark Chamber Film Showing a Typical Event................................ 44 14 The Legend for Figure 13..................... 45 15 A Special Fiducial Exposure.................. 48 16 The Projection Used to Determine the Real-Space Position of the Sparks............ 50 17 A Scatterplot of the Neutron Beam Profile at the Liquid Hydrogen Target Centerface........ 5] 18 The Difference between the Projected and the Measured Spark Positions in the Third Spark Chamber................................ 53 19 A Scatterplot of Events in Counter P1.......54 vi

Figure Page 20 A Frame of the Timing Film...... 56 21 A Light Pulser Exposure of the Timing Film... 58 22 The Difference between the Measured and the Calculated Timing as a Function of Neutron Counter...................................... 60 23 The Time-of-Flight Distributions as a Function of Neutron Counter.................. 61 24 The Path of a, Charged Particle in a Uniform Magnetic Field............................... 63 25 The Step-Size Correction to the Proton Momentum..................................... 66 26 The Error in the Determination of the Proton Momentum............................ 67 27 The Error in the Determination of the Four-Momentum Transfer................. 69 28 The Effect of the Data Cuts on the Timing Differences.............................. 72 29 The Difference between the Measured and the Calculated Timing as a Function of u......... 74 30 A Sample Background Subtraction............... 75 31 The Geometric Efficiencies for Two Beam Momenta...................................... 79 32 The Detection Efficiency of the Neutron Counters..................................... 81 33 The Neutron Beam Spectrum.................... 84 vii

Figure Page 34 The Differential Cross Sections for 2.25 GeV/c < p < 2.50 GeV/c.............................. 95 35 The Differential Cross Sections for 2.50 GeV/c < p < 2.75 GeV/c.............................. 97 36 The Differential Cross Sections for 2.75 GeV/c < p < 3.00 GeV/c.............................. 99 37 The Differential Cross Sections for 3.00 GeV/c P < 3.25 GeV/c........................101 38 The Differential Cross Sections for 3.25 GeV/c p < 4.25 GeV/c............. 103 39 The Differential Cross Sections for 4.25 GeV/c < p - 5.25 GeV/c.... 105 40 The Differential Cross Sections for 5.25 GeV/c < p < 6.25 GeV/c........ 107 41 The Differential Cross Sections for 6.25 GeV/c < p < 7.20 GeV/c.............................. 109 viii

I. INTRODUCTION A. General Comments The neutron-proton charge exchange experiment described here was a part of a more encompassing experiment designed to measure the n-p differential cross sections over a large range of' the center-of-mass scattering angle and as a function of energy. Despite its fundamental importance, very little was known about the n-p interaction above 1 GeV at the time of the conception of this experiment. The only existing data were, in fact, charge exchange data at 2.04 GeV and 2.85 GeV.1 The lack of data could be attributed, in part, to the difficulty of working with neutron beams. The experiment, which was performed in 1964, was divided into two parts as dictated by the energies of the scattered neutrons. That is, for scattering angles 4150~ in the center-of-mass system, the scattered neutrons had energies greater than 0.5 GeV and could be detected by their interactions in an array of' thick-plate spark chambers and scintillation counters. In the charge exchange region (scattering angles >1500in the center-of-mass) the scattered neutrons did not have sufficient energy to trigger such a detection system. The charge exchange data were taken with an array of thick plastic scintillation counters as neutron detectors in place of the steel chambers. Otherwise, the two parts of the experiment employed essentially identical equipment and techniques.

Only the charge exchange data. will be discussed in this report. Forithe details and results of the other phases of the experiment, the reader is referred to the published accounts.2 Previous charge exchange experiments detected only the recoil proton. Below 1 GeV it was possible to produce monochromatic neutron beams or to use time-of-flight techniques to determine the energy of the incident neutrons. Above 1 GeV a double charge exchange technique was used to set the energy of the experiment. In this technique a proton beam was directed at a target and a neutron beam taken off at zero degrees with respect to the proton beam. The neutron beam scattered off a second target which was composed of liquid hydrogen, and the protons which recoiled at small angles were detected. Charge exchange processes in both targets gave recoil protons with the full energy of the initial proton beam. By accepting only such protons, the experimenter could be assured that the n-p interaction were elastic. This experiment employed a new technique to measure simultaneously the charge exchange cross sections over a large energy range. The idea was to use a neutron beam containing a broad range of neutron energies (up to the accelerator energy) and to use the kinematics of the elastic events to determine the energy of the incident neutron on an event by event basis. To this end, both the recoil proton and the scattered neutron were detected. This

provides a powerful means of rejecting inelastic events since it is possible to measure the neutron angle and, somewhat crudely, its energy by time-of-flight. The efficacy of this technique is illustrated in Figure 1 which compares the kinematics for n-p charge exchange with those for the reaction n+pA +(1236)+n. Figure 1 also shows the kinematical limit for neutrons produced by any inelastic process. (The process n+p4n+(p+rr) in which the pion and the proton go off together gives neutrons most nearly like those produced in the elastic scattering.) We see there is a rather large range of neutron lab angles (which covers the extreme backward peak in the cross sections) from which the inelastic neutrons are excluded. It seemed, therefore, that the elastic and inelastic events could be sufficiently separated so that the differential cross sections for n-p charge exchange could be measured simultaneously for several energies. The experiment was thus of an exploratory nature in that a principle goal was to test the technique. The neutron beam used for both phases of the experiment was produced by steering the Bevatron external proton beam onto a beryllium target. The protons, which had kinetic energies of 6.3 GeV, produced neutrons with a broad energy spectrumn which peaked in the vicinity of 5 GeV. Downstream from the beryllium target a large magnet swept the remaining protons and other charged contaminants from the beam. After passing through a defining collimator the neutrons struck a liquid hydrogen target. The charge

KINEMATICS OF ELASTIC AND INELASTIC PROCESSES 96,,,, LIMIT ON NEUTRON FROM n+ p -- n*p+r u, 92 w CL 0 88z 0 n-.84 w z c0 80 w w Zn o1.75 GeV/c ACCEPTANCE LIMIT IMPOSED w BY GEOMETRY - 72. UL wO ~ ~ i.1anm Cs0EastcadIel isPoesse' Z "7.2 GeV/c 4 ~ ~ —-— n+p n+A* (1236) mi64 60 60O 20 40 60 80 100 120 140 160 180 200 220 240 KINETIC ENERGY OF THE SCATTERED NEUTRON (MeV) Fig. 1 Kinematics of Elastic and Inelastic Processes

exchange interaction produced a, proton which carried nearly the full energy of the beam particle and which proceeded at a small angle with respect to the beam line. In contrast, the scattered neutron carried very little kinetic energy (1-200 MeV) and its flight path was at approximately right angles to the beam line. The momenta of the forward-going protons were measured in a spectrometer composed of a bending magnet and four thin-foil spark chambers. If it were assumed that the interaction was n-p elastic, knowledge of the proton momentum allowed one to solve the kinematical equations for the incident neutron momentum. The scattered neutrons were detected by an array of thick plastic scintillators. In addition to indicating the presence of a neutron, the neutron detectors provided a coplanarity restriction and a crude determination of the neutron scattering angle. Further, the detectors provided time-of-flight information which was displayed on an oscilloscope and photographed. The information supplied by the neutron detectors was used in the later analysis to weed out inelastic events. B. Kinematical Preliminaries The Mandelstam variables are particularly useful for connecting experiment with theory. For the purpose of developing these Lorentz invariant variables we restrict the discussion to two-body nucleon-neucleon collisions in

which we neglect the neutron-proton mass difference. We define the Mandelstam variables s, t, and u by: P3 s=_ (P +P2P 2 t=-(Pl+P3) (1) u=- (P1+P 4)2 P1 P2 in which the four-momentum is defined by P —(, iE) (2) and ~p2 E2 - 2 P =p-E =-m (3) where p is the ordinary momentum, E is the total energy, and m is the rest mass. As we have drawn all of the four-momenta pointing in, we have not specified a scattering processo The fundamental hypothesis is that a single scattering amplitude, A(s,t,u), will describe any two-body nucleon process which one can represent byreversing the directions of any two of the four-momenta. In the case of n-p elastic scattering the processes could be represented as shown in Fig. 2. The interaction under study is usually referred to as the "s channel"o It should also be noted that the s, t, and u are not independent, but rather are constrained by

THE VARIABLES s,t,u s channel t channel u channel FP P2 P3 P4 P2 P PP P P2 P3 PP n+ p - n+p p -p n + E n+ — n+ f+ —, N + F n n p p+' f+P-* h+p PP P P P3 P4 pi P2 Pi P2 q Pi s = -(pi +p2)2 -(P p2)2 = -(PI -P2)2 t -(p p3)2 t -(PI +P3)2 t -(p _P3)2 U -( -P4)2 U ( (P)2 u = -( +P4)2 Fig. 2 The Variables s, t, u

the equation s+t+u=4m2 (4) in which m is the mass of the nucleon. We now consider an n-p scattering in the center-ofmass system and label the four-momenta. of the particles as shown. n + p * n + p P1 P2 P3 P4 P P 12 P4t In the center-of-mass systerm it can be shown that r S-(El+E2)2 t=-2p2 (-cose) u=-2p (I+coso). The differential cross section can be expressed as du/dt for foward scattering and do/du for backward scattering. Neutron-proton charge exchange scattering is backward elastic scattering. However, it should be noted that many authors reverse the definitions of t and u when discussing backward scattering so that they can express the backward

differential cross section as da/dt. Another useful relation may be obtained by evaluating u in the lab system in which case u=-2mT (6) where T is the kinetic energy of the scattered neutron in the lab system. Finally, the differential cross section as a function of angle in the center-of-mass system is related to the differential cross section as a function of four-momentum transfer by do _ p2 d (7) X~ lT Uio.

II. SURVEY OF EXPERIMENTAL DATA AND THEORY A. Experimental Data In 1962 Palevsky et al.l published the results of their n-p charge exchange experiment at beam kinetic energies of 2.04 GeV and 2.85 GeV. Although, as we shall see, quite a bit of n-p charge exchange data existed at lower energies, the attention of the physics community was focused on the multi-GeV experiments. Palevsky and his colleagues noted that the n-p backward cross section at u=O was an order of magnitude less than the p-p forward cross section at t=O. The charge exchange data also exhibited a very much sharper peak than that found in p-p scattering. The sharp peak indicated an interaction range of the order of 2 Fermis rather than the accepted nucleon size of 1 Fermi. And finally, tile data posed a problem as to which particles mediated the interaction. The one-pion exchange contribution varies as the square of the fourmomentum transfer and should,therefore, give a dip at u=O. However, the exchange of higher mass particles would have been inconsistent with the narrow peak. In 1965 the same group extended their measurements to 2.2 GeV.4 They combined their new data with their data at 2.04 GeV and plotted do/du versus -u. In this plot the extreme peaking of the data was more apparent. They parameterized the data as do = 6 9e49U 4u 06.9e+ 4.le (8) 10

11 Shortly thereafter Manning et al.5 published data for n-p charge exchange at 8 GeV/c. When plotted against -u their data showed a somewhat sharper peak than that observed at the lower energies. Further the u=0 differential cross section was found to decrease rapidly with increasing energy. The data of Friedes et al. and that of Manning et al. are shown in Fig. 3. In 1965 Wilson6 redirected attention to the low energy data in an analysis of the energy and the four-momentum transfer dependence of n-p charge exchange data. He plotted the data against -u for all energies and observed that a single curve, normalized to the u=0 values, fitted the data reasonably well from 91 MeV to 2850 MeV. He simply drew a smooth line through the data at 350 MeV to obtain the curve to which he compared all of the data. He also noted that da/du(u=0) was a strong function of energy. He concluded that, over a large energy range, the variation of the cross section with energy and the variation with four-momentum transfer were independent. In 1969 Mischke et al.7 measured the charge exchange differential cross sections for beam momenta between 600 MeV/c and 2000 MeV/c. They divided their data into fifteen momentum bins and fitted the data in each bin to d- d u epu (9) du (du) e ( 9) in which they restricted the range of u to cover the sharp peak. Combining their data with those of other experi

12 aD 4 * Friedes et al o2.3 GeV /c ond 3.0 GeV/c combined Maonninq et al _ 8.0 soV/: J cn C-) U,. N mt ~ CV'"-0..10 ~ 20.30.40.50.60 70 -U (GEV/C),42 Fig. 3 The n-p Charge Exchange Data of Friedes e t a. and of Manning et al..0 1 2 3 4 5 6 7 r i i (GV/C m rr 1 hnn — - rc z-'vr - nnaPT - PP iPn

13 menters, they showed that 8 increased from about 20 (GeV/c)- 2 at an incident momentum equal to 0.3 GeV/c to a maximum of 110 (GeV/c)-2 in the neighborhood of 0.8 GeV/co B then decreased to about 20 (GeV/c)-2 at momenta around 2 GeV/c before increasing to 70 (GeV/c)-2 at 8 GeV/c momentum. Thus the behavior at small u was considerably more complicated than that suggested by Wilson. B. Theory The nature of the nucleon-nucleon force has always presented many difficulties for theorists. Yukawa first conjectured that the force was mediated through the exchange of a particle —later identified as the pion. During the following years attempts were made, with some success, to write down a potential involving pion exchange 9 However, as the energies under consideration increased the validity and usefulness of the concept of a potential became more and more questionable. In recent years the emphasis has been on an S-matrix approach which relies heavily on phenomenological input010 Implcit in the S-matrix approach is the fact that a theory of n-p charge exchange has many constraints placed on ito For instance, as discussed in Section I-B, the amplitude which describes np-np must also describe pp+nn and np4npo F urthler, isotopic spin invariance leads to connecti.ons between np and pp cross sections. And finally, completely different reactlonsmay involve some of or all

14 of the same Regge exchanges. Adjusting the exchange parameters to fit n-p charge exchange has consequences for other reactions. In 1958 Chewll gave a prescription for extrapolating n-p charge exchange data to the pion pole and thereby determining the pion-nucleon coupling constant. At energies less than 1 GeV several experimenters performed 12-14 the extrapolation. With some difficulty they all were able to obtain values for the pion-nucleon coupling constant which were in good agreement with the values obtained from pion-nucleon scattering experiments. Therefore. it was somewhat surprising that the early papers, in the main, ignored the one-pion exchange when attempting to explain the data of Palevsky et al. However, Drelll5 had pointed out that the exchange of a single pion gave an amplitude which was proportional to u, and that the amplitude should therefore vanish at u=O. Consequently, following the publication of the data of Palevsky et al., several authors16-19 attempted to fit the data with exchanges of various combinations of elementary particles or of Regge poles, but in which no attempt was made to include u=O pion: effects. These theories were not able to fit all of the relevant data. An exception to these attempts was found in an early paper which was written by Phillips.20 He noted that one-pion exchange, through interference with a large, broad background due to other processes, could lead to

