HYPERVIRIAL THEOREMS APPLIED TO THE PERTURBATION-THEORY FOR SCREENED COULOMB POTENTIALS

By applying the hypervirial relations with the Hellman-Feynman theorem to screened Coulomb potentials, the authors derive the energy levels of atoms correct to the sixth order of the perturbation parameter λ explicitly without any calculation of perturbed wave functions. The energies of atoms up to the twentieth order of λ are also calculated by computer. In the case of the Yukawa potential, the authors demonstrate by explicit calculation that the K-shell energy converges, at least for Z5, with the value of λ0=0.85, and that the L-shell energy converges, at least for Z24, with λ0=0.70. © 1979 The American Physical Society.