ABSTRACT A MEASUREMENT OF THE POLARIZATION PARAMETER IN NEUTRON-PROTON CHARGE EXCHANGE SCATTERING FROM 2-12 GeV/c By Randal Charles Ruchti This dissertation describes an experimental measure- ment of the polarization parameter in neutron-proton charge exchange scattering for incident momenta 2—12 GeV/c and four momentum transfers 0.01 S It. 5 1.0 (GeV/c)2. Using a polarized target and a two—arm spectrometer, a sample of 1.1 x 107 triggers was collected from which 3 x 105 elastic events were extracted with a 3—constraint fit. The results show a polarization whose magnitude increases monotonically with |t| to roughly 60% for It] 2 0.6 (GeV/c)2 and which has relatively little energy dependence. A detailed comparison _Of the data with several current phenomenological models is made. A MEASUREMENT OF THE POLARIZATION PARAMETER IN NEUTRON-PROTON CHARGE EXCHANGE SCATTERING FROM 2-12 GeV/c By Randal Charles Ruchti A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1973 f “”3 ACKNOWLEDGMENTS Since a high energy physics experiment is truly a group effort, there are a number of people whom I wish to thank for their contributions or assistance: First I would like to thank my adviser Maris Abolins for his able leader- ship as spokesman for this experiment and for his guidance, encouragement, and friendship during my graduate career; second, I would like to thank fellow graduate student Jay Horowitz for his many contributions to experimental effort and data analysis; third I would like to thank Bill Reay for many helpful discussions on both phenomenology and ex- perimental techniques, Noel Stanton for discussions on fast electronics, Ron Kammerud for discussions on chambers, Jon Pumplin for discussions on phenomenology, and M. T. Lin, Ken Edwards, Ed Miller, Kurt Reibel, Don Crabb, and John O'Fallon for their part in the experiment and for helpful discussions on hardware; and lastly, I would like to thank my wife Peggy for her support through the course of this work. LIST OF TABLES LIST OF FIGURES CHAPTER I. II. III. TABLE OF CONTENTS MOTIVATION FOR THE EXPERIMENT AND INTRODUCTION TO EXISTING DATA . . THE EXPERIMENTAL CONFIGURATION . A. Incident Beam . . . . . . . . l. Integral Monitors . . . 2. Beam Cross Section Monitor 3. Beam- Target Matching . . . The Polarized Target . . . . l. Mechanisms of Polarization 2. Polarized Target Systems . a. The Glycol Target . . b. The Cryostat . . . . c. The Magnet . . . . d. Microwave System e. NMR Detection . . The Two-Arm Spectrometer . . l. The Proton Arm . . . . . 2. The Neutron Arm . . . . . 3. The Complete Trigger . . DATA COLLECTION AND ANALXSIS . A. B. C. The On-line Analysis . . . . The Off-line Allaly81s a o o o The Polarization Calculation iii Page vi CHAPTER D. Checks of the Data . . kWIUI—J Checks of the EXperimental Measurement . . Checks of the Binning Scheme . . Checks of the Polarization function of x2 . . . . . Checks on consistency with experiments . . . . . . . IV. PRESENTATION OF THE DATA . . . . . V. THEORETICAL INTERPRETATION . . . . A. Preliminaries . . . . . . . . B. Models . . . . . . . . . . . . l. 2. Elastic Amplitudes Regge Amplitudes VI. CONCLUSIONS OF THE EXPERIMENT . . A. Experimental Implication . . . B. Theoretical Implication . . APPENDIX A. KINEMATICS FOR THE n+p + p+n SYSTEM . . . . . . . . . . . . APPENDIX B. NMR POLARIZATION CALCULATION . APPENDIX C. WIRE CHAMBER SPECIFICATION . APPENDIX D. NEUTRON COUNTER SPECIFICATION APPENDIX E. PROTON MOMENTUM ANALYSIS . . . APPENDIX F. FERMI MOMENTUM CONSIDERATIONS APPENDIX G THEORY APPENDIX . . . . . . . APPENDIX H. APPROXIMATE BEAM SPECTRUM . . APPENDIX I. PPT-II FIELD MAP . - - . . - . BIBLIOGRAPHY . . . . . . . . . . . . . iv asa other Page 50 50 57 57 62 79 79 82 8h 85 101 101 101 lO2 107 110 113 120 122 124 128 131 133 LIST OF TABLES TABLE Page 1 Table Of Percentage Backgrounds in the Neutron Counters as a Function of It] . . . . . 48 2 Table of Polarization Data . . . . . . . . . . 7O 3 Table of Results of Phenomenological MOdelS o o o o o o o o o o o o o o o o o o o o 100 C-1 Wire Spark Chamber Specifications . . . . . . . lll E-l Polynomial for Proton Momentum Determination . . . . . . . . . . . . . . . . . 121 FIGURE 1 CDNCDKD-P’ IO ll 12 13 14 15 LIST OF FIGURES Definition of the Convention of the Normal to the Scatterin Plane, n = (P1 x P4)/ |P1 x PA 32 is the Beam Birection; y is the Target Quantization X18 . . . . . . . . . . . . . . . . . . Polarization Data from Reference 1 and a Comparison with the SCRAM Model . . . . . Differential Cross Section Data from Reference 5 and Comparison with the SCRAM Model . . . . . . . . . . . The Experimental Layout . . . . . . . . . The 7° Neutral Beam Line . . . . . . . . . Beam Mapper Configuration and Beam Maps . X-Ray Source Configuration . . . . . . . . Target Location Reconstructed from Straight Through Tracks into the Upstream Chambers 0 O O O O O O O O O O O O O O O 0 "Solid Effect" Energy Level Diagram . . . Polarized Target Cryostat . . . . . . . . Cryogenic Systems . . . . . . . .'. . . . Target Temperature Vs. Cavity Vapor Pressure . . . . . . . . . . . . . . . . . Microwave Plumbing Arrangement . . . . . . NMR Detector Circuit Diagram . . . . . . . NMR System Schematic . . . . . . . . . . . vi Page 13 16 l6 l9 23 25 25 27 29 32 FIGURE 16 17 18 19 20a 20b 21a 21b 22a 22b 23 24 25 26 27 28 Pulse Height Distributions for SI and S2 Counters . . . . . . . . . . . . . . . . Proton Arm Logic . . . . . . . . . . . . . Neutron Arm Logic . . . . . . . . . . . . . Two Arm Logic . . . . . . . . . . . . . . . On-line Constraints for Px, Py, and Opening Angle O O O O O O O l O O O O O O O O 0 O 0 On-line Constraint for Py Balance with Graphite Dummy Target Data Shaded . . . . . Fitted Event x2 Distributions for Both Glycol and Graphite Samples for Short Counters . . . . . . . . . . . . . . . . . Fitted Event x2 Distributions for Both Glycol and Graphite Samples for Long Counters . . . . . . . . . . . . . . . . . Neutron Counter Consistency in the Region of Overlap for the Short Counters . . . . . Neutron Counter Consistency in the Region Of Overlap for the Long and Short Counters . . . . . . . . . . . . . . . . . Uniformity of Polarization in the Target . Comparison of the Polarization Parameter Values, Calculated for Each of the Data Taking Periods Individually: Phase I ESept-Oct., 1971) and Phase II Nov-Dec., 1971) . . . . . . . . . . . . . Experimental Itl -Resolution . . . . . . . Polarization Parameter Plotted for Two Different Binning Schemes: (a) Actual Scheme used, (b) Complementary Scheme . . (N- - N+) vs X2 for 0 i X2 3 50. The Factor (N— - N+) is Essentially PO Except for Normalization . . . . . . . . . . . . . 2 PO VS x2 fOr x “f 2, )4, 6, 8’ lo 0 o o o 0 vii Page 34 36 38 MO 42 43 45 46 52 53 54 56 59 60 61 FIGURE Page 29 PO Calculated By Two Different Methods: a Method Shown in Chapter IV, b Method Used in Reference 25 . . . . . . . 63 30 Comparison of the Polarization with Previous Work: (a) This Experiment, (b) Data From Reference 1 . . . . . . . . . . 64 31 Comparison of the Differential Cross Section with Previous Work: (a) Approxi- mate Cross Section from this Experiment, (b) Data From Reference 5 . . . . . . . . . . 67 32 P0(t) vs t for 2 f PLAB f 4 GeV/c . . . . . . 71 33 P0(t) vs t for 4 : PLAB f 6 GeV/c . . . . . . 72 3A PO(t) vs t for 6 : PLAB f 8 GeV/c . . . . . . 73 35 P0(t) vs t for 8 f PLAB f 10 GeV/c . . . . . . 74 36 P0(t) vs t for 10 f PLAB f 12 GeV/c . . . . . 75 . 37 Approximate Energy Variation of Po(t) as PLAB Increases From 2-12 GeV/c . . . . . . . . 76 < 38 PO(PLAB) vs PLAB for 0.01 - 'tl 5 1.0 . . . . 77 39 PO(P ,t) vs P and It] Showing ExpePIEental Acgggtance .,. . . . . . . . . . 78 40 Helicity Picture for n+p +-p+n . . . . . . . . 81 41 Helicity Amplitude Expansion in Terms of Particle Exchange . . . . . . . . . . . . . 81 42 Fits to do/dt with Various Choices of meff(s’t) O O C O C O C O C O O C O O O C O O 86 43 How Absorption Modifies a Helicity ' Amplitude . . . . . . . . . . . . . . . . . . 86 44 V-M Fits to dO/dt (n+p + p+n) . . . . . . . . 9O 45 V-M Fits to Po(n+p + p+n) . . . . . . . . . . 91 46 V-M Fits to do/dt (p+p + fi+n) . . . . . . . . 92 viii FIGURE Page 47 V-M Prediction for Po(p+p + fi+n) . . . . . . . 93 48 Argand Plots of ¢* and‘bo for the SCRAM Model . . . . . . . . . . . . . . . . . . . . 94 * 49 Argand Plots of ¢5 and‘tO for the VAM MOdel O O C O C O C C O O O O 0 C C O O O O O 95 50 HKV Fit to dq/dt (n%p + p+n) . . . . . . . . . 96 51 HKV Fit to Po(n+p + p+n) . . . . . . . . . . . 97 52 HKVFit to do/dt (p+p+ n+n) . . . . . . . .. 98 53 HKV Prediction to Po(p+p 5+n), . , . . . . . 99 A-l Scattering in the Center of Momentum Frame 0 O O O O O O O O O O O O O O O O 0 O O 1014- A-2 Scattering in the Laboratory Frame . . . . . . 104 A-3 Coordinate Systems Used to Describe Particle Momenta: (a) Spherical Coordi- nates, (b) On-line Constraint Variables, (c) Off-line Variables. The Reference Axes are: x, Toward Neutron Arm; y, the PPT Magnetic Field Axis; z, the Surveyed Beam Direction . . . . . . . . . . . . . . . 106 C-1 Proton Arm Resolution . . . . . . . . . . . . 112 D-l Neutron Counter Acceptance, A(PLAB,t) . . . . 115 D-2 Tar et Absorption Function for Neutrons, T(t§ O O O O I O O O O O O O O O O O O O O 116 D-3 Neutron Counter Detection Efficiency, E(t) . . . . . . . . . . . . . . . . . . . . 117 D—4 Neutron Arm Resolution . . . . . . . . . . . 118 D-5 Neutron Counter Design . . . . . . . . . . . 119 E-l Polynomial Coordinates . . . . . . . . . . . 121 H-l Neutron Beam Spectrum, I(PLAB) . . . . . . . 129 H-2 Neutron Beam Resolution . . . . . . . . . . . 13o I-l PPT-II Magnetic Field Map for H = 25kG . . . 