Microscopic positive-energy potential based on the Gogny interaction

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 Schrödinger 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.

Figure 1

Differential cross sections for (a) neutron and (b) proton scattering from ${}^{40}\mathrm{Ca}$. Comparison is between data (symbols), $V^{HF}+\Delta V$ results (solid curves), and Koning–Delaroche potential results (dashed curves).

Figure 2

Same as Fig. 1 but for analyzing powers.

Figure 3

Reaction cross section for (a) proton and (b) total cross section for neutron scattering from ${}^{40}\mathrm{Ca}$. Comparison is between data (symbols), $V^{HF}+\Delta V$ results (solid curve), and Koning–Delaroche potential (dashed curve).

Figure 4

Volume integral as a function of partial waves for neutron scattering from ${}^{40}\mathrm{Ca}$: HF potential (solid curve), Hartree potential (dash-dotted curve), and Perey–Buck potential (dotted curve). Horizontal segments denote the partial-wave interval to sum up 80% of the reaction cross section at selected incident energies.

Figure 5

Partial-wave contribution $\nu$ of $\text{Im}V$ for neutron scattering from ${}^{40}\mathrm{Ca}$ scattering at 9.91 MeV as a function of radius and partial waves: $V^{HF}+\Delta V$ potential (solid curve), $V^{HF}+\text{Im}[V^{RPA}/2]$ potential (dash-dotted curve).

Figure 6

Differential cross sections $\sigma \left(\theta \right)/{\sigma }_{\text{Ruth}}$ for proton incident on ${}^{40}\mathrm{Ca}$. Comparison between data (symbols), $V^{HF}+\Delta V$ (solid curves), and $V^{HF}+\text{Im}[V^{RPA}/2]$ results (dashed curves).