Non UBC
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TRIUMF
Huber, Garth Murray
Proton induced pion production has been investigated in a series of experiments using the Medium Resolution Spectrometer at TRIUMF. Data were obtained for the ⁷Li(p̄, π⁺)⁸Li*, ¹²C(p, π⁺)¹³C*, ¹³C(p, π⁻)¹⁴O*, ¹³C(p, π⁺)¹⁴C*, and ¹⁶O(p̄, π⁺)¹⁷O* reactions at Tp = 250 , 354 and 489 MeV, and are compared with previously published results taken at other energies above and below the ∆₁₂₃₂ resonance region. Because the signatures of the ∆₁₂₃₂ resonance should be the least ambiguous in this energy range, theoretical calculations which include ∆₁₂₃₂ degrees of freedom should be able to describe these results, if they are to have any hope at describing the experimental situation at all. At fixed four-momentum transfers squared of t > 0.45 GeV²/c², the (p, π⁺) differential cross sections exhibit a maximum near the invariant mass of the ∆₁₂₃₂. This energy dependence is similar to that shown by the pp → dπ⁺ reaction at equivalent center of mass energy and four-momentum transfer squared, and thus it provides strong evidence of a NN →NNπ⁺ process in the (p, π⁺) reaction mechanism. Unlike the (p, π⁺) reactions, the differential cross sections of the (p, π⁻) reactions decrease with increasing energy through this region. This difference is consistent with an interpretation of the (p, π⁻) reaction mechanism as a NN → NN π⁻ process in which non-resonant amplitudes are dominant in this region. Analyzing power angular distributions for many states of the ⁷Li(p̄, π⁺)⁸Li* and ¹⁶O(p̄, π⁺)¹⁷O* reactions exhibit broad similarities with those of the p̄p → dπ⁺ reaction. Interpretation of this trend is complicated by other analyzing power angular distributions which have entirely different shapes. Data were also obtained for the inclusive pion production reactions to the continuum. Double differential cross sections display an energy dependence similar to that of the pp → dπ⁺ reaction, and analyzing power angular distributions are similar to those of the p̄p → dπ⁺ reaction. This is consistent with earlier interpretations of a quasi-free NN → NNπ⁺ process occurring within the nuclear environment. Theoretical calculations have been performed for two of the exclusive reactions studied in this work. A resonant two nucleon model, and a relativistic stripping model using a ∆-hole potential, both do a better job of describing the differential cross section data at the ∆₁₂₃₂ invariant mass than at lower energies. Both calculations can only be said to qualitatively describe the broad features of the analyzing power data. Thus, the results presented in this thesis indicate that there are some effects of the ∆₁₂₃₂ resonance in the (p, π⁺) reaction, but that these effects are less clear in the (p, π⁻) reaction.
Proton Induced Pion Production from Light Nuclei in the Region of the a 1232 Resonance Garth Murray Huber A Thesis Submitted to the Faculty of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics Faculty of Science University of Regina February 18, 1988 © Garth M. Huber , 1988. UNIVERSITY OF REGINA FACULTY OF GRADUATE STUDIES AND RESEARCH CERTIFICATION F THESIS WORK We, the undersigned, certify that Garth Murray Huber, candidate for the Degree of Doctor of Philosophy has presented a thesis on "Proton Induced Pion Production from Light Nuclei in the Region of the A 1232 Resonance", that the thesis is acceptable in form and content, and that the student demonstrated a satisfactory knowledge of the field covered by the thesis in an oral examination held on February 9, 1988. External Examiner: Dr. B.M.K. Nefkens, Internal Examiners: U c//~ Dr. G.J. Lolos, Co-Supervisor Dr. S.I.H. Naqvi, Co-Supervisor UNIVERSITY OF REGINA FACULTY OF GRADUATE STUDIES AND RESEARCH PERMISSION TO USE POSTGRADUATE THESES TITLE OF THESIS: Proton Induced Pion Production from Light Nuclei in the Region of the a 1232 Resonance NAME OF AUTHOR: Garth Murray Huber FACULTY: Faculty of Graduate Studies and Research DEGREE: Doctor of Philosophy In presenting this thesis in partial fulfilment of the requirements for a postgraduate degree from the University of Regina, .I agree that the Libraries of this University shall make it freely available for inspection. I further agree that permission for extensive copying of thi s thesis for scholarly purposes may be granted by the professor or profes sors who supervised my thesis work, or in their absence, by the Head of the Department or the Dean of the Faculty in which my thesis work was done. I t is understood that any copying, publication or use of this thesis or part s thereof for financial gain shall not be allowed without my written permission. It is also under-stood that due recognition shall be given to me and to the University of Regina in any scholarly use which may be made of any material in my thesis. SIGNATUREDATE: 9 l /961! 7 Abstract Proton induced pion production has been investigated in a series of experiments using the Medium Resolution Spectrometer at TRIUMF. Data were obtained for the 7Li(p,rr+)8Li*, 12C(p, rr+)13 C*, 13 C(p, rr-)1 4O*, 13 C(p , rr+)14 C*, and 16 O(p , rr+)17 O* reactions at Tp = 250 , 354 and 489 MeV, and are compared with previously pub lished results taken at other energies above and below the ~ 1232 resonance region . Becau se the signatures of the ~1232 resonance should be the least ambiguous in this energy range, theoretical calculations which include ~ 1232 degrees of freedom should be able to describe these results, if they are to have any hope at describing the experimental situation at all. At fixed four-momentum transfers squared oft > 0.45 GeV2 /c2, the (p, rr+) differen-tial cross sections exhibit a maximum near the invariant mass of the ~1232· This energy dependence is similar to that shown by the pp -t drr+ reaction at equivalent center of mass energy and four-momentum transfer squared, and thus it provides strong evidence of a NN -t NNrr+ process in the (p, rr+) reaction mechanism. Unlike the (p, rr+) reactions, the differential cross sections of the (p, rr-) reactions decrease with increasing energy through this region. This difference is consistent with an interpretatio n of the (p, rr-) reaction mech-anism as a NN -t NNrr- process in which non-resonant amplitudes are dominant in this region. Analyzing power angular distributions for many stat es of the 7Li(p, rr+)8Li* and 16O(p, rr+)17 O* reactions exhibit broad similarities with th ose of the pp -t drr+ reaction. Interpretation of this trend is complicated by other analyzi ng power angular distributions which have entirely different shapes. Data were also obtained for the inclusive pion producti on reactions to the continuum. Double differential cross sections display an energy depende nce similar to that of the pp -t drr+ reaction, and analyzing power angular distributions are similar to those of the pp -t drr+ reaction. This is consistent with earlier interpretation s of a quasi-free NN -t NN rr+ process occurring within the nuclear environment. Theoretical calculations have been performed for two of the exclusive reactions studied in this work. A resonant two nucleon model, and a relati vistic stripping model using a ~-hole potential, both do a better job of describing the differential cross section data at the ~ 1232 invariant mass than at lower energies. Both calculations can only be said to qualitatively describe the broad features of the analyzing power data. Thus, the results presented in this thesis indicate that there are some effects of the 6.1232 -;;sonance in the (p, rr+) reaction, but that these effects are less clear in the (p, rr-) reaction . ii -Dedicated to my Parents lll Acknowledgements There are no words with which I can fully express my appreciation to Dr. George J. Lolos for being my primary co-supervisor. During the five years that I have known him, I have come to appreciate his fine physics intellect. He surely has better physics insight than any other person I know. Furthermore, he has always treated me with utmost fairness and honesty, being the most supportive supervisor that a studen t could hope to have . Finally , I consider him a valued friend. I would also like to thank Dr. S.I.H . Naqvi for his help as my co-supervisor. I was indeed very lucky to have them as my co-supervisors. I also wish to thank Dr. Patrick L. Walden of TRIUMF and Dr. Robert D. Bent of IUCF for the time that they have spent going through drafts of (p, 1r+) papers submitted for publication. The material from these manuscripts formed the backbone of this thesis , and as such their suggestions have become an intrinsic piece of this work. Thanks are due to Dr. M. Javed Iqbal for the summer we worked together on his Two Nucleon Model code, and to Dr. E.D. (Tim) Cooper for his explanations of the finer points of (p, 1r) theory . As these two theorists have very different viewpoints on the direction of (p, 1r) theory , the summer that I spent with them at TRIUMF was a very educational experience. I would also like to thank the members of my superviso ry committee, and the (p , 1r+) group for their support and help. The staff of TRIUMF should be thanked for the use of the MRS spectrometer and beam time. I especially want to thank Dr. Dieter Frekers for his help with the LISA analysis system, which made the dat a analysis a much simpler task. Finally, I wish to thank my family for their love and support. This work would have been much more difficult without them. This work has been supported in part by NSERC Postgraduate Scholarships and by NSERC research grants. IV Contents Abstract .. Dedication . Acknowledgements Table of Contents . List of Figures List of Tables . 1 Introduction 1.1 Motivation for Investigating (p, 1r) Reactions 1.2 Previous Experimental Results 2 The Experiment 2.1 Selection of the Proton Beam ..... . 2.2 Measurement of the Beam Polarization . 2.3 The Principle of Dispersion Matching 2.4 Experimental Targ et . . . . . . . . . . 2.5 The Medium Resolution Spectrometer 2.6 Spectrometer Detection System 2.6.1 Front End Chamber 2.6.2 Veto Scintillators . . 2.6.3 Vertical Drift Chambers 2.6.4 Focal Plane Scintillators 2.6.5 Determination of Aquisition System Live Time 2.7 Beam Current Normalization .... . . . ... . .. . V lll IV V Vlll XU 1 1 3 12 12 13 13 17 18 19 19 20 20 20 21 23 3 Data Analysis 3.1 Drift Chamber Decoding Routine 3.2 Determination of Wire Chamber Efficiencies . 3.3 Particle Identification . . 3.4 Trajectory Reconstruction 3.5 Corrections for Improving the Resolution 3.6 Correction for Pion Decay ....... . 3. 7 Determination of the MRS Solid Angle . 3.8 Calibration of the Focal Plane . 3.9 Calculation of Observables . 3.10 Error Analysis ...... . 4 Observations on the Experimental Spectra 4.1 12 C(p, 1r+)13 C* Spectra. 4.2 16 O(p,1r+) 17 O* Spectra 4.3 7Li(p, 1r+)8Li* Spectra . 4.4 13 C(p, 11"-)14 0* and 13 C(p, 1r+)14 C* Spectra 5 Results 6 Differential Cross Sections 6.1 Observations on the (p, 1r+) Differential Cross Sections 6.2 Energy Dependence of (p, 1r+) Differential Cross Sections 6.3 Energy Dependence of (p, 1r-) Differential Cross Sections 6.3.1 Discussion . . . . . . . . 6.4 Continuum d2a /dS1dE1r Results 7 Total Cross Sections 7.1 Energy Dependence of the Total Cross Section 7.2 Spin Dependence of the Total Cross Section 7 .3 Continuum da / dE1r Results 8 Analyzing Powers 8.1 Types of Angular Distributions Vl 24 24 25 28 30 31 34 36 37 37 39 41 41 44 45 45 52 65 65 67 71 79 80 84 84 86 86 89 89 8.1.1 Category 1 (pp-+ d1r+-like) . .... . 8.1.2 Category 2 (Flat at Forward Angles) . 8.1.3 Category 3 (Oscillating above 250 MeV) 8.1.4 Exceptions ........ . ..... . 8.2 Energy Dependence of the Analyzing Powers 8.3 Continuum Results 9 Theoretical Models 9.1 Non-Relativistic Single Nucleon Model 9.2 Non-Relativistic Two Nucleon Model . 9.2.1 9.2.2 9.2.3 The Model of Keister and Kisslinger The Model of lq bal and Walker . . . The ORCHID Model of Dillig, Conte , Bent and Alons 9.3 Relativistic One Nucleon Model ..... 9.3 .1 Application to 16 O(p, 1r+)17 Og.s. 10 Summary and Conclusions Bibliography A Software A.I Data Analysis . A.1.1 A Recipe for the Analysis of (p, 1r) Data using LISA A.1.2 Insert Routine Used in Main Data Analysis A.1.3 Analysis Conditions . . . . . A.2 Rate Dependent Efficiency Analysis A.2.1 Insert routine Used in the Efficiency Analysis A.2.2 Logical Conditions ... A.2 .3 Data Skimming Routine A.3 pp -+ d1r+ Transformation Routine B Tables of Data C Tables of Continuum Data vii 90 91 92 92 93 93 96 96 97 101 102 107 109 112 117 121 127 127 127 129 134 136 136 138 142 142 155 169 List of Figures 1.1 Pioneering 12 C(p, 1r+)13 C* spectra at Tp = 185 MeV shown as a function of the excitation energy of the residual 13 C nucleus. . . . . . ·. . . . . . . . . . . 2 1.2 Schematic representation of the angular distribution data for a variety of (p,1r+)reactions ................................... 4 1.3 (p, 1r+) and (p, 1r-) spectra leading to the same final nucleus showing the previously unsuspected (p, 1r-) selectivity. . . . . . . . . . . . . . . . . . . . 5 1.4 Stripping model diagrams for the A(p, 1r+)A + 1 and A( d,p )A+ 1 reactions. 7 1.5 Analyzing powers for some (p, 1r+) transitions. 8 1.6 10 B(p, 1r+)11 Bg.s. differential cross sections at seven energies plotted as a func-tion of the momentum transfer. . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.7 Differential cross sections of the 10 B(p, 1r+)11 Bg.s. reaction versus incident proton energy at four different fixed three-momentum transfers .. 10 2.1 TRIUMF Proton Hall and Beam line 4B. . . . . . . . 14 2.2 Schematic of the Beam line 4B In-Beam Polarimet er. . 15 2.3 Interpolated AcH 2 /AH curve for the beam line 4B In-Beam Polarimeter. 15 2.4 The Medium Resolution Spectrometer ....... . ...... . 2.5 Schematic figure of the data aquistion electronics for the MRS. 19 22 3.1 Cross section views of the Front End Chamber (FEC) and a focal plane Vertical Drift Chamber (VDC). . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Spectrum of TDC times for one wire in the FEC. 3.3 Spectrum of TDC times for one wire in VDCl. . 3.4 A plot of time of flight through the spectrometer versus energy loss in the 27 27 focal plane paddles showing the relative location of pions and protons. . . . . 29 viii 3.5 Schematic diagram showing the effect of magnetic field abberations upon the experimental resolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.6 Plots of focal plane position (XF) versus horizont al FEC co-ordinate (YO) before and after the kinematical correction is applied. . . . . . . . . 3.7 Typical off-line analyzed pion focal plane spectra at Tp = 489 MeV. 33 35 3.8 Legendre polynomial fit to the results of a pp - drr+ focal plane scan. 38 4.1 12 C(p, rr+) 13 C* focal plane spectrum. . . . . . . . . . . . . . . . . . . . 42 4.2 12 C(p, rr+) 13 C* focal plane spectrum taken with the QDDM spectrometer at IUCF ............................ . ............ 43 4.3 12 C(p, rr+) 13 C* spectrum obtained at Tp = 200 MeV using the QDDM spec-trometer at IUCF .......... . 4.4 16 O(p, rr+ )17 O* focal plane spectra .. 4.5 Final result of the peak fitting program showing all of the 17 0 states for which data have been extracted. . . . . . 4.6 7Li(p, rr+)8Li* spectrum ......... . 4. 7 250 Me V 13 C(p, rr±) focal plane spectra. 4.8 354 MeV (p, rr+) focal plane spectrum from the first run of the 13 C(p, rr±) 44 46 47 48 49 experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.1 Differential cross sections and analyzing powers for the 7Li(p, rr+)8Lig.s. re-action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.2 Differential cross sections and analyzing powers for the 7Li(p, rr+ )8Li0_9808 reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.3 Differential cross sections and analyzing powers for the 7Li(p, rr+)8Li2_255 re-action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.4 Angular distributions of the 12 C(p, rr+) 13 Cg.s. reaction plotted versus the square of the four-momentum transfer (t ). . . . . . . . . . . . . . . . . . . . 56 5.5 Angular distributions of the 12 C(p , rr+) 13 C3_09 ,3_68,3 _85 reaction plotted versus the square of the four-momentum transfer (t).. . . . . . . . . . . . . . . . . 57 5.6 Angular distributions of the 12C(p, rr+) 13 C9_50 reaction plotted versus the square of the four-momentum transfer (t) ..................... 58 ix 5. 7 Differential cross sections and analyzing powers for the 16 0(p, 1r+ )17 Og.s. re-action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.8 Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 00_871 reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.9 Differential cross sections and analyzing powers for the 16 0(p, 1r+ )17 0 5.218 reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.10 Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 0 7_757 reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.11 Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 0i 5 .78 reaction . .... . 5.12 Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 0i7_1 reaction ..... . 6.1 Differential cross section versus center of mass energy at a constant square of four-momentum transfer (t = 0.50GeV 2 /c 2 ) for the 12C(p, 1r+) reaction leading to the ground state as well as the 9.50 Me V excited state. 63 64 . 69 6.2 Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 0 7_757 reaction plotted versus center of mass energy . . . . . . . . . . . . . . . . . . . 72 6.3 Differential cross section versus center of mass energy at a constant four -momentum transfer (t = 0.50 GeV2 /c 2) for the 13 C(p, 1r±) reactions leading to the ground states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.4 Differential cross section versus center of mass energy at a constant four-momentum transfer ( t = 0.50 Ge V2 / c2 ) for the 13 C(p , ,r±) reactions leading to several high excitation final states. . . . . . . . . . . . . . . . . . . . . . . 75 6.5 Invariant matrix element plotted versus center of mass energy at a constant four-momentum transfer (t = 0.50 GeV2 /c 2 ) for the ground state transitions as well as the pp -t d1r+ reaction. . 77 6.6 Invariant matrix element plotted versus center of mass energy at a constant four-momentum transfer (t = 0.50 GeV2 /c 2 ) for high-spin final states. . . . . 78 6. 7 Energy dependence of the double differential cross section for three different continuum reactions at a constant missing four-momentum. . . . . . . . . . . 82 X 7.1 Energy dependence of the total cross section of the 12 C(p, 7r+) reaction lead-ing to three final states of 13 C plotted versus the center of mass energy. . . 85 7 .2 Reduced total cross section, as explained in the text, as well as the total cross section for the 16 O(p, 7r+) reaction leading to several different states of 17 O*. 87 7.3 Angle integrated differential cross section of the 16 O(p, 7r+)X continuum ver-sus center of mass energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.1 Analyzing powers of the continuum reaction versus missing four-momentum transfer squared. . . . . . . . . . . . . . . ... 9.1 4°Ca(p, 7r+)41 Cag.s. calculations of Tsangarides. 9.2 12 C(p, 7r+)13 Cg.s. calculation of Tsangarides ... 9.3 A collection of DWBA analyzing power results for the 12 C(p, 7r+)13 Cg.s. re-95 98 99 action. . . . . . . .· . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 100 9.4 The two nucleon model and_ PWBA diagrams used by Keister and Kisslinger. 102 9.5 12 C(p, 7r+)13 Cg.s. calculation at Tp = 200 MeV by Keister and Kisslinger. . 103 9.6 Pre and post-emission diagrams calculated in the TNM model of Iqbal and Walker. . ...................................... 105 9.7 Two nucleon model calculation by Iqbal and Walker for the 12 C(p, 7r+)13 C9_50 reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 9.8 Full calculation of the 3He(p, 7r+)4Heg.s. reaction at Tp = 200 MeV with the ORCHID model. .................................. 108 9.9 PWBA calculations of the 3He(p, 7r+)4Heg.s. reaction showing the sensitivity of the ORCHID model to the type of bound state wave function used ..... 110 9.10 Relativistic stripping calculation of the 16 O(p,7r+) 17 Og.s. reaction by Cooper and Sherif. . .................................... 111 9.11 Relativistic single nucleon model calculation by Cooper and de Takacsy. 113 9.12 Relativistic stripping calculation for the 16 O(p, 7r+)17 Og.s. reaction by Cooper and Matsuyama at 200, 250, 350 and 450 MeV .................. 114 9.13 Infinite series of diagrams for the ~-hole stripping calculation of Cooper and Matsuyama . . .................................... 115 xi ' List of Tables 3.1 Sources of error, and their assigned values for the 16 O(p, 1r+)17 O* experiment. 40 B.1 A list of differential cross sections and analyzing powers for the 7Li(p, 1r±) reactions leading to some final states of 8 Li* and 8 B*. . ............ 156 B.2 A list of values for the differential cross sections and total cross sections of the 12 C(p, 1r+) reaction leading to various final states of 13 C* .......... 158 B.3 Differential cross sections for selected final states of the 13 C(p, 1r±) reactions. 159 B.4 A listing of the states of 17 0* by analyzing power category . . . . . . . . . 161 B.5 A list of differential cross sections, analyzing powers and total cross sections for the 16 O(p, 1r+) reaction leading to some final states of 17 O*. . . . . . . .. 162 C.1 A list of values for the double differential cross sections of the 13C(p, 1r±)X reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 C.2 A list of values for the double differential cross sections and analyzing powers of the 16 O(p, 1r+)x reaction ... .. .......... . ............ . 171 xii Chapter 1 Introduction 1.1 Motivation for Investigating (p, 1r) Reactions It has been approximately 17 years since the first exclusiv e (p, 1r+) angular distributions were obtained with the Uppsala University cyclotron in Sweden [Da71]. As figure 1.1 shows, different energy levels of the residual 13 C nucleus are populated with differing strengths, and the relative population of these states depends on the scattering angle. Over the next few years, the reaction was studied more intensely, and it was hoped that exclusive (p , 1r) reactions on light nuclei would eventually become a useful spectroscopic tool for study-ing the high momentum components of nuclear wave functi ons provided that the reaction mechanism was well understood. This is because the exclusive (p, 1r) reaction is charac-terized by a momentum transfer that is large compared to the nuclear Fermi momentum. Unfortunately, this problem has turned out to be more difficult than was first envisaged. Although the reaction mechanism has proved to be more complicated than was first imagined, the exclusive (p, 1r) reaction has continued to receive experimental and theoreti-cal scrutiny. Such an effort is justified on the ground that an answer to the problem of how the nucleus coherently absorbs the large momentum transfer characteristic of (p, 1r) reactions will be important to the study of large momentum transfer processes in general. However , a key problem complicating the study of the (p, 1r) reaction is the interplay between reaction mechanism and nuclear structure. Any hope of tapping the wealth of information hidden in the exclusive (p, 1r) reaction hinges on our ability to unravel the underlying reaction mech-anism from the nuclear structure effects. Since this problem has not yet been solved , some 1 . 400 200 12ccP,n1 13c ,s• lab . . .. .. . . ' 7~ HO ..... , -~·-,!,() ., . . I 761 .. . .. . .. ' . ··· ..• ·· ••• • l l { ......... •• • • .......... !:~:--:.,. !':~~-------£ O~-+--+---+-i-+--+--+---+----1i:-:--:-:-·+ ··-··~··_t--+--+---+--i-+--+--+---+-j .,.bl~ 100 "~ 50 12C(p,n,1lc 90° lab. + + ++ + + + ++++ + ++ + + + + ++ 0 L-_ ..... 3----2L--..L.1 ---'o-'---:-2_____..__.,_, ---'-s':-....._~e:--..__~,o=-...._-:,2:---'.__7:,,~-::,s~ Figure 1.1: Pioneering 12 C(p , rr+) 13 C* spectra at Tp = 185 MeV shown as a function of the excitation energy of the residual 13 C nucleus. This figure is taken from reference [Da71] and all errors shown are statistical. 2 experimenters have simply made use of the large momentum transfer reached in the (p, 1r-) [Ca87a,Gr84] and (p, 1r+) [Az87,Ko87] reactions as a spectroscopic tool for the discovery of previously unidentified high excitation states. 1.2 Previous Experimental Results Most of the early interest in (p, 1r) reactions was in positi ve pion production. This was partly because the differential cross section of the (p, 1r+) reaction is large enough so that it can be readily studied experimentally. In addition, (p, 1r+) angular distributions exhibit dips and wiggles whose shapes can vary greatly between different nuclear final states (see figure 1.2). The (p, 1r-) distributions, on the other hand, have considerably less spectacular features, and their differential cross sections are at least a factor of ten smaller than the corresponding (p,1r+) reactions. Thus, the (p,1r-) reaction was largely ignored by early experimenters. Interest in (p, 1r-) reactions was recently heightened by the results of a systematic study at the Indiana University Cyclotron Facility (IUCF) that revealed an unexpectedly strong selectivity of the reaction for the population of a closely spaced cluster of high-spin two-particle one-hole (2p-lh) final states [Vi83] (shown in figure 1.3). This feature was sub-sequently explained within the context of a NN - NN1r- reaction model [Br83]. Many further signatures of a NN - NN1r- process in the (p, 1r-) reaction mechanism were also seen at IUCF, such as the behavior of the analyzing powers of the 12 •13 •14 C(p, 1r-)13 •14 •15 0g .s. transitions [J a82] and the stable analyzing power shape for (p, 1r-) reactions to high-spin stretched 2p-lh states on a variety of nuclear targets [To85]. Thus, some people now believe that the (p, 1r-) reaction is reasonably well described by a NN - NN1r- reaction mechanism [Thr87]. Ironically, the reaction mechanism of the experimentall y more easily accessible (p , 1r+) reaction is less well understood. This is partly because stripping mechanisms, which can contribute to the (p, 1r+) reaction, can not directly contribute to the (p, 1r-) reaction because of charge conservation. The stripping process is based on an analogy with another high momentum transfer process, the ( d,p) reaction, and is the simplest possible model of the (p , 7r+) reaction ( shown in figure 1.4 ). Despite evermore sophisticated calculations of nuclear (p, 1r+) reactions [Al87,Cp86a,Iq85,Ke84], agreement between calculation and experiment is 3 / 30 60 90 120 150 180 8,, (deg) Figure 1.2: Schematic representation of the angular distribution data for a variety of (p, ,r+) reactions. The curves correspond to: a) 12C(p, ,r+) 13 Cg.s. at 200 MeV, b) 4°Ca(p, ,r+) 41 Cag.s. at 200 MeV, c) 9 Be(p, ,r+) 10 Be3_0 at 185 MeV, d) 9 Be(p , ,r+) 10 Beg.s. at 185 MeV, e) 16 0(p,1r+) 17 0 3_8 at 185 MeV, f) 9 Be(p,1r-) 1°C3_0 at 185 MeV, g) 13 C(p,1r-) 14 0g .s. at 185 MeV , h) 9 Be(p, ,r-) 1°Cg.s. at 185 MeV. This figure is taken from reference [Fe81]. 4 480 I I I I I I I I I 48 Ti (p, '77"+ t9Ti Ep= 206 MeV 0 320 ~\ elab= 30 .. 1'1 160 I I 11 11 - ,''\ I ~~¼\ 0 ' I .Q 105 11 C I I ,, ' • I -I~ - 11 u.J 48Co (p, ir-) 49 Ti I' -c I d Ep= 206 Mej ,:, b 70 1,' 1 N ,:, 3~ 0---:--,---,-~1:---,,--,--,--,--r--r-~--i-~I -,--,-..:..:.-.....,:...-1 15.0 10.0 5.0 0.0 Excitation Energy (MeV) Figure 1.3: (p, rr+) and (p, rr-) spectra leading to the same final nucleus showing the pre-viously unsuspected (p, rr-) selectivity. This figure is taken from reference [Vi83]. 5 only fragmentary, and systematic studies of a large number of cases will likely be necessary to gain a full understanding of the (p, 11"+) reaction mechanism. One of the first major discoveries about the (p, 11"+) reaction was made at TRIUMF [Au78). Using a polarized proton beam, it was determined that the analyzing powers of the (p, 11"+) reactions studied are very similar to that of the pp -+ d7l"+ reaction after transformation to the nuclear kinematical frame (see figure 1.5). Although, subsequent exceptions to this general behavior were found [Sj81a,Lo82c,Zi85), the hypothesis that the (p, 11"+) reaction is similarly explained by a NN -+ NN7l"+ process occurring within the nuclear environment is still very appealing. More evidence is still necessary to confirm or refute this hypothesis. Measurements of the energy dependence of the (p, 11"+) differential cross sections were also made. Most of this work concentrated on the (p, 11"+) reaction near threshold. As shown in figure 1.2, in this energy range the shape of the angular distribution depends strongly upon the nuclear state selected. For an angular distribution which falls smoothly with angle, it was found that the differential cross section rises uniformly with energy near threshold (see figure 1.6). Later it was shown that the differential cross section of this reaction rises smoothly up to the ~1232 invariant mass, and then falls slowly thereafter (see figure 1.7). For angular distributions with dips and bumps, however, the energy dependence was not extensively studied, and it was not known whether all (p, 11"+) reactions exhibit the same energy dependence. Furthermore, the energy dependence of the (p, 11"-) reaction, whose reaction mechanism is considered by some to be already understood, is not known in this energy range [Hoi81). Of major importance to the study of the (p, 1r+) and (p, 1r-) reaction mechanisms are studies in the ~l232 resonance region using target nuclei whose structure is known with some reliability. In this energy region signatures of the ~1232 resonance via the NN -+ NN 71" reaction, if present, should be the least ambiguous. This should make the separation of nuclear structure effects from the those of the reaction mechanism more reliable, so such measurements should aid in the understanding of the (p, 71") reaction mechanism. A simple calculation shows that the peak of the ~ 1232 excitation will occur at a beam energy of 321 Me V if the beam proton and 12 C target combine to form a mass 13 nucleus with one nucleon excited to a mass of 1232 MeV. Experimentally, most of the work on targets heavier than 3He has been near the pion 6 p Stripping Model H7TN n A (Z,N) (p, 7r+) A(Z,N) (d,p) - - - --rr+ A+I (Z,N+ I) A+I (Z,N+I) Figure 1.4: Stripping model diagrams for the A(p,11"+)A + 1 and A(d,p)A+l reactions. The shaded ovals indicate optical potential distortions. This figure is taken from reference [Ts79]. 