132 ix CHAPTER I MOTIVATION FOR THE EXPERIMENT AND INTRODUCTION TO EXISTING DATA In neutron-proton charge exchange scattering, both the incident and target nucleons have spin 1/2, and one expects polarization effects to influence the final state distribu- tion of events. A typical method for experimentally meas- uring the polarization parameter is to use an unpolarized neutron beam and a polarized proton target. At the Argonne Zero Gradient Synchrotron, the neutron beam has a broad momentum spectrum which depends on produc- tion angle and is usually contaminated with Y-rays and a few KE:mesons. The polarized target, which consists of glycol or similar organic material as well as a cryostat structure, generates a large background of events from the diversity of material present. These complications can be accommodated nicely however, first by careful collimation and filtration of the incident beam, and second by using a two-arm spectro- meter which measures completely the four-momenta of the final state particles. The yield of events from a polarized target is given by do do (1 + TonPO) 2 where (do/dt)o is the unpolarized differential cross section, + T is the target polarization, n is the normal to the scatter- ing plane specified by convention, and PO is the polarization parameter. The direction n is chosen as n = (P: x P4)/(Pl x P4] where P1 and Pg are the incident and outgoing neutron momenta respectively (see Figure 1 and Appendix A), a choice which is consistent with that of np elastic scattering. The polariza- tion parameter is a measure of the asymmetry exhibited by the distribution of final state events when the target polariza- tion T is parallel (+) and antiparallel (+) to the vector n: d do p0=_.1T;_ at. — 615+ II d 99. HE++dt+ There exists only one previous set of measurements of the polarization parameter,l covering a momentum domain 1-5 GeV/c; the data are shown in Figure 2. The same convene tion for a was used, and the polarization valuesobtained were cOnsistent with zero in the forward direction and mono- tonically decreasing with It] to |t| “.5, the acceptance limit. Over the measured energy range, the polarization parameter was approximately independent of energy. The data have interesting implications for theory, and although a de- tailed discussion of phenomenology is deferred until chapter 5, there are some salient features worth mentioning here. +-< OUTGOING NEUTRON OUTBOlNG PROTON INCOMING NEUTRON Figure 1. Definition of the Convention of the Normal to the Scattering Plane, fi = ($1 x Pu)/ |P1 x Pal; z is the Beam Direction; y is the Target Quantization Axis. 0.0 -O.4 -O.8 m (Gevxc)2 + 0.2 0.4 0.6 0.8 LG I I I T I I I I I I *' 2-3 GeV/c I tl (GeV/c)2 0.4 . 0.6 0.8 l.O - 4-5 GeV/c — Figure 2. Polarization Data from Reference 1 and a Comparison with the SCRAM Model. 5 A non—zero polarization requires contributions from¢> and A2 exchange (and possibly lower lying trajectories) in the n + p + p + n reaction. Using these as well as w- ex- change, a recent model, the Strong Cut Reggeized Absorption Model (SCRAM),2-AL was able to follow the trend Of the Robrish data out to a |t| of roughly 0.5 (GeV/C) where the data ended. SCRAM was also able to fit the differential cross section5 for |t| s 0.4 (GeV/c)2 but proved to be in error for larger momentum transfers (see Figure 3). A polarization measurement with broad energy and momen- tum transfer coverage would provide a better test of phenom- enology -- especially in the interesting region 0.4 5 |t| 5 1.0 (GeV/c)2,and could determine if the apparent energy independence of the polarization parameter persists for higher incident momenta. This dissertation describes such an exper- iment, the measurement of the polarization parameter in up charge exchange scattering for incident neutron momenta 2-12 GeV/c and four-momentum transfers 0.01 5 |t IS 1.0 (GeV/c)2, the particulars of which are now discussed. 10 11111111 1 10 J 1 LLIIJI 11111111 1 10 11111111 .iJ da/dt (mb/(GeV/Cf) SCRAM MILLER.” al. 8 GOV/c .O 0.2 O.u 036 I l r I I I I I I I 018:" 1.0 1.2 It! (GeV/C)2 Figure 3. Differential Cross Section Data from Reference 5 and Comparison with the SCRAM Model CHAPTER II THE EXPERIMENTAL CONFIGURATION Before covering the details of the apparatus a brief summary of the experimental arrangement is appropriate (see Figure 4). A neutron beam of broad momentum spectrum was incident on a polarized target. 0f the initial particles only the four-momentum of the target proton (m2, 0) was known (see Appendix A for kinematics). The final state neutron and proton were detected by a conventional two-arm Spectrometer which completely measured their three-momenta. This information allowed us to make a 3-constraint fit on our data sample, permitting a clean separation of elastic events from background. A. Incident Beam The experiment was performed in the 70 neutral beam at the Argonne ZGS (see Figure 5). By scraping the circu- lating proton beam with a 0.25" long beryllium target,6 a beam of neutrons was produced at 3/40 with a broad momentum spectrum peaked near 11 GeV/c7’ 8 (see Appendix H). This targeting scheme produced roughly 106 neutrons per 4 x 1011 protons incident on the internal target. The external beam was cleared of charged contaminants by several sweeping 7 snort: a .. mysmns ///////// V” m\\\ I1- umou \ g mmmmm r mvno 7-?!” mos mm mm 2- an 2- con IH‘”r anygfirt Th1\m$% ‘% LIGEON L/éé‘éZ/f: 0 501 T (MDT "MET MT SIM Figure 4. The Experimental Layout. SWEEPINO MAGNETS 1 \35m warren \ POLARIZED TARGET I46 ". Figure 5. The 7° Neutral Beam Line 10 magnets and passed through a y-ray filter (A) of two radiation lengths of lead. Laterally the beam was Shaped by four over— defining collimators (Cl-C4), creating a 0.94 x 1.25 in2 spot at the position of the polarized target, 145 ft. down- stream of the internal ring target. To reach the polarized target, the neutron beam passed through a hole in the PPT magnet yoke. This scheme allowed optimal placement of detec- tors around the target cryostat. Two characteristics of the beam were important: First a measurement of the total neutron flux was required for event normalization; second a cross sectional map of the beam was required just upstream of the target to make certain that the beam and target were matched and to assure that no obs- tructions lay in the beam, casting Shadows in the target vicinity. To measure these characteristics several counter arrangements were used. 1. Integral Monitors The simplest method of measuring intensity is to stop the entire beam in some thick converter and detect conversion products in scintillation counters. However high beam rates and high inelasticity of the interactions in the detector produce a rate dependence in this type of monitor. An alterna- tive is to put a thin converter into the beam and sample a fraction of the neutrons. Since counting rates are much lower the rate problem is avoided, but the low detection efficiency for neutrons requires that this type of monitor be conti- nuously checked relative to some measure of the total flux 11 to guard against changes in beam characteristics. The problem is resolved by using both types of monitors. The first relative monitor OMON consisted of three 0.25 x 6 x 6 in3 scintillators. The counter 0M1 served as charged particle veto; counters 0M2 and 0M3 detected conver- sion products from a .25 in. thick aluminum sheet placed up- stream of 0M2. Omon logic was satisfied if OMONsOMI‘0M2-0M3 Obtained. Typical counting rates were 2.5 K per ZGS pulse and neutron detection efficiency was-2%. By including into coincidence with OMON an additional 0.25 x 6 x 6 in3 counter 0M4 located 60 in. downstream of 0M1, the relative monitor HIMON was formed: HIMONeOMON-OM4. The longer axial length of the conversion telescope allowed sensitivity to beam neutrals of higher momenta since only highly collimated interaction products could satisfy the logic. As it monitored a more limited region of the momen- tum spectrum, its ratio relative to OMON was an indication of internal targeting changes. The final integral monitor was the calorimeter which was designed to detect beam neutrons with 98% efficiency. It consisted of eight 3.25 x 25 x 25 in3 layers of iron and 0.375 x 25 x 25 in3 layers of scintillator forming a giant sandwich. Just upstream of the apparatus was placed an 0.375 x 25 x 25 in3 scintillation veto counter to guarantee that only conversions from incident neutrals would be counted within the calorimeter volume. The calorimeter logic was de- fined as: CAL55A°(Cl+C3+C5+C7)-(C2+C4+C6+C8) which specified 12 a 3.25 in. minimum range for charged conversion products from an n-Fe interaction. To minimize the anticipated rate problem, the photomultiplier pulses were clipped short right at the counter. Reflection problems from the clipping were mini- mized by attenuating the signals input to the calorimeter fast logic and by raising the discriminator levels on each of the units to reject low pulses. Typical counting rates for 5 CAL were 1.1 x 10 per ZGS pulse. The calibration of OMON relative to CAL was performed at low beam intensity to avoid any rate dependence in CAL.8 Then the ratios CAL/OMON and HIMON/DMON provided the stabi- lity criterion for the relative monitor OMON, and OMON was used as the normalization for the experimental events. 