Vibrational–Rotational Structure of Supersingular Plus Coulomb Potential A/r4 − Z/r

Abstract

The vibrational–rotational states of the supersingular plus Coulomb potential A/r 4 − Z/r are variationally constructed using a nonorthogonal basis of atomic hydrogenic eigenfunctions modulated by an exponential factor exp(−α/r), ensuring the correct behavior in the vicinity of the supersingularity. The construction is carried out in two successive stages. The first stage is restricted to trial functions without radial nodes, leading to a variational optimization of the parameters of the basis for each value of the angular momentum. The second stage uses the complete basis to construct linear trial functions and to formulate the variational problem in terms of secular equations, yielding the successive vibrational and rotational states. Numerical results for the corresponding energy levels are presented for different combinations of the intensity parameters of the potential.