Revised result for the ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate for astrophysical rp-process calculations

The ${}^{32}\mathrm{Cl}$(p,γ)${}^{33}\mathrm{Ar}$ reaction rate is of potential importance in the rp process powering type I x-ray bursts. Recently, Clement et al. [Phys. Rev. Lett. 92, 172502 (2004)] [1] presented new data on excitation energies for low-lying proton unbound states in ${}^{33}\mathrm{Ar}$ obtained with a new method developed at the National Superconducting Cyclotron Laboratory. We use their data, together with a direct capture model and a shell model calculation, to derive a new reaction rate for use in astrophysical model calculations. In particular, we take into account capture on the first excited state in ${}^{32}\mathrm{Cl}$, and we also present a realistic estimate of the remaining uncertainties. We find that the ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate is dominated entirely by capture on the first excited state in ${}^{32}\mathrm{Cl}$ over the whole temperature range relevant in x-ray bursts. In the temperature range from 0.2 to 1 GK the rate is up to a factor of 70 larger than the previously recommended rate based on shell model calculations only. The uncertainty is now reduced from up to a factor of 1000 to a factor of 3 at 0.3–0.7 GK and a factor of 6 at 1.5 GK.

Figure 1

The contributions of various individual resonances and through direct capture (DC) to the ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate as functions of temperature. In the legend, resonances are labeled with their excitation energy in ${}^{33}\mathrm{Ar}$. The upper panel shows contributions from ground-state capture; the lower panel shows contributions from capture on the first excited state in ${}^{32}\mathrm{Cl}$ in each case weighted with the relative population of the respective target state. In addition, both panels show the same total ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate for comparison. Contributions from ground-state capture via the 3.36-MeV resonance and from capture on the first excited state via the 3.46-MeV resonance are too small to appear in this graph.

Figure 2

Total ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate from this work (solid area) and previous shell model rate without experimental data (hatched area). The width of the area reflects the estimated uncertainty.

Figure 3

Ratio of the ${}^{32}\mathrm{Cl}$($p,\gamma$)${}^{33}\mathrm{Ar}$ reaction rate of this work to the rate calculated by Herndl et al. [14].

Figure 4

Stellar enhancement factor derived in this work (solid line) and from the statistical model code NON-SMOKER (dashed line).