Microscopic positive-energy potential based on Gogny interaction

TL;DR

This paper introduces a novel microscopic approach to nucleon elastic scattering using the Gogny interaction within Green's function formalism, accurately modeling reaction cross sections up to 30 MeV.

Contribution

It is the first to consistently incorporate the Gogny effective interaction into the complex optical potential calculation for scattering.

Findings

Successfully reproduces differential and integral cross sections for $^{40}$Ca up to 30 MeV

Highlights the importance of intermediate single-particle resonances in reaction modeling

Identifies limitations at higher energies due to real potential volume integral issues

Abstract

We present nucleon elastic scattering calculation based on Green's function formalism in the Random-Phase Approximation. For the first time, the Gogny effective interaction is used consistently throughout the whole calculation to account for the complex, non-local 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 section. 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 $^{40}$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 much too high volume integral of the real potential for large partial waves. Moreover, this works opens the way for future effective interactions suitable simultaneously for both nuclear structure and reaction.