Use of dimension-dependent potentials for quasibound states

Abstract

Dimensional perturbation theory is applied to the calculation of complex energies for quasibound (resonance) eigenstates, using a modified dimension-dependent potential so that the infinite-dimensional limit better reflects the physical (three-dimensional) nature of the resonant eigenstate. Using the previous approach of retaining the D=3 form of the potential for all spatial dimension D, highly accurate results are obtained via Padé–Borel summation of the expansion coefficients when they are complex, but a lesser degree of convergence is found when quadratic Padé summation is applied to real expansion coefficients. The present technique of using a dimension-dependent potential allows complex expansion coefficients to be obtained in all cases, and is demonstrated to provide a marked improvement in convergence. We illustrate this approach on the Lennard-Jones potential and the hydrogen atom in an electric field.