Case Studies in Atomic Physics

Contents

Chapter 1. Detailed Balancing in the Time-Dependent Impact Parameter Method


1. Introduction


2. Time-Reversal in the Impact Parameter Method


2.1. Time-Reversal with A Time-Independent Hamiltonian


2.2. Time-Reversal with Prescribed Relative Motion


2.3. Detailed Balance in the Impact Parameter Method


2.4. Symmetry Under Reflection


2.5. Moving Eigenfunctions


3. The Coupled State Approximation


3.1. Expansion in Time-Independent Functions


3.2. Microreversibility Relations Involving Identical Intervals


3.3. Microreversibility Proof For Moving Expansion Functions

Acknowledgment

References

Chapter 2. Mechanisms of Electron Production in Ion-Atom Collisions


1. Introduction


2. Measurement of Doubly Differential Cross Sections and Electron Spectra


3. Direct Coulomb Ionization


4. Autoionization and the Auger Effect


5. Electron Promotion


6. Charge Transfer to Continuum States

References

Chapter 3. The Production of Inner-Shell Vacancies in Heavy Ion-Atom Collisions


1. Introduction


2. The Molecular Orbital Model


2.1. The Born-Oppenheimer Approximation


2.2. Molecular Orbital Correlation Diagrams For Diabatic States


2.3. Excitation Mechanisms


3. An Evaluation of The Experiments and the Data


3.1. Differential Measurements of Single Atomic Collisions


3.2. Spectroscopic Measurements and Total Emission Cross Sections


3.3. The Relationship Between Total Cross Sections and Differential Measurements


4. Applications For Inner-Shell Excitations

Acknowledgments

References

Chapter 4. Hyperfine and Zeeman Studies of Metastable Atomic States by Atomic-Beam Magnetic-Resonance


1. Introduction


2. Experimental Considerations


2.1. General Principles


2.2. Apparatus


2.3. Experimental Procedure


3. Theoretical Considerations and Interpretation of Experimental Results


3.1. Choice of Calculational Basis ; Derivation of Eigenvectors


3.2. G Values For Atomic States


3.3. Hamiltonian For The Hyperfîne Interaction


3.4. Evaluation of Matrix Elements; Theoretical Expressions For Hyperfineinteraction Constants


3.5. Off-Diagonal Hyperfine Structure and the Zeeman Effect


3.6. Comparison of Theoretical and Experimental Hyperfine-Interaction Constants


4. Concluding Remarks


4.1. General Comments


4.2. Outlook For The Future

References

Chapter 5. Coupled Integral-Equation Approach to Nonrelativistic Three-Body Systems with Applications to Atomic Problems


1. Introduction


2. Kinematic Theory of Three-Body System


2.1. Coordinates and Momentum Variables


2.2. Three-Body Kinematic Description


2.3. Lippmann-Schwinger Equation


2.4. Description of Multichannel Collision


2.5. Problems with Multichannel Lippmann-Schwinger Equations


3. Coupled Integral-Equation Formulation


3.1. Green's-Function Approach


3.2. Faddeev Equations


3.3. Watson Equations


3.4. Lovelace Equations


3.5. Newton Equations


3.6. Iterated Equations


3.7. Further Variations On Coupled Equations


4. Reduction of The Coupled Equations


4.1. On-Shell Reduction


4.2. Partial Wave Decomposition


4.3. Eigenfunction Expansion


4.4. Multiple-Scattering Expansions


5. Three-Body Coulomb Systems


5.1. Long-Range Coulomb Interaction


5.2. Off-Shell Two-Body Coulomb Amplitude


5.3. Mixed-Mode Reduction


5.4. Screening Approximation


5.5. Final-Channel Interaction


6. Methods of Approximation


6.1. Matrix-Inversion Method


6.2. Fredholm Reduction Method


6.3. Double-Expansion Method


6.4. Eikonal Approximation


7. Application to Atomic Problems


7.1. Three-Body Bound States


7.2. Three-Body Resonances


7.3. Collision Amplitudes


7.4. Differential and Total Cross Sections

Acknowledgments

References

Author Index

Subject Index