Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions

ISBN-13: 9783642646553 / Angielski / Miękka / 2014 / 249 str.

Klaus Bartschat; K. Bartschat; I. E. McCarthy

Opis

Computational Atomic Physics deals with computational methods for calculating electron (and positron) scattering from atoms and ions, including elastic scattering, excitation, and ionization processes. Each chapter is divided into abstract, theory, computer program with sample input and output, summary, suggested problems, and references. An MS-DOS diskette is included, which holds 11 programs covering the features of each chapter and therefore contributing to a deeper understanding of the field. Thus the book provides a unique practical application of advanced quantum mechanics.

Spis treści

1. Electron-Atom Scattering Theory: An Overview.- Abstract.- 1.1 Introduction.- 1.2 Potential Scattering.- 1.3 Perturbation Approaches.- 1.4 The Close-Coupling Expansion.- 1.5 Computer Program for Potential Scattering.- 1.5.1 Description of the Input Data.- 1.5.2 Test-Run Data.- 1.6 Summary.- 1.7 Suggested Problems.- Acknowledgments.- References.- 2. Core Potentials for Quasi One-Electron Systems.- Abstract.- 2.1 Introduction.- 2.2 Theory.- 2.3 The Algorithm.- 2.4 Computer Program.- 2.4.1 Program Structure.- 2.4.2 Description of the Input Parameters.- 2.5 Test Run.- 2.6 Summary.- 2.7 Suggested Problems.- Acknowledgments.- References.- 3. Energies and Oscillator Strengths Using Configuration Interaction Wave Functions.- Abstract.- 3.1 Introduction.- 3.2 Hydrogen-Like Ions.- 3.2.1 Angular Momentum.- 3.2.2 Commuting Operators.- 3.2.3 Fine Structure.- 3.3 Two-Electron Atoms and Ions.- 3.3.1 Wave Functions for Two-Electron Ions.- 3.3.2 Variational Principle.- 3.3.3 Application to the Two-Electron Ground-State Energy.- 3.4 Many-Electron Atoms and Ions.- 3.4.1 Hartree’s Method.- 3.4.2 The Hartree-Fock Method.- 3.5 Configuration Interaction Methods.- 3.5.1 Optimization of the Expansion Coefficients.- 3.5.2 Optimization of the CSF.- 3.5.3 Correlation Energy.- 3.5.4 Choice of Configurations.- 3.5.5 Calculation of Several States Simultaneously.- 3.6 Transition Probabilities and Oscillator Strengths.- 3.6.1 Dipole Approximation.- 3.6.2 Length and Velocity Forms.- 3.6.3 The Effect of Electron Correlation.- 3.6.4 Selection Rules.- 3.7 The Codes.- 3.7.1 Running of the Codes.- 3.7.2 Sample Radial Data.- 3.8 Examples.- 3.9 Summary.- 3.10 Suggested Problems.- 3.10.1 He-Like Ions.- 3.10.2 Be-Like Ions.- 3.10.3 Ground State of Carbon.- References.- 4. The Distorted-Wave Method for Elastic Scattering and Atomic Excitation.- Abstract.- 4.1 Introduction.- 4.2 Theory.- 4.2.1 Distorted-Wave Series.- 4.2.2 Discussion of Distorting Potentials Ui and Uf.- 4.3 First-Order Amplitudes.- 4.3.1 Inelastic Scattering.- 4.3.2 Elastic Scattering.- 4.4 Partial-Wave Expansion of the T Matrix.- 4.4.1 Inelastic Scattering.- 4.4.2 Elastic Scattering.- 4.4.3 Differential Cross Sections.- 4.5 Computer Program.- 4.5.1 Radial Mesh.- 4.5.2 Numerical Technique.- 4.5.3 Program Input.- 4.5.4 Sample Input and Output.- 4.6 Summary.- 4.7 Suggested Problems.- Acknowledgments.- References.- 5. Distorted-Wave Methods for Ionization.- Abstract.- 5.1 Introduction.- 5.2 Theory.- 5.3 Reduction of the (e,2e) Amplitudes to Computational Form.- 5.3.1 Distorted-Wave Born Approximation: Direct Amplitude.- 5.3.2 Radial Partial Waves.- 5.3.3 Exchange Amplitude.- 5.3.4 Radial Integration.- 5.3.5 Distorted-Wave Impulse Approximation.- 5.4 Computer Program.- 5.4.1 Input.- 5.4.2 Calculation of the Differential Cross Section.- 5.4.3 Sample Input.- 5.4.4 Sample Output.- 5.5 Summary.- 5.6 Suggested Problems.- Acknowledgments.- References.- 6. The Close-Coupling Approximation.- Abstract.- 6.1 Introduction.- 6.2 Theory.- 6.2.1 The Close-Coupling Equations.- 6.2.2 Boundary Conditions and Cross Sections.- 6.3 The Numerical Solution of the Close-Coupling Equations.- 6.3.1 The Power-Series Expansion About the Origin.- 6.3.2 Asymptotic Correction Procedures.- 6.4 The Born Approximation.- 6.5 Computer Program.- 6.5.1 The Radial Meshes.- 6.5.2 Numerical Procedures.- 6.5.3 Convergence Criteria.- 6.5.4 Program Input.- 6.5.5 Sample Input and Output.- 6.6 Summary.- 6.7 Suggested Problems.- Acknowledgments.- References.- 7. The R-Matrix Method.- Abstract.- 7.1 Introduction.- 7.2 General R-Matrix Theory.- 7.3 Electron-Hydrogen-like Ion Scattering.- 7.4 Computational Solution of the Electron-Hydrogen-Like Ion-Collision Problem.- 7.4.1 The Inner Region.- 7.4.2 Outer Region Problem.- 7.5 Computer Program.- 7.5.1 Description of Input Data for the Program Package PACK1.- 7.5.2 Description of Input Data for PACK2.- 7.5.3 Sample Input and Output.- 7.5.4 Notes on Running the Codes.- 7.6 Summary.- 7.7 Suggested Problems.- Acknowledgments.- References.- 8. Momentum-Space Convergent-Close-Coupling Method for a Model e-H Scattering Problem.- Abstract.- 8.1 Introduction.- 8.2 Theory.- 8.2.1 Close-Coupling Equations.- 8.2.2 Target-State Manifold.- 8.2.3 Ensuring the Uniqueness of Solution.- 8.2.4 Momentum-Space Convergent-Close-Coupling.- 8.2.5 Cross Sections.- 8.3 Numerical Solution.- 8.3.1 Diagonalizing the Target Hamiltonian.- 8.3.2 Calculating V Matrix Elements.- 8.3.3 Solution of the Coupled Equations.- 8.4 Computer Program.- 8.4.1 Input.- 8.4.2 Output.- 8.4.3 Typical Usage.- 8.5 Summary.- 8.6 Suggested Problems.- References.- 9. The Calculation of Spherical Bessel and Coulomb Functions.- Abstract.- 9.1 Introduction.- 9.2 Spherical Bessel Functions.- 9.3 Recurrence Relations for Spherical Bessel Functions.- 9.4 Evaluation of the Continued Fraction.- 9.5 The Programs SBESJY and RICBES.- 9.6 Recurrence Relations for Coulomb Functions.- 9.7 The Program C0UL90.- 9.8 Test Data.- 9.8.1 Sample Input Data.- 9.8.2 Sample Output Data.- 9.9 Summary.- 9.10 Suggested Problems.- Acknowledgments.- References.- 10. Scattering Amplitudes for Electron-Atom Scattering.- Abstract.- 10.1 Introduction.- 10.2 Definition of the Scattering Amplitudes.- 10.3 Convergence of Partial Wave Expansions.- 10.3.1 Effective Range Theory for Elastic Scattering.- 10.3.2 Unitarized Born Approximation for Excitation.- 10.3.3 Exponential Fitting.- 10.4 Symmetry Properties of Scattering Amplitudes.- 10.5 Computer Program.- 10.5.1 Description of the Input Data.- 10.5.2 Test Runs.- 10.6 Summary.- 10.7 Suggested Problems.- Acknowledgments.- References.- 11. Density Matrices: Connection Between Theory and Experiment.- Abstract.- 11.1 Introduction.- 11.2 Scattering Amplitudes.- 11.3 Density Matrices.- 11.4 Irreducible Tensor Operators and State Multipoles.- 11.4.1 Basic Definitions.- 11.4.2 Coupled Systems.- 11.4.3 Time Evolution of State Multipoles: Quantum Beats.- 11.4.4 Time Integration over Quantum Beats.- 11.5 Observables.- 11.5.1 Generalized ST U Parameters.- 11.5.2 Generalized Stokes Parameters.- 11.6 2S ? 2P° Transitions.- 11.6.1 General Description of an Excited 2P° State.- 11.6.2 Relationship to Experimental Observables.- 11.7 Computer Program.- 11.7.1 Description of the Input Data.- 11.7.2 Test Run.- 11.8 Summary.- 11.9 Suggested Problems.- Acknowledgments.- References.

