Level assignments of $^{11}$Be$^{\ast }$ through $\beta $-delayed low energy neutron emissions

The low energy neutron emissions from $^{11}$Be$^{\ast }$ were studied in the $\beta $-n and $\beta $-n-$\gamma $ coincidence measurements from a \textit{spin-polarized} $^{11}$Li$_{gs}$. The spin-parity assignments for the $^{11}$Be$^{\ast }$ states were made based on the fact that the allowed $\beta $-transition from the polarized $^{11}$Li shows $\beta $-decay asymmetry depending on the spin value of the daughter state in $^{11}$Be. The experiment was performed at TRIUMF ISAC, where approximately 55{\%} nuclear-polarized $^{11}$Li beam was available. The $\beta $-decay asymmetries were measured in coincidence with the delayed neutrons from $^{11}$Be$^{\ast }$ and/or the subsequent $\gamma $-rays from $^{10}$Be$^{\ast }$. In the $\beta $-n coincidence, very low energy neutrons with E$_{n}$ = 73 (5) keV and 17 (1) keV were observed. From the $\beta $-decay asymmetries in coincidence with the respective neutron, the spins and parities of the neutron emitting states in $^{11}$Be were unambiguously determined to be 3/2- and 5/2-, respectively. From the $\beta $-n-$\gamma $ coincidence the level energies of the $^{11}$Be states were determined to be E$_{x}$ = 3.951(6) and 3.890(1) keV, respectively. The I$^{\pi }$ assignment for the former is consistent with that in the literature, whereas the latter is in contradiction to the previous assignment (3/2+) based on the $^{9}$Be(t,p)$^{11}$Be$^{\ast }$ reaction data.