Relation between Nucleon Density and Nuclear Potential

The relationship between nuclear density and potential is determined, taking account of the saturating character and the finite range of the two-body forces. The former characteristic alone leads to the nonlinear relation between nuclear density and potential pointed out by Wilets, and accounts for an increase of potential radius over density radius of about 5×${10}^{-14\mathrm{}}$ cm. The finite-range effect is estimated by using pseudo-potentials to represent the two-body interaction operators generated by the two-body potentials. The combined effects of nonlinearity and finite range give an increase in the rms potential radius which is very close to that observed experimentally. The fall-off distance of the potential surface predicted is, however, somewhat greater than that empirically determined. It is pointed out that this discrepancy may be removed if proper account is taken of the nonlocal character of the nuclear potential.