Theoretical analysis of $^8$Li + $^{208}$Pb reaction and the critical angular momentum for complete fusion

TL;DR

This paper provides a theoretical analysis of the $^8$Li + $^{208}$Pb reaction, focusing on the dependence of complete and incomplete fusion processes on projectile binding energy and incident energy, using advanced modeling techniques.

Contribution

It introduces a generalized sum-rule model with an incident-energy dependent cutoff angular momentum $L_c$, extending previous models to energies near and below the Coulomb barrier.

Findings

Complete fusion is insensitive to variations in projectile binding energy.

Incomplete fusion strongly depends on projectile binding energy.

A fitted expression links $L_c$ to the critical angular momentum $L_{crit}$, enabling better modeling at sub-barrier energies.

Abstract

In a theoretical approach, the complete and incomplete fusions are investigated by considering the $^8$Li+$^{208}$Pb reaction. By decreasing the projectile ground-state binding energy $\varepsilon_b$ from its known experimental value, the complete fusion is shown to have insignificant dependence on such variations, whereas the incomplete fusion strongly depends on that. The complete and incomplete fusion cross sections are calculated by using a combination of both continuum-discretized coupled-channel and sum-rule models. To this end, an incident-energy dependent cut-off angular momentum $L_c$ is first obtained by using the available complete fusion experimental data, within an approach which is extended to model results obtained for other incident-energies. An approximated fitted expression linking $L_c$ to the well-known critical value $L_{\rm crit}$ derived by Wilczy\'nski [Nucl. Phys. A 216 (1973) 386] suggests a generalization of the corresponding sum-rule model to energies around and below the Coulomb barrier.