15 a sharp backward peak. He chose the background amplitudes to fit the data. With the realization that absorptive effects could drastically alter the effects of one-particle exchange,21 theorists reconsidered one-pion exchange. It was noted that absorption corrections could change the one-pion contribution at u=O from a dip to a peak. Unfortunately, the many attempts to fit the n-p charge exchange data with absorptive corrections indicated the presence of a 22-24 secondary maximum which was not evident in the datao Another difficulty was that, as noted above, the charge exchange peak persisted to very low energies —-even below the threshold for any inelastic processes. Thus absorptl.ve effects could not explain the low energy datao Other schemes to alter the u=O contribution to the scattering amplitude involved conspiracies and daughter 25 27 trajectories. 25-2 A conspiracy requires two trajectories with opposite parities which coincide at u=O0 Daughter trajectories form an infinite series of trajectories whose spin values at u=O are depressed by 1,2,3,oo units from the parent trajectory. However, it was recognized that these mathematical constructs represented weaknesses in 26,28 the theory and were not well motivated physically' A more physically motivated model was developed by Byers and Yang29 and was applied to n-p charge exchange by Byers.3 Their "coherent droplet" model combines

absorptive effects for small impact parameters with one-pion exchange for longer range interactions. At the present time several theorists are attempting to fit a large number of processes, including n-p charge exchange, using Regge pole exchanges and Regge cuts.28'3 The cuts are due to absorptive effects. The processes and exchanges which they consider are summarized in Table I. Their efforts seem to be meeting with some success. One difficulty which remains is that of explaining the presence of the sharp peak at low energies where absorptive effects can play no role. At high energies absorptive effects modify the low partial waves the most. It has been suggested32 that for low energies the elastic unitarity requirement modifies the lower partial waves in qualitatively the same way as do absorptive effects at higher energies. In concluding this survey it should be noted again that the attempt to understand the nucleon-nucleon force has been beset with many difficulties. However, progress has been made. It now seems clear that one-pion exchange effects must be considered in attempts to describe the n-p backward peak. Further, it seemsclear that absorptive effects must somehow be included. Finally, the realization that many diverse processes must be considered simultaneously presents an exciting challenge to theorists.

17 Processes Exchanges + Charged YPp 4 n r, p, A Photoproduction yn 4 u p Neutral YP 4 p P. w Photoproduction yp 4 r0 p Nucleon-Nucleon np 4 pn iT, p, A Charge Exchange pp 4 nn Backward Pion + p 4 Scattering u p 4 P1'- N, A u p nflu0 Backwaird yP * u n N, A Photoproduction yp uo p Table I Processes and Exchanges31

III. EXPERIMENTAL APPARATUS AND PROCEDURES A. Neutron Beam Neutrons were produced by focusing the Bevatron external proton beam onto a beryllium target. Approximately 5-7x1010 protons with 6.3 GeV kinetic energy were supplied during each 300 msec flat-top beam spill. The repitition rate was about nine pulses per minute. The beryllium target presented a cross section to the proton beam of 1/4 inch by 3/8 inch and was 8 inches long, or about 0.68 collision lengths, so that approximately 50% of the protons scattered in the target. Figure 4 shows the layout of the neutron beam production area. The proton beam size and position were monitored in two ways. For the first method, a mask composed of two thin scintillation counters mounted on 53AVP photomultiplier tubes as shown in Fig. 5 were placed immediately upstream of the beryllium target. The outputs from these counters were displayed on an oscilloscope. For the second method, a thin piece of clear plastic scintillator was placed directly in front of the target and viewed through a closed circuit TV system. The target, the counter mask, and the beam spot could be seen. With these two methods, shifts of the beam spot of about 1/16 inch could be detected, and the beam size could be monitored. The structure in the beam spill was also monitored with the oscilloscope display of the outputs from the mask counters. 18

Pb CONVERTER Be TARGET IC! ____ __ PROTON1 BEAMPOBEAMO POTON DEFINING I.D. BENDING MAGNET BEI 1 5/1j"I. COLLIMATOR SHIELDING NEUTRON BEAM Fig. 4 The Neutron Beam Production Area

SCINTILLATOR > Be ( I6" THICK ) TARGET LUCITE ~S UPP ORT 53 AVP 53 AVP 53 AVP ig. 5 The Beryllium Target Sciihtillator Mask

21 The beryllium target was also viewed by a three-counter telescope, called monitor B, which was placed about 7 feet below and aimed. at the target. The telescope B, in conjunction with others to be described later, was used to monitor the intensities of the neutron and the proton beams. A broad energy spectrum of neutrons was produced at the beryllium target. In addition, unwanted particles were produced copiously. The charged contaminants were removed by the large bending manget, M4D, which immediately followed the beryllium. M4D had a field gap that was 84 inches long, 15 inches wide, and 4 inches high. Nominally run at 1000 amperes (14 kilogauss at midfield), M4D deflected the proton beam away from the neutron collimator and into the shielding. Three pieces of 1/8-inch thick lead were placed in the gap of M4D as shown in Fig. 4 to serve as converters for gammas. Separating the lead allowed an electron-positron pair to be swept aside with less chance of radiating, thereby increasing the efficiency of the converter. M4D was followed by a 9 inch by 12 inch C magnet which further swept the charged pairs from the beam. The shielding wall was composed of 5 feet of steel followed by 10 feet of "heavy" concrete. The neutron beam was defined by a three-piece collimator imbedded in the wall. The first two sections had inside diameters of 5/8 inch while the final section had an inside diameter

22 of 1 inch. All sections were 5 feet long. The exit from the second section, which formed the defining aperture, was 23 feet from the beryllium target. The inside diameter of the final section was not directly illuminated by the beryllium target; it served to reduce beam halo by stopping many of the particles which underwent small-angle scattering in the defining collimator. The solid angle subtended by the collimator was 4xlO-6 steradians. An angular spread of about 2 milliradians was expected. A preliminary survey indicated. increasing neutron flux for decreasing angles with respect to the proton beam line; however, for safety reasons the collimator was aligned at 1~ with respect to the proton beam. This was done because the Radiation Control Group at the Bevatron did not want a magnet failure to allow the full proton beam into the experimental area. The size, spread, and position of the neutron beam was determined by placing Polaroid 3000 film at the collimator exit and at the back of the experiment cave. The Polaroid at the collimator exit was exposed during some test runs by placing some polyethylene immediately in front of the Polaroid. Neutrons which scattered in the polyethylene produced charged particles which exposed the film. The downstream Polaroid was exposed. during the course of the experiment. It was placed downstream from the M monitor telescope and from the 3-inch aluminum block. Thus many charged particles were generated which

23 could expose the film. Sample Polaroids are shown in Fig. 6 and a plan view of the experiment is shown in Fig. 7. The back of the experimental cave was 184 inches downstream from the collimator exit. At the collimator exit the beam was found; to be about 0o9 inch in diameter and very sharply defined. The downstream Polaroid showed the beam size to be about 1o2 inches which gives a full angular spread to the beam of about 2 milliradians as predicted from the collimator dimensions, An anticounter, Al, was placed at the collimator exit to insure that the beam particles were neutrally charged. The counter was 3 inches on a side and 1/8 inch thick. The anticounter also marked the entrance to the main experimental area as shown in Fig. 7. Bo Liquid Hydrogen Target The liquid hydrogen target was placed in the beam with its center 1 foot from the collimator exit. The target was 4 inches long and 2 inches in diameter. Figure 8 shows the target assembly. The liquid hydrogen was contained in a Mylar flask with 0.005 inch-thick walls. The flask was wrapped with 10 layers of aluminized Mylar and 10 layers of aluminum foilo Each layer of the wrapping was 0~00025 inch thick0 The flask was enclosed by an 8 inch diameter vacuum jacket. The beam entrance port was made of 0 020 inch Mylar, the sides through which scattered nelltrons passed were made of 0o040 inch aluminum, and the forward

-~~~~~~21 (a) 1 inch (b) Fig. 6 Beam Exposures of Polaroids (a) Collimator Exit (b) _Back Wall

NEUTRON DETECTOR A2,A 3N7 I MSHi WING &ME Al LH - - NE NE MONITTORS G I AL I" I. D. LEAD COLLIMATOR HPi MONITORS SPARK CHAMBERS P3 SPARK CHAMBERS P2 9 xr 36 BENDING MAGNET PLAN VIEW OF EXPERIMENT Fig. 7 A Plan View of the Experiment

ALUMINUM VACUUM JACKET MYLAR C —7 f ~~~FLASK FEED LINES J NEUTRON BEAM MYLAR BEAM PORT _____-i__ I LIQUID HYDROGEN TARGET ASSEMBLY Fig. 8 The Liquid Hydrogen Target Assembly

27 exit dome was made of 0.020 inch aluminum. Liquid hydrogen was supplied from a nearby reservoir and allowed to boil off at atmospheric pressure. The flask could be readily emptied to make "target empty" runs. The liquid hydrogen target was viewed by three monitor telescopes: G, H, and M. The G and M telescopes consisted of three small counters in coincidence, while the H telescope consisted of two counters. The G and H telescopes were about 1 foot from the target and viewed it from below. The M telescope was in the neutron beam line and about 184 inches downstream from the target. A three-inch thick block of aluminum was placed just in front of the M telescope to increase its counting rate and decrease its dependence on the charged beam contaminants which were generated during passage of the neutron beam through the system. C. Proton Spectrometer A charge exchange collision in the target volume resulted in a neutron with kinetic energy from 1 to 250 MeV coming off at nearly 900 in the lab, while the proton moved forward, with nearly all of the energy of the incident particle. Two thin-foil spark chambers immediately following the target gave the proton recoil angle and established its direction as it entered the momentum analyzing magnet. Two more thin-foil chambers after the magnet provided the remaining parameters needed for the

28 momentum determination. Scintillation counters P1, P2, and P3 indicated the passage of a charged particle through the system. The slow neutron was detected in an array of thick scintillation counters. The front spark chambers had an active area of 22 inches in the horizontal direction by 6 inches in the vertical direction; while the corresponding dimensions for the back chambers were 39 inches by 11 inches. Each chamber had four active 3/8-inch gaps. The plate material was 0.001 inch aluminum foil. The frames were made of Plexiglas~ In general, it is desirable to have the Plexiglas as thin as possible in order to minimize displacement of the track images due to misalignment of the frames. For this reason the frames on the short sides (through which one viewed the length of the chambers) were made 3/41 inch thick; however, the long frames at the top and the bottom of the chambers were made 1.5 inches thick in order to provide extra strength. Mylar windows which were 0.005 inch thick were glued to an extra frame which, in turn, was connected to the spark chamber proper by a Mylar diaphragm, or hinge as we labeled it, which went all the way around the frames. A cross sectional view of the hinge is given in Fig. 9. The chambers were filled with a 90% neon-10% helium mixture at a pressure slightly greater than atmospheric. The excess pressure ballooned the Mylar windows outward. The hinges isolated the foil plates from the stresses due to the ballooning so that the foils did not wrinkle0

29 MIYLAR HINGOE" IYL mAR _'I: I ra il 1 1Al FOIL LUCITE )aei FRAMES Fig. 9 The Hinge Construc tionl of the Spark Chambers

30 The chambers were constructed in a 48~ F environment and were operated at about 700 F. Plexiglas has a larger coefficient of expansion than does aluminum. Therefore, the aluminum foil was stretched taut when the chambers were warmed to operating temperatures. The aluminum foil was glued to the frames with Silastic RTV 891.33 Three counters in triple coincidence were used to detect the passage of a proton through the system. The first of these, P1, was placed between the front pair of chambers and the magnet. Because of its proximity to the magnet the photomultiplier for this counter was protected by a 3/8-inch thick steel tube in addition to the standard mu-metal shield. Counter P1 was 1/8 inch thick and 8 inches long. It was tapered from 1.75 inches near the beam to 3.6 inches at the light pipe. Counters P2 and P3 were placed immediately downstream from the last spark chamber. Both counters were 1/2 inch thick. P2 was 9-1/8 inches high and 39 inches long, while in an effort to cut down on accidentals, P3 was made 35 inches long and. tapered. It was 2.5 inches high at the beam end and 11.5 inches high at the light pipe. Note that the neutron beam traversed the proton spectrometer. Therefore, special precautions had to be taken in order to minimize the material in the beam's path and, consequently, in order to minimize the accidental rate. Counter P1, for instance, was made thinner

31 than the other counters in the system. Further, counters P1 and P3 were shaped to give a coplanarity restriction in the trigger. The analyzing magnet, Bev II, had an 8.25-inch gap with pole tips which were 36 inches long and 29 inches wide. The Lawrence Radiation Laboratory Magnet Test Group produced a series of maps of the vertical component of the magnetic fields.3 In particular, maps were obtained for each of six currents (392,588,855,960,1084, and 1203 amperes). A map consisted of 7 elevations (0., ~2., ~2.8, and ~3. inches about the gap midplane). At each elevation there were 2800 measurements distributed over an inch grid. The field was measured at each point to ~0.2%. For the charge exchange experiment the magnet was operated at 523 amperes which provided a nominal field integral of 4.77x105 gauss-inches. The current was monitored using a 33 micro-ohm shunt and a potentiometer. A 2 GeV/c particle was bent about 10 degrees and a 7 GeV/c particle was bent about 3 degrees. D. Optics Front-surface mirrors were used to view all chambers. Figure 10 shows the placement of the mirrors and the complex foldings of the light path required to reduce the images to a single 35 mm frame and to equalize the optical path lengths from all chambers to about 400 inches. Two views of each chamber, a "direct" view and a "stereo" view, were obtained.

