Microscopic optical potential for ${}^4\mathrm{He}$ scattering based on the effective Skyrme interaction

Microscopic optical potential of ${}^4\mathrm{He}$ interaction with nuclei is constructed by means of the single-folding model using the nucleon-nucleus optical potentials, which earlier were successfully applied to describing the neutron and proton scattering and are obtained from approximate calculations of the mass operator of the one-particle Green's function with the effective Skyrme nucleon-nucleon forces. The ${}^4\mathrm{He}$ scattering processes are described in a self-consistent approach based on the standard and extended Skyrme forces, which simultaneously provide a satisfactory description of nuclear structure and nucleon-nucleus scattering. The performed calculations reasonably describe experimental data on differential cross sections of the elastic and inelastic $\alpha$-particle scattering on different target nuclei in the mass-number range from ${}^{28}\mathrm{Si}$ to ${}^{208}\mathrm{Pb}$ at different projectile energies below or about 100 MeV, as well as the energy dependences of $\alpha$-particle reaction cross sections on nuclei in a wide energy range.

Figure 1

Differential cross sections $\sigma \left(\theta \right)\equiv d\sigma \left(\theta \right)/d\mathrm{\Omega }$ of the elastic $\alpha$-particle scattering on ${}^{58}\mathrm{Ni}$ nuclei at several energies calculated by the single-folding $\alpha A$ MOP with different $NA$ potentials. Experimental data are from Refs. [37, 38].

Figure 2

The same as in Fig. 1, but on ${}^{90}\mathrm{Zr}$. Experimental data are from Ref. [39].

Figure 3

The same as in Fig. 1, but for ${}^{120,124}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ target nuclei. Experimental data are from Refs. [40, 41, 42, 43].

Figure 4

The same as in Fig. 1, but for ${}^{58}\mathrm{Ni}, {}^{90}\mathrm{Zr}, {}^{124}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ target nuclei at 104 MeV. Experimental data are from Refs. [44, 45].

Figure 5

Radial dependences of the (a) real $V\left(R\right)$ and (b) imaginary $W\left(R\right)$ parts of different optical potentials (for details see the text) for the $\alpha +{}^{58}\mathrm{Ni}$ scattering at the projectile energy 58 MeV.

Figure 6

The same as in Fig. 5, but at the projectile energy 104 MeV.

Figure 7

Reaction cross sections ${\sigma }_r$ for the $\alpha$-particle interaction with ${}^{28}\mathrm{Si}, {}^{58}\mathrm{Ni}, {}^{120}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ nuclei as functions of the energy $E_{\alpha }$ calculated by the $\alpha A$ MOP with the SkOP4 force, by the SFM using the global $NA$ potential KD2003, as well as by means of the global $\alpha A$ potential. Experimental data are from Refs. [49, 50, 51].

Figure 8

Differential cross sections calculated using the $\alpha A$ MOP with the SkOP4 force for the elastic $\alpha +{}^{28}\mathrm{Si}$ scattering at 45 MeV as well as for the inelastic scattering with exciting the first $2^{+}$ state of ${}^{28}\mathrm{Si}$ nucleus. Experimental data are from Ref. [53].

Figure 9

The same as in Fig. 8 (the elastic cross section is normalized to the Rutherford one), but for ${}^{58}\mathrm{Ni}$ target nuclei at (a) 58 and (b) 104 MeV, with dashed curves calculated with the Gaussian $\alpha$-particle density (6) and the dotted ones with the model-free density SOG from Ref. [33]. Experimental data are from Refs. [37, 44].

Figure 10

The same as in Fig. 8 (the elastic cross section is normalized to the Rutherford one), but for ${}^{58}\mathrm{Fe}$ target nuclei at 64.5 MeV. Experimental data are from Ref. [54].

Figure 11

Differential cross sections calculated with the SkOP4 force at 40 MeV for the elastic $\alpha +{}^{90}\mathrm{Zr}$ scattering as well as for the inelastic scattering with exciting the first $2^{+}$ and $3^{-}$ states of ${}^{90}\mathrm{Zr}$ nucleus. Experimental data are from Ref. [55].

Figure 12

Differential cross sections calculated with the SkOP4 force at 79.1 MeV for the elastic $\alpha +{}^{208}\mathrm{Pb}$ scattering as well as for the inelastic scattering with exciting the first $3^{-}$ state of ${}^{208}\mathrm{Pb}$ nucleus. Experimental data are from Ref. [56].