Collision theory

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

1. Introduction	p. 1
1.1 The Principles of Quantum Mechanics	p. 1
1.2 Some Specific Operators	p. 9
1.3 Eigenstates of a Free Particle	p. 16
1.4 Relativistic Quantum Mechanics	p. 21
2. Symmetry Operations on the Schrodinger Equation	p. 32
2.1 Translations of Coordinates	p. 32
2.2 Coordinate Rotations	p. 36
2.3 Coordinate Reflections	p. 40
2.4 Charge Conjugation	p. 41
2.5 Displacement in Time	p. 44
2.6 Time Reversal Invariance	p. 51
3. The Description of Scattering Processes	p. 58
3.1 Preparation of the Initial State	p. 59
3.2 Integration of the Schrodinger Equation for Scattering Processes	p. 67
3.3 Evaluation of the Scattering Cross Section	p. 76
3.4 Physical Interpretations of [psi](t)	p. 95
4. Further Description of Scattering Processes	p. 111
4.1 Description of the Channels of a Reaction	p. 111
4.2 Wave Function Symmetrization for Systems of Identical Particles	p. 119
4.3 Symmetrization of the Wave Packet States for a Scattering Interaction	p. 133
4.4 Evaluation of the Scattering Cross Section	p. 141
4.5 Examples	p. 148
4.6 Further Description and Simplification of the Matrix Elements of J	p. 164
5. Formal Scattering Theory	p. 173
5.1 Limiting Process and Transition Probabilities	p. 174
5.2 The S-Matrix and Further Formal Theory	p. 186
5.3 Integral Equations for the Determination of the S-Matrix	p. 197
5.4 Scattering from Two Potentials	p. 202
5.5 The S-Matrix and the Interaction Representation	p. 209
5.6 The Reaction Matrix and the Heitler Integral Equation	p. 215
5.7 Application to Quantum Field Theory	p. 218
6. The Two-Body Problem with Central Forces	p. 221
6.1 Coordinate Transformations from the Laboratory to the Barycentric Frame of Reference	p. 221
6.2 Partial Wave Analysis and the Scattering Phase Shifts	p. 226
6.3 Nonrelativistic Potential Scattering	p. 243
6.4 Examples	p. 252
6.5 Analytic Properties of Partial Wave Amplitudes	p. 269
6.6 Effective-Range Theory	p. 286
6.7 Approximation Methods	p. 299
6.8 The Potential Scattering of Relativistic Particles	p. 339
7. Scattering by Noncentral Forces	p. 344
7.1 Kinematical Description of Scattering by Noncentral Forces	p. 345
7.2 Application to the Scattering of Spin Zero by Spin One-Half Particles	p. 358
7.3 Scattering Reactions	p. 372
7.4 The Scattering of Two Spin One-Half Particles	p. 384
7.5 The Density Matrix and the Scattering of Polarized Particles	p. 398
7.6 The Solution of the Dirac Equation in a Central Field	p. 420
8. The Lifetime and Decay of Virtual States	p. 424
8.1 Stationary State Perturbation Theory	p. 425
8.2 The Decay of a Prepared State	p. 431
8.3 Examples of the Decay of a Prepared State	p. 460
8.4 Preparation of an Unstable State by Scattering Interactions	p. 474
8.5 General Theory of the Lifetime of Scattering States	p. 485
8.6 The General Theory of Resonant Scattering	p. 498
9. Miscellaneous Applications	p. 510
9.1 Relativistic Description of the Scattering of Spin One-Half Particles by a Force Center	p. 510
9.2 The Scattering and Photoproduction of Pi-Mesons from Nucleons	p. 518
9.3 The Theory of Final State Interactions	p. 540
9.4 Applications of Formal Scattering Theory to Field Theory	p. 553
10. Introduction to Dispersion Theory	p. 557
10.1 Historical Background	p. 557
10.2 Formal Considerations	p. 563
10.3 Nonrelativistic Theory	p. 567
10.4 Dispersion Relations in Nonrelativistic Theory	p. 585
10.5 Two-Dimensional Representation	p. 598
10.6 Dispersion Relations in Relativistic Field Theory	p. 621
11. Scattering by Systems of Bound Particles	p. 679
11.1 Scattering from a Single Weakly Bound Particle	p. 680
11.2 Scattering by a Small System of Bound Scatterers	p. 708
11.3 Multiple Scattering by a System of Bound Particles	p. 749
11.4 Use of a Pseudopotential to Describe Elastic Scattering	p. 780
11.5 Coherence and Incoherence in Multiple Scattering Phenomena	p. 804
11.6 Deuteron Stripping and Pick-Up Reactions	p. 833
11.7 The Scattering of Charged Particles by Atoms	p. 850
Appendices
A Table of Wigner Coefficients	p. 867
B Collisions Involving Three Incident Particles	p. 868
C Completeness and Orthogonality of Channel States	p. 872
D Computational Methods for Scattering at Low Energy	p. 879
E The Jacob-Wick Expansion of the Scattering Matrix	p. 882
F Evaluation of the Amplitude for Nucleon-Nucleon Scattering in Terms of Phase Shifts	p. 899
G.1 Nonrelativistic Dispersion Relations for Combinations of Ordinary and Exchange Potentials	p. 903
G.2 Solution of a Class of Integral Equations	p. 908
Index	p. 913

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