An improved calculation for screened Coulomb potentials in Rayleigh-Schrodinger perturbation theory

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Abstract
Earlier works on screened Coulomb potentials using Rayleigh-Schrodinger perturbation theory have been re-examined. Instead of working with the usual Hulthen potential as the unperturbed Hamiltonian, the authors propose that a scaled Hulthen potential with modified strength and screening coefficient represents the lowest-order approximation for the static-screened Coulomb and exponential cosine-screened Coulomb potentials. The scale parameter appearing in the new Hulthen potential is then determined from the notion of the virial theorem and intuitive physical arguments. It is found that the accuracy of the predicted energy eigenvalues for the bound s states improves significantly even when the screening parameter is large and quite close to its critical values for which the quantum state becomes just bound. In spite of the simplicity of the approach, the numerical results compare fairly well with those obtained from rigorous analytic approximation methods.