The $^{30}$P($p,\gamma$)$^{31}$S reaction rate is critical for modeling the final elemental and isotopic abundance of ONe nova nucleosynthesis, the calibration of proposed nova thermometers, and the identification of presolar nova candidate grains. Unfortunately, the rate is essentially unconstrained experimentally, despite numerous studies using a variety of experimental techniques, largely due to uncertainties in the spins and parities of the narrow, isolated $^{31}$S proton capture resonance states that likely govern the proton capture reaction rate.The beta decay of $^{31}$}Cl, which preferentially populates important $l = 0$ $^{30}$P proton capture resonances in $^{31}$S, is a useful tool for studying the properties of these states. Using an accelerated beam of $^{31}$Cl, we have observed the beta-delayed gamma decay of a number of $^{31}$S states up to excitation energy $E_x = 7200$, including states within the $^{30}$P($p,\gamma$)$^{31}$S Gamow window for peak nova temperatures. Herein we report the results of this study, including: the production of a $^{31}$Cl beta decay scheme with over twice as many $^{31}$S gamma transitions as the most recent literature scheme; the observation of isospin mixing of a resonance with isospin $T = 1/2$ at $E_x = 6390.2(7)$ keV with the nearby $T = 3/2$ $^{31}$S isobaric analog state (IAS), giving it an unambiguous spin and parity of $3/2^+$; and the clear identification of the second $T = 3/2$ $^{31}$S state and the results of several tests of the isobaric multiplet mass equation for both the lowest and second-lowest $A = 31, T = 3/2$ quartets.
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