A simple model potential description of the alkaline earth isoelectronic sequences

We have developed a simple model potential with a hard core and the correct larger-tau Coulombic behaviour, to describe the interaction of an electron with a closed shell. One has an exact, analytic ground state wave function for this potential. This potential is used to develop two-electron perturb ed and unperturbed wave functions, with the correct asymptotic behaviour an d cusp conditions. These wave functions allow us to obtain accurate values for the two-electron energies, polarisabilities, hyperpolarisabilities, and dispersion coefficients of alkaline earth sequences. Many of these results are the only ones available in the literature.