Modern Three-Hadron Physics

ISBN-13: 9783642810725 / Angielski / Miękka / 2012 / 252 str.

A. W. Thomas

Opis

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"

Spis treści

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 .- 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.