Zero-Range Potentials and Their Applications in Atomic Physics

Inhaltsverzeichnis

• 1 Basic Principles of the Zero-Range Potential Method.
• 1.1 Introduction.
• 1.2 Formulation of the Method.
• 1.3 The One-Center Problem and Its Simple Applications.
• 1.4 Separable Potentials and Scattering of Slow Electrons by Atoms.
• 2 Trajectories of the Poles of the S-Matrix and Resonance Scattering.
• 2.1 Preliminary Remarks.
• 2.2 Trajectories of the Zeros of the Jost Function for ? = 0.
• 2.3 The S-Matrix in a Two-Pole Approximation.
• 2.4 The Case of ? ? 0 and Perturbation Theory for a Bound State Close to the Continuum.
• 2.5 Trajectories of the Poles of the S-Matrix in the Case of ZRP and Separable Potentials.
• 3 Zero-Range Potentials for Molecular Systems. Bound States.
• 3.1 Many-Center Problems without External Fields.
• 3.2 Potential Curves for a Two-Center System and Some Applications.
• 3.3 Analytic Properties of the Potential Curves and Trajectories of the Poles of the S-Matrix.
• 3.4 Perturbation Theory in the Presence of an External Electric Field.
• 3.5 Perturbation Theory in the Presence of an External Magnetic Field.
• 3.6 Solution of the Schrödinger Equation with the Help of ZRPs.
• 4 Scattering by a System of Zero-Range Potentials and the Partial Wave Method for a Nonspherical Scatterer.
• 4.1 The Partial Wave Method.
• 4.2 Behavior of the Phases at Low Energy.
• 4.3 The Variational Principle.
• 4.4 Scattering by a System of ZRPs.
• 4.5 ZRPs in the Theory of Multiple Scattering.
• 5 Zero-Range Potentials in Multi-Channel Problems.
• 5.1 Zero-Range Potentials for a Many-Component Wavefunction.
• 5.2 Singlet-Triplet Splitting and Cross Sections for Elastic and Inelastic Scattering.
• 5.3 Energy Terms of the e + H2 System and Trajectories of the Poles of the S-Matrix for a Two-Channel Problem.
• 5.4 Electron Scattering by Molecules in the Separable PotentialApproximation.
• 6 Motion of a Particle in a Periodic Field of Zero-Range Potentials.
• 6.1 One-Dimensional Lattice in a Three-Dimensional Space. Bound States.
• 6.2 Electron Scattering by Long Linear Molecules.
• 6.3 Two-Dimensional Lattice in Three-Dimensional Space.
• 6.4 Three-Dimensional Lattice and the Method of Ewald.
• 7 Weakly Bound Systems in Electric and Magnetic Fields.
• 7.1 Weakly Bound Systems in a Homogeneous Electric Field.
• 7.2 Weakly Bound Systems in a Homogeneous Magnetic Field.
• 7.3 Weakly Bound Systems in Crossed Electric and Magnetic Fields.
• 7.4 A Combination of ZRPs and a Coulomb Field.
• 8 Electron Detachment in Slow Collisions Between a Negative Ion and an Atom.
• 8.1 ZRPs in Time-Dependent Quantum Mechanical Problems.
• 8.2 Linear Approximation in Detachment Theory.
• 8.3 Account of the Finite Size of the Colliding System.
• 8.4 Production of Negative Ions in Three-Body Collisions.
• 9 Time-Dependent Quantum Mechanical Problems Solvable by Contour Integration.
• 9.1 General Time-Dependent Problems Solvable by Contour Integration.
• 9.2 Adiabatic Approximation and Trajectories of the Poles of the S-Matrix.
• 9.3 Ionization in Slow Atomic Collisions.
• 10 Nonlinear Approximations in the Theory of Electron Detachment.
• 10.1 Nonlinear Problems Solvable by Contour Integration. Sudden Approximation.
• 10.2 Quadratic Approximation in the Theory of Electron Detachment.
• 10.3 Quadratic Approximation (General Case).
• 11 Time-Independent Quantum Mechanical Problems.
• 11.1 Account of the Quantal Motion of the Nuclei in Detachment Theory.
• 11.2 Time-Independent Quantum Mechanical Problems Solvable by Contour Integration.
• References.