Thermonuclear reaction rate of ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ from Monte Carlo calculations

The ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ reaction impacts the break-out from the hot CNO cycles to the $rp$ process in type-I x-ray bursts. We present a revised thermonuclear reaction rate, which is based on the latest experimental data. The new rate is derived from Monte Carlo calculations, taking into account the uncertainties of all nuclear physics input quantities. In addition, we present the reaction rate uncertainty and probability density versus temperature. Our results are also consistent with estimates obtained using different indirect approaches.

Figure 1

Level scheme of the compound nucleus ${}^{22}\mathrm{Mg}$ (b) with the ${}^{18}\mathrm{Ne}+\alpha$ (a) and ${}^{21}\mathrm{Na}+p$ (c) thresholds (approximately to scale). The energies are given in MeV. The energy range of the classical Gamow window is indicated for three temperatures, $T_9=1.0$, 1.5, and 2.0 by red arrows.

Figure 2

Astrophysical S factor of the ${}^{18}\mathrm{Ne}{(\alpha ,p)}^{21}\mathrm{Na}$ reaction versus center-of-mass energy $E$, calculated from the resonance properties listed in Table 1 (thick red line). For comparison (dashed blue line), Ref. [4], so-called reference (for details see [4]); (dash-dotted green line) Hauser-Feshbach statistical model, taken from [33]. The experimental data points shown are derived from the reverse ${}^{21}\mathrm{Na}(p,\alpha ){}^{18}\mathrm{Ne}$ reaction [7, 8] and represent the ground-state contribution ${}^{18}{\mathrm{Ne}}_{\mathrm{g}.\mathrm{s}.}(\alpha ,p){}^{21}{\mathrm{Na}}_{\mathrm{g}.\mathrm{s}.}$ only. The contributions of the two resonances at 1400 and 1567 keV are shown with dashed and dash-dotted dark-red lines, respectively. The total widths $\Gamma$ are indicated by horizontal dark-red arrows. See the text.

Figure 3

Ratio between the reaction rate $N_A\langle \sigma v\rangle$ from different studies normalized to the reference rate $N_A{\langle \sigma v\rangle }_{\mathrm{ref}}$ from [4]. The conversion of the experimental data from the reverse ${}^{21}\mathrm{Na}(p,\alpha ){}^{18}\mathrm{Ne}$ reaction to the shown $N_A\langle \sigma v\rangle$ data points is explained in [4]. The line “Salter average” marks the average result from [7] (ground-state contribution only), “Salter average $\left(\times 3\right)$” corrects for contributions of excited states (for details, see [4, 7]). The new result (thick red line) and its uncertainties (thin red lines) are close to the previous recommendation which is $0.55 N_A{\langle \sigma v\rangle }_{\mathrm{ref}}$ [4] (dark gray bar). A theoretical prediction in the statistical model is also shown (green dash-dotted) [33]. For further discussion, see text.

Figure 4

Same as Fig. 3, but with the additional uncertainty from the spin assignments $J^{\pi }$ in Table 2. The new reaction rate $N_A\langle \sigma v\rangle$ using variable $J^{\pi }$ assignments is slightly higher than the first calculation with fixed $J^{\pi }$ in Fig. 3 but remains close to the previous recommendation which is $0.55 N_A{\langle \sigma v\rangle }_{\mathrm{ref}}$ [4] (dark gray bar).

Figure 5

Contributions of individual resonances to the reaction rate $N_A\langle \sigma v\rangle$. Only few resonances contribute significantly to $N_A\langle \sigma v\rangle$ in the most important temperature range around $T_9=$ 0.5–2. The black dashed line corresponds to the total contribution of all other resonances not explicitly displayed in the plot.

Figure 6

Reaction rate $N_A\langle \sigma v\rangle$ for a $0^{+}$ resonance with ${\theta }_{\alpha }^2=0.46$ in ${}^{22}\mathrm{Mg}$ as a function of resonance energy $E$ for three temperatures $T_9=1.0$ (a), 1.5 (b), and 2.0 (c) (from top to bottom). The data point indicates $E=1567$ keV which was assigned as a mirror of the $0^{+}$ state in ${}^{22}\mathrm{Ne}$ at $E^{*}=10052$ keV. The arrows indicate the position of the usual Gamow window. For further discussion see text.