The Pion-Nucleon System

The Pion-Nucleon System

B. H. Bransden
R. G. Moorhouse
Copyright Date: 1973
Pages: 552
https://www.jstor.org/stable/j.ctt13x0vfc
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    The Pion-Nucleon System
    Book Description:

    Synthesizing the theoretical and experimental advances in pion-nucleon interactions over approximately the last twelve years, the authors offer here a timely account of the hadronic interactions of pions and nucleons and of the structure of nucleons. Because of the hadronic SU3 symmetry, the book also treats the structure of baryons in general, and so contains much material external to the specific field of pion-nucleon interactions. Thus the book's subject can be stated as the hadronic structure of baryons as illustrated particularly by pion-nucleon interaction.

    Following an introductory discussion of isotopic spin, the authors proceed to chapters that treat low energy pion scattering by nucleons and the photoproduction of pions; forward and fixed momentum transfer dispersion relations; analytic properties of scattering amplitudes; formation of nucleon resonances; symmetries and classification of particles and resonances; current algebra, sum rules, and superconvergence relations; scattering at higher energies; pion-nucleon dynamics; pion-nucleon inelastic scattering; and the form factors of the nucleon and the pion.

    Each chapter is followed by abundant references to the original literature. The level of the writing is suitable for students at the graduate level, and the presentation is even and self-contained. On balance, the authors have prepared a useful consolidation and review of this difficult and changing area of investigation.

    Originally published in 1973.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6744-8
    Subjects: Technology, General Science

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. PREFACE
    (pp. v-vi)
    B. H. B. and R. G. M.
  3. Table of Contents
    (pp. vii-2)
  4. A NOTE ON UNITS AND CONVENTIONS
    (pp. 3-6)
  5. CHAPTER 1 INTRODUCTION
    (pp. 7-20)

    The proton,p,is a positively charged spin ½ particle of mass 938.3 MeV/c² and the neutron,n,is a neutral spin ½ particle of mass 939.6 MeV/c². They each have, by conventional definition, positive parity, P = +1 (Sakurai, 1964). The positively and negatively charged pions, π±, are spin 0 particles of mass 139.6 and the neutral charge pion, π0, is a spin 0 particle of mass 135.0. The parity of all three pions is found to be negative, P = -1 (Sakurai, 1964; Nishijima, 1963; Kallen, 1964). Pions and nucleons interact strongly, and this interaction is responsible for...

  6. CHAPTER 2 LOW ENERGY PION SCATTERING BY NUCLEONS AND THE PHOTOPRODUCTION OF PIONS
    (pp. 21-88)

    In this chapter, we discuss the low energy scattering of pions by nucleons and the associated process of photoproduction of pions from nucleons. The low energy region, for this purpose, is the energy region in which inelastic scattering is inappreciable The low energy experiments are analyzed with the help of the quantum theory of scattering, making use, in particular, of partial wave expansions. It is assumed that the reader has some acquaintance with this theory,¹ but to establish our notation and conventions a summary of some of the more important results that are required is given below

    The probability Pba...

  7. CHAPTER 3 FORWARD AND FIXED MOMENTUM TRANSFER DISPERSION RELATIONS
    (pp. 89-126)

    In this chapter, we shall examine the properties of elastic scattering amplitudes when the energy is allowed to take complex values. It will be shown that the scattering amplitude is an analytic function of the energy, apart from certain cuts and poles, and that this analyticity enables us to write integral relations between the real and imaginary parts of the scattering amplitude, called dispersion relations, that prove to be most powerful aids to the analysis and understanding of experimental data. We shall first discuss briefly some properties of a function f(v) of a complex variablev, that is analytic in...

  8. CHAPTER 4 ANALYTIC PROPERTIES OF SCATTERING AMPLITUDES
    (pp. 127-166)

    In the last chapter, it was shown that the scattering amplitudes for two-body collisions at fixed momentum transfer were analytic functions of energy except for cuts and poles on the real axis. This analyticity was sufficient for the derivation of certain dispersion relations, which were of great importance in the analysis of scattering data. A further advance in understanding can be achieved by studying the continuation of the momentum transfer to complex values, and indeed it is possible that the analytic properties of the scattering amplitude as a function of all its variables may be sufficient to determine the dynamics...

