THE UNIVERSITY OF MI CHIGAN COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report NEUTRON-PROTON, NEUTRON-DEUTERON, AND NEUTRON-NUCLEUS TOTAL CROSS SECTIONS AT 4.0 GeV/c AND 5.7 GeV/c E. F. Parker L. W. Jones ORA Project 03028 supported by: NATIONAL SCIENCE FOUNDATION GRANT NO. GP-13265 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION AINN ARBOR November 1969

This report was also a dissertation submitted by the first author in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan, 1969.

ABSTRACT Neutron total cross sections have been measured for H2, D2, He, Be, C, Al, Fe, Cu, Cd, W, Pb, and U at 5.7 + 0.6 Gev/c incident momentum. The hydrogen and deuterium cross sections were also measured at 4.0 + 0.6 Gev/c. The deuteron screening factor was determined from the hydrogen and deuterium cross sections. The resulting values are compared with the previous experimental evaluations and theoretical predictions. The total cross section vs atomic number data were fitted to an optical model. The experiment was performed at the Bevatron of the Lawrence Radiation Laboratory. iii

ACKNOWLEDGEMENTS I would like to thank Professor Lawrence W. Jones for his continual guidance during the entire course of this experiment. His support and encouragement have been of inestimable value to me in my graduate studies. I would like to express my gratitude to Professor Michael Longo and Dr. Bruce Cork for their invaluable contributions to the planning and performance of this experiment. I am particularly indebted to Dr. H. Richard Gustafson, Fred Ringia, and Carl Cork for their help in the setting up and running of this experiment. I am grateful to Bob Edwards, Walter Hartsough, and the entire staff of the Lawrence Radiation Laboratory Bevatron for the expert skill and cooperation so necessary to the successful setting up and running of this experiment. It is with pleasure that I dedicate this thesis to my wife, Lois, whose faith, encouragement, and hard work made it possible. iv

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS.............................., iv LIST OF TABLES...................vi................. i LIST OF FIGURES............................ vii LIST OF APPENDICES................................ ix I. INTRODUCTION............o.................. 1 A. Objective................................ B. Summary of Previous Results.............. 1 C. Theory....3................... 3 D. Report Outline........................... 6 II. EXPERIMENTAL SETUP AND APPARATUS............ 8 A. Experimental Arrangement................. 8 B. Beam................a................. 10 C. Beam Monitor.............................. 11 D. Transmission and Anticoincidence Counters 14 E. Ionization Calorimeter................. 15 F. Electronics.............................. 18 G. Targets............................ 20 III. DATA ANALYSIS......................... 24 A. Attenuation Cross Sections............... 24 B. Corrections.............. 24 C. Extrapolation to Zero Solid Angle........ 28 IV. RESULTS......................... 32 A. Measured Total Cross Sections.......... 32 B. Comparison with Other np and nd Data..... 33 C. Deuteron Screening Correction............ 37 D. Charge Independence...................... 41 E. Nuclear Total Cross Sections............. 41 V. CONCLUSIONS............................... 53 APPENDICES................................. 55 LIST OF REFERENCES...................... 67 vr

LIST OF TABLES Table Page I Theoretical Values of (r -2) for Various Choices of b...................5................ II Transmission Counter Solid Angles.............. 15 III Solid Target Properties........................ 23 IV Chemical Composition of Al Target............. 27 V Corrected Attenuation Cross Sections for the Four Transmission Counters..................... 29 VI Cross Sections Obtained from the three Extrapolation Techniques..................... 31 VII Total Cross Sections........................ 32 VIII Deuteron Screening Term...................... 40 IX Comparison of o(nn), u(pp) and a(nd), a(pd) at and 6 Gev/c............................ 41 vi

LIST OF FIGURES Figure Page 1 Experimental Layout........................... 9 2 Attenuation Cross Section for 0.625 in. Pb Target as a Function of y-Ray Filter Thickness 12 3 Beam Monitor Diagram.......................... 13 4 Ionization Calorimeter and Transmission Counter Assembly.............................. 16 5 Ionization Calorimeter........................ 17 6 Electronics Diagram........................... 19 7 Liquid Target................................. 22 8 Measured Attenuation Cross Sections vs Rate for the Four Transmission Counters............ 26 9 Neutron-Proton Total Cross Section............ 34 10 Deuterium. Total Cross Section................. 35 11 Proton-Proton Total Cross Section............. 36 12 Deuteron Screening Factor..................... 38 13 Glauber Screening Term........................ 39 14 Best a vs A Absorption Model Fit.............. 43 15 Optical Thickness for He, C, Al, Cu, Cd, and Pb........................................ 44 16 Beryllium Total Cross Section................. 46 17 Carbon Total Cross Section.................... 47 18 Aluminum Total Cross Section.................. 48 19 Copper Total Cross Section.................... 49 20 Lead Total Cross Section...................... 50 21 6 vs Momentum for Be, C, Al, Cu, and Pb...... 51 A-1 Actual and Calculated Attenuation Curves for a 3.7 and 5.4 Gev Peak Energy Neutron Beam.... 56 vii

Figure Page A-2 Incident and Effective Neutron Spectra for a 3.7 Gev Beam Energy.....................57 A-3 Incident and Effective Neutron Spectra for a 5.4 Gev Beam Energy..................... 58 viii

LIST OF APPENDICES Appendix Page I CALORIMETER RESPONSE........................ 55 II RATE EFFECT................................. 59 III BEAM RATE MEASUREMENT....................... 61 IV CALORIMETER BACKSCATTER..................... 63 V GEOMETRIC RESPONSE FUNCTION FOR THE TRANSMISSION COUNTERS..................... 65 ix

CHAPTER I INTRODUCTION A. Objective This thesis is a report of a neutral beam experiment performed at the Bevatron in the fall of 1968. Neutron total cross sections for twelve elements were measured at 5.7 Gev/c incident laboratory momentum. The total cross sections of two of the elements, hydrogen and deuterium, were also measured at 4.0 Gev/c. The deuteron screening factor and the charge independence of strong interactions were investigated as well as the atomic number dependence of neutron-nucleus total cross sections. B. Summary of Previous Results Proton-proton total cross sections have been measured at closely spaced momenta from 1 to 28 Gev/c1-11 with generally good agreement among the various data sets. Proton-deuteron total cross sections have been measured3'5'6'8'12 in this same momentum range. The agreement among the various data sets is generally good; however, there appears to be a systematic error in one of the two most extensive experiments3'5 that causes the at (pd) values of Bugg et al.3 to be about 2 mb larger than the values of Galbraith et al.5 The other pd measurements do not indicate which of these two data sets is incorrect as they are about equally divided in their agreement with these data.