MIRROR FOLDINGS TO CAMERA _..- PROTON TARGET _-~~j - - - -MIRROR -h~~~~_ -_ P4 P3 P2 P SPARK CHAMBERS SPARK CHAMBERS Fig. 10 The Mirror Foldings

33 Each view of each spark chamber was delimited by fiducials which were made by masking plastic electroluminescent panels35 with a machined aluminum plate. The panels were driven by a 500 volt, 5 khz square wave of 36 10 msec duration. In addition to the fiducials described above, "see-through" fiducials were provided for each view. These fiducials, powered with ordinary 110 volt ac, were turned on for a few frames at the beginning of each roll. Because they were viewed through the entire chamber and the Plexiglas frames, the "see-through" fiducials aided in mirror alignment and were particularly useful in later analysis. The camera also viewed a supplementary information bank which contained several important elements. First of these was a pair of large fiducials designed primarily to aid in automatically scanning the film. There was also a mechanical decimal frame counter and a neon flash-lamp binary frame counter. Neon lights also indicated which neutron counter fired for that event. The camera used was a fast, pulsed camera which could take up to 5 pictures during the 300 msec beam spill.37 A 240 mm lens was used at an f/8 aperture. The demagnification was about forty. E. Neutron Detector In contrast to the high energies of the recoil protons, the scattered neutrons had energies in the MeV range,

34 that is, from 1 MeV to 250 MeV. Because of these very different energies and because of the neutral charge of the neutron, very different techniques were employed for the detection of the neutrons. The heart of the system was an array of five thick scintillation counters. In order to be detected a neutron had to scatter in the scintillator and transfer enough energy to a charged particle (or particles) that it might produce sufficient light. Each plastic scintillator was 24 inches wide, 6 inches thick, and 12 inches high. The light pipes were mounted on the tops of the counters as shown in Fig. 11. The front face of the array was about 53 inches from the center of the hydrogen target, and a line drawn from the center of the array to the center of the target made an angle of 80.1 degrees with respect to the beam line. Thus the array extended beyond the 90 degree limit for neutrons and down to angles of about 67 degrees. Kinematics restricted inelastic neutrons to counters 2t and 5 (those nearest 67 degrees). However, gaimmnas which resulted from TTO decay could count in all of the counters. The photomriultipliers used were RCA 6810A's. They were operated at approximately -2100 volts. The threshold for nei.tron detection, that is, the discriminator levels and the turbe voltages for each counter, was set by using a 49 microclLrie T1 source. The discriminators were set to a threshold of 0.5 volt. In order to set the tube voltage for a counter the thallium source was centrally attached to the

35 NEUTRON COUNTER \ UVT Lucite Light Pipe,~ —Scintillotor12" Fig.4" -11 A D Fig. 11 A Diagram of a Neutron Counter

counter at which spot the light-tight wrapping was held to a minimum. The tube voltage was adjusted until the system counted 5000 triggers per second. This trigger rate was far above noise levels and at the same time, was far below the thallium decay ra~te. Thus we felt we were counting only the upper portion of the beta energy spectrum. In other words we set the threshold for each counter to detect 0.76 MeV betas, which was the maximum energy of the betas produced by the thallium. Because of saturation effects in the scintillator the 0.76 MeV betas simulated 2 MeV protons. The threshold settings were frequently checked by the same procedure. As noted above, information denoting the counter or counters which detected a neutron was displayed in the main experimental area and photographed along with the spark chamber tracks for each event. In addition, timing signals were displayed on a Tektronix 517 oscilloscope and photographed with a separate camera. Two anticounters, A2 and A2', were used to insure that the particle entering the neutron counters (or their light pipes) was neutral. Counter A2 was 13 inches high, 21 inches long, and 1/2 inch thick. Counter A2', which shielded the neutron counters' light pipes, was also 21 inches long, but was only 6 inches high and 3/8 inch thick. The light pipes for A2 and A2 and A2 were placed as far as possible from the neutron beam in order to minimize the number of particles which scattered into them.

37 The neutron counters were shielded from the accelerator background and from particles scattered out of the neutron beam by an arrangement of paraffin, boron, and lead which surrounded the counters on the top and bottom and all sides save that facing the target. Boxed paraffin formed the bulk of and outer perimeter of the shielding. Three-inch borax bricks served as the second ring of defense. Boron has a high cross section for thermal neutrons and gives off a low energy gamma. Three-inch lead bricks formed the innermost ring of shielding. F. Electronics The fast electronics logic is shown in block form in Fig. 12. The 100 megahertz circuitry was composed, in the main, of commercially available modules from General Applied Science Laboratories. At the start of the beam spill the circuitry was gated on by a timing pulse from the accelerator. The neutral charge of the beam was assured by the anticounter Al. Counlters PI, P2, and P3 recorded the passage of a charged particle through the proton spectrometer. A null signal from anticounters A2 and A2' plus a signal from any one of or any combination of the neutron counters indicated the presence of an associated neutral particle. An event trigger, then, was defined as Al Pi P2 P3 A2 T' Ni (i=1,...,5).

38 Al PI P2 P3 A2 A2' P COINC l — FAN IN TO NEUTRON COINCIDENCES, TO NEUTRON COINCIDENCES ACCIDENTALS, AND SCOPE DISPLAY AND ACCIDENTALS NI N2 N3 N4 N5 LIMITERS — F DISCRIMINATORS- D P. COINCIDENCES-'- N N l SCOPI SCALER DRIVERS — FAN OUT- (FFO rF 0 SCALER) F GANG SC6 CIRCUITRY TRIGGER LIGHTS ~ SPARK GAP TRIGGER TRIGGER BLOCK DIAGRAM OF ELECTRONIC LOGIC Fig. 12 A Block Diagram of the Electronic Logic

39 A sub-coincidence, here called the P-coincidence, was formed by placing the proton spectrometer counters, P1, P2, and. P3, in coincidence; and by placing the counter at the collimator exit, Al, in anticoincidence. The P-coincidence signal was split for use in other logic units. The P-coincidence signals, with the proper delays, were fed. into a coincidence module for each of the five neutron counters along with the signal from the appropriate neutron counter. The signals from the two counters, A2 and A2', in front of the neutron detecter array were combined and. placed in anticoincidence with each neutron counter. The coincidence widths were separately set for each neutron counter. They were calculated to be wide enough for each counter to accept all of the charge exchange events which could physically reach that counter with energies above threshold. The outputs of the five N coincidences defined above were added so that a signal from any one (or any combination of counters) defined an event. Once an event had been defined the signal was split to initiate several actions. The first of these was to gate off all coincidences including the beam monitors for 60 msec to allow time to record the event, advance the camera, etc. before the advent of a new event. During that time interval a spark gap was triggered to pulse the spark chambers. The fiducials were flashed, as were the frame and pulse counters and the neutron counter display. Then

40 the film in the fast camera was advanced. In the meantime, the 517 oscilloscope trace was also triggered so that the timing information might be recorded. If the event were the first of the several that might be detected during a beam pulse, a delay gate was triggered. The delay gate triggered a push-pull amplifier that was connected to the vertical deflection plates of the oscilloscope. This had the effect that the timing information for the first event of a beam pulse was recorded at the top of the film; while subsequent events had their timing information displaced downward on the same frame. The reason for placing on a single frame the timing information for all events which occured during a beam spill was that the oscilloscope camera had a slow advance mechanism. After about 1/2 second delay, that is, after the 300 msec beam spill was surely over, the delay gate reset the push-pull amplifier, advanced the film in the oscilloscope camera, and flashed the binary frame counter for the next beam pulse. The timing information consisted of signals from the P-coincidence and from each of the neutron counters. Scalers recorded the number of events, as well as the P- and N-coincidence counts, and the counts from the monitor telescopes B, G, H, and M. Accidentals rates were also recorded. The accidentals rate was monitored by forming two coincidences with neutron counter 5. One coincidence had the proper delays while the other, Nacc,

41 had the P-coincidence signal delayed an extra 100 nanoseconds. The lengths of the various timing delay cables were set by using a system of corona lamps.38 A lamp was centrally attached to each scintillator required to define an event. All lamps were driven by a common source, but calculated relative delays were inserted to simulate the time sequence of a real event. The photomultiplier outputs were viewed on an oscilloscope and delays were inserted in the fast logic to properly align the signals forming each coincidence. The light pulsers were also used to frequently monitor the performance of the electronics. G. Data Collection Approximately 5-7x10 protons struck the beryllium targetJ during each 300 msec beam spill. Two to three pictures were taken during each beam spill for a total of about 66000 pictures with liquid hydrogen in the target. Periodically the target was emptied and a "target empty" run waes made. Over 7500 pictures were taken in this mode. The "target empty" trigger rate was about 1/3 of the T"targut full" rateo Thie Lawrence Radiation Laboratory Photographic Services Group developed each roll of film within an hour or two after exposure. A quick check could then be made of the performance of the spark chambers, the fiducials,

42 and the other components of the system. A number of pictures were taken with the magnet turned off. The purpose of these pictures was to establish a straight line through the system. A number of pictures were taken with the B monitor telescope serving as the sole trigger. Presumably these pictures had nothing to do with real events in the target, so these pictures were used to determine the frequency of spurious tracks in the spark chambers. Periodically the thresholds of the neutron counters were checked and were reset with the thallium beta source. The fast electronics logic was checked by pulsing the corona lamps. The light pulser timing was recorded on the oscilloscope film as an aid to later analysis. A 50 megahertz sine wave was recorded on the same film to provide sweep calibration. During the run the accidentals counting rate averaged about 15% of the neutron counter N5 rate. Presumably the accidental events did not- reconstruct as elastic events and therefore, their only effect was on the data collection rate.

IV. ANALYSIS A. Spark Chamber Film A typical frame of the spark chamber film is shown in Fig. 13 and the various elements of the scene are labeled in Fig. 14. The condensing and folding effects of the mirrors make it somewhat difficult to follow the path of the proton except in the stereo views. The spark chamber film was prescanned to determine which events should be measured. Events were rejected for any of the following reasons. a) There were no tracks in any one view. About 7% of the frames fell into this category. b) There were multiple tracks in any one view. About 42% of the frames were rejected for this reason. c) More than two neutron counters were triggered or two non-adjacent counters were triggered. Approximately 2% of the frames were rejected by this criterion. d) The proton obviously scattered off the magnet pole tips (as seen in the stereo views), or the sparks were of very poor quality. Only 2% of the frames fell into this category. A missing track would have introduced large errors in the 43

.... 13 A Frame of the Spark Chamber Film Showing a Typical Eve4z Fig. 13 A Frame of the Spark Chamber Film Showing a Typical Event

FIDUCIAL BINARY FRAME COUNTER ROLL NIUMBER iiI L352 396 DECIMAL FRAME COUNTER NEUTRON DETECTOR FLAG FIDUCIALS PROTON PA;TH iFI i 1 Ie f 5 3~~~~~~~' 1 9 Fig. 14 The Legend for Figure 13

46 solutions for the proton momentum and the scattering angle, if indeed, solutions would have been possible. Similarly, criterion c) limited the errors allowed in the scattered neutron angle and in the timing. A scattering of the proton in the magnet would have obviously destroyed the credibility of the event reconstruction. Approximately 80% of the frames rejected were rejected due to the presence of extra tracks. Multiple track events were rejected because of the difficulties in correlating tracks and because we felt most of these events were inelastic. This feeling was based on a scan of the film taken by triggering on the B monitor telescope which looked at the beryllium target in the proton beam. Since such a coincidence should have been uncorrelated with events, elastic or inelastic, which occured in the liquid hydrogen target, the spark chambers should not have shown tracks. The paucity of tracks observed in the test run confirmed the idea that most of the multiple tracks observed in the regular ruins were associated with inelastic processes and were not random in nature. In any case, no u-dependent biases should have been introduced by ignoring multiple track frames. About 22000 frames were measured for further analysis. The film was measured on a semiautomatic scanning machine. The film was placed on a moveable stage and projected onto a glass viewing screen. The film was magnified about twenty times. The stage could be moved

47 to align the point of interest with a cross hair on the viewing screen. Encoders translated the position of the stage into a form which was automatically punched onto IBM -4 cards. The least count of the device was 1.25x10 inch on the film which was 0.005 inch in event space. A master fiducial set was measured at the beginning of each roll. Twenty-eight fiducial points were measured several times on a single frame to obtain an excellent master fiducial set. Four widely spaced fiducials were chosen from this set and measured for the other frames of interest on that roll of film. Three of the fiducials were used to solve, via a least-squares technique, for the translation, rotation, and magnification parameters required to fit each frame to the master fiducial set. The fourth fiducial was used to check on measuring errors. Events with excessive measuring errors were discarded. Thie point in the middle of each track in each of the eight views was measured. Punched onto cards along with the fiducial and spark locations, were the frame number, the neutron counter (or counters) number which fired, and a code indicating the person performing the measurements. The cards were read onto magnetic tape for computer processing. Each event was mapped onto the master fiducial set and then the real-space positions of' the sparks were determined. Figure 15 is an example of the special fiducial pictures taken at the beginning of each roll of film. It shows the "direct" fiducials which were flashed for

ID Fig. 15 A Special Fiducial Exposure

49 every picture taken and the "see-through" fiducials which were illuminated only for the special exposures. By using both sets of fiducials one could determine the position of the optic axis for each view. Figure 16 shows that simple projection revealed the real-space coordinates of the sparks. Corrections were made for the passage of the light through the Plexiglas frames. Minor adjustments were made in the real-space coordinates of the tracks. The first of these was obtained by projecting small angle tracks from the front chambers to the hydrogen ta rget centerface. We considered only tracks which made a small angle ( with tangents ~0.05) with respect to the neutron beam line; thus, the actual interaction point could be disregarded and a good beam profile at the target centerface could be obtained. Slight adjustments (0.050 inch) had to be made in the solutions for the spark positions in the front chambers in order to center the beam profile in the known beam position. Figure 17 is a sca ttergram of the adjusted beam profile. The dashed circle outlines the expected beam position. Events were expected at a radius 0.1 inch larger than the beam radius because of the projection angles of the events. However, about 6% of the events fell out of this region and were persumably due to interactions in material other than the hydorgen. The data cuts described in Sect. IV-E reduced the fraction of events which originated outside of the beam area to less than 1%.

