J. A. Sordo

Research in atomic structure

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.

Research in atomic structure: A configuration interaction program with relativistic corrections

Abstract The RIAS computer program implements the recent formulation for the evaluation of the matrix elements of the complete atomic Hamiltonian operator (S. Fraga et al., Phys. Rev. A 34 (1986) 23). The SL, J or F levels may be obtained by diagonalization of the interaction energy matrix constructed from appropriate SMSLML functions. The program allows for accurate determination of the energy levels of any neutral or ionized atomic system.

Transformation of Operators to Tensor Form

The evaluation of the matrix elements of the Hamiltonian operator through the use of the reduced matrix elements formulation presented in the preceding Chapter requires that its terms be transformed into tensor form (see Section 4.2).

Summary of Theoretical Results

The complete formulas for the matrix elements of all the terms of the Hamiltonian operator are presented below.

Angular Functions: Coupling of Angular Momenta

The HF functions are constructed as combinations of Slater determinants built from spin-orbitals defined by

Tensor-Operator Formulation

psi n\ell m\ell ms = \phi n\ell m\ell \eta ms

Matrix elements of the Breit Hamiltonian

(1) where \({\eta _{{m_s}}}\) is the spin function (either α or β) and the HF orbital \({\phi _{n\ell }}_{{m_\ell }}\) may be expressed as