Halo effects in the Li 11 ( p , t ) Li 9 reaction

I investigate the $^{11}\mathrm{Li}(p,t)^{9}\mathrm{Li}$ two-neutron transfer reaction at ${E}_{\mathrm{lab}}=33$ MeV within the distorted wave Born approximation (DWBA). The $^{11}\mathrm{Li}$ and $^{3}\mathrm{H}$ nuclei are described in the hyperspherical formalism, as $^{9}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}n+n$ and $p+n+n$ configurations, respectively. The calculation of the cross section is shown to be much more complicated than in one-neutron transfer reactions, owing to the three-body structure of $^{11}\mathrm{Li}$. The $^{11}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}p$ and $^{9}\mathrm{Li}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}t$ scattering wave functions are determined with the continuum discretized coupled channel (CDCC) method. Approximations derived from equivalent local potentials are used to compute the transfer cross section at the DWBA. The model reproduces experimental data reasonably well, considering that there is no adjustable parameter. I show that the cross section is fairly sensitive to the long-range part of the $^{11}\mathrm{Li}$ wave function, and therefore to its halo structure.