An atomic program for energy levels of equivalent electrons: lanthanides and actinides

Abstract

A program written in C is presented to carry out brute force calculations in order to derive energy levels for an equivalent electronic configuration. Relativistic effects are partly neglected except for the spin-orbit interaction. Since the main relativistic effects are indirect, i.e. causing a contraction of the core which in turn causes the outer shells to expand, they are included to a high degree through the use of appropriate Slater integrals. The program is especially useful for primarily unfilled f-shells of the rare-earth or actinide ions. Modifications of the program to include spin −spin, spin −other orbit, Breit interaction etc. is straight forward. The program is also general in the sense that there is no need to find out or generate any Racah coefficients of fractional parentage. The complete energy matrix is diagonalized with all operators interacting simultaneously thus allowing mixing of all quantum numbers. This result in all energy eigenvalues and eigenvectors that in turn for example are partly responsible for the polarized dipole, quadrupole, … transitions within the unfilled shell. Free ion configuration interaction is accounted for through the use of standard CI operators. The Stark splitting can be studied via the standard crystal field Hamiltonian. Magnetic field influence on the energy levels may also be studied.