2. Beam Cross Section Monitor At a location six feet upstream of the polarized tar- get, the relative magnitude and lateral extent of the beam were measured with a beam mapper, a mechanically moveable telescope of three 0.063 x l x 4 in3 scintillation counters arranged as shown in Figure 6. The upstream counter BMl acted as a charged particle veto; counter BM2 was itself the converter and, coupled with BM3, formed the conversion telescope: BM=BMI3BM2-BM3. The telescope was moved horizon- tally and vertically through the beam, and profiles were re- corded (see Figure 6). Once a profile was taken, the counter telescope was positioned at the nominal beam center with a transit or level scope. The spatial distance between this point and COUNTS COUNTS BEAM 400 .. 300... 200... IOO .- 400.. 300_ 200 .. IOO _ COUNTER THICKNESS me" LATERAL EXTENT OF BEAM IN Y (INCHES) I.O LATERAL EXTENT OF BEAM IN X (INCHES) Figure - 1.0 0 Beam Mapper Configuration and Beam Maps. 14 the midpoint of the counter distribution determined the physi- cal displacement of the actual beam center from the surveyed 7° neutral line. The width of the distributions determined the lateral extent of the beam near the target. With this device we were able to collimate the beam onto the target with a Spot 0.94 x 1.25 in2 to within t.O3 in. accuracy (roughly one counter thickness). 3. Beam-Target Matching The experimental target of dimensions 0.8 x 1.0 x 2.0 in3 was located 145 ft downstream from the internal beryl- lium target. Since it was situated within a cryostat, con- ventional survey techniques could not determine if it was correctly positioned in the beam. An initial check of the target location was made using an x-ray source (see Figure 7). Inngsten crosshairs were surveyed into position on the beam line up and downstream of the target. An uncollimated, point x-ray source was placed in the beam line just upstrehm of the crosshairs and allowed to expose polaroid film downstream. After a few trials with the x-ray unit in different locations, the crosshairs were aligned on the film, implying that the source was positioned directly on beam line center. The glycol polarized target also appeared in the exposures, and its position relative to beam center could be determined by measurement on the film. During actual eXperimental running, the target loca- tion was checked whenever a new one was installed in the 15 Figure 8. Target Location Reconstructed from Straight Through Tracks into the Upstream Chambers. l6 BEAM 4L \ L,-/ m 7 rs‘~\ \ \_POINT X'RAY TUNGSTEN POLAROID SOURCE CROSSHAIRS Figure 7. X-Ray Source Configuration GOO '- 500 LATERAL 40° EXTENT IN Y (INCHES) 300 200 IOO 0 1‘“? 1 . 1 -'.5 005 Ls 2.5 400 r- LATERAL 300 '- EXTENT IN X (INCHES) ZOO '- IOO*- 1 . I “1.5 ‘05 O 05 I5 Figure 8 17 cryostat by turning off the polarized target and bending mag- nets and allowing the spark chambers to trigger on straight charged particle tracks. These tracks were then extrapolated back to the target position in a computer analysis and directly measured the effective target size and hence the ex- tent to which the beam and target lateral areas were matched (Figure 8). B. The Polarized Target The polarized target used in the experiment was the Argonne Polarized Target Facility PPT-II9 consisting of po- tassium-dichromate doped ethylene glycol at liquid “He tem- perature and 25 kG field. The discussion naturally Splits into two sections: What is the mechanism for proton polarization, and what hard- ware does one need to achieve it. I will temporarily defer equipment aspects and proceed with a qualitative discussion of the "theory". 1. Mechanisms of Polarization Targets typically consist of two main components, a source of free protons to be polarized and a doping agent which provides unpaired electron Spins. When the sample is placed in a magnetic field the electron level is split in two with level separation‘hweHue being the electron Larmor frequency. In addition, for each particular electron level there are two sublevels corresponding to the two possible spin orientations of the proton. 18 Dynamic orientation of nuclei involves manipulation of electron spin states to achieve a desired proton Spin configuration. The simplest illustration of this type of scheme is the "solid effect", shown in Figure 9.10’ 11 Suppose we have the electron and proton system in a strong magnetic field H with Larmor frequencies e and n respect- ively. If the electron line is sufficiently narrow, one can distinguish the two sublevels we+wn, w —wn, and there are e three classes of possible transitions: (i) transitions with single electron flip, no proton flip (CA, DB). These transitions occur rapidly as the elec- tron Spin is relaxed yielding a phonon of energy wszAzwDB to the target lattice. (ii) transitions with single proton flip, no electron flip (DC, BA). Nuclear relaxation occurs more Slowly than electron relaxation (1). (iii) transitions with simultaneous electron and proton flip (DA, CB). In the absence of electron-nucleon dipolar couplings these are forbidden. To produce a desired proton polarization through the "solid effect", one uses microwave rf to force one of the 19 .1... -..._ Emawmam Ho>oq mwnocm :pommmm oaaom: .m Gasman I 2O forbidden transitions AD or BC to occur. Since the type (i) transition is swift, the excited electron quickly relaxes to its ground state with the proton spin in the final orienta- tion desired. This Simple explanation works fine for targets such as LMN(La2Mg3(N03)2-24 H20) doped with neodymium because for that material the electron resonance line is sufficiently narrow that the proton sublevels are resolved.ll Ethylene glycol presents a more difficult problem simply because the electron line width is ~l50 gauss broad, leaving the two proton sub- levels unresolved. An immediate consequence is that applying rf to the electron state can populate both nuclear spins since transitions BC and AD will both be induced. In fact there are additional complications from the presence of other electrons nearby. First the Larmor frequencies for the elec- trons in the target are all assumed to be me. This is jus- tified to the extent that our magnetic field is uniform over the target volume (:3 Gauss) and potassium dichromate doped ethylene glycol has isotropic properties (a fairly reasonable assumption considering that gig: = 1.99 and Seff = 1/2 for this material, very close to free electron values).12 Should there be an anisotropy of either external ' magnetic field or target composition, additional mechanisms for dynamic nuclear polarization are possible.11 Second, the electron Spin we are dealing with is not an isolated entity, but can be expected to have spin-spin interactions with neighboring unpaired lattice electrons. If one collects these 21 "neighbors" into a Spin-spin interaction reservoir and de- fines a Boltzmann temperature for the system, it can be shown11 that electron Spin-spin interactions and rf-induced spin—spin interactions can lower the collective temperature. If one describes the protons collectively as a nuclear Zeeman reservoir, then the previously forbidden transitions AD, CB provide the thermal contact between the Zeeman and spin-Spin systems and tend to equalize their temperature. Hence by inducing forbidden transitions with rf, one not only produces proton polarization through a poorly re- solved "solid effect", but also by the cooling of the nuclear Zeeman temperature through thermal contact with a low temper- ature electron spin-spin reservoir. For a specific setting of the external magnetic field, a particular microwave fre- quency will maximize the proton Spin up population, another the spin down population. Having qualitatively described some possible mecha- nisms for dynamic nuclear orientation, it remains to show how the polarization was experimentally created, maintained, and measured. The polarized target facility consisted of five major components: the target, cryostat and cryogenic support sys- tems, magnet, microwave rf system, and NMR detection system. All of the details of the systems are contained in various Argonne reports9 so only salient features will be considered. 22 2. Polarized Target System a. The Glycol Target The target material was ethylene glycol (CHQOH)2 doped with 10% by weight of potassium dichromate K20r207. The glycol acts as the source of free protons, the potassium dichromate as the source of unpaired electrons through the presence of the CrV radical. This particular target is liquid at room temperature and hence requires a containing material prior to cool down in the cryostat. The choice was air-mattress-like tubular bags of FEP (fluorinated-ethylene polymer) which were easily folded into the target shape re— quired, yet permitted a large amount of surface area to be exposed to the liquid “He bath, essential to uniform cooling. The target shape was parallelepiped, 5 cm long by 2 cm high by 2.5 cm wide, a shape dictated by the desired thickness of the target in the beam direction (5 cm.) and the available space for the target material within the exist- ing PPT-II cryostat which was of the horizontal continuous flow type (see Figure 10). These requirements were resolved by placing the cryostat at a 500 angle with respect to the beam center-line. The target weight was 31 grams of which 3 grams were the FEP container bags. Since the bags were folded to form the target, a considerable amount of the target volume con- tained no glycol at all. After accounting for the packing fraction of the target, the effective density of the glycol was 0.85 gm/Cm3. Once the slight overmatch of the beam area ’ MICROWAVE CAVITY :\ WAVEGUIDE OUTER 0° \\‘\ SHELL ' . \ HEAT SHIELD ‘\/ HELIUM ENVELOPE_\ \ I% 1 N11 I"i M"e 10. Polarized Target Cryostat OD 24 t0 the target area was included, the effective number of tar- get protons was 2.04 x 1023/bm2. b. The Cryostat The cryostat within which the target and its 5 mil thick Be-Cu microwave cavity were placed was composed of several coaxial shells (Figure 10): The innermost Shell was the liquid helium jacket of 12 mils stainless steel; the in- termediate liquid nitrogen insulating jacket was Of 5 mils Cu; the outer shell was a 16 mil aluminum vacuum jacket. In all the beam had to pass through .23g/cm2 of cryostat struc- ture in order to reach the target, which removed about 0.6% of the incident neutrons. Liquid 4He was continuously transferred from a 50 liter storage dewar to the cavity. The role of the helium 13-14 and separator vacuum systems (Figure 11) was to main- tain adequate cavity liquid level and vapor pressure. At “He 2pm), the cavity pressure typical pumping rates (27 gas measured by Mcleod gauge ranged between 150-350 microns corresponding to a target temperature of 1.0-1.150K (see 15 Figure 12). Although liquid “He temperatures are not the last word.in polarized target technology, enough thermal effects were suppressed to allow roughly 40% of the target protons to be polarized. Ho VACUUM SEPARATOR SEPARATOR VACUUM LIO HO O TARGET CAVITY MCCLEOD GAUGE INSULATING VAcuquPUWI ' ‘ Figure 1]. Cryogenic Systems 2.0-3 l.5 - d T(°K) .. LO... / 0.9- 0.8 ~ 0.7 ‘ I O 250 400 600 P (MICRONS) Figure 12. Target Temperature VS. Cavity Vapor Pressure. 