The central-field configurational model

Abstract

In the central-field configurational model, the basis functions of the atomic states are products of a radial part, an angular part, and a spin part. They must obey the antisymmetry principle. They can be gathered into electronic configurations. The atomic states (wavefunctions) are the eigenvectors of the H Hamiltonian, which is essentially the sum of the electronic kinetic energies, of the electrostatic interactions between the nucleus and the electrons, and of those between the electrons, plus the magnetic interactions between the orbital and spin magnetic moments of the electrons. They are obtained by diagonalizing H over the basis functions of a single configuration (in intermediate coupling), or of several configurations (in configuration interaction). The (3p ² + 3d ²) mixing is taken as an example.

For the matrix elements of H, the radial integrals are computed with the central-field radial functions. The angular coefficients are computed by means of Racah’s tensor-operator formalism, recalled in App. A. The relativistic approach is reviewed. As a very large number of levels ought to be taken into account statistical methods are attractive. Their use is discussed.