The neutron-rich ${}^{11}\mathrm{Li}$ halo nucleus is unique among nuclei with known separation energies in its ability to emit a proton and a neutron in a $\beta$-decay process. The branching ratio toward this rare decay mode is evaluated within a three-body model for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e., a lower bound $6\times {10}^{-12}$ obtained with a pure Coulomb wave and an upper bound $5\times {10}^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausible values between $0.8\times {10}^{-10}$ and $2.2\times {10}^{-10}$, with most probable total energies of the proton and neutron between 0.15 and 0.3 MeV.

• Received 11 October 2010

DOI:https://doi.org/10.1103/PhysRevC.82.054318