The data on the neutron-proton total cross section above 1 Gev/c are limited to 15 points,13-21 half of which lie below 4 Gev/c. The neutron-deuteron total cross section data are even more limited with only 8 points2-19 above 1 Gev/c and only 4 points above 1.5 Gev/c. The nucleon-nucleus total cross sections for a few elements have been covered reasonably well below 3 Gev/c'3' 9,15,16,18,19,22 but the data above 3 Gev/c21'23-26 are limited in extent and agreement. The results of the experiments of Atkinson et al.21 at 6 Gev/c and Pantuyev et a.l.24 at 8.3 Gev/c are in considerable disagreement with the trend of the other experimental results. The results of the 19 Gev/c proton measurement25 and the 27 Gev/c neutron measure26 ment differ by 10% to 20%. This is difficult to understand in view of charge independence, and the slow variation of the nucleon-nucleon cross section in this momentum range. It is difficult to compare the results of Engler et al.23 with other experiments since that experiment was performed with a neutron beam having a very broad momentum distribution. The authors specify their data as corresponding to a mean momentum of 10 Gev/c; however, the very wide momentum spread limits the value of this specification. Their data are in good agreement with the 19 Gev/c proton data;25 however, with a factor of two difference between the specified momenta and the assumption of equal neutron and proton cross sections, one would expect the 10 Gev/c data to be about 5% higher, at least for the light elements, as is the case with the nucleon

nucleon cross sections. All of the data discussed in the above paragraphs are presented graphically in Chapter IV. C. Theory The deuteron cross section is equal to the sum of the np and pp cross sections minus a correction, 6, that, in the semiclassical view, allows for the eclipsing of one nucleon by the other in the deuteron; i.e. a(pd)=[a(pp)+a(np) ][l-6 (1) and a(nd)=[o(nn)+a(np)][l-6]. (2) 27 Glauber27 has developed a model that considers the effects of elastic scattering in the "high energy limit" to estimate the size of this screening factor. He obtained the following approximate expressions: o(pd)=a(pp)+a(np)-(r- 2)(1-a )a(np)c(pp)/4w (3) and o(nd)=a(nn)+a(np)-(r (l-a )a(nn)a(np)/4n, (4) np nn where a is the ratio of the real to imaginary part of the zero degree scattering amplitude and - 2 ~ Re[ -xn( ) ~fxp ( ) ]d q/2'Re[ fxn(0)~f x (0) ( 5) where S(q) is the deuteron form factor, and the f's are the elastic scattering amplitudes at momentum transfer q. We

assume that the np scattering amplitude has the same form as the pp amplitude, and that the imaginary part of the scattering amplitude can be written as Im[f(q)]=Im[f(O)]e-bq /2 (6) where q2 is the four-momentum transfer squared. We also assume that the real part of the amplitude is proportional to the imaginary part of the amplitude for small q2 so that Re[f(q)]= a(O) Im[f(q)]. (7) Experimentally, above 2 Gev/c, b is found to be a weakly momentum-dependent parameter. With these assumptions we can write (r I )= 2l S( q).eb d q (8) Table I lists values of (r-2) calculated from Eq. (8) using a fit to the Gartenhaus wave function for the deuteron.28 Since experimentally b is found to be between 6 and 10 (Gev/c)-2 above 2 Gev/c, we conclude that (r 2> is essentially constant above 2 Gev/c. Its calculated value is, however, dependent upon the assumed deuteron wave function. For example with a Hulthen wave function and a b of 9.6, Bugg et al.3 derive a value of 0.034 mb-1.

TABLE I Theoretical Values of (r-2) for Various Choices of b -2 b (r > 2.0 (GeV/c)-2.031 mb1 4.0.030 6.0.028 7.0.027 8.0.027 10.0.025 12.0.022 If we combine Eq. (1) and (3) we get 6=(r2) (1-nppp )a (pp)o (np)/4 (a (pp)+a (np )) e(r -2o(pp)/8w' 1.6(r -2mb (9) since anp.aP<<1 3,29 and o(np)%o(pp)%40mb. We therefore conclude that the Glauber model predicts an energy-independent screening correction factor of about 0.05. Pumplin and Ross30 have expanded the Glauber model to include the screening effects associated with inelastic intermediate states of the incident nucleon. They conclude that the effects are not important below 5-10 Gev/c because of the coherence requirement that kRtl, where R is the radius of the nucleus, and k is the three-momentum transfer required to

produce an inelastic state of mass m with an incident laboratory momentum K, i.e. k;m2/2K. Above 5-10 Gev/c the effect should increase with energy, yielding a decrease in the c(pd) cross section of 1.8 mb at 30 Gev/c. This translates into an increase in 6 from about 0.05 below 5-10 Gev/c to 6%0.06 at 30 Gev/c. The total cross sections of more complex muclei can also be expressed in terms of the nucleon-nucleon cross sections, i.e. a(pA)=[(A-Z)a(np)+Za(pp)1][l-6 (10) and o(nA)=[(A-Z)a(pp) np+Z(np)][l-6] (11) assuming charge symmetry [a(nn)=a(pp)]. As in the deuterium case, 6 allows for the elastic and inelastic shadow effects. Pumplin and Ross30 have also calculated these effects for A=9,64, and 207 and conclude that inelastic effects are insignificant below 5-10 Gev/c but can give 6 a significant energy dependence above 10 Gev/c. Specifically they calculate a 50% increase in 6 for Be at 30 Gev/c relative to its low momentum value. They predict an increase of about 10% in o for Pb. D. Report Outline The scheme of this report is as follows: Chapter II contains a detailed description of the experimental apparatus and set-up, Chapter III discusses the data analysis and the variaus correction factors that had to be considered and

Chapter IV discusses the results in terms of a simple absorption model and also compares them with most of the available nucleon total cross section measurements above several hundred Mev. The deuteron and nuclear screening factors are also evaluated and compared with the theoretical predictions.

CHAPTER II EXPERIMENTAL SETUP AND APPARATUS A. Experimental Arrangement Fig. 1 is a diagram of the experimental layout on the floor of the Bevatron. The neutron beam was produced in a 6 in. x 1/4 in. x 1/4 in. Be target mounted in the Bevatron vacuum tank and was defined by a 10 ft. length 5/8 in. diameter collimator located in the shield wall. Charged particles were removed from the beam by the large C-type ( 36 in. pole length) electromagnet located just downstream of the machine port, and a small (24 in. pole length) permanent magnet located just downstream of the defining collimator. The large magnet had a field strength of about 20,000 gauss and the permanent magnet had a strength of about 1200 gauss. In order to reduce the background radiation near the monitor counters, the magnet gap was filled with lead except for a 4 in. x 4 in. tunnel along the beam line, and a 5 ft. x 1 ft. x 6 in. Pb block with a 1 in. diameter collimator was located just upstream of the magnet. A 1 in. diameter, 5 ft. length collimator was placed downstream of the defining collimator to minimize any halo from scattering off the collimator walls. The solid targets, i.e. Be-U, were mounted on a platform located where the beam exits from the shield wall, and the liquid target was located 2 ft. downstream of the shield wall. The transmission counters and the calorimeter assembly were mounted on a cart and track that allowed the target-calorimeter

Ionization Calorimeter Transmission Counters DI-D4 I/2"Fe Converter Plate Liquid Target A2 Al ) I"Collimator Concrete Shield Wall ermanent Magnet Permanent Magnet /~ o5/8 " Collimator C C tjC -," Monitor C) / t Ct~gnet Y - Filter l"Collimator Vacuum Tank Port -Bevatron Beam 0 10 20feet -Be tgt Fig. 1 Expe rirnental I.ayout

10 separation to be varied by about 20 ft. This feature was included primarily for utilization in a small angle elastic scattering experiment that followed this total cross section experiment. For this experiment the converter plate-solid target position separation was 313.5 in. and the distance between the converter plate and the center of the liquid target was 262.5 in. The beam monitor was located in the beam just upstream of the shield wall and consisted of a 1/2 in. thick block of CH2 viewed by a three counter telescope. Specific details of these various components are given in the following paragraphs. B. Beam The beam line was at an angle of 2.5 degrees relative to the proton beam direction at the Be target. The distance between the Be target and the center of the defining collimator was 575 in. and the distance from the collimator center to the converter plate was 480 in. The beam was 1.12 in. in diameter at the converter plate and had no noticeable halo. The momentum distribution of the beam was not measured in this experiment; however, the small angle neutron spectrum from Be has been measured under quite similar circumstances31 and was found to be well represented by an empirical fit to the data on the production of inelastic protons by protons on Be;32 i.e.

