Proton and $\gamma$- partial widths of astrophysically important states of $^{30}$S studied by the $\beta$-delayed decay of $^{31}$Ar

Resonances just above the proton threshold in $^{30}$S affect the $^{29}$P$(p,\gamma)^{30}$S reaction under astrophysical conditions. The ($p,\gamma$)-reaction rate is currently determined indirectly and depends on the properties of the relevant resonances. We present here a method for finding the ratio between the proton- and $\gamma$- partial widths of resonances in $^{30}$S. The widths are determined from the $\beta -2p$ and $\beta -p-\gamma$-decay of $^{31}$Ar, which is produced at ISOLDE, CERN. Experimental limits on the ratio between the proton- and $\gamma$- partial widths for astrophysical relevant levels in $^{30}$S have been found for the first time. A level at 4689.2(24)keV is identified in the $\gamma$-spectrum, and an upper limit on the $\Gamma_{p}/\Gamma_{\gamma}$ ratio of 0.26 (95% C.L.) is found. In the two-proton spectrum two levels at 5227(3)keV and 5847(4)keV are identified. These levels were previously seen to $\gamma$-decay and upper limits on the $\Gamma_{\gamma}/\Gamma_{p}$ ratio of 0.5 and 9, respectively, (95% C.L.) are found, where the latter differs from previous calculations.