Quantum defects and the 1/ndependence of Rydberg energies: Second-order polarization effects

The principal result of this paper is a general expression for the second-order dipole polarization energy of a Rydberg electron resulting from the term -${\mathrm{\alpha }}_1$/${\mathit{r}}^4$ in the asymptotic potential, where ${\mathrm{\alpha }}_1$ is the core polarizability. It is shown that the second-order term contributes even as well as odd powers of 1/n in a 1/n expansion of the energies for Rydberg states. The results are used to extend the interpretation of the terms in a quantum-defect expansion. It is shown that the Ritz expansion for the quantum defect, which contains only even inverse powers of the effective quantum number ${\mathit{n}}^{\mathrm{*}}$, provides a powerful method for deducing the even-order terms in the second-order energy. Least-squares fits to high-precision variational calculations for the Rydberg states of helium, using 1/n and quantum-defect expansions, are presented. The results reveal well-defined ‘‘Ritz defects,’’ which represent the degree to which the data cannot be represented by a Ritz expansion for the quantum defect. The implications for extrapolations of quantum defects are discussed. Finally, it is shown that the second-order polarization energy plays a significant role in understanding the quantum defects for the alkali metals.