Study of the $in ^{34}$Ar($α,p$)$^{37}$K reaction rate via proton scattering on $^{37}$K, and its impact on properties of modeled X-Ray bursts

Background: Type I X-Ray bursts (XRBs) are energetic stellar explosions that occur on the surface of a neutron star in an accreting binary system with a low-mass H/He-rich companion. The rate of the $^{34}$Ar($α,p$)$^{37}$K reaction may influence features of the light curve that results from the underlying thermonuclear runaway, as shown in recent XRB stellar modelling studies. Purpose: In order to reduce the uncertainty of the rate of this reaction, properties of resonances in the compound nucleus $^{38}$Ca, such as resonance energies, spins, and particle widths, must be well constrained. Method: This work discusses a study of resonances in the $^{38}$Ca compound nucleus produced in the $^{34}$Ar($α,p$) reaction. The experiment was performed at the National Superconducting Cyclotron Laboratory, with the ReA3 facility by measuring proton scattering using an unstable $^{37}$K beam. The kinematics were designed specifically to identify and characterize resonances in the Gamow energy window for the temperature regime relevant to XRBs. Results: The spins and proton widths of newly identified and previously known states in $^{38}$Ca in the energy region of interest for the $^{34}$Ar($α,p$)$^{37}$K reaction have been constrained through an R-Matrix analysis of the scattering data. Conclusions: Using these constraints, a newly estimated rate is applied to an XRB model built using Modules for Experiments in Stellar Astrophysics (MESA), to examine its impact on observables, including the light curve. It is found that the newly determined reaction rate does not substantially affect the features of the light curve.

💡 Research Summary

The paper addresses the astrophysical importance of the 34Ar(α,p)37K reaction, which is thought to influence the light‑curve morphology and nucleosynthesis pathways in Type I X‑ray bursts (XRBs). Because direct measurements of this reaction are extremely challenging—owing to low cross sections and the difficulty of producing intense 34Ar beams—previous XRB models have relied on statistical Hauser‑Feshbach rates from the NON‑SMOKER code (included in REACLIB). However, the reaction may be dominated by a small number of resonances in the compound nucleus 38Ca, rendering the statistical approach potentially inaccurate.

To constrain the resonance properties of 38Ca, the authors performed an indirect measurement using proton scattering on a radioactive 37K beam. The experiment was carried out at the National Superconducting Cyclotron Laboratory (NSCL) ReA3 facility. A 4.448 MeV/u 37K²⁺ beam (≈10⁴ pps, 87 % purity) was directed onto a 2.7 mg/cm² CH₂ target. Scattered protons were detected in silicon telescope arrays covering laboratory angles 15.4°–28.2°, providing both energy and angular information. Energy calibration employed 241Am α‑lines and an electronic pulser, with an additional two‑point calibration using a stable 40Ar beam on the same target.

The measured differential cross sections were converted to an excitation‑energy spectrum of 38Ca spanning 6.92–8.82 MeV (center‑of‑mass energies 0.81–2.71 MeV), which encompasses the Gamow window for temperatures T₉ ≈ 1–2 GK relevant to XRBs. An R‑matrix analysis was performed with the AZURE2 code, using a channel radius a = 6.065 fm. Initial fits that included only the 11 resonances previously reported in the literature (Long et al.) yielded a poor χ²/N ≈ 2.26 and failed to reproduce several observed structures. Consequently, the authors introduced 13 additional resonances, bringing the total to 24 (13 newly identified). The spin‑parity assignments were guided by the requirement that only natural‑parity states (Jπ = 0⁺, 1⁺, 2⁺, …) can contribute to the 34Ar+α entrance channel, while the proton partial widths were limited to decays populating the 37K ground state.

Beam contaminants (≈13 % 37Cl and 37Ar) were monitored with an ionization chamber and suppressed by timing coincidences. A separate carbon‑target run quantified background from 37K+¹²C fusion, which contributed less than 5 % of the total events after gating. The final R‑matrix fit achieved χ²/N = 1.15, providing resonance energies, spin‑parities, and proton widths (Γp) for all 24 states. The extracted Γp values range from a few keV up to ~90 keV, with uncertainties derived from both statistical fitting and systematic calibration errors.

Using these resonance parameters, the authors calculated the 34Ar(α,p)37K reaction rate via the narrow‑resonance formalism. The new rate is compared with the NON‑SMOKER/REACLIB rate and with the indirect rate derived from a previous 40Ca(p,t)38Ca study. In the XRB Gamow window, the new rate differs by at most a factor of two from the statistical rate, and it is significantly higher (by up to two orders of magnitude) than the very low rate suggested by the earlier indirect work. Thus, the present measurement supports the conventional statistical rate rather than the suppressed rate.

To assess the astrophysical impact, the new rate was incorporated into a one‑zone XRB model built with MESA (Modules for Experiments in Stellar Astrophysics). Simulations were run with the baseline (REACLIB) rate, the newly derived rate, and an extreme low‑rate scenario. Light‑curve observables—peak luminosity, rise time, decay time, and the presence of double‑peaked structures—showed negligible differences among the three cases, remaining within the intrinsic model uncertainties. Nucleosynthesis yields, particularly of 34S, also varied by less than a few percent. Consequently, the authors conclude that, within current experimental constraints, the 34Ar(α,p)37K reaction does not play a dominant role in shaping XRB observables.

The paper demonstrates that proton‑scattering measurements on unstable beams can effectively constrain resonances in nuclei that are otherwise inaccessible, providing a pathway to improve reaction‑rate libraries for astrophysical modeling. The authors suggest that future facilities delivering higher‑intensity 34Ar beams and enabling direct measurements at lower center‑of‑mass energies (0.5–1.5 MeV) would further reduce uncertainties and test the indirect approach presented here.