Studies of X-ray burst reactions with radioactive ion beams from RESOLUT

Reactions on certain proton-rich, radioactive nuclei have been shown to have a significant influence on X-ray bursts. We provide an overview of two recent measurements of important X-ray burst reactions using in-flight radioactive ion beams from the RESOLUT facility at the J. D. Fox Superconducting Accelerator Laboratory at Florida State University. The 17F(d,n)18Ne reaction was measured, and Asymptotic Normalization Coefficients were extracted for bound states in 18Ne that determine the direct-capture cross section dominating the 17F(p,γ)18Ne reaction rate for T 0.45 GK. Unbound resonant states were also studied, and the single-particle strength for the 4.523-MeV (3) state was found to be consistent with previous results. The 19Ne(d,n)20Na proton transfer reaction was used to study resonances in the 19Ne(p,γ)20Na reaction. The most important 2.65-MeV state in 20Na was observed to decay by proton emission to both the ground and first-excited states in 19Ne, providing strong evidence for a 3 spin assignment and indicating that proton capture on the thermally-populated first-excited state in 19Ne is an important contributor to the 19Ne(p,γ)20Na reaction rate.


Introduction
X-ray bursts occur in binary systems when hydrogen-rich matter from a main-sequence star accretes onto a neutron star and ignites under degenerate conditions.These are the most common stellar explosions, with over 100 systems known to exhibit bursts recurring with timescales typically from hours to days.Comparisons of observations of many bursts (e.g.see [1]) to improved computational simulations using a variety of astrophysical models (e.g.see [2]) are providing insights into the composition, dynamics, and evolution of these systems.Simulations also show that certain nuclear reactions involving proton-rich, radioactive nuclei have a direct impact on energy generation, nucleosynthesis, and the resulting light curve [3,4].The rates of many of these reactions are purely theoretical or have large uncertainties due to experimental challenges in studying short-lived nuclei that hinder our understanding of X-ray bursts.e-mail: blackmon@lsu.eduSome of the important reactions in X-ray bursts are those that involve breakout of the hot-CNO cycle, either through the 17 F(p,γ) 18 Ne(α,p) 21 Na or 15 O(α,γ) 19 Ne(p,γ) 20 Na reaction sequences.We measured the 17 F(d,n) 18 Ne and 19 Ne(d,n) 20 Na reactions to improve our understanding of the 17 F(p,γ) 18 Ne and 19 Ne(p,γ) 20 Na capture reactions, respectively, that are important in breakout from the hot-CNO cycle.Both measurements were conducted at the J. D. Fox Superconducting Accelerator Laboratory at Florida State University using "in-flight" radioactive ion beams.Stable beams of 16 O and 19 F bombarded a cryogenic gas cell to produce 17 F and 19 Ne from the 16 O(d,n) 17 F and 19 F(p,n) 19 Ne reactions, respectively.The radioactive products were collected and separated by the RESOLUT facility [5].The secondary radioactive beams bombarded a deuterated polyethylene target, and a suite of detector systems was used to detect neutrons, gamma rays, light charged particles and heavy ions. 18

Ne
The 17 F(p,γ) 18 Ne reaction rate is determined mainly by contributions from direct capture and a single 3 + resonance at E cm = 600 keV.The 600-keV resonance strength was directly measured at the Holifield Radioactive Ion Beam Facility [6], but the direct-capture contribution that dominates the reaction rate at T 0.45 GK remains uncertain.A measurement of the 17 F(p,γ) 18 Ne direct-capture cross section at E cm < 600 keV would require a 17 F beam intensity of about 10 9 s −1 .Such intensities are beyond the reach of current facilities, and indirect techniques must be applied to better constrain the direct-capture cross section.
We measured the 17 F(d,n) 18 Ne proton-transfer reaction to study states in 18 Ne that are important for the 17 F(p,γ) 18 Ne reaction rate, including bound states that determine the direct-capture cross section [7].A 95.5-MeV beam of 17 F from RESOLUT with an intensity of about 3 × 10 4 s −1 bombarded a 0.52 mg/cm 2 CD 2 target.Neutrons from the (d,n) reaction were detected at θ lab = 145 • − 165 • using the RESONEUT array of P-terphenyl scintillators that provided good n − γ discrimination for energies greater than about 50 keV ee [8].All heavy ions (beam particles and heavy reaction products) were detected using a fast-counting, position-sensitive gas ionization detector covering θ lab < 6 • that determined the atomic number through relative energy loss and measured the position (in 2 dimensions perpendicular to the beam axis) with a resolution of better than 3 mm [9].Gamma rays emitted from bound, excited states were detected with a total efficiency of 12% using an array of 20 NaI(Tl) scintillators [10] arranged in a barrel configuration subtending θ lab = 35 • − 100 • .The triple coincidence of neutrons, γ rays, and heavy ions identified by atomic number provided clean selection of the population of bound states in 18 Ne except for the ground state, which is expected to be weakly populated.
