Application of the Bruyères Jeukenne-Lejeune-Mahaux model potential to composite nuclei with a single-folding approach

A single-folding (SF) model analysis has been performed for $\alpha$ and deuteron elastic scattering from ${}^{58}\text{Ni}$, ${}^{90}\text{Zr}$, ${}^{116}\text{Sn}$, and ${}^{208}\text{Pb}$ at incident energies between 10 and 100 MeV/nucleon with the Lane-consistent Bruyères Jeukenne-Lejeune-Mahaux model nucleon-nucleus potential. The energy dependence of a set of only three potential parameters was derived, and the resulting global optical model potentials were found to account well for $\alpha$ and deuteron elastic scattering within their studied energy ranges. The energy dependence of a real potential form factor is found to be important for describing $\alpha$-nucleus scattering within large energy ranges. Corrections due to the compositeness of projectiles to the SF potentials were studied and were compared with theoretical estimations through the renormalization factor. Systematic differences in renormalization factors between $\alpha$ particles and deuterons were observed.

Figure 1

SF potential for ${}^4\mathrm{He}$ elastic scattering from ${}^{90}\mathrm{Zr}$ at 141.7 MeV calculated with different values of the range parameter $t_{\mathit{ri}}$.

Figure 2

Energy dependence of $t_{\mathrm{ri}}$ for ${}^4\mathrm{He}$ and deuteron with heavy targets.

Figure 3

Energy dependence of $N_r$ and $N_i$ for an $\alpha$ particle and a deuteron with heavy targets.

Figure 4

Comparison between optical model calculations and experimental data of ${}^4\mathrm{He}$ elastic scattering from ${}^{58}\mathrm{Ni}$, ${}^{90}\mathrm{Zr}$ (triangles for the ${}^{116}\mathrm{Sn}$ target at 288 and 340 MeV), and ${}^{208}\mathrm{Pb}$ at different energies. The solid and dashed curves were calculated with local and global potential parameters, respectively. Different data sets are offset by factors of ${10}^n$ with an $n$ variable for optimum view. The ${}^{58}\mathrm{Ni}$ data at 25 MeV, ${}^{90}\mathrm{Zr}$ data at 25 MeV, and ${}^{208}\mathrm{Pb}$ data at 23 MeV are from Refs. [79, 80, 81]. Experimental error bars are not shown in these figures.

Figure 5

Same as Fig. 4 but with deuteron projectiles. The ${}^{58}\mathrm{Ni}$ data at 20 MeV, ${}^{90}\mathrm{Zr}$ data at 15 MeV, and ${}^{208}\mathrm{Pb}$ data at 28.8 MeV are from Refs. [63, 64, 82].

Figure 6

Comparison between optical model calculations and experimental data for $\alpha$ elastic scattering at around 140 MeV as an example of a detailed view for the degree of agreement with model calculations and data. Note that the c.m. angles are ${\theta }_{\mathrm{c}.\mathrm{m}.}$ in this figure.

Figure 7

Comparison between optical model calculations and experimental data for $\alpha$ elastic scattering at 340 MeV. Note that the c.m. angles are ${\theta }_{\mathrm{c}.\mathrm{m}.}$ in this figure.

Figure 8

Comparison between optical model calculations of total reaction cross sections and experimental data for the $\alpha$ particle. The target nuclei are indicated in the figure. The experimental data are from Refs. [83, 84].

Figure 9

Comparison between optical model calculations of total reaction cross sections and experimental data for the deuteron. The target nuclei are indicated in the figure. The experimental data are from Refs. [85, 86, 87].

Figure 10

Comparison between optical model calculations and experimental data for deuteron elastic scattering at 56 MeV. Note that the c.m. angles are ${\theta }_{\mathrm{c}.\mathrm{m}.}$ in this figure.

Figure 11

JLMB model description of proton elastic scattering from ${}^{90}\mathrm{Zr}$ with different finite-range Gaussian parameters. The experimental data are from Ref. [88].

Figure 12

Volume integrals per interaction pair of optical model potentials for a proton (solid curves), a neutron (dashed curves) with the JLMB model, and a deuteron (open triangles) and $\alpha$ (solid squares) with global SF model parameters.

Figure 13

Moduli of the $S$ matrix for proton, deuteron, and $\alpha$-particle elastic scattering from ${}^{58}\mathrm{Ni}$ at 80 MeV/nucleon calculated with the JLMB model and the global parameters obtained in this paper.