APPARENT CAMERA POSITION I I i I APPARENT DIRECT SPARK FIDUCIALS POSITION I; I - " I APPARENT + CAMERA 7. a POSITION SEE-THROUGH PTIC FIDUCIALS, AXE S Fig. 1a6 The Projection Used to Determirne the Real-Space Position of the Sparks

51 DISTRIBUTION OF SMHRLL RNGLE EVENTS RT TRRGET CENTERFRCE 0 0.-_ I.. l 6 u,~~~~~~ 9 tr,~~~~~~ o *~ N-0 L).. **p r*4Ir~* CD ~ uJ~~~~~~~~~~~~~~~~~~~~.0~ b0.. ISO, *(I *Np'-1~~.0-.5.00 ~.5.-o Fig. 17 A Satterplot of -the Neutron Beam Profile at the Liquid Hydrogen Target Centerfac-e t~~~~i * jC -+ ~~~~~~~~~~~~~~~~ Fig.~~~~~ e'7e ecterpo ~f ~h etolRemPoie..,.?i ydoe TreiCnera~

A second correction involved the relative positions of the front and back spark chambers. A-number of pictures were taken with the magnet turned off, thereby producing "straight-throughs". These tracks defined a set of straight lines through the system. These pictures were measured and the real-space track coordinates were determined in the usual manner. Then the tracks in the frort two chambers were connected by a straight line which was extended into the regions of the back chambers. The positions of the sparks in the back chambers were compared to the position of the extended line. Figure 18 shows the horizontal component of the error in the third chamber. The positions of the sparks in the back chambers were adjusted accordingly. The cause of the large shift was -unknown, but after the adjustment no significant error in the measu..red angles is thought to occur. One of the reasons for thinking that no significant track positioning errors remained, was that the distribution of the differences between the calculated and measured times-offlight for the neutrons which triggered covunter N1 was centered at zero. The calcula,ted time-of-flight wa;s a function of the proton scattering angle and the proton mcomentuim. An investigation of the width of the peak in Fig. 18 indicates the measurement errors in each spark chamber were slightly less than 0.030 inch in the horizontal plane. Similar errors were made in the vertical plane measurements. Figure 19 is a scattergram of tracks projected from

53 PROJECTED MINUS MEASURED X P3.20.18.16.14 O.12 0.06 oo| -1.00 -.60 -.20.20.60 1.00 INCHES Fig. 18 The Difference netween the Projected and the Measured Spark Positions in the Third Spark Chamber

Z (INCHES2 -3.00 -2.00 O.00.00 1.O0 2.O0 3O0 IiIt''- Ij to ":: ~~' t' e o' e to ~'~'.,,'7.'. I Ptt:rt...<..-t:.g.~t.,'.,-:,' ~ ~ ~ $ ~ b i~~~~~~~~~~~~t II to~ ~~ r r~~~~~~~~~~~~~~~~~~~~~*rC+ 4 t". i'..A.- I k~(~~~~~~~~~~~~~~~~~~~T * "~I ~e ~~ -:e.f.''. V',,''~~'*': " V''':. ~..,.., 0 ct ( X. to to tn xD z I ~; to..',,,, \~,:;W to~~~~~~~~~~~~~~~~It ~ " ~r 1'~' "'r"'I, I:: ~...' ]..$'~ $ I ~ ~ t ~ s$,,.U to'. I I ~z ~,t~ ~ ~) 3:~ ~ ~~~~~~~~,, ~.:.' ~~ ~.rtr ~.), ~ ~ ~ e I~~ I 4.'.''...,:'~ 1. ~ ~, - - D3 ~ ~ ~ ~ E'r qr'~3!~.'''. ~ ~.' <~~ ~~~~~~~~~~~~ ~.r. c,_~.:',..'~': to'.~.".~ ~.,~;.'. ID *f J*,)tZI~~~~~~~~~~ r J I to t'.%."..'' ~,'. ~,~.? 4'.',' to''" to"' to ~to.. r0~ ~ ~. d=' -II ~5'....'t.:' "'.',..,;'_ /'.'.' r.'' CS~~~~~ ~ ~~~~~~~~~~~~~~~~ ~ ee. ~~j ~~~ O ~ ~~~~~~~~~I...' ~ ~;.. r'~~...q,.. t.O'E I:-.'..:..~.,. e$ ~e.' e ~ to3'~ to t t/,,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~t o ~~I''...,'.",..'."",:'"" I ~ "1 ~r ~~';~ %'' *' *' r~~~~~~~~~~~~.., ~'.. ~Ji....~I,e ~~~ e d~ L _-.-;, r-..: (~,-,. -~ to LI ~3 I,-.... ir~~~~~~~~~l

55 the front two spark-chambers into counter P1. The outline of the counter is shown by the dashed line. The counter was designed to be slightly oversize. Such scattergrams serve as good checks on the measurements and corrections used. B. Timing Film Figure 20 shows a picture of the oscilloscope screen which displayed the timing information. In fact, the top trace belongs to the event for which the spark chamber film is shown in Fig. 13. The other traces correspond to events which occured later during the same beam pulse. They were displaced downward with the push-pull arrangement described in the section on electronics. The neutron pulses are the smaller pulses which occur to the left of the frame, and the proton pulses are the larger pulses near the right-hand side. Because of the manner in which the oscilloscope was triggered, faster neutrons produce longer distances between the neutronproton pulses. The blobs at the base of the picture are the binary lights. All of the measurements were made by projecting the film onto a glass screen. A special centimeter rule was aligned with the trace base line and the measurements were made from the leading edge of the neutron pulse to the leading edge of the proton pulse at about 2/3 the height of the pulses. (The velocities of the protons were essentially the velocity of light. Therefore, the measured timing was directly related to the neutron time-of-flight.) The measuring

..............................~:~i~~;~ i..............................................................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::~i::::i:::::i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::ii~~~~~~~~~~~~~~~.Picp:::::~~~~~~~~~~~~~~~~~~~~~~~~~......:~:~:~~: ~~~i~~~~~~~~~~~~~iii~~~~:~i:~:. ~~~.......:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Xp;..........................% ~ i.:::j:::i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......................~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~533~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............-~iii ----------— ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:: -$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F a e 0..e7

57 system was calibrated and the uniformity of the sweep rate was checked by similarly measuring the signal from a; 50 mHz sine wave generator. The sweep rate was found to be uniform. The distance-to-time conversion factor was found to be 5.01 nanoseconds per centimeter. The errors on the distance measurement resulted in errors of about ~3 nsec in the timing. An additional error of perhaps i4 nsec was introduced because the N signal came from a discriminator rather than directly from the photomultiplier. Large pulses from the photomultiplier would appear to arrive at the discriminator earlier than small pulses. Each neutron counter was exposed to neutrons with a. large range of energies. Light pulsers were attached to each counter and were timed to simulate events with energies corresponding to the middle of' the energy acceptance of each counter. Timing pictures were made of the signals generated by the light prLlsers as shown in Fig. 21. From the left, couinter N5 is represented by the first pulse, and so on to coniter Ni, and finally at the far right is the broad pulse from the P-coincidence. The light pulser timing was measured for each counter. Since the light pulser delays were arranged to simiulate events in the middle of the timing range for each neutron counter, it was possible to calculate a real time-offlight and associate it with the proper light pulser. The target to counter time-of-flight for an event was then calculated by using the following formula. T = (Tcentral + Tpulser)i - Tscope (10)

.................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................. II..............................................................................................................................................................................................................I.............................................................I............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................I I-...................................................................................................................... I11 1.1.11.................................................................................................................. I...................................................................................................................................................................................................................................................................................................................................... - -------------------------...... - ---------------------................................................................. Pu e T'm4 nzlser'.E'Xposu-re o a,

59 Tcentral is the time-of-flight associated with the light pulser. Tpulser is the light pulser timing as measured from the oscilloscope trace. The subscript, i, indicates which neutron counter fired. T is the timing measured for scope the particular event under consideration. The proton scattering angle and momentum completely determined the kinematics of the scattering if one assumed that the scattering were n-p elastic. Therefore, the timeof-flight of the neutron could also be calculated and compared to the measured value. Distributions of the differences between measured and calculated times-of-flight were plotted for each neutron counter. In some cases the distribiltions did not center on zero so small empirical corrections were made to the above formula.. These corrections varied from -4 to +1 nsec. Figure 22 shows these difference distributions for each of the neutron counters after the corrections have been made. Figure 23 shows the measured time-of-flight distributions for the counters. In the difference plots a neuJtron which was faster than calculated would give a positive point on the graph. In Fig. 23 photons should give a peak centered at 5 nsec. This can be seen clearly in the distributions for counters 2 and 3. Photons were timed out for coulnter 1, and the photon peak merges with the neutrons for counters 4 and 5. C. Proton Momentum Determination The momentum of the proton was determined through the

60 DELTA TIME FOR COUNTER 1 S. -0.oo -20.00 -10.00 0o.oo 20.00 00.00 NANOSECONOS DELTA TIME FOR COUNTER 2 DELTA TINE FOR COUNTER 3 I1 zr~oo ~ -00.00 -3.00 -00.00 00ri.00 3Ol.00 00.00 -50.00 -30.00 -00.0 0 00.00 30.00.00 NANOSECONS NANOSECONDS DELTA TINE FOR COUNTER 4 DELTA TINE FOR COUNTER 5 8 _ —_ u! s - -o.00 -0.0 —.0 10.00 10.00 30.00.00.00 -0.00 -10.00 10.00 30.40 00.00 NANOSECONDS NANOSECONDS Fig. 22 The Difference between the Measuired and the Calculated Timing as a Function of Neutron CoI-nter

61 TINE-OfILIG4T OISTRIBUTION FOR COUNTER I INE-Wf-FLIGHT DISTRIIUTION FOA COUNTER 2 t. TIME* 1-FLIGHI OTlRBUlTION F OR COUNTER TIE-OF-FLIGHT OISTRIBUTION FOR COUNTER 4 ~e,e.0,,oo,oeo ~oo4.000 o,4ee 7ee 91.00' e.oo 1,,.OO TIRIE-OF-FLIGHT OISTRIeUJTION FOR COUNTER S:.00 LO 0.6 a0. oo 20.6 o. 6o.6 6.6o 7.o 0 e.6 6.oo leo.oo NMOSECONm5O Fig. 23 The Time-of-Flight Distributions as Function of Neutron Counter

62 usual equation p=eBr/c. For a uniform field B of length L this can be written in the form B*L (11) (1.31x10 )(2sinO/2) in which the momentum, p, is given in GeV/c and B-L is given in gauss-inches. Figure 24 illustrates the derivation of the above formula. The uniform field approximation was used as a starting point to determine the proton momentum by a method of iteration. As mentioned, the Magnet Test Group provided maps of the vertical component of the magnetic field for various currents. (The horizontal components of the magnetic field were neglected in this experiment since these provided only a small vertical focusing.) Since at these currents the magnetic field varied linearly with the current, a map was generated for the operating current, 523 amperes, by using the following formula f5=3 52 3 B523 392 )B392 (12) for which a map was provided at i392 amperes. This new map was folded about the three orthogonal planes which intersected at the center of the magnet gap and averaged. This procedure yielded a map containing only 1/8 as many points as in the original, and thus wa-s of a size more easily handled by computers. No errors were introduced by this procedure since the magnetic field was symmetric (within a few tenths of a percent) about the gap center. The actual calculation of the proton momentum proceeded

L e B P ~~R eB L P c 2 sin(e/2) Fig. 24 The Path of a Charged Particle in a Uniform Magnetic Field

64 by the following steps. A first guess of the momentum was made using Equation (11) where B'L was replaced by the integral jB.dl through the center of the magnet. The integral was 4.77x105 gauss-inches. The angle, 0, was the angle between a straight line drawn through the sparks in the front chambers and a line drawn similarly in the back chambers. The initial parameters for the computer stepping procedure were the first approximation to the momentum, the angle 0, and a position which was the spark location in chamber three. The proton was stepped from the back to the front through the magnetic field in 1.7-inch steps. The direction of the steps was parallel to the 36-inch sides of the gap. At each step position the magnetic field was calcullated by interpolating from the known fields at the nearest eight points which defined a surrounding box. The proton was then projected along a straight line to the next step position and a new angle determined with the aid of Eq. (11). This procedure gave a series of chords to the real curved trajectory. In this way the proton was projected from the back chambers to each of the front chambers and an aiming error obtained for each. Using the aiming error in one of the chambers, the computer performed an appropriate modification to the first approximation value of the momentum and repeated thie stepping procedure with the new momentum. This procedure was repeated until two values of the momentum were obtained —-corresponding to momenta which gave 0.005 inch,

or less, position errors in each of the front chambers. The two momenta were averaged and corrected for the finite step size. The correction for the step size was determined in test calculations by varying the step size from 1.7 inches to 0.085 inch. Typical results are presented in Fig. 25. The top line represents the momentum found by projecting into the front chamber; the bottom line is the similar thing for the second chamber, and the dotted line represents the average. Presumably the fact that all three lines do not coincide cain be traced to the effects of measurement errors. The value of the momentum for zero step size could be found by multiplying the 1.7-inch value of the momentum by 1.018. This factor was found to be independent of the momentum. An insignificant correction was made for energy loss in the liquid hydrogen and other material throughY which the proton passed before entering the magnetic field. The error in the proton momentum determination was dule, in the main, to spark measurement errors. Coulomb scattering effects were less significant. The proton momenttun errors ranged from about 2% to about 7% as shown in Fig. 26. Actually thie errors varied slightly with angle. D. Kinema.tics If one assimes that the interaction were n-p elastic, then the proton momentum and scattering angle completely determine the collision kinematics. This can be seen if we restrict the discussion to the plane of the interaction.

66 5.55 5.50 a) 0 ~o'5.40' P2 5.30 - 5.300.5 1.0 1.5 STEP SIZE ( INCHES) Fig. 25 The Ste p-Size Correction to the Protol Mo rnt ~ ~z m.

ERROR IN PROTON MOMENTUM DETERMINATION I0 9 8 7 6 5 41 4 31 1 L, I. I. I a. a - a a _ 0 I 2 3 4 5 6 7 8 9 10 P (GeV/c) Fig. 26 The Error in the Determination of the Proton Momentum

68 Then the conservation of energy and momentum supplies three equations for which there are three unknowns: the incoming neutron momentum, the scattered neutron momentum, and the angle of scatter for the neutron. The three equations were cast a;s /P'" + m = M p + m + p + m i beam n p n /2 p p' beam = n cose n + p cosp, (13) P= sine =0p sine. Pn sin6n p p Once these equations were solved all other quantities of interest could be calculated. In particular, the four-momentum transfer squared, u, could be calculated as a function of p and 0 The incoming;. neutron momentum was essentially the same as the scattered proton momentum, and so the errors were identical for the two. The errors for the four-momentlmu transfer were a function of the beam momentum. Representative errors are shown in Fig. 27. For beam momenta above 5 GeV/c and for four-momentuim transfers less than 0.03 (GeV/c)2 the four-momentlml transfer was recalculated from the neutron time-of-flight. The errors for this procedure are given by the dotted lines. E. Data Cuts and Subtractions Three cuts were independently made on the data in order to weed out inelastic events. The cuts were a coplanarity cut, a counter cut, and a timing cut.

ERRORS IN FOUR MOMENTUM TRANSFER DETERMINATION 36 32 26 24 20~ 0 PuOO GeV/c 16 Px5.OO GeV/c Pr3.00 GoV/c.00.04.08.2.16.20.24 2.32 3.40.44.4 lul (GeV / c) Fig. 27 The Error in the Determination of the Four-Momentium Transfer

70 The size of the neutron counters and their placement, together with the size of the beam, combined to give the system a ~7.5 degree maximum planar~ acceptance about the horizontal plane. No coplanarity information other than the trigger requirement was available from the neutron couaters. A coplanarity "chi square" term was calculated according to 0 if Icpj | 7.5~= 0.1325 radians 2 XCP (14) ( 11 - 0.1325 2 if I1rn > 0.1325 radians k O where cp was determined from the tracks in the two front proton spark chambers. The expected error, a, was a function of the proton momentlun and angle. It contains the effects of Coulomb scattering of the proton and measuring errors in the spark locations. Events were kept for which X was less than or equal to one. Each cotunter had a certain angular acceptance due to the counter size and the target length. If upon solving the kinematics, the angle of the scattered neutron did not lie within the range of acceptance of the neutron counter which had been triggered, tihe event was thrown out. If two adjacent neutron counters fired the angular limits were taken for the counter for which the difference between the measured and the calculated times-of-flight were a minimum.