Blurb

"Computational Atomic Physics" deals with computational methods for calculating electron (and positron) scattering from atoms and ions, including elastic scattering, excitation, and ionization processes. After an introductory chapter on atomic collision theory, two chapters are devoted to the bound-state wavefunctions. A description of perturbative methods is followed by discussions of the standard non-perturbative close-coupling theory, the R-matrix method, and the recently developed "convergent-close-coupling" approach. The details of calculating accurate Coulomb and Bessel functions are treated as well. Finally, the calculation of scattering amplitudes is discussed and an introduction to the density-matrix theory is given. The book provides a practical application of advanced quantum mechanics. The abstract equations of general scattering theory are reduced to numerically solvable differential and integral equations, and computer codes for the solution are provided. Numerous suggested problems in the text and ten programs on a diskette contribute to a deeper understanding of the field. The diskette The 10 program packages included on a 3 1/2" MS-DOS diskette are written in standard FORTRAN 77 and run on any computer that fulfills the following system requirements: 16MB RAM, MS-DOS 3.30 or higher; 486 DX processor with numerical coprocessor. The FORTRAN 77 source files allow for modification of the programs; therefore a FORTRAN 77 compiler is also needed. Example input and output files are provided for the text cases. * COREPOT core potentials * CIV3 atomic structure * DWBA first order distorted wave program for excitation * DWBIA first order distorted wave program for ionization * CCPA close-coupling for positron-atom scattering * RMATREX R-matrix program for electron-atom scattering * CCC convergent close-coupling * COUL90 Coulomb and Bessel functions