26 c. Magnet The glycol target sat in the center of a 3 in. gap be- tween the pole tips of a Varian magnet. The field was main— tained at 25 kG with a measured inhomogeneity of: 3 Gauss over the target volume. The field was measured and stabilized to i.l Gauss by means of a Hall probe feedback system and a map of the radial field is presented in Appendix I. d. Microwave System The source of microwaves for spin pumping was a French built COE4¢B carcinotron, a back-wave oscillator. In this device microwaves are generated by passing a beam of elec- trons through a copper interaction structure. By suitably tuning the electron beam one can adjust the power and fre- quency delivered to the wave guide, typically 1.5 Watts at ~70.6 GHz during running conditions. The microwaves of appropriate frequency then passed through a standard plumb- ing arrangement to the target cavity (Figure 13). A phase sensitive feedback amplifier in combination with wavemeters in the waveguide system then maintained the carcinotron at a stable line voltage, which insured a stable output 16 frequency. e. NMR Detection The actual value of the polarization was measured by nuclear magnetic resonance. The NMR system was a standard RLC circuit in which the target, wrapped with five turns of 27 LOAD POSITIVE J. ENHANCE- I 0.008 MENT \ WAVEMETER DIRECTIONAL ATTENUATOR COUPLERS fl-I-'->. CARCINOTRON ‘ I o .9 \ 6’ .0 0‘ NEGATIVE 0" ENHANCEMENT DVO’ E-N TUNER 6 a FLARE ARM FOR REFLECTED POWER CRYOSTAT TARGET ' CAVITY Figure 13. Microwave Plumbing Arrangement 28 wire, was a component with equivalent circuit shown in Figure 14. The large external resistance RE (7.5 kn) essentially determined the current -— hence the NMR system was a constant current Q-meter.l Proton Spins in the target absorb energy from the cir- cuit as the frequency of the signal generator passes through the proton resonant frequency, wn' This energy absorption is described electrically as a complex susceptibility, and the target-coil system is assigned a complex inductance: L = LO(1 + 41m) = LO(l + 41m(x' _ ix")) where n is the filling factor, the amount of volume within the coil that the target occupies, and x' and x" are the real and imaginary parts of the susceptibility x. The frequency average Cd‘x" is proportional to the amount of power absorbed from the circuit, and hence to the degree of spin alignment of the protons: T = £f¢ 0 dc»: tanh (+g8H/2kT) (3) T 4 O VTE(w) where g is the g factor for the proton, 8 = eh/2mc is the nuclear magneton, k is the Boltzmann factor, and T is the target temperature in OK. The expression for the enhanced polarization (1) is then given by: ” V(00 - V O dw szTE 0 V0“; I“ VTE(w') - Vo dw. O VTE(“') The proton resonance was swept every five minutes by the NMR system, and Signals for both the voltage V(u) and its derivative with respect to frequency dV(w)/dquere sent to the electronics trailer. The dV(w)/dw signals were gen- erated by a set of "tickler" coils on the pole ‘tips of the magnet, and were used extensively in the measurement of the target polarization because of their sensitivity in the proton resonance rcgionw Zen. For example, rather than rely on a direct measurement of VTE(u') whose size is very small, one uses instead w'dv (0)") VTEIw') = 1 ____..___TE CM"- II 0 dw 1? The V(w) and dV(w)/duIsigna1s were recorded in two ways: first, on paper tape for use in an off-line analysis 31 developed by the Argonne staff, and second, by fast logic interfaced to the on-line DDP-24 computer which optically displayed the polarization and wrote the NMR values onto magnetic tape as a part of the experimental data vector. The actual calculation of the target polarization was performed by calculating the various integrals as Riemann sums. In the fast logic scheme, two points on an NMR sweep were re- corded during the first event trigger of a given ZGS beam spill, and four numbers per point wemalead into blind scalers: The NMR frequency w, the V(w) signal, the dV/dw signal, and a 21 MHz clock. The latter number was used to normalize the other three, to insure equal Aw spacing in the Riemann sums. How this system was tied into the existing NMR system is shown in Figure 15. Several paper tape recordings were made during each data run (*3 hrs. in length) as a check of the interfaced on- line scheme which monitored the polarization continuously. The two methods agreed to within AT = 2%. Once every twenty- four hours, ten target thermal equilibrium sweeps were re- corded to calibrate the NMR system and determine 5. For these measurements the microwaves were turned off, and the data taking was suspended temporarily. The polarization di- rection of the target was reversed every successive data run to eliminate any experimental bias; within each run, the pol— arization fluctuated by 14%. On the basis of the NMR measurement, the average target polarization was determined to be 39% for positive enhancement 32 oflmeozom Empmhm mzz .ma ouowfim an: 5.2. 41 2.3-26 L. F233: H 2.5.9 TI g >28 3.... .— r r f fl 3:32.11 Ia 3:52: , 72.21.33 _ o» a.» >u 7 flFIIIM— r a. .83 a H 3.. Sn: 223.53: a... 2.1. FlamxfiL o» o; > L . 1w _ cocoa a: "e. Ana...“ 1 . UJCU. JOKPZOU . I. U .33 »uzuaoucug \/.\ .33» 59:6 :5. r rerun: # . , 523.. Owen E _ 33 and 40% for negative enhancement.2O Relative to an absolute calibration of the target polarization by a double scattering experiment, the NMR measurement was accurate to 7% of the target polarization value: s 40 i 3%.21"23 C. The Two-Arm Spectrometer The detection of the final state neutron and proton was performed with a two-arm spectrometer. l. The Proton Arm: The proton was detected by a coincidence between four counters, 51, S2, S3, S4 and had its momentum and direction specified by a wire chamber magnetic Spectrometer. The corri- dor for protons into the upstream chambers was defined by counters Sl(1/8" x 3" x 5") and S2(1/8" x 5" x 7") located 21 in. and 41 in. from the target respectively. Single pro- tons were selected by pulse height cutS on these two dE/dx counters which rejected multiply ionizing events; approxi- mately five percent of the 81 and two percent of the S2 singly ionizing distributions were cut out by this method (see Figure 16). To minimize triggers on final states of higher multi- plicity, anti-counters were extensively employed. In the vi- cinity of the target, wide angle charged particles were vetoed by a group of four 0.125 in. thick scintillation coun- ters which formed a tight fitting box around the cryostat ex- cept for a small downstream opening to allow protons into the forward Spectrometer. The rejection of events in the upstream 34 10001 sinOI“ 800-1 doubles m I- z m 5400— ‘ / 200~ s'a I \/H \ o I Y I I T V l 4E U 1 U I I O 50 . IOO ISO SI PULSE HT. (ADC channel no.) 8001 shout «mbhs 600- ; uncut m 400- I 5 \ Zm‘ \\\ S. HI'CUI ‘~\ \ s| a 32 III-an \ \- O T I T I T V‘ T I ‘T I T T j— 0 50 I00 V1 '1 $2 PULSE HT. (A Dc channel no.) S-COUNTER PULSE HT. SPECTRA igure lb. Pulse Height Distributions for SI and S2 Counters. 35 chambers containing Y-rays and divergent charged particles was effected with two Y-sensitive hole counters Fl, r2 con- sisting of 0.5 in. lead converter and 0.375 in. scintillator with apertures which allowed particles within the proton cor- ridor to pass unhindered. A large y-sensitive counter r3 vetoed strays on the side of the beam line opposite to the proton spectrometer. A schematic of the proton arm logic is shown in Figure 17. The quantity TS was the proton triggen whereas the ratio T:S/S (where T:S is T delayed 120 Inna: relative to S) was a measure of random blocking by all veto counters (except those near the neutron counters); from such blocking, approximately 10% of the possible triggers were lost. The Spark chambers were arranged in four modules con- taining three x.and y (horizontal and vertical) planes each. Spark and fiducial information were read out magnetostrict- ively, preamplified at the wands, and sent to the computer trailer. Each chamber was viewed by a number of sealers, allowing the digitization Of four Sparks per plane in the chamber modules upstream of the magnet, two per plane in the modules downstream (spark chamber specifications are presented in Appendix C). Fringe fields near the two magnets necessi- tated the shielding of some of the magnetostrictive wands in the upstream chamber modules to prevent signal attenuation or inversion. Once a complete track was indicated by the chambers, the proton momentum was calculated using a l4-term polynomial 3L oawoq 8.3 sonosm .5 msowam on... I 3.5.. c. on... a. (In 1 an I _ 00.0 50 II Kuwat .l UOJ5‘ g... 1.x... N” cuothoao Zahara 00.0 A I .50 : 0.84 a: 0 35:0?