Dynamical Collision Theory and Its Applications - 1st Edition - ISBN: 9780120442737, 9780323140713

Dynamical Collision Theory and Its Applications

1st Edition

Authors: Sadhan Adhikari
eBook ISBN: 9780323140713
Imprint: Academic Press
Published Date: 28th July 1991
Page Count: 508
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Dynamical Collision Theory and Its Applications reviews some of the powerful methods that have evolved for calculating the predictions of dynamical collision theory. Topics range from scattering theory to potential scattering, three- and four-particle scattering, multiparticle scattering, many-particle Lippmann-Schwinger equations, and the connected-kernel approach. This book is comprised of nine chapters; the first of which introduces the reader to the quantum theory of scattering. This topic is followed by a discussion on two-particle potential scattering and various methods for calculating off-shell two-body amplitudes as well as approximating them by finite-rank forms. The next chapters focus on the interpretation and applicability of the multichannel, multiparticle Lippmann-Schwinger equations, along with the known N-particle connected-kernel integral equations and their physical predictions. Descriptions of contemporary field-theoretical and relativistic approaches, such as the Dirac phenomenology for intermediate energy nucleon-nucleus scattering, are included. The singularity structure of multiparticle amplitudes and the associated dispersion-relation techniques are also considered. This book concludes by describing the relationship between the conventional (optical potentials, multiple-scattering theories, and the coupled-reaction channel and resonating-group methods) and the few-body approaches. This text is primarily intended for chemists, physicists, and graduate students interested in general scattering theory; intermediate and low-energy hadron and nuclear physics; atomic and molecular physics; statistical mechanics; and physical and quantum chemistry. There are a number of topics in this book that will be interesting to both mathematicians and particle physicists, as well as advanced graduate students in courses that involve collision theory.

Table of Contents


Chapter 1 Scattering Theory

1.1. Introduction

1.2. Elastic and Inelastic Scattering

1.3. Quantum Theory of Scattering

1.4. Asymptotic Completeness: The

1.5. The Asymptotic Condition

1.6. Dynamical Strategies

1.7. Transition Operators

1.8. Integral Equations, Subtraction Techniques

1.9. Unitarity, Singularities, and Disconnected Structure

1.10. Symmetries

1.11. Permutation Symmetries

Appendix (1)

References and Notes (1)

Chapter 2 Potential Scattering

2.1. Introduction

2.2. Time-Independent Realization of Scattering

2.3. Lippmann-Schwinger Equation

2.4. Spectral Representations; Off-Shell Unitarity

2.5. Partial-Wave Dynamical Equations

2.6. Multichannel Collisions

2.7. Relativistic Integral Equations

References and Notes (2)

Chapter 3 Solution Methods and Techniques: Potential Scattering

3.1. Introduction

3.2. General Calculational Questions

3.3. Singularity Removal

3.4. Solution by Iteration

3.5. Convergence

3.6. Collision Integral Equation Approach to the Bound-State Problem

3.7. Variational Principles for the Scattering Amplitudes

3.8. Separable Expansions and Degenerate-Kernel Schemes

3.9. Numerical Applications of Expansion Methods

References and Notes (3)

Chapter 4 Many-Particle Lippmann-Schwinger Equations

4.1. Introduction

4.2. Homogeneous and Inhomogeneous Equations

4.3. Alternative Interpretations of the LS Equations

4.4. The Basic Set of LS Equations

4.5. Scattering Equations for Three or More Noninteracting Clusters in the Initial State

4.6. Discussion

References and Notes (4)

Chapter 5 The Connected-Kernel Approach

5.1. Introduction

5.2. Interactions, Transition Operators, Green Functions, and Wave Functions

5.3. Three-Particle Equations

5.4. N-Particle Equations. I

5.5. N-Particle Equations. II

Appendix (5)

References and Notes (5)

Chapter 6 Singularity Structure of Multiparticle Amplitudes

6.1. Introduction

6.2. Singularities of the Two-Particle Amplitudes

6.3. Singularities of the Three-Particle Amplitudes

6.4. Efimov and Thomas Effects

References and Notes (6)

Chapter 7 Solution Methods and Techniques: Three-Particle Scattering

7.1. Introduction

7.2. Numerical Methods

7.3. Results for the Three-Nucleon System

7.4. Photodisintegration of

7.5. Deuteron-Alpha Collisions

7.6. Three-Body Treatment of the NN-πd-πNN System

7.7. Applications to Atomic/Molecular Collision Processes

References and Notes (7)

Chapter 8 Solution Methods and Techniques: Four-Particle Scattering

8.1. Introduction

8.2. Integral Equations for the (3 + 1) → (3 + 1) Reactions

8.3. Explicit Momentum-Space Scattering Equations

8.4. Numerical Calculations

References and Notes (8)

Chapter 9 Solution Methods and Techniques: Multiparticle Scattering

9.1. Introduction

9.2. The Method of the Optical Potential

9.3. Multiple-Scattering Algorithms

9.4. Bound-State Approximations

9.5. Generalized Reaction Theories

References and Notes (9)




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Academic Press
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About the Author

Sadhan Adhikari

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