# Case Studies in Atomic Physics 4

## 1st Edition

**Editors:**E McDaniel

**eBook ISBN:**9780444601346

**Imprint:**North Holland

**Published Date:**1st January 1975

**Page Count:**465

## Description

Case Studies in Atomic Physics IV presents a collection of six case studies in atomic physics. The first study deals with the correspondence identities associated with the Coulomb potential: the Rutherford scattering identity, the Bohr-Sommerfeld identity, and the Fock identity. The second paper reviews advances in recombination. This is followed by a three-part study on relativistic self-consistent field (SCF) calculations. The first part considers relativistic SCF calculations in general, and in particular discusses different configurational averaging techniques and various statistical exchange approximations. The second part reviews the relativistic theory of hyperfine structure. The third part makes a number of comparisons between experimental results and values obtained in different SCF schemes, with exact as well as approximate exchange. The next case study on pseudopotentials compares the results of model potential and pseudopotential calculations. The final study reviews, on a kinetic basis, the behavior of low density ion swarms in a neutral gas.

## Table of Contents

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

## Details

- No. of pages:
- 465

- Language:
- English

- Copyright:
- © North Holland 1975

- Published:
- 1st January 1975

- Imprint:
- North Holland

- eBook ISBN:
- 9780444601346