A semi-empirical model for computing radial matrix elements in one-electron atoms and ions

An easily tractable model is proposed to compute radial matrix elements between discrete states of one-electron atoms or ions. Assuming a closed-shell core, polarization effects are included in the model, and core penetration is accounted for empirically. The required inputs for this algorithm are the energies of the involved levels, and the core size and polarisabilities. Ignoring core polarization, the derived Coulomb matrix elements (possibly between levels with non-zero quantum defects) agree with those tabulated elsewhere in the literature. The method is then applied to dipolar and quadrupolar transitions in alkali atoms and singly-ionized alkaline-earth elements; it proves to be in fair agreement with available experimental data. An accuracy test of the method is proposed.