Shell-model studies of the astrophysical $rp$-process reactions ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ and ${}^{34g,m}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$

Background: Dust grains condensed in the outflows of presolar classical novae should have been present in the protosolar nebula. Candidates for such presolar nova grains have been found in primitive meteorites and can in principle be identified by their isotopic ratios, but the ratios predicted by state-of-the-art one-dimensional hydrodynamic models are uncertain due to nuclear-physics uncertainties.

Purpose: To theoretically calculate the thermonuclear rates and uncertainties of the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ and ${}^{34g,m}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$ reactions and investigate their impacts on the predicted ${}^{34}\mathrm{S}/{}^{32}\mathrm{S}$ isotopic ratio for presolar nova grains.

Method: A shell-model approach in a ($0+1$) $\hslash \omega$ model space was used to calculate the properties of resonances in the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ and ${}^{34g,m}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$ reactions and their thermonuclear rates. Uncertainties were estimated using a Monte Carlo method. The implications of these rates and their uncertainties on sulfur isotopic nova yields were investigated using a postprocessing nucleosynthesis code. The rates for transitions from the ground state of ${}^{34}\mathrm{Cl}$ as well as from the isomeric first excited state of ${}^{34}\mathrm{Cl}$ were explicitly calculated.

Results: At energies in the resonance region near the proton-emission threshold, many negative-parity states appear. Energies, spectroscopic factors, and proton-decay widths are reported. The resulting thermonuclear rates are compared with previous determinations.

Conclusions: The shell-model calculations alone are sufficient to constrain the variation of the ${}^{34}\mathrm{S}/{}^{32}\mathrm{S}$ ratios to within about 30%. Uncertainties associated with other reactions must also be considered, but in general we find that the ${}^{34}\mathrm{S}/{}^{32}\mathrm{S}$ ratios are not a robust diagnostic to clearly identify presolar grains made from nova ejecta.

Figure 1

Experimental spectroscopic factors, ${\mathrm{C}}^2{\mathrm{S}}^{+}=(2J_f+1){\mathrm{C}}^2\mathrm{S}$, for single-proton transfer on the target ${}^{34}\mathrm{S}$. The results below 5.8 MeV are from Ref. [19], and the results from 6.2 to 7.4 MeV are from Ref. [7]. The dotted line shows the value of the proton separation energy.

Figure 2

Theoretical spectroscopic factors, ${\mathrm{C}}^2{\mathrm{S}}^{+}=(2J_f+1){\mathrm{C}}^2\mathrm{S}$, for single-proton transfer on the target ${}^{34}\mathrm{S}$. The states with $T=3/2$ are indicated by a cross on top. The dotted line shows the value of the proton separation energy.

Figure 3

Spectroscopic factors, ${\mathrm{C}}^2{\mathrm{S}}^{+}$, for $L=0,1$ in the excitation energy region of importance for the reactions rates. For a given spectroscopic factor, $L=0$ is about a factor of 10 stronger than $L=1$ in the reaction rate due to the smaller centrifugal barrier. For this reason, the values for $L=0$ have been multiplied by 10 to show their relative importance to $L=1$. The bottom panel shows the theoretical values for ${}^{34}\mathrm{S}$ to ${}^{35}\mathrm{Cl}$. The peaks are labeled by their order in the excitation energy spectrum. The middle panel shows the experiment values from Ref. [19] for $E_x<5.8$ MeV and from Refs. [7] and [8] for $E_x>6.3$ MeV. Experimental results are not known for the region between 5.8 and 6.3 MeV. The line at 6.8 MeV labeled by a down arrow is given in Ref. [8] by ${\mathrm{C}}^2{\mathrm{S}}^{+}<4$. The arrows at the bottom show the range of excitation energy important for the ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ reaction starting at $S_p=6.371$ MeV, and the ${}^{34g}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$ starting at $S_p=5.896$ MeV in the mirror nucleus ${}^{35}\mathrm{Ar}$. The upper panel shows the spectroscopic factors for ${}^{34m}\mathrm{Cl}\left(3^{+}\right)(p,\gamma ){}^{35}\mathrm{Ar}$. The arrow starting at $S_p=6.042$ MeV shows the range of excitation energy of importance for that reaction. These spectroscopic factors lead to a reaction rate for ${}^{34m}\mathrm{Cl}\left(3^{+}\right)(p,\gamma ){}^{35}\mathrm{Ar}$ that is about a factor of 4 larger than that for ${}^{34g}\mathrm{Cl}(0^{+}$)($p,\gamma ){}^{35}\mathrm{Ar}$ in the region around $T9=0.2$ GK.

Figure 4

Top panel: The calculated reaction rate for ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ vs temperature $T9$ (GK). The upper and lower black lines show the low and high rates obtained from the Monte Carlo calculations. The middle black line shows the rate obtained directly from the input in Table 1. The results from positive parity states only are shown by the red dots. Bottom panel: The contribution of individual resonances in Table 1.

Figure 5

The calculated reaction rates for ${}^{34}\mathrm{S}(p,\gamma ){}^{35}\mathrm{Cl}$ compared with the rate [8] based on experimental data from Ref. [7] and the Hauser-Feshbach rate from Ref. [21].

Figure 6

Top panel: The calculated reaction rates for ${}^{34g}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$ vs temperature $T9$ (GK). The upper and lower black lines show the low and high rates obtained from the Monte Carlo calculations. The middle black line shows the rate obtained directly from the input in Table 2. The results from positive-parity states only are shown by the red dots. The results are compared to the Hauser-Feshbach rate from Ref. [21]. Bottom panel: The contribution of individual resonances in Table 2.

Figure 7

Top panel: The calculated reaction rates for ${}^{34m}\mathrm{Cl}(p,\gamma ){}^{35}\mathrm{Ar}$ vs temperature $T9$ (GK). The upper and lower black lines show the low and high rates obtained from the Monte Carlo calculations. The middle black line shows the rate obtained directly from the input in Table 3. The results from positive-parity states only are shown by the red dots. The results are compared to the Hauser-Feshbach rate from Ref. [21]. Bottom panel: The contribution of individual resonances in Table 3.