Discrete contributions to static dipole polarizabilities of excited bound states of non-relativistic hydrogen-like atoms

Abstract

The static dipole polarizability α _{d, i} for an arbitrary bound state i of the non-relativistic hydrogen-like atom has been known for a long time from, e.g; the second-order perturbation theory treatment of the Stark effect. A reliable result for the ground state requires both summation over the discrete spectrum and inclusion of the continuum contribution. This continuum contribution is known to decrease for excited states, but a systematic study of this decrease has not been available so far. We present here representative results from a systematic study of α _{d, i} , which was performed as a first test of a new algorithm for the radial integrals involved. Partial sum approximations of the discrete contribution yield the total α _{d, i} with a relative error of less than 1% for all states i with principal quantum number n≥5. Corresponding results for the relativistic case, for which the radial integral algorithm was developed, will be presented elsewhere.