  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.