11 d2N 2[0.47Pb 0 5640.44 0.47Pb -303(p0(P)2 P 1.0+ 2 P(0 dpdQ P b P p (12) where Pb is the momentum of the incident beam, and 6 is the production angle. The beam intensity was typically about 2 4 to 5 x 10 neutrons per spill. A small y-ray contamination can produce a significant error in the total cross section, and great care was taken to assure that there was no significant y-ray component. This was accomplished by measuring the attenuation cross section for a 0.625 in. thick Pb target as a function of y-ray filter (Pb) thickness. The radiation length in lead is much shorter than the nuclear collision length; therefore, the beam attenuation factor for the 0.625 in. Pb target will be strongly dependent upon the y-ray to neutron ratio. This ratio is strongly dependent on the amount of filtration. When it has been reduced to a negligible value, the beam attenuation factor will become independent of the filter thickness. The resulting data are shown in Fig. 2. On the basis of these data a 3 in. lead filter was placed in the beam at the sweeping magnet. C. Beam Monitor The beam monitor and its associated logic are shown in Fig. 3. The anticounter was a 2 in. x 2 in. x 1/2 in. scintillator mounted on a 6810A PM tube and the three counters in the telescope were 1.25 in. x 1.25 in. x 0.125 in.

12 9 8 z a: 7 o6 L_ cn (J 0 u 4 z wI II I 0.5 1.0 1.5 2.0 2.5 3.0 Pb FILTER THICKNESS (INCHES) Fig. 2 Attenuation Cross Section for 0.625 in. Pb Target as a Function of y-Ray Filter Thickness

MO CH2 Mi M2 M3 2 1 | | | BEAM DISC * SCALER*** "AND" GATE MoMI M2M, M MoMI M3 MoM, Mi Mo M2 M3 Mo M2M3 MI M2 M2M * Chronetics 104 Quad Disc. ~** All "And"Gates were Chronetics Model 113's *** All Scalers were LRL "Jackson" Scalers Fig. 3 Beam Monitor Diagram

14 scintillators mounted on 53AVP PM tubes. The converter was a 0.5 in. thick by 1.5 in. diameter CH2 disc. A very small fraction (1l%) of the incident neutrons interacted in the CH2 converter and produced a forward-going spray which was detected in the telescope, thereby giving a count rate directly proportional to the incident neutron intensity. The anticounter was used to assure that the monitor was counting incident neutrons and not charged particles. Although M1.M2 M3.M~ was the primary monitor, the various double coincidences were scaled and recorded to have a continuous check on the stability of the monitor counters. Counter instabilities were nCgligible throughout the experiment. D. Transmission and Anticoincidence Counters Anticoincidence counters were located just upstream and downstream of the targets. The upstream counter was a 1.5 in. x 1.5 in. x 1/16 in. scintillator mounted on a 6810A PM tube and was used to veto events due to any charged particles in the beam. The downstream counter was a 4 in. x 4 in. x 1/16 in. scintillator mounted on a 6810A PM tube and was used to veto events due to charged particles coming out of the target. The four transmission counters were 0.25 in. thick discs having 1.5 in., 2.5 in., 4.5 in., and 7.75 in. diameters and mounted on 6810A PM tubes. They were mounted in series between the converter plate and the body of the calorimeter as shown in Fig. 4. The axes of the counters were coincident with the beam center line to within 0.1 in. The two smallest

15 counters were fitted into 0.25 in. thick lucite sheets so that regardless of where a neutron hit a counter, it had previously passed through the same amount of material. The 4.5 in. counter light pipe was large enough to cover the 7.75 in. counter. The solid angles and mean Itl (fourmomentum transfer) ranges subtended by these four counters relative to the geometric centers of the liquid and solid targets are given in Table II. TABLE II Transmission Counter Solid Angles Counter Solid Angles (sterad.) Mean t Range (Gev/c)2 Diameter liquid solid (inches) liquid solid 5.7Gev/c 4.OGev/c 5.7Gev/c D4-1.5 2.6x10-5 1.8x10-5 2.2x10-4 l.lxlO-4 1.6x10- 4 75 -5 -4 -4 -4 D3-2.5 7.x10 5.0xlO 7.5x10 3.7x104 5.lxlO D2-4.5 2.3x10 -4 1.6x10- 4 2.5x10 3 1.3x!0 3 1.8x10-3 D1-7.75 6.8x10 -4 4.8x10 4 7.8x10-3 4.0x10o3 5.5x10 3 E. Ionization Calorimeter The calorimeterl consisted of 14 aluminum plates interleaved with scintillators as shown in Figs. 4 and 5. The scintillators were 32 in. x 22 in. x 0.25 in. sheets of Pilot Chemical Co. type F plastic scintillator. The scintillators were divided into two interleaved groups of seven which were summed optically and viewed by an RCA 4522 PM tube, a 5 in. Discussions on the theory and applications of calorimeters are given in Ref. 33 and 34.

16 Scintillators PM Tube Al Sheets - LAN\\\ \\\ I O.5"Fe ~Th~DD2 Converter Plate i D4 0.5" Fe Converter Plate Sheets I " I'UDI- D4 Scintillator Fig. 4 Ionization Calorimeter and Transmission Counter Assembly

Fig. 5 Ionization Calorimeter

18 diameter, 12 stage tube with a bialkali photocathode. The outputs of the two PM tubes were passively summed. The Al sheets were 19 in. x 19 in. x 1.25 in. The original design called for Fe instead of Al absorbing layers; however, an experimental evaluation showed that Al yielded a slightly better resolution than Fe at Bevatron energies. The response characteristics of the calorimeter are discussed in Appendices I, II, III, and IV. F. Electronics Fig. 6 is a diagram of the electronics for this experiment. The labels "50% Cal" and "10% Cal" signify that the input attenuation for the two calorimeter discriminators was such that only the upper 50% and 10% of the calorimeter output pulses could trigger their respective discriminators. The effective neutron spectra for these two attenuation levels are shown in Appendix I. The largest transmission counter, D1, was in coincidence with the 10% Cal and in anticoincidence with the anticounters. The Cal(10%)'DlA output was then put in coincidence with the 4.5 in. disc counter, D2. This output in turn was put in coincidence with the 2.5 in. disc counter, D3, and finally this output was connected in coincidence with the 1.5 in. disc counter, D1. This coincidence cascade was duplicated for the 50% Cal. The 50% calorimeter was included primarily as a check on the operation of the 10% logic and as a convenience for making various tests during data runs.

