Isospin Mixing Reveals $^{30}$P($p,\gamma$)$^{31}$S Resonance Influencing Nova Nucleosynthesis

The thermonuclear $^{30}$P($p,\gamma$)$^{31}$S reaction rate is critical for modeling the final elemental and isotopic abundances of ONe nova nucleosynthesis, which affect the calibration of proposed nova thermometers and the identification of presolar nova grains, respectively. Unfortunately, the rate of this reaction is essentially unconstrained experimentally, because the strengths of key $^{31}$S proton capture resonance states are not known, largely due to uncertainties in their spins and parities. Using the $\beta$ decay of $^{31}$Cl, we have observed the $\beta$-delayed $\gamma$ decay of a $^{31}$S state at $E_x = 6390.2(7)$ keV, with a $^{30}$P($p,\gamma$)$^{31}$S resonance energy of $E_r = 259.3(8)$ keV, in the middle of the $^{30}$P($p,\gamma$)$^{31}$S Gamow window for peak nova temperatures. This state exhibits isospin mixing with the nearby isobaric analog state (IAS) at $E_x = 6279.0(6)$ keV, giving it an unambiguous spin and parity of $3/2^+$ and making it an important $l = 0$ resonance for proton capture on $^{30}$P.