7 -•pp- '7Td. -0 ·2 A'f t -0 ·4 f*k -0 ·6 10 t 0 Be1, 10 -0 ·8 A Be(3-3 • 13c • f f Heer(B) -1·0 0 30 60 90 120 150 180 LAB. ANGLE (DECREES) Figure 1.5: Analyzing powers for some (p, ,r+) tr ansitions : 9 Be(p, 1r+)10 Beg.s., 9 Be(p, 11'+)10Be3_4 , and 12C(p, 11'+)13 C*(average of 3 excited states). Also shown by the solid line is the analyzing power of the pp --+ d1!'+ reaction (kinematically transformed). This figure is taken from reference [Jo79]. 8 -.... V'l ' ..0 C ....... IO 450 500 550 600 qcm (MeV/c) TP (MeV lab) • 145 4 r • 150 6 l . 151 2 x 153.8 [o0 159.1 160.1 • 165 .7 r t. 182 .0 · h 182.5 197.4 650 700 Figure 1.6: 10B(p, 1r+)11 Bg.s . differential cross sections at seven energies plotted as a function of the momentum transfer. The curves are best fits to the data using Legendre polynomial s; each curve is labeled with the corresponding pion center -of-mass energy. This figure is taken from reference [Pil79]. 9 10 I ,oa' +l 118 t p. n ' EJ. .-···· t q<• ·- ··- , S 10 HeY/( __ a SSO _ o SM --- • ,so /~,--~-~ l' ... ____ , -.__ __ . __ ---200 400 600 800 Tp (MeV) Figure 1. 7: Differential cross sections of the 10 B(p, ,r+ )11 Bg .s. reaction versus incident proton energy at four different fixed three-momentum transfers. The arrow denotes the ~1232 invariant mass . This figure is taken from reference [Cv81]. production threshold, in the region of 150 to 250 MeV, alt hough there have been a lim-ited number of measurements at higher energies, primarily in the region above 600 MeV [Fe81]. On 12C, which is experimentally one of the most studied targets, there is a gap between 250 and 800 MeV in which the only angular distri bution that has been obtained is for the 12C(p,,r+) 13Cg.s. reaction via the time reversed (,r+ ,p) reaction at an equivalent proton energy of 332 MeV [An81]. Thus, there is a large dynamic range in which very few measurements have been taken for either the (p, ,r+) or (p, ,r-) reaction. Similarly, it has not been shown whether the (p, ,r-) reaction exhibits an energy dependence similar to that of the (p, ,r+) reaction. It would thus be desirable to have complete measurements across the Ll1232 region for both the (p, ,r+) and (p, ,r-) reaction s for the investigation of such questions relating to the dynamical behavior of the two pro cesses. This thesis contains the results of a study performed at TRIUMF to learn more about the (p , ,r+) and (p, ,r-) reactions in the energy region where the effects of the ~ 1232 resonance should be the most pronounced. The target nuclei 12 C and 160 were chosen because their closed shell structure simplifies theoretical calculations, and therefore the results of this 10 investigation should be easier to interpret. Data were also collected with a 7Li nucleus, for reasons to be explained later. The polarization measurements taken with the 160 and 7Li nuclei are the first ever obtained for a (p, 11"+) reaction on a nucleus with A > 2 in this energy range. In addition, the differential cross section of the 13 C(p, 11"-)14 0* and 13C(p, 11"+)14 C* reactions were studied at a constant four-momentum transfer squared of t = 0.50 GeV2 /c 2 • By choosing mirror final states, effects due to differences in the final state nuclear structure are minimized, and any differences in the energy behavior of the (p, 11"-) and (p, 11"+) differential cross sections at the same four-momentum transfer should reflect differences in reaction mechanism behavior rather th an nuclear structure . 11 Chapter 2 The Experiment To elucidate the role of the ~I232 resonance in the (p, rr+) and (p, rr-) reactions, three ex-periments were performed at TRIUMF using the Medium Resolution Spectrometer (MRS) with polarized and unpolarized proton beams over a period of three years. In this chapter the various experimental components and techniques are presented. 2.1 Selection of the Proton Beam The TRIUMF cyclotron is a sector focussing isochronous cyclotron [Cr77] which accelerates H- ions. The external beam energy is chosen by appropriately setting the location of a stripper foil located inside the TRIUMF cyclotron. As the H- ions pass through the foil, the two electrons are stripped off, and the positive charge resulting of the protons causes them to naturally exit the cyclotron. Proton beams with energy between 185 and 508 Me V kinetic energy are available. Although the cyclotron is capable of producing up to 140 µA of beam, during unpolarized running periods almost all of this beam is transported to the meson hall, and in most cases less than 100 nA of beam is transported down beam line 4B into the proton hall, where the MRS is located. To keep within this intensity when 140 µA of normal unpolarized n- beam is present within the cyclotron , a whisker foil of 0.001" radius is used , but during polarized beam periods when less than 1 µA of circulating n-beam is present in the cyclotron , a larger foil of 0.030" width and 0.001" thickness can be used. The beam intensity is selected either by raising or lowering the stripper to intercept a portion of then- beam, or by varying the beam height at the stripper location by means 12 of the magnetic field trim coils inside the cyclotron. 2.2 Measurement of the Beam Polarization The polarization of the proton beam is monitored continuou sly by an in-beam polarimeter (IBP) located on beam line 4B in the proton hall (see figure 2.1). For the 12 C(p, 1r+)13 C and 13 C(p, 1r±) experiments polarimeter #1 was used. For the 16 0(p, 1r+)17 0 experiment , however, a riew polarimeter was used which is located downstream of polarimeter #1. The two polarimeters operate in an identical manner, each consisting of a CH2 target of 1.383 mg/cm 2 thickness and two pairs of counter telescopes, each in coincidence with a recoil counter, that count proton-proton elastic scattering event s (see figure 2.2). The beam polarization is given by the equation p = #Left - #Right AcH2 (#Left + #Right) (2.1) where Actt 2 is the analyzing power of proton elastic scattering on CH2, This number is determined for the incident proton energy from a fit to thr ee AcH2 / Att calibration points [Ab85] as shown in figure 2.3. The value, AH, is determined from a phase shift analysis of p-p elastic scattering data [Ar87]. For the polarized proton experiment, beam polarization was typically 73% at 250 Me V, and approximately 60% at 354 and 489 Me V. This was a lower than the usual beam polarization, and was due to problems with the polarized ion source during the experiment. The uncertainty in the beam polarization is estimated to be approximately 1.5%, as determined from the accuracy of the p-p elastic scattering analyzing powers, and from the accuracy to which the three calibration points in figure 2.3 are known. 2.3 The Principle of Dispersion Matching Located between the two in-beam polarimeters is the inter mediate beam focus , 4BTL The characteristics of the final beam spot are measured with the use of a wire chamber monitor which can be remotely inserted into the proton beam at this location. The elements of beam line 4B are tuned to produce either an achromatic tu ne at 4BT1, which has a typical beam spot size of 2mm x 2mm, or a dispersed tune. A dispersed tune is one with the protons distributed according to their momentum along the length of the beam spot and 13 , ....... --., r.:::--:--:--~ ..... ,.. 4""·"'. --:,,-, _.-. . ~'"", -.:- , -:-••• --:_.,,.::-:-,-.-r:-. • -:-, .,,-:-.. :-: ••• ;-;:-.c-::.--::-, ,. .--=--:----:-,, •••. ,-.. --;-,~,:-;.~.-;.:;-, ..... .:--:,-:-. •••--:-• .,:-:. ,-:-.:.r--:-, .'-.. ! L ; . • • . • , . .. ., • . · . > . ' L ' .. . • . ....... . ..,.,~.,., ,..., , •.~ .. ., ••t • " .,.r•'•~'• .. • . ... ,..,, .•,• •.• • -111,1..a •••• ,, / - 1'1• "ICIIJtOa .. ... , / IL4C NEUTRON ~REA -....., .... _ ... , .. -....... •~ .. · ......... ·.· .. •.•······ ··-............. ··"~·~·-· .... ··~· .. -.. • .:. . • ... -....... .:·,, --.... , .. Figure 2.1: TRIUMF Proton Hall and Beam line 4B. 14 -~ ~) . ,, , ... R3 L2 L1 BEAM I l1•l2·l3 • ACCl~NTALS R1·R2·R3 CH2 ACCl~NTALS TARGET R2 RI L3 Figure 2.2: Schematic of the Beam line 4B In-Beam Polarimeter. 1.00 ~-------'- ____ _.__ __ _,_ ___ --+ 0.98 ::c:0.96 <l:: ....___,__N :r u <l:: 0.94 0.92 ! I 0.90 ~---------r-------r----- , 150 250 350 450 550 T (MeV) p Figure 2.3: Interpolated AcH2 / AH .curve for the beam line 4B In-Beam Polarimeter . 15 perpendicular to the scattering plane. It is advantageous to use a dispersed tune in order to fully utilize the resolution of the MRS. If one places th e dispersed beam spot on the experimental target such that the highest momentum protons are located at the top of the beam spot, and the lowest momentum protons are at the bottom, and if the momentum dispersion of the produced pions is exactly the same as the dispersion of the spectrometer's dipole magnet, then pions produced from the large momentum protons will fall on the same location of the spectrometer's focal plane as the pions produ ced from the small momentum protons. In effect, this reduces the momentum spread of the proton beam to zero, and the finite experimental resolution obtained will be due to the intrinsic resolving power of the spectrometer. If an achromatic tune is used, the resolution obtained by the MRS will be determined primarily by the momentum spread of the proto n beam. The condition for dispersion matching is determined from the kinematics of the reaction studied, and from the optical properties of the spectrometer. The beam tune dispersion required is where · d = -( Ds )(PB)( dps )MR Ms PS dpB (2.2) Ds/Ms = dispersion to magnification ratio of the spectrometer, which is 11 cm/% for the MRS PB = momentum of the proton beam PS = momentum of the central ray through the spectrometer, in this case pions (dps/dpB)MR = amount that the scattered particle's momentum changes when the beam momentum is changed but the recoil mass is held constant. This quantity is determined from relativistic kinematics. The length of the beam spot on the experimental target is determined by the product of the ()nergy spread of the proton beam from the cyclotron and the dispersion of the beam line tune. If the cyclotron beam has a momentum spread of 0.1 %~P /P, then a -20 cm/% tune will produce a beam spot length of 2 cm. If the beam produced by the cyclotron has a considerably larger momentum spread, then the beam spot length will be larger than the 2.5 cm length that can be reliably handled by the beam line. Using a larger beam spot would result in abnormally large backgrounds caused by the beam scattering in the beam pipe, and this scattering would adversely affect the accuracy of the beam current 16 normalization. In this case, the only way to reduce the size of the beam spot is to reduce the dispersion of the beam line tune. Although the (p, 1r) reaction at 354 MeV requires a beam dispersion of -23 cm/% for perfect dispersion matching, in most cases the momentum spread of the proton beam only allowed a dispersion of -12 cm/% to be used. Thus, the resolution obtained by the MRS was not as good as it could have been if perfect dispersion matching was obtained. In one instance during data taking the momentum spread of the beam from the cyclotron was so large that a dispersion of only -8 cm/% could be safely achieved. Located between 4BT1, where the first momentum focus is formed, and 4BT2 where the experimental target is located, is the twister. At 4BT1 the beam dispersion is in the horizontal plane. However, since the MRS is a vertical bending spectrometer, the dispersion of the proton beam on the experimental target must be in the vertical plane. This rotation is accomplished by a set of six 4" quadrupoles called the twister. The effect of the twister is to transfer the focus from 4BT1 to 4BT2 with a magnificati on of 1, and at the same time to exchange the horizontal and vertical phase space. Other than the 90° rotation of the beam spot, no other characteristics of the beam are changed between 4BT1 and 4BT2. 2.4 Experimental Target The experimental target is located at 4BT2 in a scattering chamber under continuous vacuum. The location and size of the beam spot (typically 2.5cm x 0.3cm XY in dispersed mode) was visually monitored periodically with a ZnS scint illator momentarily located at the target position. For this series of experiments the following targets were used: Research grade natural carbon target of 92mg/cm 2 thickne ss, 13 C target of 99% enrichment and 94 mg/cm 2 thickness, 7Li16 O1 H target of 100 mg/cm 2 thickness, 7 Li target of 208 mg/cm 2 thickness. The systematic error corresponding to non-uniformities in these target thicknesses, and errors in the measurement of these thicknesses, is estimat ed to be less than 1 %. When the 7 Li16 O1 H target was used, the location of events in t he pion focal plane due to the 7Li(p,1r+) 8Li* reaction interfered with the most highly excited states of the 16 O(p,1r+) 17 O* reaction at only the most forward angles. For these angles, data from the metallic 7Li target 17 were collected and subtracted from the 7Li 160 1 H target data . In order to take advantage of the resolution available by the MRS, the target angle with respect to the beam was chosen at each spectrometer angle setting so that the maximum energy loss of the proton beam in the target would be appro ximately equal to the maximum energy loss of the detected pions. An error of 2° in the targe t angle calibration corresponds to a relative uncertainty in the target thickness of about 4%. Because of reliability prob-lems associated with the target angle readout system duri ng the oxygen experiment, the uncertainty in the effective target thickness for that data set is estimated to be ±14%. This uncertainty was estimated by making two measurements at the same spectrometer angle and proton energy in which the target position and spectr ometer angle were moved and then reset to their original positions. Any difference between the two measurements was attributed to the error in obtaining the original target posit ion. 2.5 The Medium Resolution Spectrometer The MRS, as shown in figure 2.4, is a 1.4 GeV /c Quadrupole-Dipole system. The purpose of the quadrupole magnet is to focus the scattered particle beam so that the solid angle of the spectrometer is not limited by the geometrical acceptance of the dipole magnet aperture. Therefore, the ratio of quadrupole to dipole field strengths must be optimized for proper focussing of the scattered pions, and this ratio must be kept constant within the experiment, as the dipole field is changed, to assure that focussing is maintained. This ratio is determined by analyzing the trajectory of each scattered particle through the spectrometer, and forming a scatter plot of the particle's position on the spectromet er focal plane (XF) versus the angle in the bend plane at which the particle's trajectory crosses the focal plane (Ope). On this plot, the focal plane position will be globally independent of Ope if the focal plane is actually located at the position used by the on-line , softwa re calculation. It is customary for all experimenters to adjust the Q/D ratio so that the MRS focal plane is always placed at the same physical location. 18 1-1 (l) ..0 s Cll .c u bJ) -~ 1-1 (l) Cll tJ C/) 1-1 (l) ..0 s Cll ..c u "O r..i 0 (l) :>-M (l) (/) (/) (l) :>-S2 S1 Figure 2.4: The Medium Resolution Spectrometer. 2.6 Spectrometer Detection System The spectrometer detection system consists of a multiwire drift chamber located in front of the spectrometer's entrance quadrupole magnet (the Front End Chamber or FEC), and two vertical drift chambers (VDC) followed by two planes of plastic scintillators located near the focal plane of the spectrometer . Each of these components will be discussed in detail according to their position along the scattered particle trajectory. 2.6.1 Front End Chamber The FEC consists of four wire planes, giving position measu rements in the vertical {XO, XO' in the spectrometer bend plane) and horizontal {YO, YO' in the non-bend plane) directions. Each plane consists of 16 pairs of alternating anode and cathode wires with the primed 19 planes offset from the unprimed planes by one half of the anode spacing. This indicates whether the incident particle passed to the left or to the right of a struck wire, and also allows off-line interpolation of the particle position between the wires using drift times to an accuracy of 0.5 mm. These interpolated particle positions are labelled XO and YO. Software cuts are placed on the FEC quantities XO and YO during the off-line event-by-event analysis to define the spectrometer's geometric acceptance. 2.6.2 Veto Scintillators There are two scintillators located adjacent to the entrance to the dipole magnet. If the acceptance is not limited by the FEC, then the slit veto scintillators will define the accep-tance of the MRS in the non-bend plane. For the experimen t s of this work, however, it was the FEC which provided the acceptance definition. The dipole vessel veto scintillator which lines the radial surface of the dipole magnet vessel serves as a veto of events which scatter off of the inner radial surface of the dipole magnet. 2.6.3 Vertical Drift Chambers The most important elements of the MRS focal plane instrumentation are the two VDCs, which are placed along the bend plane at 45° with respect to the scattered pion trajectory through the spectrometer. Each VDC consists of two crossed wire planes X and U which give positions in the bend plane (X) and the 30° to X directions. During the off-line analysis this information is transformed into perpendicular X and Y planes (Xl, Yl and X2, Y2) with a resolution of 150 µm in the X direction. Each plane in the lower chamber (VDCl, closest to the focal plane) contains 160 wires while each plane in the upper chamber (VDC2) contains 176 wires. 2.6.4 Focal Plane Scintillators Ten focal plane scintillator paddles are located directly above the VD Cs. If desired, a portion of the spectrometer focal plane can be ignored by turning off the appropriate paddle. A clock (TDC - Time to Digital Converter) started by the OR of these 10 scintillators, and stopped by a registered event in the FEC, provides time of flight information through the spectrometer. Hardware cuts are placed on this quantity via the DACS on-line aquisition 20 system [Ti84] to ensure that only events with a time of flight characteristic of a pion are written on magnetic tape. In addition, pulse height information via an ADC (Analog to Digital Converter) on each of the ten paddle scintillators provides a measure of the particle's energy loss within the scintillator. This information was used in the off-line analysis to ensure that the events of interest were due to pion production. The information from another TDC, started by the FEC and stopped by the RF pulse from the cyclotron, ensured that the observed particle was produced by a beam burst from the cyclotron. A 1 to 4 ns wide pulse of beam is delivered from the cyclotron every 43 ns. Two large scintillators located at the entrance of the focal plane polarimeter form the second scintillator plane. A discriminator on the pulse height from this plane was used to prevent large pulse height events (mostly protons) from being written on magnetic tape. Energy loss and time of flight information from this scintillator provided a further off-line criterion for pion identification. The two planes of scintillators, along with one plane of the front end chamber (FEC), and one plane of the first of the two vertical drift chambe rs (VDCl) provided the event definition. Symbolically, this logical trigger definition was (XO+ XO'+ YO+ YO') X (FPO+ · · · + FP9) x Xl x (SlLo + SlHI) (2.3) A schematic of the aquistion electronics is shown in figure 2.5. 2.6.5 Determination of Aquisition System Live Time Because the CAMAC scalers of the MRS are not inhibited when the data aquisition system is busy, all scalers have to be corrected by the live time of the instrument. This live time was measured by two independent methods. The live time can be simply measured by taking the ratio of the number of busy latches that the data aquisition electronics generates, divided by the number of event triggers. The MRS electronics also contain provision for generating pseudo-events electronically; the ratio of the number of th ese pseudo-events actually seen by the aquisition system, divided by the number of pseudo-events generated, gives a second determination of the live time. In most cases the two different methods were within 4% of each other, so this is the value of the uncertainty quoted for the aquisition system live time. The live time varied between 60% and 98%, dependin g on the event rate. During the (p, 1r-) runs the live time was approximately 98%. 21 10 10' YO TO' Dipole Vet o ----------TP C tnout S11 t Veto TDC Input FPP 51.52 11 ( 1.0+11 I) F Front E.nd aeanticur {not •h own) Scintillator Prone E.nd Veto Sc Int. Sl ow Au ll.. Tri, select delay TRM IN, TkM,.__. ____ _. •elect width fast (' lf'llf Figure 2.5: Schematic figure of the data aquistion electronics for the MRS. 22 2.7 Beam Current Normalization Beam intensity was monitored by a secondary emission monitor (SEM), as well as with the in-beam polarimeter, both of which had been previously calibrated against a Faraday cup. The SEM is located downstream of 4BT2 just before the proton beam dump. It collects electrons from surface emission as the proton beam passes through several aluminum foils. The number of electrons emitted by each proton is proport ional to the energy loss of the proton within the foils (i.e. it depends upon proton velocity). When both monitors worked properly , agreement between the two monitors for total charge on target was about 2%. During the 16 O(p, ,r+)17O* experiment, the SEM consistently gave a lower value for total charge on target than the in-beam polarimeter by 17 ± 4%. This deviation is consistent with that seen previously by other experimenters using the MRS [Fr86], and the stability of the ratio between the two beam normalizations leads one to believe that it was due to the thin polarimeter target, which has been known to wrinkle after an extended time period in the beam. Therefore, the SEM was used for the total charge on target, and the beam normalization is believed to be accurate to within ±2%, the accuracy of the SEM calibration with respect to the Faraday cup. 23 Chapter 3 Data Analysis After an experiment was completed, magnetic tapes containing the detector information were shipped to the University of Regina for analysis. Since the MRS is a complex instru-ment, the data analysis was complicated. This chapter discusses the methodology involved in analyzing data taken with the MRS. 3.1 Drift Chamber Decoding Routine All information from the three MRS wire chambers was written on magnetic tape in the form of wire number and drift time for only the wires in each chamber that were struck. As the chambers are pressurized with an Argon-Isobutane-Methylal-Freon gas mixture, these are the times that it takes the isobutane ions to drift from the particle's trajectory through the wire chamber to the anode wires. The TDCs measuring the drift times are used in common stop mode (with the stop signal supplied by the MRS event trigger) so that long drift times correspond to small TDC values and small drift times correspond to large TDC values. This information is used to calculate the particle position at some median plane located within the chamber, and in the case of the VDCs, it allows the extraction of a trajectory angle through the chamber as well. The FEC consists of two planes of wires and a cathode plane, as shown in the top half of figure 3.1. These two wire planes allow the interpolation of the particle position on the median plane to an accuracy of 0.5 mm. Before any drift decoding proceeds, however, the TDC value for each FEC wire is checked to see if it is within an acceptable range, as shown 24 in figure 3.2, to eliminate random hit events. After this check, the particle position is inter-polated between each two adjacent FEC wires that were 'hi t ' , and then each interpolated position is checked to see if it is outside the MRS acceptance as defined by off-line software. This last check is used to determine which cluster should be ignored in the case of a multiple cluster event on the FEC. The event is discarded if more than one cluster is located within the MRS acceptance. Each VDC consists of one wire plane and two cathode planes, as shown in the bottom half of figure 3.1. Since the VDC is placed at 45° with respect to the particle trajectory , many wires within each VDC are 'hit'. The TDC value of each VDC wire is checked to see if it is less than a certain acceptable value, as shown in figure 3.3. Any cluster which contains fewer than 3 hit wires and more than 5 hit wires is ignored. In addition , any cluster that does not have a 'V ' in its time spectrum (two decreasing drift times followed by one longer drift time) is also ignored. This check is done because the ions' drift time to the anode wire should decrease until the particle passes through the wire plane, and then the drift time should increase. This is a very efficient method for discriminating between a bonafide cluster and a cluster due to a random hit withi n the same event. If all events with more than one cluster were rejected, then many otherwise good events would have to be discarded. Finally, the interpolated wire positions are checked to see if they are within the MRS momentum acceptance. 3.2 Determination of Wire Chamber Efficiencies As stated in the previous chapter, the trigger for putting an event on tape consisted of coincidences from the two planes of scintillators, along with any one plane of the FEC , as well as the X plane of VDCl, provided that the time of flight and energy loss in the top scintillator were within the set hardware limits. This arrangement provided a ratio of good events to bad events on each tape (as explained in section 3.1) of approximately 1:3. Although it was possible to increase the proportion of good events on tape by including more planes of the chambers into the event trigger, this would have inhibited the determination of the rate dependent efficiency of each of the drift chambers . The rate dependent efficiency 25 • 0 ,...o Cathode Wire ,,, ... Anod~ Wi re P.1rti c le Particle Cathode Plan e • • • • . . . hode Plan e FEC Prim~d Plan~ of Wi r~s 0 Cathod e Plane 0 • Unpri med Plan e of Wires VDC • • • • • • \ Cua rd Wire Figure 3.1: Cross section views of the Front End Chamber (FEC) and a focal plane Vertical Drift Chamber (VDC). 26 300------~--_,_ _____ ~~---250 i I 2001 j ,so~ w 100~ 50 I i 0 -+---~------"!"3=-----r------------.----+-fl) -+-J 100 150 200 250 300 TDC for a FEC wire 350 Figure 3.2: Spectrum of TDC times for one wire in the FEC . 400 30-+---~--...__ _ ___. _ _,__ _ _._ __ ~--"i'-25 20 i 15 I ~ > w 10 5 0 -f-----r----....---~---.-----r-----~---''+-0 50 100 150 200 250 300 350 TDC for a VDC wire Figure 3.3: Spectrum of TDC times for one wire in VDCl. 27 of the FEC, for example, was defined to be Number of Pion Events which had Good Hits in all 3 Chambers 1JFEC = Number of Pion Events which had Good Hits in VDCl and VDC2 (3.1) The efficiency of the two VDCs was defined in a similar, cyclic, manner. All events which were used for the determination of differential cross sections and analyzing powers were required to have a good hit in each chamber, and the number of events observed was corrected for the loss of events due to the wire chamber inefficiencies. Despite the high proportion of bad events on tape, a good hit in one chamber was highly correlated with a good hit in all three chambers. The product of the efficiency of all three chambers was typically 75% for (p, 7r+) runs, and 50% for (p, 71"-) runs, although at extreme back angles the product fell to as low as 35%. This decrease in efficiency was shared equally between all three chambers, and was primarily due to increased beam current during the (p, 7r-) runs, or at back angles, in order to reduce the running time, resulting in increased singles rates from background. The rejection of events with multiple clusters on the FEC is the primary contribution to a FEC rate dependent efficiency not equal to unity. Furthermore, there is a contribution to the FEC inefficiency from events with missing FEC hits since the MRS trigger requires a hit on only one plane of the FEC, and the TDC value of this hit is not checked to see if it is in the appropriate windows until the off-line analysis. To invest igate the effect of including one plane of the FEC and the X plane of VDCl in the MRS trigger, the efficiency of each wire chamber plane was calculated individually, but any effect of the inclusion of these elements in the event trigger was found to be much smaller than the ±2% uncertainty estimated for this efficiency calculation (see section A.2.2 for complete rate dependent efficiency information for a typical data taking run). Of the three chambers, the FEC always had a slightly lower efficiency than the two VDCs; this was expected since the singles rates on this chamber were the highest of all. 3.3 Particle Identification The particles which caused the events to be written on tape are identified by several dif-ferent means. A two dimensional plot of the time of flight through the spectrometer versus the energy loss in the focal plane paddle scintillators provides the first identification. Al-28 Figure 3.4: A plot of time of flight through the spectrometer versus energy loss in the focal plane paddles showing the relative location of pions and protons. This spectrum was taken from an early data taking run in which the hardware rejecti on of large pulse height events (protons) was not available. The hardware limits imposed upon the time of flight are clearly visible. though the energy loss in the paddles and the time of flight are both proportional to the particle velocity, the relatively small momentum acceptance characteristic of the magnetic spectrometer ensures that protons and pions are clearly separated in figure 3.4. All events shown in this figure satisfy all the requirements placed upon all of the spectrometer's cham-bers . If a plot is made in which the chamber information is ignored, then the pion peak . can not even be distinguished because of all of the random hits. The proton band shown in this plot is probably due to remaining accidental coincidences which have good hits in all of the chambers. Low energy protons due to other reactio ns would have a longer time of flight and would appear on the extreme left side of this figure if they were not eliminated by the hardware restrictions on the time of flight. A software box drawn around the pion peak shown in figure 3.4, as well as one formed 29 around a similar peak for the second plane of scintillators, ensures proper particle identi-fication. Additional cuts are placed on the TDC started by the FEC and stopped by the RF pulse from the cyclotron to ensure that the observed particle was produced by a beam burst from the cyclotron. This condition was not placed on the events shown in figure 3.4. 