  9. CHAPTER 5 FORMATION OF NUCLEON RESONANCES
    (pp. 167-216)

    Characteristic of hadron experiments is the occurence of particularly strong interactions in some channels at some energies. These resonances may first be seen for example as peaks in total cross sections in πNor K¯N scattering experiments, or as departures from expected distributions in phase space (Dalitz) plots in three (or more) body final states (see Chapter 10). Further investigation shows that the resonances occur in states for which all the strong interaction quantum numbers (J,P,I, etc.) are good. Consequently they may be regarded as particles with masses high enough to be formed from, and to decay into,...

  10. CHAPTER 6 SYMMETRIES AND CLASSIFICATION OF PARTICLES AND RESONANCES
    (pp. 217-284)

    As outlined in Chapter 1, the interaction of pions and nucleons is charge independent. The symmetry appears to be perturbed only by comparatively weak forces of the order of the electromagnetic interactions. It is a reasonable hypothesis that the specifically hadronic interactions are exactly charge-independent, and that the observed deviations are due to the electromagnetic interactions. The charge independence can be best described as a symmetry in isospin, which is mathematically identical to spin in ordinary space. The pion is assigned total isospin 1, giving three independent isospin states of the pion. These are linear combinations of the three physical...

  11. CHAPTER 7 CURRENT ALGEBRA AND SUM RULES
    (pp. 285-318)

    In the last chapter we were concerned with particles and resonances as multiplets (that is, bases of representations) of symmetry groups SU2, SU3, or SU6 and with their interactions as approximately invariant under SU2, SU3, or SU6. However these symmetries may also play a part in elementary particle physics not as a group, but as an algebra of equaltime commutations ofcurrents(Gell-Mann, 1962). When one sandwiches such a relation between state vectors, and inserts a complete sum over states between the currents or other operators of the commutator, one obtains a sum rule that may enable one to utilize...

  12. CHAPTER 8 SCATTERING AT HIGHER ENERGIES
    (pp. 319-380)

    One of the features of elementary particle scattering is that for center of mass momenta greater than 0.5 GeV/c the differential cross sections for the observed elastic scatterings have a marked peak at forward scattering angles in the center of mass system. As collision energies increase, the forward peak increasingly dominates the elastic cross section, the greater part of which is contained in a decreasingly small forward angle (with the exception that when the particles are alike, as in proton-proton scattering the differential cross section is necessarily symmetric between forward and backward directions). The forward, ordiffraction, peaking is shown...

  13. CHAPTER 9 PION-NUCLEON DYNAMICS
    (pp. 381-424)

    The ultimate goal towards which the study of elementary particles strives is the provision of an adequate dynamical theory. At first, following the ideas of Yukawa, attempts were made to describe the pion nucleon system in terms of a Lagrangian field theory,¹ similar in structure to the successful theory of quantum electrodynamics. Qualitatively the strong attractive forces between nucleons can be understood in terms of the exchange of (virtual) pions, in lowest order pictured in the Feynman diagram of Fig. 9-la, while thep₃₃ resonance in pion-nucleon scattering can be attributed to nucleon exchange (Fig. 9-lb). The quantitative implementation of...

  14. CHAPTER 10 PION-NUCLEON INELASTIC SCATTERING
    (pp. 425-458)

    In earlier chapters, the analysis of the elastic scattering of pions by nucleons has been discussed in some detail, while some features of inelastic scattering at very high energies were outlined in Chapter 8. Neither the experimental information, nor its interpretation, is as complete for scattering into individual inelastic channels as for elastic scattering, but some progress has been made in understanding some of the principal features of these processes. The first inelastic threshold is at a laboratory pion kinetic energy of Tπ= 180 MeV. Above this energy single pion production is possible:

    π + N → π +...

  15. CHAPTER 11 THE FORM FACTORS OF THE NUCLEON AND PION
    (pp. 459-508)

    The structure of a composite particle, such as a nucleus, can be characterized by, amongst other things, the way in which the charge and magnetic moment of the particle is distributed. These distributions can be measured by allowing the composite particle to interact with an electromagnetic field. In particular, these distributions are connected with differential cross sections for the scattering of charged particles by the composite particle. The most suitable charged particles to use as probes in the experimental investigation of form factors are electrons, as these are structureless and do not take part in the strong nuclear interaction that...

  16. APPENDIX A ANGULAR MOMENTUM
    (pp. 509-516)
  17. APPENDIX B FORMALISM FOR PION PHOTOPRODUCTION
    (pp. 517-522)
  18. AUTHOR INDEX
    (pp. 523-530)
  19. SUBJECT INDEX
    (pp. 531-538)