Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Section Data for the $^{12}$C+$^{208}$Pb System at Near-Coulomb-Barrier Energies by using a Folding Potential

TL;DR

This study uses an extended optical model with a folding potential to analyze elastic scattering and fusion data for the $^{12}$C+$^{208}$Pb system near the Coulomb barrier, successfully reproducing experimental results without normalization.

Contribution

It introduces a comprehensive analysis method decomposing the polarization potential into direct reaction and fusion parts, satisfying dispersion relations and revealing a threshold anomaly in the imaginary potentials.

Findings

Elastic scattering and fusion data are well reproduced without normalization.

Both DR and fusion polarization potentials satisfy dispersion relations.

Imaginary parts of potentials change rapidly at the strong absorption radius.

Abstract

Simultaneous $\chi^{2}$ analyses are performed for elastic scattering and fusion cross section data for the $^{12}$C+$^{208}$Pb system at near-Coulomb-barrier energies by using 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 also that both DR and fusion parts of the polarization potential determined from the $\chi^{2}$ analyses satisfy separately the dispersion relation. Furthermore, it is shown that the imaginary parts of both DR and fusion potentials at the strong absorption radius change very rapidly, which results in a typical threshold anomaly in the total imaginary potential as observed with tightly bound projectiles such as $\alpha$-particle and $^{16}$O.