3.4 Trajectory Reconstruction The bend and non-bend plane angles (0 and</>) at which the scattered particle's trajectory crossed the spectrometer's focal plane are measured from the difference in VDC co-ordinates X2 - Xl and Y2 - Yl. These angles are also calculated from the drift times within each of the two VDCs. The redundancy of these three different measurements of 0 and </> allow for the off-line rejection of events whose trajectories had drast ically changed between VDCl and VDC2. This is a particularly valuable tool for rejecting events in which the pion had decayed. A ray-trace study of the MRS indicates that rays passing through the low momentum region of the focal plane are bent more than rays passing through the focal plane's high momentum region. Therefore, the bend-plane angle 0 has a dependence upon momentum which must be removed before software cuts may be placed to reject events whose angle was outside the geometric confines of the spectrometer. The variable Ope incorporates a correction proportional to the focal plane position (XF) to eliminate this dependence. Software cuts are also placed on the non-bend plane angle¢. Because (p, 1r-) reactions have very low cross sections, background problems warrant careful consideration. The FEC provides a high degree of redundancy as it allows a complete ray-trace through the spectrometer back to the target, a distance of about 11 m. Therefore, all background sources not originating from the illuminated target spot can be eliminated. In addition, when using a magnetic spectrometer the proton background problem associated with (p, 1r+) experiments is reduced in (p, 1r-) experiments due to the negative charge of the pions. This, coupled with the redundancy of the cuts applied in the off-line event-by -event analysis , made it possible to observe states with differential cross sections as low as 0.1 nb/sr in the 16 0(p,1r+) 170* experiment. The calculated target position in the vertical and horizo ntal directions is determined by 30 the relations XI = a * XO + b * Bpc YI= C *YO+ Yl (3.2) where a,b and c are parameters. Listings of the actual computer code used to calculate these, as well as the other variables, can be found in section A.1.2. A ray-trace study shows that XI must be independent of Bpc for all events originating from the target. XI and YI must also be configured to be independent of XO and YO so that the software cuts on XI and YI will not cut into the geometrical acceptance of the MRS defined by XO and YO. 3.5 Corrections for Improving the Resolution The focal plane co-ordinate of the event (XF) is calculated from the Xl position, taking into account the distance and orientation of the MRS focal plane with respect to VDCl. Several corrections are made to XF to increase the resolutio n obtained. A two dimensional plot of XF versus Bpc indicates that the focal plane positio n has a local dependence upon the angle at which the particle's trajectory crossed the focal plane of the spectrometer. This dependence is due to abberations in the MRS dipole's magnetic field and is corrected by adding quadratic terms in Bpc to the focal plane co-ordinate. The physical cause of this position dependence is illustrated in figure 3.5. A plot of focal plane position versus the horizontal FEC co-ordinate (YO) is essentially a plot of momentum versus pion scattering angle, and allows for a correction of the kinematic change in pion momentum across the ±2° angular acceptance of the MRS. This correction is proportional to Sin(BMRS) (3.3) where the symbols indicating the kinematical quantities are self explanatory. As this equa-tion shows, the amount of kinematical broadening is propor t ional to the mass of the target nucleus (mA), and is therefore much larger for the pp --t d1r+ calibration runs than for the nuclear (p, 1r) runs. Figure 3.6 shows how this kinematical broadening was eliminated for the pp - d1r+ reaction. A plot of vertical beam spot illumination (XI) versus the focal plane position is used to set the software correction for the dispersion mismatch caused by using a -12 cm/% or 31 Quadru pole Abbe ration Correctio ns > L ____________ _, Focal Plan e Figure 3.5: Schematic diagram showing the effect of magnetic field abberations upon the experimental resolution. These abberations are reduced by software corrections during the off-line analysis. This figure has been adapted from reference [Thr84]. 32 C 1000 0 (/) 0 CL 750 u w LL 500 I I . • 0 .. . . . ~ggg;, :: . . . . • o~• ... • . . . . • 0 CJ • • • • · • • o oa • · · · . • · • er Do• • · · · · · - o ~o · .. · : :-~~HD: :: . • •OCJOCJ• · • · • CJOD • • • : ~ffi;; : : : . · • o r:JOC • · · . 0 1100 .. . •OCQOa • • ··· DODO• · · •OOCJCJ •• · • 0 Ca• • , • ••DOD• •• . · :-9~5 g : : : . ·•one • - . : : ~80:,; . · • • • 0 0 • • · •OD• • . .• 0. -250+---~-~------~ .1200 2400 3600 4800 6000 ,--.. 0 >-......... C 1000 0 en 0 CL 750 u w LL 500 Focal Plane Position (XF) . • 0,. • . . cue.. . . • o Do • • · · • · • •OOC• • • • • • . : : ~ffig; : : .. : . . • • DC)QO • • • • • • • • · • • • OD a• • • • • • · • . · · • a CJOO • · · ... coco ... .. • • DCCC•• · · • • • ••• · : ; : : ; : : : : : : ; : : : : : . : : : : : • 0 oo • • • · • • • • • • • • • • • •ODOD• • • • • • • • • • • • • • • • • ' D 000 • ' ' ' ' • " ' ' 0 ' • • o 00 CJ• • • • • • CJ o D • • . . .. : : ;,e:-B;.;. : . . : ••CCC•• · • •• ••OCJC• •• • • • • •DC, 0 • • • • • • coo O • · · • • 0 0 • • · • ooa • . . • , • a a a • • , , 250--+----- ----------, 1200 2400 3600 4 800 6000 Foca l Plane Pos ition (XF) Figure 3.6: Plots of focal plane position (XF) versus horizontal FEC co-ordinate (YO) for the pp ..... d11"+ reaction before and after the kinematical correction is applied. A projection showing the effect of the correction on the focal plane resolution is shown above each plot. 33 smaller beam line tune. This correction becomes less effective as the quality of the beam energy spread deteriorates because the beam spot size becomes more circular in size as the dispersion of the tune is reduced . Four typical off-line, event by event analyzed pion spectra at 489 MeV after all resolution related corrections have been applied are shown in figure 3.7. Solid angle, energy loss, time of flight , target beam spot and particle trajectory conditions have been applied. The energy resolutions for these spectra were typically 200 ke V, and because of the imperfect dispersion matching of the spectrometer, was due primarily to the energy spread of the proton beam delivered from the TRIUMF cyclotron. In one run the resolution was 300 keV; this poorer energy resolution was due to a larger than usual energy spread of the incident proton beam from the TRIUMF cyclotron (0.35% 6.p/p instead of 0.2% 6.p/p ), resulting in a lower beam dispersion (-8 cm/%) being used. 3.6 Correction for Pion Decay Most of the muons resulting from pion decay within the spectrometer were eliminated via the beam spot, particle trajectory and solid angle cuts ; net events observed were then corrected for this pion decay loss within the spectrometer. This pion survival fraction is calculated by the relation ,,, _ e-lM/-rpc _ e-196.7/p 71"S - -where l = the path length of the MRS (11 m) M = the mass of the pion (139.57 MeV /c 2) T = the lifetime of the pion (26.02 ns) p = the momentum of the pion in MeV /c c = the speed of light in vacuum (0.2998 m/ns) and was approximately 35% at 250 MeV, 50% at 354 MeV, and 65% at 489 MeV. (3.4) It is not possible for the cuts imposed to reject those muons resulting from pions which decay close to the spectrometer focal plane . This means that the pion survival fraction shown above is only correct if an effective spectrometer path length shorter than the actual 11 m path length is used. However, no Monte Carlo calcula tions to determine this effective 34 w -0 C: -0 "' b N -0 40 20 e ~20° LAB 2008+--~~~ ............... - ...__,___._~_.___._ .... ........ __ 13C(p Irr+) 14c 1500 1000 500 1500 1000 500 1608-i--_.___._~~ ............... - ___________._~_.___._ .. ...... ... _ 160(p,rr+) 110 1200 800 400 Q._2 22 28 34 40 Excitation Energy (MeV) Figure 3.7: Typical off-line analyzed pion focal plane spectra at Tp = 489 MeV. The 16 O(p, 1!"+)17 0 spectrum was obtained at OLAB = 23°. 35 path length were performed, and there is therefore an error in the pion survival fraction used due to this difference between the actual and effective MRS path lengths. The uncertainty in the pion survival fraction w~ estimated from the numbe r of events located on the high momentum side of the ground state, which can only be populated by muons via pion decay or pion multiple scattering. For the data obtained in the 12C(p, rr+)13 C* and 13 C(p, rr±) experiments, these events were estimated to comprise approximately 5% of the total events on the focal plane, so this was taken to be the uncertainty in the pion survival fraction. For the data taken during the 16 O(p, rr+)17 O* experiment the RF timing, veto scintillator, and 0 and </J redundancy cuts were implemented for the first time, and the resulting spectra had far fewer events to the left of the ground state. The error in the pion survival fraction for these results was taken to be 3%. 3. 7 Determination of the MRS Solid Angle The spectrometer acceptance was calibrated at 500 Me V using the pp - drr+ reaction, whose cross section is known to an accuracy of ±2% [Gi85]. The proton energy was chosen so that pions from this reaction would have approximately the same momentum as pions from the 12 C(p, rr+)13 C* reaction at 354 MeV. (The momentum of pions produced from other reactions studied in this work is very similar to this, and the 12 C nucleus was chosen just as an example). The effective solid angle of the spectrometer, determined by this method, was 2.1 msr, with a standard deviation of 0.1 msr between independent calibrations for the first two experiments, and this was taken to be the uncertainty in the calibration. This solid angle was found to be independent of beam spot size and pion momentum ranging from 185 to 290 MeV /c within this same 6% uncertainty. For the oxygen experiment, the effective solid angle was determined by this method to be 2.8 msr, which compares well with the 3.0 msr geometric solid angle of the MRS spectrometer as determined by the FEC cuts. The 6% uncertainty used for the previous experiments was used again for this experiment as this is approximately the amount that the 2.8 msr effective solid angle differs from the 3.0 msr geometric solid angle. It is not understood why the solid angle used in the oxygen experiment differs so much from that used in the previous experiments. Since all data presented here are normalized to the pp - drr+ reaction, the quality of the data presented in this work should not be affected. 36 The effective solid angle as determined by this method is expected to be smaller than the geometric solid angle determined by the FEC because of scattering losses within the wire chambers, and reaction losses in the focal plane paddles. These effects would have to be included in a proper Monte Carlo analysis of the MRS geometric solid angle. Losses due to scattering off the dipole faces are expected to be small because of the use of the quadrupole magnet. 3.8 Calibration of the Focal Plane The shape of the spectrometer focal plane was measured with scans of the pp - d7r+ reaction peak by varying the spectrometer dipole magnetic field. A Legendre polynomial fit to the results of this scan (see figure 3.8) allowed the efficiency of each focal plane co-ordinate to be calculated, and all net counts observed in the off-line analysis were corrected for the decrease in collection efficiency away from the center point. An uncertainty of ±2% has been estimated for the accuracy of this Legendre polynomial fit from the uncertainties in the Legendre polynomial coefficients. 3.9 Calculation of Observables The differential cross section for one spin state is given by ~(i) = Net(i) (df!LAB) df!c.m. (Prot(i) )P1J1rs1JLIVE7JCH( i)1JFocD-f!MRS df!c.m. where Net = net counts after background subtraction Prot = number of spin up protons on target according to SEM calibration p = effective density of target in Nuclei/barn (taking into account the target angle) 1J1rs = pion survival factor 1JLIVE = data aquisition system live time 1JCH = product of FEC · VDCl · VDC2 efficiencies during spin up 'IJFOC = the efficiency of peak channel relative to the focal plane center D-f!MRS = solid angle of MRS in the LAB frame in steradians df!LAB/df!c.m. = jacobian of nucleon-nucleus frame The arrows indicate spin up and spin down quantities, respectively. 37 (3.5) u 0 LL. 0 .8 0.6 0.4 0.2 0 4500 9000 13500 18000 Focal Plane Position (XF) Figure 3.8: Legendre polynomial fit to the results of a pp -+ drr+ focal plane scan from the 16 O(p, rr+)17 O experiment. 38 Then the unpolarized differential cross section was calculated via the relation da _ ~(i) + ~(l) dn c.m. - 2 (3.6) since the polarization of spin up and spin down protons was measured to be equal. The statistical error in the unpolarized differential cross section is given by dCTerr = Net(j) Net(l) (Prot( j) )7Jch ( i)Factor )2 + -(P-r-ot_( _l )-) T/_ch_(_l )-F-ac-to-r-)2 (3.7) where anLAB Factor = P1J1rs1JLIVE1JFOc~i1MRS( df! ) c.m. This formula assumes that the net counts and the background counts are not correlated. In truth, many of these background counts are correlated to the net counts since there are bonafide events in the underlying continuum due to the inclusive pion production process . The error, however, in the calculation of these statistical errors is assumed to be small. The analyzing power is given by the relation A - ~(j) - ~(!) NO - P(d,t~m. (i) + di:.m. (l)) (3.8) where P denotes the polarization of the incident proton beam, and the statistical error in the analyzing power is given by 1 Aerr = p 2Net(j) 2 2Net(l) 2 ( (Net(i) + Net(!)) 2) Net(l) + ( (Net(j) + Net(!))2) Net(j) (3.9) Differential cross sections and analyzing powers (where available) may be found for all states investigated in appendix B, and for the continuum data in appendix C. 3.10 Error Analysis Typical systematic and relative errors for these experiments are summarized in table 3.1. All of the listed uncertainties have been discussed in the previous two chapters except th e uncertainty due to the inconsistent placement of cuts in the off-line event -by-event analysis. This uncertainty was estimated by analyzing some data twice, once with normal solid angle , beam spot, and particle trajectory cuts , and once with the se cuts set drastically different . This test determined the maximum sensitivity of the differential cross-sections presented here to errors in the data analysis. 39 Table 3.1: So urces of error , and their assigned values for the 16 O(p, 1r+)17 O* experiment. Systematic Uncertainties Solid Angle ±6% Pion Survival Factor 3% Uncertainty in pp ---+ d1r+ Cross Sections 2% Target Thickness 1% Total Systematic Uncertainty ±7% Relative Uncertainties Effective Target Thickness ±14% Maximum Sensitivity to Errors in the Data Analysis 8% Aquisition System Live Time 4% Integrated Beam Current 2% Wire Chamber Efficiency 2% Focal Plane Relative Efficiency 2% Total Relative Uncertainty ±17% 40 Chapter 4 Observations on the Experimental Spectra Because the (p, 1r) reaction is characterized by a momentum transfer that is large compared to the nuclear Fermi momentum, it can be used as a tool for_ the study of high excitation states which are difficult to reach with other reactions. This chapter discusses some of the states which were visible in the pion spectra taken in this series of experiments. The first experiment which was completed for this work investigated the 12 C(p, 1r+)13 C* reaction. A pion spectrum at Tp = 354MeV and (}LAB = 21° from this experiment is shown in figure 4.1. This figure is clearly dominated by the 9.50 MeV, 9/2+ state, which is predominantly of a stretched two particle-one hole configuration (2p-lh) with respect to the 12 Cg.s. core. This selectivity for the population of a particular state is similar to that previously reported in (p, 1r-) reactions [Vi83], and is in contrasf to the experimental spectrum of the same reaction at Tp = 200MeV and (}LAB = 25° shown in figure 4.2, in which the five lowest energy peaks all have approximately the same strength, regardless of the spin of the 13C configuration. The striking difference between these two figures indicates that this selectivity is a phenomenon which does not occur in all kinematical regions. Similar effects have been seen previously in other experiments at TRIUMF [Lo84b]. The narrowness and the centroid of the 3.68, 3.85 MeV cluster in figure 4.1 indicates 41 400 + N 12c(p, rr+) 13c• ' C1> I 0 T =354 MeV N I() p + ' C1> 0 =21° N LO 300 ' ll) LAB If) ll'l If) r--co +·+ I') NN (/) ,, -+-' I r--n §200 N ' C1> co r') '<tCD 0 co ,-.: r-: u CD I') + I + N 100 N N ' I() 0 --1-.-..i..,-..,...~-~----,=-.......------.----.------,----.------,------.-~ -2 2 6 10 14 18 22 26 Excitation Energy (MeV) Figure 4.1 : 12 C(p , ,r+) 13 C* focal plane spectrum. 42 '2c I :- (p "7T'~) C ~co ~N ' ;e~ Ep•200 MeV 8'-==25° ' a, .., ,-..;~ -• N r-:= • 8 a:; = N + co 0 0 ' N -..... a, = ,.., 0 2CO ,.,,;= ,.,; c.Q ,.,; er, ... a + 170 qy + = ICO c.Q I") ,._ = 6 4 Elcitation Energy (MeV) Figure 4.2: 12C(p , 71'+)13C* focal plane spectrum taken with two bites of the QDDM spec-trometer at IUCF . This picture is taken from reference [So80]. 43 ,2c (p, rr+) '3c 386 3 09 TP = 200 MeV gs l3t8 l 1 .\ 4 3 0 -Ex (MeV) Figure 4.3: 12 C(p, ,r+) 13 C· spectrum obtained at Tp = 200 MeV using the QDDM spec-trometer at IUCF. Because the momentum acceptance of the QDDM spectrometer is very small, only the region from 0 to 4 MeV can be observed within a single momentum bite. The asymmetric peak shapes indicate that the resolution obtained was determined mainly by proton straggling in the target. This figure was taken from reference [Be81). that this peak is dominated in strength by the single particle 3.85 MeV state, which has the higher spin. This agrees with the observations of Soga et al. [So81] at Tp = 156MeV, who were able to resolve the states of this cluster for the first time (see figure 4.3). In figure 4.1, the peaks at 11, 12 and 14 MeV previously reported by Dahlgren et al. [Da73b] at 185 MeV are also visible. The 21.4 MeV state, which has been recently reported to have an unusual zero analyzing power at 200 MeV [Ko87), is only clearly visible at forward angles as its differential cross section falls faster than that of the continuum at larger angles. 4.2 16 0(p, 1r+)17 0* Spectra The three spectra shown in figure 4.4 were taken at a fixed four-momentum transfer squared oft = 0.45GeV2 /c 2 • The states of 17 0 which dominate all three spectra are the ground state !+, and the 5.218 MeV ( r), 7.757 MeV v-, 15.78 MeV (1l-) and 17.1 MeV G-) excited states. Those spins which are within parenthesis are only tentative assignments. Note that the strongly populated states have known, or tentatively assigned, high spins, as expected from the large momentum transfer characteristic of this reaction. Thus, in this kinematical range, this reaction selectively populates high spin states in a manner similar 44 to the 12 C(p, 1r+)13 C* reaction. Because of the small momentum acceptance of the MRS Spectrometer, the 250 Me V spectrum shown in figure 4.4 is a composite of two separate momentum bites covering the full range of excitation energies shown. The broad high excitation peaks in the 354 and 489 MeV spectra are from the 7Li(p, 1r+)8Li reaction due to the LiOH target; the 250 MeV spectrum has had contributions due to this reaction subtracted from it. These three spectra look very similar because they were all taken at the same four-momentum transfer. The rough energy dependence of the reaction can be seen directly by comparing the y-axis scales in figure 4.4. Because of the close spacing of the 170 states, a peak fitting routine [Ro78] was used to extract differential cross section and analyzing power distributions for 23 different final states at each of the three energies. A spectrum showing a typical fit used to extract data for these states is shown in figure 4.5. The energy assignments for the stronger states labelled in figure 4.5 have an uncertainty of ±50 keV, and have been taken from reference [Aj86a]. 4.3 7Li(p, 1r+)8 Li* Spectra A 7Li(p, 1r+ )8Li* spectrum taken with the pure metallic 7Li target is shown in figure 4.6. Because of the small size of this nucleus, nuclear states are widely separated and few in number. All possible nuclear states of the 8Li nucleus are populated, so not much can be said about the selectivity of the (p, 1r+) reaction here. However, the nuclear structure of the 6.53 MeV excited state does exhibit some interesting behavior. Although this state is clearly visible in figure 4.6, there is no similarly populated sharp peak corresponding to its isospin analogue state in previously published 7Li(p, 1r-)8B* spectra [Ca87a,Ke86]. There must be some characteristic of the nuclear structure of this st ate which makes it inaccessible to the (p, 1r-) reaction. Pion spectra are shown for the 13 C(p, 1r±) reactions in figure 4.7, and for the 13 C(p, 1r+)14 C* reaction in figure 4.8. Both spectra shown in figure 4.7 are dominated by a 3- state near 6 MeV excitation, which is described by a two-particle one-hole configuration (2p-lh) with 45 160(p,7T+)170* t=0.45 GeV2/c 2 600-~.._._.._._~~.._._~--~~~ T =250 MeV p 400 e LA8= 680 ,,...--..,,. > 200 Q) 2 2 0 0 8 -~....__.___.__...~.......__..~~___.___,,~ .. .... ............... ---+ (J) 1500 _o S 1000 250 , 1 I T =354 MeV p 0 LA8=4Qo 0~1 3 7 Excitation 11 15 19 23 Energy (MeV) Figure 4.4: 16O(p, 11"+)170· focal plane spectra. 46 L'l ......, 40------~----------------'---......... _ __.___,_..._ i60(p,7T+) 170• 30 T =354 MeV p 8 =70° LAB r--.. LO r--.. t'--$1 0 §20 0 N ..... LO r--.. 0 0 0 r--.. co 0 10 I""') ..... 0) lO • '<t-I""') lO (]) co r--.. r--.. -.:t- '<t-I""') -.:t- - r--.. LO • r--.. N I""') ..... "' co lO co ..... lO '<t- - 0) I""') N r--.. co 0 CO I""') N ..... l{) '<t-l""')N 0 co .......... LO "' co . CT> -.:t-0 4- ................. ~.....c,J ....... ""'--llit-,'-l,-..z;a~J...#0,..at,..l,,.a....,..:L.4-..l.Jll,........,.&-.t,.L.l,-,l,,.J:......-a .......... ...Jo.....-~ -1 3 7 11 15 19 Excitation Energy (MeV) Figure 4.5: Final result of the peak fitting program showing all of the 17 0 states for which data have been extracted. The total fit to the spectrum, also shown here, included smaller peaks for which data have not been extracted. This spectrum has had background and contributions due to the continuum subtracted from it, and was then smoothed by a cubic spline routine. 47 120 + + 7Li(p,1r+)8Li· N I") 0 LO T =354 MeV 0 LO p N 0 =20° 90 0 N LAB + ..... CJ) 0'.) I") +-' 0 LO C 60 co I.D :::J 0) 0 0 u 30 0 ---------.----r~-,------r-..-----r--...-----.--r--~--,.---.....------,---,----+-- 2 0 2 4 6 8 10 12 14 Excitation Energy (MeV) Figure 4.6: 7Li(p,11'"+)81i• spectrum. The energy resolution is approximately 250 keV. respect to the 13 Cg.s.· As stated previously, at 250 MeV the momentum acceptance of the MRS spectrometer is not large enough to allow pion energies corresponding to transitions to states from zero to 23 MeV excitation to be collected simultaneously. At this energy, 13C(p, 11'"+)14 C* data were obtained with two magnetic field settings of the spectrometer, of which only data from the highest field setting are shown in figure 4.7. At 354 MeV, the acceptance of the spectrometer was large enough to view the entire energy range shown in figure 4.8. The high spin 11.67 and 14.87 MeV states dominate the (p, 11'"+) spectrum shown in figure 4.8, as one would expect considering the large momentum transfer of this reaction. Like the 21.4 MeV state of 13C, the 23.2 MeV state of 14C has been previously observed [Ko87) to have an unusual zero analyzing power. The absence of a strongly populated mirror state in 140 near 23 MeV excitation at 354 and 489 MeV indicates, by isospin arguments, that this is not a T=2 state, and confirms arguments presented in reference [Ko87]. There is, however, in figure 3.7, a broad structure of about 4 MeV width in the 13C(p, 11'"-) spectrum near 23 MeV excitation. This structure is prominent in a previously published spectrum obtained at 200 MeV [Ko87). There is a similar structure 48 (f) -+-' T =250 MeV 0 =29° p ~B 25-+---'-___._~_.___,_.__~__.____.~.~~~ 13C(p,rr-) 140* i 20 15 10 5 + 0 I .-t'1 0) co + N + N 0) 0) C 0.......-..,..... . .. --~~~~r,LaJJ!fJL-.~~~.._~11U14-~100____.___.__._~~_.__~_.__._i...__._~~ 8 13C(p;rr+) i4c• I t'1 80 60 40 20 0_1 + 0 0 0 0 t'1 co I I .- N 0) «t-o "'1 + CO N N 0 t'1 (X) cri (X) + I -.;;f--.;;f-.- CD II) .-0 -, 1 3 5 7 9 11 13 15 Excitation Energy (MeV) Figure 4.7: 250 MeV 13 C(p, 11"±) focal plane spectra. 49 160 13C( p ,-rr+) 14c• I LO N T =354 MeV I") BP =35° I " N '<t- co 120 LAB .-" I <.O t") .-.-Cl) t") ...... r--. C: 80 <.O :::J + 0 I + OLO u NN ·~ I t")~ .- ..... .-.-~N LO 0) nn 52 i~ + .. 40 0 "co 0 u ,1 <.O 0 0 -1 3 7 11 15 19 23 27 Excitation Energy (MeV) Figure 4.8: 354 MeV (p, ,r+) focal plane spectrum from the first run of the 13 C(p, 1r±) experiment . The spin assignment of the 11.67 and 14.87 MeV states is taken from reference [Ko87]. 50 structure near 25 MeV excitation energy in the 13 C(p, rr+) spectrum shown in figure 3.7. A broad structure has also been seen previously at 19 MeV excitation in the 9 Be(p , rr-) 10 C reaction [Lo82b]. The 13.50 and 14.05 MeV states of 14 C* shown in figure 4.8 are reasonably populated but are not listed in the nuclear level tables of Ajzenberg-Selove [Aj86b]. These states are also visible in the pion spectrum obtained in reference [Ko87] at 200 MeV. Because of the close spacing of the populated levels of 14C near 6 MeV , the peak fitting routine was once again used to deconvolute these states. This procedure was a necessity because of the poorer resolution spectra obtained in the second run of the 13 C(p, rr±) exper-iment, but was also performed on the spectra from the first run in order to be consistent. The poorer resolution in the second run of this experiment was due to the larger than usual energy spread of the proton beam already noted in sections 2.3 and 3.5. For the states shown in figure 4.7, the peak fitting routine was used to deconvolute the 6.09 MeV and 7.34 MeV states from the 6.73 MeV peak of 14 C. It should be noted that the 6.73 MeV state is close in energy to a cluster of other states (6.59, 6.90, 7.01 MeV). The deconvolution routine shows that these states are most probably weak in comparison to the 6.73 MeV state, so no attempt was made to subtract their strengths from the 6.73, 3~ peak. For the 13 C(p , rr-) spectra , no attempt was made to deconvolute the 6.79 MeV state of 14 0 from the 6.27 MeV peak because of poor statistics. 51 Chapter 5 Results This chapter presents some of the experimental results of Appendix B in graph form. Each experimental observable will be discussed separately in the following chapters, and will refer to the figures presented here. Because of the large amount of data presented in this work, figures for every final state have not been provided; the characteristics of all states can be represented by the few samples shown here. Data are presented in order according to the mass of the target nucleus and the excitation energy of the final nuclear state. 52 104 7Li(p,1r+)8Li ,...-.._ 2+ I,_ g.s., (/) 103 "" • ...0 C ......__,,. D • C ·•• D ,; 102 .... -0 A DA "" ... 12 • • b ... .... * -0 ... 1 100.7 0.6 0.5 0.4 0.3 t (GeV2/ c2) 1.0 --- - --- ·- · I,_ Q) 0.5 3 0 I (l_ • 0.0 C 01 • C :I :±II ! ! ·-N >. :I -0.5 i:i I :I ... :I 2 ' <( • & • - 1·n.7 0.6 0.5 0.4 0.3 t (GeV2/ c 2) Figure 5.1: Differential cross sections and analyzing powers for the 7Li(p, 1r+ )8Lig.s. reaction. Plotting symbols indicate the incoming proton energy and source of data as follows: A 200 MeV Reference [Ca86]; D 250 MeV [This Work]; • 354 MeV [This Work];* 489 MeV [This Work]. 53 ,.--.._ L (/) " ..0 C L 7L'( +)BL'* o I p '7f I 0.9808, 1+ 10 ~--~----0.7 0.6 0.5 0.4 0.3 t (GeV2/ c 2) 1. 0 .J..._ __ ____.L, ___ ....J..1 ___ --L'----+ 0.5-0 o_ 01 0.0-c N 0 -0.5 -C <( ... I I I 0.6 0.5 0.4 0.3 t (GeV2 / c2) Figure 5.2: Differential cross sections and analyzing powers for the 7Li(p, ,r+ )8Li0_9808 reac-tion. Plotting symbols are as in figure 5.1. 54 L Q) 0 Q_ 01 C N 0 C <( 104 --1----__.__ __ .___~---+ 7L·( +)sl·* I p,7T I 2.255, 3+ • • • * 1 1°o~.7--0~.6--0-.5---0~.4--0-.3 t (GeV2/c 2) 1. 0 -----·--------~·---~·-----,... 0.5-0.0--0.5--·- ~= - -· ·-,- - - -• !l!! i C / f ... . . . . I. i . ,.· ··o.. .