Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Section Data for the 7Li+208Pb System at Near-Coulomb-Barrier Energies using the Folding Potential

TL;DR

This study extends optical model analyses to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies, successfully reproducing elastic scattering and fusion data using a double folding potential without normalization, and decomposing the polarization potential into direct reaction and fusion parts.

Contribution

The paper introduces an extended optical model approach for $^{7}$Li+$^{208}$Pb, separating polarization potentials into DR and fusion components, and validates the model against experimental data without normalization.

Findings

Both DR and fusion polarization potentials satisfy the dispersion relation.

The real part of the fusion potential is attractive, while DR is repulsive at most energies.

The model reproduces experimental data without adjusting the folding potential.

Abstract

Simultaneous $\chi^{2}$ analyses previously made for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system is extended to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies based on the extended optical model approach, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and that both the DR and fusion parts of the polarization potential determined from the $\chi^{2}$ analyses satisfy separately the dispersion relation. Further, we find that the real part of the fusion portion of the polarization potential is attractive while that of the DR part is repulsive except at energies far below the Coulomb barrier energy. A comparison is made of the present results with those obtained from the Continuum Discretized Coupled Channel (CDCC) calculations and a previous study based on the conventional optical model with a double folding potential. We also compare the present results for the $^7$Li+$^{208}$Pb system with the analysis previously made for the $^{6}$Li+$^{208}$Pb system.