— m.. I 024 :2: o» I I m 1 95> on:— 00.0 .50 0 £5349" uni: .0... 1;: .m s... _ .m 9: 4 on... was? 3 .IEEE w I w 5...... J” I: >J¢I< OIUIOPIOIH 80.; 08.8; Rug.— :42 2.3 n use: 2.2....» .5 III . on... 1.1, 5:38 I 1.. x0.“ 3:3: I uni... II \F 0 55...... I. 3...... A... /_ w I a... 1 N c . I 530.. s 8......» no.2... . all on. 5A.... 3... 2:...» 530.. 1i W on... 53.5.... all 22:3: ill 2:3: x0. x0. 2.3 024 Al 2-..; z a... A: an... A1 w 9* t 3.3.53.3: & W 61.. on... :31. 0 (x. 116.11 2:2... out; I “A #w 2253:. xnd cuticoII 3...... A... - \. I w .1 ._ 1...... I n a an}... /— I .II 39 3. The Complete Trigger: With a coincidence between neutron and proton arms in the two-arm logic (Figure 19), the complete trigger was satis- fied, firing the Spark chambers. Digitized chamber informa- tion, neutron counter pulse heights and timing information, and NMR information were then read into an on-line DDP-24 computer which recorded the data on magnetic tape and which, between beam spills, analyzed a portion of the data and dis- played monitors of equipment and event constraints. #0 $44.08 0.0»...(8‘ 0042 080 0» a: oamoq Ep< 038 .m. mxswfim 2:3... 2.2... 5!... :oc»:.: ......‘ .08....» 0008‘ cut: “(to 1000.8h030IIOIh308 008020500 laboglgcbaul 0000.3...030 take; u: can»? to (I... o\ IO 8 6 4 2 maximum x 1. "I 2 2 Figure 2b. Po rs x for X fin 7%— O O evewrs n03 ‘ o N 00 0 Ni O. m a: 5 62 4. Checks on consistency with other experiments: The method of computing the polarization parameter discussed in Section C is different than that of Robrish, et al.,25 but the two techniques turn out to be numerically equivalent at our level of statistics as shown in Figure 29, where the polarization is determined from our data using both schemes. Once this check was made, our polarization data were then compared with the data of Robrish, et al., for the two momentum bins where the experimental data overlap (Figure 30). Although the momentum coverage is slightly different, the results are consistent. Finally the data samples for positive and negative target polarization were used to calculate No(As, At), the unpolarized event rate, and hence the differential cross section. The experimental expression for dO/dt is: N AP At (10' (APIJAB’At) : O( IAB, )0 l l a? I(AI-”LAB) CTGT CN(APLAB,¢t) p l I? where the several terms are defined as follows: NO(APLAB,At) is the unpolarized event rate calculated in Section C. I(APLAB) is the incident beam flux measured in neutrons per OMON (see Appendix I). qTGT is the effective number of target centers per unit area (2.04 x 1023/Cm2). CN(APLAB:At) is a composite correction factor for the neutron arm given as: 63 .mm mwflmhmkmm CH meD UO£P®E ADV “>H smpmmno Ca csozm cocpmz Amv o m "noozpoz pCmsmmmaQ 039 am Umpmaooamo .mm muomfim 3 an: .5 8:52 o I 0 Home. .5 8:52 o o\>00 mum I ad: I w W a + ++ 4.3L... .I .. .3. e T _ a _ _ _ e r a 30.0 O; 040 “Av ’Av NAV «A0\>mov _: III (GeV/c)2 0.2 0.4 0.6 0.8 I.0 00$ I I I I I I I I I fl C) 3! 0+0 ¢ This expt ¢*¢ I Robrish eI 0|. "0.4 *- 2- 3 GeV/C ~08~ 2-4 GeV/C |t| (GeV/ciz 0.0vq I OIZ I 0.4 I Die I 0i8 I do 5) ¢°+¢ +¢ €> This expt ¢ + ¢ 4, + Robrish eial. -04- + 4’5 GOV/C *0-3— 4-6 GeV/c Figure 30. Co parison of the Polarization with Previo«s Work: (a) This Fxperirent, (r) Data Fro: Reference 1. where: where: 65 CN(APLAB,At) = A(APLA_B,At)dQ(NTYPE, At)T( At)E( At) A(AP&AB,At) is the neutron counter acceptance for the bin (APLAB,At). (See Appendix D). dQ(NTYPE,At) is the solid angle subtended by the par- ticular neutron counter array (NTYPE) at the target. A T(At) is the target absorption correction calculated for the long and short neutron counters (see Appendix D). E(At) is the detection efficiency of the neutron coun- ters. (See Appendix D). Cp is a composite correction factor for the proton arm given as: Cp : Cpl. Cp2 C is the correction for pulse height cuts on the two pl dE/dx counters in the proton arm: 0.95 for SI and 0.98 for S2. Cp2 is the correction for the spark chamber spectro- meter efficiency (0.98). Since the differential cross section was to be used as a Check on the polarization measurement, several simplifying assumptions were made: First, the incident momentum spectrum I(APLAB) was assumed to be the same as that measured by E. L. Miller, et al.,5 a fair assumption since the ZGS internal targeting scheme was the same for both experiments (quoted error on 1(APLAB) is 110%). Second, the absorption T(At) of 66 the slow recoil neutrons from the charge exchange process (by cryostat walls, liquid helium, target veto counters, etc.) was calculated for the horizontal (x, z) scattering plane only; the same absorption was presumed to hold for neutrons emitted at various angles A above and below the horizontal plane, where i Z 170. The uncertainty introduced into dO/dt by this assumption is It) dependent, worst for small ltl where neutrons have a better than 50% chance of being lost, and best for higher it |2 0.1(GeV/c)2 where the absorption becomes small. Estimated uncertainty in the value of the absorption is éT/T z 110% for 0.01 f It] : 0.1(GeV/c)2 and éT/T zi5% for larger ltl values. Third, the neutron counter acceptance A( PLAB’ At) was estimated from the graph in Appendix D rather than from an event monte carlo, with un- certainty dA/A :i5%. Hence the differential cross section calculated here should have an uncertainty of roughly i20%. Since the above approximations hold best for events detected in the long neutron counters,the cross sections obtained should be most trustworthy for It] 2 O.l(GeV/c)2. The results of this analysis were compared with the Miller data (Figure 31). For It! 2 0.1(GeV/c)2, the two sets of data agree in both PLAB and It) dependence to within 20%. On the other hand, the small |t| short neutron counter data, sensitive to the slowest recoil neutrons and events ‘above and below the horizontal plane, do not show as good an agreement indicating a failure in the approximation ID ID IIIIIII I dcr/di (mb/(GeV/C)2) (b) HEAVY LINES ARE TREND OF MILLER,oIal. (0) S=SHORT CTR DATA L'LONG CTR DATA -1« IO ._ .. BGeV/c IIGOV/C I ‘I‘ I 4I It I LI T ‘I I 0.0 0.2 U.H 0.6 0.8 1.0 2 |I|(GeV/C) Figure 31- Comparison of the Differential Cross Section with Previous Work: (a) Approxi- mate Cross Section from this Experiment, (b) Data From Reference 5, 68 arguments for small ItI. However in the region where the approximations hold best,I tI32 O.l(GeV/c)2, the results suggest that we really have np charge exchange events. CHAPTER IV PRESENTATION OF THE DATA The 300,000 elastic events with x2 f 10 were then used to calculate the polarization parameter. The results, binned into five different intervals of laboratory momentum, are presented in Table 2 and Figures 32-36. The distinctive fea- tures are: For fixed energy, the polarization magnitude grows monotonically with It k for fixed momentum transferl tl, a slight energy dependence is exhibited, with evidence of a trend toward larger polarization magnitudes as PLAB increases. In particular if one draws the empirical curve suggested by Robrish, et al. IP01: _L__I._"C 2mn on the plots of the data (Figure 37), the agreement is no longer good for PLAB > 6 GeV/c, indicating a trend toward rising polarizations. For example at ItI l .7(GeV/c)2, A|PO|/APLAB : .O3(GeV/c)-l GeV/c. Attempts at parametrizing the energy dependence of for the momentum range 4fPLAB512 PO shown in Figure 38 by simple functions of PLAB all resulted in equally poorx2 values for the fits. Hence no definitive conclusions on the exact form of the energy dependence were drawn. A three dimensional summary of PO(PLAB,At) is shown in Figure 39. 69 70 .mm maomfim op Comma mHmOSpcopmm Ca myoppoq* mmfi.amom.I eAH.Hm:m.I Axv o.HIms. mmfi.asms.I mofi.ammm.I mofi.amse.I Anv ms.Iom. mso.aoH:.I soo.asmm.I moo.asH:.I mmo.ammm.I flaw ow.-me. mmo.nmmm.I mmo.smmm.I mmo.wom:.I omo.aosm.- Aev m:.-mm. mao.ammm.I oso.asme.I meo.aom:.I Heo.amam.I emo.amfim.I Amv mm.-mm. omo.am::.I omo.nmsm.I mmo.a:©m.I sao.ammm.I :mo.nmmm.I Auv mm.Iom. mso.amsm.I meo.asom.I mao.nomm.I 0:0.aoam.I smo.ooam.I on om. ma. mmo.ammm.I omo.aomm.I omo.aomm.I mmo.namA.I mmo.a::m.I gov mH.IoH. omo.aomH.I omo.amsH.I omo.nHmH.I omo.smHA.I on.no:H.I on 0H.Imo. emo.a©mH.I :mo.ammA.I emo.nmmH.I mmo.nwso.I mao.nAmH.I gov mo.Imo. mmo.no mmo.n@oo.+ wmo.womo.I omo.aHoH.I smo.amso.I *on mo.IHo. 3-2 SIm mIo SI: aim ESE I: spam Soapmmflamaom mo manna .m mHDmB 71 .o\>mm : w mdqm I m sou p n> Auvom .mm snows; V In 0\>m..o VIN .1 m.o.l . 038 TN + is- _o B cmtnom + 0+0 0 . o I as mi 0 + mmfi r L _ b p _ _ _ _ . 0.. mo ed to «+0 00 «same z. 'KDcI 72 .o\>ow m w mdqm w 3 now p.m> Apvom .mm muowfim J 0\>m0 0!? I . 0\>m0®l¢ 0 + 0 1 _O.—macmtnom + 0 O + 0 g xm m2... 0 +0 I. r _ _ _ L _ _ _ _ W 30 AV. mgu .wAv .vAv qu «3209 E mKVI .ngo 'lOd 73 .o\>oo m w mega w 6 son a m> onoa .em magmas J o\>mo mIm I m.oI —o— _O.. .0. .0. _o.. 1 ¢ ‘I’ 'IOd no no to No «898. :_ I/u o\»oo oH I mag V a w w sou o m> onod .mm magmas J 0.0 I v.0 I pa2mmvnvrImw .. + + O 0 I 0 O I o 1 00 r b h _ L L P b _ o._ no no to No «same z. 0.0 'TCMd 75 .o\>ou ma I warm w 0A sou a m> onoa .mm magmas V o\>mo NTO. I 0 l a a a a .. .v 0 OJ _ r _ . _ _ p _ OJ md $6 and N6 AL ass/8. :. mdl to... 0.0 '10:! 