Examination of the role of the ${}^{14}\mathrm{O}\left(\alpha ,p\right){}^{17}\mathrm{F}$ reaction rate in type-I x-ray bursts

The ${}^{14}\mathrm{O}\left(\alpha ,p\right){}^{17}\mathrm{F}$ reaction is one of the key reactions involved in the breakout from the hot-CNO cycle to the rp-process in type-I x-ray bursts (XRBs). The resonant properties in the compound nucleus ${}^{18}\mathrm{Ne}$ have been investigated through resonant elastic scattering of ${}^{17}\mathrm{F}+p$. The radioactive ${}^{17}\mathrm{F}$ beam was separated by the Center for Nuclear Study radioactive ion beam separator (CRIB) and bombarded a thick ${\mathrm{H}}_2$ gas target at 3.6 MeV/nucleon. The recoiling light particles were measured by three $\Delta E\text{−}E$ silicon telescopes at laboratory angles of ${\theta }_{\mathrm{lab}}\approx 3{}^{\circ },10{}^{\circ }$, and $18{}^{\circ }$. Five resonances at $E_x=6.15$, 6.28, 6.35, 6.85, and 7.05 MeV were observed in the excitation functions, and their spin-parities have been determined based on an $R$-matrix analysis. In particular, $J^{\pi }=1^{-}$ was firmly assigned to the 6.15-MeV state which dominates the thermonuclear ${}^{14}\mathrm{O}\left(\alpha ,p\right){}^{17}\mathrm{F}$ rate below 2 GK. As well, a possible new excited state in ${}^{18}\mathrm{Ne}$ was observed at $E_x=6.85\pm 0.11$ MeV with tentative $J=0$ assignment. This state could be the analog state of the 6.880 MeV $\left(0{}^{-}\right)$ level in the mirror nucleus ${}^{18}\mathrm{O}$, or a bandhead state $\left(0{}^{+}\right)$ of the six-particle four-hole (6p-4h) band. A new thermonuclear ${}^{14}\mathrm{O}\left(\alpha ,p\right){}^{17}\mathrm{F}$ rate has been determined, and the astrophysical impact of multiple recent rates has been examined using an XRB model. Contrary to previous expectations, we find only a modest impact on predicted nuclear energy generation rates from using reaction rates differing by up to several orders of magnitude.

Figure 1

Schematic diagram of the experimental setup at the scattering chamber, similar to that used in Ref. [49].

Figure 2

(a) Identification plot for the beam particles before the ${\mathrm{H}}_2$ target via the TOF technique. Two groups of particles appear for a single beam, since the data for two extraction cycles of the cyclotron are plotted together. (b) Identification plot for the recoiled particles via the $\Delta E\text{−}E$ technique. See text for details.

Figure 3

The center-of-mass differential cross sections for elastically scattered protons of ${}^{17}\mathrm{F}+p$ at angles of (a) ${\theta }_{\mathrm{c}.\mathrm{m}.}\approx {155}^{\circ }\pm {18}^{\circ }$, and (b) ${\theta }_{\mathrm{c}.\mathrm{m}.}\approx {138}^{\circ }\pm {22}^{\circ }$. The (red or gray) solid curved lines represent the best overall $R$-matrix fits. The locations of inelastic scattering events for the 6.15-MeV state are indicated as the asterisks. The indicated background spectra (from the Ar gas run) was subtracted accordingly. Additional $R$-matrix fits for the 6.15- and 6.85-MeV states are shown in (c) and (d), respectively. See text for details.

Figure 4

Ratios between the present reaction rates and previous calculations [19, 25, 35, 39].

Figure 5

Nuclear energy generation rates during one-zone XRB calculations using the K04 thermodynamic history [22]. Results using the “Present” rates [black line for the lower limit (LL) of “Present−”, grey line for the upper limit (UL) of “Present+”] and the “Hahn−” rates [25] (red dotted line) are indicated. The result with the Wiescher et al. [19] rate is also shown for comparison (labeled as “W87”).