β decay ofLi11intoLi9and a deuteron within a three-body model

The β-decay process of the ${}^{11}\mathrm{Li}$ halo nucleus into ${}^9\mathrm{Li}$ and $d$ is studied in a three-body model. The ${}^{11}\mathrm{Li}$ nucleus is described as a ${}^9\mathrm{Li}$ $+n+n$ system in hyperspherical coordinates on a Lagrange mesh. Various ${}^9\mathrm{Li}$ $+d$ potentials involving a forbidden state, a physical bound state, and a resonance near 0.25 MeV in the $s$ wave are compared. With an added surface absorption, they are compatible with elastic scattering data. The transition probability per time unit is quite sensitive to the location of the resonance. For a fixed resonance location, it does not depend much on the potential choice at variance with the ${}^6\mathrm{He}$ delayed deuteron decay. The calculated transition probability per time unit is larger than the experimental value but the difference can be explained by a slightly higher resonance location and/or by absorption from the ${}^9\mathrm{Li}$ $+d$ final channel.