Coupled-channels analyses for $^{9,11}$Li + $^{208}$Pb fusion reactions with multi-neutron transfer couplings

TL;DR

This paper investigates the influence of multi-neutron transfer processes on fusion reactions involving lithium isotopes and lead, using coupled-channels models to reproduce experimental data and highlight the importance of two-neutron transfers, especially for halo nuclei.

Contribution

It introduces a coupled-channels analysis incorporating multi-neutron transfer couplings for $^{9,11}$Li + $^{208}$Pb fusion reactions, emphasizing the role of halo structure and transfer channels.

Findings

Two-neutron transfer significantly affects fusion cross sections.

Coupled-channels model reproduces experimental data.

Multiple transfer channels are crucial for halo nuclei.

Abstract

We discuss the role of two-neutron transfer processes in the fusion reaction of the $^{9,11}$Li + $^{208}$Pb systems. We first analyze the $^{9}$Li + $^{208}$Pb reaction by taking into account the coupling to the $^{7}$Li + $^{210}$Pb channel. To this end, we assume that two neutrons are directly transferred to a single effective channel in $^{210}$Pb and solve the coupled-channels equations with the two channels. By adjusting the coupling strength and the effective $Q$-value, we successfully reproduce the experimental fusion cross sections for this system. We then analyze the $^{11}$Li + $^{208}$Pb reaction in a similar manner, that is, by taking into account three effective channels with $^{11}$Li + $^{208}$Pb, $^{9}$Li + $^{210}$Pb, and $^{7}$Li + $^{212}$Pb partitions. In order to take into account the halo structure of the $^{11}$Li nucleus, we construct the potential between $^{11}$Li and $^{208}$Pb with a double folding procedure, while we employ a Wood-Saxon type potential with the global Aky\"uz-Winther parameters for the other channels. Our calculation indicates that the multiple two-neutron transfer process plays a crucial role in the $^{11}$Li + $^{208}$Pb fusion reaction at energies around the Coulomb barrier.