Energy calculations of low-vertical bar m vertical bar diamagnetic hydrogen states with dimensional perturbation theory - art. no. 025405

摘要

In a previous article [J. R. Walkup, M. Dunn, and D. K. Watson, Phys. Rev. A 58, 4668 (1998)] dimensional perturbation theory (DPT) was applied to circular Rydberg states of diamagnetic hydrogen to investigate avoided crossings in its energy spectrum as both the field strength and magnetic quantum number m were swept. Because the DPT perturbation parameter delta = 1/(D + 2m + 1), where D is the dimensionality of the system, is inversely related to m, one might assume that for a given field strength DPT would be effective only when m is large. However, the field-strength expression used in DPT is scaled as a function of m, so it is not obvious a priori whether the effectiveness of DPT diminishes when m is significantly reduced for a given physical field strength. It is shown that for many states of diamagnetic hydrogen DPT can still produce strongly convergent and accurate energy values when m is small, even when m = 0 (delta = 1/2). For those regions where even Pade summation failed to converge adequately, a technique is presented based on economized rational approximants. [References: 28]