<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> -delayed neutron spectroscopy of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>In</mml:mi><mml:mprescripts /><mml:none /><mml:mn>133</mml:mn></mml:mmultiscripts></mml:math>

The decay properties of $^{133}$In were studied in detail at the ISOLDE Decay Station (IDS). The implementation of the Resonance Ionization Laser Ion Source (RILIS) allowed separate measurements of its $9/2^+$ ground state ($^{133g}$In) and $1/2^-$ isomer ($^{133m}$In). With the use of $\beta$-delayed neutron and $\gamma$ spectroscopy, the decay strengths above the neutron separation energy were quantified in this neutron-rich nucleus for the first time. The allowed Gamow-Teller transition $9/2^+\rightarrow7/2^+$ was located at 5.92 MeV in the $^{133g}$In decay with a logft = 4.7(1). In addition, several neutron-unbound states were populated at lower excitation energies by the First-Forbidden decays of $^{133g,m}$In. We assigned spins and parities to those neutron-unbound states based on the $\beta$-decay selection rules, the logft values, and systematics.