Vibrational-rotational analysis of super singular plus quadratic A/r4 + r2 potential

Most works on super singular potentials have focused on the study of the ground state. In this paper, a global analysis of the ground and excited states for the successive values of the orbital angular momentum of the super singular plus quadratic potential is carried out, making use of centrifugal plus quadratic potential eigenfunction bases. First, the radially nodeless states are variationally analysed for each value of the orbital angular momentum using the corresponding functions of the basis; the output includes the centrifugal and frequency parameters of the auxiliary potentials and their eigenfunction bases. In the second stage, these bases are used to construct the matrix representation of the Hamiltonian of the system, and from its diagonalization the energy eigenvalues and eigenvectors of the successive states are obtained. The systematics of the accuracy and convergence of the overall results are discussed with emphasis on the dependence on the intensity of the super singular part of the potential and on the orbital angular momentum. (author). 6 refs, 2 tabs