Bound state spectra of the 3D rational potential

We present bound state spectra of the 3D rational potential, V(r)=r² + λr²/\(1+gr²\), 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 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 higher excitations and 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 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.