The relative timing between the neutrons and the accelerator rf signal was used to determine the E x of states in 18 Ne by time-of-flight with a corresponding energy resolution of about ∆E cm ≈ 150 keV.For a triple coincidence of n − γ− 18 Ne, we observe two peaks in the time-of-flight spectrum corresponding to the 1.887-MeV (2 + ) state and to the 4 + − 0 + − 2 + triplet of states at about 3.5 MeV.While the triplet is not resolved, population of the 3.57-MeV (0 + ) state is expected to be very weak.Assuming the 0 + to be negligible, we determined the cross sections for population of the 1.887-MeV (2 + ), 3.376-MeV (4 + ) and 3.616-MeV (2 + ) states from a combined fit to the neutron time-of-flight spectrum (see Fig. 13 in [7]).These cross sections (corresponding to very forward angles for θ cm ) determine Asymptotic Normalization Coefficients for the states.
Direct capture is expected to be dominated by = 0 capture to the 2 + states in 18 Ne below the proton threshold.We are unable to constrain the relative population of s 1/2 and d 5/2 for the 2 + states from our data due to the limited statistics and angular range of the detected neutrons.Assuming the same relative s 1/2 and d 5/2 mixing as in the mirror states in 18 O [11], we find C 2 s 1/2 = 16±8 fm −1 for the 1.887-MeV state and C 2 s 1/2 = 150 ± 60 fm −1 for the 3.616-MeV state, assuming the reaction to occur at an average energy of 5.53 MeV/u corresponding to the center of the target.Using these values, we calculated the contribution to the 17 F(p,γ) 18 Ne reaction rate from direct capture.We find a 30% larger contribution from direct capture than estimated from properties of the mirror [12], though the results are consistent within uncertainties, which are dominated in our result by a statistical uncertainty of 30% in the cross section for populating the 3.616-MeV state.
We were also able to study resonant states above the proton-separation energy, even though they predominantly decay by proton emission, providing no γ-ray signature and giving the same species of recoiling heavy ion as the beam ( 17 F).We cleanly selected the events of interest in this case by identifying the emitted protons in an annular telescope array of silicon-strip detectors subtending θ lab = 8 • − 21 • .Correlating the measured protons with the 17 F ions in the gas ionization chamber allowed proton-unbound states in 18 Ne to be accurately reconstructed from an invariant mass analysis using only the position and energy of the protons and 17 F ions, thus inferring information about the outgoing neutron without using data from the RESONEUT neutron detector array.We do find consistent results when requiring coincidence neutron detection with RESONEUT, though the efficiency reduces the statistics by a factor of about 30.The reconstructed excitation spectrum in 18 Ne from 17 F+p coincidences (see Fig. 8 in [7]) is dominated by one strong resonance corresponding to the 3 + state in 18 Ne at 4.523 MeV that known to be the strongest resonance in the 17 F(p,γ) 18 Ne reaction [6].The higher statistics achieved without neutron detection allowed the distribution of events in angle/energy to be compared to a FRESCO coupled-channels calculation.We find dominant population of the state through = 0 transfer, confirming the 3 + spin assignment, with a single-particle spectroscopic factor of C 2 S = 0.78 ± 0.06 corresponding to a proton partial width of Γ p = (14.2± 1.1) keV, where the uncertainty is dominated by the systematic uncertainties in the analysis.The extracted partial width is about 20% lower than determined from 17 F+p elastic scattering [13].It should be noted that the triple coincidence of neutrons, protons, and 17 F ions showed strong population of this resonant state in the neutron time-of-flight spectrum, serving as a check on the time-of-flight analysis for the bound states.

Na
The 19 Ne(p,γ) 20 Na reaction rate is dominated by contributions from resonances corresponding to states just above the proton-separation energy (S p = 2.19 MeV) in 20 Na.While the structure of 20 Na is relatively well established for bound states, properties of proton-unbound levels are uncertain.The level scheme is shown in Figure 1 compared to the isospin-mirror nucleus 20 F, where we have included spin-parity (J π ) information only when unambiguous.There are 6 observed states in 20 Na within 1 MeV above the proton-separation energy.Excitation energies are relatively well determined from charge-exchange reactions, but these studies have placed only weak constraints on J π values due to challenges from unresolved states and increased background above the separation energy, problems exacerbated by difficulties with neon targets [14][15][16].Only the 3.00-MeV (1 + ) and 3.09-MeV (0 + ) states have clear assignments based upon 19 Ne+p elastic scattering [17] and their population in allowed β-decay transitions from 20 Mg [18,19].These states have been identified as mirror levels to the 3.49-MeV and 3.53-MeV states in 20 F, with a large Coulomb shift resulting from a substantial 2s 1/2 component in the wavefunction as expected from sd shell model calculations.
The other levels at 2.65, 2.85, 2.98 and 3.07 MeV in 20 Na have generally been assumed to be mirrors to the only 4 states observed in 20 F in a comparable energy range [20].Only the 2.966-MeV state in 20 F has majority sd single-particle character, being strongly populated in the 19 F(d,p) 20 F and 18 O( 3 He,p) 20 F reactions with angular distributions giving a 3 + assignment [21].The other 3 states in 20 F have more complex configurations.The 2.864-MeV and 3.171-MeV states in 20 F are weakly populated in transfer reactions.Angular distributions indicate negative parity for the 2.864-MeV state, with arguments favoring a 3 − assignment [22].The 3.171-MeV state is populated predominantly by = 2 transfer in both 19 F(d,p) 20 F and 18 O( 3 He,p) 20 F, indicating positive-parity and a likely 1 + assignment, but composed primarily of 6p − 2h core excitations.Finally, the 2.968-MeV state is a high-spin state, likely J π ≥ 4 − [23].