71 A final cut was made by constructing a. "chi square" term for the timing information as follows 2 /measured timing - calculated timingN2 Xtiming \ Ct 1 5) As was explained in an above section, the measured timing was taken from the oscilloscope trace and the calculated timing was obtained from the kinematical reconstruction of the event. The expected error, ot, contained terms which reflected timing measurement errors, pulse height effects, and the neutron counter traversal time. Only events were kept for which Xtiming was less than or equal to one. From an analysis of the data generated by the Monte Carlo program which is discussed in Sect. IV-F, it was estimated that about 25% of the elastic events were removed by the data cuts described above. The fraction of elastic events cut was found to be independent of beam momentum and of four-momentum transfer. Figure 28 demonstrates the effect of these cuts. It shows the distribution of the difference between the measured and the calculated timing for events with Jult 0.025 (GeV/c)2 Each event is represented by a nunber which indicates which neutron counter was triggered. As can be seen, each of the three cuts independently discriminated strongly against the obviously inelastic events under the secondary peak. The inelastic events were presumably gammas from r~decay. However, two points should be made. First, the efficacy of the timing cut is reduced in the larger lul bins as can be

---------------------------------------- __ —--------------- - ~~~~0~ 1 i~~~~~~ 1L9ai,t~va 2i32 1 all 2 *,!- tu~t(O.US. Lk~It, ~ ~ ~ ~ ~ M ]....._m _'................ ~ ~mtT~,=uT......l 31....... 7IJ" I,.... 2' " I, "I~ I334 3 1 722 ~1~223 I I!4;;;-;~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~0 r'2'f... NS. 4. 2 23 2 - Sll - I~~~~r ~ -2-l T m --- _ _ 4433313 33 IS la33 33 2113t 21 4!S34Sj ~19 1~* J I MMr! ay 21,21~~~~~~~~~ 3C 3 122122211111 ".2-12"ISIS4 31533S2 2111 43S I 14 I 3 233 31. 3233 3~~~~~~~~~~~~~~~~~~~41 4S3 4-1S3 14 333 3312ZI2217 3133jj~ j 3 JJJJJJJJJ]___4__1.3.... 3 - ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~21,J 7 - - - _171M "31 3331 —' - - - - - - -333 ----------------- - A I IM12244JCAR$33 i $ 2 1. 31.; 33! I3 3333CI 2122~~~~~~~~~~~~~~~~~~~~2'3~11 3233 I( I 322 223J l 31313 333333 2 3332 3 5 717 4 1? 1113 33 1 - ~~iii~iil~illlli fr4)13~~r15~~1)31~ J~Z't'ZfTIillllii.Tfl H)Pl~ I:~ 2222212111111~~21222 I)'t~~ili;'~r~~~l~ 11~II1 111~~~~~~11()~~11 2~~)~Militia 33 2333323322 333331131 3331 31! 2 32!3 1331133 33Ii i 1122121 232323322313 3 33333322 3 33 2333322...................,........2....... 333 3323333332133 3 3......+ 3.............. 51? *I~~~~~~~~~~194S?111 4 - 1 I1 ~ ~ ~ ~ ~ ~.'1 233333 333332Ir 332333333 233333 3 333333333319 31 23 3 3 f 111 I 3332333333 3 3333323 2 3 3 3 3:~'3 3.3.13.223'33 3'I3 I3 331332313 333 13 3 3 3 - I 3 1 1 1 -33 -3 -' 32 3322 33 23 333333 -1O -33 - -21 -33 33 33 23 33 33 iit3 ~~~~~~~~~, 3 —1 ----! - - - - - - -- ----- ---- -1 -- -- --- ~. ~ ~ ~........ -,...33.3.3..3...3,-i. b, -......I }~"........_ ___ __ __ -....... 1 3 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ) 3 ~i~ii;~alll! I.... I............~~~~~~~~~~~c t t 3 4 oS.-T2i'-I.... IC.... 11r.... Fi, g2.2 Th EfP oAe ai CUTi n D Lf eT.........~ Ifil1ll c I TI1+Tf~ t.233333 - ----- ____ 3223..i21 _ -' -...lt: ~~~~~~~~~~~~~~2,3322 3232332 r t iiii~~~~~~~~~~~~i32 3333333i, -—.-, J 2332" 11112111 1 ))~~~~ ~~ ~~~~~~~~~~~~~~~~~~~~~~~171331 ririiiri~~~~~~~~~~~~i~ I 3li233232 122221122 -- - -— ~lill' --- -~ --- -- - 2;22?ijillI 3,?........ - 3' 32333333332....' --.722 33 3 3 -- - 211311131'". i Ili~~li~itZL~~Jt I~iifiitt t,~ I II 2i % 4! il! 111' I141*~tilliitii~iiii~ l&S~LS ~~ll~llqlH!42!!i~S~!~)?lt~l~l?41!l14~ I iliii~i~iliJijjljllll I FrrCSR~~~~~~lllnfc~~rnn Fig. 28 The Effect of the Datca C ut~s on the Timing Differences

73 seen in the uncut distributions in Fig. 29. As Jul increases, the inelastic peak moves under the elastic peak. Thus, for large Jul we are forced to rely on the counter and the coplanarity cuts to reduce the inelastic background. Secondly, in all Jul bins after the counter and coplanarity cuts were made, a background persisted which extended under the elastic peak. Consequently, a background subtraction was made to the data. The cuts described above throw out individual events. The subtraction was made to the cross sections as a whole, but as a, function of beam momentumn and four-momentulm transfer. The subtraction was determined by binning the data —-after the coplanarity and counter cuts had been made —-in bins of incident momentum and folur-momentum transfer as shown in Fig. 30. An effort was made to extend the tails of the background distribultion tunder the peak by drawing a. smooth line a.s shown. The events under that line and within the limits of the timing cut were counted and then the appropriate fraction subtracted from the cross section. The subtractions ranged from about 5% for the highest momentum bins to 15% for most of the rest of the data. As the statistical errors in the data were >10%, uncertainties in the subtractions were not considered significant. F. Geometric Detection Efficiency In order to determine cross sections from the numbers of events it was necessary to know the detection efficiency

74 -— C —- * —~ —- ---- ----------- ----- I j"/~~~~~~~~~~~~I ~~~~~~~~~L~~~n~~~h I llln~~~~~~~~~~y.il ~~~~~~~*nnn~~~ ~~~~r-~r l ~~~~i' I --------— ~~~~~~... (: -----:.;~~~~~~~~~~~~~~~~~~~~~rc~rrrr ".7...:,= —-~'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!... rrrl *~n~e~~~ ~c'i) r~~~r~ r~~~~~~ r~~rr~~~'~rn~ ~L~r -.i bp.....- - - - - - - - - - "-, - - -.-: - -......... uu::~~~~~~~~~~~~~ ~.~~~~~~~~.;;~''Ct', ~, —' ilk''C,-L I~C l~iI.I IC~i rC~LCn~~:~ ~, n~*r;~~~:~= ~I~.~~~~~"E:E'"`''' "~....... " 4.3 ~~~~~h~~~~~~~Ln rnncn =~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ r~~~~~~~~~~j~r. I1IC' =~~~~~~~~~~~~~LI =:,, ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~ i ~~~~~~~~~~~~~~~~~I~7~~~~~~~~r~~~~~~~.p rr~:~Z~'.`'~C~CX ~ E r n.C.~h~~~~~E ~::~1~~ ~~~~~~ ~ -rrrrl,r C~ Il~q3r-~~i~~~~~~~~~~~~~~~~~~~~~~~~~5r~ i:,1 l-I ~)Ct ____L,.....,, ~','-.....~~~~~~"X,c! _ _ ~ ~ rr'`''':;..... n~~~r~~F'i ~=, I

75 I I, XI I o! +uIC~~~~ 0 | x I Ii3 xx zQ* I,; | x 0* 54KJ C) r,, X xxI 4 X^~~~~~~~X XXS,XC X X X X,, I ~ XX XX JK X X, X X',, J XXXXXXXXXXXXXX XXx ~U I X X X X X X X X ^ X X X X X X X X XX X X XXX X X XX Xi, 5 XXXXXXXXXXX XX Ix ZI k Oo x i x I X. O * I I A I o,I.,(..

76 of the neutron counters and the solid angle of the system. The neutron detection efficiency will be discussed in another section. The solid angle, or geometric efficiency, of the experiment was investigated via Monte Carlo techniques. Appropriate random number generators were used to simulate the experiment. For a given computer run, the incident neutron momentum and the center of mass scattering angle, or four-momentum transfer, were fixed. With these quantities fixed, many events were generated with randomly chosen planar angles, random secondary scatterings, and so forth. All important features of the experiment were simulated on the computer. The ratio of accepted events to generated events was calculated for each range of u and of beam momentum. This fraction was then used to correct the data. A description of the salient features of the Monte Carlo program follows. The beam size, the beam divergence, and the beam atteritu.ation in the liquid hydrogen target were simulated. The plane of the scattering was randomly chosen with. the restriction that the neutron always be scattered to the side on which the neutron counters stood. (Restricting the planar angle to an hemisphere saved valuable computer time a.s a little investigation had shown that no events were accepted from the other hemisphere. The detection efficiency found in this way had to be divided by two when completing the absolute cross sections.) Once the interaction point and plane had been set the directions of the scattered neutron

77 and proton were determined. The fate of the scattered neutron was investigated next. Random rescattering of the neutrons in the liquid hydrogen were generated according to a parameterization of the low energy n-p cross sections prepared by Clements and Winsberg.39 Most of the rescattered events did not strike the neutron counters. Further attenuation in the target dome, the air, and the anticounter Al were simulated. In an effort to save computation time, scattered neutrons with kinetic energies -1 MeV were rejected. This could be done since the neutron detection efficiency of the neutron counters was zero for such low energy neutrons. If the neutron did not strike a. counter a new event was generated; otherwise, the counter which was struck was recorded and the fate of the proton was then investigated. Coulomb scattering effects and energy loss effects for the proton were simulated in the liquid hydrogen, the target flask, the target dome, the spark chambers, and the scintillators. The proton was stepped through the magnet in 0.097inch steps. The coordinates of the proton in each of the spark chambers were recorded. Tests were made to insure. that the proton passed through each of the three scintillators in the proton spectrometer. If not, a new event was generated. If the neutron went into a neutron counter and the proton passed properly through the spectrometer, the event was considered as having been recorded on film. From this point on the Monte Carlo program simulated the

78 analysis of the rea~l data. That is, measurement errors were randomly generated and were tacked onto the spark chamber coordinates. The kinematics of the event were then reconstructed as for the actual data. Further, the counter, coplanarity, and timing cuts were made. If the event survived all of these it was considered accepted and was properly binned. At the end of the run the ratio of accepted events to generated events was calculated. This ratio, called the "geometric detection efficiency", is presented in Fig. 31 for two beam energies and as a function of fourmomentum transfer. The errors are based on the statistics on the number of Monte Carlo accepted events. The dashed line is a, smooth curve drawn through the data. G. Neutron Detection Efficiency The thick plastic scintillator, the photomultiplier, and the a.ssociated circuitry constituted a system whose detection efficiency had to be calculated. That is to say, only a fraction of the neutrons striking a scintillator scattered in such a way as to produce charged particles with enough energy to prod.ce pulses above the threshold of the system. The ratio of detected neutrons to neutrons striking the counter is called the neutron detection efficiency and was calculated with the aid of a FORTRAN program developed 40 by Kiurz. Kurz's program treats both initial and secondary scattering effects on both hydrogen and carbon in the

79 BEAM ENERGY 3.0 GeV 0 6.-' -| o!-s. U~~~~., U. 4. c 3. w f 2.I_ \I 0.I A.0.1.2.3.4.5 FOUR MOMENTUM TRANSFER lul BEAM ENERGY 5.5 GeV e6. >'5. -',r-' w -- \ LLI ~ /e ~ % U. 4. o3 ~.' 2.'T.0..2.3.4.5 FOUR MOMENTUM TRANSFER lul Fig. 31 The Geometric Efficiencies for Two Beam Momenta

80 scintillator. Saturation effects in the production of scintillation light are considered as well. The program assumes a cylindrical shape for the scintillator with the neutrons uniformly and normally illuminating the circular face. The results of the program have been experimentally verified for several counter systems.4041 Our counters were each 15 cm long and, for the purposes of the calculation, were assuned to be 9.2 cm in radius. This value for the radius gives the area of the face of each counter. As the detection efficiency was a weak function of the counter radius, no significant errors were introduced by assuming a. circular cross section for each counter. The detection threshold was taken to be 0.7 MeV for electrons. The threshold energy was taken to be slightly lower than the 0.76 MeV maximum energy carried by the betas produced by T1 decay in order to reflect the actua.l beta energy spectrum and the counting rates at which the thresholds were set. Because of saturation effects these electrons simulated 2 MeV protons. The results of the calculation are presented in Fig. 32. The first peak is due to the rise from threshold and to the falling n-p cross sections, while the second peak is due to the onset of n-C interactions. Errors in the detection efficiency of ~10% of the calculated value are associated with the uncertainties in the cross sections ucsed in the calculations. Somewhat smaller errors are involved in determining the threshold and in neglecting edge effects.

DETECTION EFFICIENCY OF PLASTIC SCINTILLATOR B3 1 11 1.32 -SIZE: 9.2 cm radius 14.9 cm thick THRESHOLD: 0.70 MeV e- from TI 204.28.24z U.2 U.) w Z J6C-) w.08.04.oc0 I I I I I I I~~~~~~~~~~~~~ -A 20 40 60 80 100 120 140 ISO ISO 200 220 240 NEUTRON KINETIC ENERGY (MeV) Fig. 32 The Detection Efficiency of the Neutron Counters

82 It is important to note that all of the counters were set at the same threshold, and therefore, the detection efficiency was the same for all counters. Since the neutron energy is related to u by Eq. (6), errors in the efficiency would cause u-dependent errors, but these would be independent of the beam momentum. The statistical errors in our measured cross sections are typically >10% so the uncertainties in the neutron detection efficiency are not expected to be important. H. Data Contaminants Contamination of the data from inelastic collisions was investigated via, Mont Carlo techniques. The program which was used to calculate the geometric detection efficiency was modified for these calculations. The three processes in this category that were investigated were n + p A A (1236) -+ n + p + To Tr 4 y + y n + p 4 p + A~ (1236) A0~ n + r TT 4 y + y, and n + p 4 d + To no Y + y. The total cross section for each of the above processes was assumed to be about ten times as large a.s thie elastic charge exchange cross section. No energy dependence was considered.