19 D4 D3 D2 D1 I Al. A1 A2lp / /Beam Mixer -i I Mixer 50n Mixer Scaler Atten: All Disc are Chronetics Br Cal(lDlD2A ModI el 101. D) Linetics Model 113. FCal(50 1A Spc Inc model 1(400 NS)1. G=Cal(10%).D1.D2A Scalers Bs-I are LRL H=Cal(50%o) D1 D2D3A "Jackson Scale s. I DCal(50%o).D1.D2 D3'D4 Ah Figo 6 Electronics Diagram " a " a ") I C icaler A =Cal(1O%)-D1. Note: All Disc. are Chronetics

20 The "delayed Cal(10%).D1.A" coincidence was included to give a continuous measure of the accidentals rate and also an indication of the instantaneous beam intensity for making rate corrections on the data (see Appendix II). The delayline length was equal to one period of the Bevatron RF system, i.e. about 400 ns. The scaler data were typed out and punched on paper tape at the end of each run. For the solid targets a complete in-out sequence was limited to about 10 minutes with about 30 seconds required to record the data and change the target. For the liquid targets the sequence was extended to about 20 minutes because of the longer time required (X3 minutes) to change the target state. These short cycle times were used to minimize the effects of any temporal drifts in the equipment. One such variation was caused by temperature changes in the calorimeter discriminator. Although the Chronetics logic is relatively temperature-insensitive, small temperature-induced changes in the triggering level coupled to a very steep pulse height spectrum (see Fig. A-1) were found to produce significant effects in the 10% calorimeter count rate relative to the monitor. For this reason great care was taken to avoid short-term temperature changes in this discriminator, and, the discriminator temperature was continually monitored and displayed on a strip-chart recorder. G. Targets The liquid target is sketched in Fig. 7. The flask

21 was emptied for the target "out" runs by closing the flask vent and increasing the pressure above the liquid by adding helium gas to force the liquid into the reservoir. The target "out" runs for liquid hydrogen were therefore not actually with an empty flask but rather with the flask filled with a gaseous helium and hydrogen mixture at one atmosphere. Helium was also used to empty the flask in the liquid helium runs; however, deuterium gas was used for the liquid deuterium runs. In the liquid hydrogen and liquid helium runs the flask vent was opened to the atmosphere; however, in the liquid deuterium runs a closed-loop arrangement was required to avoid loss of the deuterium. Since the deuterium was condensed from the gaseous state by passing it over a condenser at LH2 temperature, the LD2 system equilibrium pressure was 0.5 atmospheres. Helium was added to the system to bring the pressure up to 0.75 atmospheres. Although it would have been quite helpful to have been able to measure the temperature of the gas in the flask during the target "out" runs, repeated attempts to do so failed. As stated above, the flask was 48 in. long at room temperature with no pressure inside. However, this length must be corrected for the expansion produced by the pressure differential (1 atmosphere) and the contraction produced by the temperature reduction from essentially 300 degrees K to 20 degrees K. The following correction factors were obtained from the Lawrence Radiation Laboratory mechanical engineering group:35

22 Flask Vent, \Reservoir Al Vacuum Jacket -Fill Line 0.015" Cu Heat Shield-, Mylar- I- I Beam l iask-48"x 3" Diameter 0.0 1 F 0.015" Mylar Multilayer Aluminized Mylar Insulation Mylar ~Reservoir Flask Vent Reservoi Flask Fill Line Mylar Window - Fl JsVacuum Jacket Flask Fig. 7 Liquid Target

23 thermal contraction 0.155 inches pressure expansion 0.350 inches/atmosphere. The corrected flask lengths are 48.195 in. for the liquid hydrogen and helium runs and 48.11 in. for the liquid deuterium runs. The temperature of the liquid hydrogen and deuterium was determined by the liquid hydrogen boiling at one atmosphere in the reservoir. This resulted in a density of 0.0707 + 0.0001 g cm-3 for hydrogen36 and 0.1708 + 0.0003 g cm-3 for deuterium.37 The liquid helium temperature was determined by the liquid helium boiling at one atmosphere resulting -3 38 in a density of 0.1255 g cm 3 The physical characteristics of the solid targets are given in Table III. TABLE III Solid Target Properties Element Thickness Density (inches) (g cm-3) Be 3.690 1.854 C 3.000 1.768 Al 3.012 2.77 Fe 0.9922 7.871 Cu 1.000 8.974 Cd 1.663 8.65 W 0.9233 19.3 Pb 1.504 11.34 U 0.4014 18.97

CHAPTER III DATA ANALYSIS A. Attenuation Cross Sections The attenuation cross section measured by a counter having a solid angle AQ is given by the simple attenuation equation a (AQ)=nln(Io/Ii) (13) where Ii is the intensity with the target in, Io is the target out intensity, n is the density of nuclei in nuclei per cm, and x is the target thickness. The total cross section is obtained by extrapolating the attenuation cross section to zero solid angle. The standard approach is to simultaneously measure attenuation factors for a series of counters having different solid angles, then fit these data to some model. The zero solid angle attenuation cross section predicted by the best fit to the data is then taken to be the total cross section. B. Corrections Before the true attenuation cross section could be obtained several corrections had to be made on the raw data. The most significant correction required was the the rate effect discussed in Appendix II. This correction factor was determined by measuring the attenuation cross section for the Be target at a number of different rates and using the measured cross sections vs rate to obtain the relationship between the rate and the correction factor. The rate was 24

25 taken to be proportional to the target in and out average of the Delayed Cal(10%).Dl.A to Cal(10%).Dl.A ratio, hereafter called the "accidentals rate." Appendix III discusses the reasons for using this quantity as a measure of the rate. The aa (measured) vs accidentals rate data for the four transmission counters are shown in Fig. 8. The straight lines are least squares fits to the data using the linear expression Pa (measured) = a a(l+aR) (14) The average of the four values of a was taken as the correction factor for all elements and counters. Eq. (14) is derived in Appendix II. The best fit value of a was 0.031 + 0.005. Most of the data required about a 2% rate correction. A correction of the order of 1% was applied to the attenuation cross sections measured by the 7.75 in. counters D1, in order to compensate for a gradual falloff in the calorimeter output amplitude towards the edge of the absorber plates. This correction was of little significance since Dl has little influence on the extrapolation to zero solid angle. None of the targets were chemically analyzed specifically for this experiment; however, they were all obtained from the Lawrence Radiation Laboratory metal stores whose stock is specified by the Standards and Specification Group, Mechanical Engineering, Livermore Site, Lawrence Radiation Laboratory. According to these specifications the Cd, W and Pb targets were free of contaminants to the 0.1% level by weight. The

315 DI D3 300 310 E.0 E 295 o 305 % b o b 290 300 285 0 0.5 1.0 1.5 0 0.5 1.0 1.5 ACCIDENTALS RATE (%) ACCIDENTALS RATE (%) 3 1 O ~~- "' D4 iu-,I o 310 D2 D4 305 - 285 E E E 300 280b' b 295 275 0 0.5 1.0 1.5 0 0.5 1.0 1.5 ACCIDENTALS RATE (O/) ACCIDENTALS RATE (%) Fig. 8 Measured Attenuation Cross Sections vs Rate for the Four Transmission Counters

