Correlated uncertainties in Monte Carlo reaction rate calculations

Abstract

Context. Monte Carlo methods have enabled nuclear reaction rates from uncertain inputs to be presented in a statistically meaningful manner. However, these uncertainties are currently computed assuming no correlations between the physical quantities that enter those calculations. This is not always an appropriate assumption. Astrophysically important reactions are often dominated by resonances, whose properties are normalized to a well-known reference resonance. This insight provides a basis from which to develop a flexible framework for including correlations in Monte Carlo reaction rate calculations. Aims. The aim of this work is to develop and test a method for including correlations in Monte Carlo reaction rate calculations when the input has been normalized to a common reference. Methods. A mathematical framework is developed for including correlations between input parameters in Monte Carlo reaction rate calculations. The magnitude of those correlations is calculated from the uncertainties typically reported in experimental papers, where full correlation information is not available. The method is applied to four illustrative examples: a fictional 3-resonance reaction, 27 Al(p, γ) 28 Si, 23 Na(p, α) 20 Ne, and 23 Na(α, p) 26 Mg. Results. Reaction rates at low temperatures that are dominated by a few isolated resonances are found to minimally impacted by correlation effects. However, reaction rates determined from many overlapping resonances can be significantly affected. Uncertainties in the 23 Na(α, p) 26 Mg reaction, for example, increase by up to a factor of 5. This highlights the need to take correlation effects into account in reaction rate calculations, and provides insight into which cases are expected to be most affected by them. The impact of correlation effects on nucleosynthesis is also investigated.

High-resolution study of levels in the astrophysically important nucleus Mg26 and resulting updated level assignments

“…However, the energy resolution of these experiments is insufficient to resolve some of the states observed by Moss [6]. Rather, the discernment that additional states are present comes from the differential cross sections and comparisons to other experimental studies of 26 Mg. The 22 Ne( 6 Li,d) 26 Mg reaction has been measured at a number of different beam energies [10,[12][13][14]. This reaction should preferentially populate natural-parity isoscalar states with large α-particle reduced widths, i.e.…”

“…In the absence of existing direct measurements at lower temperatures, the knowledge of the properties of resonances in 26 Mg may be used to better-constrain the 22 Ne+α reaction rates. To this end, a number of experimental studies have been performed to probe the properties of levels in 26 Mg. A brief summary of these experi-mental studies is given so that comparisons to the states observed in the present experiment may be made later. The 26 Mg(p, p ) 26 Mg reaction has been measured at a low proton energy [6].…”

“…To this end, a number of experimental studies have been performed to probe the properties of levels in 26 Mg. A brief summary of these experi-mental studies is given so that comparisons to the states observed in the present experiment may be made later. The 26 Mg(p, p ) 26 Mg reaction has been measured at a low proton energy [6]. The reaction mechanism for this reaction is not selective [7,8].…”

“…[6,7] may be used as a reference for other experimental works as to how many states are present and the excitation energies of the states. The 26 Mg(p, p ) 26 Mg reaction has also been measured at a higher proton energy (E lab p = 200 MeV) for the purpose of determining the M 1 strength distribution in 26 Mg [9]. This experiment may be used to identify known 1 + states which, being of unnatural parity, cannot contribute to the astrophysical 22 Ne+α reaction rates, for the purposes of excluding said states from the rate calculation.…”

“…The 26 Mg(α, α ) 26 Mg reaction using E α = 200 MeV has been performed twice on roughly comparable experimental setups [10,11]. Ref.…”