Studies on bound-state spectra of Manning-Rosen potential

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states, accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral (CPS) method. All 55 eigenstates with a <= 10 are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a non-uniform, optimal spatial radial discretization. A detailed investigation has been made on energy changes with respect to screening and other potential parameters. A systematic estimation of critical screening parameters is given for these eigenstates. Special emphasis has been given to higher states and in the vicinity of critical screening region. A thorough comparison with literature results is made wherever possible. This surpasses the accuracy of all other existing methods currently available. Several new states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered.