Four-body CDCC analysis of $^6$He+$^{209}$Bi scattering near Coulomb barrier energies

In 2003, Keeley et al. analyzed the elastic scattering of $^6 $He on $^{209}$Bi target at 19.0MeV and 22.5MeV by the continuum-discretized coupled-channels method (CDCC). In the analysis the $^2n$+$^4$He+$^{209}$Bi three-body model, where $^2n$ denotes dineutron, was adopted. This three-body CDCC analysis, however, failed to reproduce the experimental data of the elastic cross section of $^6$He+$^{209}$Bi. In the present paper, $^6$He+$^{209}$Bi system is described by $n$+$n$+$^4$He+$^{209}$Bi four-body model and the four-body CDCC analysis, including nuclear- and Coulomb-breakup channels explicitly, is carried out. The three-body ($n$+$n$+$^4$He) continuum states of $^6$He are discretized by the pseudostate method, i.e., pseudostates obtained by diagonalizing the internal Hamiltonian of $^6$He with Gaussian basis functions are assumed to be discretized-continuum states of $^6$He. We show that the four-body CDCC well reproduces the angular distribution of elastic scattering data and the total reaction cross section at the both incident energies.