Nonperturbative dynamical-group approach to screened Coulomb potentials

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Abstract
In this paper we consider screened Coulomb potentials of the Yukawa type and treat them using a scaling variational method based on the SO(2, 1) subgroup of the full SO(4,2) dynamical group of the point Coulomb problem. In this formulation the tilting angle is treated as a variational parameter and the relevant matrix elements of the Yukawa potential can be expressed as matrix elements of an analytically continued finite SO(2, 1) transformation of the parabolic type. We calculate the energy eigenvalues, wave functions (essentially scaled Coulomb wave functions), and normalization factors. Our energy eigenvalues are more accurate than those found by the analytic perturbation theory of McEnnan et al., while the normalization factors are less accurate. Thus our method may be considered as complementary to the analytic perturbation theory.