27 Be and Fe targets contained about 1% contamination, the most significant contaminants being Mn in the Fe and 0 in the Be. The closeness in A between the contaminants and the targets coupled with the weak A-dependence of the errors generated by the contaminants makes the error that results from ignoring them only of the order of 0.1% to 0.2%. This was not the case with aluminum as can be seen in Table IV, and a correction was required. TABLE IV Chemical Composition of Al Target Element % by Weight Mg 1.7<, <2.3 Cu 0.9<, <1.5 Cr 0.17<,<0.4 Mn <0.3 Fe <0.7 Sn <0.6 Zn 3.5j1, _4.2 Corrections were made for the various contaminants by dividing them into four groups according to atomic weight: those close to Al, Fe, Cu, and Cd in atomic weight. The target in readings for the four counters were then corrected for the additional attenuation produced by the contaminants. A correction had to be made on the liquid target data to allow for the effects of the gas in the flask in the target

28 empty runs. This correction factor can be accurately determined if the temperature and composition of the gas is known; however, in this experiment the temperature was not measured. If we assume that the gas was totally helium, at 70 degrees K, in the hydrogen runs the correction would be 0.5%. If the gas were at 50 degrees K, the correction would be 0.8%, and 1.6% for 20 degrees K. Since a considerable quantity of room temperature helium was introduced to force the liquid out of the flask it seems reasonable not to expect the gas to be at the liquid temperature. Similarly one would not expect the gas to be above 70 to 80 degrees K, the temperature of the liquid nitrogen-cooled radiation shield. Therefore a temperature of 50 + 20 degrees K was assumed. This corresponds to a correction factor of 0.8 + 0.4% for the hydrogen and helium data. Since deuterium gas at 0.75 atmospheres was used in the deuterium runs the correction factor was 0.7 + 0.4%. C. Extrapolation to Zero Solid Angle The corrected attenuation cross sections for the four counters are given in Table V. The uncertainties shown are the statistical errors of the raw data.

29 TABLE V Corrected Attenuation Cross Sections for the Four Transmission Counters Element Cross Sections (mb) Statistical D1 D2 D3 D4 uncertainty H (6Gev/c) 42.56 42.17 41.43 38.91 0.74% H (4Gev/c) 43.19 42.90 42.41 40.16 0.6 % D (6Gev/c) 77.6 77.0 75.1 70.1 0.52% D (4Gev/c) 80.1 79.3 78.3 73.8 0.6 % Be 298.7 294.7 285.0 273.4 1.0 % He 140.3 138.3 133.5 123.5 0.8 % C 367.4 362.7 350.3 321.1 1.0 % Al 710.4 695.1 649.0 478.1 1.35% Fe 1229 1184 1071 931.0 1.35% Cu 1371 1311 1181 1018 1.15% Cd 2051 1941 1707 1453 1.0 % W 2861 2672 2294 1964 0.9 % Pb 3101 2888 2470 2107 0.8 % U 3456 3182 2706 2311 1.05% Three extrapolation methods were tried. The first assumed that the measured attenuation cross sections decrease linearly with solid angle so that the total cross section is given by ot=a (i)+ [oa(i)-a (i+l)].AO(i)[AQ(i+l)-A2(i)]- L (15) where a (i) is the attenuation cross section measured by the ith counter, An(i) is the solid angle of the ith counter with AQ(i)<AE(i+l). This is only valid if do/dQ is constant over

30 the solid angles subtended by the counters. Therefore it is only applicable to the smallest counters for the high A targets but is good for all four counters for the low A targets. The second method assumed that the difference between the attenuation cross section and the total cross section is due to small angle elastic scattering and that du/dO is represented by the expression for scattering from a, totally absorbing disc, i.e. t= taa(i)+[E 2 FI2J(Rke) fi(0) dQ (16) where fi(e) is the geometrical response function of the ith transmission counter (see Appendix), and R is the nuclear radius. Actually allowance should be made for the fact that the neutron beam was not monoenergetic. However that refinement represents a neglilible improvement in this case. Total cross section values were calculated using Eq. (16) for all four values of aa(i), treating R as a free parameter. Very good agreement could be obtained between the four values of at for reasonable R values for all of the heavy targets. The at values calculated from the larger counters for the lighter elements, however, were slightly smaller than the smaller counter values. This is to be expected since no inelastic term is included in Eq. (16). This was not noticeable for the heavy targets since the elastic correction is so large. However for the lighter elements where the elastic correction is small, the inelastic term is not compeletely negligible for the largest counter.

31 The third approach was to make a least squares fit to a polynomial in Itl, i.e. oa(i)=ot+atl+b ltI2+cltl3. (17) The total cross section values yielded by these three extrapolation methods were averaged to obtain the final cross sections, and the spread among the methods was taken as a measure of the uncertainty. In all cases this spread was small compared to the statistical uncertainty of the data. Table VI shows the cross sections obtained from these three methods for several elements. TABLE VI Cross Sections Obtained from the Three Extrapolation Techniques Element Extrapolation Method Percentage #1 #2 #3 spread H 42.57 42.40 42.40 + 0.2 D 77.92 77.73 77.90 + 0.13 Cu 1410 1400 1410 + 0.35 Cd 114 2112 2121 + 0.2 U 3608 3618 3634 + 0.35

CHAPTER IV RESULTS A. Measured Total Cross Sections The total cross sections resulting from the analysis procedures discussed in Chapter III are listed in Table VII. The uncertainties represent the uncertainties associated with the various correction factors discussed in Chapter III and the statistical uncertainty of the experimental data combined in quadrature. TABLE VII Total Cross Sections Element Z A Total cross section (mb) 5.7 Gev/ 4.0 Gev/c H 1 1 42.5+0.6 43.1+0.6 D 1 2 77.8+1.3 80.3+1.9 He 2 4 142+3 Be 4 9 301+5 C 6 12 370+6 Al 13 27 718+13 Fe 26 56 1250+20 Cu 29 64 1410+30 Cd 48 112 2120+30 W 74 184 2970+70 Pb 82 207 3240+50 U 92 238 3620+60 32

33 B. Comparison With Other np and nd Data Figs. 9 and 10 show the available np and nd total cross sections above 1 Gev/c. The Bugg et al. 3 Foley et al., and Galbraith et al.5 pp data are shown in Fig. 11. As can be seen, the np values from this experiment are somewhat higher than the Engler et al.13 results. However since their experiment did not contain a neutron energy selecting element, this discrepency may be due to the fact that their values are averages over an energy range where the cross section is changing fairly rapidly. Their nd data also appears low relative to the pd data. The 5.7 Gev/c nd value of this experiment is in good agreement with the Galbraith et al.5 6 Gev/c pd cross section, and our 4.0 Gev/c nd value is consistent with the Bugg et al.3 4.0 Gev/c pd value. It is interesting to compare the energy dependence of the np cross section (Fig. 9) with the pp cross section (Fig. 11). The nucleon-nucleon, antinucleon-nucleon, and K —nucleon total cross sections can be expressed in terms of the cross sections for pure isospin states, I = 0 and I = 1. The pp, pn, K n, and K p cross sections are pure I = 1 cross sections and the np, K p, pp, and K n cross sections are made up of equal parts of I = 0 and I = 1 cross sections. Experimentally it is found that, in the case of K-nucleon and antinucleonnucleon cross sections, the I = 0 cross section is equal to or larger than the I = 1 cross section.5 If the same is true for the nucleon-nucleon interactions the np cross section

