Bound state spectra of the 3D rational potential

Abstract

We present bound state spectra of the 3D rational potential, $V(r)=r^2 + \lambda r^2/(1+gr^2)$, $g>0$, by means of the generalized pseudospectral method. All the thirty states corresponding to $n$=0--9 are considered for the first time for a broad range of coupling parameters. These results surpass the accuracy of \emph{all} other existing calculations published so far except the finite-difference method, which yields similar accuracy as ours. Variation of energies and radial distribution functions is followed with respect to the interaction parameters. Special emphasis has been laid on \emph{higher} excitations and \emph{negative} values of the interaction, where relatively less work has been reported. The energy sequence is found to be different for positive and negative interaction; numerically following a mirror-image relationship \emph{usually}, if not always. Additionally, twenty energy splittings arising from certain levels belonging to $n$=0--9 are systematically studied as functions of the potential parameters. Several new states (including the higher ones) are presented.