An energy-independent nonlocal potential model. II. The asymmetry term

We analyze the single-particle bound-state properties and the elastic scattering of protons and neutrons in various groups of isotopes, ranging from C up to Sn, by means of an energy-independent nonlocal optical model. The potential is obtained as an extension of the one used in the analysis of N = Z nuclei, the new term being a Lane-type potential with the same geometrical parameters as the isoscalar one. The radius of the potential is determined by the fit of single-particle energies and charge distribution in one nuclide of each group and it is given by $\text{R}{}_{\mathrm{N}}\text{= 1.16 (A?1)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{F}$. The well depths of the equivalent local potential are fitted to a large set of single-particle energies, measured in stripping and pick-up reactions, and show an energy dependence which is consistent with a unique nonlocal energy-independent potential having isoscalar nonlocality $\text{β ? 1F}$ and isovector nonlocality $\text{β}{}_{\mathrm{T}}\text{? 1.6F}$. In particular, the bound-state data can determine the isovector part of the potential with fair accuracy, provided that proton and neutron, T> and T<, particle and hole states are analyzed: its average value at zero energy shows an increasing behavior from C to Mo. The nucleon point distribution and r.m.s. radii corresponding to this model potential have been calculated in various nuclei.