-·· ··o. &.-· ······ ·&ll. '-. / &.! ... ... i ---I I I 0.6 0.5 0.4 0.3 t (GeV2/ c2) Figure 5.3: Differential cross sections and analyzing powers for the 7Li(p, 11"+ )8Li2.255 re-action. Plotting symbols are as in figure 5.1. Also shown are analyzing powers for the pp -+ d?r"+ reaction [Gi85,Hof83,Mat83,May85,Sah83] transformed to the nuclear kinemat-ical frame at equivalent center of mass energy and four-momentum transfer. The solid line indicates the pp-+ d?r"+ analyzing power at 200 MeV, the dotted line at 250 MeV, and th e dashed line at 354 MeV. The 489 MeV analyzing power is not shown for the sake of clarit y; it is quite flat and positive with a magnitude of approxima tely 0.25. 55 103 ,2C(p,1r+) 13c g.s . • i I ,. ,,--.... 102 c. I L • I Cl) "- . j ..0 I C ...__,, f ft iii 01 • C: tJ -0 D lg [J D "- 101 t i 2 b -0 !! rm~~£~ £ 1 10° 0.7 0.5 0.3 0.1 -0.1 t (GeV 2/ c2) Figure 5.4: Angular distributions of the 12C(p , 7r+)13Cg .s . reaction plotted versus the square of the four-momentum transfer (t). Plotting symbols indicate the source of data as follows: • [So81] 156 MeV; l:::, [Da73b] 185 MeV; A [Hoi80] 200 MeV; D [Lo84b] 250 MeV; [This Work] 250 MeV; • [This Work] 354 MeV; * [This Work] 489 MeV; o [Na82] 800 1'1eV. 56 104 ~? ...,., +)i3c· ! -c \ p '7T 3.09,3 .68 ,3.85 103 181 • ----I... D • ~· (/) • "- =;U I ..0 • c:, ~-C .:. J 0 C 0 ' 102 i :J .____,, • • D ;.... • f~ • C: ! "'O "- f :lQ:::lQ 0 b a a! ' "'O 101 2 T ' 10° - -- - · 0.7 0.5 0.3 0.1 -0.1 t (Ge V2/ c 2) Figure 5.5: Angular distributions of the 12 C(p, ,r+ )13 C3_09 ,3_68 ,3_85 reaction plotted versus the square of the four-momentum transfer (t). This triplet of states is plotted, rather than the 3.09 MeV or 3.68, 3.85 MeV states separately, so that the 250 MeV data of reference [Lo84b] may be used to help show the systematics of the 12 C(p, 1r+)13 C* reaction. Plotting . symbols indicate the source of data as in figure 5.4. 57 104 __ ___L_ i2c\'"' n+/ 3c• • 9.50 • 103 • 181 • • ,,,.--.... ... I.... ... (/) ~lt •• "-. ..0 A & D o C 102 ....__,, I At:, ... 0 • c9 C: • oD D -0 0 D D • "-. • b C -0 10 1 Q 2 10° 0.7 0.5 0.3 0.1 -0.1 t (GeV 2/ c 2) Figure 5.6: Angular distributions of the 12 C(p, 1r+)13 C9_50 reaction plotted versus the square of the four-momentum transfer (t). Plotting symbols indicat e the source of data as in figure 5.4 except • [So81] 166 MeV. 58 10 160 ( p '7f +) 17 0 g.s. 0 0 0 0 156 MeV 200 •0 250 DD D • • 354 • • • * MeV * MeV 1. 0 ___ _._ __ ...___----I_ I.... (1) 0.0 0.0 0 156 MeV 0 200 Me\/ 3: 0 1.0 -+---------+-Q_ Cl 250 MeV O'IO.O C: D a D D D ; 1.0 -+------------c <( 0.0 a• I • • 354 MeV I • 1.0 ------------* 0.0 10°------T--t-489 MeV i -1.0 ---~--------0.7 0.5 0.3 t 0. 1 0.7 0.5 0.3 0.1 (GeV2/ c2) Figure 5.7: Differential cross sections and analyzing powers for the 16 O(p, 1r+)17 Og.s. reac-tion. The 156 MeV data are from references [Sj81a,Sj81b), the preliminary 200 MeV data are from reference [Az87), the 250, 354, 489 MeV data are from this work, and the prelimi-nary 800 MeV data are from reference [Na82]. Differential cross sections are not displayed on a common scale for sake of clarity. 59 ,,--..... 102 "' ...0 C '--" 10 1 C: -0 "'-10 1 b -0 Cl .~ • Cl • 160(p rr+)170* ' 0.871 250 D D 354 MeV ! • • ! I i L Q) 1.0--+---....._ __ ....__ __ 1-156 MeV 0.0 1.0~--------~ 250 MeV 3: 0.0 0 Q_ O') 1.0 ~-----tlt--B-':::;__-----~ C N >--0 0.0 C ! 354 MeV !! 1.0--+----------+--1-0 .0 10--1+----.--,--~-~- -1.0--+----.------1--489 MeV 0.7 0 .5 0.3 t 0.1 0.7 0.5 0.3 0.1 (GeV2/ c2) Figure 5.8: Differential cross sections and analyzing powers for the 16 0(p, 1r+)17 00_871 re-action. The 156 MeV data are from references [Sj81a,Sj81b], the 185 MeV data are from reference [Da74], the 250, 354, 489 MeV data are from this work, and the preliminary 800 MeV data are from reference [Na82]. Differential cross sections are not displayed on a common scale for sake of clarity. 60 160(p rr+)170* ' 5.218 103 1.0 • Cl OCl Cl • g 0.0 Q Q l w • r----102 250 MeV Cl L. 1.0 L. Q) Cf) 5 ! ! "'-- I 0 ...0 Ci 0 Q_ C I •• '--./ 010 .0 . •,· C: • C u I N "'-- >-_g 10 1 0 354 MeV C <( 1.0 48 9 MeV 0.0 i: t 10° -1. 0 0 .7 0.5 0.3 0. 1 0.7 0 .5 0.3 0 .1 t (Ge\/ 2/ c 2) Figure 5.9: Different ial cross sections and analyzing powers for the 16 O(:p, 11"+ )1; 0 5_218 re-action. All data shown are from this work. 61 160(p 7T+)170* ' 7.757 103 1.0 200 MeV • ••• 200 MeV D ... 0.0 • • D ... • • •D D 250 MeV 1.0 • D 250 MeV ;----... D I.._ I.._ • Q) (f) 3 0.0 '-...,__ 102 MeV 0 0 ..0 • o_ D C • D '----"' 0, 1.0 • * C 102 • N I '-...,__ MeV >- • • b • 0 0.0 I -0 * <><> 354 MeV 1.0 I 489 MeV MeV <> 0.0 i * i 10° I -1.0 0.7 0.5 0.3 0.1 0.7 0.5 0.3 0.1 t (Ge\/ 2/ c 2) Figure 5.10: Differential cross sections and analyzing powers for the 16 O(p,1r+) 17 O7_757 re-action. The preliminary 200 MeV data are from reference [Az87], the 250, 354 and 489 MeV data are from this work, and the preliminary 800 MeV data are from reference [Na82]. The smooth line is the analyzing power of the pp -+ d,r+ reaction based on the polynomial fits of references [Gi85,Hof83,Mat83,May85,Sah83] with th e appropriate kinematical trans-formation to the nuclear frame. Differential cross sections are not displayed on a common scale for sake of clarity. 62 160(p 7T+) 170* ' 15.78 104 1.0 200 MeV I 0.0 ....... I 1& oa 103 • 1.0 D ... .,,---. o• L D L Q) (fJ ... 3 0.0 0 00 o * "' 0 D ...0 D a Q_ C Da 250 MeV '-" 10 2 ... 0) 1.0 C: C • N I ""'O && .& D • "' >, • • ... • ••• b 0 0.0 C ""'O • <{ 354 MeV 10 j 489 MeV I 0.0 1 * if 10° -1.0 0.7 0.5 0.3 0.1 0.7 0.5 0.3 0.1 t (GeV 2/ c 2) Figure 5.11: Differential cross sections and analyzing powers for the 16 0(p, 1r+)11 Oi5.78 reaction. All data shown are from this work except the preliminary 200 MeV data from reference [Az87]. 63 . 160(p TI+) 170* ' 17 .1103 ..L 1.0 200 MeV • 0.0 .u I~ A &I Cl • A C 1.0 250 MeV ,,,--.._ 102 Cl • I..... I..... i Q) Q Cl) A ?: 0.0 0 0002 '--..,_ I 0 .0 & A o_ C ai • CJ) 1.0 Cl C C N i -a >-. • ' '--..,_ I • _g 101 0 0.0 •• •• ' C <( 354 MeV ! 1.0 f i 0.0 I :i 489 MeV 10° -1.0 0.7 0.5 0.3 0.1 0.7 0.5 0.3 0.1 t (GeV2/ c2) Figure 5.12: Differential cross sections and analyzing powers for the 16 0(p, 7r+ )17 Oi 7.1 re-action. All data shown are from this work except the preliminary 200 MeV data from reference [Az87]. 64 Chapter 6 Differential Cross Sections This chapter discusses the differential cross section data taken in this series of experiments. 6.1 Observations on the (p, 1r+) Differential Cross Sections Figures 5.4 through 5.6 show 12 C(p, 1r+)13C* data from this work, as well as some previously measured angular distributions [Da73b,Hoi80,Lo84b,Na82,S o81] taken at different incident proton energies above and below the Ll1232 region. The use of this previously published data allow the systematics of the data to be more readily apparen t . Differential cross sections are also presented for the 16 O(p, 1r+) reaction leading to six separate states of 17 0* in figures 5.7 to 5.12, and for the 7Li(p,1r+)8Li* reaction leading to th ree discrete states in figures 5.1 to 5.3. These distributions are plotted versus the Mandelstam variable t, which is the square of the four-momentum transfer. Together with the Mandelstam variable s, which is the square of the center of mass energy, these two variables completely determine the kinematics of a two body collision. Thus, the only kinematic variables needed to describe the scattering matrix are s and t. Unlike the more commonly used kinematic variables q ( the three momentum transfer) and Tp (the beam kinetic energy), both of the Mandelstam variables are relativistically invariant. These variables were first pub licly used by B.M.K. Nefkens to emphasize the reaction mechanism aspects of a nuclear reaction, an example of which may be found in [Ne83]. In the lab system for an A(p, 1r )A+ 1 reaction, these variables are given 65 by s = m; +mi+ 2EpmA (6.1) t = m; + m; - 2(EpE,r - p; ·p-;.) One must keep in mind that at energies close to pion production threshold, only a small range of four-momentum transfers is accessible, and that this range increases in size, and is restricted to smaller values oft, as the proton energy is increased. Unlike Soga et al. [So81], who multiplied the 185 MeV 12 C(p, 1r+)13 C data of reference [Da73b] by 1.27 to correct for perceived differences in instrum ental normalizations, it was not found necessary to multiply any of the data presented in figures 5.4 to 5.6 by any arbitrary factor. It has been noted, however, that the data of reference [Da 73b] are reported in the lab frame rather than the center of mass frame, and the appropriate transformation of this data to the center of mass frame has been made. Figure s 5.4 to 5.6 do not reveal any gross errors in the normalization of this data, rather the 185 MeV 12 C(p, 1r+)13Cg.s. data of reference [Da73b) agrees reasonably well with the 183 MeV data of reference [Gr83] after taking into account the statistical errors. Note that as the proton energy is increased, the angular distribution of every state becomes more exponential-like, even if at energies closer t o threshold the angular distri-bution exhibited a very pronounced back angle peak, such as is shown in figures 5.5 and 5.7. At very large momentum transfers (t < 0.2 GeV 2 /c 2 ), the differential cross sections of some states flatten out with a magnitude less than 10 nb/ sr; this is shown in figures 5.4 and 5.8. Other than this behavior, the smoothly falling shape of the angular distributions at 354 Me V and higher energies is reasonably independent of nuclear final state. At 800 MeV, angular distributions obtained with targets from 6 Li up to 4°Ca have been observed [Se87] to fall more or less exponentially with a slope of a( q) ex: q-(to± 2), where q is the three-momentum transfer. A careful analysis of figures 5.4 to 5.6 shows that low spin states are comparable in strength to 2p-lh high spin states in only a limited kinematical area of small Tp and forward angle; in other areas 2p- lh high spin states dominat e the exclusive pion production cross section. Thus, this demonstrates graphically the reason for the stark contrast between the 12 C(p, 1r+)13 C'" spectra at 200 and 354 MeV as discussed in Chapter 4. The selectivity of both the (p, 1r+) and (p, 1r-) reactions for high spin 2p-lh states appear to be very 66 similar, and the empirical explanation for the non-selectivity of (p, ,r+) reactions [Vi83] does not appear to hold globally. This explanation suggested that pn -+ pp,r- processes should preferentially populate 2p-lh states in (p, 1r-) reactions since there are no competing processes, but that (p, ,r+) reactions have many competing NN -+ NN ,r+ processes involving target nucleons from a variety of orbitals, and that this may cause lp and 2p-lh states to be populated with comparable strength. 6.2 Energy Dependence of (p, 1r+) Differential Cross Sec-tions The energy dependence of the differential cross section depends on the shape of the angular distributions at low energy (Tp < 225 MeV). For the states whose low energy distributions fall smoothly with angle, as shown in figures 5.4, 5.6 and 5.11, for example, the differential cross section has its largest values at 354 MeV in the range of 0.7 > t > 0.3GeV 2 /c 2 • This enhancement is at an energy near the invariant mass of the ~ 1232 , and confirms the findings of Convert and Dillig shown in figure 1.7. For the 7Li(p, 1r+)8Lig.s. and 7Li(p, ,r+)8Li2_255 reactions, shown in figures 5.1 and 5.3, the differential cross sections rise with energy from 200 Me V to approximately the ~ 123 2 invariant mass at 354 Me V, and then level off. This slightly different energy dependence is similar to that of the elementary pp -+ pn,r+ process, whose cross section levels off at energies above the ~ 1232 resonance [Loc70]. It is not clear why the differential cross section of the 7Li(p, 1r+)8Li* reaction should fall proportionally less above the ~ 1232 invariant mass than the 16O(p, ,r+) 17 O* reaction, but reduced final state distortions due to the lighter residual nucleus is a possible explanation. Those states which exhibit a pronounced back angle peak at lower energies, as shown in figures 5.5, 5.7, and 5.8, also have their largest differential cross sections near 354 MeV, but only for momentum transfers below the location of the first minimum ( t 0.5 Ge V2 / c2 ). At smaller values oft the 200 and 250 MeV differential cross sections are much larger than the 354 MeV differential cross sections. Although the 200 MeV 8Li0_9808 data shown in figure 5.2 do not exhibit a large angle peak, the differential cross sections do not fall as rapidly at large angles as they do at 200 MeV in figures 5.1 and 5.3, so this state can be considered to be in this category. The origin of the large angle peaks at lower energy is not fully known, 67 but it is believed to be related to the nuclear structure of these states [Ku87]. In the region t < 0.3GeV 2 /c2, some reactions, such as the 16 O(p, 1r+)17 Oi 5.78 reaction shown in figure 5.11, continue to show an enhancement at the .6.1232 invariant mass in this region of high momentum transfers. The great majority of reactions, however, have lower differential cross sections at 354 Me V than at 250 Me V for t < 0.3 Ge V2 / c2 • In order to more easily observe the energy dependence of the differential cross section at t=0.50 GeV2 /c 2 , results for the 12 C(p , 1r+)13Cg.s. and 12 C(p, 1r+)13 C9_50 reactions are plotted in figure 6.1. Plotting the differential cross section at a constant four-momentum transfer permits, to a first approximation, the separation of the reaction mechanism from the nuclear structure effects [Cv81]. The quantity vs - m12c, where s is the relativistic Mandelstam variable corresponding to the square of the center of mass energy, is a measure of the excitation energy available to the system. If this energy has been used to excite a nucleon to a .6. 1232 resonance, then a signature of this process would be expected to manifest itself at the appropriate invariant mass ( vs - m12c = 1.232 GeV). Figure 6.1 indicates an enhancement in the differential cross section which levels off near this energy. To relate this enhancement to the role of the .6.1232 and the NN -+ NN 1r+ process, the differential cross section of the pp -+ d1r+ reaction was transformed to the nucleon-nucleus frame. The transformation assumes that the nucleus emits a proton directly into the incident beam. Using the constraint that the pp -+ d1r+ reaction between this emitted proton and the beam proton must create a pion with the same momentum and scattering angle (in the p-A lab frame) as that produced by the A(p, 1r+ )A+ 1 reaction, conservation of momentum conditions are used to solve for the energy of the proton emitted by the nucleus. The residual nucleus is off-shell. The incident proton energy and pion lab angle are then transformed from the p-A lab frame to the p-p lab frame so that the pp-+ d1r+ differential cross section may be calculated from published fits to the data. Finally, the pp -+ d1r+ differential cross section is corrected for the nuclear body Ja cobian instead of the p-p frame Jacobian. A listing of the computer program used for this t ransformation may be found in section A.3. At energies close to pion production threshold, the assumption that the target nucleus emits a proton directly into the incident beam is clearly valid. This is because the reaction must utilize the Fermi momentum of the nuclear proton if it is to proceed at energies below 68 ;: ~j --'------::!=--!-----'---+ I "2 7 01 (f) ' , '-.. 35 -g °"o• ,2c(p,1r+),3c '---" 0------.-----....-------= 9-·5_·4 12 00 ,----~-------'-------+ C u '· 900 " _g 60 0 300 I ... DOD II C, 12c(p 1r+)13c• ,,---._ t:,. ' 9.50 L Q+------.-----....----~~ 100Ct----~---_.__----+ .D • t:,.. ::i_ 75 0 '---" C 500 u '"' 250 b u • 1"91 ct • • 0 0 0 0 1.3 (GeV) • 1.4 Figure 6.1: Differential cross section versus center of mass energy at a constant square of four-momentum transfer (t = 0.50GeV 2 /c 2 ) for the 12 C(p, 1r+) reaction leading to the ground state as well as the 9.50 MeV excited state. Plotting symbols indicate the source of data as follows: 0 [Gr83] 183, 190 MeV; b. [Da73b] 185 MeV; A [Hoi80] 200 MeV; D [Lo84b] 216, 225, 237, 250 MeV; * [An81] 246, 332 MeV; • [This Work) 250, 354, 489 MeV. The differential cross sections shown were obtained from the dat a using either an exponent ial or · Legendre polynomial fit to the distributions . Also shown are differential cross sections for the pp - d1r+ with modifications as explained in the text. Plotting symbols indicate the source of data as follows: t::. [Bos82), • [Gi85], o [Hof83), • [Ric70), D [Rit81) . The data from references [Bos82,Ric70,Rit81) were extracted from Legendre polynomial fits contained in reference [Jo82). 69 that of the free NN - NN7r+ threshold. At incident proton energies above this threshold ( approximately 280 Me V), it is no longer necessary for th e reaction to utilize the Fermi momentum of the nuclear protons. Nevertheless, the assumption that the nucleus emits a proton directly into the incident beam maximizes the p-p center of mass energy, and as a result, this configuration is expected to still play an important role above the free NN - NN7r+ threshold, although all other configurations in which the beam proton and the nuclear proton do not collide head-on will become increasingly important. For the 16 0(p, 7r+) reaction to 23 MeV excitation in the continuu m, this transformation requires the nuclear proton to have a momentum of 203 ± 2 Me V / c at t=0.5 Ge V2 / c2 for all incident proton energies from 200 MeV to 489 MeV. At t=0.4 GeV2 / c2 the transformation requires a nuclear proton momentum of 238 ± 4 MeV /c, and for t=0.2 GeV2 /c 2 the transformation requires a nuclear proton momentum of 297 ± 9 Me V / c for incident proton energies between 250 and 489 MeV. Thus, as the momentum transfer is increased, it becomes less likely to find a proton in the nucleus with the required momentum, and the model loses validity. As such, the model is only meant to describe the qualitative tr ends of the nuclear (p, 7r) data, and not the details. The result of this transformation, which was to stretch out the high energy tail of an otherwise symmetric peak, is shown at the bottom of figure 6.1. Note that the addition of pp - pn7r+ contributions to the pp - d7r+ plot will further enhance the high energy tail and cause it to resemble the nuclear (p, 7r+) data even more closely. Therefore, these excitation functions seem to indicate that the .6. 1232 does play an important role in the (p, 7r+) reaction via the NN - NN7r+ reaction mechanism. The energy dependence of the 16 0(p, 7r+)17 0 7_757 reaction is shown for 5 different val-ues of t in figure 6.2. Also shown in this figure by the solid lines are the differential cross sections of the pp - d7r+ reaction via the transformation to the nuclear frame described above and normalized to the 16 0(p, 7r+)17 0b 57 result. As can be seen for t > 0.45 GeV2 /c2, both the pp - d7r+ and 16 0(p, 7r+)17 0 7_757 reactions exhibit a pro-nounced peak at the .6.1232 invariant mass. Note also that at much larger momentum trans-fers (t < 0.35GeV2 /c 2 ), the pp - d7r+ reaction does not exhibit this enhancement, and neither does the 16 0(p, 7r+)17 0b 57 reaction, as the 250 MeV data point ( .Js-m1so = 1.17 Ge V) has a larger . differential cross section than either of the 354 or 489 Me V data points. 70 r This energy dependence is also seen for the 12 C(p, rr+)13 C* reactions in figures 5.4 and 5.6 for t < 0.3 GeV2 /c 2 . The 16O(p, rr+)17 Oi 5_78 reaction shown in figure 5.11, however, continues to show an enhancement at the .6.1232 invariant mass at these high momentum transfers, even though the pp -t drr+ reaction, as shown in figure 6.2, does not. This energy dependence is very difficult to interpret. Thus, at four-momentum transfers squared in the range t > 0.45GeV 2 /c2, most states exhibit an enhancement at the .6. 1232 invariant mass which is similar to that exhibited by the pp drr+ reaction after transformation to the nuclear kinematical frame. At larger momentum transfers (t < 0.35GeV 2 /c 2 ), some states still exhibit an enhancement in differential cross section at the .6.1232 invariant mass. Most of the states, however, do not show an enhancement, exhibiting instead a differential cross section that falls with energy from 250 to 489 MeV, similar to that shown for the pp -t drr+ reaction in figure 6.2. It should be kept in mind that the required nucleon momentum, as dictated by the pp -t drr+ transformation, becomes excessively large in this range of small t values, and therefore, any observed similarities may be fortuitous. \_ 6.3 Energy Dependence of (p, 1r-) Differential Cross Sec-tions Plots of differential cross section versus center of mass energy at a constant four-momentum transfer are shown for the 13C(p, rr-)1 4Og.s. reaction in figure 6.3, and for the 13 C(p, rr-)1 4O6_27 ,6 _79 reaction in figure 6.4. Also shown for comparison is the energy de-pendence of the 13 C(p, rr+)14 Cg.s. reaction in figure 6.3, and the 13 C(p, rr+)14 C6_73 and 13C(p, rr+)14 C:h_2 reactions in figure 6.4. By choosing mirror final states, effects due to differences in nuclear structure are minimized, and any differences in _the energy behavior of the (p, rr-) and (p, rr+) differential cross-sections at the same four-momentum transfer should primarily reflect differences in reaction mechanism behavior rather than nuclear structure. However, this comparison is only valid to first order since the (p,rr+) and (p,rr-) reactions are not mirrors of each other, and therefore they can sample different isospin components of a given mirror pair of final states. The cross sections shown in figures 6.3 and 6.4 at t = 0.50 GeV2 /c 2 were obtained by 71 160 ( p 7T +) 17 0. ' 7.757 10 4--,;--~-~~---l:- 1.0 --+---'---'---'---+-t=0 .6 103 ;t=0 .6 0 .0 / fr- 1.0 10~ I ,' J t = 0.5 ;r· J ~ --,,....--.... 4 t= 0 .5 L O.O J. 'v/ L 2 b-Q; D i', 101 ,rl · E~ i.o-+j-t=_o ..:.·----t .__S 10~ .a. D 0>0 .0 j C t = 0.4 -~ j • o \ -u j ' i 10~ i? 1.0 J ! -u ~ t = 0. 3 CJ....--rr---i- < o.oJ 10~ j 1l_ 3 .i-t= 0.3 l J 1.0 ......_ _______ ._ 101 ,-o, --- E ,J 10 01 I I I r -l.C i t=O.~ i 1.0 1.1 1.2 1.3 1.4 1.0 i.1 1.2 1.3 1.4 Vs - m (Ge\/) 150 Figure 6.2: Differential cross sections and analyzing powers for the 160(p, ,r+) 17 Ob 57 reac-tion plotted versus center of mass energy. Plotting symbol s indicate the source of data as follows: A reference [Az87] 200 MeV; D [This Work] 250,35 4,489 MeV. Plotted differential cross sections were calculated using Legendre polynomial fits to the data; plotted analyzing powers were calculated using associated Legendre polynomial fits to the data. The solid . lines are the differential cross sections and analyzing powers of the pp -+ d,r+ reaction based on the polynomial fits of references (Gi85,Hof83,Mat83,May 85,Sah83] with the appropriate kinematical transformation to the nuclear frame. The pp -+ d,r+ differential cross sections have been normalized to the 354 Me V 17 0 7_757 data point, except at t = 0.6 Ge V2 / c2 , which was normalized to the 250 MeV data point. 72 interpolation using fits to the data listed in table B.3. For the previously published data with bombarding energies below Tp = 250 MeV [Da73a,Hoi80,Ja82,Ko87,Vi83], Legendre polynomial fits to the angular di.stribution results were used. For Tp = 250 MeV and above, which are the data from this work, an exponential was fitted to the cross section at the two angles measured. For the Tp = 354 and 489 MeV (p , rr-) results, where the cross section was measured at only one angle, the relative exponential fit to the 250 MeV data was used. Since the data in this experiment were measured close to t = 0.50 Ge V2 / c2 , the error involved in this interpolation should be minimal. Plotting the differential cross section at a constant four-momentum transfer permits, as discussed previously, the first order separation of the reacti on mechanism from the nuclear structure effects [Cv81]. Any differences in the energy behavior of the (p, rr-) and (p, rr+) differential cross sections can then be attributed mainly to the reaction mechanism. Both figures 6.3 and 6.4 show that at t = 0.50GeV 2 /c 2 the (p, rr+) reactions have an enhancement in the differential cross section near the invariant mass of the ~ 1232 ( Js-m13c = 1.232GeV), as one would expect from the findings of the previous section. For comparison, the differ-ential cross section of the pp ---t drr+ reaction, in which th e ~ 1232 resonance is known to play a dominant role, is plotted at a constant momentum transfer oft = 0.50 GeV2 /c 2 at the bottom of figure 6.3 after transformation to the nuclear frame. It is easily seen that the energy dependence of the pp ---t drr+ reaction is strikingly similar to the energy dependence of the (p, rr+) reactions, and, as noted before, the addition of pp ---t pnrr+ contributions to the pp ---t drr+ plot would enhance the high energy tail and cause it to more closely resemble the 13 C(p, rr+) energy dependence. In contrast, the differential cross sections of both (p, rr-) reacti?ns in figures 6.3 and 6.4 show no enhancement near the invariant mass of the ~l232· These are the first measurements of the energy dependence of the (p, rr-) reaction in this dynamical region. .) Note that the pp ---t drr+ transformation to the nuclear kinematical frame is a plane wave calculation, and that one would expect distortions to play a major role at resonant energies, possibly modifying the energy dependences shown here. However, for both the (p,rr+) and (p,rr-) reactions on 13C, the incoming channel distortions are common, and the distortions in the outgoing channel between rr+ - 14 C and rr- - 14 0 are assumed to have similar dynamic behaviors. Thus, although distortions as final state interactions are energy 73 8 _..___ 13C(p,1r-) 140 6 ~I g.s. ,,,--...._ 4 L (J) 2 I-_Q ' C 0 '---" 75 C -u b 50 --0 25 I ,,,--...._ t::.• 13C(p,1r+) 14c ~1008 0.:9. • A _Q • :i_ 750 '---" 0 c 500 0 • 0 • --0 0 250 • • • b • pp~dn+ ""O ~-7 ct Fs1.2 1.3 1.4 s - m13 (GeV) C Figure 6.3: Differential cross section versus center of mass energy at a constant four-momentum transfer (t = 0.50 GeV2 /c 2 ) for the 13C(p, 1r±) rea~tions leading to the ground states . Plotting symbols indicate the source of data as follows: 6. [Da73a] 185 MeV; o [Ja82] 190 MeV; .& [Hoi80] 200 MeV; • [This Work] 250, 354, 489 MeV. Also shown are the differential cross sections for the pp --+ d7r+ reaction with modifications as described in the text . Plotting symbols for this reaction are as in figure 6.1. The error bars reflect statistical uncertainties only. 74 401 13c( - )14o• p '7T 6.27,6.79 301 20 i 10 0 I ,..---..._ 0 L 750 ; (/) ...0 500.; C I '-/ ; ' i C 250 ~ • -0 i 13C(p 1r+) 14c• b o: ' 6.73 -0 600 i ' L I I 4001 200 ~ • I i 13c(p 1r+) 14c• ~-1 • ' 23.2 1.2 1.3 1.4 Fs - m,3 ( Ge\') C Figure 6.4: Differential cross section versus center of mass energy at a constant four-momentum transfer (t = 0.50 GeV2 /c 2 ) for the 13 C(p , 1r±) reactions leading to sev-eral high excitation final states. Plotting symbols are the same as in figure 6.3 except: 0 (Vi83] 191 MeV; + [Ko87] 200 MeV. 75 dependent, the comparisons of the (p, 1r+) and (p, 1r-) reacti ons at the same energies should be almost insensitive to the effects of the final state interactions and the comparisons at fixed values of t should be the best one can do in minimizing the non-dynamical variables. Unfortunately, the combination of the small (p, 1r-) cross section and the 2.1 msr spec-trometer solid angle made it impractical to obtain a distribution of (p, 1r-) differential cross sections over a large angular range (corresponding to a large range oft values). However, in the previous section it was shown that for the 12 C(p, 1r+)13 C* and 16 O(p, 1r+)17 O* reactions the energy dependence of the differential cross section at constant momentum transfer is independent of the value oft chosen within the range 0.7 > t > 0.45GeV2 /c 2 . No angular distribution results exist for the 13C(p, 1r+)14C* reaction at higher energies. Nevertheless, the energy dependences shown for the 13C(p, 1r+)14C* reactions should not be very sensi-tive to the value oft chosen within this range. Although angular distributions for (p, 1r-) reactions are not available over a similarly large energy range, recently published (p, 1r-) angular distributions [Ca87b,Hoi86,Ke86,Thr87] which include target nuclei from 7Li to 48 Ca do not exhibit dips and wiggles. This leads us to expect that the energy dependences of the (p, 1r-) reactions shown are similarly insensitive to the momentum transfer chosen within this range oft values. Although the energy dependen ces of the two (p, 1r-) reactions are somewhat different, the most important feature is the lack of an enhancement of cross section in the ~1232 region. This common feature of two transitions to two entirely different final states indicates that, in addition to any differences which nuclear structure may cause, there is a substantial dynamical difference between the (p, 1r-) and (p, 1r+) reactions. As an added measure for comparison, the squares of the invariant matrix elements were extracted from the differential cross sections in order to remove any effects due to an increase in phase space as the energy increases. This extraction was done using the equation for A(p, 1r )A+ 1 reactions in general (6.2) wheres is the Mandelstam variable previously described, and the other symbols are standard and referring to the center of mass frame. The results are plotted in figures 6.5 and 6.6. These plots clearly indicate again that there is a significant underlying difference between the (p, 1r-) and (p, 1r+) reaction mechanisms. 76 400+---~---_._ __ ----,. 1.3c ( p) rr -) 140 300 ! 2001% g.s. 100~ i I o-1----------.-----·~ '-...../2000~, ---___._----~---~ N I 2 150C1 i 1000J socj I & 0 ,,-__ 24( 1 +-----~-----------1-L 0 180 "" 120 N 60 • • • 0 0 0 . • 0 • pp~dn+ 0 t:tJ ct 1.1 1.