δ -Function Model for the Two-Nucleon Interaction

An interaction of the form VLJST(r)=Σ(vᵢrᵢ)δ(r-rᵢ) is used to make a fit to the Livermore X phase shifts (0-460 MeV). Only states with L≤2 are considered; coupling between states is at present neglected but effective central ³S₁ and ³D₁ interactions are given. No more than four terms (per state) are required. In states which have a repulsion the position of the innermost δ function can be chosen arbitrarily within wide limits; e.g., for the ¹S₀ state 0.1542≤rᵢ≤0.95 F. Families of hard-core interactions in which rc and r₁ are arbitrary are also determined. We find 0.1542≤rc≤0.7 F for the ¹S₀ state. All ¹S₀ interactions give essentially the same D-state phase shifts within the same energy range (these differ from ¹D₂ experimental phase shifts). The main virtues of this type of potential are the ease with which the parameters may be determined and its relative simplicity in calculations for A≥3 and nuclear matter. It may also be written in the separable form $〈rLJST|V|{r}^{{'}}LJST〉={Σ}({{v}ᵢ}{{r}ᵢ}){δ}(r{-}{r}ᵢ){δ}({r}^{{'}}{-}{r}ᵢ)$.