Proton capture on ${}^{30}\mathrm{P}$ in novae: On the existence of states at 6.40 MeV and 6.65 MeV in ${}^{31}\mathrm{S}$

We use a high-resolution ${}^{32}\mathrm{S}(d,t)$ measurement to investigate the claimed existence of a 6401(3) keV state in ${}^{31}\mathrm{S}$ that may affect the ${}^{30}\mathrm{P}(p,\gamma )$ nuclear reaction rate in oxygen-neon (ONe) novae. Our data are shown to exclude the null hypothesis—that the state does not exist—with high significance. Additionally, the data also suggest the existence of a hitherto unreported state at 6648(4) keV. This state corresponds to a ${}^{30}\mathrm{P}(p,\gamma )$ resonance at 517(4) keV, located below the higher edge of the Gamow window for peak nova temperatures of about 0.4 GK.

Figure 1

${}^{32}\mathrm{S}(d,t)$ spectrum at ${\theta }_{\mathrm{lab}}={55}^{\circ }$. This histogrammed spectrum was rebinned by a factor of 3, only for visualization purposes. The purported 6401-keV state in ${}^{31}\mathrm{S}$ is labeled in red. The 6648-keV state is a new level reported in this work. Nominal values for the other states are taken from Ref. [23].

Figure 2

Left panel: Fit results for the ${55}^{\circ }$ data assuming the null hypothesis, which does not include a state at 6401 keV. The FWHMs of these peaks were constrained as described in the text. Right panel: A similar fit to the same data assuming that an additional state exists in the 6400-keV region.

Figure 3

Histogrammed distribution of $f\left(q_0\right|0)$ obtained from ${10}^5$ synthetic data sets, under the assumption of the background-only hypothesis $\left(H_0\right)$ for the ${55}^{\circ }$ data. The experimental value is $q_{0,\mathrm{obs}}=123.8$.

Figure 4

Fits to the ${45}^{\circ }$ data, compared similarly as in Fig. 2.

Figure 5

Fit results in the 6636-keV region. Left panel: Assuming a single peak corresponding to the 6636-keV state (the null hypothesis). Right panel: On including an additional peak corresponding to $E_x\approx 6648$ keV (the alternative hypothesis).

Figure 6

Calculated ${}^{30}\mathrm{P}(p,\gamma )$ reaction rates for the two resonances discussed in this work, at $E_r=270$ keV and $E_r=517$ keV. For comparison, we also show the contribution of the important 259-keV resonance reported in Refs. [8, 9]. Although the $\omega \gamma$ for this resonance is reported with 60% relative uncertainty [8], we evaluate the rate using its central value. We forgo uncertainty bands in this plot because of the reasons specified in Ref. [45]. The total reaction rate is for all significant resonances, obtained using the shell model results from Refs. [46, 47] when experimental information was lacking.