Studying the structure of the neutron-unbound $^{12}$Li

The decay-energy spectrum of $^{12}$Li was measured in a neutron-fragment coincidence experiment at the National Superconducting Cyclotron Laboratory at MSU. $^{12}$Li was produced in the two-proton knockout reaction from a $^{14}$B secondary beam at 54 MeV/u. $^{12}$Li is neutron unbound and decays into $^{11}$Li and a neutron. The $^{11}$Li fragments were detected with position sensitive detectors behind the sweeper magnet, while the Modular Neutron Array (MoNA) was used to detect the emitted neutrons. The decay energy of $^{12}$Li was reconstructed event-by-event from the four-momentum vectors of the two products. Two resonances were observed in the invariant-mass spectrum at $\sim$200 keV and $\sim$500 keV. The measurement of the structure of $^{12}$Li is an essential first step for the understanding of the two-neutron decay mode of $^{13}$Li. The latter was also measured during the experiment in the one-proton knockout reaction from $^{14}$Be and the analysis is in progress.