-'iII Iii1"11 I' 111I11I... IO'I L Kreisler 43 X Eng/er + Polevsky V Atk inson 42 A Khachaturyon ~' ~ 1 v Booth % E 41 ODzhelepov Nedzel Z Ashmore 0 40 0 This Experiment HORunge I (I) cn C/3 3A 0 -- 35 34 1.0 10.0 MOMENTUM (Gev/c)

L Kreisler o _ _ + Galbraith - (Proton) 0 Be//ettini - (Proton) X Engler 80- V P/levsky - oa V Booth E - Dozhe/epov * Nedze/ T Z * Ashmore 275 - ugg- rProton) + TTT c o0 0 This Experiment 1 H65 I —I v 60m 1.0 10.0 MOMENTUM (Gev/c)

XX X Bugg Foley H ^47 x Fo/ey + Ga/braith t045L XXX x 45 o 03 o 44 X 0u x o O42 FH 43 X n 0 "39e~~~~~~~ ++ 1 41 39 1.0 10.0 MOMENTUM (Gev/c)

37 should be equal to or greater than the pp cross section. A comparison of Figs. 9 and 11, however, shows that a(np) seems to oscillate around a(pp) with o(np) less than a(pp) below 3.5 Gev/c and again from about 12 to 27 Gev/c. It must be noted, however, that only the 22 Gev/c np point is definitely below the pp curve and without it there would be little evidence for a crossover. C. Deuteron Screening Correction One can use Eq. (1) through (4) and the assumption of charge independence to calculate values for the deuteron screening correction factor, 6=.[(pp)+a(np)-a(nd)]/[a(pp)+a(np)] and the quantity (r- 2)(1- anpapp)=4[(pp)+a(np)-a(nd)]/a(pp)a(np) from the cross sections listed in Table VII. The results are shown in Table VIII. Also included are values obtained using the preliminary np data of Runge39 et al. Figs. 12 and 13 show the values of these quantities obtained from the earlier experiments. The theoretical values shown in these figures are those calculated by Bugg et al.3 for a Hulth6n wave function and a value of 9.6 for b in Eq. (8). The earlier data exhibit a strong energy dependence contrary to the theoretical predictions of Glauber27 or Pumplin and Ross.30 If the values obtained with the Bugg et al.3 pd data are omitted the remainder of the nucleon data are consistent with

A Kreis/er - Fo/ey I I I I I I I I I I 0 Galbraith - Kreisler Theoretical Volue V Palevsky - Bugg 10 0 Eng/er - Foley Gao/braith - Eng/er 9-X ugg - Po/levsky o | Bugg - Eng/er 8 ugg - Booth N 7_+ Galbraith 7 +~ 5 ++ 0I 0 MOMENTUM (Gev/c)

l I i I I I I I I I I 8A Kreisler - Foley -- Theoretical value 0 G/braith - Kreisler V Pa/evsky - Bugg 7 0 Engler -Foley ~u L | / Diddens - Engler 0 ~ 6 Diddens -Palevsky di x Y V Ashmore -Engler 7 * Galbraith - Engler 55 X Bugg- Palevsky E f |) Bugg - Engler T Og g,4 * Bugg- Booth a. + Galbrait r+ DOta aa ker r1 t C-T Ct 3 I CI 10 MOMENTUM (Gev/c)

40 TABLE VIII Deuteron Screening Term 6 2 t (pp) at((p) Ct(pd) ot(nd) (r-2) 6xl Gev/c) (mb) (mb) (mb) (mb) (l-a ) x102mb - 6 40.65 42.5X 77.45 4.1 6.8 +0.6 +0.6 +1.3 +1.1 +1.6 6 it 77.8x 3.8 6.4 +1.3 +1.1 +1.6 6 40.83 79.13 3.0 5.0 +.12 +.25 +0.5 +0.7 6 77.8X 4.0 6.6 +1.3 +1.0 +1.4 4 42.13 43.1x 80.93 3.0 5.0 +.12 +0.6 +.25 +0.5 +0.7 4 " 80.3x 3.4 5.7 +1.9 +1.4 +1.9 8 40.05 40.639 76.25 3.4 5.5 +0.6 +1.0 +1.3 +1.3 +1.7 13 39.25 39.839 74.25 3.8 6.1 +0.6 +1.0 +1.3 +1.3 +1.7 17 38.75 38.739 73.25 3.5 5.8 +0.6 +1.0 +1.3 +1.4 +1.7 22 38.35 37.539 71.65 3.7 5.5 +0.6 +1.0 +1.3 +1.4 +1.7 theoretical value 3.4 5.4 x this experiment

41 a constant or weakly energy dependent screening factor except for the 27 Gev/c point of Kreisler et al.14 The agreement among the values in Table VIII is quite good and. is consistent with a constant or nearly constant screening factor. The agreement with the theoretical values is also quite good. D. Charge Independence The nn total cross section can be evaluated from Eq. (4) using the Galbraith et al.5 experimental value for the Glauber screening term, i.e. 0.042+0.003 mb-1. From charge symmetry it is expected to equal the pp cross section. We also expect a(pd)=a(nd) from charge symmetry. Table IX compares these cross sections. The agreement is good. TABLE IX Comparison of o(nn), a(pp) and o(nd), o(pd) at 4 and 6 Gev/c Momentum ao(p) a(nn) a(od) o(nd) (Gev/c) (mb) (mb) ((mb) 4 42.1+.123 43.5+2.4X 80.9+,.243 80.3+1.9x 6 40.6+.65 41.2+1.7x 77.4+1.35 77.8+1.3x 6 40.8+.123 79.1+.243 x this experiment E. Nuclear Total Cross Sections 40 Sievers has derived a rather simple expression for fitting nuclear total cross section data in terms of two parameters, the nucleon radius, ao, and the nucleon mean free path in nuclear matter, xo. The expression is 5= 2r{R2- 2Cl-(XR+l)eXR1/X2} (18)

42 where R=aA /3, A is the atomic weight and X=2/xo. This is obtained in an optical model, by integrating, for zero degree scattering, the familiar small angle, large max integral max 41 approximation for the scattering amplitude, i.e. f(e)=ikf/b a(b) J (kbe)db, (19) 0 assuming a totally absorptive interaction. With this assumption the partial wave amplitude, a(b), (where b is the impact parameter) becomes the absorption probability which should depend upon the amount of nuclear matter traversed by the particle, i.e. a=(l-ex/ o), (20) where x is the total path length of the particle in the absorbing medium. If we now assume that the direction of the incident particle is unchanged in traversing the nucleus Eq. (20) becomes a(b)=(l-e xo ) (21) Combining Eq. (19) and (21) and integrating we get Eq. (18). Eq. (18) was fitted to the total cross sections listed in Table VII using a trial and error least squares method. The best fit is shown in Fig. 14 along with the experimental points. The best fit parameters are ao=1.27+0.01f, which is in good agreement with the values of 1.2f to 1.3f obtained from electron scattering, and x =3.0+0.2f. The optical thickness vs impact parameter for six elements is shown in Fig. 15.

PIJ TaPO1AI uoildJosqV v so saD j 11 ~ T, TOTAL CROSS SECTION (mb) ol 0 0 0 0 0 0 0 0!11q \I q III X l I liiil l l I I Iittl l I It( 2l ---- Et

44 (O L U 0I SS3N>3IHJ lVOidO Fig. 15 Optical Thickness for He, C, A 1, Cu, Cd and Pb - _~<1:~~~ C'd and Pb

45 As can be seen, He is quite transparent while Pb is almost totally opaque. The nuclear radii obtained from this value 1/3 of ao, i.e. R=aoA, are in quite good agreement with the radii which yielded the best agreement between the four values of at obtained when using Eq. (16) to extrapolate the attenuation cross sections to zero solid angle in Chapter III. F. Comparison With Other Nucleon-Nuclear Data nd +-he Energy Dependence of the Total Cross Sections In order to show how the results of this experiment compare with previous experiments the available nucleonnuclear total cross section data were collected and are presented in Figs. 17 through 21 for those elements for which considerable data exist. Also included are the preliminary results from a recently completed CERN neutron experiment39 that included an ionization calorimeter for energy selection. The dashed lines are included in the figures only to guide the eye. The only previous measurement at about 6 Gev/c is that of Atkinson et al. which seems to be incorrect. The agreement between this experiment and the preliminary results from CERN is very good. Fig. 21 is a plot of the nuclear screening correction factor, 6, for several elements calculated using Eq. (11) and the pp, np, and n-nuclear data presented in this chapter. The calculated values of Pumplin and Ross3 are included. The data are consistent with a constant 6, especially in the case of lead and aluminum. However, it must be noted that the

j~~~. ~''111II I IIII11 % Jones 320 0 Belletf/ni - (Proton) X Engler CDw ~ + Longo - (Proton) Coor ~o O D ozhe/epov T 300 * Nedze/ / E] This Experiment - ~o L, 280O'") 0[ o 260 0 240 220 II I II 11I I I..... I I Iill 1.0 10.0 MOMENTUM (Gev/c)

:I I I'I" I I I'111 11 m I Jones 0 Bellettini - (Proton) 380- x Engler A Pantuyev T + Longo- (Proton) I E _ Iv coor 3%=w I/go - (Proton) 360 B6ooth P O o DOzhe/epov o* Nedzel Lo )) Ashmore Wl 0[ This Experiment J ~340- v Runge ~) / i I / 0 300 280 L I I1 1.0 10.0 MOMENTUM (Gev/c)

c? A dones -760 0 Bellettini - (Proton) X Eng/er > E A Pantuyev 740 V Atkinson Z + Longo - (Proton) ~'0 0 p720 *Coor — 720I - ~F Booth o Z O Dzhe/epov of 700 * Nedze/ C) Ashmore 680 Runge 0 680 Ch0 --- Bugg - (Proton) ~ )6 0 O This Experiment CO 660 0 640 580 620 600 580' 1.0 10.0 MOMENTUM (Gev/c)

.r' 1.6 t, Jones o Bellettini- (Proton) X Engler Q) A & Pantuyev + a () |V Atkinson Z 1.5 + Longo - (Proton) ~ I ~*Coor o m Y Booth > - I O Dzhelepov Q Z ~ *Nedzel 0d ~ 1.4 mo Ashtore F0 E]o This Experiment 03 I.3I / 1.1 1.0 10.0 MOMENTUM (Gev/c)

111111| | 11' I I I I' III j - -?9A Jones 0 Be/lettini x Eng/er, () 3 &A Pantuyev 3.2 V Atkinson ~< V Booth I 0 Dzh elepov nQz ~Nedzel Ashmore o0 3.0 0 Th/s Experiment uz I Runge' LJ1.0 10,0 MOMENTUM (Gev/c) 2.8 0 2.6 1.0 10.0 MOMENTUM (Gev/c)

51.7 Pb T T x.6 X 4 Pumplin a Ross I.6.5 I I Al.3 4 rC.3 I.2.2 1 5 10 15 20 25 30 MOMENTUM (Gev/c) Fig. 21 S M'eomentum for Be, C, Al, Cu, & Pb.

key points between 10 and 22 Gev/c are based on preliminary data. The data are not inconsistent with the Pumplin and Ross model. Except for the 27 Gev/c point the average values of 6 for the data shown in Fig. 2 fit an A0'26 expression quite well for A->12. This suggest the following empirical equation for relating nucleus cross sections to the nucleon-nucleon cross section; 26 a(nA)=[(A-Z)a(pp)+ Za(np)][1-0.155A 1 (22) (pA)=[(A-Z)a(np)+ Zo(pp)][1-0.155A 261 (23)

CHAPTER V CONCLUSION The neutron-proton and neutron-deuteron total cross sections have been measured to an accuracy of 1.5% at 4.0 and 5.7 Gev/c. These cross sections, along with those obtained by Runge et al.37 show that a(np)_a(pp) below 10-15 Gev/c. The experimental data between 10-15 Gev/c and 27 Gev/c indicate o(np)~a(pp), which is contrary to the available data on the relative sizes of the pure I=O and I-=l amplitudes. The region above 15 Gev/c should be investigated further to determine if this is indeed true and whether or not o(np)2a(pp) above 27 Gev/c. The deuteron screening factor was evaluated and was found to be consistent with the theoretical predictions. The experimental uncertainties are, however, too large to prove or disprove the existence of an inelastic contribution of the size predicted by Pumplin and Ross.30 The neutron-nuclear total cross sections were measured for He, Be, C, Al, Fe, Cu, Cd, W. Pb, and U at 5.7 Gev/c. These data fit a totally-absorbing optical model quite well. All of the available high-energy nucleon-nuclear total cross section data were used to evaluate the nuclear screening factor a~s a. function of momentum for several elements. These data are consistent with a momentum independent screening factor; however, the uncertainties are too large to disprove the existence of a momentum dependence of the size predicted

54 by Pumplin and Ross.30 A reevaluation of the 27 Gev/c cross section should clarify this question.

APPENDIX I CALORIMETER RESPONSE Since a high-energy monoenergetic neutron beam is not technically feasible the energy resolution of the calorimeter could only be determined indirectly. This determination was made by trying to find an energy resolution fnction that, coupled to the incident neutron spectrum, would produce a good fit to the measured calorimeter attenuation or integral pulse height distribution curves (see Fig. A-i). It was assumed that the incident neutron spectrum was given by Eq. (12) up to 0.3 Gev/c of Pb and then fell linearly to zero at Pb (see Figs. A-2 and A-3). It was also assumed that the energy resolution of the calorimeter was energy independent, i.e. a monoenergetic neutron beam:would give a Gaussian pulse height spectrum with a FWHM, AE, equal to some constant, C, times the neutron energy, E. Fig. A-1 shows attenuation curves taken at two Bevatron energies along with the fit obtained for C=1.5. This indicates that the calorimeter resolution was + 75%. The output of the calorimeter was fanned out to two discriminators, one set to trigger only on the largest 10O of the calorimeter output pulses, the other set to trigger on the largest 50%. The effective neutron spectra for these two discriminator settings for Bevatron energies of 3.7 and 5.4 Gev are shown in Figs. A-2 and A-3.

