The ${}^{18}$Ne($\alpha$,$p$)${}^{21}$Na breakout reaction in x-ray bursts: Experimental determination of spin-parities for $\alpha$ resonances in ${}^{22}$Mg via resonant elastic scattering of ${}^{21}$Na+$p$

The ${}^{18}$Ne($\alpha$,$p$)${}^{21}$Na reaction provides a pathway for breakout from the hot CNO cycles to the $rp$ process in type-I x-ray bursts. To better determine this astrophysical reaction rate, the resonance parameters of the compound nucleus ${}^{22}$Mg have been investigated by measuring the resonant elastic scattering of ${}^{21}$Na+$p$. An 89 MeV ${}^{21}$Na radioactive ion beam was produced at the CNS Radioactive Ion Beam Separator and bombarded an 8.8 mg/cm${}^2$ thick polyethylene target. The recoiled protons were measured at scattering angles of ${\theta }_{\mathrm{c}.\mathrm{m}.}\approx 175{}^{\circ }$ and 152${}^{\circ }$ by three $\Delta E$-$E$ silicon telescopes. The excitation function was obtained with a thick-target method over energies $E_x$(${}^{22}$Mg) = 5.5–9.2 MeV. The resonance parameters have been determined through an $R$-matrix analysis. For the first time, the $J^{\pi }$ values for ten states above the $\alpha$ threshold in ${}^{22}$Mg have been experimentally determined in a single consistent measurement. We have made three new $J^{\pi }$ assignments and confirmed seven of the ten tentative assignments in the previous work. The ${}^{18}$Ne($\alpha$,$p$)${}^{21}$Na reaction rate has been recalculated, and the astrophysical impact of our new rate has been investigated through one-zone postprocessing x-ray burst calculations. We find that the ${}^{18}$Ne($\alpha$,$p$)${}^{21}$Na rate significantly affects the peak nuclear energy generation rate and the onset temperature of this breakout reaction in these phenomena.

Figure 1

Experimental center-of-mass differential cross section for resonant elastic scattering of ${}^{21}$Na+$p$ at a scattering angle of ${\theta }_{\mathrm{c}.\mathrm{m}.}$$\approx$175${}^{\circ }$. It also shows a best overall $R$-matrix fit.

Figure 2

Sample $R$-matrix fitting results for some resonances above $\alpha$ threshold. The (red) thicker lines represent the best fits. The relevant channel spin $s$ and orbital angular momentum $\ell$ values are indicated.

Figure 3

Ratios between the present rate and previous ones (Görres 1995 [14], Chen 2011 [15], Chae 2009 [20], He 2009 [22], Matic 2009 [18], Mohr 2013 [19], and statistical-model calculation HF 2000 [46]).

Figure 4

Nuclear energy generation rates during one-zone XRB calculations using the K04 thermodynamic history [47]. Results using the present rate (black solid line), the Chae et al. 2009 [20] rate (red dashed line) and the Görres et al. 1995 [14] rate (blue dotted line) are indicated.