83 The total cross sections did not enter in the Monte Carlo program directly, but were used in estimating the absolute background. The four-momentum transfer dependence of the 10u 42 production was taken to be e. The incident neutron momentum was randomly chosen, but was constrained to reflect the distribution shown in Fig. 33. 2 This beam spectrum was obtained from an analysis of the data, from the other phase of this experiment. The width of the resonance was taken to be 160 MeV rather than 120 MeV in an attempt to include the background under the resonance peak. In the same vein, isotropic decay of the resonance was simulated. Isotropic decay of the pion into two gammas was required. The gammas, as well as the neutrons, were tracked to the neutron cotunters. Events which triggered both the neutron counters and the proton counters, i.e., simuiated events for which pictures were taken during data collection, gave distributions in four-momentum transfer which tended to peak at u=O. However, the three cuts made on the data eliminated the peaking and reduced the backgrounm.d to a, level that was estimated to be,20% of the elastic events. This was further julstification for the background subtraction which was discussed in Sect. E above. The process n + p - A + n was found to be the most serious source of contamination. It accounted for about 75% of the background. Processes involving beam contaminants were investigated and found not to contribute to the background. The reactions considered were

350 300 250 200 2 1 50 0 00 50 QCI ~ ~ ~ ~~ICDN KNTCEEG GV Fig. 33 The Neutron Beam Spectrum w I00 Iz U)O 50 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 INCIDENT KINETIC ENERGY (6eV) Fig. 33 The Neutron Beam Spectrum

85 IV+ p 4 +t p and y + p 4 y + p. I. Target Empty Correction Finally, the target empty events were investigated. The target empty trigger rate was 1/3 of the target full trigger rate. However, the cuts made on the data discriminated more heavily against the target empty events. The few remaining target empty events assumed the appearance of a broad background when examined as a function of incident momentunm and four-momentum transfer. They represented something under 10% of the cross section under the elastic pea1k. Therefore, it was assumed that the background subtraction described above removed the target empty contribution to the cross sections.

V. RESULTS AND CONCLUSIONS A. Differential Cross Section Formula The formula which was used to calculate the differential cross sections is do _ X Y Z A (16) du -(piN/M)(B) (I (g/2) (En)(F/6p) Ap Au in which the sum is over all events and in which du du(pu) = the differential cross section as a function of beam momentum and of four-momentum transfer squared. X = film scanning efficiency correction = 1.12 Y = correction for events not measured due to the presence of extra tracks = 1.2 Z = Z(p,u) = background subtraction factor p = density of liquid hydrogen = 7.08x0- 2 g/cm3 1 = length of liquid hydrogen target = 10.2 cm N = Avogadro's number = 6.02x1023 protons/mole M = molecular weight of hydrogen = 1.008 g/mole lN/M = 4.33x10-4 protons/millibarn A = A(p,u) = correction for (p,u) bins for which the ranges of p or u are restricted by kinematics or detection efficiencies to be less than the bin sizes. A = 0 or from 1 to 2. c /2 = solid angle or geometric detection efficiency. 86

87 The factor 2 comes from the fact that the Monte Carlo calculation was restricted to one hemisphere. en = neutron detection efficiency. Events were not considered for which the product (cg/2)(en) was less than half the maximum value. F/6p = F(p)/6p = fraction of the beam spectrum per momentum bin. The beam spectrum was determined in the forward scattering portion of the experiment. The results are presented in Fig. 33. Ap = incident momentum bin size for which the cross section was being calculated. Au = four-momentum transfer bin size for which the cross section was being calculated. B = number of counts on monitor B. I = neutrons in beam per count on monitor B. The determination of this number is discussed in the next section. B. Normalization Normalization refers to the process of determining the numbers in the above formula or of fixing absolutely the scale of the differential cross section in some other way. In practice the difficult quantity to determine is usually the beam flux. It is always difficult to determine

88 the flux of a neutron beam. It is especially so when the beam spectrum encompasses a wide range of energies as in this experiment. Consequently, no effort was made to directly determine the flux. Instead, the forward-scattered data were normalized to the n-p total cross sections via the optical theorem.2 The plan was to normalize the charge exchane data to the forward data. The original hope was to make the connection between the forward data and the charge exchange data in one of two ways. One possibility was that the ranges of the four-moment-um transfer for the two phases of the experiment would overlap so that the differential cross sections could be smoothly joined. The detection efficiencies were sulch that no overlap existed. The second method involved a convoluted calculation which depended on the target sizes, the monitor rates, the detection efficiencies, arnd other physical parameters of' the two experiments. This method also did not work. We felt that it was not appropriate to normalize the data to the data of Friedes et al. or that of Manning et al.5 since their normalizations are not certain. Therefore, our data are not normalized. However, the relative normalizations between incident momentumn bins are fixed since the neutron beam spectrum was known. Again the reader is referred to Fig. 33. Above 6 GeV/c, uncertainties in our beam spectrum introduce errors in the relative normalizations of about ~50%. Similar errors are introduced in the

89 relative normalizations of the data for momenta below 2.5 GeV/c. C. Results and Conclusions The differential cross sections are given in tabular form in Tables II-XI and in graphical form in Figs. 34-41. The cross sections were not plotted for 1.75 GeV/c to 2.25 GeV/c as they did not possess enough points to present interesting plots. The errors quoted are statistical errors only. Several points should be made about the data. First of all, the normalization is not determined; however, that fact in no way effects the u dependence of the data. Secondly, the neutron detection efficiency limits the range in four-momentum transfer to JuJ > 0.01 (GeV/c)2 which is outside most of the sharp backward peak seen in other data. Evidence for a sharp backward peak does exist in the data however. Thirdly, the data from 2.25 GeV/c to 3.00 GeV/c show a strong energy dependence in the shape of the cross sections. The data from 2.25 GeV/c to 2.50 GeV/c and from 2.75 GeV/c to 3.00 GeV/c show backward peaks, while the data in the 2.50 GeV/c to 2.75 GeV/c bin show a dip. Fourthly, the data above 3.25 GeV/c indicate the existence of a plateau in the differential cross sections at a four-momentum transfer of about 0.08 (GeV/c)2. And finally, the data for large lul may be characterized as

90 d~.e5u. (17) The strange energy dependence of the differential cross sections between 2.25 GeV/c and 3.00 GeV/c, and, the existence of a plateau in the differential cross sections at Ju = 0.08 (GeV/c)2 are the most striking features of the data. Future experiments should carefully investigate the n-p charge exchange differential cross sections in these regions. Our data, together with that of Mischke et al.7 show that the behavior of the charge exchange cross section between 1 and 7 GeV/c is much more complicated than previously realized. Not only does the slope of the sharp peak vary rapidly with energy, but the shape of the cross section just outside of the peak varies in an apparently complicated way. In conclusion, we offer a critique of the techniques employed in this experiment. The advantages of this technique are given below. 1) This technique offers a higher data taking rate. The data were taken in 100 hours of running time. 2) The ratio of events to triggers is much better. Our ratio was l0 1, while the ratio for Manning et al. was 10-3. 3) The technique can be easily extended to higher energies. Experiments employing this technique are currently being performed at the AGS and at the

91 ZGS. 4) With some refinements of the technique a recent experiment used. this technique to study polarization in n-p charge exchange. 5) This technique measures simultaneously the cross sections for a large range of neutron energies. There are two principle disadvantages to the technique. 1) The neutron counter detection efficiency must be known. 2) It is difficult to measure the cross sections for small u. In particular, the u=O values of the differential cross sections cannot be measured.

CRUSS SECTIONS FUR 1.75 GEV/C TO 2.00 GEV/C ABS U bINS NUMBER ABSU SIGMA ERROR COSINE SIGMA ERROR O Tu (v/cY)2- Cos, ff 0. -Tu O. -- --- 0..O - -' -- - 0.0 — 0.0 -.. —-- -0.00 -- --- -0.0- -' o.oJLU0 TO 0.02000 45 1.5135E-02 3.6497E 01 5.4407E 00 -9.8618E-01 6.3792E 00 9.5095E-0l U.U 1-JUU u 0.035000 50U.4Y8t1-0uz b4UZL U1 5.430fft 00 -90.169OE-01 6.6415E 00 9.3925E-01 u.O300u TU 0.44000 28 3.414dE-02 2.5774E 01 4.8708E 00 -9.6916E-01 4.5516E 00 8.6016E-01 0.04000 TO —.05 —- 4....-S0E —253 7 Z 3..58.. U873OE 00 -9.5819E-01 5 —-5~.45E 70 1..- E-!0.J5OUO TO o.07d00 41 5.5537E-02 3.5658E 01 5.5688E 00 -9.4964E-01 6.2747E 00 9.7994E-0O 0.07 000- TO 0,090- 0. --- --..; —— —--. —-.0 —--- -.... _ _.O 0.09000 TO 0.11000 0 0.0 0.0 0.0 0.0 0.0 0.0 U0IluV ou V0.3V 0 - o. 0 0.U 0, 0. O.1o o.00.13000 TO 0.15Q00 0 0.0 0.0 0.0 0.0 0.0 0.0 O. 15l00 TO O. 17t00o - 0 —-- -'- O --- - --- ---- -.- -- 0.17000 TO 0.1900 0 0 0. 0 0.0 0.0 0. 00.0 0. I9UOO TO 0.21 00f O. u-.0 - --.-.-.. -O —- -. — -. _ 0.21000 T0 0.23000 0 0.0 0.0 0.0 0.0 0.0 0.0 U.:UU TU 025v00 0.0 0U, 0.0 0.U 0.0 uoo id 0.25000 TO 0.27000 0 0.0 0.0 0.0 0.0 00 0.0 - 0.2100 TOa- 0.2 000 —- - -. —1- 1),- - -------------— o- —. --------— w. —— 0 --- -- 0.29000 TO u.3100U 0 00 0.u 0.0 0.0 0.0 0.0 031000 TO e, t..... 0 0 —-. —- ---- 0. --. — - 0.0 —... — —..... 0.33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 0- 0.3000 TO u.i7t000 0 0.0 0.0 O.e 0.0 0. 0 u.0 0.31000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 o0.39 U TO 0.41,000 —--.....0'- O.0.. -.. o.- - 0...0.0.0. 0.41000 TO 0.43000 0. 00.0 0.0 0.0 O.0 0.0 206 WEIGHKTED -AVERAGE MOMENTUM - =- —...:I-B9-G E -. - _ _... StEA KINeItIC EKNERGY = I.M GEY S = -7 1 { - - - ------.' -- -- ---—. —--—. - Table II The Differential Cross Sections for 1.75 GeV/c < p < 2.00 GeV/c

CROSS SECTIONS FOR 2.00 GEVIC TO 2.25 GEV/C ABS U BINS NUMBER ABSU SIGMA ERROR COSINE SIGMA ERROR M_ _t ~~~~du cs3 f o ~~ou Gro oT44Gt~o~ -~ o,___ __o____ 0.0.........TO 00100 0 0.....0...0. 0o0. 0o0 *0o 0.01000 TO 0.02000 29 1.5d8l1E-02 2.5851E 01 4.8004E 00 -9.8742E-01 5.2110E 00 9o6766E-O1 0.0/Uoou ~u 0.03000 3. 2.L85t:-U, 3.0 7i i,956;' uU -9.dU34E-OI b.1549E 00 1.0119E 0 0.03000 TO 0.04000 33 3.5563E-02 2.6899E 01 4.6826E 00 -9.7193E-01 5.4378E 00 94659E-Ol 0-0.134-000 TO0 0.05C -......F.... — 50-8 1 —02...; i -..30... —9 L5E —-- — X3 3..947E-UU- 2 F 302 327EL0 - 7E.6 10.05000 TU 0.07000 34 5.5344E-02 2. 1541E 01 3.6942E 00 -9.5712E-01 4.4371E 00 7.6096E-01 - 170 —TOO T0;. -U -.- - - O.0.O-. -- 0.09000 TO O.11U00 0 0.0 0.0 0.0 0.0 0.0 0.0. =in0 Tu 0. i000 0 0.0U..u 0.0 00 -o - o. 0.1.000 TO 0.15000 0 0.0 0.0 0.0 0.0 0.0 0.0 -o.19000-700 — w. —00 0.0 O.0 -. — O —. 0.11000 TO 0.19000 0 0.0 0.0 0.0 0.0 0.0 0.0 -.19O~01O 0.ZIUOO 0 -__ _.0_0.00.0 0.0 0.21000 TO 0.23000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.23000 TO 0.25000 0 0.0 0.0 0.0 0.0 0.0 U* WU 0.25000 TO 0.27000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.27000'7 TO 0.9u O — O. 0,o 0.0- 0 —-.-1 —-3 —0 -0 -.0.29u00 TO 0.31000 0 0.0 0.0 0.0 0.0 0.0 0.0.3O -31000 TO - -3300 -- 0.0 0.T - -0 o - o. -.. 0.33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 IJ.s7UU TO 0.37000 - u.0 u-u -~ u-u u-u 0uOa 0.37000 TO 0.397000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.37000 TO 0.39000 0 0.0 0.0 0O0 0- 0 0 —0 0o0 -0;39'0 TO - -O-,q 1-0- 0 ~*~ -0 O. 0* O.0 0.41000 TO 0.43000 0 0.0 0.0 0.0 0.0 0.0 0.0 151 WEIGHTED AVERAGE MOMENTUM = 2.098 GEV/C BEAM KINETIC ENERGY = 1.359 GEV S 6.077 (GEV)**2 Table IIi The Differential Cross Sections for 2.00 GeV/c < p < 2.25 GeV/c

