Energy spectra and asymptotic laws of the radial screened Coulomb potential

Abstract

The energy spectra and corresponding asymptotic laws of the radial screened Coulomb potential V(r)=−exp⁡(−C/r)/r are investigated by employing the generalized pseudospectral method. Our numerical calculations manifest full convergence for all investigated bound states with the screening parameter C ranging from zero to infinity, but show significant discrepancies with previous predictions. Based on the Hellmann-Feynman theorem, we analyze the asymptotic behavior of the energy spectra for screening parameters close to zero. We further propose an empirical reciprocal law for energies when the screening parameter approaches infinity. We finally conclude that for the radial screened Coulomb potential there do not exist finite values of critical screening parameters at which the bound states merge into the continuum.