Relativistic Heavy-Particle Collision Theory de Derrick S.F. Crothers

Relativistic Heavy-Particle Collision Theory

Derrick S.F. Crothers

If a heavy particle ion (atom, molecule, muon) collides with another in the gas phase at speeds approaching the speed of light, the time-dependent Dirac equation equation must be used for its description, including quantum electro-dynamic, special relativity and magnetic coupling effects.
In this book we study one electron in the variety of rearrangement collisions: radiative and non-radiative capture, ionization, capture by pair (one electron, one positron) production and antihydrogen production. Our relativistic continuum distorted-wave theory accounts extremely well for the simultaneous behaviour of the electron with respect to the nuclear charges of the projectile and the target.
This is the first book developed in this subject. Containing many diagrams and tables, and fully referenced, it goes beyond chapters in previous books. The relativistic continuum distorted-wave theory developed by the authors group, is shown to be fully Hermitean. Detailed mathematics are provided in nine appendices.

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Cuprins

1. Heavy-Particle Ion-Atom Collisions.- 1. Introduction to Non-Relativistic Collisions.- 2. Introduction to Relativistic Collisions.- 3. Lorentz Transformations.- 4. The Dirac Equation.- 5. Dirac Equation in a Central Field.- 2. Relativistic Electron Capture.- 1. Distorted Wave Theories of Nonradiative Capture.- 2. Relativistic OBK Theory.- 3. Relativistic Continuum Distorted Waves.- 4. The Relativistic Symmetric Eikonal Model.- 5. Asymmetric Theories.- 6. Results and Discussion.- 3. Second-Order Theories.- 1. Second-Order Theories of Relativistic Electron Capture.- 2. Relativistic OBK1 and Peaking Approximations.- 3. The Relativistic Bates Approximation.- 4. Relativistic OBK2.- 5. The Relativistic Impulse Approximation.- 6. Half-on-Shell OBK2.- 4. Radiative Electron Capture.- 1. Introduction to Radiative Electron Capture.- 2. Collision System.- 3. Distorted-Wave Method.- 4. 2s Bound-State Wavefunctions.- 5. Target Roothan-Hartree-Fock Bound States.- 6. Results and Discussion.- 5. Relativistic Ionization.- 1. Introduction to Relativistic First Born and Distorted-Wave Born Approximations.- 2. Implications of Assuming a Straight Line Trajectory.- 3. Spin Flip/Non-Hip Considerations.- 4. Derivation of the Cross-Section Formulae.- 5. Residual Interaction for RDWB (Prior) Approximation.- 6. Matrix Elements.- 7. Results and Conclusions.- 6. Relativistic Continuum Distorted Waves.- 1. Introduction to Relativistic Continuum Distorted Wave-Eikonal Initial State and (Post) Distorted Wave Born Approximations.- 2. RCDW Wavefunctions.- 3. Derivation of the Residual Interaction.- 4. Matrix Elements.- 5. Computational Details.- 6. Results and Conclusions.- 7. Processes Involving Pair Production.- 1. Introduction to Transitions Involving Electron-Positron Pair Production.- 2. CrossingSymmetries.- 3. Physics of Ionization and Pair Production Capture.- 4. Wavefunctions for Processes Involving Pair Production.- 5. Results and Conclusions.- 6. Antihydrogen Production.- Appendices.- A. Thomas Double Scattering.- B. RCDW Bethe-Integrals.- 1. Target Centred Integrals.- 2. Projectile Centred Integrals.- C. Eikonal Integrals.- 1. Target Centred Integrals.- 2. Projectile Centred Integrals.- D. The Relativistic Field-Free Propagator.- E. Asymptotic Formulae.- 1. Nonflip.- 2. Flip.- F. The Relativistic Impulse Approximation.- G. RDWB Matrix Elements.- H. Continuity Relation.- I. Matrix Element Checks.- References.