Microscopic positive-energy potential based on the Gogny interaction

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 consis- tently 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 Schrodinger equation for the scattering process is solved without localization procedures. The method is ap- plied 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. Nuclear structure and nuclear reactions are two aspects of the same many-body problem, although in practice they are often addressed as different phenomena. A con- sistent, quantitative and predictive account for both is still a challenging open problem in nuclear physics. The description of nucleon-nucleus elastic scattering based solely on the nucleon-nucleon (NN) interaction is an im- portant step forward toward this unification. Depending on projectile energy and target mass, vari- ous strategies have been adopted in order to treat micro- scopically elastic scattering. Nuclear matter models (1) provide reasonable descriptions of nucleon elastic scat- tering at incident energies above 50 MeV (2), even up to �1 GeV (3). The Resonating Group Method within the No-Core Shell Model, has successfully described nucleon and deuteron scattering from light nuclei (4). These mod- els have recently been extended to include three-nucleon forces for nucleon scattering from 4 He (5). The Green's Function Monte Carlo method has been used to describe elastic scattering from 4 He (6). These models yield en- couraging results but are still restricted to light targets at low energies. The Self-Consistent Green's Function (SCGF) method has been applied to microscopic calcu- lation of the optical potentials for proton scattering from 16 O (7, 8). The coupled-cluster theory has been applied to proton elastic scattering from 40 Ca (9). These last two methods are limited to closed-shell nuclei. Work on Gorkov-Green's function theory is in progress to ex- tend SCGF to nuclei around closed-shell nuclei (10, 11). An alternative method consists of using microscopic ap- proaches based on the self-consistent mean-field theory and its extensions beyond mean-field. In nuclear physics, they are usually based on energy density functionals built from phenomenological parametrizations of the NN effec- tive interaction, such as Skyrme (12, 13) or Gogny forces (14-17). These approaches have successfully predicted a broad body of nuclear structure observables for nuclei ranging from medium to heavy masses. This wealth of developments can be extended to reaction calculations based on NN effective interaction. The so-called Nuclear Structure Method (NSM) for scattering (18-22) relies on the self-consistent Hartree-Fock (HF) and Random- Phase Approximations (RPA) of the microscopic opti- cal potential. The former is a mean-field potential and the latter is a polarization potential built from target- nucleus excitations. A strictly equivalent method, the continuum particle-vibration coupling using a Skyrme in- teraction, has been recently applied to neutron scattering from 16 O (23), but neglecting part of the residual inter- action in the coupling vertices. Other approaches are in progress, where optical potential is approximated as the HF term plus the imaginary part of the uncorrelated particle-hole potential neglecting the collectivity of tar- get excited states (24, 25). We report on optical potential calculations using NSM (18). Here the optical potential V consists of two compo- nents, V = V HF + �V.