This paper reports some results obtained in an attempt to determine a nucleon-nuclear potential of the Morse function type that contains velocity-dependent, spin-orbit splitting, energy-dependent, centrifugal interaction, etc., terms. The single-particle energy formula for all nuclei in the Morse-type potential well has been shown as convenient as in the harmonic type and as reliable as perhaps Hartree-Fock calculations. In particular the neutron separation energies for ¹⁶O and ⁴⁰Ca have been calculated and compared with the recently published results obtained from similar calculations and compared with the recently published results obtained from similar calculations and also with the other theoretical and experimental works. The results are found to be in very good agreement with the data and are consistent with the other calculations except with those published recently.