Atomic Structure Theory: Lectures on Atomic Physics

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9783540680109: Atomic Structure Theory: Lectures on Atomic Physics

This book provides a hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrödinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements. The book also contains numerical methods for solving the Schrödinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations.

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From the Back Cover:

Atomic Structure Theory is a textbook for students with a background in quantum mechanics. The text is designed to give hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrödinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements. Numerical methods for solving the Schrödinger and Dirac eigenvalue problems and the (Dirac)-Hartree-Fock equations are given as well. B-spline basis sets are used to carry out sums arising in higher-order many-body calculations. Illustrative problems are provided, together with solutions. FORTRAN programs implementing the numerical methods in the text are included.

About the Author:

Frank M. Freimann Professor of Physics, University of Notre Dame, 1992-present

Professor of Physics, University of Notre Dame, 1958-present

Chairman: Department of Physics, University of Notre Dame, 1982-1985

Chairperson: Division of Atomic, Molecular, and Optical Physics, American Physical Society, 1988-1989.

Alexander von Humboldt Senior U.S. Scientist Award, University of Frankfurt, 1982-1983;

Technical University of Dresden1994; Technical University of Dresden 2001.

Gordon Godfrey Fellow, University of New South Wales, Sydney, 2000, 2005

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Johnson, Walter R.:
Verlag: Springer, Berlin (2007)
ISBN 10: 3540680101 ISBN 13: 9783540680109
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Buchbeschreibung Springer, Berlin, 2007. Gebundene Ausgabe. Buchzustand: Sehr gut. 312 Seiten; Buch ist in einwandfreiem Zustand ! Contents Angular Momentum 1 1.1 Orbital Angular Momentum - Spherical Harmonics 1 1.1.1 Quantum Mechanics of Angular Momentum 2 1.1.2 Spherical Coordinates - Spherical Harmonics 4 1.2 Spin Angular Momentum 8 1.2.1 Spin 1/2 and Spinors 8 1.2.2 Infinitesimal Rotations of Vector Fields 9 1.2.3 Spin 1 and Vectors 10 1.3 Clebsch-Gordan Coefficients 12 1.3.1 Wigner 3j Symbols 16 1.3.2 Irreducible Tensor Operators 17 1.4 Graphical Representation - Basic rules 19 1.5 Spinor and Vector Spherical Harmonics 22 1.5.1 Spherical Spinors 22 1.5.2 Vector Spherical Harmonics 24 Problems 26 Central-Field Schrodinger Equation 29 2.1 Radial Schrodinger Equation 29 2.2 Coulomb Wave Functions 31 2.3 Numerical Solution to the Radial Equation 35 2.3.1 Adams Method (ADAMS) 37 2.3.2 Starting the Outward Integration (OUTSCH) 40 2.3.3 Starting the Inward Integration (INSCH) 42 2.3.4 Eigenvalue Problem (MASTER) 43 2.4 Quadrature Rules (RINT) 46 2.5 Potential Models 48 2.5.1 Parametric Potentials 49 2.5.2 Thomas-Fermi Potential 51 2.6 Separation of Variables for Dirac Equation 55 2.7 Radial Dirac Equation for a Coulomb Field 56Contents 2.8 Numerical Solution to Dirac Equation 60 2.8.1 Outward and Inward Integrations (ADAMS, OUTDIR, INDIR) 61 2.8.2 Eigenvalue Problem for Dirac Equation (MASTER) 64 2.8.3 Examples using Parametric Potentials 65 Problems 66 Self-Consistent Fields 71 3.1 Two-Electron Systems 71 3.2 HF Equations for Closed-Shell Atoms 77 3.3 Numerical Solution to the HF Equations 88 3.3.1 Starting Approximation (HART) 88 3.3.2 Refining the Solution (NRHF) 90 3.4 Atoms with One Valence Electron 93 3.5 Dirac-Fock Equations 97 Problems 104 Atomic Multiplets 107 4.1 Second-Quantization 107 4.2 6-j Symbols Ill 4.3 Two-Electron Atoms 114 4.4 Atoms with One or Two Valence Electrons 118 4.5 Particle-Hole Excited States 123 4.6 9-j Symbols 126 4.7 Relativity and Fine Structure 128 4.7.1 He-like Ions 128 4.7.2 Atoms with Two Valence Electrons 132 4.7.3 Particle-Hole States 133 Problems 134 Hyperfine Interaction & Isotope Shift 137 5.1 Hyperfine Structure 137 5.2 Atoms with One Valence Electron 142 5.2.1 Pauli Approximation 144 5.3 Isotope Shift 146 5.3.1 Normal and Specific Mass Shifts 148 5.4 Calculations of the SMS 149 5.4.1 Angular Decomposition 149 5.4.2 Application to One-Electron Atoms 151 5.5 Field Shift 152 Problems 155Contents XI Radiative Transitions 157 6.1 Review of Classical Electromagnetism 157 6.1.1 Electromagnetic Potentials 157 6.1.2 Electromagnetic Plane Waves 159 6.2 Quantized Electromagnetic Field 160 6.2.1 Eigenstates of Mi 161 6.2.2 Interaction Hamiltonian 162 6.2.3 Time-Dependent Perturbation Theory 163 6.2.4 Transition Matrix Elements 164 6.2.5 Gauge Invariance 168 6.2.6 Electric-Dipole Transitions 169 6.2.7 Magnetic-Dipole and Electric-Quadrupole Transitions . . 175 6.2.8 Nonrelativistic Many-Body Amplitudes 182 6.3 Theory of Multipole Transitions 185 Problems 192 Introduction to MBPT 195 7.1 Closed-Shell Atoms 197 7.1.1 Angular Momentum Reduction 199 7.1.2 Example: Second-Order Energy in Helium 202 7.2 B-Spline Basis Sets 203 7.2.1 Hartree-Fock Equation and B-splines 206 7.2.2 B-spline Basis for the Dirac Equation 207 7.2.3 Application: Helium Correlation Energy 208 7.3 Atoms with One Valence Electron 209 7.3.1 Second-Order Energy 210 7.3.2 Angular Momentum Decomposition 211 7.3.3 Quasi-Particle Equation and Brueckner Orbitals 212 7.3.4 Monovalent Negative Ions 214 7.4 Relativistic Calculations 216 7.4.1 Breit Interaction 217 7.4.2 Angular Reduction of the Breit Interaction 218 7.4.3 Coulomb-Breit Many-Electron Hamiltonian 221 7.4.4 Closed-Shell Energies 221 7.4.5 One Valence Electron 223 7.5 CI Calculations 224 7.5.1 Relativistic CI Calculations, 226 7.6 MBPT for Divalent Atoms and Ions 227 7.6.1 Two-Particle Model Spaces 227 7.6.2 First-Order Perturbation Theory 230 7.7 Second-Order Perturbation Theory 231 7.7.1 Angular Momentum Reduction 233 Problems 234XII Contents 8 MBPT for Mat. Artikel-Nr. 248557

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