Measurement of ${}^{17}\mathrm{F}$($d,n$)${}^{18}\mathrm{Ne}$ and the impact on the ${}^{17}\mathrm{F}$($p,\gamma$)${}^{18}\mathrm{Ne}$ reaction rate for astrophysics

Background: The ${}^{17}\mathrm{F}(p,\gamma ){}^{18}\mathrm{Ne}$ reaction is part of the astrophysical “hot CNO” cycles that are important in astrophysical environments like novas. Its thermal reaction rate is low owing to the relatively high energy of the resonances and therefore is dominated by direct, nonresonant capture in stellar environments at temperatures below 0.4 GK.

Purpose: An experimental method is established to extract the proton strength to bound and unbound states in experiments with radioactive ion beams and to determine the parameters of direct and resonant capture in the ${}^{17}\mathrm{F}(p,\gamma ){}^{18}\mathrm{Ne}$ reaction.

Method: The ${}^{17}\mathrm{F}(d,n){}^{18}\mathrm{Ne}$ reaction is measured in inverse kinematics using a beam of the short-lived isotope ${}^{17}\mathrm{F}$ and a compact setup of neutron, proton, $\gamma$-ray, and heavy-ion detectors called resoneut.

Results: The spectroscopic factors for the lowest $l=0$ proton resonances at ${\mathrm{E}}_{\mathrm{c}.\mathrm{m}.}=0.60$ and 1.17 MeV are determined, yielding results consistent within $1.4\sigma$ of previous proton elastic-scattering measurements. The asymptotic normalization coefficients of the bound $2_1^{+}$ and $2_2^{+}$ states in ${}^{18}\mathrm{Ne}$ are determined and the resulting direct-capture reaction rates are extracted.

Conclusions: The direct-capture component of the ${}^{17}\mathrm{F}(p,\gamma ){}^{18}\mathrm{Ne}$ reaction is determined for the first time from experimental data on ${}^{18}\mathrm{Ne}$.

Figure 1

Angular kinematics and angular distribution for an $l=0$ proton transfer for the ${}^{17}\mathrm{F}(d,n){}^{18}\mathrm{Ne}^{*}$ reaction in inverse kinematics, populating a state at 4.5-MeV excitation energy. The primary $y$ axis and thin-solid-line graph represent the neutron energy, and the secondary $y$ axis and thick-solid-line graph represent the differential cross section in the laboratory system, as predicted by a coupled-reaction-channel (CRC) calculation.

Figure 2

Schematic of the experimental setup for the ${}^{17}\mathrm{F}(d,n){}^{18}\mathrm{Ne}$ radioactive-beam experiment.

Figure 3

Neutron pulse-shape discrimination spectrum for a single resoneut detector, representing ${\gamma }^{-2}$ and neutrons emitted from a ${}^{252}\mathrm{Cf}$ source. Also drawn is the gate used to select neutron-based events in the analysis.

Figure 4

Sample beam composition observed in the gas ionization chamber, characterized according to the partial energy loss (dE) and residual energy $E$ detected in the active sectors of the chamber but excluding the position-resolving sections. This spectrum represents data taken without the ${\mathrm{CD}}_2$ target. During the experiment the beam composition was continuously sampled at a 1/1000 downscaled trigger rate.

Figure 5

Beam time-of-flight signal, measured between the silicon time signal and the accelerator RF reference signal. Contaminant ${}^{16}\mathrm{O}$ and ${}^1\mathrm{H}$ (proton) beam particles are identified in addition to the ${}^{17}\mathrm{F}$ beam of interest. Protons are created in reactions at the production target, selected at the same rigidity as the beam, and can strike the inner rings of the silicon detector. The gate on ${}^{17}\mathrm{F}$ events is shown, which was used for beam identification in the subsequent analysis.

Figure 6

Light charged particles identified in the $\mathrm{\Delta }E-E$ silicon detectors according to their characteristic energy losses and selected by gating on incident ${}^{17}\mathrm{F}$ beam particles, identified through the time-of-flight analysis displayed in Fig. 5.

Figure 7

Heavy-ion particles identified in the gas ionization chamber according to their characteristic energy losses, with the signals equivalent to those in Fig. 4. Events were selected by gating on incident ${}^{17}\mathrm{F}$ beam particles (see Fig. 5) and a coincident proton. A gate is drawn identifying the ${}^{17}\mathrm{F}$ reaction products. Note that the peak around 50-MeV energy corresponds to the strong, 0.6-MeV proton resonance observed in this experiment.

Figure 8

Center-of-mass resonance-energy spectrum reconstructed from the invariant-mass analysis of the detected coincident $\mathrm{proton}+{}^{17}\mathrm{F}$ events. The spectrum is dominated by a peak at 0.60 MeV. Inset: Energy spectrum expanded in the region of the state expected at 5.09 MeV. Both spectra show a fit hypothesis of the two resonance peaks and a polynomial background.

Figure 9

The ${}^{17}\mathrm{F}+p$ energy distribution for the state at 4.5 MeV is fit with the simulated spectrum assuming that the state is populated by either $l=0$ or $l=2$ proton transfer.

Figure 10

Time-of-flight (tof) signals of neutron detection analyzed relative to the accelerator RF reference for ${}^{17}\mathrm{F}$-based events triggered by a silicon detector. Shown is the raw distribution, including the $\gamma$-based events at 0.6-ns tof and the events detected in coincidence with an identified proton, a heavy ion, and applied $\gamma$ discrimination through the pulse-shape analysis.

Figure 11

Energy loss and residual energy detected in segments of the gas ionization chamber, equivalent to those displayed in Fig. 4 and Fig. 7, selected for neutron-$\gamma$ coincidence events (blue symbols) and neutron-proton coincidence events (red symbols). A separation between $Z=9$ and $Z=10$ regions is obtained in the reaction residues marked by the dashed-line regions. Separated at higher energies, the spectrum also contains background events from random coincidences with beam particles of ${}^{17}\mathrm{F}$ and ${}^{16}\mathrm{O}$ and beam-particle pileup events.

Figure 12

Excitation energies of states populated by the $(d,n)$ reaction reconstructed using the neutron time-of-flight measurement (see text). (a) Events detected in coincidence with a proton and a ${}^{17}\mathrm{F}$ reaction residue. (b) Events detected in coincidence with a $\gamma$-ray and a ${}^{18}\mathrm{Ne}$ reaction residue. The dashed line in (b) represents an upper-limit estimate for events from uncorrelated background in the time spectra.

Figure 13

The observed spectrum compared with three peaks at the locations of ${}^{18}\mathrm{Ne}$ bound states $2_1^{+}$, $4_1^{+}$, and $2_2^{+}$. Peak areas are consistent with expectations from the simulation based on spectroscopic factors from the mirror reaction [17].

Figure 14

Direct-capture reaction rate calculated using the ANCs measured in this work and the calculated astrophysical $S$ factors.