Proton decays from $α$-unbound states in $^{22}$Mg and the $^{18}$Ne($α, p_{0}$)$^{21}$Na cross section

Abstract

Background: Type I X-ray bursts provide an opportunity to constrain the equation of state of nuclear matter. Observations of the lightcurves from these bursts allow the compactness of neutron stars to be constrained. However, the behaviour of these lightcurves also depends on a number of important thermonuclear reaction rates. One of these reactions, 18 Ne(α, p) 21 Na, has been extensively studied but there is some tension between the rate calculated from spectroscopic information of states above the α-particle threshold in 22 Mg and the rate determined from time-reversed measurements of the cross section.Purpose: The time-reversed measurement of the cross section is only sensitive to the ground state-to-ground state contribution. Therefore, corrections must be made to this reaction rate to account for the contribution of branches to excited states in 21 Na. At present this is done with statistical models which may not be applicable in such light nuclei. Basing the correction of the time-reversed cross section on experimental data is much more robust. Method:The 24 Mg(p, t) 22 Mg reaction was used to populate states in 22 Mg. The reaction products from the reaction were analysed by the K600 magnetic spectrometer at iThemba LABS, South Africa. Protons decaying from excited states of 22 Mg (Sp = 5502 keV) excited states were detected in an array of five double-sided silicon strip detectors placed at backward angles. The branching ratio for proton decays to the ground state of 21 Na, Bp 0 , was determined by comparing the inclusive and exclusive spectra. Results:The experimental proton decay branching ratio to the ground state of 21 Na from excited states in 22 Mg were found to be a factor of about two smaller than the ratios predicted by Hauser-Feshbach models. Using the experimental branchings for a recalculation of the 18 Ne(α,p0) 21 Na cross section leads to a considerably improved agreement with previous reaction data. Updated information on the disputed number of levels around Ex ≈ 9 MeV and on the possible 18 Ne(α,2p) 20 Ne cross section at astrophysical energies is also reported. Conclusions:The proton decay branching of excited states in 22 Mg to the ground state of 21 Na have been measured using the K600 Q2D spectrometer at iThemba LABS coupled to the double-sided silicon-strip detector array CAKE. Using these experimental data, the modeling of the 18 Ne(α,p0) 21 Na cross section has been improved. The result is not only in better agreement with previous cross section data but also consistent with a recent direct measurement of 18 Ne(α,p) 21 Na. This strengthens the case for the application of statistical models for these reactions.