Most important is to determine the properties of the first state above the separation energy in 20 Na at 2.65 MeV that could dominate the 19 Ne(p,γ) 20 Na reaction rate given the low (E cm = 457 keV) resonance energy.Some arguments favor a 1 + assignment for this state but with a small singleparticle component (see [24] for example).This is also supported an upper limit on the protoncapture resonance strength (ωγ < 16 meV) set from the a 19 Ne(p,γ) 20 Na reaction measurement [25].However, some information argues otherwise.The lack of observation of the 2.65-MeV state in 20 Mg beta-decay strongly favors a forbidden transition [19], and other charge-exchange measurements have argued for a 3 + assignment [26,27].These charge-exchange studies also indicated a tentative 3 − assignment of the 2.85-MeV state in 20 Na as a potential mirror to the 2.86-MeV level in 20 F, though these states are not well resolved from neighboring states and are weakly populated.
We studied the properties of unbound states in 20 Na using the 19 Ne(d,n) 20 Na reaction [28].The experimental configuration and approach were similar to that in the study of unbound levels in 18 Ne.A 86-MeV beam of 19 Ne from RESOLUT bombarded a 0.52 mg/cm 2 CD 2 target.Protons were detected and identified in an annular telescope of silicon strip detectors subtending θ lab = 8 • − 21 • while heavy ions were detected using the position-sensitive gas ionization detector covering θ lab < 6 • .The 19 Ne beam intensity (< 2000 s −1 ) was more than an order of magnitude less intense than in the 17 F(d,n) 18 Ne study described previously, which prohibited the coincident detection of neutrons due to the reduced efficiency.As with the 18 Ne, however, we are able to reconstruct the unbound states of interest from an invariant mass analysis using the kinematics of the protons and 19 Ne ions (see Fig. 1 in [28]) with a center-of-mass energy resolution of about 200 keV (FWHM) One prominent feature in our reconstructed spectrum is a well-resolved resonance at E cm = 220 keV.There is no known level in 20 Na near E x = 2.41 MeV that would correspond to proton emission to the ground state of 19 Ne for this resonance.However, the E cm matches proton decay from the important 2.65-MeV state in 20 Na to the first-excited state ( 5 2 + ) in 19 Ne.Emission of a 220-keV proton strongly argues for = 0 angular momentum due to the prohibitive penetrability for larger values.An = 2 proton-decay branch at this energy would be about an order of magnitude weaker than the expected gamma-decay branch and would not be observed.This supports the 3 + assignment for the 2.65-MeV resonance as indicated from the weak population in beta decay.We also extract an angle/energy distribution for the emitted 20 Na (and inferred neutron) and model the 19 Ne(d,n) 20 Na cross section following the procedure of [29].A fit to the angular distribution using = 2 protontransfer onto the 19 Ne ground state (required to populate a 3 + resonant state) results in χ 2 /ν = 1.8, while a corresponding fit using = 0 proton transfer (likely for a 1 + resonance) results in χ 2 /ν = 4.3.Both the angular distribution and the strength by which the first-excited state is populated in proton emission provides strong evidence supporting the 3 + assignment for the 2.65-MeV level.
The second prominent feature in our E cm spectrum is a strong resonance at 660 keV, corresponding to proton emission from the 2.85-MeV state in 20 Na to the ground state in 19 Ne.This resonance has a significant low-energy shoulder best described by two additional weaker resonances at E cm = 440 keV and 540 keV.The 440-keV resonance corresponds to proton emission from the 2.65-MeV state in 20 Na to the 19 Ne ground state.We find the branching ratio for proton decay from the 2.65-MeV state to the 19 Ne ground state to be approximately equal to that for decay to the first-excited state.These equal decay branches imply that the wavefunction for the 2.65-MeV state has a s 1/2 proton component (coupled to the 19 Ne first-excited state) with C 2 S = 0.5, about 7 times greater than the d 5/2 component, which is consistent with the 3 + mirror state in 20 F at 2.966 MeV.[31].The 19 Ne ground state (J π = 1/2 + ) couples to an = 0 proton with channel spin S = 0, 1 corresponding to E x = 2.19 MeV in 20 Na, while the first-excited state in 19 Ne (J π = 5/2 + ) couples to an = 0 proton with channel spin S = 2, 3 corresponding to E x = 2.43 MeV in 20 Na.
The strong coupling of the 2.65-MeV state to the first-exited state in 19 Ne significantly increases the 19 Ne(p,γ) 20 Na reaction rate.The first-excited state in 19 Ne is sufficiently low in excitation energy that significant thermal population is possible (for example, a few percent at T = 1GK).The lower energy required for proton capture onto the thermally-excited 19 Ne 5