1. Introduction. Atomic Processes in Astrophysics 2. Radiative Transitions in an Atomic Potential 3. Polarization of Atoms. Polarization Radiation and Light Scattering 4. Atom in a Static Electric Field 5. Atom in a Magnetic Field and Crossed F-B Fields 6. Atom in a Variable Electric Field 7. Atom under Influence of Stochastic Peturbations 8. Relaxation and Decay of Atomic States 9. Excited Hydrogen-Like Atom in Electric Fields of Charged Particles. Foundation of Classical and Quantum Spectral Line Broadening Theory 10. Quasiclassical Theory of Atom - Charge Particle Collisions 11. Collision of the Atom with Atomic Particles in External Fields 12. Atomic Kinetics References Index
Introduction. Atomic Processes in Astrophysics 2. Radiative Transitions in an Atomic Potential 3. Polarization of Atoms. Polarization Radiation and Light Scattering 4. Atom in a Static Electric Field 5. Atom in a Magnetic Field and Crossed F-B Fields 6. Atom in a Variable Electric Field 7. Atom under Influence of Stochastic Peturbations 8. Relaxation and Decay of Atomic States 9. Excited Hydrogen-Like Atom in Electric Fields of Charged Particles. Foundation of Classical and Quantum Spectral Line Broadening Theory 10. Quasiclassical Theory of Atom - Charge Particle Collisions 11. Collision of the Atom with Atomic Particles in External Fields 12. Atomic Kinetics References Index
List of contributors Preface 1. Rydberg atoms in astrophysics A. Dalgarno 2. Theoretical studies of hydrogen Rydberg atoms in electric fields R. J. Damburg and V. V. Kolosov 3. Rydberg atoms in strong fields D. Kleppner, Michael G. Littman and Myron L. Zimmerman 4. Spectroscopy of one- and two-electron Rydberg atoms C. Fabre and S. Haroche 5. Interaction of Rydberg atoms with blackbody radiation T. F. Gallagher 6. Theoretical approaches to low-energy collisions of Rydberg atoms with atoms and ions A. P. Hickman, R. E. Olson and J. Pascale 7. Experimental studies of the interaction of Rydberg atoms with atomic species at thermal energies F. Gounand and J. Berlande 8. Theoretical studies of collisions of Rydberg atoms with molecules Michio Matsuzawa 9. Experimental studies of thermal-energy collisions of Rydberg atoms with molecules F. B. Dunning and R. F. Stebbings 10. High-Rydberg molecules Robert S. Freund 11. Theory of Rydberg collisions with electrons, ions and neutrals M. R. Flannery 12. Experimental studies of the interactions of Rydberg atoms with charged particles J. -F. Delpech 13. Rydberg studies using fast beams Peter M. Koch Index.
Equivalent derivations of time-dependent pertubation theory; Fermi golden rule; the Born approximation for scattering from Fermi golden rule; survival probability of a state in a time-independent perturbation; positronium in static and oscillating magnetic fields; hydrogen atom in a time-dependent electric field; a model for inelastic scattering of a projectile with a target; semiclassical treatment of the electromagnetic field; ionization of the hydrogen atom by an electromagnetic wave; cross sections for stimulated absorption and emission in hydrogen; spontaneous emission and selection rules with an application to the 2p to 1s transition in hydrogen; theory of the line width; formal scattering theory; S- and T-operators.
1. The origin of the quantum theory Planck's radiation formula 2. The nuclear theory of the atom Bohr's theory of the hydrogen spectrum 3. The correspondence principle the photo-electric effect Einstein's deduction of Planck's formula 4. The adiabatic principle of Ehrenfest the stationary states of a periodic system 5. General dynamical theory 6. Contact transformations the Hamilton-Jacobi differential equation 7. The use of angle variables multiply periodic systems 8. The relativity theory of the fine structure of the hydrogen lines electron in a central field 9. The Stark effect 10. The Zeeman effect 11. The series spectra of the elements 12. The multiple structure of series lines theory of the Ritz formula 13. Arc and spark spectra excitation of lines by electrons or radiation 14. X-ray spectra 15. Absorption spectra and absorption edges Bohr's table of the atomic structures of the elements 17. Band spectra in the infra-red 18. Band spectra in the optical region molecular rotation and specific heat 19. The Keplerian orbit the Delaunay elements 20. The astronomical theory of perturbations and atom mechanics 21. General perturbation theory 22. The effect of electric and magnetic fields on the spectra of elements of higher atomic number. Recent developments of the quantum theory: the doublet theories of Sommerfield and Lande the dispersion theory of Kramers the quantum-kinematics of Heisenberg Index of authors.
This volume offers a timely look at Rydberg states of atoms in external fields and dielectronic recombination. Each topic provides authoritative coverage, presents a fresh account of a flourishing field of current atomic physics and introduces new opportunities for discovery and development. Topics considered include electron-atom scattering in external fields; observations of regular and irregular motion as exemplified by the quadratic zeeman effect and other systems; Rydberg atoms in external fields and the Coulomb geometry; crossed-field effects in the absorption spectrum of lithium in a magnetic field; precise studies of static electric field ionization; widths and shapes of stark resonances in sodium above the saddle point; studies of electric field effects and barium autoionizing resonances; autoionization and dielectronic recombination in plasma electric microfields; dielectronic recombination measurements on multicharged ions; merged beam studies of dielectronic recombination; Rydberg atoms and dielectronic recombination in astrophysics; and observations on dielectronic recombination.
