Atomic and Molecular Scattering

1st Edition - January 28, 1971
Editor: Berni Alder
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 4 4 9 - 9

Methods in Computational Physics, Volume 10: Atomic and Molecular Scattering presents the digital methods used in producing quantitative results from the theory of atomic and… Read more

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Methods in Computational Physics, Volume 10: Atomic and Molecular Scattering presents the digital methods used in producing quantitative results from the theory of atomic and molecular scattering. This volume contains seven chapters that specifically consider the methods that produce quantum mechanical wavefunctions from which cross sections are deduced. Chapter 1 covers the solutions of the systems of coupled integro-differential equations using the Hartree and Hartree-Fock methods for atomic structure calculations and the eigenfunction expansion method for electron-atom collision calculations. Chapter 2 treats the translation of the formal results into a generally applicable, efficient, and numerically stable method for solving quantum-mechanical scattering problems. Chapter 3 discusses the exponential method of solution as applied in inelastic scattering, the reaction coordinates for a collinear reactive system, and the modifications of the computational method required for reactive scattering. Chapter 4 outlines the theory and the calculational techniques involved in the use of algebraic expansions in scattering problems, while Chapter 5 deals with the solution of the close-coupled equations. Chapter 6 evaluates the collision between two quantum-mechanical systems with internal structure using the quantum-mechanical operator equations. Lastly, Chapter 7 focuses on the principles and applications of classical trajectory methods.

Contributors

Preface

Numerical Solutions of the Integro-Differential Equations of Electron-Atom Collision Theory

I. Introduction

II. The Integro-Differential Equations

III. Solutions in the Asymptotic Region

IV. Iterative Methods

V. Reduction to a System of Coupled Differential Equations

VI. Reduction to Systems of Algebraic Equations

VII. Approximate Solutions

VIII. Computer Programs

References

Quantum Scattering Using Piecewise Analytic Solutions

I. Introduction

II. Constructing Zeroth-Order Solutions

III. Evaluation of Accuracy

IV. Matching Boundary Conditions

V. Computational Estimates and Efficiency

IV. Comparison with Numerical Methods

References

Quantum Calculations in Chemically Reactive Systems

I. Introduction

II. Inelastic Scattering

III. Coupled Equations in Reaction Coordinates

IV. Computational Methods and S Matrix

V. Numerical Examples

VI. Conclusion

Appendix

References

Expansion Methods for Electron-Atom Scattering

I. Introduction

II. Calculation of Scattering Cross Sections

III. Determination of Scattering Wavefunctions

IV. Matrix Elements and Integrals

V. Computational Details and Results

Appendix A. Function Definitions

Appendix B. Evaluation of Special Functions

References

Calculations of Cross Sections for Rotational Excitation of Diatomic Molecules by Heavy Particle Impact: Solution of the Close-Coupled Equations

I. Introduction

II. General Theory

III. Numerical Methods

IV. Computer Program

V. Discussion

Note Added in Proof

Appendix: Evaluation of Coupling Matrix Elements

References

Amplitude Densities in Molecular Scattering

I. Introduction

II. Integral and Differential Equations for the Amplitude Density Functions

III. Stability of the Amplitude Density Equations

IV. The Voltera Equation

V. Differential Equations for the T Matrix

VI. Complex Arithmetic

References

Classical Trajectory Methods

I. Introduction

II. The Technology of the Method

III. Applications

References

Author Index

Subject Index

Contents Of Previous Volumes