~ 1.'3 1.4 (GeV) Figure 6.5: Invariant matrix element ( as explained in the text) plotted versus center of mass energy at a constant four-momentum transfer (t = 0.50GeV 2/c 2 ) for the ground state transitions as well as the pp -+ d1r+ reaction. Plotting symbols are the same as in figure 6.3. 77 300 200 100 0 ,,,-...30001 L I ~20001 I -...._,,, I N 1000 ~ I 2 Q i 3000 2000 1000 ~.1 n • • I /1.2 VS -13c( -),4o• p '7T 6.27,6 .79 • • 1.3 1.4 m,3c (GeV) Figure 6.6: Invariant matrix element ( as explained in the text) plotted versus center of mass energy at a constant four-momentum transfer (t = 0.50 GeV2 /c 2 ) for high-spin final sta tes. Plotting symbols are the same as in figure 6.3. 78 6.3.1 Discussion The NN-+ NN1r- dominance of the (p, 1r-) reaction mechanism has been a widely accepted assumption (Thr87]. The role of the .61232 resonance in the (p, 1r-) reaction, however, is currently an open question (Pia86,Vi87]. The striking differences between the (p, 1r-) and (p, 1r+) energy dependences shown in figures 6.3 to 6.6 suggest that the role of the .61232 is distinctly different in the two reactions. It is well known (Be82,Bu84,Ca86,Jo84,Tho80] that the dominant amplitude of the pp-+ pn1r+ reaction in the .6.1232 resonance region is pp( 1 D2)-+ .6.N(5 S2) -+ pn( 3S1)+P-wave1r+. This specific channel is forbidden for the pn -+ pp1r- reaction by angular momentum and parity conservation and by the Pauli exclusion principle. The allowed .6.1232 channels for 7r- production in a two nucleon mechanism are pn(3P 0 ) -+ .6.N(3P0 ) -+ pp( 1S0 ) + S -wave 1r- and pn(1 D2) -+ .6.N(5S2) -+ pp( 3P 2) + S - wave 1r- involving P-waves for either the intermediate .6.N or final NN state, as well as other channels involving still higher partial waves. These resonant amplitudes are much smaller than the one above that dominates the pp -+ pn1r+ reaction (Ca86], and may be masked in the (p, 1r-) reaction by non-resonant amplitudes. A recent analysis of analyzing power data for (p, 1r-) reactions on nuclei [Vi87] together with a phase shift analysis of differential cross sections for low-energy 1r- absorption by a 1S0 , T=l proton pair in 3He [Pia86] suggests that the pn -+ pp1r- reaction at low energies may be dominated by the non-resonant pn( 3D1, T = 0)-+ pp(1S 0 ) + P - wave 1r-transition, which cannot lead to an intermediate .6.N(T = 1, 2) state. This may be the reason for the lack of an enhancement of the (p, 11"-) reaction near the invariant mass of the .6.1232. It should be noted that other considerations, such as the possible influence of higher energy 1rN resonances accessible only by the (p, 1r-) reaction, or possible differences in 1r+ and 1r- absorption by the nuclear medium, may further influence the energy dependence of the (p, 1r-) reaction. Alternatively, the possibility exists that the (p, 1r-) reaction may be a two step process involving pion single charge exchange. In this case, recent results from pion-nucleus single charge exchange studies at LAMPF [Ro87] may have direct bearing on this discussion. This reference indicates that in the ( 1r+, 1r0 ) reaction on a wide variety of nuclei the .6.1232 resonance is manifested by the suppression of cross section in the .6.1232 region due to increased absorption of the outgoing pion in the nuclear medium. 79 Detailed model calculations are needed to clarify the role of the ~1232 in the A(p, 11"-)A+ 1 reaction. 6.4 Continuum d 2a / dOdE1r Results Each of the (p, 7r+) spectra in figure 3.7 is characterized by a large number of populated states superimposed upon an inclusive pion production continuum. This continuum starts near 8 MeV excitation and increases linearly in strength with excitation energy. The p+A-+ Ag.s. +n+ 7r+ reaction has a threshold of 8.18 MeV excitation in the 13 C(p, 7r+) reaction, and has a threshold of 4.15 MeV excitation in the 16 O(p, 7r+) reaction. On the other hand, the p +A-+ (A- l)g.s. + d + 7r+ reaction does not contribute unt il 23.49 MeV excitation in the 13C(p, 7r+) reaction, and does not contribute until 14.05 MeV excitation in the 16 O(p, 7r+) reaction. Since the slope of the continuum does not increase at the onset of (p, 7r+d) contributions in the 13C(p,7r+) 14 C spectrum (23.49 MeV) in figure 3.7, this must indicate that the (A - 1) + d + 7r+ final state does not contribute significantly to the continuum at this range of pion momenta. In contrast to the (p, 7r+) spectra, only a weakly pop ulated cluster of states near 6 MeV stands out in the (p, 11"-) spectrum at Tp = 489 MeV. While the ratio of 7r+ /11"-cross sections leading to discrete states at this energy is approximately 60, the ratio leading to the continuum is only 30. This compares with a 7r+ /11"-ratio of approximately 10 for both the inclusive and exclusive reactions at 200 MeV [Ko87]. Thus , at higher energies the (p, 11"-) reaction leading to discrete states is suppressed in relation to the (p, 11"-) reaction leading to the continuum. This may result from Pauli blocking effects that are more restrictive in exclusive 11"-production, due to the identity of the final two nucleons in the elementary pn -+ pp7r- process, than in exclusive 7r+ production, which involves the elementary pp -+ pn7r+ process. This argument does not explain, however, why the 7r+ /11"-ratio is approximately the same for both the inclusive and exclusive reactions at 200 MeV. It should be noted that all continuum data presented in this work are for a one Me V wide slice of pion continuum centered about some specified equivalent excitation energy as if there were a two body final state in which the recoil nucleus remain ed intact. Unfortunately, this is not the standard way to present continuum data. The two most comprehensive sets of data on inclusive 7r+ and 11"-production [Cr80,Cc72] were motivated by the need of data for the 80 optimal design of pion beam lines at the meson factories; hence their data are presented as a function of the pion lab energy for a set of constant pion lab angles. Recent inclusive pion production measurements [Bi85,DiG85,Fa86] have continued this practice. This makes it inconvenient to relate the results of these studies to the exclusive pion production case. The reason for this is that the exclusive reaction do-/ df! results are presented for the population of a particular nuclear final state versus pion scattering angle, and hence the pion lab energy varies within a data set as the pion scattering angle changes. By comparing data at a constant excitation energy, the internal total energy of the recoil nucleus is fixed, and a comparison of these data to the exclusive pion production data may yield some hints about the nature of the reaction mechanism. Figure 6. 7 shows the energy dependence of the double differential cross section for three different reactions at a constant missing four-momentum squared of t = 0.50 Ge V2 / c2 • Also shown for comparison by the solid lines is the differential cross section of the two body pp - d7!'+ reaction transformed to the nuclear frame and normalized to the 354 Me V data point. Note that at t = 0.50 GeV2 /c 2 the double differential cross section of the inclusive (p, 11'+) reactions increase with energy up to the ~ 1232 invariant mass at a rate that is identical to that of the pp - d7!'+ reaction. Above this invariant mass, however, the 13C(p, 11'+)X and 16 O(p, 11'+)x reactions do not fall as fast with energy as the elementary pp - d7!'+ process. This behavior is expected since the cross section of the pp - pn11'+ reaction is known to level off at energies well above the ~ 1232 resonance [Loc70]. Plotted at the bottom of figure 6. 7 is the t = 0.30 Ge V2 / c2 energy dependence of the 16 O(p, 11'+ )X reaction at an equivalent excitation energy of 19 Me V, as -well as that of the pp - d7!'+ reaction after transformation to the nucleon-nucleus frame. The choice of t = 0.30 Ge V2 / c2 emphasizes the energy dependence at larger pion scattering angles than the 0.50 Ge V2 / c2 data referred to above. As shown in figure 6. 7, the energy dependence of the 16 O(p, 11'+)X reaction is much flatter between 250 and 354 MeV than it was at t=0.5 Ge V2 / c2 • However, the pp - d7!'+ process qualitatively describes this flatter energy depen-dence, just as it does in the exclusive case. The very small double differential cross section that the inclusive reaction exhibits at 489 MeV (vs - mA = 1.4 GeV) is not understood. Plotted at the top of figure 6.7 is the energy dependence of the 13 C(p, 11'-)x reaction at t = 0.50 Ge V2 / c2 • The energy dependence of this reaction is different from that observed at 81 t=0.50 GeV2/c 2 48 2 36 24 .....--... 12 13C ( p, rr-)x C > G) so8 2 I 600 I..... Cf) 400 "'-- 200 _Q 13C (p, rr+)x C 1208 t:: 900 w C ""O 600 C 300 ""O 160 ( p 'rr+)x "'-- 0 b t=0.30 GeV2/c 2 N ""O 250 200 150 C 100 50 160(p, rr+)x C 9. 1 1.2 1.3 1.4 Vs mA (GeV) Figure 6.7: Energy dependence of the double differential cross section for a one MeV wide slice of pion continuum at 19 MeV excitation for three different reactions at a constant miss-ing four-momentum oft = 0.50 GeV2 /c 2 , and for one reacti on at a missing four-momentum oft = 0.30 GeV2 /c 2 • The solid line is the differential cross section for the two-body pp --+ d1r+ reaction at equivalent missing four-momentum squared after transformation to nuclear kinematics and solid angle and normalized to the 354 MeV data point. 82 t = 0.50 Ge V2 / c2 for either the inclusive (p, rr+) or the pp -+ drr+ reactions. This difference may indicate that the 6.1232 resonance plays different roles in rr+ and rr- production. It should be pointed out , however, that the maximum differential cross section of the exclusive 13 C(p, rr-) 14 O reaction occurs in the 200 to 250 MeV region (see figures 6.3 and 6.4), whereas the maximum double differential cross section shown for the 13 C(p, rr-)x reaction in figure 6.7 occurs near 350 MeV. Thus , the energy dependence at a constant value oft is different depending on whether the residual nucleus is left in its ground state, an excited state , or is left unbound. Since by fixing t to a constant value shou ld, to first order, keep nuclear structure effects constant, it is unclear what dynamical effect is causing the different (p, rr-) energy dependences. The (p, rr+) energy dependences, however, are very similar for both the inclusive and exclusive reactions. 83 Chapter 7 Total Cross Sections If the differential cross sections are integrated over the scattering angle, the total cros~ section of the reaction is obtained. This chapter discusses the observed characteristics of this quantity. 7 .1 Energy Dependence of the Total Cross Section Figure 7 .1 shows the energy dependence of the total cross section for several 12 C(p, 1r+ )13 C* reactions plotted versus ../s-m12c- The total cross sections were determined by fitting the angular distributions previously shown with Legendre polynomials, the zeroth order pa-rameter giving the total cross section because of the normalization requirement of Legendre polynomials. Po( Cos( 0c.m.)) er=------ (7.1) Figure 7.1 does not show a maximum near the invariant mass of the ~ 1232 , rather the maximum cross section occurs about 100 MeV lower than this, at a beam energy of about · Tp = 225MeV. Another interesting feature of figure 7.1 is that the shape of the energy dependence is reasonably independent of final state. A similar energy dependence is also seen for the 16 O(p, 1r+ )17 O* reactions shown in figure 7 .2; in this figure the location of the maximum total cross section varies with final nuclear state within the range of 200-250 MeV. In the region t > 0.45 GeV 2 /c2, to which the (p,1r) reaction is largely restricted at 225 MeV, the 354 MeV differential cross section is larger than the 225 MeV differential cross section at the same value oft. However, at 354 MeV the (p,1r) reaction can reach 84 *• ------9 :O; ,._ . 0 '---" '0 0 C +-----~----~------+ 0 :0 4 ___, u (J :03 'f" \.;J Cf', :02 er; ,....._ V L . ,2c( +) 13c• P 'rr 3 .09 ,3.68,3.85 • • 0 u 'iO ' -----...------...-------+ _____ ...._ ____ _._ ___ --+ 12c (p 7T +) 13c• ..2 et,.AQLJD • ' 9.50 0 i03 f-0 -.o, +------,--------.-------+ -,.00 ~ -25 1.50 s - m12c (GeV) ,.75 Figure 7.1: Energy dependence of the total cross section of the 12C(p, 1r+) reaction leading to three final states of 13 C plotted versus the center of mass energy. Plotting symbols indicate the source of data as in figure 6.1 except: 12C(p, 71"+)13Cg.s. : • (So81] 156, 159 MeV; 0 [Gr83] 170, 183, 190 MeV; • [This Work] 354 MeV. o [Na82] 800 MeV. 12C(p, 71"+)13 C3_09 ,3_68 ,3_85 : Same as for the ground state except• [So81] 156, 159, 170 MeV. 12C(p, 1r+)13 C9_50 : Same as for the ground state except • [So81] 166 MeV. The data shown in figure 7.1 from reference [Lo84b] have the highest uncertainty in the fit because no measurements were taken at angles smaller than Oc.m. = 49°, where the contribution to the cross section is the largest. 85 a range of very large momentum transfers which can not be reached at 225 MeV. In this region the 354 MeV differential cross sections are very small. Thus, the 100 MeV shift of the maximum total cross section from the invariant mas s of the ~1232 is probably due to an interplay between the increase in differential cross section due to the ~1232 seen at small momentum transfers, and the decrease in differential cross section characteristic of the larger momentum transfers that the reaction is restricted to at the higher energies . If this deviation is indeed due to the interplay between these two variables, then inclusive (p, 1r+) nuclear reactions such as 12C(p, 1r+)X, which do not require t he extra nucleon to be bound , should show the influence of the NN - NN1r+ channel at lower momentum transfers , while exclusive reactions will show a peak below the invariant ma ss of the ~1232 · 7.2 Spin Dependence of the Total Cro ss Section It has been noted in references (Cv83] and (Zi85] that the population of final states in the (p, 1r+) reaction is roughly proportional to the number of spin states in the outgoing channel 2JA+l + 1. Because of the large momentum transfer charact eristic of (p, 1r+) reactions , one would expect high angular momentum states to be promin ent and saturated to their full 2J A+l + 1 statistical weighting. This qualitatively describes the well known suppression of low spin states in (p , 1r) reactions; other high spin states which are not strongly populated (eg. 17 Oi4.1s (~+)) are presumably suppressed by some other mechanism, for example, the nuclear structure of that state. Plotted in figure 7.2 is the reduced total cross section ( 2h!i +i )CT for some of the most strongly populated states of the 16 O(p, 1r+ )17 O* reaction. Also plotted for comparison, at the bottom of figure 7.2, are the total cross sections of these states. As figure 7.2 shows, the reduced total cross sections are indeed more clustered together than the total cross sections. 7.3 Continuum do-JdE1r Results Figure 7.3 shows the energy dependence of the angle integra ted differential cross section for two 1 MeV wide slices of the 16 O(p, 1r+)x reaction centere d at 19 and 21 MeV excitation . The energy dependence shown here is very similar to the energy dependence of the total cross section for exclusive 16O(p, 1r+ )17 0 reactions leading to discrete states. This behavior 86 103 +-----'----------1.-------4-b + 1 i 1011 X b 10QT; ____ -.--------,------+-104+------'--'----L-- ' ---~ ... + 0~ 0 O D • xx X 0 • 0 X ... + • g X + L.. 101-+--------,------r----= 0 -+ 1.00 1 2· s s· Fs. 1. 0 1.75 s - m160 (GeV) Figure 7.2: Reduced total cross section, as explained in the text, as well as the total cross section for the 16 O(p, 71"+) reaction leading to several different states of 17 O*. Plotting symbols indicate the final state of 17 O* as follows: 0 110 5+ 110 • 1 + • 110 • (9-) 110 • 11- ... 110 • (13-) 110• (1-) g.s . 2 , X 0.871 2 , 5.218 2 , + 7.757 2 , - 15.78 2 , o 17.1 2 · The spin assignment for the 15.78 MeV state was taken from reference [Bl84]. 87 > (l) 2 "' ...0 C ...__... w -0 "' b -0 104-- ___ .....,_ _ _ ~1.__ ___ ..__ ___ .._1 ___ .._ ___ _ 103 -• D • D • D 102 --t-----r---~-----r----,-----,--------+-I I 1.1 1.2 1.3 Fs - m (GeV) 16Q 1.4 Figure 7.3: Angle integrated differential cross section of the 16 O{p, ,r+)X continuum versus center of mass energy for two 1 MeV wide slices of continuum. Plotting symbols indicate the equivalent excitation energy as follows: D 19 MeV; • 21 MeV. should be expected since these data were taken at the maximum momentum end of the pion's kinematical range. Thus, the neutron and recoil nucleus are restricted to small values of momentum, and the inclusive reaction is forced to mimic the large momentum transfer seen in exclusive (p, ,r) reactions. If one took cont inuum data such that both the pion and the neutron could share the increase in available energy as the incident proton energy is increased (perhaps by holding the difference between the neutron and pion energy constant), then the maximum cross section might occur closer to the ~ 1232 invariant mass ( Js - mA = 1.232GeV), and not near 250 MeV. A 16 O(p, ,r+n) 16 O coincidence experiment in which both the 1r+ and the neutron are observed, and their energies measured, would have to be performed to confirm this hypothesis. 88 Chapter 8 Analyzing Powers The 16 O(p, 7r+)17 O* and 7 Li(p, 7r+)8Li* reactions were the only ones in this work investigated with polarized proton beam. This chapter discusses the analyzing power data gathered for these reactions. 8.1 Types of Angular Distributions As stated in the Introduction, one of the first major discoveries about the (p, 7r+) reaction concerned its sensitivity to the spin of the incident proton, as seen in its non-zero analyzing power distributions. Some early measurements of (p, 7r+) ana lyzing powers were very similar to those of the pp ---+ d7r+ reaction after transformation to the nuclear kinematical frame (Au78). Subsequent experiments showed that this pp ---+ d7r+ -like behavior is not exhibited by all (p, 7r+) reactions, but that some states have their own characteristic analyzing power distributions [Lo82c,Sj81a,Zi85). However, these experiments at lower energy only measured the analyzing powers of a select number of final states, so it was not known whether there was any systematic rule regarding the exceptions to the pp ---+ d7r+ -like analyzing powers. In this work the analyzing powers of a large number of final states have been measured and it has been found that the analyzing powers of the 16 O(p,7r+) 17 O* and 7Li(p,7r+)8Li* reactions do not have a common angular distribution , but fall into several broad categories. 89 8.1.1 Category 1 (pp ----+ d7r+-like) The most common type of analyzing power distribution is one having a dip near t = 0.4 GeV2 /c 2 at 250 MeV, a positive and fairly flat distribution at 354 MeV, and a negative flat analyzing power at 489 Me V. Almost half of the states investigated had analyzing power distributions following this general pattern, of which the 7Li(p, 1r+)8Li2_255 reaction shown in figure 5.3, and the 16 O(p, 1r+)17 O7_757 reaction shown in figure 5.10 are outstanding examples. The analyzing powers of both of these reactions share many similarites with the analyzing power of the pp --+ d1r+ reaction after transforma tion to the nuclear kinematical frame. Other states in this category also have broad similarities to the analyzing power of the pp --+ d1r+ reaction, but the similarity is not as striking. Many of the states which exhibited this pattern are believed to be primarily of two particle-one hole (2p-lh) structure. At 250 MeV, the 17 0 7.757 state exhibits a much more negative dip in the analyzing power than the pp --+ d1r+ reaction, and the minimum for the pp --+ d1r+ reaction occurs at slightly lower value oft. It has been noted previously [Hoi79] that the (p, 1r+) analyzing powers in this category have a larger amplitude dip than the pp --+ d1r+ reaction. The larger dip is believed to be due to the distortions of the nuclear environment upon the underlying reaction mechanism. If this is the case, then the amplitude of the dip in the 7Li(p, 1r+)8Li* reactions should be smaller since the target nucleus is lighter. This is indeed the case for the 7Li(p, 1r+)8Li2_255 reaction shown in figure 5.3, which has a similar nuclear structure. Recent analyzing power measurements of the pd --+ t7r+ reaction [Lo84a,Lo82a] are also very similar to those of the pp --+ d1r+ reaction. At 354 Me V, the analyzing powers of both reactions turn positive and have approx-imately the same magnitude, although the 16 O(p, 1r+)17 O7_757 reaction displays a dip at t = 0.35 GeV2 /c 2 which is not evident in the pp--+ d1r+ da ta. At 489 MeV, the analyzing power of the 17 0 7_757 reaction once again becomes negative, while that of the pp --+ d1r+ · reaction remains positive. Clearly, the evidence for an unde rlying pp --+ d1r+ mechanism in the 16 O(p, 1r+)17 O7_757 reaction is stronger at 200 MeV than at the higher energies, although the free two body process qualitatively describes the data up to 354 MeV. The analyzing powers of the 7Li(p, 1r+)8Lig.s. reaction shown in figure 5.1 are similar to those of figure 5.3, except that the dips in the 200 and 250 Me V data are more pronounced, and the 354 MeV data show a deep dip near t = 0.4 GeV2 /c 2 • This similarity is prob-90 ' ably because the 8 Lig.s. and 8Li2.255 states are known [Ca86] to have the same dominant configuration [(1r1p3; 2 )(v1p3; 2 )3]. The 8 Li2_255 state contai ns a small (24%) admixture of a two particle-one hole (with respect to the target 7Li nucleus) [(1r1p3; 2 )(v1p1; 2)2(v1p3; 2 )] configuration which can be populated only by two nucleon or higher order mechanisms. While this configuration can only be populated via pn - nn1r+ contributions, which have a very small isospin strength, the analyzing power is an interference effect, rather than a coherent one, like the differential cross sections. Thus, thi s small 2p-lh admixture could enhance the NN - NN ,r+ contribution to this transition and cause the analyzing power angular distributions shown in figure 5.3 to more closely resemble the pp - d1r+ curves than do the 8Lig.s. distributions shown in figure 5.1. The 8 Li0_9808 state shown in figure 5.2 has a predominant [( 1r1p3; 2 )(v 1p1; 2)(v 1p3; 2 ) 2] configuration [Ca86]. Although at 200 MeV the analyzing powers for the transitions to all three final states of 8Li* are very similar, at higher energy each state portrays an individual character. There is a general trend, however, for the analyzing powers of all three states to become more positive as the incoming proton energy increa ses from 200 to 354 MeV. This is also observed for the 16 O(p, 1r+)17 O* reaction and appears to be a systematic feature of nuclear (p, 1r+) reactions. The pp - d1r+ analyzing powers also exhibit a similar trend (see figure 5.3). 8.1.2 Category 2 (Flat at Forward Angles) The next most common type of analyzing power angular distribution is exemplified by the 17 Oi 5.78 state in figure 5.11, and by the 170i7.1 state in figure 5.12. These analyzing power distributions are flatter at forward angles than any of the other distributions shown elsewhere in this work, perhaps with the exception of the 17 0 5_218 state shown in figure 5.9. These analyzing power distributions share similarities with the very flat 200 MeV analyzing power distributions reported for the 13 Ci1.4 and 14 Ch2 states in reference [Ko87]. Despite the difference between the shape of these distributions, and those in category 1, one observes once again that the mainly negative analyzing powers at 200 Me V become positive by 354 MeV, and then become negative again at 489 MeV. 91 8. 1.3 Category 3 ( Oscillating above 250 Me V) The third type of analyzing power distribution has large oscillations from 250 to 489 Me V, as shown by the 170 0_871 state in figure 5.8. The 250 MeV analyzing power distribution shown in this figure has a negative forward angle dip which is not visible in category 1 analyzing powers like the 170 7.757 state shown in figure 5.10. Thus, t he frequency of the 250 MeV analyzing power oscillation in figure 5.8 is much larger than the frequency of the 250 Me V analyzing power oscillation in figure 5.10. Data for other states not shown in this work at higher excitation have less dramatic analyzing power oscillat ions. Many of the states which exhibited this type of analyzing power distribution were primarily of single particle (lp) or three particle-two hole (3p-2h) structure. Once again we see that the analyzing powers at 354 MeV are generally more positive than those at 250 and 489 MeV. 8.1.4 Exceptions Two states which do not seem to fit into any of the previously described categories are the 17 Og.s. and 170 5_218 states. As shown in figure 5.7, the 170 ground state has a rapidly oscillating analyzing power at all energies from near-threshold, at 156 MeV, to well above the Ll1232 invariant mass, at 489 MeV. The 157 MeV 17 Og.s. analyzing power measurements [Sj81a) display a pp -+ d1r+-1ike shape because only a very small range of four-momentum transfers are accessible at this low energy. As the energy is increased, a larger range of t values become accessible, and more oscillations in the analyzing power results become apparent. This type of energy dependence was not displayed by any other state studied in this work. Although the analyzing power oscillations exhibited by this state at 250, 354 and 489 MeV are very similar to that of the 17 0 0_871 state shown in figure 5.8, it should be noted that at 250 MeV the oscillations of the 17 0g .s . are about a quarter oscillation out of phase with the oscillations of the 17 0 0_871 state, while the two analyzing power distributions appear to oscillate with the same frequency. The other state which does not seem to fall into any of t hese analyzing power categories is the 17 0 5_218 state shown in figure 5.9. The analyzing powers for this state are entirely positive at 250 MeV, positive but on average of smaller magnitude at 354 MeV, and entirely negative at 489 MeV. In summary, the analyzing power angular distributions of many 2p-lh states have some 92 resemblance to those of the pp -+ d7r'+ reaction. However, there are also many states of differing nuclear structure which have entirely different analyzing power distributions. 8.2 Energy Dependence of the Analyz ing Powers Although the specific types of analyzing power angular dist ributions can not be explained on the basis of nuclear structure, it is intriguing to note that regardless of the type of distribution, analyzing powers at 354 MeV are more positive than those at 250 and 489 MeV (with the exception of the 17 0 5_218 state shown in figure 5.9). In figure 6.2 the energy dependence of the analyzing power for the 16 O(p, 11'+)17 0 7_757 reaction is shown at several different four-momentum transfers. The energy dependence of the analyzing powers for this reaction is better described by the pp -+ d7r'+ curves shown by the solid lines in the same figure than those of the differential cross sections. Note that in the region t > 0.35GeV 2 /c2, both the 16O(p,11'+)17 Ob 57 reaction and the pp-+ d7r'+ reaction have an analyzing power energy dependence in which the analyzing power is most positive near the ..6.1232 invariant mass. This could be interpreted as anot her signature that is consistent with the characteristics of a NN -+ NN 71'+ process. The analyzing power energy dependence of many of the other states do not resemble the pp -+ d7r'+ reaction so clearly. The striking similarity to the pp -+ d7r'+ reaction in figure 6.2 may be because the 17 0 7_757 state is primarily a stretched 2p-lh configuration to which only two nucleon processes can contribute. 8.3 Continuum Results Continuum results, which do not require the neutron in a two nucleon process to be bound, may shed further light upon the origin of these analyzing powers. Figure 8.1 shows the analyzing power of the 16 O(p, 7r'+)X reaction plotted versus the missing four-momentum squared at incident proton energies of 250, 354 and 489 Me V. Also shown for comparison are the previously published 13 C(p, 7r'+)x analyzing powers [Ko87] at 200 MeV, as well as the pp -+ d7r'+ analyzing powers transformed to the nucleon-nucleus kinematical frame (solid lines). The plots at each incident energy are of the analyzing powers for several 1 MeV wide slices of continuum near 20 MeV excitation. The analyzing powers shown do not 93 change very much within the range of excitation energies plotted. They are best described by the pp - d1r+ curve ( after transformation to the nuclear frame) at low missing momenta (t > 0.45 GeV2 /c 2 ) and this description becomes less accurate as the missing momentum is increased (smaller t). However, the pp - d1r+ analyzing power still provides a qualitative description of the 489 MeV data. Korkmaz et al. [Ko87) interpreted the exceptional description of the 200 MeV forward angle analyzing powers by the pp - d1r+ curve as eviden ce that 1r+ production within the nucleus can be viewed as a quasi-free two-body process . Falk et al. [Fa86) also noted that the 400 and 450 MeV forward angle 12 C(p, 1r+)x anal yzing powers are very close to what would be observed via a pp - d1r+ quasi-free process . As the square of the missing momentum is increased, nuclear distortions presumably play a larger role and the quasi-free model is no longer relevant. Also, it is not unreasonabl e to expect that more nucleons may become involved in the momentum sharing process at the higher momentum transfers. This hypothesis may be supported in fact by measurements of the inverse reaction, pion absorption on nuclei leading to multinucleon emission. 94 13C ( p, 7T +) X 1.0 +-----'------'---~--__._ ___ .._ __ ---r 0.5 0.0 -0.5 200 MeV -1.0 +----~--~---...-------------1.0---~--~----- -~--~---L Q) 3: 0 o_ 0.5 0.0 -0.5 II a 250 MeV -1:g _ ___._ _____.