First Direct Measurement Constraining the ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ Reaction Cross Section for Mixed Hydrogen and Helium Burning in Accreting Neutron Stars

The rate of the final step in the astrophysical $\alpha \mathrm{p}$ process, the ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ reaction, suffers from large uncertainties due to a lack of experimental data, despite having a considerable impact on the observable light curves of x-ray bursts and the composition of the ashes of hydrogen and helium burning on accreting neutron stars. We present the first direct measurement constraining the ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ reaction cross section, using the Jet Experiments in Nuclear Structure and Astrophysics gas jet target. The combined cross section for the ${}^{34}\mathrm{Ar},\mathrm{Cl}(\alpha ,\mathrm{p}){}^{37}\mathrm{K},\mathrm{Ar}$ reaction is found to agree well with Hauser-Feshbach predictions. The ${}^{34}\mathrm{Ar}(\alpha ,2\mathrm{p}){}^{36}\mathrm{Ar}$ cross section, which can be exclusively attributed to the ${}^{34}\mathrm{Ar}$ beam component, also agrees to within the typical uncertainties quoted for statistical models. This indicates the applicability of the statistical model for predicting astrophysical $(\alpha ,\mathrm{p})$ reaction rates in this part of the $\alpha \mathrm{p}$ process, in contrast to earlier findings from indirect reaction studies indicating orders-of-magnitude discrepancies. This removes a significant uncertainty in models of hydrogen and helium burning on accreting neutron stars.

Figure 1

Calculated two-body kinematics for the $(\alpha ,\mathrm{p})$ reaction on the three beam constituents (${}^{34}\mathrm{Ar}$, blue solid; ${}^{34}\mathrm{Cl}$, red dash; ${}^{34}\mathrm{S}$, green bold solid), with the events that met the selection criteria from the current experiment overlaid in black, for the lower beam energy. The upper panel (a) shows the energy versus angle dependence for the identified proton events (black circles) compared with the calculated kinematics curves. The lower panel (b) shows those same events projected into a ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ $Q$-value spectrum (black histogram), again compared against the locations of the known levels in ${}^{37}\mathrm{K}$,Ar,Cl. While the resolution is not sufficient to differentiate between excited states in ${}^{37}\mathrm{K}$ and ${}^{37}\mathrm{Ar}$, the (combined) p0 channel is clearly delineated. The ground state of the contaminant ${}^{34}\mathrm{S}(\alpha ,\mathrm{p}){}^{37}\mathrm{Cl}$ reaction falls at a reconstructed $Q$ value of about $-3\mathrm{MeV}$. In brown is a simulation of the reconstructed $Q$ value using the partial cross sections ($\mathrm{p}0,\mathrm{p}1,\dots ,\mathrm{p}N$, corresponding to reactions proceeding through the final nucleus ground state, first excited $\text{state}\dots N$th excited state, respectively) as predicted by TALYS but with the total cross section normalized to reproduce the number of events seen in the measurement, for comparison.

Figure 2

Combined experimental cross sections derived in the current work, compared with Hauser-Feshbach statistical calculations using the default parameters in TALYS. In the upper panel (a), the TALYS calculations for the combined ${}^{34}\mathrm{Ar},\mathrm{Cl}(\alpha ,1\mathrm{p}){}^{37}\mathrm{K},\mathrm{Ar}$ cross section is shown in black solid, and the p0 contribution in black dashed. Similarly, the ${}^{34}\mathrm{Ar}(\alpha ,2\mathrm{p}){}^{36}\mathrm{Ar}$ reaction is shown in the lower panel (b). The horizontal error bars represent the uncertainty on the beam energy; the target thickness was about 200 keV in the center of mass.

Figure 3

X-ray burst light curve in luminosity per gram of accreted matter predicted by one-zone model [8] for a ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ reaction rate reduced by a factor of 100 and multiplied by a factor of 10 (shaded black), and for the same reaction rate reduced and multiplied by a factor of 2 (shaded gray). The inset enlarges the burst peak. The small kink around 55 seconds stems from a switch between tabulated data and an analytic approximation used in the opacity calculation.

Figure 4

Impact of variations of the ${}^{34}\mathrm{Ar}(\alpha ,\mathrm{p}){}^{37}\mathrm{K}$ reaction rate on the final composition of the nuclear ashes in steady state burning at a local accretion rate of $40{\dot{m}}_{\text{Edd}}$ [5]. Shown are the ratios of final abundances, summed by mass number, as functions of mass number relative to the baseline calculation for a variation of the reaction rate by a factor of 10 (solid red), 0.01 (dashed red), 2 (solid black), and 0.5 (dashed black). Ratios are only displayed for total abundances larger than ${10}^{-6}\mathrm{mole}/\mathrm{g}$.