Electron Correlation Dynamics in Atomic Collisions

Online revised edition

This online version contains some corrections and updates from the original version of "Electron Correlation Dynamics in Atomic Collisions" available from Cambridge University Press (England) or (New York) at a cost of about $80.

ISBN 0 521 48020 5

Title page

Preface

Chapter 1: Introduction

  1.1 Probability of a transition

     1 Single particle probability

     2 Two particle probability

     3 N particle binomial probability

     4 Multinomial probabilities

  1.2 Cross sections and reaction rates

     1 Differential cross sections and transition probabilities

     2 Total cross section

  1.3 Quantum features

     1 The Hamiltonian

     2 The electronic wave amplitude

     3 The transition probability

  1.4 Correlation

     1 Definition of correlation

     2 Correlated probabilities

     3 Other applications

Chapter 2: Single Electron Transition Probabilities

  2.1 Formulation

     1 Complete atomic system

     2 Atomic electrons

     3 Evolution of an electron

     4 Partial wave expansion

  2.2 Excitation probabilities

     1 1s - 2s,2p transitions

     2 n,l,m -> n,l',m' transitions

  2.3 Mass transfer probabilities

     1 n,l,m -> n',l ',m' transitions

     2 1s - 1s transitions

     3 Special features of electron capture

  2.4 Ionization probabilities

     1 Continuum of the target

     2 Continuum of the projectile

  2.5 Long range Coulomb effects

     1 Continuum of target and projectile

  2.6 Other methods

     1 Strong electric fields

     2 Strong projectile fields

     3 Over the barrier model

  2.7 Observations

  2.8 Appendix

     1 Classical cross sections

     2 Tables of ionization cross sections and probabilities

Chapter 3: Formulation of multi-electron transition probabilities

  3.1 Terms in the Hamiltonian

  3.2 The many electron wavefunction

     1 Separation of the electronic from the nuclear wavefunction

     2 Interaction representation

     3 The evolution operator

  3.3 Transition probability and cross section

     1 Multi-electron effects and electron correlation

     2 Scattering, relaxation and asymptotic regions

     3 Waves and particles

     4 Long range Coulomb terms

     5 Exclusive and inclusive cross sections

     6 The active electron approximation

     7 Electron exchange

  3.4 Methods of computation

  3.5 Classification of multiple electron transitions

  3.6 Appendix

     1 Separation of electronic terms

Chapter 4: Independent electron approximation

   4.1 Single atoms

     1 Full atomic Hamiltonian

     2 Uncorrelated Hamiltonian

     3 Binomial distributions

     4 Comparison to experiment

  4.2 Systems of atoms

     1 Full Hamiltonian for systems of atoms

     2 Independent subsystems

  4.3 Time dependent Dirac Fock

Chapter 5: Statistical methods

  5.1 Statistical energy deposition model

  5.2 Fokker Planck method

     1 Fokker Planck equation

     2 Application to atomic collisions

     3 Simple model

  5.3 Maximum entropy method

  5.4 Intermediate systems

Chapter 6: Correlated multi-electron transition probabilities

  6.1 Correlation

     1 Asymptotic states

     2 Scattering operator

     3 Analytic expressions

     4 Multi-center correlation

     5 Dielectronic processes

  6.3 Shake probabilities

     1 Simple shake factors

     2 Generalized shake factor

     3 High energy ratios in helium

  6.4 The Liouvillian

     1 The Hamiltonian as a generator of dynamics for little systems

     2 The Liouvillian as a generator of dynamics for big systems

Chapter 7: Perturbation expansions

  7.1 Formulation

     1 Binomial distributions with shake

     2 Time ordering

     3 Spatial correlation

  7.2 Method of expansion in the scattering potential V

     1 Scattering amplitude

     2 Pseudostates

     3 One electron amplitudes in pseudostates

  7.3 Many body perturbation theory

     1 Diagrams and matrix elements

  7.4 Observations

     1 Z^3 terms

     2 Cross sections and ratios

Chapter 8: Projectiles carrying electrons

  8.1 Formulation

     1 Basic ideas

  8.2 The first Born approximation

     1 The effective projectile charge

     2 Virtual impact parameter method

     3 Application to the independent electron approximation

  8.3 Examples

     1 Screening terms

     2 Antiscreening terms

  8.4 Impulse approximation

  8.5 Observed results

Chapter 9: Reactions with photons

  9.1 Introduction

  9.2 The Hamiltonian

     1 Dipole approximation

     2 L,V and A forms of the dipole operator

  9.3 Photoionization (Photo effect)

     1 Gauge dependence

9.4 Compton and Raman scattering

     1 Compton scattering

     2 Compton scattering and photoionization

     3 Raman scattering

  9.5 Observations

  9.6 Appendix

     1 Gauge transformations

     2 Two electrons in a magnetic field

     3 Two electrons in an electromagnetic field

     4 Mathematical scattering factors

     5 Expansion parameters

     6 Names of processes

Chapter 10: Relations between charged particle and photon reactions

  10.1 Multipoles

     1 Ratios of cross sections

     2 Compton and charged particle scattering

  10.2 Dipole terms

  10.3 Dipole and non-dipole terms

     1 Ratios of cross sections differential in energy transfer

     2 Ratios of total cross sections

  10.4 Observations

Appendices

  A.1 Hydrogenic wavefunctions

     1 Spherical harmonics

     2 Coordinate space

     3 Momentum space

  A.2 A special integral

  A.3 The Green function

  A.4 Equivalence of observables in the particle and wave pictures

  A.5 Binomial and multinomial moments

  A.6 N body systems

References