Bound state spectra of the 3D rational potential

TL;DR

This paper computes the bound state spectra of a 3D rational potential using a generalized pseudospectral method, providing highly accurate results for a wide range of states and interaction parameters, including higher excitations and negative interactions.

Contribution

The study offers the first comprehensive calculation of 30 states for the 3D rational potential across various parameters with high accuracy, surpassing previous methods.

Findings

Accurate bound state energies for 30 states (n=0--9) across broad parameters.

Energy sequences differ for positive and negative interactions, often mirror-image.

Systematic analysis of energy splittings and presentation of new states.

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.