Velocity-Dependent Nuclear Potentials for Singlet-Even States

Abstract

The usual models for the two-nucleon interaction involve a potential which includes a repulsive hard core at short distances and as a result, the treatment of the many-body problem is mathematically complicated. Peierls, Levinger, and others have suggested that ordinary perturbation theory may be useful if the two-body interaction can be described by a well-behaved potential. We attempt to provide such a description of the singlet-even states in terms of a potential of the form $-V_{0}J\left(r\right)+\left(\frac{\lambda }{M}\right)\left[p^2\omega \mathrm{}\right(r)+\omega \mathrm{}(r\left)\mathrm{}{p}^2\right].\mathrm{}$ $J\left(r\right)\mathrm{}$ and $\omega \mathrm{}\left(r\right)\mathrm{}$ are well-behaved functions of the relative separation and p is the operator for the relative momentum. The effective range and zero-energy scattering length along with the ${}_{}{}^1{}_{}{}^{}S$, ${}_{}{}^1{}_{}{}^{}D$, and ${}_{}{}^1{}_{}{}^{}G$ phase shifts in the energy range 20 to 340 Mev are calculated and adjusted to fit the experimental values. We can fit the low energy parameters and the ${}_{}{}^1{}_{}{}^{}S$ phase shifts very well. Agreement with the ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^1{}_{}{}^{}G$ phase shifts is plausible but less satisfactory. Suggestions for improving the fit are made. The treatment is nonrelativistic and Coulomb effects are ignored.