Full-folding optical potential for nucleon scattering at low energies

The inclusion of a microscopic Optical Model Potential (OMP) in the frame of various nuclear reaction models for the description of the pre-equilibrium emission is a difficult task. Therefore, the simplest 1 fm range Yukawa interaction has been chosen to describe the effective nucleon-nucleon (NN)-interaction leading to particle-hole excitations in the frame of the Feshbach-Kerman-Koonin model. Its strength, V0, is the only free parameter adjusted to reproduce the experimental data. The large discrepancies still present at low incident energies (Ei<50 MeV) in the systematics of the phenomenological V0 values prove the necessity to consider a more realistic NN-interaction, as well as the corresponding folded real part of the OMP. First, we have considered the density and energy-dependent effective interactions DDM3Y and BDM3Y based on the g-matrix elements of the Reid and Paris NN-potentials which seem to be most successful for the nucleon-nucleus scattering within the low-density nuclear matter. Secondly, the point-like nucleon assumption of the single folding method has been replaced by considering a realistic density distribution of the incident nucleon. This has been done by a Double Folding (DF) procedure with effective NN interactions based on realistic NN potentials. Finally, the real part of the OMPs have been obtained on the basis of realistic effective interactions. Instead of introducing phenomenological form factor we use the DF procedure which accounts for the extended structure of the nucleon. In the case of the optical potential calculations this procedure will lead to results similar to those in which the cut-off method has been applied. The effects of both nucleon and nuclear density distributions, as well as of the related quantities like the kinetic-energy density τ(r) and various approximations of the average relative momentum kav(r) on the corresponding double-folding real OMP at lower incident energies (Ei<100 MeV), have been comparatively analysed. Also, the corresponding double-folding real OMPs obtained from the different types of density dependence of the effective NN-interactions have been compared. A good agreement with the phenomenological potential of Lagrange-Lejeune, as well as with the parametrization of Jeukenne-Lejeune-Mahaux (JLM) for both neutron and proton double-folded potentials is obtained. In conclusion, this analysis has shown that the DF procedure using the nucleon-density Fermi distribution and average relative momentum leads, at lower energies, to real OMPs, in good agreement with both the phenomenological potentials and the JLM parametrization for the neutron- as well as proton-nucleus scattering. (authors)