Measurement of the ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ cross section at $E_{\mathrm{c}.\mathrm{m}.}\approx 2.1–5.3\mathrm{MeV}$

Background: The ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction plays an important role as the trigger reaction for the x-ray burst.

Purpose: The direct measurement of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ was made for studying the resonant states in ${}^{18}\mathrm{Ne}$ and determining the reaction rate of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ at astrophysical temperatures.

Methods: The differential cross section of the ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction was measured using a 2.5-MeV/u ${}^{14}\mathrm{O}$ radioactive beam and the thick target method in inverse kinematics. Three sets of $\mathrm{\Delta }E-E$ Si telescopes were installed and coincidence measurements were performed. We analyzed single-proton decay events using the time-of-flight (TOF) information of the recoiling protons.

Results: The excitation function of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ was acquired for excitation energies between 7.2 and 10.4 MeV in ${}^{18}\mathrm{Ne}$ by considering the two channels which decay to the ground state and first excited state of ${}^{17}\mathrm{F}$. Several new, as well as previously known, states in ${}^{18}\mathrm{Ne}$ were observed and their resonance parameters were extracted from $R$-matrix analysis. The contributions of four resonances over the excitation energy range, $7<E_x<8.2\mathrm{MeV}$, to the ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}$ reaction rate were calculated.

Conclusions: We observed very strong single-proton decay events, but did not observe strong double-proton decay events as in a previous study by Fu et al. The reaction rates contributed by the 7.35-, 7.58-, and 7.72-MeV states were estimated to be dominant at temperatures $T_9>2$. Among these three states, the 7.35-MeV state was found to enhance the reaction rate by a factor of 10 greater than the other two resonance states.

Figure 1

Schematic view of the experimental setup.

Figure 2

Secondary beam identification. The $y$ axis and $x$ axis represent TOFs between two PPACs and RF time (the timing between F0 and F3), respectively.

Figure 3

Particle identification in $\mathrm{\Delta }E-E$ telescope.

Figure 4

Geometrical efficiency which the present detector system detects two protons simultaneously (dotted line) and the efficiency for detecting the single proton (solid line).

Figure 5

Energy distribution of single- and double-proton events. The $x$ axis represents the energy summation of the $\mathrm{\Delta }E-E$ detector.

Figure 6

Threshold energy of $p$ decay, $2p$ decay, and $\alpha$ and the energy level of ${}^{18}\mathrm{Ne}$. Several excited levels are also shown with the excitation energies.

Figure 7

TOF between the PPAC and the central telescope plotted against the energy of protons. The upper panel represents the experimental data and the lower panel shows the simulation results at zero degrees.

Figure 8

Proton spectra of $p_2-p_3$, when all the protons go to the second state (solid line) and third state (dotted line) of ${}^{17}\mathrm{F}$.

Figure 9

Fitted curves of excitation function of ${}^{14}\mathrm{O}(\alpha ,p){}^{17}\mathrm{F}_{\mathrm{g}.\mathrm{s}.}$ with 10 different $J^{\pi }$ combinations in $7<E_x<8.2$ MeV. The resonance at $E_x=8.10$ MeV was fixed with $0^{+}$. The solid line in the bottom figure represents the best fitted curve.

Figure 10

Reaction rates contributed by four resonances observed in this study, 6.15- and 7.05-MeV states. The resonant parameters of 6.15- and 7.05-MeV states were adopted from Refs. [23] and [3], respectively.

Figure 11

Excitation function of ${}^{14}\mathrm{O}(\alpha ,p_0){}^{17}\mathrm{F}_{\mathrm{g}.\mathrm{s}.}$ with eight different $J^{\pi }$ assignments in $E_x>8$ MeV. The solid line in the bottom figure represents the best fitted curve.