Nucleon–nucleus real potential of Woods–Saxon shape between −60 and +60 MeV for the 40 ⩽ A ⩽ 208 nuclei

Abstract

Nucleon differential elastic scattering cross sections, total proton reaction cross sections and single-particle energies of nucleon bound states for 40Ca, 90Zr and 208Pb nuclei are reanalysed in terms of the dispersive optical model at energy from −75 MeV to 60 MeV. The real effective Woods–Saxon potential, which corresponds to the real part of the dispersive optical model potential, is studied with respect to its dependence on A, Z, E and on projectile nature (proton or neutron). For the first time, a parametrization of the Woods–Saxon real part of the nucleon–nucleus optical potential is proposed for the 40 ⩽ A ⩽ 208 nuclei in an energy range from −60 MeV to +60 MeV, which obviously includes the Fermi energy range. The parametrization reflects the dispersion relation between the real and imaginary parts of the optical model potential through the energy dependence of the radius parameter of the real part of the potential. The method of determining the imaginary part of the optical model potential, which is symmetrical relative to the Fermi energy, is also proposed for the nuclei with 40 ⩽ A ⩽ 208. Differential elastic scattering cross sections, total neutron interaction cross sections, total proton reaction cross sections and single-particle energies of the nucleon bound states are calculated in terms of the proposed nucleon–nucleus potential parametrization for some of the (n + A) and (p + A) (40 ⩽ A ⩽ 208) systems and compared with the available experimental data, yielding a fairly good agreement.