Research in Atomic Structure

ISBN-13: 9783540562375 / Angielski / Miękka / 1993 / 143 str.

S. Fraga; M. Klobukowski; J. Muszynska

Opis

This work offers a formulation for the prediction of the energy levels of many-electron atomic systems within the framework of a configuration interaction treatment, with consideration of the most important relativistic corrections as well as the interaction with magnetic fields.

Spis treści

Theoretical Foundation.- 1 Hamiltonian Operator and Eigenvalue Equations.- 1.1 Hamiltonian operator.- 1.1.1 Extended Breit Hamiltonian operator.- 1.1.2 Generalized Hamiltonian operator.- 1.2 Eigenvalue equations.- Basic Theoretical Formulation.- 2 Angular Functions: Coupling of Angular Momenta.- 2.1 One-electron functions.- 2.2 SL-functions.- 2.3 JMJ- and FMF-functions.- 2.4 Selection of functions.- 3 Tensor-Operator Formulation.- 3.1 Tensor operators.- 3.2 Wigner-Eckart theorem.- 3.3 Reduced matrix elements.- 3.4 Matrix elements.- Application of the Basic Formulation.- 4 Transformation of Operators to Tensor Form.- 4.1 Basic operators.- 4.1.1 Operators s(1), ?(1) and C(k).- 4.1.2 Other common operators.- 4.2 Transformation rules.- 4.3 Application.- 4.4 Summary.- 5 Matrix Elements.- 5.1 General formulation.- 5.2 General expressions.- 5.2.1. SMSLML-coupling.- 5.2.2. JMJ-coupling.- 5.2.3. FMF-coupling.- 5.3 Examples for specific interactions.- 6 Summary of Theoretical Results.- 6.1 Electronic energy.- 6.2 Mass variation.- 6.3 Specific mass effect.- 6.4 One-electron Darwin correction.- 6.5 Two-electron Darwin correction.- 6.6 Electron spin-spin contact interaction.- 6.7 Orbit-orbit interaction.- 6.8 Spin-orbit coupling.- 6.9 Spin-spin dipole interaction.- 6.10 Magnetic dipole and Fermi contact interactions.- 6.11 Electric quadrupole coupling.- 6.12 Magnetic octupole coupling.- 6.13 Zeeman effect (low field).- 6.14 Zeeman effect (high field).- 6.15 Zeeman effect (very high field).- 6.16 Stark effect.- 6.17 Nuclear-mass dependent orbit-orbit interaction.- 6.18 Nuclear-mass dependent spin-orbit coupling (electron spin).- 6.19 Nuclear-mass dependent spin-orbit coupling (nuclear spin).- Implementation.- 7 Practical Details.- 7.1 Selection of configurations.- 7.2 Determination of radial functions.- 7.3 Selection rules.- 7.4 Mass corrections.- 8 Numerical Examples.- 8.1 Accurate energies.- 8.2 SLJ energy levels.- 8.3 Hyperfine-structure splittings.- 8.4 Nuclear-mass dependent corrections.- References.- Reference texts.- Data sources.- Units and Constants.- Constants.- Units.- Notation and Symbols.