Background: The uncertainty in the ${}^{29}$P($p,\gamma$)${}^{30}$S reaction rate over 0.1 $\le$ $T$ $\le$ 1.3 GK was previously determined to span approximately four orders of magnitude due to the uncertain location of two previously unobserved 3${}^{+}$ and 2${}^{+}$ resonances in the $E_x=4.7$–4.8 MeV region in ${}^{30}$S. Therefore, the abundances of silicon isotopes synthesized in novae, which are relevant for the identification of presolar grains of putative nova origin, were uncertain by a factor of 3.

Purpose: (a) To investigate the level structure of ${}^{30}$S above the proton threshold [4394.9(7) keV] via charged-particle spectroscopy using the ${}^{32}$S($p,t$)${}^{30}$S reaction and in-beam $\gamma$-ray spectroscopy using the ${}^{28}$Si(${}^3$He, $n\gamma$)${}^{30}$S reaction to calculate the ${}^{29}$P($p,\gamma$)${}^{30}$S reaction rate. (b) To explore the impact of this rate on the abundances of silicon isotopes synthesized in novae.

Methods: Differential cross sections of the ${}^{32}$S($p,t$)${}^{30}$S reaction were measured at 34.5 MeV. Distorted-wave Born approximation calculations were performed to constrain the spin-parity assignments of the observed levels, including the two astrophysically important levels. An energy-level scheme was deduced from $\gamma$-$\gamma$ coincidence measurements using the ${}^{28}$Si(${}^3$He, $n\gamma$)${}^{30}$S reaction. Spin-parity assignments based on measurements of $\gamma$-ray angular distributions and $\gamma$-$\gamma$ directional correlation from oriented nuclei were made for most of the observed levels of ${}^{30}$S.

Results: The resonance energies corresponding to the states with 4.5 MeV $\lesssim$ $E_x$ $\lesssim$ 6 MeV, including the two astrophysically important states predicted previously, are measured with significantly better precision than before. The spin-parity assignments of both astrophysically important resonances are confirmed. The uncertainty in the rate of the ${}^{29}$P($p,\gamma$)${}^{30}$S reaction is substantially reduced over the temperature range of interest. Finally, the influence of this rate on the abundance ratios of silicon isotopes synthesized in novae are obtained via 1D hydrodynamic nova simulations.

Conclusions: The uncertainty in the ${}^{29}$P($p,\gamma$)${}^{30}$S reaction rate is reduced to the point that it no longer affects the silicon isotopic abundance ratios significantly, and, thus, the results of our nova hydrodynamic simulation for the nucleosynthesis in the Si-Ca mass region are more reliable than before.

• Received 3 October 2012

DOI:https://doi.org/10.1103/PhysRevC.87.065801