Bound eigenstates for two truncated Coulomb potentials

Abstract

The eigenvalue problem for two particles interacting through the attractive truncated Coulomb potential, V(r)=-${\mathrm{Ze}}^{2}$/(${r}^{p}$+${\ensuremath{\beta}}^{p}$${)}^{1/p}$, for p=1 and 2 is solved numerically. Energy eigenvalues accurate to within eight to six significant figures for the states 1s to 4f are calculated as a function of the truncation parameter \ensuremath{\beta}. It is found that the level ordering satisfies ${E}_{\mathrm{nl}}$>${E}_{\mathrm{nl}\mathcal{'}}$ for l'. Systematics of the eigenvalues are studied and it is found that for each l value the energies are well represented by a Ritz type of formula.