__ _._____. __ ._ __ N 0.5 O 0.0 C -0.5 <( 0.5 0.0 -0.5 0.6 354 MeV 489 0.5 0.4 0.3 t (GeV2/ c2) -MeV 0.2 0.1 Figure 8.1: Analyzing powers of the continuum reaction versus missing four-momentum transfer squared. The 200 MeV data is from a recent publication by Korkmaz et al. [Ko87]. For the 200 MeV data, the circles are for 20 MeV excitation and the solid triangles are for 22 MeV excitation. For the higher energy data, the open squares are for 19 MeV excitation, the solid diamonds are for 21 MeV excitation, and the open triangles are for 23 MeV excitation. 95 Chapter 9 Theoretical Models In the 17 years that the (p, 1r+) reaction has been studied, there has been much theo-retical investigation, and many differing opinions on the merits of one theoretical model over another. During this period, theoretical models have become considerably more so-phisticated. Nevertheless, agreement between theoretical models and experiment is only fragmentary, and many questions pertaining to the separation of nuclear structure and re-action mechanism effects have yet to be answered. Thus, theories have followed, rather than led experiments in understanding the global systematics of the (p, 1r+) reaction. 9.1 Non-Relativistic Single Nucleon Model The simplest possible model that can be formed of the (p, 1r+) reaction is the plane-wave stripping mechanism. This model , shown in figure 1.4, is ba sed upon another high momen-tum transfer stripping process, the ( d,p) reaction. This calculation predicts a zero analyzing power at all angles. If optical potentials are used to distort the incoming proton and out-going pion plane-waves (Distorted Wave Born Approximation (DWBA)), then non-zero analyzing powers are possible. Many different DWBA calculations have been performed, of which the model by Tsangarides [Ts79] is perhaps the most complete. The stripping model of Tsangarides is able to qualitatively reproduce the main features of the A(p, 1r+)A + 1 reaction over a wide range of nuclei at energies close to threshold. Figure 9.1 is a good example of this, showing how the DWBA calculation reasonably reproduces the magnitude and shape of the differential cross section, but that this agreement gets worse as the proton 96 energy is increased. All parameters used in this calculation, as well as all of the other calculations shown in this thesis, are constrained by other types of scattering experiments, and their normalizations are absolute. Figure 9.2 shows several calculations of the 12C(p,ir+) 13Cg.s. reaction at Tp = 200 MeV using different sets of parameters for the proton optical potential. As the diagram shows , the calculated magnitude of the differential cross section is somewhat sensitive to variations of these parameters, but that the shape of the analyzing power is even more sensitive to variations in the proton optical potential parameters. Indeed, this point is made even more clearly in figure 9.3, which shows four different DWBA calculations for the 12 C(p, 1r+)13 Cg .s. analyzing power by different authors. It is hard to believe that all of these calculations are essentially the same in their physics input, and that all of them are trying to describe the same set of experimental data. This extreme sensitivity to variations in parameters should not come as too much of a surprise as the analyzing power is created solely by the distorting potentials and has no intrinsic non-zero value in a distortion free PWBA calculation. Variations in the pion optical potential parameters affect the differential cross sections more than they do the analyzing powers. Furthermore, the calculation is very sensitive to the choice of wave function for the bound neutron. This sensitivity to variations of the optical potential parameters is a major problem with the DWBA model and stems from the large momentum transfer characterized by the (p, 1r) reaction . In the stripping picture, the momen t um of the incoming proton is not shared explicitly with any of the other nucleons in the nucleus. Thus, the neutron from the p --t n1r+ process has much larger momentum than the nuclear Fermi momentum. This makes the small and not very well understood high momentum components of the distorted incoming proton wave function and the bound neutron wave function very important, and the calculation is overly sensitive to variations in parameters which· change these small components. 9.2 Non-Relativistic Two Nucleon Model A model which explicitly shares the large momentum transfer between three bound state wave functions is not expected to be so sensitive to variations in the optical potential parameters. This follows since each participating nucleon will absorb a momentum transfer 97 -... en ' .0 C -~100 C: '0 ' b '0 2 40 41 _ Ca(p,v+) Cag. 1 .(7/2 ) - OLP ).•1 'n • 1.16, ~n· .5 0 60 90 120 150 180 BcM TL p (MeV) 185.3 172.8 163.3 160.0 153.5 148.2 ·143.6 140.1 Figure 9.1: 4°Ca(p, 1r+ )41 Cag.s. calculations of Tsangarides. This figure is taken from refer-ence [Ts79]. 98 -.:,o .D C -.4 -1. • ....... . ........ ........ + •2c < 7T+) '3c u12-, p, g.L ! TRIUMF Tp •20~ MeV --- OLP >-•I Vp ------OL P ).•O vJ 2 -·-·OL P ).•I Vp .... ~. .... .. :--,..... , • 'n•l.l8 ......... ' ·-.. . .:::....._ .., a a • .5 ~---...., n ·-·-.. .... . :::---. .... _ ::-,...... -------- ;_"--- --~ ...... _ 40 60 80 BLAB 100 ' 120 140 I OLP >-•I Vp 'n•l.l8 I -----OLP >-•O Vp 0n•.5 -·-· OLP ). • I vi 60 80 100 120 Figure 9.2: 12C(p, ,r+) 13 Cg.s. calculation of Tsangarides using several different sets of pa-rameters for the proton optical potential. This figure is taken from reference [Ts79]. 99 1.0 ..--------------------. 0.8 0.6 0.4 02 A., ao -02 -0 .4 -0 .6 -OB -t .O .__ _ __. __ ___.._ _ ......_ _ _.__ __ .L..-_--l 0 Figure 9.3: A collection of DWBA analyzing power results for the 12C(p, rr+)13Cg.s. reaction at Tp = 200 MeV. This figure is taken from reference [Fe81]. comparable to its Fermi level momentum. This is a region where the nuclear wave functions and potentials are well known, so a variation of the potential parameters will not significantly alter the results of the calculation. Unfortunately, these calculations are very tedious to perform, so only a handful of microscopic calculations have been done to date. Thus the sensitivity of the model to nuclear structure effects, and the energy range for which the model has been most successful, have not been tested as extensively as they were for the DWBA model. In addition, each of these calculations involve different simplifying approximations, so the results of one calculation can not be easily compared with those of another to gain a better picture of the systematics of the model. Fearing [Fe81], is one of a larger group of people who got around the difficulty of this model by performing phenomenological calculations in which actual pp -+ drr+ data are used to determine the amplitude of the NN-+ NNrr+ vertex ; these are combined with dis-torted proton and pion waves to determine the nuclear (p, rr+) differential cross section and analyzing power. This model is commonly known as the Distorted Wave Impulse Approxi-mation (DWIA). However, what is really required is the off-shell NN-+ NNrr+ amplitudes, 100 for which a model must be used, rather than the on-shell NN ---+ NN1r+ amplitudes de-termined phenomenologically. Nevertheless, this type of calculation has had reasonable success, but for the purposes of this work this discussion shall concentrate solely upon the microscopic calculations in which the NN ---+ NN 1r+ vertex is determined from theoretical calculations. 9.2.1 The Model of Keister and Kisslinger The first microscopic calculation was performed by B.D. Keister and L.S. Kisslinger [Ke84]. Their model incorporated the two ~ 1232 resonant two nucleon diagrams shown in figure 9.4, as well as two plane wave stripping diagrams also shown in the same figure. One possible concern is the problem of double counting between the DWBA and the TNM contributions since both calculations use distorting potentials. The purpose of the optical potentials is to subtract flux from the incoming and outgoing channels; this accounts for losses due to absorption and other rescatterings within the nucleus. The parameters for the optical potentials are determined via fits to the elastic (p,p) or ( 1r+, 1r+) scattering data. Thus, implicitly contained within the DWBA calculation are the TNM diagrams, since the two nucleon model is in essence a pion production model in which one internal pion rescattering is calculated explicitly. The DWBA calculation simply incorporates these internal pion rescatterings via the pion distortions, and, therefore, the sum of the DWBA and TNM amplitudes will contain the pion rescatterings twice. If, however, plane waves are used for the outgoing pion wave function in the single nucleon diagrams, but distorted waves are used in the two nucleon diagrams, then the problem of double counting will not occur. Keister and Kisslinger applied their calculation to the 12 C(p, 1r+)13 Cg.s. reaction at Tp = 200 MeV (see figure 9.5). The major approximation employed in this calculation is that the intermediate ~1232 resonance is not allowed to propagate within the nucleus (i.e. the ~ 1232 is produced and then decays at the same point in co-ordinate space). Although the effect of this approximation could not be investigated, they did investigate the sensitivity of their calculation to the propagation of the virtual pion within the nucleus. This means that the two participating nucleons in the NN ---+ N~ process must also lie at the same point. They found that if the virtual pion is static, then the differential cross section calculation is four orders of magnitude larger than if the virtual pion is allowed to propagate 101 -~----Figure 9.4: The two nucleon model and PWBA diagrams used by Keister and Kisslinger. This figure is taken from reference [Ke84]. throughout the nucleus. When doing this test, they further assumed that the virtual static pion had the same momentum as the final outgoing pion. This is a poor approximation since the momentum of the internal virtual pion should be determined from conservation of momentum conditions at each interaction vertex, and should not be just one constant value. A peculiar finding was that the Keister and Kisslinger model was sensitive (by a factor of 2.5) to the use of Woods-Saxon or harmonic oscillator bound state nuclear wave functions. This may be because they ignored the spin-orbit term of the Woods-Saxon potential. Their final conclusion was that their two nucleon model calculation was just as sensitive to variations in calculation parameters as the DWBA was. This came as a surprise because the TNM is believed to be intrinsically less sensitive to variations in the potential parameters than the DWBA, and this is the main motivation for performing these calculations. The sensitivity of the model to variations in the potential parameters may be because of the simplifications involved. 9.2.2 The Model of Iqbal and Walker The more recent calculation by M.J. Iqbal and G.E. Walker [Iq85] does not make the approximation of a static intermediate Ll1232 . This calculation, however, includes only 102 IO 3 .---,,----,---,,---.---,----,-----r----r---, 2 10 :;; ' .0 C -0 10 ' b -0 1.0----.---,---,---,---,---,---,-----, 0 .5 <! -0 .5 t-,, i f t t t \ ~Vf ! - I. 0 1,__2...Jo--4..1.0~::_6..1.0 _ B_._O _ Io..L..0--12.L..o--, 4'-o-,"'"'6-0___,I B0 Bc.m. (deg) Figure 9.5: 12C(p, ,r+)13Cg .s. calculation at Tp = 200 MeV by Keister and Kisslinger . The dashed curve is the PWBA contribution, the dash-dot curve is the two-nucleon contribution , and the solid curve is their coherent sum. This figure is ta ken from reference [Ke84). 103 two nucleon diagrams of the 6.1232 resonant type, and does not incorporate any single nucleon diagrams. Thus, this model is primarily intended for application to the 6. 1232 resonance region, where all other competing processes are assumed to be small. The only other approximation is that the interaction of the 6. with the many-nucleon environment is assumed to be a local function of the nuclear density. The intermediate mesons can be either 7r or p-mesons, although the p-meson exchange contribution was determined to be a very small contribution. Originally, this model calculated differential cross sections for the two TNM diagrams included in the model of Keister and Kisslinger. However, it has been recently extended by M.J. Iqbal and the author for the calculation of differential cross sections and analyzing powers for the four diagrams shown in figure 9.6. Two of these diagrams, also calculated by Keister and Kisslinger, are post-emission diagrams in which the physical pion is created after the incident proton interacts with the nucleus. The other two diagrams shown in this figure are pre-emission diagrams in which the physical pion is emitted before the incident proton interacts with the nucleus. These last two diagrams are essentially spontaneous pion production, but are part of a complete set of time ordered diagrams, and thus their inclusion is desirable. Although a 'back of the envelope' calculation before proceeding with the implementation of these two pre-emission diagrams indicated that at some energies they could contribute up to 20% of the total cross section, the final calculation showed that any contribution due to these diagrams is negligible. This is because the 6. 1232 is very far off the mass shell in the pre-emission diagrams. Present limit ations of the model are that it can only perform calculations for spin zero target nuclei, and that it can not be reliably applied to energies above the 6.1232 resonance. This is because the model uses a Chew-Low formalism for the 6.1232 wave function, and this formalism does not predict a decrease in the pp -+ d1r+ cross section at energies above the ~1232 resonance. Further work is necessary in order to generalize the model for target nuclei of arbitrary spin, and to incorporate a formalism which is valid at energies above the 6. 1232 resonance. This model has been applied to the 12C(p, 1r+)13C9_50 reaction from Tp = 200 up to 354 MeV. This is an appropriate reaction to investigate becaus e the final state has a predom-inantly two particle-one hole configuration which cannot be reached by stripping mecha-nisms. Results for this calculation are shown in figure 9. 7. The agreement of the TNM 104 Taqs~t !::miss lon + I I I / / 6 , .p~~JA+I Pre.-Emh1:i. ion ,. f Diagraa11 A \ Post-Eaiss i.on Diagra.m:ai , , , + ,' I , 6 , p ---i=::::::::::::::1. ____ J 1.{ A+I Pro jc..:tih t:missio n • .,' ' , 6 P-+ J , . / A+l I A I ~/ ,.[ Figure 9.6: Pre and post-emission diagrams calculated in the TNM model of Iqbal and Walker. with the experimental data is clearly superior at 354 MeV than at 200 or 250 MeV. This could indicate that diagrams which include an intermediate .6.1232 resonance are more im-portant to the reaction mechanism at 354 MeV than at energies in the 200-250 MeV range. However, any explanation for the discrepancy between the calculation and experiment at these lower energies must not only take into account neglected non-resonant contributions, but must also include the role of single nucleon diagrams which are not included in this calculation. Also note that the analyzing power calculation qualitatively describes the ex-perimental data, including the change in the sign of the analyzing power at the energy of the .6.1232 invariant mass, although at 250 MeV there is a large angle oscillation in the analyzing power which is not predicted by the calculation. Unlike the model of Tsangarides, the analyzing powers calculated by the lq bal and Walker model were sensitive to pion distortions rather than proton distortions, and the differential cross sections were reasonably insensitive to either. The model was investigated for sensitivity to the use of Woods-Saxon or harmonic oscillator wave functions and this was found to be only a 1% effect, in direct contradiction to the sensitivity found by Keister and Kisslinger. This difference is likely due to the fact that Keister and Kisslinger ignored 105 UC(p 7T+) 13c• 10• 10• I 4 9.50 10• 10 _..__ L Cl) 103 103 • 103 103 " .. .. ..0 ...... C ... .. '-" ,al .. ,01 101 101 • a c:: "CJ ",o, 10, 10, 10, b "CJ 200 MeV 250 MeV 300 MeV 100 100 100 100 1.0 1.0 1.0 1.0 L (L) 00.5 0.5 0.5 0 .5 0... O'lO.O 0 .0 0.0 C N ~-5 .5 .5 C I I <t: -1.0 -1.0 -1.0 -1.0 0 60 120 180 0 60 120 180 0 60 120 180 0 60 120 180 8 (deg) c.m. Figure 9. 7: Two nucleon model calculation by Iqbal and Walker for the 12 C(p, 1r+)13 C9_50 re-action. The experimental data shown are from the following references: A reference [Hoi80]; D reference [Lo84b]; • [This Work];* [Zi84]. This calculati on was performed assuming that the 2p-lh component of the 13 C9_50 state is unity, and only includes intermediate pion exchange. 106 the spin-orbit term of their Woods-Saxon potential. In conclusion, this model is not as sensitive to variations in the potential parameters as either t he DWBA model or the TNM model of Keister and Kisslinger, and as such, there is a hope that something can really be learned from this model. The improved agreement between calculation and experiment near the invariant mass of 61232 is promising, but more work needs to be done to verify the conclusions one can draw with this model. 9.2.3 The ORCHID Model of Dillig, Conte, Bent and Alons The ORCHID model originally begun by M. Dillig [Al87,Dil85] has been under development for approximately 6 years and has only recently come to completion. This model has been designed primarily to investigate the (p, 1r) reaction near t hreshold. It incorporates both PWBA and TNM terms, as does the model of Keister and Kisslinger. Both pions and p-mesons are used as the intermediate exchange particles, but the 6 1232 resonance does not propagate through the nucleus. Unlike either of the prece eding two nucleon models, the calculations are performed in momentum, rather than co-ordinate, representation. This is designed to make the model more flexible for the investigation of the dynamical effects of the reaction, such as the effect of using static propagators for the exchange particles, and the inclusion of the 6-nucleus interaction in the 6 propa gator. It is one of only a few calculations [Cv85,Dil85,Ku86] to be applied to the (p, rr-) reaction. This model has, at present, only been applied to the 3He(p, rr+)4Heg.s. reaction, where stringent tests can be applied to locate errors in the coding of the computer program. There are plans to eventually apply this model to heavier target nuclei such as 12C and 16 0. The 4 Heg.s. is a single particle state, so it is expected that both SNM and TNM processes will contribute. Preliminary results indicate that the two processes are approximately equal in magnitude (see figure 9.8), however, for heavier nuclei, the relative importance of the . SNM contribution to single particle states may diminish because of the larger momentum transfers involved. So far, this model has been only used to illustrate the relative importance of the various amplitudes, and no effort has been made to optimize the potential parameters for max-imum agreement with experiment, and no indication has been given of the sensitivity of the calculation to the input parameters. Because of this, no definite conclusions can be 107 -.c C -e . u q -0 ' b -0 3 4 4 He (p, ,r+) He Tp=200 MeV 10 ---· ______ --;..,... ____ __ ' 103 .... , . ' ' ' 102 101 I ' \ • • • • -----<?o + -I 0 60 120 ec.m. (deg) 180 Figure 9.8: Full calculation of the 3He(p, ,r+)4 Heg.s . reaction at Tp = 200 MeV with the ORCHID model using the 'realistic' wave functions. The dashed curve is a single nucleon model calculation with full proton and pion distortions (DWBA). The solid curve is the sum of a SNM with pion plane waves and a projectile emission TNM involving intermediate pion exchange only. The dot-dash curve is the sum of a SNM with pion plane waves and a full TNM with both pion and p-meson exchange. This figure is taken from reference [Al87]. 108 made about the physics information contained in the mod el. However, ORCHID model calculations show that the PWBA portion is extraordinarily sensitive to the type of bound state wave function used (see figure 9.9), and is sensitive to the distortion parameters used as well. The TNM diagrams, however, are not as sensitive to parameter variations as the SNM diagrams are, a feature that one would expect by the large differences in momentum transfered per nucleon involved in these two processes. 9.3 Relativistic Orie Nucleon Model A model unlike any of the other models described here is the relativistic stripping calculation by E.D. Cooper and H.S. Sherif [Cp82]. It calculates only the projectile emission SNM diagram shown in figure 1.4, and neglects the less important t arget emission diagram. It uses the Dirac impulse approximation for the incoming proton-nucleus interaction, Dirac-Hartree wave functions for the neutron bound-state, and a Stricker-Mc Manus-Carr potential, which is derived from the Klein-Gordon equation, for the outgoing pion-nucleus interaction . Figure 9.10 shows the results of this calculation for the 16 0(p, 1r+ )17 Og.s . reaction at en-ergies close to threshold. As observed, this calculation does a respectable job of predicting the experimental differential cross sections at Tp = 185 MeV, but the agreement between experimental results and calculation deteriorates as the energy is decreased towards thresh-old, although it is still not as poor as some of the other calculations presented here. The analyzing power shape is not described as well by the calculation, and seems to be quite sensitive to the proton distortions used [Cp82]. For final sta tes with more complicated nu-clear structure, such as 170~ _871 and 13 Cg.s., the calculation performs more poorly. This is partly because of configuration mixing effects for states with complicated nuclear structure. As first discussed by Miller [Mi74], configuration mixing can present a problem because the single nucleon model emphasizes the high momentum components of the nuclear wave func-tions. Therefore, it is necessary to consider these high momentum components of the final state wave function, even though they may have very small spectroscopic weighting factors which are very poorly understood. For states with complicated nuclear structure, such as those with large 2p-lh contributions to which only the TNM and higher order processes may contribute, the SNM can only populate the single particle components of these states , and may be forced to play a less important role. 109 -VI ' .D C: -e u C: "'C ' b "'C 4 3He(p,1r+) 4He Tp•200 MeV 10 .-----.----,--...------.----. •• • ...... ,cf 10 Saxon 103 •• • ' ONM, plane waves • • ' ' ' • • ,,, • ' • Realistic -- static - - non-static 10'..__.. _ __.__ ....... _____ __ 0 60 IW I~ Bc.m. (deg) Figure 9.9: PWBA calculations of the 3He(p, rr+)4Heg.s. reaction showing the sensitivity of the ORCHID model to the type of bound state wave function used for static and non-static calculations. The 'realistic' wave function is a Hartree-Fock wave function which differs only marginally from the Woods-Saxon wave function at large radii. This figure is taken from reference [Al87). 110 1000 100 1000 100 I C _, 1000 bJC: 'C 'C 100 1000 100 10 0 165 MeV • •~ I -~·"\.1/ ----- PS • ------------... ... AO .... ',, ', I ! 157 MeV I 154 MeV ',,,,! i .... ----ao 120 160 6c.m. +0 .6 .------------------, •0.A +0 .2 ·O 2 ·0 .A ·0 .6 ·0 .1 ·1 00 16Q (p, 71'+) 17Q g.1. -PV ----- PS AO 10 8c.m. Tp • 157 MeV 120 160 Figure 9.10: Relativistic stripping calculation of the 16 O(:p, 1r+)17Og.s. reaction by Cooper and Sherif. The solid curves are calculated using pseudo-vector coupling for the 1r-N vertex; the dashed curves are for pseudo-scalar coupling. This figure is taken from reference [Cp82]. 111 Preliminary calculations in progress [Cp86b) will hopefully shed light on the question of the relative importance of these single nucleon diagrams. Shell model calculations using a Nilsson model with band mixing predict that the 13 q;_50 state contains a 1g9; 2 - 12 Cg.s. core configuration with a spectroscopic factor of about 2% (Cp87). Thus, through this small single particle contribution, it is theoretically possibl e for the SNM to populate this predominantly 2p-lh state. A plane wave relativistic strip ping model calculation leading to this final state, assuming a spectroscopic factor of 2%, is shown in figure 9.11. Since one expects SNM contributions to play a more important role at lower energies (i.e. lower momentum transfer) than at the higher energies, the inclusio n of SNM diagrams could bring the calculated TNM differential cross section at 354 MeV shown in figure 9.7 closer to the experimental data and thus deemphasize the successful tre nd observed with the TNM at 354 MeV. 9.3.1 Application to 16 O(:p, 1r+)17 Og.s. Relativistic stripping model calculations for the 16 O(p, 1r+)17 Og.s. reaction by E.D. Cooper and A. Matsuyama (Cp86a) are compared in figure 9.12 with differential cross section and analyzing power data from the present work and reference [Az87). Unlike the calculations by Cooper and Sherif shown in figure 9.10, this calculation uses a non-relativistic ~-hole potential for the outgoing pion-nucleus distortions. In thi s method, the distorted waves are calculated from basic principles by summing the infinite Watson's scattering series. With the other optical potentials the distorted waves are obtained by fits to previously obtained ( 1r+, 1r+) scattering data, although they also could in principle be obtained by summing the infinite scattering series. Therefore, with t his calculation, the distinction between SNM and TNM is blurred, as some of the diagrams explicitly included in the TNM are implicitly included in via the ~-hole calculation (see figure 9.13). As in the Cooper and Sherif model, the proton distortions are calculated from first principles via the Dirac impulse approximation, and the NN --t N interaction is neglected. Comparing the differential cross section calculations with the experimental data, it is immediately apparent that the agreement between theory and experiµient is superior at 354 MeV, and deteriorates at energies far below the invaria nt mass of the ~ 1232 (200, 250 Me V). This behavior is in contrast to the earlier relativistic stripping model calculations of 112 104 ---l.--_____j __ _.i_ __ .,___------t-12c ( P 7T +) 13c * ' 9 .50 • T ==354 ~1eV p • • • x .02 0 45 90 ~35 180 e ( deg) c.m. Figure 9.11: Relativistic single nucleon model calculation by Cooper and de Takacsy. This calculation was performed assuming that the spectroscop ic factor of the 1g9; 2 -12 Cg.s. component of the 13C9_50 state is unity; the calculation is shown with data from this work assuming that the spectroscopic factor of this component is 0.02. 113 ~, '--... b "'O 200 MeV ,004--- ____ --J.. L (l) 1.0 ...__......___. _ __._ 00 .5 0... 0'\0 .0 c:: N ,so(p,n+) 170 g.s. 1)3~-'------'--+ D ,02 a 0 , 250 MeV 10 4-----------. 350 MeV ~D..._ ___ _._.__.. 1.0 +--..___--:'----+ lO+--~---.. 0.5 0.5 0 .0 t 0.0 10,..__..J..__..J..__. 102 450 MeV ,oo._ _____ • 1.0 ...... --'---_.___. 0.5 0.0 ~-5 0.5 .5 0.5 C:: I I -to +-------+-1.0 -to -1.0 +-------+ 0 60 120 180 0 60 120 180 0 40 BO 120 0 30 60 90 6 ( deg) c.m. Figure 9.12: Relativistic stripping calculation for the 16 O(p, 11'+)17 Og.s. reaction by Cooper and Matsuyama at 200, 250, 350 and 450 MeV. The 200 MeV data is taken from reference [Az87), all other data shown is from this work. 114 1.1 )1.2) 1.3) I I (a) (d) (a) (a) + ( b) + ( e) + ( b) + ( b) I I I I I I I I I I I + + + + (c) I I I ( f) (c) ( C} +• +• +• Figure 9.13: Infinite series of diagrams for the ~-hole stripping calculation of Cooper and Matsuyama. Series 1.1 are diagrams included in the calcul ation, of which 1.1 b) is a TNM diagram included in the calculation by Iqbal and Walker. Series 1.2 and 1.3 are not included in the ~-hole calculation, however, diagram 1.2 a) is a TNM diagram included in the calculation by Iqbal and Walker. This figure is taken from reference [Cp86a). 115 Cooper and Sherif [Cp82], in which agreement between data and calculation was fairly good for energies below 185 Me V. Since the only difference between these two models is the use of the .6.-hole potential, rather than a local Stricker-Mc Manus-Carr potential for the outgoing pion distortions, it is reasonable to assume that this is the cause of the improved agreement in the .6.1232 region . In fact, as shown in reference [Cp86a], a local potential calculation at 350 Me V overestimates the 354 Me V experimental data by approximately one order of magnitude. Thus , the differential cross section for the local potential calculation rises rapidly with energy, and only agrees with experimental data at energies fairly close to pion production threshold. The .6. - hole potential calculation , on the other hand, overestimates the 200 MeV differential cross section and rises much more slowly with energy. Figure 9.12 also shows that the .6.