Morse Function and Velocity-Dependent Nuclear Potentials

Abstract

We have found approximate analytic solutions and an eigenvalue formula for Schr\"odinger's equation with velocity-dependent potentials by using the well-known Morse function as an "effective" potential. The method is applied to neutron bound states in ${\mathrm{O}}^{17}$ and ${\mathrm{Ca}}^{41}$ and the results are compared with the numerical solutions of Wyatt, Wills, and Green, with recent experimental data, and with the results of a recent Hartree-Fock calculation. The method should be applicable to many nuclear problems in the mass range $10<~A<~50$ which require realistic nuclear wave functions, as well as to other problems in nuclear and particle physics.