76 Iummmf Q: on on on L0 00 I I I T T I j ¢ This expt. 0 ish oi OI. 4“ afihfiWt POL POL oz on as as I I0 .00 0 -O.4Ir- ¢¢¢ .J 2 _ I I I «I e-Ioom: L '05 " IO-IZ GeVl: + h- 39. Approxi ate Energy Variation of P3(t) as PEAR Increases Fro~ 2-12 CeV/c. 77 .o.H w _o_ w Ho.o sou mans m> Amaqmvo 3\>.82..d 0.: on o.» ,on o.» a .mm magmas 0.. a - 1 q u /.. /.._ xv»... u 3.3. ........... .. . z. 23 :9 < 8 +{IIHIIII ../ 2.35.. «2.5.. :26 mdi on on No- 0.0 10P>3_N>4.08 I QB and I t I, .-.\ . 3 {If}, I") '8 LT: bowing Experimental Acceptance. I“O\Pj S Figure 39. CHAPTER V Theoretical Interpretation A. Preliminaries: A correct theoretical description of the np + pn sys- tem must reproduce the polarization parameter which is large (IPOI ~O.6 at It] ~O.6(GeV/c)2) and essentially energy inde- pendent, must reproduce both the t and s dependence of the differential cross section, and must reproduce the polariza- tion and differential cross section for the line reversed reaction pp + fin. The reaction np + pn involves two particles of spin 1/2 in both the initial and final states. If one writes down a transition amplitude ¢ = (K314IMIA1A2> where the Aj are the helicities of the external nucleons (see Figure 40), then one can construct 16 possible s-channel helicity ampli- tudes.26 However symmetry of the strong interaction under time reversal, parity, angular momentum, and isospin conser- vation reduce this number to five that are linearly indepen- dent. The conventional choices27 for these five are: N x o1 = <++Im|++> O O x}: 0 2 79 80 N X o3 = <+—|m| +- > 0 0 4,“: <+-ImI-+> 2 O ¢5=<++lmI+-> l u where N = |(A4-A2) (x3-xl)| is the net helicity flip in the diagram, and x = liq-K2I+IX3-KlI-N. The differential cross section and polarization para- meter are composed of bilinear combinations of these helicity amplitudes: 4 2 2 912: 1 ,3 Mil +4I¢5I (1) dt 128flPcmS s i=1 2 Im¢ *¢ p0 d2 = 52 o , where do = (¢l+¢?+¢3'¢4) (2) t l28wP S cms -i(- It should be noted that the relative phase between ¢5 and ¢o is a crucial quantity. For the case in which ¢5*, ¢o are at right angles in an Argand diagram, POdO/dt is maximized, conversely a relative colinearity of ¢5*, $0 will imply very small polarization values. Each helicity amplitude OJ is a superposition of allowed particle exchange amplitudes. In particular for a n-meson to be exchanged, the equal masses of the proton and neutron require a spin flip at each nucleon vertex, res- tricting the pion to the $2 and ¢4 amplitudes only. Other leading exchanges, such as the natural spin-parity p and A2 in general contribute to all five helicity amplitudes. PI PIAZ n,X4 TOTAL my”, (8,?) - nrxl pr>‘3 Figure 40. Helicity Picture for n+p + p+n P Tn BORN _ I mx’l‘ ($,I)' n {p ms: I p ., . A'I‘s’- nnlp ngpp 23:3? 9 pin + 9 Min + pin n = I mXII-I-(s’t) nN*{p n njp n} ‘p N*'n 'N n ‘N‘n I" ,I I ”51.“:4 nN}p nlpp IIIN p REGGE- I I REGGE |"Ip = I + 00. Figure 41. Helicity Amplitude Expansion in Terms of Particle Exchange. 82 From inspection of the expressions for do/dt and Podq/dt, one can conclude: pion exchange alone can produce no polarization because it cannot contribute to ¢53 con- versely the non—zero polarization data imply that natural spin-parity exchange be present -- hence large 0, A2 contri- butions (and perhaps other more low lying trajectories) are to be expected. However the pion, which is presumed to be the important factor in the forward peak of the differential 5, 28, 29 cross section, can influence the magnitude and sign of the polarization through its coupling strength and contri- bution to the overall phase of ¢o' In the expression POdO/dt then, the p and A2 exchanges will control the magnitude and phase of 05, and n, p, and A2 exchanges will determine Io: For each particle exchange there are two possible couplings, flip and nonflip, corresponding to the net nu- cleon helicity flip at the vertex in the Feynman diagram. Of the three particle exchanges considered, only the a- coupling is rigidly specified within the framework of these models: ggonflip = 0.0, gflip = gnnp' The first is zero to satisfy parity conservation, the second is measured in pion- 3O nucleon scattering. B. Models A helicity amplitude may be written as a series of Feynman graphs (Figure 41). The simplest theoretical descrip- tion is to consider only the Born term, a one particle ex- change approximation. For the two amplitudes to which the 83 pion contributes, one gets: ¢ t = ¢ t = 2 ItI 2( I n( I s ItI + mi which predicts a zero in the cross section at t=0. Since w—Reggeon exchange contains a similar functional form: 0. 2 ¢2(t) = M“) = g ”If: m“? c (t) (0 lm it too predicts a forward dip. Hence to get a useful descrip- tion for dO/dt and PO one must look beyond the Born term and consider rescattering diagrams. By interference among the Regge poles and the additional contributions from rescattering, one hopes to fill in the forward dip in the differential cross section. It should be mentioned that one must avoid a strictly dual picture for the nppn system as welL,e.g.,astfimas-chan- nel is exotic, the Dual Absorption Model319 32 predicts the imaginary parts of all the helicity amplitudes to be zero (or very small), implying that PO(ItI) ~O for all ItI. In what follows, only the Born term plus contribu- tions from the Regge-Pomeron graphs (Figure 41) will be con- sidered; Regge-Regge graphs will not be included. In parti- cular, the Regge-Pomeron corrections will in general have sizeable real and imaginary parts. After expanding a given particle exchange amplitude mi: (s,t) in partial waves,2 including elastic scattering with the Sopkovich prescription,33 and rewriting the partial wave series as a Hankel transform over impact parameter b 84 (see Appendix G for details), one gets: meTAL (s,b) = miiggfism) SEL(s,b) 2 . EL where SEL(s,b) = l + l_EEE§. m (s,b), and A, u are the heli- “riff—S— city flips of the external nucleons: A = A4'A2’ u = A3-A1. Combining expressions gives: TOTAL REGGE . EL IIIM (s,b) = mAu (s,b)(l+wi m (s,b)) LI" {8 - The original Regge exchange amplitude is modulated by an elastic scattering correction term as yet to be specified. The various phenomenological models differ in their choice of parametrization of m§EGGE (s,b) and.mEL(s,b) -- common variants are presented in Appendix G. Different combinations of these amplitudes were tried in an attempt to fit the pol- arization and cross section data. 1. Elastic Amplitudes: Figure 42 shows attempted fits to the differential cross section using the various elastic amplitudes listed in Appendix G. Independent of the parametrization of the Regge amplitude, those elastic amplitudes which consider the first two rescattering graphs only in Figure 41 (weak cut), and hence do not estimate the contribution of the diffraction elastic intermediate states, cannot generate a strong forward 34, 35 However if one includes an estimate of the re- peak. maining graphs (except Regge-Regge) which contain the diffrac- tive intermediate states with the same internal quantum num- bers as the nucleon, then one can generate a strong enough 85 cut. In the case of SCRAM,2 the effect of the additional graphs was incorporated by taking the simple elastic absorp- tion (G-1) and multiplying it by a coherent inelastic factor A, where A is greater than one and has in general different values for each particle exchange and helicity amplitude.3 The physical effect of A > I is to enhance the absorption at small impact parameter, and sharpen the edge at r --1 fm (see Figure 43). More recently, a model proposed by Hartley, Kane and Vaughn (HKV)36_38 splits the elastic scattering am- plitude into two components, a central core and edge piece, with additional contribution from the diffraction elastic states included as an edge effect only. This is made expli- cit by two terms, P and D, in this parametrization (G-4). Each of these models (SCRAM and HKV) is capable of generating the forward peak in the cross section. 2. Regge Amplitudes: The original motivation for the strong cut formulation was to generate dip structure in cross sections through dif- fractiVe means, rather than having to rely on nonsense-sense- signature-zeros of Regge amplitudes}I Hence one should not use an NWSZ Regge amplitude with the strong cut formalism. (Attempts at trying to use both have resulted in the wrong sign and incorrect ItI behavior of the polarization para- meter.39) The appropriate Regge pole forms are either G—6 or G—8 which have no NWSZ features. As shown in Figures 3 and 43, this model will fit both do/dt and PO for It] values less than 0.A, but fails for larger |t| primarily because of the 10 —— q --I -I u .2 I 10 86 do-/d’I (mb/(GeV/Ciz) DATA FROM MlLLER,otaI. 8 GOV/c HKPR III-MI l T I 0.0 0.1 032 2' 0.'3 ' OTII |t| (GeV/C) Figure 42. Fit? to dO/dt with Various Choices of me (s,t). |‘I 4 -'REBCIEAINN. --'X'“0 0.4 where the differential cross section is too high. The expression for the polarization parameter: 2 Po 3% = 2 Im¢5* d>O/(l28IIPCms 8) suggests several possibilities: First, the overly large values for dO/dt as determined from the fit for ItI 3 0.4 may render PO small; second,II5 may become inherently small at largeI tI; and third, the vectors‘I5* and ¢C)may become relatively co- linear as It I+-l.O. A study of the first possibility requires forcing dO/dt to the correct slope and size. To do this the vertex— modified (VAM) form for the Regge amplitude (047) was em- ployed which makes additional assumptions about the exchange amplitude coupling constants. They were treated as exponen- tially damped with |t|, the |t| dependence being different for a vertex with nucleon helicity flip or non—flip: ” 2 EV = gv exp (€V(t'mj)) gT sT exp (Emit-m§)) where gv, gT are the magnitudes of the vector, tensor (non- flip, flip) couplings, mj is the exchange particle mass, and ev, 5T depend only on helicity flip and not particle exchange. Such a choice preserves the form of the original amplitude near the particle pole and could possibly allow 0 and A2 coupling constants to be more nearly equal. The technique 88 produces good fits to the differential cross section for nppn 2 over the range 0.0 : |t| 5 l.O(GeV/c) and 3.0 i PLAB < 24.0 GeV/c, but does not reproduce the differential cross sec- 40, 41 very well (Figures 44 and 46)- What tion for pp + fin the fits predict Po(np+pn) and Po(pp+fin) to be are shown in Figures 45 and 47. However the relative phase between ¢; and $0 is consi- derably altered from the SCRAM case, and PO is much too small for It] 3 0.2 (see Figure 45). Hence the magnitude of ¢5 and the relative phase between a; and ¢o are the key quan- tities -- their dependence as functions of (t) are shown in Figures 48 and 49 for SCRAM and V-M models. The results show a relative colinearity of the phasers in the range 0.6 5 ItI S 0.8, and compounded with the relatively small size of M5|at large |t|, PO is forced to die away for ItI Z O.6(GeV/c)2. The remaining options are: to revise the size of the A2 contribution (the least peripheral exchange) and to in- troduce an appropriate t-dependent real part into the elas- tic scattering which will allow more flexibility in the phase determination of ¢5 and $0, in an attempt to boost the large ItI values of PO. One method devised with these ideas in mind is the previously mentioned HKV approach using G-4 and G-8 as the elastic and Regge amplitudes. In this model, the elastic scattering form (G-4) has been constructed to re— produce the high energy CERN ISR proton-proton elastic 89 scattering data,42 and appears to be able to generate the differential cross section for 0.0 5 ItI 5 l.O(GeV/c)2 and sizeable polarization magnitudes for larger ItI (30.6). Typical fits for dO/dt and Po(t) are shown in Figures 50-53. A summary of the "merits" of the various phenomenol- ogical models is presented in Table 3; none except the HKV scheme appears to satisfactorily fit both the polarization and differential cross section. The form of the HKV Pomeron however, reveals that a detailed phenomenological description of the polarization in nucleon-nucleon scattering is compli- cated when treated as a strong cut Reggeized problem. Though one may obtain a fit to the data which is much improved over previous cut models, it is not clear one has gained insight into the mechanism(s) responsible for the polarization seen. 90 do/d’I (mb/(GeV/CV) 1 O 101 10 a GoV/c I LJILI I DATA FROM MILLER,” al. 5.8,“ GOV/c DAVIS,” aI. l9,27.3 GOV/c ILIIIIII I T T l T T I 0.0 0.2 0.4 0.6' 2 IHIGOVC) Figure 44. V-M Fits to dO/dt (n+p +p+n). PC". 0 1 III (GeWCIz o (”i 0.2 0.4 0.0 as to -OI4— I’ ¢ ¢ _. I + I} + '08" 8-IOGeV/C ._ FIT A1'Eieovwc III (GeV/CI’.‘ ‘ oz 0.4 0.0 0.0 . .0 00 -(M4 ¢, ‘¢ «6 I. I I ‘0-3‘” IO-IZGeV/C I I5 FIT A1'IIGMNVC Figure 45. V-M Fits to Po(n+p + p+n). 92 da/d’r (mb/(GeV/C)2) l 1 10 10 0 10 1 0 l E 10 - 7GBV/C i 0.0 ' 031 T 0T2 .. /5GeV/c _ . 7GoV/c 10 1 i SBoV/c/ " : v -2 DATA FROM ‘ i 10 __. ASTBURY.otoI.,560V/c(x) )t : 7GoV/c(o) : 960V/c(o) ’ 4 LEE,etal..7.7660V/c(+) x 0.0 T 032 ' ofu ‘ 076 ‘ 038 ' 130 ' 1327 m (Ge-awe)?- Figure 46. '\/-M Fits to do/dt (13+p + 5+n). 93 .Ac+m + a+mvom uom Coapofivmum zu> .5: mgswam 1.6.. 0.. ad ad to «o .. r\_\L“L _ P _ P _ ad «A0\>mmu E . 1 1.3 I1 £3 a «on. 29553.. .36 'NDd SCRAM Model. 5 967A > 5 2 - .004 L .9 " -.004 I T I I .7 '6 on --.004 d-.I ,oa ‘ 4 mnmnsa on ' ‘-.008 ‘ -05 CURVES IS "I IN 3 2 ' .07 .. (GoV/c)2. .09 .. J—.0I2 '3 .4 -08 - 06 ’0‘ “.2 '2 l I I I I I I I fi 9‘2, ' . 7 .0 .03 _ Figure 148. Argand Plots of ¢* and ¢0 for the PARARTIR ON CURVES '3 .N I” Qccflwcfiz. 4-02 * Figure 49. Argand Plots of ¢ Model. 5 and tho for the V-M 10 1 lJlJHJ 1 10 lllJllll l 10 l I [lJiHl 96 dcr/dT (mb/(GeV/c)2) 1 1 0 l l [[1111] 100 [ 111L111] DATA FROM MILLER.“ al., 8 GOV/c FTT AT'B‘GOVVO T l I T l T I l l l l l .0~ 0.2 0.u 015 0.8 1.0 1.2 III (GeV/c)2 Figure 50. HKV Fit to da/dt (n+p + p+n). POL FIT AT! “We ‘03" 6'86er .- 0.. '" 8-IOGeV/c FIT AT 0 GOV/c Figure 51. HKV Fit to Po(n+p + p+n). 98 do-/ d1 (mb/ (GeV/c)2) 1 1 10 __ 10 ~ 0 e 10 ___1 0 «I» E 10 __ -1 3 012 r -1 10 .2 g -2 DATA FROM 10 __ ASTBURY.otoI.,7GeV/c m 3 LEE,” al.,7.76 GeV/c (H T : FIT AT 8 GOV/c 1 g 0.0 ‘ 032 ' ofu ‘ 0T6 T ofa T 130 ' 112'7 m (GeV/c)2 Figure 52. HKV Fit to dO/dt (5+p + am). Ac+m + e+mvom op seepeflemem >xm .mm mesmfim To «8509 E 0\>ooo mom zoFoEmma tdl 0.0 to 0.0 10:! 100 Table 3. Table of Results of Phenomenological Models Weak Cut Models: dO/dt: POL: No forward peak of sufficient strength. Wide It] (2 O.l(GeV/c)2) Respectable. Can fit polarization with assumptions of additional exchanges such as AD HOC X-Meson. Strong Cut Models: SCRAM: d0 /dt: POL: V-M: do/dt: POL: HKV: dO/dt: POL: Comment: Can fit small It] (‘50.4(GeV/e)2) behavior; fails for larger |t |due to large pion cut. Correctly predicts energy dependence. Can fit small It] ( $0.4(GeV/c)2) behavior; fails for larger It Iwith polarization too small. Can fit behavior for 0.0 f It] E l.O(GeV/c)2; however forward peak predicted for ppfin is too strong. Energy dependence is OK. Fit to polarization is useless for It I 3 O.25(GeV/c)2. Good fits to 8 GeV/c for 0.0 S ltl s l.O(GeV/c)2 for both nppn and ppfin. Fit to polarization is respectable with possible problems for O f It] i 0.15(GeV/c)2 and It I2 O.8(GeV/c)2. This model is superior to the other cut models tried. CHAPTER VI CONCLUSIONS OF THE EXPERIMENT A. Experimental Implication The polarization for the reaction n+p + p+n is roughly energy independent with a tendency toward slightly higher pol- arization values as incident momentum is increased over the measured range 2-12 GeV/c. The trend suggests that the pola- rization will be large at higher energies. B. Theoretical Implication The data imply important natural spin-parity contribu- tions for the generation of polarization. It is also clear from the differential cross section measurements that an ex- changed Reggeon must be accompanied by a complex elastic re- scattering correction to obtain an adequate fit to the data for 0.0 5 |t| 5 l.O(GeV/c)2. Current strong cut parametri- zations of the rescattering can yield fits to the neutron- proton charge exchange data; however in their present form they do not necessarily lead to an understanding of the under- lying mechanisms of polarization observed in this reaction. lOl APPENDICES 102 APPENDIX A KINEMATICS FOR THE n+p + p+n SYSTEM The kinematics for the reaction n+p + p+n may be speci- fied by the Mandelstam variables: 8 = (P1 + P2)2 2 t = (P1 - P3)2 = (P2 - P4) 11 = (P1 - IDA-)2 where the four momenta are defined in Figure Al. Specializ- ing to the laboratory (Figure A2), and using the equal mass approximation m : mn = m we can obtain: P s = 2m(m+E1) t = -2mT4 where T4 is the kinetic energy of the outgoing neutron. Another useful quantity is the approxima- tion: t z — 132632 for 632 small and IPl I’m, |r3|>m3 and |§1I~|§3 I = p, and where 6 is the usual polar angle, measured rela- tive to the direction P1. In this experiment all four momenta were known except for the incident beam P1 = (El, P1). The three momentum of each particle in the reaction was described during various analyses by several different sets of variables. These choi- ces are shown in Figure A3 for regular polar coordinates, on- line coordinates, and fitting program coordinates. Regular 103 A cartesian reference axes are shown in each diagram, with z the direction of the beam line, y the vertical direction above the experimental floor and the direction of positive target polarization, and i directed toward the neutron spectrometer. 104 outgoing proton P36 outgoing proton . . 9cm: Incident neutron P. c P2,; target proton P40 outgoing neutron Figure A-l. Scattering in the Center of Momentum Frame. P4 recoil neutron Incident neutron PI Figure A-2. Scattering in the Laboratory Frame. 105 Figure A-3. Coordinate S stems Used to Describe Particle Momenta: (al Spherical Coordinates, (b) On- line Constraint Variables, (c) Off-line Variables. The Reference Axes are: x, Toward Neutron Arm; y, the PPT Magnetic Field Axis, 2, the Surveyed Beam Direction. 106 (a) (c) Figure A-3 107 APPENDIXvB NMR POLARIZATION CALCULATION The enhanced target polarization is given as a fre- quency average over the imaginary part of the complex sus- ceptibility, determined from the NMR measurement: T = E f” x" dw where ELis a proportionality constant determined from the thermal equilibrium target polarization and x = x' - Jx" is the target susceptibility. The NMR System used was a parallel circuit, constant current Q-meter. Hence one may write the circuit impedance as: l _ l ._ _ + JwC Z R + .ijo(l + limx) where n is the filling factor, w is the circuit frequency.17 Using the assumption that x' is very small and using the usual definition Q =¢0Lo/R, one obtains 1 ~ 1 l E PC1+E1IQx"-I-JQ+%§ which after inversion becomes Z = RQLQ - 3(1 + thx")) (l + 4nQX") In the absence of microwaves, and with the NMR far from proton resonance, x' = x" = O and: %=RMQ-w and hence _Z___ = (g - j(l + lian") ZO (Q - J) (1 + HFQX 108 Since we have a constant current Q-meter: IV/Vo |= IZ/ZOI. Thus 2 = Q2 +41 + hug-thl2 (1 + Q72) (1 + MQ x")2 L V0 which may be immediately solved for x" (let V/Vf,= IV/VOI) 2 - . 