Low-energy nucleon-nucleus scattering within the energy density functional approach

The description of nucleons scattering off doubly closed-shell nuclei ${}^{16}\mathrm{O}$ and ${}^{208}\mathrm{Pb}$ at energies below 50 MeV is carried out in a fully self-consistent framework of the particle-vibration coupling approach. The applications are performed with commonly used Skyrme-type effective interactions. Nucleon-nucleus optical potentials are thus calculated without ad hoc adjusted parameters. These potentials are then solved with standard optical model codes (dwba98 in the present case). Empirical nucleon-nucleus elastic angular distributions are thus successfully reproduced.

Figure 1

Diagrammatic representation of the self-energy $\mathrm{\Sigma }\left(\omega \right)$ and the second-order self-energy ${\mathrm{\Sigma }}^{\left(2\right)}\left(\omega \right)$. $\alpha$ and $\beta$ can be either particles or holes.

Figure 2

Angular distributions of the neutron elastic scattering by ${}^{16}\mathrm{O}$ at 28 MeV. The interaction ${\mathrm{SkM}}^{*}$ has been used. The solid (long-dashed) curve shows the results of PVC calculations with (without) the SOP. HF and cPVC results (extracted from Ref. [10]) are denoted by the dot-dashed and short-dashed lines, respectively. Experimental data are taken from Ref. [30].

Figure 3

Calculated $W(R,s=0)$ by ${}^{16}\mathrm{O}$ at different incident energies. The interaction ${\mathrm{SkM}}^{*}$ has been used.

Figure 4

Calculated $W(R,s=0)$ by ${}^{208}\mathrm{Pb}$ at different incident energies below 50 MeV. The interaction SLy5 has been used.

Figure 5

Calculated $W(R,s=0)$ by ${}^{208}\mathrm{Pb}$ at $E=14.5$ MeV. The interaction SLy5 has been used. The solid line corresponds to OP calculations; the dashed line, to results taken from Ref. [7].

Figure 6

Contributions of the multipole modes to angular distributions of neutron elastic scattering by ${}^{208}\mathrm{Pb}$ at incident energy $E=14.5$ MeV. The interaction SLy5 has been used. HF results are denoted by the solid line. Short-dashed, dotted, long-dashed, dotted/short-dashed, and dotted/long-dashed lines correspond to calculations with the maximum multipolarity $L_{\max }=1$, 2, 3, 4, and 5, respectively. Experimental points are taken from Ref. [30].

Figure 7

Angular distributions of neutron elastic scattering by ${}^{208}\mathrm{Pb}$ at different incident energies below 50 MeV. The interaction SLy5 has been used. Solid curves show the results of OP calculations. Experimental points are taken from Ref. [30].