A new analytical solving for electric polarizabilities of hydrogen-like atoms

TL;DR

This paper introduces an analytical method based on the transition-matrix approach to precisely calculate electric multipole polarizabilities of hydrogen-like atoms, including excited states, by solving an integral equation exactly.

Contribution

It presents an exact analytical solution for electric multipole polarizabilities of hydrogen-like atoms using the transition-matrix approach, extending previous formulas to excited states.

Findings

Exact analytical solutions for all electric multipole polarizabilities.

Reproduction of the Dalgarno-Lewis formula for ground state.

Method applicable to excited bound states.

Abstract

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno-Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states.