Hydrogen atom with a Yukawa potential: Perturbation theory and continued-fractions--Pade approximants at large order

Journal Article · Sat Feb 01 04:00:00 EST 1986 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.33.1433· OSTI ID:6286430

Vrscay, E R

A simple power-series method is developed to calculate to large order the Rayleigh-Schroedinger perturbation expansions for energy levels of a hydrogen atom with a Yukawa-type screened Coulomb potential. Perturbation series for the 1s, 2s, and 2p levels, shown not to be of the Stieltjes type, are calculated to 100th order. Nevertheless, the poles of the Pade approximants to these series generally avoid the region of the positive real axis 0 < lambda < lambda(, where lambda( represents the coupling constant threshold. As a result, the Pade sums afford accurate approximations to E(lambda) in this domain. The continued-fraction representations to these perturbation series have been accurately calculated to large (100th) order and demonstrate a curious ''quasioscillatory,'' but non-Stieltjes, behavior. Accurate values of E(lambda) as well as lambda( for the 1s, 2s, and 2p levels are reported.

• Research Organization: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
• OSTI ID: 6286430
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 33:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular &amp; Chemical Physics-- Atomic &amp; Molecular Properties &amp; Theory
74 ATOMIC AND MOLECULAR PHYSICS
ATOMS
CONTINUED FRACTIONS
ELEMENTS
ENERGY LEVELS
HYDROGEN
NONMETALS
NUCLEAR POTENTIAL
PADE APPROXIMATION
PERTURBATION THEORY
POTENTIALS
RAYLEIGH-SCHROEDINGER FORMULA
YUKAWA POTENTIAL