Semimicroscopic analysis of ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ elastic scattering at 76 to 318 MeV

Using the α-cluster structure of colliding nuclei, the elastic scattering of ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ at energies from 76 to 318 MeV has been investigated by the use of the real folding cluster approach. The results of the cluster analysis are compared with those obtained by the CDM3Y6 effective density- and energy-dependent nucleon-nucleon (NN) interaction based upon $G$-matrix elements of the M3Y-Paris potential. A Woods-Saxon (WS) form was used for the imaginary potential. For all energies and derived potentials, the diffraction region was well reproduced, except at $E_{\mathrm{lab}}=135$ and 154 MeV at large angle. These results suggest that the addition of the surface (DWS) imaginary potential term to the volume imaginary potential is essential for a correct description of the refractive structure of the ${}^6\mathrm{Li}$ elastic scattering distribution at these energies. The energy dependence of the total reaction cross sections and that of the real and imaginary volume integrals is also discussed.

Figure 1

A comparison of the radial shapes of the real microscopic nuclear potentials (DFC1 and CDM3Y6) and the WS imaginary potentials used in our calculations at $E_{\mathrm{lab}}=76\text{–}318\mathrm{MeV}$. The dotted line is the real DFC1with (WS+DWS) imaginary potentials.

Figure 2

A comparison between the measured ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ elastic differential cross sections and theoretical predictions obtained by using the CDM3Y6 and DFC1 potentials at $E_{\mathrm{lab}}=76$, 99, 135, 154, 210, and 318 MeV. The dotted line is theoretical prediction using DFC1 with (WS+DWS) imaginary potentials. The data are taken from Refs. [13, 17, 18, 49].

Figure 3

Energy dependence of the best-fit parameters $N_{\mathrm{R}}$ and $V_{\mathrm{R}}$. Panels (a) and (b) show the results of energy dependence for the normalization coefficients ($N_{\mathrm{R}}$) of the CDM3Y6 potential and the real repulsive depths ($V_{\mathrm{R}}$) of the α-α interaction in the DFC1 potential, respectively.

Figure 4

The volume integral per interacting nucleon pair for different optical potentials of the ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ interaction obtained with CDM3Y6 and DFC1 and imaginary WS potentials plotted versus incident energy. The solid curve represents the Satchler expression obtained with the SIY effective NN interaction [48]. The dotted curve represents Nadisen et al.’s expression obtained with WS potentials [18].

Figure 5

Energy dependence of the total reaction cross sections, ${\sigma }_R$, extracted from the present analysis using CDM3Y6 and DFC1 potentials in comparison with those deduced from elastic scattering calculations of El-Azab [3, 4].