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: $v=-V_0{J}_1\mathrm{}\left(r\right)-\left(\frac{\lambda }{M}\right) \mathrm{p}·J_2\mathrm{}\left(r\right)\mathrm{}\mathrm{p}$, where $J_1\mathrm{}\left(r\right)\mathrm{}$ and $J_2\mathrm{}\left(r\right)\mathrm{}$ are two short-range functions. For simplicity $-J_2\mathrm{}\left(r\right)\mathrm{}$ is assumed to be a square well of unit depth. The Schrödinger equation is solved (neglecting Coulomb forces) for three different choices of $J_1\mathrm{}\left(r\right)\mathrm{}$. Numerical results for the phase shifts are given for these three potentials ($v_1, v_2, \mathrm{and} v_3$) for the singlet $S$, $D$, and $G$ states. Reasonably good fits are obtained.