Calculation of Stark effect energy shifts by Pade approximants of Rayleigh Schrodinger perturbation theory

Abstract

Pade approximants give Stark effect energies for excited states of hydrogen that are considerably more accurate than simple perturbation theory. In one example, Pade approximants for an n=25 state lie within the experimental uncertainty, while simple perturbation theory lies outside. In a second example, Pade approximants for an n=30 state fall inside the theoretical ionisation width, while simple perturbation theory falls outside. This behaviour appears to be general.