-hole potential calcula t ion of reference [Cp86a] quali-tatively predicts the oscillations of the analyzing power data. Here, the agreement between experimental results and calculation is clearly superior at 200 MeV rather than at the higher energies. In particular, the calculations at 250 and 350 MeV are out of phase with the data , and the calculation at 450 Me V completely fails to reproduce the continued oscillations of the 489 MeV data. Note that the local potential calculation at 350 MeV greatly under-estimates the magnitude of the analyzing power oscillations, and has the wrong frequency of oscillation as well. The authors of this model are unable , at present , to account for the failure to predict the oscillations at 489 MeV, or for the error in phase in the 250 and 350 MeV analyzing power calculations. Nevertheless, this model has been the most successful to date in qualitatively describing some experimental result s over a large energy range. " 116 Chapter 10 Summary and Conclusions The 7Li(p, rr+)8Li*, 12 C(p, rr+)13 C*, 13 C(p, rr+)14 C*, 13C(p, rr-) 14 O* and 16 O(:p, rr+ )17 O* reactions have been investigated at incident proton energies of 250, 354 and 489 Me V using the MRS spectrometer at TRIUMF. These energies were chosen because they span the A1232 resonance region, and as such, the effects of the A123 2 resonance should be the least ambiguous, if they are present at all. The present work has shown that at a constant value of the four-momentum transfer squared, the energy dependence of the (p, rr+) differential cross sections varies little from reaction to reaction. All states investigated exhibit an energy dependence, in the range t > 0.45 GeV2 /c2, in which the differential cross sections are shown to increase with energy up to the A 1232 invariant mass and then to either slowly fall or remain constant. A similar type of energy dependence is exhibited by the pp ---+ drr+ reaction at equivalent center of mass energy and four-momentum transfer squared. This is interpreted as strong evidence of a NN ---+ NA ---+ NN rr+ reaction mechanism where most of the incoming momentum is shared amongst two nucleons. At larger momentum transfers (t < 0.35 GeV2 /c 2 ), the (p, rr+) energy dependences are less uniform. Most of the states whose low energy distributions fall monotonically with angle have an energy dependence in which the 250 Me V data points have the largest differential cross section. This same type of energy dependence is also displayed by the pp ---+ drr+ reaction after transformation to the nuclear frame, and by the 16 0(p, rr+ )X reactions at t=0.3 GeV2 /c 2 • A few other states, however, continue to exhibit an enhancement at the invariant mass of the A 1232 in this region. This behavior could not be explained. Those 117 states which have pronounced large angle bumps in their low energy differential cross section distributions have very complicated energy dependences in this region. These large angle bumps are probably nuclear structure related, and one should note that at higher energies these states revert back to the exponential drop characteris tic of all the other states. The energy dependence of the 13 C(p,1r-)1 4 O* reaction was investigated at a four-momentum transfer squared oft = 0.50 GeV2 /c2, and no enhancement was seen at the b.1232 invariant mass, unlike all of the (p, 1r+) reactions. The energy dependence of the two states of 14 0 investigated, however, did have minor differences between them. The energy dependence of the 13C(p, 1r-)x continuum reaction, shown in figure 6.7, did have its maximum double differential cross section near the b. 1232 mass, but the energy dependence of the reaction was otherwise unlike that of the pp -+ d1r+ reaction. It is not clear what is the nature of the dynamical effect causing these differences between the three 13 C(p, 1r-) reactions explored here. The common feature of all three 13C(p, 1r-) reactions, however, is that the energy dependence is different from that of pp -+ d1r+ and (p, 1r+) reactions. This difference may be explained if the large b. 1232 ampli tudes accessible to the (p, 1r+) reaction via the pp -+ (pn)3s11r+ reaction are forbidden in the (p, 1r-) reaction via the pn -+ (pp )1 80 11"- reaction because of angular momentum and parity conservation and be-cause of the Pauli exclusion principle. The much weaker b. 1232 amplitudes which remain in the (p, 1r-) reaction may be of less importance than other non-resonant amplitudes. Extraction of the total cross section is possible by integrating the differential cross sections obtained over the scattering angle. The maximum total cross section was not found at the b. 1232 invariant mass, but at a lower energy in the 200 to 250 MeV range. This shift in the energy at which the maximum total cross section occurs is likely due to an interplay between a rising cross section at lower momentum transfers due to the influence of the b. 1232 resonance in the reaction mechanism, and a declining cross section due to the influence of the large momentum transfers reached at higher energy. These total cross sections scale according to the number of spin orientations in the final state (2JA+l + 1). The (p, 1r+) analyzing powers do not exhibit a common angular distribution, but were classified into several categories. Hints at the diversity of the (p, 1r+) analyzing power distributions had been seen prior to this experiment [Hoi81], but never before have enough nuclear final states been investigated from one target nucleus for some of the systematics 118 to be identified. In addition, this was the first time that (p, 7!"+) analyzing powers were obtained in this energy range for target nuclei with A > 2. The most common category was one in which the analyzing power distributions behaved in a manner very similar to that of the pp --t d7!"+ reaction. The continuum (p, 7!"+) reactions also exhibit analyzing powers which look very similar to the pp --t d7l"+ reaction, and this has been interpreted as evidence of a quasi-free NN --t NN7!"+ process occurring within the nuclear environment. Other analyzing power categories include distributions which are flat and near-zero at forward angles, and other distributions with rapid oscillatio ns. However , it was noted that the distributions of nearly every state had values which were on average negative at 250 Me V, positive at 354 Me V, and negative or at least less positive at 489 Me V. It was also noted that the pp --t d7!"+ reaction, after transformation t o the nuclear frame, exhibits a similar energy dependence. Theoretical calculations by two different models have been performed and compared with some of the data presented in this work. 16 O(p , 7!"+ )17 Og .s . differential cross-sections and analyzing powers have been calculated at 200, 250, 350 and 450 by Cooper and Mat-suyama. This is a relativistic stripping calculation which uses a A-hole potential for the pion distortions . The model was shown to perform satisfactorily in predicting the differ-ential cross sections near the A 1232 invariant mass, but the agreement between theory and experiment is not as good at energies far below the A 1232 invariant mass (200, 250 Me V) . The improved agreement in the A 1232 region appears to be largely due to the implicit inclusion of the A 1232 resonance in the model via the A-hole potential. The calculation performs satisfactorily in predicting the rapid oscillations in the analyzing power of this re-action. Overall, this model has been the most successful to date in qualitatively describing experimental data over a large energy range. Calculations were also performed for the 12 C(p, 7!"+)13 qj_50 reaction with the two nu- . cleon model of Iqbal and Walker, which only incorporates diagrams explicitly involving an intermediate A 1232 resonance. This is a final state whose dominant configuration is a two particle -one hole amplitude that can only be reached via a two nucleon mechanism. The model makes a good prediction of the differential cross sections of this reaction near the A 1232 invariant mass (354 MeV), but considerably underestimates the magnitude of the dif-ferential cross section at lower energy (200 and 250 MeV). This could mean that the cross 119 section predicted by the model increases with energy and only happens to pass through the data near 354 MeV, or it could also indicate the relative importance of the ~1232 resonance at these energies. An extension of this model which does not use a Chew-Low formalism for the ~1232 wave function is necessary to verify this claim. The calculation does a fair job of predicting the pp -+ d7r+-like analyzing power of this reaction at forward angles. A plane wave relativistic stripping calculation was also performed for this reaction as-suming that this dominantly 2p-lh state has a 2% single part icle admixture. The calculation shows that the stripping mechanism can contribute substant ially to this reaction at forward angles, even in the ~ 1232 resonance region. Since the plane wave stripping mechanism am-plitudes can be added to the two nucleon mechanism amplitudes without fear of double counting (provided that they are added with the correct relative phase), this calculation may account for the portion of the differential cross section not accounted for by the res-onant two nucleon mechanism calculation. Further work with the ORCHID model will hopefully clear up the question of the relative importance of these two amplitudes. Thus, this work has shown that there are some effects of the ~ 1232 resonance in the (p, 7r+) reaction, but that these effects are less clear in the (p, 71"-) reaction. Further work will have to be done to study the range of validity of the conclusions made here. Further experiments are being planned for the ~ 1232 resonance region at TRIUMF and at the IUCF Cooler using target nuclei ranging from 3He to 4°Ca, and more efforts are being made to study the continuum reaction in which the missing particle is detected. 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Measday, Phys. Rev. D 12, 3550 (1975). [Tho80] A.W . Thomas, R.H. Landau , Phys. Rep. 58c, 121 (1980). [Thr84) T.G . Throwe, Ph .D. thesis, Indiana University (1984). [Thr87) T.G. Throwe et al., Phys. Rev. C 35, 1083 (1987). [Ti84) J. Tinsley , J . Rogers , TRIUMF Design Note TRI-DN-84-28 'Introduction to DACS'. [To85) H. Toki, K.I. Kubo, Phys. Rev. Lett. 54, 1203 (1985). [Ts79) M.C. Tsangarides, Ph. D. thesis, Indiana Universit y (1979). [Vi83] S.E. Vigdor et al., Nucl Phys. A396, 61c (1983). [Vi87) S.E. Vigdor , W.W. Jacobs., E. Korkmaz, Phys. Rev. Lett. 58 , 840 (1987). [Zi84) W.A . Ziegler, private communication. [Zi85) W.A. Ziegler et al., Phys. Rev. C 32 , 301 (1985). W.A. Ziegler, Ph.D. thesis, University of British Columbia (1985). 126 Appendix A Software This appendix contains more details on the programs used to analyze (p, 11") data taken with the MRS spectrometer. The interested reader should also familiarize himself with the details of the LISA analysis package [Fr84] as well as the MRS user's manual [Hi86]. A.1 Data Analysis A.1.1 A Recipe for the Analysis of (p, 7r) Data using LISA 1. Create a version of LISA incorporating the appropriate INSERT subroutine used to calculate all of the needed variables ( a listing of the INSERT routine used for the analysis of the 160(p, 11"+)170* data is located in section A.1.2). 2. Mount a pp -+ d11"+ data tape. 3. Define the order of the data words as they are stored within an event on tape ( event structure). 4. Define all needed spectra, conditions, parameters, co-ordinates and scalers. 5. Do a LIVE display of TTB versus ESUM (SPID) and set the appr .opriate pion window (BLOP). Do the same with time of flight versus energy loss on the Sl scintillator. 6. Rewind the tape, and while gated on pions, look at a spectrum of the drift times for a wire on the FEC and on the VDC to ensure that the drift parameters are set correctly (SETDRIFT). Also look at the FEC (X0,Y0) and VDC (Xl ,X2) to ensure that the FMSK parameter, upper and lower acceptance limits and the software cuts (WI) are set properly. 7. Rewind the tape, and while gated on pions, check that the RF cut (TRF) and veto 127 scintillator cuts are placed correctly. Also check that the angles (Ope, </>) and ' difference in angles between the two VDCs (ITHD, IPHD) are calculated within the plotting scale. 8. Rewind the tape, and check that the focal plane parameters (F and TILT) are set correctly by ensuring that the pp -t d1r+ line is vertical on a plot of thetapc versus the focal plane position (XFTH). 9. Rewind the tape, and the place correct software cuts on all of the angles. Also check that the kinematic correction is set correctly (XFYO). 10. Rewind the tape, and while gated on all of the cuts set correctly so far, check that the ray tracing to the target is set correctly by looking at (YIYO), (XITH) and (XIXO). 11. Rewind the tape, and set the correct software cuts on XI and YI. While gated on the logical and of all of these cuts (EVENT), check that the dispersion matching correction (XFXI) and abberation corrections (XFTH) are set correctl y. 12. Rewind the tape, and verify that all parameters, software cuts and drift routine param-eters are set correctly. Dump all of these settings for later use. 13. Create another version of LISA with INSERT and EVBEV subroutines for the calcu-lation of rate dependent efficiencies and the creation of disk files containing skimmed data (listings of the routines used to analyze the 16 0(:p, 1r+)170* data are in section A.2.1). 14. Do steps 2-6 above with this new version of LISA, and dump these settings to disk for use when skimming tapes. 15. Use the version of LISA created in steps 13-14 to create skimmed pp -t d1r+ disk files, and then use the version of LISA created in steps 1-12 anal yze this data. 16. From the pp -t d1r+ data, determine the effective solid angle of the spectrometer, and a Legendre polynomial fit to the relative focal plane efficiency (77Foc). 17. Repeat step 15 for all of the (p,1r) data taken during the experiment, ensuring at all times that all parameters, software cuts, . and drift routine values are set correctly for each . individual run. 18. Integrate the number of counts under each peak via LISA (INT) if the individual peaks are resolved, or deconvolute the states via a fitting routin e (FITPEAK) if the individual peaks are not resolved. 19. Determine the final differential cross-sections and analy zing powers. 20. Write manuscript and publish data in Phys. Rev. C. 128 A. 1.2 Insert Routine Used in Main Data Ana lysis Thi s subroutine was linked with the LISA off-line event-by-event analysis system to calculate all of the variables and all of the corrections to them that were described in sections 3.3 to 3.5. subroutine insert(*) ex366.for (experiment 366) written by dieter frekers with modifications by garth huber, nov/86 include 1 lis$share:evtcom 1 include 1 lis$share:dskcom 1 include 1 lis$share:concom 1 include 'lis$share:daccom' data vdcdist data x1c0 data tetx1 data tetx2 data ivs / 5472./ / 7392./ /.09137/ /.09137/ /23/ start of vdc values in kbuf if(ieventtype_1.eq.1)then return scaler event if(ieventtype_2.eq.0)return 1 return if not event type 2 return if the hitpattern is bad kbuf(S0) = hitpattern ipuls = iand(kbuf(1),4096) if(ipuls.eq.4096)return ihitbit = para(99)+.5 ireturn = iand(hitpattern,ihitbit) if(ireturn.ne.0) return 1 now define all parameters needed tan_delta = para(1) ! tangent of fp tilt angle delta 129 focal_f = fact_yOsq = y_OO = para(2) para(3) para(4) fact_for_kinematic=para(5) a good value is -.05 offset of fp at x=O a good value is -1550. this is for the quadr. yo-correction II II II II II II y_001 = para(4)•para(5) fact_ theta_sq= para(7) !quadr. term in xfthpc-correction tetapc_02 = para(8) II II II II fact_theta_4= para(9) !4th power term in xfthpc-correction tetapc_041 = para(10) !1st 4th pwr offset-term in xfthpc-corr tetapc_042 = para(11) !2nd 4th pwr offset-term in xfthpc-corr fact_xi_xO = para(12) fact_xi_ tepc= para(13) xi_offs = para(14) fact_yi_y1 = para(15) fact_yi_yO = para(16) yi_offs = para(17) xfxt = para(25) xfxt_offs = para(26) disp = para(35) disp_offs = para(36) iwire = para(44) iwireoffec = para(45) 130 kbuf(71) = itimeofwire kbuf(72) = itimeofwireplus1 kbuf(73) = itimeoffecwire kbuf(74) = itimeoffecwireplus1 kbuf(75) = itimeoffecwireminus1 i_plow = para(46) i_phigh = para(47) tet0 = para(48) !/-175.44/ tetpcxf = para(49) !/-0.0062/ !=-.0070 for lac tetpc0 = para(50) !/ 95./ !=114.for lac fp_offs = para(51) offset for display of uncorr. xf fp_scale = para(52) scaling factor tetpc_scale = para(53) factor for display of tetapc tetpc_offs = para(54) offset for display of p-corr. tetapc y_offset = para(55) offset for y coordinates xi_scale = para(56) xi_disp_offs= para(57) yi_scale = para(58) yi_disp_offs= para(59) phi_scale = para(60) phi_offs = para(61) y0_offset = para(62) td_scale = para(63) 131 td_offs = para(64) phid_scale = para(65) phid_offs = para(66) esum_prot = para(70) !proton rejection parameter · ttb_offs = para(71) xf_offs_2 = para(72) !offset for 2d plots now define y coordinates on the vdcs and put them for u y1 = 1.732052•kbuf(ivs+5)-2.•kbuf(ivs+2)+2315.08 y2 = 1.732052•kbuf(ivs+3)-2.•kbuf(ivs+4)+2829.54 yy1 = y1+y_offset yy2 = y2+y_offset kbuf(ivs+2)=yy1 kbuf(ivs+4)=yy2 phi = y2-y1 define intrinsic angle differences to take into account pions which decay between vdc1 and vdc2, and hence change direction between them intr_thetad = intrinsicangle(6)-intrinsicangle(4) kbuf(ivs+13) = (intr_thetad+td_offs)•td_scale intr_phid = intrinsicangle(3)-intrinsicangle(5) kbuf(ivs+14) = (intr_phid+phid_offs)•phid_scale calculate esum on focal plane paddles ipmax=O do 70 i=i_plow,i_phigh if (kbuf(i).gt.esum_prot)goto 70 if (kbuf(i).ge.ipmax) ipmax=kbuf(i) 70 continue kbuf(100)=ipmax 132 !x1-x2 !u1-u2 do the same for the s1 scintillator ipmax=0 do 701 i=20,21 if (kbuf(i).gt.eswn_prot)goto 701 if (kbuf(i).ge.ipmax) ipmax=kbuf(i) 701 continue kbuf(101)= ipmax kbuf(2) = kbuf(2)+ttb_offs !offset to ttb to center pion blop calculate raw focal plane position x1c = kbuf(ivs+5)+x1c0 q1 = vdcdist•x1c-focal_f•(x1c-kbuf(ivs+3)) q2 = vdcdist-(x1c-kbuf(ivs+3))•tan_delta if (q2.eq.0) return xf = q1/q2 calculate theta and correct to get theta_pc teta = tetx1•(kbuf(ivs+3)-kbuf(ivs+5))+tet0 tetapc = teta+tetpcxf•xf+tetpc0 tetapcx0=tetapc •(kbuf(ivs)-para(79))•par a (80)+para(81) kbuf(ivs+12) = tetapcx0 thetapc_display=(tetapc+tetpc_offs)•tetpc _scale kbuf(ivs+6) =thetapc_display calculate target position xi = kbuf(ivs)•fact_xi_x0+fact_xi_tep c•tetaPC+xi_offs 133 kbuf(ivs+8)=(xi+xi_disp_offs)•xi_scale yi = fact_yi_y1•y1 + fact_yi_yO•kbuf(ivs+1) +yi_offs kbuf(ivs+9)=(yi+yi_disp_offs)•yi_scale corrections to the focal plane position 1 1 1 1 1 1 xfpc = xf + (kbuf(ivs+1)-y_00)**2*fact_y0sq + fact_for_kinematic•kbuf(ivs+1)-y_001 + fact_theta_sq•(tetapc-tetapc_02)••2 + fact_theta_4•(tetapc-tetapc_041)••2 * (tetapc-tetapc_042)••2 + xfxt•(kbuf(ivs+12)-xfxt_offs) + disp•(xi-disp_offs) scale factors for various variables kbuf(ivs+7)=(xfpc + fp_offs)•fp_scale kbuf(ivs+10)=(phi+phi_offs)•phi_scale kbuf(ivs+11)=kbuf(ivs+1)+yO_offset !quadratic yo corr !kinematic corr !aberration corrs !xO•thpc-term !dispersion corr kbuf(48) = kbuf(ivs+7)+xf_offs_2 !add offset for 2d plots kbuf(49) = kbuf(ivs)+para(91)•xi+para(92) !this is xOc return A.1.3 Analysis Conditions These variables were then subject to conditions during the off-line analysis. A sample listing of these conditions , and the number of events that passed each test, is shown below. As stated in section 3.1, there were also restrictions placed on the drift times of each VDC and FEC wire, as well as on the accepted location of hits within each chamber. LISA STATUS INFORMATION from: 6-DEC-86 12:26:45 134 ---------RUN= XE71 output header 3X30.DMP *************************CONDITIONS************************* Number of conditions defined: 29 [ Windows/bitmasks: 19] [ complex conditions: 10] MSK 1 (PULS) KOOR= 1 (DCR) [MASK = 4096] #(T) 6482 MSK 2 (UP ) KOOR= 1 (DCR) [MASK = 128] #(T) 36801 MSK 3 (DOWN) KOOR= 1 (DCR) [MASK= 256] #(T) 27489 MSK 4 (OFF) KOOR= 1 (DCR ) [MASK = 512] #(T) 12893 CON 5 PUP=PULS•UP #(T) 2443 CON 6 PDN=PULS•DOWN #(T) 2796 CON 7 POFF=PULS•OFF #(T) 1054 BLP 8 (PION) BLOP[X: 2 (TTB) / Y: 100 (ESUM) ] #(T) 68602 BLP 9 (PIS1) BLOP[X: 6 (TS1 ) / Y: 101 (ES1 ) ] #(T) 72140 CON 10 (XO ) KOOR= 23 (XO )[ 460, 1164]#(T) 73028 CON 11 (YO ) KOOR= 24 (YO )[ 247, 1208] #(T) 73173 CON 12 (THPC) KOOR= 29 (THPC)[ 437, 1672] #(T) 68817 CON 13 (PHI) KOOR= 33 (PHI ) [ 116, 459]#(T) 66587 CON 14 (IPHD) KOOR= 37 (IPHD)[ 176, 447]#(T) 70830 CON 15 (ITHD) KOOR= 36 (ITHD) [ 184, 447]#(T) 70874 CON 16 (TRF ) KOOR= 3 (TRF )[ 96, 146]#(T) 71642 CON 17 (TSLT) KOOR= 4 (TSLT)[ 1091, 1098]#(T) 77814 CON 18 (ESLT) KOOR= 8 (ESLT)[ 8443, 8505]#(T) 79516 CON 19 (TDIP) KOOR= 5 (TDIP)[ 1091, 1098]#(T) 75654 CON 20 (EDIP) KOOR= 9 (EDIP)[ 20, 32] #(T) 78087 CON 21 (XI ) KOOR= 31 (XI )[ 388, 826] #(T) 66173 CON 22 (YI ) KOOR= 32 (YI )[ 269, 943]#(T) 63212 135 CON 23 PI=PION•PIS1•TRF•ITHD•IPHD #(T) ·: 64436 CON 24 SOLID=THPC•PHI•XO•YO #(T) 64135 CON 25 VETOS=TSLT•ESLT•TDIP•EDIP•(-PULS) #(T) 67199 CON 26 EVENT=PI•SOLID•VETOS•XI•YI #(T) 51256 CON 27 UPEVT=EVENT•UP #(T) 24340 CON 28 DNEVT=EVENT•DOWN #(T) 17180 CON 29 OFFEVT=EVENT•OFF #(T) 8225 ....................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Rate Dependent Efficiency Analysis The insert routine listed in section A.1.2 will only do calculations if all of the chambers registered good hits (i.e. the hitpattern was not bad). To extract the rate dependent drift chamber efficiencies, the data had to be analyzed a second time with a routine that did not require the hitpattern to be good. (The hitpattern is a 16 bit word defined by the drift chamber decoding routine. Each bit of the word is set according to whether the appropriate chamber registered a good event .) A.2.1 Insert routine Used in the Efficiency A nalysis subroutine insert(•) ex366eff.for insert routine for lisa efficiency calculation written by garth huber include 'lis$share:evtcom' include 'lis$share:dskcom' include 'lis$share:concom' include 'lis$share:daccom' data vdcdist / 5472./ data x1c0 / 7392./ data ivs /23/ start of vdc values in kbuf if (ieventtype_1.eq.1)then return 136 now if (ieventtype_2.eq.0)return 1 kbuf(50) = hitpattern ipuls=iand(kbuf(1),4096) if (ipuls.eq.4096)return define all parameters needed kbuf(71) = itimeofwire kbuf(72) = itimeofwireplus1 kbuf(73) = itimeoffecwire kbuf(74) = itimeoffecwireplus1 kbuf(75) = itimeoffecwireminus1 i_plow = para(46) i_phigh = para(47) esum = para(70) ttb_offs = para(71) calculation of esum for focal plane paddles ipmax=0 do 70 i=i_plow,i_phigh if(kbuf(i).gt.esum)goto 70 if(kbuf(i).ge.ipmax)ipmax=kbuf(i) 70 continue esum10=esum/10. if (ipmax.le.esum10) ipmax=esum+esum10 !force bad events above cut kbuf(100)=ipmax kbuf(2) =kbuf(2)+ttb_offs !add offset to ttb return 137 end A.2.2 Logical Conditions This section lists the logical conditions that were placed upon the pion events for the calculation of the chamber efficiencies as described in section 3.2. This is a sample listing of the number of events that passed each logical test on the hitpattern in a 354 Me V, 0LAB = 30°, 16 0(p, rr+)17 0* run. LISA STATUS INFORMATION from: 4-DEC-86 11:04:12 ---------RUN= XE71 output header E366MUL.DMP, 3X30 *************************CONDITIONS************************* Number of conditions defined: 63 [ Windows/bitmasks: 30] [ complex conditions: 33] MSK 1 (PULS) KOOR= 1 (OCR ) [MASK = 4096] #(T) 6482 BLP 2 (PION) BLOP[X: 2 (TTB ) / Y: 100 (ESUM) ] #(T) 92819 MSK 3 (UP ) KOOR= 1 (OCR ) [MASK= 128] #(T) 58982 MSK 4 (DOWN) KOOR= 1 (OCR) [MASK = 256] #(T) 48358 MSK 5 (OFF) KOOR= 1 (DCR) [MASK = 512] #(T) 22239 CON 6 PUP=PULS•UP #(T) 2443 CON 7 PDN=PULS•DOWN #(T) 2796 CON 8 POFF=PULS•OFF #(T) 1054 MSK 9 (MIXO) KOOR= 50 (HIT) [MASK = 1] #(T) 18219 MSK 10 (MIYO) KOOR= 50 (HIT) [MASK = 2] #(T) 12781 MSK 11 (MIU1) KOOR= 50 (HIT) [MASK= 4] #(T) 25470 MSK 12 (MIX2) KOOR= 50 (HIT) [MASK = 8] #(T) 24377 MSK 13 (MIU2) KOOR= 50 (HIT) [MASK= 16] #(T) 24310 MSK 14 (MIX1) KOOR= 50 (HIT) [MASK = 32] #(T) 24796 138 MSK 15 (MUXO) KOOR= 50 (HIT ) [MASK = 256] #(T) 5682 MSK 16 (MUYO) KOOR= 50 (HIT) [MASK= 512] #(T) 7577 MSK 17 (MUU1) KOOR= 50 (HIT) [MASK= 1024] #(T) 905 MSK 18 (MUX2) KOOR= 50 (HIT) [MASK= 2048] #(T) 915 MSK 19 (MUU2) KOOR= 50 (HIT) [MASK= 4096] #(T) 987 MSK 20 (MUX1) KOOR= 50 (HIT) [MASK= 8192] #(T) 857 CON 21 (HOUT) KOOR= 50 (HIT ) [ 65536,9999999 99]#(1) 70738 CON 22 INPI=PION•(-HOUT)•(-PULS) #(T) 51421 CON 23 FECG=INPI•(-MIXO)•(-MIYO)•(-MUXO)•(-MUYO) #(T) 47227 CON 24 V1GD=INPI•(-MIX1)•(-MIU1)•(-MUX1)•(-MUU1) #(T) 49748 CON 25 V2GD=INPI•(-MIX2)•(-MIU2)•(-MUX2)•(-MUU2) #(T) 49911 CON 26 FV1G=FECG•V1GD #(T) 45846 CON 27 FV2G=FECG•V2GD #(T) 45978 CON 28 V12G=V1GD•V2GD #(T) 48841 CON 29 ALLG=FECG•V1GD•V2GD #(T) 45035 CON 30 V12X=V12G•(-MIXO)•(-MUXO) #(T) 46466 CON 31 V12Y=V12G•(-MIYO)•(-MUYO) #(T) 46331 CON 32 FV1X=FV1G•(-MIX2)•(-MUX2) #(T) 45381 CON 33 FV1Y=FV1G•(-MIU2)•(-MUU2) #(T) 45335 CON 34 FV2X=FV2G•(-MIX1)•(-MUX1) #(T) 45465 CON 35 FV2Y=FV2G•(-MIU1)•(-MUU1) #(T) 45343 MSK 36 (XOO) KOOR= 50 (HIT ) [MASK= 65536] #(T) 15045 MSK 37 (X01 ) KOOR= 50 (HIT ) [MASK = 131072] #(T) 19800 MSK 38 (YOO ) KOOR= 50 (HIT) [MASK = 262144] #(T) 4626 MSK 39 (Y01 ) KOOR= 50 (HIT) [MASK= 524288] #(T) 7403 MSK 40 (U1 ) KOOR= 50 (HIT ) [MASK = 1048576] #(T) 224 MSK 41 (X2 ) KOOR= 50 (HIT) [MASK = 2097152] #(T) 891 MSK 42 (U2 ) KOOR= 50 (HIT) [MASK = 4194304] #(T) 326 MSK 43 (X1 ) KOOR= 50 (HIT) [MASK = 8388608] #(T) 530 MSK 44 (FECT) KOOR= 50 (HIT) [MASK =16777216] #(T) 61817 MSK 45 (VDCT) KOOR= 50 (HIT) [MASK =33554432] #(T) 22540 139 CON 46 (TOT) KOOR= 50 (HIT)[ 0,999999999]#(T) CON 47 TOTL=TOT•(-PULS) #(T) CON 48 PTOT=PION•TOTL #(T) CON 49 MULT=(MUXO+MUYO+MUU1+MUX1+MUU2+MUX2)•(-PUL #(T) S) CON 50 MISS=(MIXO+MIYO+MIU1+MIX1+MIU2+MIX2)•(-PUL #(T) S) CON 51 GOOD=(-MULT)•(-MISS)•(-PULS) CON 52 (HIT) KOOR= 50 (HIT)[ #(T) 1,999999999]#(T) CON 53 RETR=HIT•GOOD #(T) CON 54 RETP=HIT•INPI #(T) CON 55 XOMU=MUXO+(XOO+XOl+FECT)•(-MIXO) #(T) CON 56 YOMU=MUYO+(YOO+YOl+FECT)•(-MIYO) #(T) CON 57 X1MU=MUX1+(Xl+VDCT)•(-MIX1) #(T) CON 58 U1MU=MUU1+(Ul+VDCT)•(-MIU1) #(T) CON 59 X2MU=MUX2+(X2+VDCT)•(-MIX2) #(T) CON 60 U2MU=MUU2+(U2+VDCT)•(-MIU2) #(T) CON 61 MUL=(-PULS)•(XOMU+YOMU+X1MU+U1MU+X2MU+U2MU #(T) ) CON 62 MULR=MUL•RETR CON 63 MULN=MUL•(-RETR) #(T) #(T) 134585 128103 92819 12644 37967 80260 86048 31723 6764 52961 56491 2763 2929 3206 3505 66644 31158 35486 ....................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conditions 1-35 give the number of events with missing or multiple clusters in each of the wire chambers, subject to the conditions on TDC values and active area as described in section 3.1. By observing the number of events passing these logical conditions, we see that the number of multiple hit events on the two VDCs ( conditions 17-20) is very much smaller than the number of multiple hit events on the FEC ( conditions 15,16). However, the number of missing hit events on the VDCs (conditions 11-14) is significantly larger than the number of missing hit events on the FEC ( conditions 9,10). Thus, the inefficiency of the VDCs is determined primarily from the number of events with missing hits, and the 140 inefficiency of the FEC is determined by the number of events with multiple hits. This finding seems reasonable since the FEC is located very close to the target. From ALLG and V12G the efficiency of the FEC is calculated to be 92.2%. From ALLG and V12Y the efficiency of the XO plane of the FEC is determined to be 97.2%, and from ALLG and V12X the efficiency of the YO plane of the FEC is 96.9%. Thus TJxo X 7JYo=94.2%. This compares well with the 92.2% figure determined above for the FEC, and shows that the inclusion of one plane of the FEC in the MRS trigger has not given the FEC an artificially large efficiency. Similarly, from ALLG and FV2G the efficiency of VDCl is 97.9%, and from ALLG and FVlG the efficiency of VDC2 is 96.9%. Furthermore, the efficiency of the Xl plane is 99.3% from ALLG and FV2Y, and the efficiency of the X2 plane is also 99.3% from ALLG and FVl Y. Therefore, the inclusion of Xl in the MRS trigger has not adversely affected the efficiency calculation. The Xl plane has an efficiency not equal to unity because of contributions from multiple cluster events, and missing hit events due to the drift routine cuts on TDC values and active area. Conditions 36-45 give the number of events that did not pass each drift routine condition (i.e. the active area conditions, and the TDC value conditions). A portion of the multiple hit events, however, can be retrieved if the other cluster does not pass one of these drift routine conditions. The number of events which have been retrieved is given by condition 53. From MUL and TOTL we see that the total number of events on this tape which had multiple clusters in one of the wire chamber planes is 52.0%, and from MULR and MUL we see that 46.8% of these multiple hit events have been retrieved. However, most of these retrieved multiple hit events are not pions as RETP is only 6764. Thus, from RETP and INPI it can be seen that only 13.2% of these good pion events have been retrieved by the drift routine. It should be noted that conditions 1-35 only include events which have not been retrieved by the drift routine. Conditions 55-63 give the total number of events with multiple clusters, including both those that have not been retrieved by the drift routine, as well as those which have been retrieved. 141 A.2.3 Data Skimming Routine While the chamber efficiencies were extracted via the above routine, a smaller data file was created on disk containing a high proportion of good data. All off-line analysis from which observables were extracted used these skim files as input. subroutine evbev(•) skim366.for for creating skim data tapes written by garth huber 20 include 'lis$share:evtcom' include 'lis$share:daccom' include 'lis$share:concom' include 'lis$share:flacom' include 'lis$share:outcom' include 'lis$share:bufcom' include 'lis$share:dskcom' if (ieventtype_1.eq.1) goto if (icon(1).eq.1) goto 20 if (icon(S0).eq.1) return if (kbuf(100).gt.para(70)) call out1 return end 20 return !save scalers !save pulsers !don't save missing hits !don't save high eloss evts !write event to disk A.3 pp --+ d?r"+ Transformation Routine This is the program described in section 6.2 which transforms pp - d1r+ differential cross sections and analyzing powers to the nucleon-nucleus kinernatical frame. ! ppria.for 142 program to calculate pp->dpi cross sections shifted by nuclear kinematics and solid angle using equations from segre, p.937 and the rutherford lab kinematics handbook section by w.s.c. willia.ms written by pat walden and modified by garth huber, 1987 implicit real•8(a-h,j-z) dimension pl(11),d(11) factor=1.0/(4.0•3.1415926) !masses of internal sub-process m1=938.28 m2=1875.63 write(6,105) !target !recoil 105 format(/,' Choose the reaction desired:', * /,t5,'1) 12C(p,pi+)',/,t5,'2) 13C(p,pi+)',/,t5, * '3) 160(p,pi+)',/,t5,'4) 7Li(p,pi+)') read(S,•)ire write(6, 110) 110 format(' Excitation:',$) read(S,•)ex if (ire.eq.1) then mb=938.28 mt=11174. 