Figure 1

Energy level scheme for the ${}^{19}\mathrm{F}$($\alpha ,p$)${}^{22}\mathrm{Ne}$ reaction. The entrance channel ($\alpha {+}^{19}$F) has a threshold of 10.47 MeV with respect to the ground state of ${}^{23}\mathrm{Na}$. The compound state can decay either via the $p_0$ channel to the ground state of ${}^{22}\mathrm{Ne}$ or by the $p_1$ channel to the first excited state of ${}^{22}\mathrm{Ne}$. The subsequent emission of a 1.27-MeV photon from the decay of the first excited state ($2^{+}$) to the ground state ($0^{+}$) of ${}^{22}\mathrm{Ne}$ can also be observed. The dark rectangle above ${}^{23}\mathrm{Na}$ represents the energy region studied in this work. White regions above and below it correspond to energies where the cross sections were extrapolated.Reuse & Permissions

Figure 2

Proton spectra for ${}^{19}\mathrm{F}$($\alpha ,p$)${}^{22}\mathrm{Ne}$ at ${135}^{°}$ for three beam energies (label at the right upper corner of each box). The upper spectrum shows both proton groups at the reference resonance. Both peaks appear clean of background and are easy to identify. The spectrum at $E_{\mathrm{lab}}=1100$ keV shows two groups of protons, still well isolated from the background. Finally, a spectrum at $E_{\mathrm{lab}}=792$ keV, where no proton groups were positively identified is shown. The integrated charges are (in μC) 1981, 180647, and 519252, respectively.Reuse & Permissions

Figure 3

Experimental yield curves for the ${}^{19}\mathrm{F}$($\alpha ,p_0$)${}^{22}\mathrm{Ne}$ channel and the $R$-matrix fits (solid lines). Different curves are offset by a factor of 100. Vertical axis units are relative yields. The labels to the right of each curve are described in Table .Reuse & Permissions

Figure 4

Experimental yield curves for the ${}^{19}\mathrm{F}$($\alpha ,p_1$)${}^{22}\mathrm{Ne}$ channel and the $R$-matrix fits (solid lines). Different curves are offset by a factor of 100. Vertical axis units are relative yields. The labels to the right of each curve are described in Table .Reuse & Permissions

Figure 5

Calculation of error bars. (a) Bootstrap histogram used to compute the error bars with a 95% confidence level. The horizontal axis corresponds to the raw ${\chi }^2$ value associated to the set of central-value parameters. Each bin contains intervals $\Delta {\chi }^2=20$. A total of 40 000 subsets were sampled from the experimental set with a Monte Carlo method. Note that the curve does not correspond to a normal distribution. However, the centroid corresponds to the raw value of ${\chi }^2$ associated to the best $R$-matrix fit (${\chi }_{\min }^2=20,535$). An area corresponding to 95% of the total integral is below ${\chi }_{95}^2=22,774$ (vertical line). (b) Sample ${\chi }^2$ vs. parameter value (γ) curve. The horizontal line represents ${\chi }_{95}^2$, whereas the dotted vertical lines are, from left to right, the lower limit, central value, and upper limit of the parameter, respectively. An equivalent curve was generated for each of the formal parameters.Reuse & Permissions

Figure 6

$R$-matrix calculated total cross sections for ${}^{19}\mathrm{F}$($\alpha ,p$)${}^{22}\mathrm{Ne}$. Both ${}^{19}\mathrm{F}$($\alpha ,p_0$)${}^{22}\mathrm{Ne}$ (upper panel) and ${}^{19}\mathrm{F}$($\alpha ,p_1$)${}^{22}\mathrm{Ne}$ (lower panel) curves are shown with uncertainty bands, as computed by sampling the 95% confidence interval nuclear parameter space with a Monte Carlo method. The strong oscillations in the upper and lower limits of the bands are an artifact of the finite number of samples (10 000) taken with the Monte Carlo method.Reuse & Permissions

Figure 7

The experimentally determined ${\gamma }_{\alpha }^2$ as a function of center-of-mass energy, presented in sets of $J^{\pi }$.Reuse & Permissions

Figure 8

Monte Carlo simulated low energy $S$ factor for ${}^{19}\mathrm{F}$($\alpha ,p$)${}^{22}\mathrm{Ne}$ for three different sample resonance interference assumptions.Reuse & Permissions

Figure 9

The new rate for the ${}^{19}\mathrm{F}$($\alpha ,p$)${}^{22}\mathrm{Ne}$ reaction compared to the phenomenological rate listed in the literature (CF88) [8], the Hauser-Feshbach predictions, and Lugaro et al.'s [13] rate.Reuse & Permissions