$\alpha$-unbound levels in ${}^{34}\mathrm{Ar}$ from ${}^{36}\mathrm{Ar}(p,t){}^{34}\mathrm{Ar}$ reaction measurements and implications for the astrophysical ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ reaction rate

The ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ reaction has been identified in several type-1 x-ray burst (XRB) sensitivity studies as a significant reaction within the $\alpha p$ process, possibly influencing not only the abundances of burst ashes but also the bolometric shape of double-peaked light curves coming from certain XRB systems. Given the dearth of experimental data on the ${}^{30}\mathrm{S}(\alpha ,p)$ ${}^{33}\mathrm{Cl}$ reaction at burst temperatures, we have performed high energy-resolution forward-angle ${}^{36}\mathrm{Ar}(p,t){}^{34}\mathrm{Ar}$ measurements in order to identify levels in ${}^{34}\mathrm{Ar}$ that could appear as resonances in the ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ reaction. Energies of levels identified in this work, along with model-based assumptions for spin assignments and spectroscopic factors, were then used to determine a rate for the ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ reaction based on a narrow-resonance formalism. The rates determined in this work are then compared with two standard Hauser-Feshbach model predictions over a range of XRB temperatures.

Figure 1

${}^{34}\mathrm{Ar}$ spectra as seen in the focal plane of the Grand Raiden spectrograph at ${\theta }_{\text{lab}}=0^{\circ }$ for two different magnetic field settings [panels (a) and (b)]. With these two magnetic field settings a full energy region from the g.s. to 11 MeV in excitation energy is covered in ${}^{34}\mathrm{Ar}$. Both spectra shown have been gated on energy loss and time of flight. Additionally, an empty gas cell spectrum has been included (normalized to the ${}^{10}\mathrm{C}$ g.s peak located at $\sim 5.3$ MeV) to show possible sources of contamination peaks. Each peak has been labeled according to whether it has been identified as background (red online), has been observed in previous works (blue online), or has been observed for the first time in this work (orange online). Additional spectra were recorded at ${\theta }_{\text{lab}}=8^{\circ }$ and ${11}^{\circ }$ to help separate background peaks from peaks of interest in ${}^{34}\mathrm{Ar}$.

Figure 2

Calculated proton particle widths in the ${}^{33}\mathrm{Cl}+p$ system as a function of center-of-mass energy, for a given range of orbital angular momenta, $\ell =0–4$. A proton center-of-mass energy range of 3.2–6 MeV approximately corresponds to an excitation energy range of 7.8–10.6 MeV in ${}^{34}\mathrm{Ar}$.

Figure 3

Spin distributions for selected excitation energies in ${}^{34}\mathrm{Ar}$ based on the BSFG parameters used in talys 1.8. [38].

Figure 4

(a) $\alpha$-spectroscopic factors for states in ${}^{34}\mathrm{Ar}$ calculated using the shell model as described in [44] (shown in gray), along with the mapped values to states observed in this work (overlaid). (b) Level density of observed states in ${}^{34}\mathrm{Ar}$ from this work and previous works.

Figure 5

(a) The two median ${}^{30}\mathrm{S}(\alpha ,p){}^{33}\mathrm{Cl}$ reaction rates as a function of stellar temperature calculated in this work, median rate 1 (non-$\alpha$ clustering) and median rate 2 (with $\alpha$ clustering), along with statistical model calculated rates, non-smoker${}^{\mathrm{WEB}}$ v5.0w and talys 1.8. (b) All rates are normalized to the non-smoker${}^{\mathrm{WEB}}$ v5.0w rate.