1Oii 5,4 Gev 0 Actual Attenuation Curve - Ca/culated Attenuation Curve wF~~~ 1 ~3.7 Gev — F- 0.1 0.01 0 4 8 12 16 20 24 28 ATTENUATION (Db) Fig. A-1 Actual and Calculated Attenuation Curves for a 3o 7 and 5.,4 Gev Peak Energy Neutron Beam

MOMENTUM (Gev/c) I 2 3 4 I I (0 5 z 3.7 Gev- 2.50 Neutron Spectrum -(D i izJ O k5 C 50 Co/-~ ~zI ~0 2 0 -0% Ca/ CD 0 I 2 3 KINETIC ENERGY (Gev)

MOMENTUM (Gev/c) 1 2 3 4 5 6....i l I I... I I I 7 5.4 Gev, 2.5~ Neutron Spectrum 6 /I > / 3 50% Co-/ Z 2/ //0% Ca/ / / 0 I 2 3 4 5 KINETIC ENERGY (Gev) Fig. A-3 Incident and Effective Neutron Spectra for a 5 7 Gev Beam Energy

APPENDIX II RATE EFFECT A. Signal to Noise Ratio With the 0.5 in. thick iron converter plate there was about a 10% probability that an incident neutron would undergo a conversion in the iron while there was about an 80% probability for a neutron to convert in the body of the calorimeter. Since the calorimeter discriminator rejected all but the upper 10% of the pulses from neutron conversions occuring in the iron plate, the ratio of the "signal" pulses to the "noise" pulses coming from the calorimeter was of the order of 0.01. A small ratio like this would not be a problem at the average beam intensities used in this experiment; however, because of RF structure and strong magnet ripple modulation, the beam contained spikes with intensities many times larger than the average. During these spikes the probability that the pulses from two uncorrelated neutron interactions add to produce a pulse large enough to trigger the calorimeter discriminator becomes significant. A discussion on tle effect of these pile-up pulses on the cross section measurements is given below. B. Rate Effect on Measured Total Cross Sections The probability that the pulses from two uncorrelated neutron interactions in the calorimeter will add to produce an output pulse of sufficient amplitude to trigger the

6o calorimeter discriminator is proportional to the square of the beam intensity. The measured event rate, Rm, is therefore: R =Rt (1+ aR ) (A- 1 ) where R is the true event rate and a is a constant proportional to the pulse width, i.e. of the order of 108 sec. t when R is events per sec. The measured attenuation cross sections are obtained from the target in-out event rates via Eq. (13), i.e. co =[ n Ro /Ri /nx (A-2) where the subscripts "o" and "i" stand for target out and in respectively. Combining (A-l) and (A-2), expanding (1+ cRt) and dropping terms higher than the first order in Rt yields t t t Jm [In Ro/R + In(l+ mRo- mRi)]/nx = a+ a(Ro- REi)/nx (A-3) Let R= ( 1+ ) R (A-4) The targets used in this experiment typically attenuated the beam by a factor of 0.2 to 0.44, so that ct 0.3. Combining (A-2) and (A-4) yields a =[ln R o/Ri]/nx = [ln(l+e)]/nx t t t ~(Ro Ri)/R nx (A-5) and -aC(l+ aRi) (A-6) The aR term was typically 0.02.

APPENDIX III BEAM RATE MEASUREMENT The delay between D1'A and the 10% Cal which form the quantity Delayed Cal(lO%)'DlA corresponds to one period of the Bevatron RF system. This means that the pulses from D1.A from one RF bunch arrive at the Delayed Cal(lO%).DlA "and" gate at the same time as the pulses from the calorimeter from the previous RF bunch. Since any two adjacent RF bunches are approximately the same, the Delayed Cal(10%).D1A output is proportional to the accidentals rate in the normal Cal(lO%) Dl A. The number of accidental coincidences in a twofold coincidence, g, expected per spill is proportional to get n2(t) dt (A-7) where n(t) is the beam intensity at time t. The number of true coincidences is proportional to m=y n(t)-dt (A-8) which is what the monitor measures. For a constant beam intensity the monitor measures the beam rate; however, in this experiment the beam was strongly modulated so the monitor was not a good indicator of the average instantaneous rate. To see that the Delayed Cal(lO%).Dl.A is a better indicator consider the three spill profiles below; n (t) 4'61

62 n(t) 4h1 IO 10 8 n(t) 6 4 2_ Since each contains the same number of particles the monitor would not differentiate between them. The Delayed Cal(lO).Dl-A would rank them in the ratio 1:2.5:5, which is a reasonable estimate of the effective rates. The ratio Delayed Cal(lO)' DlAA/Cal(0).D1 D-A is therefore a measure of the average rate.

APPENDIX IV CALORIMETER BACKSCATTER Another problem resulting from conversions in the body of the calorimeter was backscattering. There is a relatively large probability that a conversion taking place in the body of the calorimeter will produce a backward-going prong or y-ray. If this radiation triggers the transmission counter an event in which the incident neutron did not interact in the converter will be incorrectly registered as a "signal" event. Backward-going radiation from "proper" conversions in the Fe converter plate can trigger the anticounter and a "signal" event will be incorrectly rejected. In order to evaluate these effects a series of beam attenuation measurements were made using the transmission counters alone, with and without the calorimeter located in the beam. The electronic logic for this study was the same as that shown in Fig. 6 except that the calorimeter was removed. The quantities scaled were D1.A, D1lD2'A, D1lD2.D3-A, and D1.D2'D3'D4'A. The D1.A rate increased by 20% when the Calorimeter was physically at its normal location. The Dl'D2'A rate increased by 2%, D1-D2*D3.A rate increased by 1%, and D1.D2*D3-D4.A increased by 0.4%. The beam attenuation factors measured with and without the calorimeter present were, however, the same within statistics. Effects due to backscatter hitting the anticounters were completely 63

64 negligible because of the large separation between these counters and the converter plate.

APPENDIX V GEOMETRIC RESPONSE FUNCTION FOR THE TRANSMISSION COUNTERS The geometric response function, fi(0), expresses the probability that a particle, scattered through an angle 0, will hit the ith transmission counter. Consider the following diagram of the beam and counter geometry. target position Beam l _ IY -- Detector Circle D\\ X Scatter Circle D is the radius of the ith transmission counter, a is the point where the neutron would hit if it had not been scattered through an angle 9, A is the distance between the center of the counter and a, S is the target-counter separation, and B is the radius of the "scatter circle" i.e. a circle with a radius equal to 9.S centered at a. From Path~~~~64

66 here on we will refer to a as the "image" point of the neutron. The probability that a neutron with an image at a will hit the detector if scattered through an angle 0 is P(e,A) oL/1 (A-9) The detector circle and the scatter circle intersect at x = (A2 B2+D2)/2A (A-10) Therefore cos(a) = (A2+ B2- D2)/2A.B (A-ll) and P(BA) = coco1ct (A - D 2 (and A) = cos-[(A2+ B2- D2)/2A'B] (A-12) If we assume that the beam has a constant intensity over its entire cross sectional area, the probability that a neutron will have an image point in an annulus of radius A and width dA is P(A) = 2AdA/R2 (A-13) where R is the radius of the beam and AR. We therefore get 1, eSs(D-R) f(9) = fcosl[(A+ +B - D )/2A.B].2A.dA/-R, (D-R)-eS-(D+R) 0, (D+R)-e S (A- 14)

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