Experimental study on the $\beta$- strength function in the decay of neutron-rich $^{133}$In

An experimental work has been recently conducted at the ISOLDE decay station (IDS), to study the neutron-unbound states in $^{133}$Sn following the beta decays of $^{133}$In. The main decay strength of $Z<50$ and $N>82$ nuclei is anticipated to be the Gamow-Teller transition transforming a deeply bound $g_{7/2}$ neutron into a $g_{9/2}$ proton. In addition, first-forbidden transitions are postulated to take noticeable strength feeding lower-lying states. In order to examine these highly excited states above neutron separation energy, the neutron time-of-flight array, VANDLE, was installed at IDS to measure $\beta$-delayed neutron-emission energies. In this contribution, we will discuss our latest results regarding the excitation energies, branching ratios, and log-ft of a series of neutron unbound states observed in the $^{133}$In decay. To gain insights into the microscopic configurations of those states and the strength distribution in $^{133}$Sn, we carried out a large-scale shell-model calculation, of which the result and its comparison with experimental data will also be presented.