Microscopic positive-energy potential based on the Gogny interaction

Abstract

We present a nucleon elastic scattering calculation based on Green's function formalism in the random-phase approximation. For the first time, the finite-range Gogny effective interaction is used consistently throughout the whole calculation to account for the complex, nonlocal, and energy-dependent optical potential. Effects of intermediate single-particle resonances are included and found to play a crucial role in the account for measured reaction cross sections. Double counting of the particle-hole second-order contribution is carefully addressed. The resulting integro-differential Schr\"odinger equation for the scattering process is solved without localization procedures. The method is applied to neutron and proton elastic scattering from $^{40}\mathrm{Ca}$. A successful account for differential and integral cross sections, including analyzing powers, is obtained for incident energies up to 30 MeV. Discrepancies at higher energies are related to a much-too-high volume integral of the real potential for large partial waves. This work opens the way to simultaneously assess effective interactions suitable for both nuclear structure and reactions.