Relativistic nucleon optical potentials with isospin dependence in a Dirac-Brueckner-Hartree-Fock approach

Abstract

The relativistic optical model potential (OMP) for nucleon-nucleus scattering is investigated in the framework of the Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-B one-boson-exchange potential for the bare nucleon-nucleon interaction. Both real and imaginary parts of isospin-dependent nucleon self-energies in the nuclear medium are derived from the DBHF approach based on the projection techniques within the subtracted $T$-matrix representation. The Dirac potentials as well as the corresponding Schr\"odinger equivalent potentials are evaluated. An improved local density approximation is employed in this analysis, where a range parameter is included to account for a finite-range correction of the nucleon-nucleon interaction. As an example the total cross sections, differential elastic scattering cross sections, analyzing powers for $n$, $p$ $+$ ${}^{27}$Al at incident energy 100 keV $\ensuremath{\le}E\ensuremath{\le}$ 250 MeV are calculated. The results derived from this microscopic approach of the OMP are compared to the experimental data, as well as the results obtained with a phenomenological OMP. A good agreement between the theoretical results and the measurements can be achieved for all incident energies using a constant value for the range parameter.