Table of Contents 1. The Origins of Quantum Mechanics 1.1 Introduction 1.2 Blackbody Radiation The Problem with Blackbody Radiation 1.3 The Nature of Light The Photoelectric Effect The Compton Effect Is it a Particle or a Wave? 1.4 TheWave Nature of Matter 1.5 The Bohr Atom 1.6 Where do we Stand? 2. Math Interlude A: Complex Numbers and Linear Operators 2.1 Complex Numbers 2.2 Operators Definition of an Operator Eigenfunctions and Eigenvalues 3. The Schrodinger Equation 3.1 Derivation of the Schrodinger Equation 3.2 The Meaning of theWave Function 3.3 The Time-Independent Schrodinger Equation Derivation of the Time-Independent Schrodinger Equation Qualitative Solutions and the Origin of Quantization 4. One-Dimensional Time-Independent Schrodinger Equation 4.1 Unbound States: Scattering and Tunneling Scattering From Step-Function Potentials 4.2 Bound Systems The Infinite SquareWell The Harmonic Oscillator Potential 5. Math Interlude B: Linear Algebra 5.1 Properties of Linear Operators 5.2 Vector Spaces Inner Products Adjoint and Hermitian Operators Basis Sets 6. The Three-Dimensional Time-Independent Schrodinger Equation 6.1 Solution in Rectangular Coordinates 6.2 Angular Momentum 6.3 The Schrodinger Equation in Spherical Coordinates 6.4 The Hydrogen Atom 7. Math Interlude C: Matrices, Dirac Notation, and the Dirac Delta Function 7.1 The Matrix Formulation of Linear Operators 7.2 Dirac Notation 7.3 The Dirac Delta Function 8. Spin Angular Momentum 8.1 Spin Operators 8.2 Evidence for Spin 8.3 Adding Angular Momentum 8.4 The Matrix Representation of Spin 8.5 The Stern-Gerlach Experiment 8.6 Spin Precession 8.7 Spin Systems with Two Particles Noninteracting Spins Interacting Spins 8.8 Measurement Theory Hidden Variables The ManyWorlds Interpretation of Quantum Mechanics 9. Time-Independent Perturbation Theory 9.1 Derivation of Time-Independent Perturbation Theory 9.2 Perturbations to the Atomic Energy Levels Fine Structure The Lamb Shift 9.3 The Atom in External Electric or Magnetic Fields The Atom in an Electric Field: The Stark Effect The Atom in a Magnetic Field: The Zeeman Effect 10. The Variational Principle 10.1 Variational Principle: Theory 10.2 Variational Principle: Application to the Helium Atom 11. Time-Dependent Perturbation Theory 11.1 Derivation of Time-Dependent Perturbation Theory 11.2 Application: Selection Rules for Electromagnetic Radiation 12. Scattering Theory 12.1 Definition of the Cross Section 12.2 The Born Approximation 12.3 PartialWaves 13. The Multiparticle Schrodinger Equation 13.1 Wave Function for Identical Particles 13.2 Multielectron Atoms 14. Some Modern Applications of Quantum Mechanics 14.1 Magnetic Resonance Imaging 14.2 Quantum Computing 15. What Comes Next? Relativistic Quantum Mechanics 15.1 The Klein-Gordon Equation Derivation of the Klein-Gordon Equation Probability Densities and Currents 15.2 The Dirac Equation Answers and Hints for Selected End-of-Chapter Exercises Index
As light passes an atom, it exerts forces on the charges, electrons, and nuclei that alter the atomic structure. These may be slight distortions (perturbations) of the electron cloud or they may be more severe, as described in subsequent sections of this monograph. We wish to determine those changes, given the radiation field, or to devise a radiation field that will produce specified changes. The changes to the atomic structure also affect the radiation that subsequently passes the atom. To describe those effects we must consider wave equations for radiation in the presence of altered atomic structure. More generally we must find self-consistent equations for the atoms and the field together, as discussed in Chaps. 21 and 22. Here we consider mathematical descriptions of the influence of coherent radiation on individual atoms, molecules, or other single quantum systems. Individual atoms Traditional sources of emission and absorption spectra, though revealing energy states of the constituent atoms and molecules, are macroscopic samples. One observes averaged characteristics of many individual particles, see Chap. 16. Quantum theory offers the basic formalism for dealing with individual atoms exposed to controlled radiation fields. Several experimental techniques provide acceptable approximations to this ideal. The following paragraphs note some of these examples. Vapors Neutral atoms or molecules in a vapor move freely along straight-line paths, interrupted by brief collisions that redirect the two collision partners. When the kinetic energies of the two partners are small, there can be no transfer of kinetic energy into internal energy of either particle – the collision is elastic .