CROSS SECTIONS FOR 2.25 GEV/C TO 2.50 GEV/C ABS U BINS NUMBER __ ABSU SIGMA ERROR COSINE _ SIGMA ERROR lUt (ae'V dO 9 C__ o.0 o.auo -..-.. o....-0 -—.o0 -- -.o 0.0 0.0 0.01000 TO 0.02000 31 1.4630E-02 2.1392E 01 3.8421E 00 -9.9038E-01 5.1813E 00 9.3058E-01 0.02000 IU U.03000 Z. Z.zbLE-u. I.(b[f9: 01 3.40M3E 00 -9.8313E-01 4.2227E 00 8.1266E-01 0.03000 10 0.04000 23 3.4866E-02 1.5557E 01 3.2438E 00 -9.7708E-01 3.7789E 00 7.8796E-01 -O-04U TO -.- -8 442 --- --.4Z. — 1 hE-O —-.6794E-U —... — 9. 067E-O —..-7316E 00 84-E 0.05000 TO 0.07000 51 6.0881E-02 1.5731E 01 2.2027E 00 -9.5957E-01 3.7761E 00 5.2876E-01 t.OTOW~~~~~~~~~~~~~~~~~~~~~~~~ —- 1-~ —-Z.6 olyo0 3+.- 0* I Y4n-m.-7.f9-2O- 0 TOO01TO 0 9 E9000 34.9tZ9E-02..- -1-IT....ItJ, 9099E- WO- 9.- 431E'-U..67OEE-0 - 4...519ZE-4 17 0.09000 TO 0.11000 34 9.9903E-02 1.2695E 01 2.1772E 00 -9.3420E-01 3.0727E 00 5.2696E-01 0.ii000 TO 0.i3000 L5!. 2i UOE-Ot L.0O6oE Vi 2.i352E 00 -9.2015E-01i 2.53: 00'.16J6E-71 0.13000 TO 0.15000 0 0.0 0.0 0.0 0.0 0.0 0.0 -O. 15toO0 -TO0 la17000 -0 —....;...00 0 0.0 0; 30...... 0.17000 TO 0.19o00 0 0.0 0.0 0.0 0.0 0.0 0.0 0.t; 90 00 - -T 0.;2t -.. —-- - - --.-.. -. -0 0. —---- - 0.21000 TO 0.23000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.23000 TO v.z5000 0 u.0 v.0 0. U. 0.0. O 0.2500U T0 0.27000 0 0.0 0.0 0.0 0.0 0.0 0.0 Or.21000 TO- 0.29000 -O- — 0 —- - --- 4~- -0;0 -- — o-~ —_ _ -_0.29000 TO 0.31000 0 0.0 0.0 0.0 00 0.0 0.0 0.31t00- TO.3o33000 - --- 0 — - -- l- ---- - o - - 0.33000 TO 0.35000. 0.0 0.0 0.0 0.0 0.0 0.0 0.3500 TO 0.37to 0.0 000 — 0.0 - 0.0 00 0.0 0.37000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 O0.39000 TO t0.4000 0 0.0. 0-0 0. o 0.41000 TO 0.43000 0 0.0 0.0 0.0 0.0 0.0 0.0 _........... _._.......................................... 243 WEIGHTED AVERAGE MOMENTUM = 2.374 GEV/C BEAM KINETIC ENERGY = 1.614 GEV ~~........................ S = 6.555 (GEV)**2 Table IV The Differential Cross Sections for 2.25 GeV/c < p 2.50 GeV/c

BERM MOMENTUM FROM 2.25 TO 2.50 GEV/C JJ c:::) U. I —. r. N' if z; i i [ * LL ) cc., i'.00.Oq.08 ~12.16.20.22.32.36 WlO -U (GEV/C) N2 Fig. 34 The Differential Cross Sections for 2.25 GeV/c < p < 2.50 GeV/c

CROSS SECTIONS FOR 2.50 GEV/C TO 2.75 GEV/C AbS U t3NS NUMBER ABdSU SIGMA ERROR COSINE SIGMA ERROR _____ cose -, 0..0.......TO -.-01010i -. --.....O ---- 00 - 0.0 0.01000 TO 0.02000 25 1.4620E-02 9.6193E OU 1.9239E 00 -9.9164E-01 2.6822E 00 5o3643E-O 0.0 0 u u.030 i 2.4'33-U02 b.UfZE UU i.''UbU UE -9.*583E-01 1.6961E 00 4. Z43E-01 0.03u00 TO U.04U00 18 3.5785E-02 6.8956E 00 1.6253E 00 -9.7915E-01 1.8852E 00 4.4435E-01 0-.- 04000 TO * -.05000 - - 22 -—. 598 8E-02Z —- -....5 —r-E73I.-25E 0... —-—.-ZZ55E 0....4-8E-0 — 0.05000 TO O.076u0 49 5.9081E-02 9.0985E 00 1.2998E 30 -9.6554E-01 2.4883E 00 3.5547E-O1 0.07T0 O U 0.909000 4T 7& 0 5Z9E Oia9361E... -9.54-Z5E-GI....2689E 0 — B — 336E- [ - 0.09000 10 0.11U00 39 1.0039E-01 9.3892E 00 1.5035E 00 -9.4107E-01 2.5503E 00 4.0831E-0l.IIU'000 10 i.3000 37 iL.20I2E-'U 9*.0o+ 00 i.o;'EU0 00 -9. UO+4-Ul'L436E 00 4.OT7LE-O1 0.13000 TO 0.15000 11 1.3573E-01 5.2470E O0 1.5820E 00 -9.2127E-01 1.4416E 00 4.3465E-01 0,1O. 5000 TO. ITCOO.0.. -.o -..-. - -.. —.o- --—.- —.. —-.- _0 _ - _ U.17000 TO 0.19000 0 0.0 0.0 0.0 0.0 0.0 0.0 0. —O00 OO o — 0 - 0 - -— 0 —- - 9 --—;0 — -- - -o o- 0.21000 TO 0.23UO0 0 0.0 0.0 0.0 0.0 0.0 0.0 u.3UOO 1TU 0.25L00C0 0.0 u00.O 0.0 u.O u0.u 0.25000 TO 0.27600 u 0.0 0.0 0.0 0.0 0.0 0.0 O.27000 TO U. 290 - - -. -. - 0 -- -- o ------ — O - 0.29000 TO 0.31000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.31-000 TO 0 —3tr00 - - --- --- - ---- -.- - - a- -- tw -. 0.33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 O.23000 TO 0.37000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.37000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.39000 TO 0.41 00 0 - 0 09.-0 0 0.0 0-. -o 0.41000 TO u.43000 0 0.0 0.0 0.0 0.0 0.0 0.0 264 WEIGHTED AVERAGE MOMENTUM = 2.610 GEV/C BEAM KINETIC ENERGY = 1.835 GEV S = 6.969 (GEV)**2 Table V The Differential Cross Sections for 2.50 GeV/c < p < 2.75 GeV/c

BERM MOMENTUM FROM 2.50 TO 2.75 GEV/C C0) Li. Lu. 0) O'3 co (.S.. N ".00.04.06. 2. l6.20.24.28.32.36.40 -U (GEV/C).M2 Fig. 35 The Differential Cross Sections for 2.50 GeV/c < p < 2.75 GeV/c

CROSS SECTIONS FOR 2.75 GEV/C TO 3.00 GEV/C ABS U BINS NUMBER ABSU SIGMA ERROR COSINE SIGNA ERROR 0 0.a O TO U..U.LO -- ch.. ——. --.. - 0-; —- 0.0 0.1OudO TO 0.0I000 34 1.5261E-02 9.7543E 00 1.6728E 00 -9.9222E-01 3.0484E 00 5o2279E-01 0i02000 1-u 0.000 2jU 2.5396t-0't02,+:)5 UU 1.6bIbE.. -9. 10tE-O I 2.3Z53E 00 4o56&3E-010.03000 TO 0.04000 18 3.4500E-02 4.5185E 00 1.0650E 00 -9.8255E-01 1.4225E 00 3.3529E-01 050T 0.T03000 2 —1 - T-5 OU 47558EE00 1.T0400E 00 -9. 686E-0o1. -— T E0 — 32274E-01 0.05000 TO 0.07000 36 6.2109E-02 4.1785E 00 6.9642E-01 -9.6833E-01 1.3047E 00 2.1745E-01 - O;OTo -T-'-.090 - 30-00-.....0 E-O —-;'8 u0"Z - — 4;-....-80E -- 6. —-9-O..E1 - ---— O.5.99..- g3Z EB3 E0.09000 TO 0.11000 31 1.0124E-01 4.3501E 00 7.8130E-01 -9.4791E-01 1.3481E 00 2.4213E-O1 U.IULO TiO 0.13000 20 I.9i,,E-O " 2.92/6LE U00 5.513EJt- -Y.393e-U 9.19 tE-01 2.053E-01 0.13000 rO 0.15000 22 1.3758E-01 3.7488E 00 7.9925E-01 -9.2914E-01 1.1595E 00 2.4721E-01 —.150 — O. 00...9.. -... —--. — -tt 0. - 1. —0 —- — 30- --- 0.17000 T0 0.19000 11 1.7926E-01 2.62b0E 00 7.9000E-01 -9.0808E-01 8.1381E-01 2.4537E-01... O-..1t067 -.21000 -,-100 - ---.. 0 0.0 O. 0 0-U.' 0_0 0.0 0.21000 TO 0.23000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.23000 TO 0.25U000.0 O. u 0.0 uO u.u U.UU m 0.25000 TO 0.27000 0 0.0 0.0 0.0 0.0 0. 0.0 0.z 270. 0TOU --. O — TO- -.. 20 00 0'- -.0 ~ — -' — 09- -- 0 -. O-.0 0.29000 TO 0.31000 0 0.0 0.3 0.0 0.0 0.0 0.0 — Of300IO — 0- 0.33(M, 0 — - - 0-' 0.0.0.0- 0-.0 —- - 0.33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.35u00 TO 0.37000 0 0.0 0.0.0 UOV 0 0.0 0 0.37000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 — O;'0 0 " OO0 0.... — 0-,-4... —o.o -0 O -.... 0. - - ---- On-l. 0.41000 TO 0.43b00 0 0.0 0.0 0.0 0.0 0.0 0.0 274 WEIGHTED AVERAGE MUMENTUM = 2.878 GEV/C BEAM KINETIC ENERGY = 2.088 GEV S = 7.444 (GEV)**2 Table VI The Differential Cross Sections for 2.75 GeV/c < p < 3.00 GeV/c

BERM MOMENTUM FROM 2.75 TO 3.00 GEV/C e0 w li "X r, Cr) C V) (V.00.04.06.12.16.20.21.28.32.36.1 -U (GEV/C) ""2 Fig. 36 The Differential Cross Sections for 2.75 GeV/c < p < 3.00 GeV/c

CROSS SECTIONS FOR 3.00 GEV/C TO 3.25 GEV/C ABS U BINS NUMBER ABSU SIGMA ERROR COSINE _ S I GMA _ RO _ Ia (~~~~~ V' fff C_ osf _ _ _ _ _ t~~.O~ tO~D.0IUU,00 U. U- 0W -- 0.000 0.0 0.01000 T0 0.02000 23 lo4315E-02 6.024t3E 00 L.2562E 00 -9.9332E-01 2.0630E 00 4e31E0 U.020UU Fu u.0300u 20 2-519E-02 5*35 U0 19L/-5[ 00 -YoU35t-0I IoI430E 00 387E0 0.03000 TU 0.040U0 16 3.5533E-U2 3.4238E 00 8.5595E-01 — 9.8382E-01 — 1.1983E 00 2.95E0 -— a0-4'0OWT~~50 474 9E-2.-46456t700 9.686S-U 1 -9.795ZE-01 1. 6ITa3E70W-Y 373E 0.05000 To 0.07000 3d 5o9665E-02 3.9003E 00 6.3270E-01 -9*722SE-01 __ o13381E 00 2.101E 0.09000 To 0.11000 31 9.9658E-02 3.79-56E 00 6.8172E-01 -9.5442E-01 l.3216E 00 2.73E0 00.LLU0 [ Eu u. 00 35 J.2000UL0L 4*58 UIJ g.69'tt-0 -9.44TIE-01 10517't3 00 Z61tO 0.13000 ITO 0.15000 18 1. -855E:-01 2.5108E 00 5.9180E-01 -9.3610E-01 8o6699E-01 2.03E0 U. 13 000 - To - 10 70 — -2- I* — "~ 44E001t0 a61~ 89440Ei-017 ~ f8E 0.17000 TO u.1900U 13 1.8077E-01 1.9543E 00 5.4202E-01 -9ol758E-01 6o8260E-01 1.83E0 - ~.19&0O1~Q~O.ZIU0W —T& 0I9976ZE —017- — 3-7Tr34E 0 -9v.4336E-0i1 073E0 0.210u0 TO 0.23000 0 0.0 0.0 0.0 0.0 0.0 0.00 0.25000 TO0u.25000 0 0.0 0.0 0.0 0.0 0.0 0. O.2100V T0 - 0.ZV0&0~~~~~~~~~~~ ~ ~~0 — - 0~~~~~O-~ 0 0- ------- o0 - - _- _ 0.29000 TU U.31u00 0 0.0 0.0 0.0 0.000 0.00' -— 0U;31000 -T0G U. 330U -0 --. —- -D- -~ 0:33000 TO 0.35000 u 0.0 0.0 0.0 0.0 0.0 0.0 0,,35v0 iu u.3,7u0 0.0 ~ O.ty0. 000 0*0 a~ U.37000 TO U.39UO0 0 0.0 0.0 0.0 0.0 0.0 0.0 - 3.Th000 TO'Or-,4 1-00 — O -- -e- - - U.0 -- 0 0 —- --— O-.0 - -— 0 -— O --- 0.41000'T0 0.43C00 0 0.0 0.0 0.0 0.0 0.0 0.0 283 WEIGHTED AVERAGE MOMENTUM 3.121 0EV/C____ __ BEAM KINETIC ENERGY 2.320 GEV____ S =7.879 (GEV)**2 Table VII-L The Differential Cross Sections for 3.00 GeV,/c < p < 3.2 5 G eV/c~

BERM MOMENTUM FROM 3.00 TO 3.25 GEV/C x 0 CD Z -. 0) L) i' a: V.. uJ Co u3" C) < P < 3.25 GeV/' < P < 3.25 GeV/c

