Collision Theory

A systematic description of the basic principles of collision theory, this graduate-level text presents a detailed examination of scattering processes and formal scattering theory, the two-body problem with central forces, scattering by noncentral forces, lifetime and decay of virtual states, an introduction to dispersion theory, and more. 1964 edition.

Marvin L. Goldberger Professor of Physics Emeritus University of California, San Diego Kenneth M. Watson Professor Emeritus Marine Physical Laboratory Scripps Institution of Oceanography University of California, San Diego

Introduction

1

(31)

The Principles of Quantum Mechanics

1

(8)

Some Specific Operators

9

(7)

Eigenstates of a Free Particle

16

(5)

Relativistic Quantum Mechanics

21

(11)

Symmetry Operations on the Schrodinger Equation

32

(26)

Translations of Coordinates

32

(4)

Coordinate Rotations

36

(4)

Coordinate Reflections

40

(1)

Charge Conjugation

41

(3)

Displacement in Time

44

(7)

Time Reversal Invariance

51

(7)

The Description of Scattering Processes

58

(53)

Preparation of the Initial State

59

(8)

Integration of the Schrodinger Equation for Scattering Processes

67

(9)

Evaluation of the Scattering Cross Section

76

(19)

Physical Interpretations of Ψ(t)

95

(16)

Further Description of Scattering Processes

111

(62)

Description of the Channels of a Reaction

111

(8)

Wave Function Symmetrization for Systems of Identical Particles

119

(14)

Symmetrization of the Wave Packet States for a Scattering Interaction

133

(8)

Evaluation of the Scattering Cross Section

141

(7)

Examples

148

(16)

Further Description and Simplification of the Matrix Elements of T

164

(9)

Formal Scattering Theory

173

(48)

Limiting Process and Transition Probabilities

174

(12)

The S-Matrix and Further Formal Theory

186

(11)

Integral Equations for the Determination of the S-Matrix

197

(5)

Scattering from Two Potentials

202

(7)

The S-Matrix and the Interaction Representation

209

(6)

The Reaction Matrix and the Heitler Integral Equation

215

(3)

Application to Quantum Field Theory

218

(3)

The Two-Body Problem with Central Forces

221

(123)

Coordinate Transformations from the Laboratory to the Barycentric Frame of Reference

221

(5)

Partial Wave Analysis and the Scattering Phase Shifts

226

(17)

Nonrelativistic Potential Scattering

243

(9)

Examples

252

(17)

Analytic Properties of Partial Wave Amplitudes

269

(17)

Effective-Range Theory

286

(13)

Approximation Methods

299

(40)

The Potential Scattering of Relativistic Particles

339

(5)

Scattering by Noncentral Forces

344

(80)

Kinematical Description of Scattering by Noncentral Forces

345

(13)

Application to the Scattering of Spin Zero by Spin One-Half Particles

358

(14)

Scattering Reactions

372

(12)

The Scattering of Two Spin One-Half Particles

384

(14)

The Density Matrix and the Scattering of Polarized Particles

398

(22)

The Solution of the Dirac Equation in a Central Field

420

(4)

The Lifetime and Decay of Virtual States

424

(86)

Stationary State Perturbation Theory

425

(6)

The Decay of a Prepared State

431

(29)

Examples of the Decay of a Prepared State

460

(14)

Preparation of an Unstable State by Scattering Interactions

474

(11)

General Theory of the Lifetime of Scattering States

485

(13)

The General Theory of Resonant Scattering

498

(12)

Miscellaneous Applications

510

(47)

Relativistic Description of the Scattering of Spin One-Half Particles by a Force Center

510

(8)

The Scattering and Photoproduction of Pi-Mesons from Nucleons

518

(22)

The Theory of Final State Interactions

540

(13)

Applications of Formal Scattering Theory to Field Theory

553

(4)

Introduction to Dispersion Theory

557

(122)

Historical Background

557

(6)

Formal Considerations

563

(4)

Nonrelativistic Theory

567

(18)

Dispersion Relations in Nonrelativistic Theory

585

(13)

Two-Dimensional Representation

598

(23)

Dispersion Relations in Relativistic Field Theory

621

(58)

Scattering by Systems of Bound Particles

679

(234)

Scattering from a Single Weakly Bound Particle

680

(28)

Scattering by a Small System of Bound Scatterers

708

(41)

Multiple Scattering by a System of Bound Particles

749

(31)

Use of a Pseudopotential to Describe Elastic Scattering

780

(24)

Coherence and Incoherence in Multiple Scattering Phenomena

804

(29)

Deuteron Stripping and Pick-Up Reactions

833

(17)

The Scattering of Charged Particles by Atoms

850

(17)

APPENDICES

A Table of Wigner Coefficients

867

(1)

B Collisions Involving Three Incident Particles

868

(4)

C Completeness and Orthogonality of Channel States

872

(7)

D Computational Methods for Scattering at Low Energy

879

(3)

E The Jacob-Wick Expansion of the Scattering Matrix

882

(17)

F Evaluation of the Amplitude for Nucleon-Nucleon Scattering in Terms of Phase Shifts

899

(4)

G.1 Nonrelativistic Dispersion Relations for Combinations of Ordinary and Exchange Potentials

903

(5)

G.2 Solution of a Class of Integral Equations

908

(5)

Index

913

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