| Abstract: | We have calculated the energies of the (7s) and (8s) states of the valence electron in the K atom by making use of a pseudopotential based on recently obtained variational solutions of the Thomas–Fermi (TF) equation for neutral atoms, and positive ions. We have chosen trial wave functions, with appropriate parameters, for the valence electron and then minimized the energies of the respective states using the pseudoHamiltonian. The exchange interaction between the K+ core and the valence electron has also been considered as a perturbation. Comparison of the calculated (7s) and (8s) energies with the experimental values shows an agreement of about 6% for the former one and of about 5% for the latter one, respectively. With the exchange correction both of these discrepancies are reduced to less than 2%. We conclude that the procedure outlined here is a promising one in dealing with problems involving a highly excited electron outside of a closed-shell ion core, a system for which a more exact quantum-mechanical treatment would be much more difficult. |
