Analytical Solutions for Velocity-Dependent Nuclear Potentials

The two-nucleon potential, with the necessary invariance requirements, is assumed to be a quadratic function of momentum: v=-V₀J₁(r)-(λM) p·J₂(r)p, where J₁(r) and J₂(r) are two short-range functions. For simplicity -J₂(r) is assumed to be a square well of unit depth. The Schr\"odinger equation is solved (neglecting Coulomb forces) for three different choices of J₁(r). Numerical results for the phase shifts are given for these three potentials (v₁, v₂, and v₃) for the singlet S, D, and G states. Reasonably good fits are obtained.