98 ms=139.58 mr=12109.61 end if if (ire.eq.2) then mb=938.28 mt=12109.61 !12C(p,pi+)13C !13C(p,pi+)14C 143 end if ms=139.58 mr=13041.01 if (ire.eq.3) then mb=938.28 mt=14895.24 ms=139.58 mr=15830.68 end if if (ire.eq.4) then mb=938.28 mt=6533.66 ms=139.58 mr=7470.95 end if mr=mr+ex write(6,112) !160(p,pi+)170 !7Li(p,pi+)8Li 112 format(/,' Input the t-value you want: ',$) read(S,•)t t=t•1.e6 114 write(6,115) 115 format(/,' Input the proton beam Tp: ',$) read(S,•)tlb elb=tlb+mb plb=sqrt(elb•elb-mb•mb) !calculate s ,u for nuclear system s=mb•mb+mt•mt+2.•elb•mt sroot=s ·qrt (s)-mt 144 u=mb•mb+mt•mt+ms•ms+mr•mr-s-t !calculate pion thetalab for nuclear system als=acosd( * (2.•mt•mt•(t-mb•mb-ms•ms) * (s-mb•mb-mt•mt)•(u-mt•mt-ms•ms) ) * I sqrt( lam(s,mb•mb,mt•mt) •lam(u,mt•mt,ms•ms)) * ) !calculate pion thetacm for nuclear system acs=acosd( * (2.•s•(t-mb•mb-ms•ms) * + (s+mb•mb-mt•mt)•(s+ms•ms-mr•mr)) * I sqrt( lam(s,mb•mb,mt•mt) •lam(s,ms•ms,mr•mr)) * ) !calculate lab momentum of pion in nuclear system pls=sqrt( lam(u,mt*mt,ms•ms) /(4.•mt•mt) ) els=sqrt(ms••2+pls••2) !calculate cm momentum of pion in nuclear system pcs=sqrt( lam(s,ms•ms,mr•mr) /(4.•s) ) !find nuclear LAB/CM jac=pcs•(pls•(elb+mt)-plb•els•cosd(als))/(sqrt(s)•pls•pls) !calculate cm energy of recoil in nuclear system ecr=(s+mr•mr-ms•ms)/(2.•sqrt(s)) pcr=sqrt(ecr•ecr-mr•mr) !calculate lab energy of recoil in nuclear system elr=(ecr•(elb+mt)-plb•pcr•cosd(acs))/sqrt(s) plr=sqrt(elr•elr-mr•mr) !calculate recoil thetalab in nuclear system alr=acosd( * * I ) 145 !assume that the nucleus emits a proton directly into the beam, and that !the sub-process creates a pion with the same momentum and lab angle as !the nuclear case. the residual nucleus is off the mass-shell. using !conservation of momentum for the sub-process, the nuclear process, and !the nuclear proton, the cm energy of the nuclear proton is ecm=(t+m1•m1-m2•m2)/(2•sqrt(t)) beta=(plb-pls•cosd(als))/(elb-els) !beta of recoil in z dir ganuna=(els-elb)/sqrt(t) !use transformation from cm to lab energy and E-2=p-2+m-2 to get a !quadratic equation for the lab momentum of the nuclear proton a=1. -beta•beta b=2.•ecm•beta/gamma c=m1•m1-ecm•ecm/gamma/ganuna plm=(-b+sqrt(b••2-4.•a•c))/(2.•a) elm=sqrt(plm•plm+m1•m1) !transform from the nuclear system to the sub-process system !first finds (using the formula for an arbitrary frame of reference) s1=(elb+elm)•(elb+elm)-(plb-plm)•(plb-plm) !solve for Tp elb1=(s1-mb•mb-m1•m1)/(2.•m1) plb1=sqrt(elb1•elb1-mb•mb) tlb1=elb1-mb !using s,t find u u1=mb•mb+m1•m1+ms•ms+m2•m2-s1-t !calculate pion thetalab for sub system als1=acosd( * * (2.•m1•m1•(t-mb•mb-ms•ms) (s1-mb•mb-m1•m1)•(u1-m1•m1-ms•ms) 146 ) * I sqrt( ) lam(s1,mb•mb,m1•m1) •lam(u1,m1•m1,ms•ms)) * !calculate pion thetacm for sub system acs1=acosd( * (2.•s1•(t-mb•mb-ms•ms) * + (s1+mb•mb-m1•m1)•(s1+ms•ms-m2•m2) ) * I sqrt( lam(s1,mb•mb,m1•m1) •lam(s1,ms•ms,m2•m2)) * ) !calculate lab momentum of pion in sub system pls1=sqrt( lam(u1,m1•m1,ms•ms) /(4.•m1•m1) ) els1=sqrt(ms•ms+pls1•pls1) !calculate cm momentum of pion in sub system pcs1=sqrt( lam(s1,ms•ms,m2•m2) /(4.•s1) !find LAB/CM jacobian of sub system jac1=pcs1•(pls1•(elb1+m1)-plb1•els1•cosd(als1)) * I (sqrt(s1)•pls1•pls1) !recalculate t for test t1=mb•mb+ms•ms-2.•(elb1•els1-plb1•pls1•cosd(als1)) s=s/1.e6 s1=s1/1.e6 t1=t1/1.e6 ) sroot=sroot/1.e3 write(6,200)pls,pcs,pls1,pcs1,tlb1,plm,al s ,acs,als1,acs1,s,s1, * sroot,jac,jac1,t1 200 format(/,' Pion lab(A) momentum ',f7.3,' MeV/c', * /,' Pion cm(A) momentum ',f8.3,' MeV/c', * /,' Pion lab(p) momentum ',f8.3,' MeV/c', * /,' Pion cm(p) momentum ',f7.3,' MeV/c', * /,' Tp (p) ',f7.2,' MeV', * /,' Nuclear proton lab momentum ',f7.3,' MeV/c', 147 * I•, Pion lab(A) angle ',f6. 2, , degrees', * I•, Pion cm(A) angle J ,f6.2, I degrees', * I. I Pion lab(p) angle I • f6 • 2, I degrees', * I. I Pion cm(p) angle 1 ,f6.2, 1 degrees', * I. I sin A frame I ,f9.4, I GeV••2 1 , * /,' sin p frame J ,f9.4, I GeV••2 1 , * I. I sqrt(s)-mA I ,f8.4, I GeV1 , * I. I LAB/CM Jae (A) I ,f6.3, * I. I LAB/CM Jae (p) 1 ,f6 .3, * I. I test t I ,f6.4, 1 (GeV/c)**2') !calculate pp->dpi differential cross section at selected energy and angle call ppanO(tlb1,acs1,cross,anO) cross=cross•jac/jac1 write(6,201)cross,an0 201 format(' *** Corrected for Difference in Jacobians ***',/, Differential Cross Section (ub/sr)= ',f7.2,/, Analyzing Power= 1 ,f7.4) goto 114 end 148 subroutine ppan0(tpr,thcm,cross,an0) this program uses a smooth line through measured Legendre polynomial coefficients to calc pp->dpi+ analyzing powers and cross-sections implicit real•8(a-h,o-z) dimension a2a0(30),a4a0(30),a6a0(30),b1a0(30),b2a0(30),b3a0(30), - b4a0(30),b5a0(30),b6a0(30),e(30),pl(7),a(7),b(6),a0(30) Sources of Data: 320, 330, 350, 400, 425 MeV E.L. Mathie et al., Nucl. Phys. A397(1983)469. 375, 450, 498 MeV G.L. Giles, Ph.D. Thesis, University of British Columbia (1985). 515.9, 542 . 1, 568 . 8, 581.8 MeV J. Hofteizer et al., Nucl. Phys. A402(1983)429, A412(1984)286. 547, 598, 648, 698 MeV A. Saha et al., Phys. Rev. Lett. 51(1983)759. 725, 765, 796, 825, 850, 876, 902, 942, 1003 MeV B. Mayer et al . , Nucl. Phys. A437(1985)630. np=25 emin=320. emax=1003. data (e(i),i=1,25) !number of pp->dpi energies I 320., 330., 350., 375., 400., 425., 450., 498.,515.9,542.1, 547.,568.8,581.8, 598., 648 . , 698., 725., 765., 796., 825., 850., 876., 902., 942.,1003./ data (a0(i),i=1,25) / 149., 280., 401., 645., 822., 1200., 149 1680. ,2310. ,2555. ,2916., 2980.,3101.,3122.,3180.,2810.,2270., 1945.,1620.,1226.,1210.,1100., 990., 859., 706., 568./ data (a2a0(i),i=1,25)/ 0.76, 0.90, 1.00, 1.10, 1.09, 1.11, 1.12, 1.07,1.070,1.048, 1.045,1.026,1.011, .970, .895, .825, .805, .803, .795, .839, .814, .790, .821, .789, .728/ data (a4a0(i),i=1,25)/ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -.06, -.10,-.035,-.056, -.060,-.090,-.103,-.145,-.217,-.237, -.244,-.213,-.242,-.242,-.240,-.238,-.237,-.317,-.299/ data (a6a0(i),i=1,25)/ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -.13, -.06,-.026, .005, 0.0, .010,-.008,-.003,-.020,-.038, -.030,-.021,-.057,-.001,-.006,-.012,-.043,-.117,-.095/ data (bla0(i),i=l,25)/-.297,-.278,-.243,-.169,-.113,-.073, .001, .136, .213, .289, .300, .351, .379, .397, .414, .360, .3213,.2689,.2382,.2053,.1771,.1707,.1461,.1270,.1365/ data (b2a0(i),i=1,25)/ .019, .036, .028, .026, .039, .011, .029, .031, .032, .036, • 041 , . 045 , • 045 , • 046 , . 051 , • 041 , .0345,.0211,.0218,.0085,.0081,-.0115,-.0153,-.0295,-.0469/ data (b3a0(i),i=1,25)/ 0.0, .005, .022, .040, .066, .057, . 083, . 112, .132, . 150, .153, .154, .162, .158, .150, .119, .1073,.0916,.0763,.0801,.0746,.0725,.0668,.0612,.0520/ data (b4a0(i),i=1,25)/ 0.0, 0.0, 0.0, .003, 0.0,-.004, .002, .007, .006, .010, 150 .011, .014, .012, .018, .026, .029, .0287,.0354,.0291,.0306,.0311,.0289,.0314,.0342,.0362/ data (b5a0(i),i=1,25)/ 0.0, 0.0, 0.0, .006, 0 .0, 0.0, . 007, . 007, . 007, . 009, .005, .008, .011, .007, .005, .004, .0026,.0055, .0038,.0038,.0079,.0080,.0057,.0107,.0119/ data (b6a0(i),i=1,25)/ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ·o.o, 0.0, 0.0, 0 .0, 0.0, .001, .001, .002, 0 .0, 0 .0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0 .0/ if(tpr.lt.emin)tpr=emin if(tpr.gt.emax)tpr=emax do 210 j=1,np check if outside range of validity if(tpr.le.e(j))goto 220 210 continue j=np+1 220 itpr=j if (itpr.gt.np.or.itpr.le.1)goto 240 diff=(tpr-e(itpr))/(e(itpr)-e(itpr-1)) if (diff . lt . (-0.5)) diff=1+diff goto 300 'middle' energy values e closer to previous one 240 if (itpr.eq . 1) diff=(tpr-e(1))/(e(2)-e(1))! energy less than e(1) if (itpr.eq.np+1) diff=(tpr-e(np))/(e(np)-e(np-1))! e > e(np) 300 a(1)=1. if (itpr.eq.np+1 .or. itpr.eq.1) goto 350 if (diff.gt.0) then ! take lower energy values cross=a0(itpr-1)+diff•(a0(itpr)-a0(itpr-1)) a(3)=a2a0(itpr-1)+diff•(a2a0(itpr)-a2a0(itpr-1)) 151 a(5)=a4aO(itpr-1)+diff•(a4aO(itpr)-a4aO(itpr-1)) a(7)=a6aO(itpr-1)+diff•(a6aO(itpr)-a6aO(itpr-1)) b(1)=b1aO(itpr-1)+diff•(b1aO(itpr)-b1aO(itpr-1)) b(2)=b2aO(itpr-1)+diff•(b2aO(itpr)-b2aO(itpr-1)) b(3)=b3aO(itpr-1)+diff•(b3aO(itpr)-b3aO(itpr-1)) b(4)=b4aO(itpr-1)+diff•(b4aO(itpr)-b4aO(itpr-1)) b(5)=b5aO(itpr-1)+diff•(b5aO(itpr)-b5aO(itpr-1)) b(6)=b6aO(itpr-1)+diff•(b6aO(itpr)-b6aO(itpr-1)) else take higher energy values cross=aO(itpr)+diff•(aO(itpr)-aO(itpr-1)) a(3)=a2aO(itpr)+diff•(a2aO(itpr)-a2aO(itpr-1)) a(5)=a4aO(itpr)+diff•(a4aO(itpr)-a4aO(itpr-1)) a(7)=a6aO(itpr)+diff•(a6aO(itpr)-a6aO(itpr-1)) b(1)=b1aO(itpr)+diff•(b1aO(itpr)-b1aO(itpr-1)) b(2)=b2aO(itpr)+diff•(b2aO(itpr)-b2aO(itpr-1)) b(3)=b3aO(itpr)+diff•(b3aO(itpr)-b3aO(itpr-1)) b(4)=b4aO(itpr)+diff•(b4aO(itpr)-b4aO(itpr-1)) b(5)=b5aO(itpr)+diff•(b5aO(itpr)-b5aO(itpr-1)) b(6)=b6aO(itpr)+diff•(b6aO(itpr)-b6aO(itpr-1)) end if goto 355 350 if (itpr.eq.np+1) then cross=aO(np)+diff•(aO(np)-aO(np-1)) a(3)=a2aO(np)+diff•(a2aO(np)-a2aO(np-1)) a(5)=a4aO(np)+diff•(a4aO(np)-a4aO(np-1)) a(7)=a6aO(np)+diff•(a6aO(np)-a6aO(np-1)) b(1)=b1aO(np)+diff•(b1aO(np)-b1aO(np-1)) b(2)=b2aO(np)+diff•(b2aO(np)-b2aO(np-1)) b(3)=b3aO(np)+diff•(b3aO(np)-b3aO(np-1)) b(4)=b4aO(np)+diff•(b4aO(np)-b4aO(np-1)) 152 b(5)=b5aO(np)+diff•(b5aO(np)-b5aO(np-1)) b(6)=b6aO(np)+diff•(b6aO(np)-b6aO(np-1)) goto 355 end if cross=a0(1)+diff•(a0(1)-a0(2)) a(3)=a2a0(1)+diff•(a2a0(1)-a2a0(2)) a(5)=a4a0(1)+diff•(a4a0(1)-a4a0(2)) a(7)=a6a0(1)+diff•(a6a0(1)-a6a0(2)) b(1)=b~a0(1)+diff*(b1a0(1)-b1a0(2)) b(2)=b2a0(1)+diff•(b2a0(1)-b2a0(2)) b(3)=b3a0(1)+diff•(b3a0(1)-b3a0(2)) b(4)=b4a0(1)+diff•(b4a0(1)-b4a0(2)) b(5)=b5a0(1)+diff*(b5a0(1)-b5a0(2)) b(6)=b6a0(1)+diff•(b6a0(1)-b6a0(2)) then all that is left is ITPR=1 ! calculate associated Legendre polynomials 355 cth=cosd(thcm) sth=sind(thcm) pl(1)=0.0 pl(2)=sth do 420 k=3,7 420 pl(k)=((2*k-3)*cth*pl(k-1)-(k-1)*pl(k-2))/(k-2) anO=O.O do 450 j=2,7 450 anO=anO+pl(j)•b(j-1) calculate Legendre polynomials pl(1)=1.0 pl(2)=cth do 421 k=3,7 153 421 pl(k)=((2*k-3)*cth*pl(k-1)-(k-2)*pl(k-2))/(k-1) an1=0.0 do 451 j=1,7,2 451 an1=an1+pl(j)*a(j) anO=anO/ an1 cross=cross*an1/4./3.1415926 write(6,460)cross,an0 460 format(' Differential Cross Section (ub/sr)= ',f7.2,/, 'Analyzing Power= ',f7.4) return end function lam(a,b,c) implicit real*8(a-h,j-z) lam=a*a+b*b+c*c-2.*(a*b+a*c+b*c) return end 154 Appendix B Tables of Data This appendix contains all measured quantities for the exclusive (p, 1r) reactions studied in this series of experiments. All quantities shown are in the center of mass frame; angles are in degrees; do-/dn are in nb/sr and O' are in nb. The numbers in parenthesis reflect statistical uncertainties only. Data are presented in order according to the mass of the target nucleus and the excitation energy of the final nuclear state. 155 Table B.l: A list of differential cross sections and analyzing powers for the 7Li(p, 1r±) reactions leading to some final states of 8Li* and 8B*. The 7Li(p, 1r-) data, as well as the 7Li(p, 1r+) results whose Bc.m. have been quoted to three significant figures, were obtained in a later experiment and are not part of this thesis. They have been tabulated here for the sake of completeness. 7Li(p, 1r+) Bc.m. s1· lg .s . s1·• 1o.9sos s1·• 12.255 Tp = 250MeV 22 445(23) 0.25(.05) 297(19) 0.24(.06) 687(29) 0.17(.04) 47 186(8) 0.09(.04) 92.6(5.5) 0.35( .06) 319(11) -.03(.03) 61 107(6) -.52(.05) 39.6(3.6) 0.16( .09) 199(8) -.14(.04) 74 68.9(6.4) -.64(.09) 14.3(3.2) 0.14( .22) 119(11) -.40(.09) Tp = 280MeV 38.8 710(20) 0.40(.04) 426(16) 0.62(.04) 952(23) 0.24(.03) 54.2 216(7) 0.01(.05) 94.9( 4.6) 0.34( .06) 327(8) -.02(.04) 67.1 64.7(1.8) -.68(.04) 17.6(0.9) 0.26( .08) 116(2) -.06(.03) 79.1 50.0(1.6) -.59(.05) 9.9(0.7) -.25(.11) 67.4(1.9) -.07(.04) 90.6 29.2(0.9) -.26(.05) 10.1(0.5) -.12(.08) 45.6(1.1) 0.04(.04) 102.0 21.5(0.7) 0.09(.05) 6.8(0.4) -.01(.09) 38.1( 1.0) 0.29( .04) 113.9 8.6(0.4) 0.47(.06) 4.9(0.3) 0.39( .08) 18.9(0.5) 0.45(.04) Tp = 354MeV 21.3 1160(50) 0.23(.06) 611(3~) 0.24(.07) 1400(50) 0.20(.05) 22 1050(45) 0.29(.04) 494(31) 0.32(.06) 1310(51) 0.33(.04) 33 554(23) 0.18(.03) 248(12) 0.32(.04) 851(23) 0.38(.06) 44 196(6) -.01(.03) 98.9(4.4) 0.22(.04) 315(8) 0.34(.05) 55 79.6(5.1) 37.9(3.6) 149(7) 0.38(.05) 57.4 101(5) 0.17(.08) 29.7(2.8) 0.55(.15) 154(6) 0.26(.06) 61 59.4( 4.0) 40.2(3.4) 107(6) 0.22(.06) 64.7 57.4(3.8) 0.25(.10) 20.8(2.2) 0.61( .15) 90.1( 4.7) 0.28(.08) 75.5 33.7(1.7) 0.24(.07) 7.7(0.8) 0.42(.15) 34.2(1.7) 0.62(.07) 84.8 24.6(1.4) 0.64(.09) 9.6(0.9) 0.79(.13) 38.6(1.8) 0.66(.07) 156 71i(p, 1r+) 0c.m. 81· lg .s . 81"* 1o.9sos 81'* 12.255 Tp = 489MeV 20.7 245(13) 0.03(.12) 115(9) 0.44(.17) 329(15) 0.07(.10) 27.6 181(9) 0.10(.11) 57.2(5.1) 0.48( .20) 219(10) 0.09(.10) 35.6 60.1(3.4) -.38(.10) 20.0(1.9) 0.13(.19) 103( 4) -.04(.08) 42.3 31.1(1.7) -.29( .11) 8.4(0.9) 0.15(.22) 55.9(2.3) -.38(.08) 48.2 25.4(1.2) -.13(.10) 3. 7( 0.5) 0.28( .24) 27.0(1.3) -.18(.09) 53.6 13.3(0.8) 0.31( .12) 3.2(0.4) -.20( .25) 22.1(1.1) 0.04(.10) 71i(p , 1r-) 0c.m. sB g .s. BB* 0 .78 BB* 2.32 Tp = 280MeV 38.8 9.1(0.8) -.31(.13) 6.3(0.7) 0.31(.14) 7.5(0.7) -.29(.14) 54.2 9.1(0.5) -.19(.10) 5.2(0.4) -.17( .12) 5.8(0.4) -.34(.12) 67.2 6.1(0.3) -.01(.08) 2.2(0.2) 0.35(.13) 3.5(0.3) -.07(.11) 79.3 4.1(0 .3) 0.08(.09) 1.4(0.1) 0.37(.15) 2.6(0.2) -.02(.11) Tp = 354MeV 21.3 18.2(1.3) -.56( .10) 20.0(1.3) 0.20(.10) 33.0(1.7) -.54(.08) 36.3 11.1(0 .6) -.24(.08) 7.6(0.5) -.04(.10) 8.3(0.5) -.52(.09) 47.2 6.6(0.4) -.33( .10) 3.4(0.3) 0.10(.14) 5.1(0.4) -.63(.11) 57.4 5.1(0 .3) -.29(.09) 2.4(0 .2) -.14( .13) 3.4(0.2) -.36(.11) Tp = 489MeV 20.7 2.9(0.4) -.14(.35) 0.6(0.2) -1.0(.66) 3.7(0.5) -.76(.30) 27.6 2.5(0 .3) -.40(.22) 1.4(0.2) 0.02( .29) 3.6(0.3) -.22(.18) 35.6 1.8(0.2) -.07( .21) 0.9(0 .1) -.15(.30) 2.5(0 .2) 0.20(.17) 157 Table B.2: A list of values for the differential cross sections and total cross sections of the 12C(p, ,r+) reaction leading to various final states of 13 C*. The systematic error in the overall normalization has been estimated at 8%, and the relative uncertainties have been estimated at 10%. 0c.m. 13c g.s. 13C* 3 .09 13C* 3 .68,3.85 13C* 6.86 13C* 7.49,7.55,7.68 13C* 9.50 Tp = 250MeV 31 331(36) 326(36) 1200(71) 464(45) 1120(69) 957(66) 62 29.1(4.1) 56.7(5.7) 136( 9) 123( 9) 220(12) 312(15) Tp = 354MeV a 326(18) 366(48) 1390(320) 415(50) 2520(70) 3480(230) 22 157(14) 171(15) 944(34) 264(19) 1520(46) 2310(56) 32 106(11) 111(11) 350(20) 123(12) 912(33) 1270(38) 37 81.7(9.8) 114(12) 238(17) 107(12) 655(28) 1020(36) 48 53.1(5.3) 80.6(6.6) 195(10) 35.6(4.3) 269(12) 322(13) 64 15.1(3.2) 21.7(3.7) 73.6(6.9) 24.9(4.0) 115( 9) 107( 8) 79 5.3(1.4) 2.1(0.9) 13.2(2.3) 2.5(1.0) 39.4(3.8) 32.3(3.6) 94 8.6(1.6) 6.1(1.3) 14.8(2.1) 1.8(0. 7) 12.6(1.9) 27.4(2.8) 114 3.9(0.8) < 1 1.2(0.4) < 1 8.1(1.1) 5.0(0.9) Tp = 489MeV 21 61.7(8.6) 87.4(10.5) 199(16) 63.2(8.9) 597(27) 786(31) 32 28.4(2.6) 54.4( 3.6) 114( 5) 17.8(2.1) 197( 7) 288( 8) 158 0c.m. 13c• 10.99 13c• 11.85 13c• 14.12 13c• 21.4 Tp = 354MeV 22 196(16) 256(19) 300(21) 1420(90) 32 164(14) 197(15) 230(17) 725(55) 37 127(12) 103(11) 144(17) 474(29) 48 58.6(5.7) 62.8(6.0) 58.8(5.9) 159(16) 64 21.9(3.7) 41.6(5.2) 16.1(3.2) 88.1(8.5) Tp = 489MeV 21 138(13) 159(14) 123(12) 446(25) 32 72.5(3.9) Table B.3: Differential cross sections for selected final stat es of the 13C(p, 7r±) reactions. The systematic error in the overall normalization has been estimated at 8%, and the relative uncertainty has been estimated at 10%. 13C(p, ?r-) Bc.m. 140 g .s . 140* 5 .17 140* 6 .27,6.79 140* 9.92 Tp = 250MeV 31 2.3(0.7) 5.8(1.2) 68.2(4.0) 17.4(2.1) 52 1.6(0.4) 3.3(0.6) 44.5(0.2) 8.2(1.0) Tp = 354MeV 32 1.6(0.4) 19.8(1.5) Tp = 489MeV 21 0.6(0.3) 4.7(0.9) 159 13e(p, 1r+) Bc.m. He g.s. 14e• 6 .09 He• 6.73 14e• 7.34 14 e • 8.32 He• 9.80 14e• 10.51 Tp = 250MeV 31 127(14) 373(25) 1180(44) 356(24) 149(16) 235(20) 344(24) 52 27.6(3.3) 122( 7) 341(12) 80.9(5.8) 54.6(4.8) 79.6(5.9) 88.7(5.6) Tp = 354MeV 30 57.9(6.4) 117( 9) 783(23) 188(11) 169(11) 112( 9) 235(13) 37 42.3(5.1) 88.0(7.1) 253(12) 80.4(6.8) 88.1(7.1) 49.9(5.5) 112(8.1) Tp = 489MeV 21 26.2(5.0) 60.2(7.2) 279(16) 62.4(7.5) 73.0(8.0) 27.8(5.0) 70.0(7.7) 32 8.1(1.6) 28.5(2.9) 75.7(4.7) 26.5(2.7) 18.4(2.4) 5. 7(1.3) 8.8(1.6) 13C(p, 1r+) Bc.m. 14e• 11.67 14e• 12.86 He• 13.5 He• 14.05 He• 14.87 He• 15.44 14e• 23.2 Tp = 250MeV 31 520(32) 52 195( 8) 65.4(4.5) 58.3(4.3) 48.2(3.9) 214( 8) 290(12) Tp = 354MeV 30 530(19) 78.5(7.2) 200(12) 224(12) 647(21) 110( 9) 597(34) 37 279(13) 36.8(0.5) 115( 8) 108( 8) 397(15) 500(20) Tp = 489MeV 21 231(14) 18.7(0.4) 66.7(8.0) 28.9(5.2) 292(16) 18.0( 4.0) 271(16) 32 45.0(3.7) 11.2(1.8) 13.3(2.0) 89.6(5.1) 21.3(2.6) 53.7(4.0) 160 Table B.4: A listing of the states of 17 O* by analyzing power category as described in section 8.1, and some of their dominant configuration amplitudes as published in [Le72]. Category 1 - pp --+ d1r+ -like 11-7.757, 2 0.89([1d512J2)5[1P1;2J- 1 - 0.41([1d5;2]4 )5([1p1;2]-3)1l2 5-3.841, 2 0.62([1d5;2J2)2[1P1;2J- 1 + 0.39([1d5;2H2s1;2])2[1P1;2J- 1 5-5.733, 2 -0.53([1d5;2J2)2[1P1;2J- 1 + 0.49([1d5;2][2s1;2])2[1P1;2J- 1 1+ 8.466, 2 unknown 9-9.15, 2 -0.83([1d5;2J2)5[1P1;2J- 1 + 0.37([1d5;2]4)5([1P1;2J- 3)1/2 9.783 unknown 11.238 unknown 13.484 unknown 14.15 unknown Category 2 - Flat at Forward Angles 15.78 unknown 11- 13-17.1,2 '2 unknown 3-8.200, 2 -0.55([1d5;2H2s1;2])2[1P1;2J- 1 + 0.47 ([1d5;2][2s1;2])2[1P1;2J- 1 7-8.967, 2 unknown 12.274 unknown Category 3 - Oscillating above 250 MeV 1+ 0.871, 2 0.78[2s1;2] + 0.39([1d5; 2]2[2s1;2])112([1p1; 2J- 2)0(T = 3/2) 3+ 4.552, 2 0.50([1d5;2J2)2[1P1;2J- 1 - 0.40([2s1;2J2)1[1P1;2J- 1 s+ 6.972, 2 0.30([1d5; 2]3)512 ([ 1 p1;2]- 2 )1 + 0.27[1d5; 2] 14.76, unknown Exceptions 5+ 0.00, 2 0.82[1d5;2] + 0.37([1d5;2]3)512([1p1;2J- 2)0(T = 3/2) 9+ 5.218, 2 +0.78([1d5;2]2)4[1P1;2J- 1 - 0.31([1d512J2)5[1P1;2J- 1 7 5+ .379, 2 -0.36([1d5;2J3)5/2([1P1;2J-2)1 - 0.29([1d512J3)5/2([1P1;2J-2)0 States with Very Bad Statistics 1-3.055, 2 -0.5 7([1d5;2J2)0[1P1;2J-l - 0.43([1d5;2]4 )o([lP1/2J-3)1/2 1+ 6.356, 2 -0.40([1d5;2J2[2s112D1/2([1P1;2J-2)1/2 - 0.27[2s1;2] 161 Table B.5: A list of differential cross sections, analyzing powers and total cross sections for the 16O(p, 1r+) reaction leading to some final states of 17 o•. Errors for this data ar e summarized in table 3.1. Oc.m. 170 g.s. 170* 0 .871 170• 3 .055 Tp = 250Me_V (7 1360(30) 282(17) 21 625(30) -.01( .05) 133(14) -.67(.09) 4.6(2.5) 0.00( .60) 45 218(11) -.78( .04) 23.2(3.3) 0.21( .17) 3.0(1.1) -.87(.41) 58 84.6(5.9) 0.30( .07) 8.1(1.8) 0.29( .24) 2.3(0.9) -.17( .42) 71 36.3(2.9) 0.66( .08) 14.9(2 .0) -1.0(.07) 2.5(0 .9) -.96(.21) 85 35.7(2.4) -.78(.06) 24.4( 2.0) - .89( .07) 1.7(0.5) -1.0(.23) 102 39.9(2.3) -.76(.05) 9.9(1.1) -.11(.12) 0.8(0.3) -1.0(.38) Tp = 354MeV (7 685(121) 100(9) 21 539(23) 0.14(.04) 61.5(7.5) 0.99(.11) 31 214(11) 0.41( .05) 41.0(4.9) 0.82(.11) 42 112(5) 0.53( .04) 15.0(1.7) 0.56(.10) 52 45.4(3.5) 0.15( .07) 3.9(1.0) -.24(.23) 0.4(0.3) 0.68( .72) 58 20.8(2.1) -.52(.10) 2.0(0.7) -.39( .36) 0.3(0.2) 1.00(.65) 63 12.5(0.9) - .80(.07) 3 .7(0.5) 0 .23(.13) 0.3(0 .1) -.69(.47) 73 7.0(0.8) 0.34(.11) 4.7(0.6) 1.00(.10) 0.3(0 .2) 0.56(.51) 83 5.9(0.6) 1.00( .08) 1.7(0.3) 1.00(.20) 0.1(0 .1) 1.00(1.0) Tp = 489MeV (7 128(26) 26.5(7.8) 24 77.4(5 .0) 0.38(.06) 17.7(2.4) - .01(.13) 1.5(0.7) 1.00(.50) 42 11.4(1.2) -.72(.10) 3.2(0.6) -.78(.20) 0.5( 0.3) 1.00( .20) 57 4.9(0 .7) 0.88(.13) 2.8(0.6) 1.00(.15) 0.3(0.2) -1.0(.56) 162 Oc.m. 170* 3.841 170* 4.552 170* 5.218 Tp = 250MeV (j 182(25) 1070(50) 21 39.8(7.2) 0.73(.18) 13.1(4.5) -1.0(.05) 416(24) 0.59(.06) 45 32.5(3.8) 0.82(.12) 11.3(2.3) 0.55(.22) 212(10) 0.77(.05) 58 18.3(2.7) 0.37(.15) 5.6(1.5) 0.44( .27) 103(7) 0.67( .05) 71 19.6(2.2) 0.07(.13) 1.9(0.8) -1.0(.45) 46.2(3.4) 0.30(.08) 85 18.2(1.8) -.74(.10) 2.7(0.7) -1.0(.11) 46.3(2.9) 0.04(.07) 102 4.0(0 .7) -.13( .21) 2.9(0.6) 0.07(.25) 18.8(1.6) 0.12(.09) Tp = 354MeV (j 180(11) 975(84) 21 117(11) 0.17(.09) 36.9(5.9) 0.52(.15) 674(26) 0.20(.04) 31 67.0(6.3) 0.09(.10) 20.8(3.5) 0.86( .14) 453(17) 0.16(.04) 42 32.2(2.4) 0.35(.07) 4.4(0.9) 0.69(.16) 162(5) 0.04(.03) 52 15.9(2.1) 0.29(.11) 0.9(0.5) 0.77(.26) 57.1(4.0) 0.09(.06) 58 11.6(1.6) 0.58( .13) 1.4(0.6) 0.89( .36) 37.0(2.9) -.03(.08) 63 6.9(0.7) 0.59(.09) 1.1(0.3) 0.95(.23) 24.2(1.2) 0.12(.05) 73 2.6(0.5) 1.00(.14) 0.7(0.3) 1.00(.08) 8.2(0.8) 0.48(.10) 83 1.1(0.2) 1.00(.14) 0.5(0.2) 0.71(.36) 2.3(0.3) 0.62(.15) Tp = 489MeV (j 46.4(7.6) 204( 42) 24 32.9(3 .2) -.44(.10) 5.0(1.3) 0.45(.22) 144(7) -.12(.05) 42 4.6(0.8) 0.16(.16) 0.5(0 .3) -.16(.46) 17.4(1.5) -.50(.09) 57 0.3(0.2) -.92(.67) 0.3(0.2) 1.00(.65) 2.5(0.5) -.50(.22) 163 0c.m. 170* 5.733 170* 6.356 170* 6.972 Tp = 250MeV (j 898(18) 663(23) 21 461(26) 0.08( .06) 387(24) 0.02(.06) 45 99.6(7.1) 0.04(.07) 17.9(3.1) -.60(.16) 102(7) 0.35(.06) 58 11.9(2.2) 0.12(.20) 4.9(1.4) -1.0(.20) 48.8(4.5) -.02(.10) 71 19.0(2.3) -.88(.10) 1.8(0.7) -.81(.32) 17.4(2.3) -.62(.11) 85 37.4(2.6) -.29(.07) 3.9(0.8) -.62(.24) 11.6(1.5) -.68(.13) 102 46.7(2.6) -.23( .06) 1.5(0.5) -.33(.30) 3.3(0.7) -.07(.21) Tp = 354MeV (j 250(16) 467(35) 21 155(12) -.19( .08) 34.9(5.9) -.24( .18) 383(19) 0.30(.05) 31 85.4(7.2) 0.09(.08) 10.5(2.5) 0.87(.21) 212(11) 0.24(.05) 42 47.5(2.9) 0.24(.06) 2.6(0.7) 1.00(.18) 48.6(3.0) 0.30(.06) 52 19.6(2.3) 0.00(.10) 0.7(0.5) -.53(.52) 12.7(1.9) 0.19(.14) 58 15.3(1.9) -.16(.13) 0.9(0.4) -.40(.47) 6.3(1.2) 0.34(.18) 63 15.2(1.0) -.54(.06) 1.0(0.3) -.48(.24) 3.7(0.5) 0.38(.13) 73 7.5(0.8) 0.73(.10) 0.4(0 .2) -.39(.52) 1.5(0.4) 1.00(.16) 83 3.8(0.4) 0.88(.11) 0.8(0.2) 0.33(.29) Tp = 489MeV (j 55.5(8.8) 27.8(11.2) 24 27.2(2.9) -.15(.11) 4.2(1.1) -1.0(.12) 21.6(2.6) -.13(.12) 42 6.1(0.9) 0.03(.14) 0 .9( 0.3) 0.08( .37) 0.1(0.1) 1.00(.32) 57 3.8(0.7) 0.98(.13) 0.5(0.2) -1.0( .46) 0.3(0.2) -1.0(.65) 164 Oc.m. 170* 7.379 170* 7.757 170* 8.200 Tp = 250MeV (7 709(14) 2810(120) 21 310(21) 0.11(.07) 1230(43) 0.19(.04) 408(25) 0.16(.06) 45 109(7) -.48( .08) 501(16) 0.19(.03) -.46(.10) 58 53.8(4.7) 0.04(.09) 217(9) -.43(.04) 29.9(3.5) -.22(.12) 71 43.8(3.4) 0.16( .08) 178(7) -.64( .03) 6.8(1.4) -.54(.18) 85 29.9(2.4) -.57(.08) 99.6(4.4) -.19(.05) 8.0(1.2) -.81(.14) 102 17 .5( 1.6) -.55( .08) 50.6(2.8) 0.27( .05) 4.7(0.8) 0.57( .18) Tp = 354MeV (7 379(44) 2220(100) 21 279(17) 0.25(.06) 1740(42) 0.37(.02) 95.7(9.8) -.03(.10) 31 134(9) 0.31( .07) 967(24) 0.41(.03) 59.9(6.0) 0.94(.08) 42 56. 7(3.2) 0.20( .06) 307(8) 0.38(.02) 18.1(1.8) 1.00(.07) 52 35.9(3.2) 0.65(.07) 96.9(5.2) 0.26(.05) 6.9(1.4) 0.64(.13) 58 18.5(2.1) 0.87(.10) 51.1(3.4) 0.07( .07) 2.4(0.7) 0.39(.30) 63 16.3(1.0) 0.45(.06) 31.0(1.4) 0.19(.05) 1.9(0.4) 0.43(.18) 73 2.6(0.5) 0.19( .19) 11.1(1.0) 0.50(.08) 0.6(0.2) 0.32(.35) 83 1.2(0.3) 0.20( .22) 4.8(0.5) 0.33(.11) 2.3(0.4) 1.00(.09) Tp = 489MeV (7 91.9(11.8) 315(87) 24 59.5( 4.3) -.09( .07) 237(9) -.09(.04) 42 9.8(1.1) -.15(.12) 17.7(1.5) -.21(.09) 57 1.2( 0.4) 1.00( .24) 3.1(0.6) -.17(.21) 1.1(0.4) 1.00(.35) 165 0c.m. 170• 8.466 170• 8.967 170• 9.15 Tp = 250MeV (J 693(40) 746(19) 682(37) 21 321(22) 0.36( .07) 397(35) 0.33( .10) 473(40) -.35(.08) 45 107(8) -.18( .10) 159(10) 0.44(.07) 77.4(7.7) -.44(.08) 58 71.7(5.5) -.15(.08) 51.8(5.6) 0.12( .12) 32.6(4.4) -.70(.13) 71 33.4(3.2) -.67( .08) 13.2(1.5) 0.09( .12) 11.7(1.5) -.68(.12) 85 11.4(1.5) -.89(.11) 8.2(1.3) 0.69( .12) 10.3(1.5) 0.17(.14) 102 17.0(1.6) -.86(.08) 4.4(0.8) 0.50(.16) 3.8(0.7) 1.00(.11) Tp = 354MeV (J 209(17) 503(84) 207(34) 21 137( 12) 0.4 7( .09) 431(21) 0.25(.05) 130(12) -.07(.09) 31 88.3(7.4) 0.38(.08) 176(11) 0.32( .06) 105(8) 0.69( .07) 42 30.1(2.4) 0.29(.07) 53.0(3.1) 0.38(.06) 32.8(2.5) 0.83(.06) 52 16.9(2.2) 0.29( .11) 19.5(2.4) 0.60(.10) 9.9(1.7) 0.83(.17) 58 13.4(1.8) 0.04(.13) 8.8(1.4) 0.03(.17) 5.5(1.1) 0.56(.19) 63 5.5(0.6) -.45(.11) 7.4( 0. 7) 0.94( .08) 4.8(0.6) -.10(.12) 73 2.4(0.5) -.06(.19) 3.1(0.5) 1.00(.13) 2.4(0.5) 0.27(.21) 83 2.1(0.3) 0.38( .17) 1.7(0.3) 0.60(.18) Tp = 489MeV (J 32.3(3.2) 50.4(11.8) 37.6(8.0) 24 19.2(2.5) -.15(.13) 36.8(3.4)-.17(.09) 20.3(2.6) 0.53(.12) 42 3.8(0. 7) 0.48( .17) 3.6(0.7) 1.00(.13) 2.2(0.5) -.67(.23) 57 0.7(0.3) -1.0(.25) 0.4(0.2) 1.00( .50) 1.3(0.4) 0.08( .28) 166 0c.m. 170• 9.783 170• 11.238 110· 12.274 170• 13 .484 Tp = 250MeV CT 515(28) 1070(60) 1220(60) 523(26) 21 188(25) 0.02(.14) 472(39) 0.22(.09) 671(47) 0.20(.08) 179(23) 1.00( .07) 45 122(9) 0.00( .08) 245(14) -.08( .05) 219(13) -.06(.06) 98.4(8.8) -.01(.09) 58 38.5(4.9) -.16(.15) 90.7(7.7) -.08( .09) 59.9(6 .3) 0.04(.11) 48.9(5.6) -.47(.11) 71 7.0(1.1) -.56(.18) 44.5(3.0) - .20(.07) 41.3(2.9) -.52( .07) 35.6(2.6) -.57(.07) 85 17.1(2.0) -.49(.12) 26.1(2.6) -.40(.10) 21.5(2 .3) -.40( .12) 32.2(2.9) -.30( .09) 102 18.4(1.5) -.40(.08) 7.9(1.0) - .85(.10) 15.0( 1.4) 0.20( .10) 11.5(1.2) 0.04(.11) Tp = 354MeV CT 218(101) 288(46) 484(54) 399(23) 21 117(11) 0.58(.09) 160(13) 0.27(.08) 366(20) 0.32(.05) 248(16) 0.35(.06) 31 146(10) 0.50(.06) 144(10) 0.36(.07) 191(11) 0.69(.05) 180(11) 0.69( .06) 42 20.9(2.0) 0.71( .08) 57.8(3.3) 0.42(.05) 43.7(2.9) 0.67(.06) 89.1(4.2) 0.51(.04) 52 6.8(1.4) 0.00(.16) 22.2(2.5) 0.68(.10) 34.2(3 .2) 0.49( .08) 28.8(2.9) 0.42(.09) 58 7.2(1.3) -.12(.18) 15.9(1.9) 0.69(.11) 23.3(2.4) 0.71(.09) 14.2(1.9) -.02(.13) 63 3.7(0.5) -.12(.14) 11.8(0.9) 0.28(.08) 10.3(0.9) 0.65( .07) 11.0(0.9) 0.58(.08) 73 2.1(0.4) -.84(.20) 2.9(0.5) 0.39(.18) 5.6(0 .7) 0.56(.12) 5.2(0.7) 0.59(.13) 83 2.6(0.4) 0.24(.15) 1.6(0.3) -.41(.20) 4.0(0.5) 0.28(.12) 1.5(0.3) 0.49(.20) Tp = 489MeV CT 38.6(5.1) 30.1(5.0) 42.4(2.0) 94.0(24.5) 24 20.3(2.6) 0.53(.12) 17.7(2.4) 0.93(.11) 25.7(2.8) -.21(.13) 67.7(4.7) -.38(.07) 42 3.5(0.7)-.81(.17) 3.1(0.6) -.16(.21) 7.1(1.0) 0.69(.12) 5.9(0.9) 1.00(.08) 57 1.2(0.4) 0.65( .27) 0.9(0.3) 0.62(.30) 0.8(0.3) -1.0(.24) 1.2(0.4) 0.90(.22) 167 Oc.m. 170* 14.15 170* 14.76 170* 15.78 170* 17.1 Tp = 250MeV (1 1200(20) 1090(130) 4160(180) 1920(130) 21 754(51) -.13(.07) 184(26) -.27(.14) 1860(83) -.18(.04) 965(60) -.17(.06) 45 133(11) -.47(.07) 292(15) 0.08( .06) 712(25) -.10(.03) 253(14) -.11(.03) 58 38.7(5.1) -.49(.12) 118( 9) - .66( .07) 438(17) -.07(.04) 179(12) -.08(.06) 71 36.0(2.6) -.66( .08) 83.5(4.1) -.61(.05) 195(7) -.03( .03) 111(6) -.07(.05) 85 42.6(3.2) -1.0(.05) 68.3(4.3) -.27(.07) 122(6) -.04(.05) 37.5(3.2) -.10(.12) 102 14.2(1.4) 0.22( .10) 37.1(2.3) 0.15(.07) 51.5(2.8) 0.32(.05) 28.0(2.1) 0.13(.12) Tp = 354MeV (1 618(138) 878(39) 2630(80) 1360(120) 21 403(21) 0.10( .05) 655(26) 0.43(.04) 1840( 45) 0.12( .03) 997(33) 0.00(.03) 31 338(15) 0.62(.04) 361(15) 0.58(.04) 1110(27) 0.09(.03) 520(19) 0.02(.04) 42 79.8(3.9) 0.24(.05) 142(5) 0.37(.04) 476(10) 0.15(.02) 236(7) 0.26( .03) 52 40.5(5.0) -.05(.09) 50.0(5.0) 0.05(.06) 188(8) 0.19(.04) 104(6) 0.12(.05) 58 25. 7(2.5) 0.63( .09) 23.3(2.4) 0.12( .10) 116(6) 0.27( .05) 58.0(3.8) 0.07( .07) 63 10.7(0 .9) -.40(.09) 27.1(1.4) 0.47(.05) 61.4(2.1) 0.49(.03) 35.7(1.6) 0.39(.04) 73 2.1(0.4) -.61(.19) 4.8(0.7) 1.00(.04) 22.4(1.5) 0.30( .06) 11.4(1.1) 0.56(.09) 83 1.1(0.2) 0.21(.25) 2.8(0.4) -.89(.13) 8.6(0.7) 0.66(.08) 4.7(0.5) 0.27(.12) Tp = 489MeV (1 99.7(26.8) 170(36) 389(74) 135(20) 24 72.4( 4.9) 0.00( .07) 117(6) -.39(.05) 275(10) -.10(.04) 89.3(5.4) -.19(.06) 42 5.9(0.9) 0.78(.11) 13.3(1.4) 0.58(.09) 34.4(2.2) -.48( .06) 14.9(1.4) 0.25(.0 8) 57 1.2(0.4) -.17(.32) 2.8(0.6) -.44(.19) 3.5(0.6) 0.09( .19) 2.4(0.5) -.08(.21) 168 Appendix C Tables of Continuum Data This appendix contains all quantities measured for the continuum in this series of experi-ments. Results are given for a 1 MeV T1r bite centered about each excitation energy and are given in the lab frame. Angles are in degrees and d20-/df!dE1r are in nb/sr-MeV. The numbers in parenthesis reflect statistical uncertainties only. 169 Table C.l: A list of values for the double differential cross sections of the 13C(p , 1r±)x reactions. Data for 13C(p, 1r-)x include contributions due to exclusive and inclusive pion production; data for 13C(p , 1r+)x are for inclusive pion production only. The systematic error in the overall normalization has been estimated at 8%, and relative uncertainties have been estimated at 10%. t3C(p, 1r-) eLAB I 15 17 19 21 23 Tp = 250MeV 49 140.7(2.7) 33.2(2.6) 44.8(3.0) 40.3(3.2) Tp = 354MeV 281 30.0(1.7) 34.9(1.9) 49.1(2.4) 56.2(2.8) 68.8(3.5) Tp = 489MeV 20 I 8.9(1.2) 12.6(1.4) 13.5(1.5) 12.6(1.4) 27.5(2.1) t3C(p, 1r+) 8LAB 15 17 19 21 23 Tp = 250MeV 49 196(8) 285(10) 419(14) 436( 14) 411(14) Tp = 354MeV 28 401(16) 678(29) 961( 43) 870(41) 1260(49) 35 211(11) 390(16) 545(19) 508(19) 715(24) Tp = 489MeV 20 248(15) 347(18) 456(20) 570(23) 568(23) 30 90.4(5.1) 136(6) 185(7) 215(8) 292(9) 170 Table C.2: A list of values for the double differential cross sections and analyzing powers of the 160(:p, ,r+)x reaction. Data are for inclusive pion production only. Errors for this data are summarized in table 3.1. OLAB 17 19 21 Tp = 250MeV 20 1300(74) 0.11(.06) 2140(100) -.04(.05) 2290(118) -.07(.05) 43 294(17) 0.16(.06) 783(31) -.04(.04) 56 310(16) -.04(.05) 297(17) -.11(.06) 68 124(6) -.21(.04) 266(9) -.26(.03) 360(12) -.36(.03) 82 119(6) -.26(.05) 207(9) -.37(.04) 134(9) -.36(.06) 99 101(4) -.25(.04) 173(6) -.31(.03) Tp = 354MeV 20 1760(47) 0.24(.03) 2500(57) 0.21(.02) 3120(66) 0.29(.02) 30 800(25) 0.23(.03) 1190(31) 0.26(.03) 1350(34) 0.22(.03) 40 388(9) 0.23(.02) 791(13) 0.24(.02) 1050(16) 0.32(.01) 50 140(7) 0.22(.04) 198(8) 0.19(.04) 269(10) 0.18(.03) 55 86.8( 4.9) 0.29(.06) 133(6) 0.11(.05) 153(7) 0.25(.04) 60 61.3(2.2) 0.22(.04) 93.4(2.8) 0.15(.03) 109(3) 0.11(.03) 70 22.6(1.5) 0.22( .07) 39.5(2.0) 0.23( .05) 47.4(2 .3) 0.25( .05) 80 8.9(0.7) 0.43(.08) 18.3(1.1) 0.33(.06) 28.4(1.4) 0.31(.05) Tp = 489MeV 23 310(11) -.07(.04) 438(13) -.04(.03) 529(14) 0.01(.03) 40 52.3(2.8) -.33(.06) 71.0(3 .3) -.16(.05) 89.0(3.7) -.18(.04) 54 12.6(1.3) 0.14(.10) 19.5(1.6) 0.03(.08) 22.6(1.7) 0.20(.08) 171 8LAB 23 25 27 Tp = 354MeV 20 3580(74) 0.27(.02) 4250(99) 0.24(.02) 30 2600(49) 0.29(.02) 2960(56) 0.34(.02) 40 960(15) 0.25( .02) 1290(19) 0.30(.02) 1330(20) 0.28(.02) 50 363(12) 0.17(.03) 545(16) 0.17(.03) 55 259(9) 0.24(.04) 390(12) 0.26(.03) 393(14) 0.19(.04) 60 176(4) 0.12(.02) 221(5) 0.24(.02) 253(6) 0.11(.02) 70 65.2(2.8) 0.34( .04) 85.9(3.5) 0.26(.04) 122(5) 0.28(.04) 80 41.3(1.8) 0.32(.04) 51.3(2.2) 0.21(.04) Tp = 489MeV 23 704(17) 0.04( .02) 844(19) 0.07(.02) 921(20) 0.10( .02) 40 124(5) -.08( .04) 184(6) -.11(.03) 204(6) -.14(.03) 54 32.7(2.1) -.02(.06) 37.0(2.2) 0.15(.06) 42.8(2.4) 0.07( .06) 172
Thesis/Dissertation
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Unreviewed
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Proton Induced Pion Production from Light Nuclei in the Region of the a ∆₁₂₃₂ Resonance
Text