Coulomb approximation for multipole polarizabilities and dispersion forces: Analytic static polarizabilities of ground and excited state atoms

Abstract

An analytic expression for the 2^j‐pole static electric polarizability of an atom is obtained in a Coulomb‐like approximation. Core effects are neglected and following Bates' and Damgaard's method for oscillator strengths, the valence orbital is approximated by the asymptotically valid Whittaker function with hydrogenic normalization. Information about the symmetry allowed excited states is introduced via an r⁻²‐type pseudopotential. This simple choice leads to an analytically tractable perturbation equation which is solved by an adaptation of the technique of Schwartz and Tiemann. The effective nonintegral quantum numbers which enter our expression for the polarizability are obtainable from spectroscopic data. Our expression yields very accurate dipole and quadrupole polarizabilities for monovalent ground and excited s‐state atoms. Reasonable though somewhat less accurate results are obtained for divalent species and monovalent p‐state systems. The method is generalizable to frequency‐dependent perturbations.