Rydberg states of helium: Relativistic and second-order corrections

In this paper the corrections of relative order (Zα${)}^2$ to all multipole polarizabilities of a hydrogenic ion of nuclear charge Z are computed, with use of third-order perturbation theory with nonrelativistic wave functions. To accomplish this, the spin-independent part of the Pauli Hamiltonian of order ${\alpha }^2$ is treated as a perturbation along with the usual Coulomb interaction expanded in a multipole series. The leading (dipole) correction is in agreement with the previous results of Zon et al. In addition, the previously discussed second-order energy shift has now been calculated analytically. Both of these corrections are applied to the high-lying Rydberg states of helium, yielding small but important corrections to the fine-structure splittings.