4.qu _.. Y2( <1 +922 - gm ) ”2.. V Q . Q Vo Assuming Q is very high and hence i. 17.2«1 Q2 vo one immediately obtains X" = — __l_(V-Vo) unQ v hence T = " 5 V-V do: K V-V WITP- I Odw where K = -E/hNQ. A similar expression will hold for the tar- get polarization at thermal equilibrium PTE‘ : K I VTE -V 0 du) P TE VTE However we can now determine K since we know PTE from the Boltzmann distribution.l6 exp (+gsH/2k'r) - exp bash/2 le P _ TE €Xp(+gBH/2kT)+ exr>( vgBH/QKT) tanh(gKH/2kT) where g is the nuclear g factor, B is the nucleam'magneton, H is the external magnetic field (25 k6), k is the Boltzmann factor, and T is the target temperature (~ 1.l°K). 109. Hence K is determined and the enhanced polarization is obtained: f V-Vo do.) tanh (+gBH/2k‘l‘) V I VTE- V0 dw VTE 110 APPENDIX C WIRE CHAMBER SPECIFICATION The wire spark chambers described here were built for use on a previous experiment.5’ 8 Each chamber consisted of a 3/8 in. GlO frame upon which were stretched two orthogonal planes of aluminum wires, 24 per inch, with wire diameter de- pending on the module: .007 in. for the two modules upstream of the bending magnet and .010 in. for those downstream. To improve the characteristics of the large chambers, a 1 mil thick aluminum foil sheet was stretched behind each wire plane with an insulation layer of 2 mil mylar in between. The chamber volumes were maintained in a recirculated atmosphere of 90% Ne-lO% He Gas. The chambers were operated at 5.1-5.4 kV high voltage which was held on storage capacitors until the fast logic event trigger enabled a Marx generator to turn on a thyratron tube, firing the chambers. A d.c. clearing field of 35 V was applied to the chambers at all times except when the thy- ratron was turned on. After each spark chamber trigger, a 600 V, 4-5 msec post-clearing field was utilized to sweep the chamber volume of ionization products. The spark chambers were equipped with magnetostrictive readout, and fiducial and spark information were digitized by a SAC 20 MHz quadscaler system. There were four scalers per plane in the upstream chambers, two per plane downstream. lll Dimension and mass specifications for each chamber module are shown in Table C-l. Table C—l. Table of Dimensions Module Chamber active Wire Effectige number area diameter mass/cm 1 14" x 12" .007" .017 gin/01112 2 lit" x 12" .007" .017 gnu/cm2 3 39" x 13" .010" .039 gin/C1112 4 50" x 24" .010" .039 gm/cm2 Resolution for the proton arm is shown in Figure C-l. A P3 (GOV/0) A¢ (DEGREES) 112 4.04 .0 to 1 13.0q 110‘ .0 l OHORTB A 9 (DEGREES) L ‘ ‘) ‘~‘~—__ IINWGS ‘3‘) I I’I 1 I' ’1 0 5.0 l0.0 9 (DEGREES) [TTTUI WTS LONG! do 9 (DEWES) p, (Boil/c) 0.02 -i .09 H 0.08- 0. I 0-1 0.|2 Figure C-l. Proton Arm Resolution. 113 APPENDIX D NEUTRON COUNTER SPECIFICATION Each neutron counter consisted of three active elements (see Figure D-5): a large block of Pilot Y Scintillator either 6" x 6" or 6" x 10" in cross sectional area and two 5 in. dia- meter Amperex 58 DVP photomultiplier tubes. To optimize the light collection at the photocathode of each tube, UVT Lucite blocks with Winston funnel light guides were used to match scintillator area to phototube area. The negative high voltage supplied to the base of each phototube varied from counter to counter depending on tube quality, individual counter light transmission properties, and pulse height requirements which were different for the long and short counter banks. The gains of the tubes for a given array were set as nearly equal as possible; typical voltages were l.75-2.0 kV (longs) and 2.0-2.35 kV (shorts). From each tube base, anode and second dynode signals were extracted. The anode signal was used for timing and was used in the pulse height analysis if the signal was unsatu— rated. However if it was saturated, the dynode signal pro- vided the measure of energy deposit in the counter. Detection efficiencies for the neutron counters were calculated for given counter geometry, neutron energy, and counter discriminator threshold from a monte carlo program developed for a previous experiment (see Figure D-3).)+3 114 Thresholds for the longs and shorts were 2.0 and 0.2 MeV respectively. Resolution for the neutron arm is shown in Figure D-h. 115 Aflgm: .muCougpooe. nopgoo coopsoz .Hun onswwm muNKGWO 0001 . . WWW _ h eObO _ 000 T T $020.4 i 950.5 9— \ “(>06 N. 0\>oo m I IITTI l [um i I 3.0 3 3mm» 8 O.— 116 .3: Ammoapsoz pom soapocsm coapmnomn< pomuafi .mun meowam «338. . N. . O. _. 0.0 0.0 ¢.O Nd 0.0 . 7 . a d . a 1|.JIIJIIJI . O 0 W 0.0 117 .Apvm .zoeofioamum cofipoepoa nopcsoo coupsmz .mun ousmfim $3: a» 00. o. . q. q 4 e .14qu n . q:1_q11 . 1.4, 0.0 memoxm ////r oozes I 1.4;u AP" (MeV/c) A¢(DEGREES) A9 (DEGREES) 118 P" (MeV/c) o 200 ~ 400 600 800 I000 o I 1 I I I I I I I j 5.— '°*' LONGS SHORTS l5~ 2° "' |t| (GeV/c)2 op 01: CAP 416 (is u: I I I l I I F I I j ’,,—e LONSS L0- fp/"—§Honrs 1° |t| (GeV/c)2 ° °~.2.°.4.°+§.2F.';° <15 LON08 sweats LO- Figure D-u. Neutron Arm Resolution. 119 .cwamoa empcsoo Conpsoz .mnm onswam :. c We _ _ _ no.3 he... 33» .5229. .8523; cpo ago; 3 . 3 263 _ / x $59.. one... :6... ¢E 3". D3 = XMPI—XI _ £_ XO-XMPO -V(XMFI-XI)2 + (30)2T‘ 1RXD_XMP0)2 + (30): (XMPO,YMPO) (XMPI,YMPI) EXIT PROTON SPECTROMETER BENDING MAGNET INCIDENT PROTON Figure E-l. Polynomial Coordinates 122 APPENDIX F FERMI MOMENTUM CONSIDERATIONS The main sources of bound protons in the glycol target are carbon and oxygen nuclei. Using a simple Fermi Gas 45 approach, one calculates the average momentum of a bound nucleon in the y (vertical) direction to be roughly 120 MeV/c (155 MeV/c is the maximum momentum). The question of interest is whether or not we can se- parate free proton events from bound proton events experimen- tally. The neutron arm acceptance will allow detection of neutrons with momenta up to 930 MeV/c (|t| ~l.O(GeV/c)2), and Fermi motion of a bound target proton can alter this appreciably. If one considers the y-momentum balance constraint be- tween the final state neutron and proton (a plot is shown in Figure 20(b)) neut prot Apy = y y 2 2 o + o pyn PYP neut prot where py , py are the y-momentum components of the neu- tron and proton, and o are their respective errors, pyn’ “pyp one can estimate how Fermi motion effects will distribute events. If we consider an event at It] 1 l.O(GeV/c)2 for which Opyn 2 15 MeV/c and opyp 1 5 MeV/c, and consider the average Fermi momentum allowed the target (120 MeV/c), then 123 Apy = 1 8a where o is the standard deviation of Apy. Hence the events produced from bound protons will produce a broad smear across the range of Apy distinguishing them from the elastic events peaked within :20. Data obtained with the graphite dummy target and shown in Figures 20(b), 21 (a—b) bear out this expectation. 124 APPENDIX G THEORY APPENDIX If one considers a helicity amplitude for a particle exchange mix(s,t), where A = 13-11 and u = A4'A2 (helicity U indices are shown in Figure 40, one may write it as an eXpan- sion over partial waves: mex(s t) = 2 (2J + l) dJ (z) mJ ex (5) All ’ J A'u All Using the Sopkovich prescription33 for including elastic scattering yields a new total amplitude: TOT J J ex e1 m (s,t) = Z(2J + 1) d (z) m (s) S (8) Au J A _ A11 11 where S is the elastic S-matrix. Now making the usual transformationfl6 >3 + I P db ‘J o cms J = Pcmsb-1/2 J d (z) 2 J (b V -t ) = Jn(b V’-t ) where n A‘U A'u I is the total helicity flip defined on page 80, we obtain ex TOT el msdb Jn(bv’-t )mAu(s,b) S (s,b). mAu (s,t) =£ (2PCme) PC Then if one writes the formal expression: TOT TOT m 2 f.— m“ (s,t) = g (2 Pcms) bdb Jn (b -t )mw (s,b) 125 we get the prescription: TOT mA (s,b) = mex(s,b) Sel(s,b) Ll Au where Sel(s,b) may be split into a piece with no scattering plus an interaction term:2 i P 81 ‘ ___JZEE eff S (s,b) =: l + u"/——S m (s,b) TOT ex . Pcms hence mAu (s,b) = mxu(s,b)(l + 1 Z;7:§r meff(S,b)) . What distinguishes the various models is their choice of Regge exchange amplitudes mfif(s,b) and effective rescat- tering amplitude meff(s,b) presumably due to the Pomeron, elastic scattering corrections, etc. 1. Elastic amplitudes, meff(s,b) Four main parametrizations were considered: G-l Elastic Absorptionzu6 -At/2 2 «- meff(s,t) = 4 P oT(i-+o ) e 5x1135A214 CHIS where A.is the slope of the elastic cross section (~10) and 5 is the ratio of real to imaginary parts in the elastic scattering (~30%). The delta func- tions emphasize that the pomeron flips no spins. The same will be true for all the other choices in this section and the 6's will be dropped for convenience. G-2 Worden Square Well:35 2 “ 2k k -b /2A . ~ meff(s,b) = 2: CkA (1 9—) e (1 +9) k=O A (1A 126 2 0-3 Strong Cut (SCRAM-HKPR): ’ 3 meff(s,b) = 4P5ms AoT(i.+tb)e-At/2, A 3 1.2 usually where A is the estimate of contributions from diffrac- tion elastic intermediate states (see Figure 41). 0‘4 gky:35‘38 meff(s,t) = P(s,t) + D(s,t) B t Bt where P(s,t) = is(AOe O + Ae JO(R./-t(ln§g - 1%) > is the Pomeron and A0 and A are related to 0T by the optical theorem, and: Bgt D(s,t) = is(A2e JO(R2 V-t(ln§3 - lg) ) is the contribution of the diffraction elastic interme- diate states whose effect is entirely generated from the edge of the proton located at radius R2“ 1n§— . o 2. Regge exchange amplitudes, mfifp (s,t): Four different Regge prescriptions were used, each of which are listed below: G—5 NWSQ: The traditional form fbr the Regge amplitude which has periodic zeros in the denominator leading to non- sense wrong signature zeros: N ex _i£ a J J t = _ 2 ‘g 1 + T6 min (S, ) ( t) gA1A3gA2A4(So) sinfloJ -iTI’OJ I47 127 G-6 Simplicity Choosing2 This is a form which has no forced amplitude zeros away from t=0 and is used in strong cut models: N+X _ X 2 OJ mexJ(s t) - (_L2__-t g1 A $1 M(S 1/2 men) A ’ ‘ 2 S x exp(-i-g-a3 (t-m§)) G-7 V—M This includes t -dependent vertex form factors to assist in fitting dO/dt: mfx (s,t) = i‘t) IaAll lexp