Resonances just above the proton threshold in ${}^{30}\mathrm{S}$ affect the ${}^{29}\mathrm{P}{(p,\gamma )}^{30}\mathrm{S}$ 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 ${}^{30}\mathrm{S}$. The widths are determined from the $\beta$2$p$- and $\beta$$p$$\gamma$-decay of ${}^{31}\mathrm{Ar}$, which is produced at the ISOLDE radioactive ion beam facility at the European research organization CERN. Experimental limits on the ratio between the proton and $\gamma$ partial widths for astrophysical relevant levels in ${}^{30}\mathrm{S}$ have been found for the first time. A level at $4689.2\left(24\right)\mathrm{keV}$ 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 $5227\left(3\right)\mathrm{keV}$ and $5847\left(4\right)\mathrm{keV}$ 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.

• Received 11 March 2013

DOI:https://doi.org/10.1103/PhysRevC.87.055808