Microscopic optical potentials for ${}^4\mathrm{He}$ scattering

We present a reliable double-folding (DF) model for ${}^4\mathrm{He}$-nucleus scattering, using the Melbourne $g$-matrix nucleon-nucleon interaction that explains nucleon-nucleus scattering with no adjustable parameter. In the DF model, only the target density is taken as the local density in the Melbourne $g$ matrix. For ${}^4\mathrm{He}$ elastic scattering from ${}^{58}\mathrm{Ni}$ and ${}^{208}\mathrm{Pb}$ targets in a wide range of incident energies from 20 to 200 MeV/nucleon, the DF model with the target-density approximation (TDA) yields much better agreement with the experimental data than the usual DF model with the frozen-density approximation in which the sum of projectile and target densities is taken as the local density. We also discuss the relation between the DF model with the TDA and the conventional folding model in which the nucleon-nucleus potential is folded with the ${}^4\mathrm{He}$ density.

Figure 1

Differential cross sections as a function of transfer momentum $q$ for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ elastic scattering at (a) $E_{\mathrm{in}}/A_{\mathrm{P}}=20–72$ MeV and (b) $E_{\mathrm{in}}/A_{\mathrm{P}}=85–175$ MeV. The cross section at each $E_{\mathrm{in}}/A_{\mathrm{P}}$ is multiplied by the factor shown in the panel. The solid (dotted) line stands the results of the DF-TDA (DF-FDA) model, whereas the dashed line denotes the results of the NAF model. The experimental data are taken from Refs.  [40, 41, 42, 43, 44, 45].

Figure 2

Total reaction cross section ${\sigma }_{\mathrm{R}}$ as a function of $E_{\mathrm{in}}/A_{\mathrm{P}}$ for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ scattering at $E_{\mathrm{in}}/A_{\mathrm{P}}=20–175$ MeV. The circles (squares) stand the results of the DF-TDA (DF-FDA) model, whereas the triangles denote the results of the NAF model. The experimental data are taken from [44, 46].

Figure 3

$R$ dependence of the absolute value of the elastic $S$-matrix element for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ elastic scattering at $E_{\mathrm{in}}/A_{\mathrm{P}}=26,85,$ and 175 MeV. The solid, dashed, and dotted lines represent the elastic $S$-matrix elements calculated with the DF-TDA model at $E_{\mathrm{in}}/A_{\mathrm{P}}=26,85,$ and 175 MeV, respectively.

Figure 4

Optical potentials for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ elastic scattering at $E_{\mathrm{in}}/A_{\mathrm{P}}=175$ MeV. The solid (dotted) line stands for the DF-TDA (DF-FDA) potential, whereas the dashed line denotes the NAF potential.

Figure 5

Optical potentials for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ elastic scattering at $E_{\mathrm{in}}/A_{\mathrm{P}}=85$ MeV. See Fig. 4 for the definition of lines.

Figure 6

Optical potentials for ${}^4\mathrm{He}+{}^{58}\mathrm{Ni}$ elastic scattering at $E_{\mathrm{in}}/A_{\mathrm{P}}=26$ MeV. See Fig. 4 for the definition of lines.

Figure 7

Differential cross sections as a function of transfer momentum $q$ for ${}^4\mathrm{He}+{}^{208}\mathrm{Pb}$ elastic scattering at (a) $E_{\mathrm{in}}/A_{\mathrm{P}}=26–85$ MeV and (b) $E_{\mathrm{in}}/A_{\mathrm{P}}=97–175$ MeV. The cross section at each $E_{\mathrm{in}}/A_{\mathrm{P}}$ is multiplied by the factor shown in the panel. The solid (dotted) line stands the results of the DF-TDA (DF-FDA) model, whereas the dashed line denotes the results of the NAF model. The experimental data are taken from [44, 47, 48, 49].