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

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 cir cular Rydberg states of diamagnetic hydrogen to investigate avoided crossin gs in its energy spectrum as both the field strength and magnetic quantum n umber m were swept. Because the DPT perturbation parameter delta = 1/(D + 2 \m\ + 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 effect ive only when m is large. However, the field-strength expression used in DP T is scaled as a function of m, so it is not obvious a priori whether the e ffectiveness of DPT diminishes when m is significantly reduced for a given physical field strength. It is shown that for many states of diamagnetic hy drogen 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 ev en Pade summation failed to converge adequately, a technique is presented b ased on economized rational approximants.