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

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 Akyüz-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.