CROSS SECTIONS FOR 3.25 t:V/C TO 4.25 GEV/C AdS U BINS NUMBER ABSU SIGMA ERROR COSINE SIGMA ERROR. - TO —OT.oo0 VI 0.. o- 0.0 0G.0....,0 0.O,0.01uO0 TO 0.oJU00 88 1.4843E-02 3.358oE 00 3.5803E-01 -9.9445E-01 1.4416E 00 1.5368E-01.Uu2000 Tu 0.03000 i 2.4.u3jV-02J. 2 t-0U.b129E-01 9..-9.YUo4t-UEl — I..T —r-.-.. 1.53Z — 0.03000 TO u,.0400 81 3.4751E-02 2.8158E UO 3.1287E-01 -9.8691E-01 1.2004E 00 1.3338E-01 — O*U4- T.+- 9-U5 96 4.4810020 2 9 -e.iSE-0O -0. a-.- 3u — I- -- z. --- 9837 -O - I-.217E 44E-4I 0.05000 TO U.0700 142 5.9905E-02 2.1908E Ou 1.8384E-01 -9.7735E-01 9.3069E-01 7.8102E-02 -- oTo-7000 — 0 — 0.0 — uu.r VO —002 1.95 1E0 1.T.73E —- -.-704BE-I - - 4 —- 3E- -. 7.71I85E —-- O.09uOu TO 0.11O00 124 1.0033E-01 2.4253E UO 2.1780E-01 -9.6211E-01 1.0298E 00 9.2483E-02 W. i, V0,u ov 0i3000 o5.9 E i. 114"0- -— E"I7- —. —-.St —5....-7.3-3 -- -Stb-UZ?. J.13000 TO U.15b00 69 1.4004E-01 l.4157E 00 1.7043E-O1 -9.4715E-01 6.0338E-01 7o2638E-02 u. l' iOuTOV -I- 1 vO -- - ---- - TO -64 -u..E- -- t397E —-- - h-44E -4t... -. t-.3-89EOV -..4.86E-2. - J.T 7I:Ju TO 0.19000 62 1.8058E-01 1.4423E 00 1.8317E-01 -9.3133E-01 6.0908E-01 7o7354E-02 d. 1 U vO-f-utr —.21000 45 - t-.9959E —01-. 714E -0i 1*4.4S -otli -9.t250 9.E — -Z592E-O01 — 6.93 —Z - - u.21000 TO U.23U00 39 2.1927E-01 8.3243E-01 1.3330E-01 -9.1981E-01 3.6483E-01 5o8419E-02.23OG ToG 22 2. 38ZOE-t —- - -. e-0i i.39oZE-0i z-S.1202E-ul 6' SU o. UU"e - Uz 0.25000 TO 0.27000 0 0.0 0.0 0.0 0.0 0.0 0.0 - -O. Z7000 TO - 0.-29000 0.0 0 — - - --- -0.0 fO- -— 0 —0 — ~- -—..-.- -.. 0.29000 TO 0.310l0 0 0.0 0.0 0.0 0.0 0.0 0.0 -.-3o000 —[- 0.33000 0 0. t0O. 0 0t.- -t -. 0 g 0.33000 TO 0.35000 0.0 00 0 0.0 00 0.00 0.35000 0.37000 0 ----- 0-0 0.0 0.0 0.u U.O 0.37000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0o0 —.0.39 0 00-T1O -T.....44000 0 — - -— O. -0 0 0. 00 -10. 0.41000 TO 0.43000 0 0.0 0.0 0.0 0.0 0.0 0.0 1126 lrTtcD AVERAGE MOMENTUM - 3.682 GEV/C BEAM KINETIC ENERGY = 2.861 GEV S = 8.894 (GEVJI**2 Table VIII The Differential Cross Sections for 3.25 GeV/c < p < 4.25 GeV/c

BERM MOMENTUM FROM 3.25 TO 4.25 GEV/C to tn Cy z C:) - LU, o -" C<) cc 0'3 C: 0'M ".00.04.08.12.16.20.24.28.32.S.310 -U (GEV/C) mi2 Fig. 38 The Differential Cross Sections for 3.25 GeV/c < p < 4.25 GeV/c

CROSS SECTIONS FOR 4.25 GEV/C TO 5.25 GEV/C ABS U BINS NUMBER ABSU SIGMA ERROR COSINE SIGMA EARRO 0 0 - TO U U U - 0.0 0. 0.01000 TO 0.02000 101 1.4872E-02 2.6516E 00 2.6385E-01 -9.9597E-01 1.5499E 00 10.5422E0 0.03000 TO 0.04000 80 3.5344E~-02 1.7426E 00 1.9483E-01 -9.9012E-01 9.9759E-01 I. II53E-0 0.05000 TO 0.U7000 154 5.9878E-02 1.5292E 00 1.2322E-'01 -9. 8354E-01 8.9002E-01 __7.1720E0 0.07000 TU-o.0 (I4 T91t 2 - 673E0-TOE~T ~ 8E0 - - 53Bi9E-0I1- T —7849E'D 0.09o00 TO 0.11000 93 9.9887E-02 1.1471E 00 1.1895E-01 -9.7247E-O1 6.6652E0OL 6.9115E0 0.13000 TO 0.15L00 62 1.3960E-01 7.8621E-01 9.9849E-02 -9.6181E-01 4.6032E-01 5.846,E0 0.1 100 o-t5 —~ O-OD ~ — t-ot38E 00 --— T.24i0E-VLO V 3330tt535E 0t -T-IZ6TEU 0.17000 TO 0o.19000 63 1.804uiE-01 8.b380E-01 l.OB83E-01 -9.502BE-01 5.0147E-01 6.3179E0 0-.1,9,0 0 0 - -a-oZ ---- 0 —---- 6 —- --- ~ -- lot965E-0t0 9I45E1tI7O 5*1 4Jb1:1 377-6Eo-3To 0.21000 TO 0.23000 50 2.1966E-01 7.0698E-01 9e9982E-02 -9o3961E-01 4oL098E-01 5.81Z2E-0 0.25000 to 0.27000 42 2.5992E-01 6.6652E-01 1.0285E-01 -9o2769E-01 3o8296E-01 5o9092E-0 0 * ZTOOO- To- 00 o 9D - -- to oe-10t-1- 50 3 ZO - -t95i-4 -~9. 25Z — Ot -3-4401-DT0V- boT9TE0 0.29000 TO 0.31(00 0 0.0 0.0 0.0 00. 0 0.0 0.0 -0 31700TIO — Oi33000 00.2 -000 u0 0-a -O- _ 0.33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 ui.i500u To 0.3I000 U 000 u.0 0.0 U.U 0.0 0.0 0.37000 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 Oo 3"OU - 10 4 ro4100 - -- -0- ----— o.o — -—.o ----— o. 0.41000 To 0.4-3000 0 0.0 0.0 0.0 0.0 0.0 0.0 1256 WEIGHTEDI AVERAGE MOMENTUM 4.739 GEV/C _________ _________ ____ __ _ BEAM KINETIC ENERGY 3.891 GEV __ _ _ __ _ _ _ _ _ _ _ _ _ __ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ S = 10828 (GEV)**2 Table IX The Differential Cross Sections for 4.25 GeV/c < P < 5.25 GeV/c

BERM MOMENTUM FROM 4.25 TO 5.25 GEV/C I" C), o T 0 r xi I. _,) L ( C: -.00.Oq.OO. 12.16.20.24.20.32.3.Wo -U (GEV/C) "-2 Fig. 39 The Differential Cross Sections for 4.25 GeV/c < P < 5.25 GeV/c

CRkOSS SECTIONS FOR 5. 25 GEV/C TO 6.25 GEV/C ABS U BINS NUMbER ABSU SIGMA ERROR CUSINE SIGMA ERROR _ 1/__ _ ___ _._. lal (&/C W-ay -0-O....T..O..01-U00 -..'-... 0 0.'VU O0 0 0.0 - 0.OlUOO TU 0.U2O00 113 1.4777E-02 1.b6662t 00 1.5674E-01 -9.9695E-01 1.2157E 00 1.1436E-01 U.vO000 TO 0.03000 ~oe 2.e~E-2 i.!u'.59 6 O a.4oo'66-ui -9o9469E-O1 1*0954E 00 I.063ME-1 O.o03OU TO U.U40OU 90 3. 522oE-02 1.2203E 00 1.2d64E-01 -9.9227E-01 8o8790E-01 9.3593E-02.0OaOO Tr- — 84.-050E -.....4 —. TIE —.5E Do L.1U"0-U1 -o9oZ4OE-O1 — 4879E-0T1 16 0 0.05uoo TO O.07000 1b2 b.0035E-02 1.3248E 00 8.0518E-02 -9.8676E-01 7.4164E-01 5.8269E2 — 0.07oouu -o-.. 9c00 1. t8 - a --- 63Eo-Z -. -'90IE0 8.6E —-- - 9. 825IE-O1.- -.32E — 0.09uO0 o10 v.11uO 112 9.9490E-02 6.1l18E-01 8.2319E-02 -9.7805E-01 6.3020E-01 5.9549E-02 6ouiloO T O.i3ouO 9i [.iit9E-0i T. Tg20E-o/ 6. jit-02 -9 I33E-0i 50b25oE-ODl 0.1300u TO U.15ou00 73 1.4023E-01 o.7148E-Ul 7.8590E-02 -9.6908E-01 4.8657E-01 5.6948E-02 O.i;utrb-f 0 -0 ~CO.1.. 7...10tJ0O.....%LOE) ~). E-0 -; 7?-....1..8 -1.t8E01 6.-8g -0iV 0.17U00 TO 0.19000 1.8o31E-01 5.b772E-01 7.3292E-02 -9.6041E-01 4.131LE-01 5.3332E-02 -.19000 T —- O-.ZiU Z.-70 — -3.-81E-i 5.89E-02 -9.5720E-0ui.31ilt-01U 4.365-Z - 0.21000 TO u.23u00 58 2.190ZE-01 5.4119E-01 7.1062E-02 -9.5223E-01 3.9619E-01 5.2022E-02 0.25000 TO O.25coo 2. vboo. 50;,;E-Oi 6.0;iorVE-02 -9.,O946E-Oi 3.233iE-01 4. 7( 0.25000 TO U.270O 44 2.5d31E-01 4.3230E-01 6.5171E-02 -9.4391E-01 3.1785E-01 4.7918E-02 -O.Z27,00.- 0;t9C S —... ——...- 2- dOE-ut - 4..tE-O 1 6.6 Z2E-02 -o 380 iE-0 i -E01o —3E-OZ 0.290OU0 TO 0.31000 15 Z.9B2iE-01 1.8956E-01 4.8945E-02 -9.3547E-01 1.3988E-01 3.6116E-02 -0.3ti000 -TO — -- 33000 -.- - -. —- 0.0 0-0 00 - o -- 0.33000 TO U.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.3500O To 0.37ftO u.O 0.0.0 0.0 0.0 0 -. 0.37000 TO 0.39000 0 U00 0.0 0.0 0.0 0.0 0O0 -01,3000- TO: O.to...........- --— 0 —. 0 --- 0 — o —0.410U0 TO 0.43000 0 0.0 0.0 0.0 0.0 0.0 0.0 13o9 WEIGHTED AVERAGE MLMENTUM 5.734 GEV/C BEAM KINETIC ENERGY = 4.870 GEV S = 12.666 (GEV)**2 Table X The Differential Cross Sections for 5.25 GeV/c < p < 6.25 GeV/c

BERM MOMENTUM FROM 5.25 TO 6.25 GEV/C L O ) a, C) I:,.00.04.08.12.16.20.24.28.32.36.W0 -U (GEV/C) m2 Fig. 40 The Differential Cross Sections for 5.25 GeV/c < p < 6.25 GeV/c

CROSS SECTIONS FOR 6.25 GEV/C TO 7.20 GEM/C ABS U BINS NUMBER ABSU SIGMA ERROR COSINE SIGMA ERROR /u/ (&A*0/c 0 — O -..-.- - OuOO 0 O.0 o.o 0.0 0"0 0o0 0'0 0.01000 TO 0.02O0 82 1o494dE-02 2o6741E 00 2.9530E-01 -9.9742E-01 2*3459E 00 2,5906E-01 -O.UY.00, O ~0.03,000 o5. ~.,,U/.4E-U0'.l.63,24, 0: 2u.ul72:-ul -V9.13I:-UlL 1.4185E O0 108015-0 O.U39u0 TU U.04b00 56 3.4S79E-02 1.4689E 00 1.9629E-01 -9.9377E-01 1.2798E 00 1.7102E-0l ---— O-~00 0.05"00. 0 4,,4]LE-02 L..953E 0U i.6bsUi —'.l86E-0I -1~395E 00.4701E-O] 0.05000 TO 0.07000 85 5.9324E-02 9.2305E-01 1.0012E-01 -9.8907E-01 7.9920E-01 8,6686E-OZ.T0 --— G. —'000 B T ---- 2B - 02'go- I f.tiiF.-Oi 9.95B-Z — -9.a5ZEE-O'- 7.1817E-018. —— a',U. 0900u lO o. ilUo0 10 9.9032E-02 8.?7d3E-O0 1.0503E-01 -9.8160E-01 7,5470E-01 9*0204E-02 0. iOu0 TO u.i.300 43 1-20/16E-O1 O.U/2E-0i 9. -O; -z:-ul 5.Z189E-OI -7.ff87E-oZ 0.13000 TO u.15U00 31 1.3913E-01 3.9057E-01 7.0149E-02 -9.738LE-01 3o3064E-01 5.9384E-02 — O.-i 010-TOO -— V. IJ0-? -~6069t -01.....-.9392E-0-...8.1199E-02 -9.6980 — ---,k1892t-01 - 6.- 1 --- 0.17000 TO U.19000 4 2 l.8146E-01 6.217tE-01 9.5943E-02 -9.6646E-01 5.3627E-01 8o2748E-0 H -— T. 1 9000 -— 0.2ZiOO 206 2o0030E-0i.'07E-02 -' -9.6347-0 3.030E-01 - 6 O 0*21000 TO 0.23000 25 2.1902E-01 4.1317E-01 8.2634E-02 -9.6004E-01 3.6113E-01 7.2226E-02 C 0.23000 la 0.25000 23 2.3?oOE-Oi 3.6452E-01 t.0029E-02 -9.6.E-O - 3.se 26t-0UL 6 O 94e:-OZ 0.25000 TU 0.27000 16 2.6038E-01 2.8273E-01 7.0683E-02 -9.5261E-01 2.4759E-01 6o1897E-02 — O,-2To (Jo.229c, 00 -- 16 2.?aOTE —- 7.1625E-02 -9.48uBf-;01-2.4887~-0O -.. 6~22TIE-OZ 0.2900u TU O.31u00 13 3,0174E-01 2.40B8E-01 6.6808E-02 -9.4389E-01 2.0650E-01 5-7272E-02 0.3100- T0 —- 33000 0.0 00 0-0 -.Oo 0~33000 TO 0.35000 0 0.0 0.0 0.0 0.0 0.0 0.0 0.35000 TO 0.37C00 0 0.0.0 0. -0 0-0 00 0~U 0.37U00 TO 0.39000 0 0.0 0.0 0.0 0.0 0.0 0.0 -— O 3900-TO' D~.-4.1t tUO 0 0. —-.... 0 0 - O. 0 - 0 0.0 O. 0 0.41000 TO U.43U00 0 0.0 u.O 0.0 0.0 0.0 0o0 746 WEIGHTED AVERAGE MCMENTUM a 6.689 GEV/C BEAM KINtTIC ENERGY = 5.816 GEV S = 14~439 (GtV)J*'2 Table XI The Differential Cross Sections for 6.25 GeV/c < p < 7.20 GeV/c

BERM MOMENTUM FROM 6.25 TO 7.20 GEV/C T I 0C ) Cr) Fig. 41 The Differential Cross Sections for 6.25 GeV/c < p < 7.20 GeV/c < P < 7.20 GeV/(2

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