Modern three-hadron physics. Topics in current physics; v. 2.

The model calculations considered here test the DWBA with a wide range of three-body models. Each of the calculations, however, considers only one or two aspects of the accuracy of the DWBA. The lack of overlap of the testing parameters limits the con- clusions which can be drawn. This is particularly true with reference to the nucleon- core potential where comparable parameters are rarely used. In spite of this limitation, we may make a few observations about the sensitivity of the model cross sections and the mechanism which produces an accurate DWBA. Specifically we may summarize the most important results as follows: 1) In these models the exact DWBA at low energies (E

1. Fundamentals of Three-Body Scattering Theory.- 1.1 Two-Body Scattering.- 1.1.1 The Schrödinger Equation.- 1.1.2 The Differential Cross Section.- 1.1.3 The Scattering Integral Equation.- 1.1.4 The Two-Body t-Matrix.- 1.1.5 The Separable Potential.- 1.2 The Simplest Three-Body Problem.- 1.2.1 Notation.- 1.2.2 The Two-Body t-Matrix in the Three-Body System.- 1.3 Three Distinguishable Particles — Wave Function Approach.- 1.3.1 The Non-Uniqueness Problem.- 1.3.2 The Solution (3?3).- 1.3.3 Scattering from a Two-Body Bound State.- 1.4 The Faddeev Equations (3?3).- 1.4.1 A Rigorous Derivation of Faddeev Equations for G (z).- 1.4.2 The Three-Body t-Matrix.- 1.5 Bound State Scattering.- 1.5.1 The Amplitudes Uij.- 1.5.2 Break-Up in Terms of Uji.- 1.5.3 Calculation of Cross-Sections.- 1.6 Unitarity.- 1.6.1 Formal Expression for disc {Uji}.- 1.6.2 Meaning for Elastic Bound State Scattering.- 1.6.3 Remarks.- 1.7 Identical Particles.- 1.8 Three-Body Scattering With Separable Interactions.- 1.8.1 General Formulation.- 1.8.2 Three Identical Particles.- 1.9 Rotationally Invariant Equations for Separable Interactions.- 1.10 Conclusion.- References.- 2. Analytic Structure of On-Shell Three-Body Amplitudes.- 2.1 Background.- 2.2 The Fredholm Representation of On-Shell Amplitudes.- 2.2.1 Definition of Amplitudes in the Separable Potential Model.- 2.2.2 Singularities of Multiple Scattering Terms.- 2.2.3 The Elastic Amplitude.- 2.2.4 The Break-Up Amplitude.- 2.2.5 The Free-Particle Amplitude.- 2.2.6 Remark on the Rotation of Contours Method.- 2.3 Analytic Continuation in Energy of the On-Shell Amplitudes.- 2.3.1 The Elastic Amplitude.- 2.3.2 Location of Singularities of the Elastic Amplitude.- 2.3.3 Minimal Three-Body Scattering.- 2.3.4 The Break-Up and Free-Scattering Amplitudes.- 2.3.5 Summary.- 2.4 On-Shell Calculations.- 2.4.1 Dispersion Relations and the N/D Method.- 2.4.2 Calculations for the Three-Nucleon System.- 2.4.3 Other Applications.- 2.5 Conclusions.- Appendi x.- References.- 3. Theory of Three-Body Final States.- 3.1 The Problem.- 3.2 Coherence.- 3.3 The Two-Body Case.- 3.4 The Three-Body Case.- 3.5 Spinless Boson Example.- 3.6 Implementing Unitarity and Analyticity.- 3.7 Three Identical Bosons Again.- 3.8 Conclusions.- References.- 4. The Boundary Condition Method.- 4.1 Fundamentals.- 4.2 Two-Particle Description.- 4.3 Boundary Conditions for Three-Particle Scattering.- 4.4 The BCF Integral Equation.- 4.5 Practical Evaluation of the Kernel.- 4.6 The Interior Region.- 4.7 Summary of the Formal Work.- 4.8 An Example.- 4.9 Discussion.- References.- 5. A Relativistic Three-Body Theory.- 5.1 Derivation of the Basic Equations — Spinless Case.- 5.1.1 Unitarity; Relativistic Two-Body Problem.- 5.1.2 Relativistic Three-Body Equations: Spinless Particles.- 5.2 Spin and Isospin.- 5.2.1 Isospin.- 5.2.2 Integral Spin.- 5.2.3 Spin-1/2 and the Pion-Nucleon Interaction.- 5.2.4 Spin-3/2 (?(1236)??+N).- 5.3 Physical Input: Blankenbecler-Sugar vs. Feynman, etc.- 5.4 Application of Relativistic Three-Body Formalism.- 5.4.1 Inelastic Effects and ?-N Resonances.- 5.4.2 Further Applications.- 5.5 Present Developments — Three-Body Phenomenology.- 5.5.1 Data Analysis of Single Pion Production in ?N Collisions in the CM Energy Range of 1300–2000 MeV.- 5.5.2 Three-Pion System.- Appendix A.- Appendix B.- References.- 6. Applications of Three-Body Methods to Many-Body Hadronic Systems.- 6.1 Tests of Reaction Mechanisms.- 6.1.1 Direct Reactions.- 6.1.2 Three-Body Formulation of the DWBA.- 6.1.3 Stripping.- 6.1.4 Elastic Scattering.- 6.1.5 Other Reactions.- 6.1.6 Summary and Conclusions.- 6.2 Three-Body Effects in Nuclear Processes.- 6.2.1 Elastic Scattering of Simple Projectiles: Optical Potentials.- 6.2.2 Deuteron Reactions.- 6.2.3 Multi-Particle Final States.- 6.2.4 Summary and Conclusions.- References.