Calculation of the spectrum of 12Li by using the multistep shell model method in the complex energy plane

The unbound nucleus ${}^{12}$Li is evaluated by using the multistep shell model in the complex energy plane assuming that the spectrum is determined by the motion of three neutrons outside the ${}^9$Li core. It is found that the ground state of this system consists of an antibound $1\mathrm{/}{2}^{+}$ state and that only this and a $1\mathrm{/}{2}^{-}$ and a $5\mathrm{/}{2}^{+}$ excited states are physically meaningful resonances.