Case Studies in Atomic Physics 4

Chapter 1. Correspondence Identities and the Coulomb Potential

    1. Introduction

    2. The Historical Importance of the Correspondence Identities

         2.1. Consequences of the Rutherford scattering identity

         2.2. Consequences of the Bohr-Sommerfeld identity

    3. Present-Day Relevance in Classical Theories

         3.1. Reasons for using classical theories

         3.2. Classical binary encounter collisions

         3.3. Classical three-body calculations

    4. Explaining the Correspondence Identities

         4.1. Explaining correspondence identities

         4.2. Providing a complete correspondence identity for the bound states of the Coulomb potential

         4.3. Explaining the Fock and Bohr-Sommerfeld identities

         4.4. Providing a complete correspondence identity for the scattering states

         4.5. Explaining the Rutherford scattering identity

    5. Relevance in Semi-Classical Theories - Understanding Quantal Effects in Terms of Classical Paths

         5.1. Interference

         5.2. Discrete energy levels and quantization

         5.3. Barrier penetration and classically forbidden processes

         5.4. Spin

    6. Further Considerations and Correspondence Identities in General

        6.1. Why does a complete correspondence identity exist?

        6.2. The relevance of dynamical symmetry in the existence of complete correspondence identities

    7. Conclusions

    Acknowledgment

    References

Chapter 2. Recombination

    1. Introduction

    2. Ionic Recombination in a Gas

    3. Mutual Neutralization

    4. Radiative Recombination

    5. Collisional-Radiative Recombination

    6. Development of Theory of Ionic Recombination in a Gas

    7. Electronic Recombination in a Gas

    8. Recombination Electrical Network Theorem

    9. Dielectroniic Recombination

    10. Collisional-Dielectronic Recombination

    11. Dissociative Recombination

    12. Final Remarks

    Acknowledgments

    References

Chapter 3. Relativistic Self-Consistent-Field Calculations with Application to Atomic Hyperfine Interaction. Part I: Relativistic self-consistent fields. Part II: Relativistic theory of atomic hyperfine interaction

    I.1. Introduction

    I.2. Relativistic Hartree-Fock Equations

         I.2.1. Relativistic hamiltonian and zero-order wavefunctions

         I.2.2. One- and two-electron integrals

         I.2.3. Relativistic Hartree-Fock equation

         I.2.4. Numerical examples

    I.3. Average of Configuration

         I.3.1. One-electron energies

         I.3.2. Total energies

         I.3.3. Summary of angular factors for average of configuration

         I.3.4. Example: 1s2 2s2 2pN configuration

    I.4. Statistical Exchange Approximation

         I.4.1. Slater exchange

         I.4.2. Electron-gas model

         I.4.3. Thomas-Fermi model

         I.4.4. Kohn—Sham model

         I.4.5. Parametrized potentials

         I.4.6. Hartree-Slater model

    Appendix A. Hartree Atomic Units

    Appendix B. Hartree-Slater Approximation

    Appendix C. Some General Theorems Concerning Statistical Exchange Approximations

    References

    II.1. Introduction

    II.2. Multipole Expansion of the Static Electro-Magnetic Field from the Nucleus

         II.2.1. Equations for electro-magnetic potentials

         II.2.2. Electric interaction

         II.2.3. Magnetic interaction

    II.3. Hyperfine Hamiltonian

         II.3.1. Non-relativistic perturbation

         II.3.2. Relativistic perturbation

    II.4. Single-Electron Systems

         II.4.1. Non-relativistic matrix elements

         II.4.2. Relativistic matrix elements

    II.5. The Effective Relativistic Hyperfine Hamiltonian

         II.5.1. The theory of Sandars and Beck

         II.5.2. The relation between the relativistic and the non-relativistic hamiltonians

         II.5.3. Explicit expressions for the effective hyperfine hamiltonians of order k=1,2,3,4

    II.6. Hyperfine Interaction for Many-Electron Atoms

         II.6.1. Breakdown of LS coupling

         II.6.2. Explicit expressions for the hyperfine interaction constants in intermediate coupling

    Appendix A. Vector Spherical Harmonics

    Appendix B. Tensor-Operator Formulas

    Appendix C. Matrix Elements of Ck and some 9-/ Symboles

    References

Chapter 4. Relativistic Self-Consistent-Field Calculations with Application to Atomic Hyperfine Interaction. Part III: Comparison between theoretical and experimental hyperfine-structure results

    III.1. Review of Experimental Techniques

    III.2. The Traditional Hyperfine Hamiltonian

    III.3. Theoretical Hyperfine Parameters and Relativistic Correction Factors

    III.4. The Procedure for Determining Effective Radial Parameters from Experiments

    III.5. Hyperfine Structure of the Alkali Atoms

    III.6. Hyperfine Structure of Copper, Silver and Gold

    III.7. Hyperfine Structure of the npN Ground-Configuration Atoms

         III.7.1. General

         III.7.2. Magnetic dipole interaction

         III.7.3. Electric quadrupole interaction

         III.7.4. Magnetic octupole interaction

    III.8. Hyperfine Structure of the 3d-Shell Atoms

    III.9. Hyperfine Structure of the 4d- and 5d-Shell Atoms

    III.10. Hyperfine Structure of the Rare-Earth Atoms

    III.11. Hyperfine Structure of the Actinides

    III.12. Summary and Conclusion

    Appendix A. Computer Program for Hyperfine-Structure Analysis

    Appendix B. Conversion Factors Between Hyperfine Interaction Constants and Hyperfine Radial Integrals

    References

Chapter 5 . Pseudopotentials in Atomic and Molecular Physics

    1. Introduction

    2. Formal Development of Pseudopotentials

         2.1. Systems with one valence electron

         2.2. Generalized pseudopotential operators

         2.3. Systems with two valence electrons

         2.4. Localized molecular orbitals

         2.5. Optical potentials

    3. Empirical Pseudopotentials

         3.1. Formal considerations

    4. The Choice of Pseudopotential

         4.1. Truncated Coulomb potentials

         4.2. Exponential potentials

         4.3. Further empirical potentials

         4.4. Statistical pseudopotentials

         4.5. Further ab initio pseudopotentials

         4.6. Summary

    5. The Calculation of Atomic Properties

         5.1. Energy levels

         5.2. Photon absorption or emission

    6. The Calculation of Molecular Properties

         6.1. Alkali molecules

         6.2. The interaction between alkali and rare gas atoms

         6.3. Rydberg states in molecules

         6.4. Further studies of molecular bound states

         6.5. Photo ionization in molecules

    7. Electron Scattering by Atoms and Molecules

         7.1. Electron scattering by neutral alkali atoms

         7.2. Low energy scattering of electrons by rare gas atoms

         7.3. Correlation effects in e -H scattering

         7.4. Electron scattering by molecules

    8. Conclusions

    Appendix 1. Computations with Pseudopotentials

    Acknowledgments

    References

Chapter 6.  Analysis for Ion Drift Tube Experiments

    1. Introduction

    2. Drift Tubes

    3. Kinetic Theory

    4. Green’s Function Method

    5. One and Two Ion Solution

    6. Sources, Detectors and Drift Regions

    7. Spectrum Analysis (One Ion)

    8. Spectrum Analysis (Two Ions)

    9. Radial Boundary Effects

    10. End Plate Boundary Effects

    11. Fast Forward-Backward Reactions

    12. General Considerations

    13. Conclusions

    Acknowledgments

    Appendix

    References

Author Index

Subject Index