Eigenenergies of the $r^2$+λ$r^2$/(1+${\mathrm{gr}}^2$) potential obtained by the shifted 1/N expansion

Energy eigenvalues are obtained for the three-dimensional potential V(r)=(1/2[$r^2$+λ$r^2$/ (1+${\mathrm{gr}}^2$)], where λ and g are parameters, using the shifted-1/N-expansion method. Results are obtained for nine sets of $n_r$ and l values corresponding to n=0, 1, 2, 3, and 4. It is found that certain levels which are degenerate in the limit λ=0 do not remain so as λ increases. This splitting is studied as a function of g and of λ. It is also shown that with a negative λ, this potential gives a sequence for energy levels which is identical with that which occurs in the shell model of the nucleus.