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Register a new userBayesian Estimation of the D(p,$gamma$)$^3$He Thermonuclear Reaction Rate
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Joseph Moscoso
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Big bang nucleosynthesis (BBN) is the standard model theory for the production of the light nuclides during the early stages of the universe, taking place for a period of about 20 minutes after the big bang. Deuterium production, in particular, is highly sensitive to the primordial baryon density and the number of neutrino species, and its abundance serves as a sensitive test for the conditions in the early universe. The comparison of observed deuterium abundances with predicted ones requires reliable knowledge of the relevant thermonuclear reaction rates, and their corresponding uncertainties. Recent observations reported the primordial deuterium abundance with percent accuracy, but some theoretical predictions based on BBN are at tension with the measured values because of uncertainties in the cross section of the deuterium-burning reactions. In this work, we analyze the S-factor of the D(p,$gamma$)$^3$He reaction using a hierarchical Bayesian model. We take into account the results of eleven experiments, spanning the period of 1955--2021; more than any other study. We also present results for two different fitting functions, a two-parameter function based on microscopic nuclear theory and a four-parameter polynomial. Our recommended reaction rates have a 2.2% uncertainty at $0.8$~GK, which is the temperature most important for deuterium BBN. Differences between our rates and previous results are discussed.
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The thermonuclear $^{19}$F($p$,$alpha_0$)$^{16}$O reaction rate in a temperature region of 0.007--10 GK has been derived by re-evaluating the available experimental data, together with the low-energy theoretical $R$-matrix extrapolations. Our new rate deviates up to about 30% compared to the previous ones, although all rates are consistent within the uncertainties. At very low temperature (e.g. 0.01 GK) our reaction rate is about 20% smaller than the most recently published rate, because of a difference in the low energy extrapolated $S$-factor and a more accurate estimate of the reduced mass entering in the calculation of the reaction rate. At temperatures above $sim$1 GK, our rate is smaller, for instance, by about 20% around 1.75 GK, because we have re-evaluated in a meticulous way the previous data (Isoya et al., Nucl. Phys. 7, 116 (1958)). The present interpretation is supported by the direct experimental data. The uncertainties of the present evaluated rate are estimated to be about 20% in the temperature region below 0.2 GK, which are mainly caused by the lack of low-energy experimental data and the large uncertainties of the existing data. The asymptotic giant branch (AGB) star evolves at temperatures below 0.2 GK, where the $^{19}$F($p$,$alpha$)$^{16}$O reaction may play a very important role. However, the current accuracy of the reaction rate is insufficient to help to describe, in a careful way, for the fluorine overabundances phenomenon observed in AGB stars. Precise cross section (or $S$ factor) data in the low energy region are therefore mandatory for astrophysical nucleosynthesis studies.
Updated stellar rates for the reaction 23Mg(p,gamma)24Al are calculated by using all available experimental information on 24Al excitation energies. Proton and gamma-ray partial widths for astrophysically important resonances are derived from shell model calculations. Correspondences of experimentally observed 24Al levels with shell model states are based on application of the isobaric multiplet mass equation. Our new rates suggest that the 23Mg(p,gamma)24Al reaction influences the nucleosynthesis in the mass A>20 region during thermonuclear runaways on massive white dwarfs.
The study of d+d reactions is of major interest since their reaction rates affect the predicted abundances of D, 3He, and 7Li. In particular, recent measurements of primordial D/H ratios call for reduced uncertainties in the theoretical abundances predicted by big bang nucleosynthesis (BBN). Different authors have studied reactions involved in BBN by incorporating new experimental data and a careful treatment of systematic and probabilistic uncertainties. To analyze the experimental data, Coc et al. (2015) used results of ab initio models for the theoretical calculation of the energy dependence of S-factors in conjunction with traditional statistical methods based on Chi-2 minimization. Bayesian methods have now spread to many scientific fields and provide numerous advantages in data analysis. Astrophysical S-factors and reaction rates using Bayesian statistics were calculated by Iliadis et al. (2016). Here we present a similar analysis for two d+d reactions, d(d,n)3He and d(d,p)3H, that has been translated into a total decrease of the predicted D/H value by 0.16%.
The thermonuclear rate of the 50Fe(p,gamma)51Co reaction in the Type I X-ray bursts (XRBs) temperature range has been reevaluated based on a recent precise mass measurement at CSRe lanzhou, where the proton separation energy Sp=142+/-77 keV has been determined firstly for the 51Co nucleus. Comparing to the previous theoretical predictions, the experimental Sp value has much smaller uncertainty. Based on the nuclear shell model and mirror nuclear structure information, we have calculated two sets of thermonuclear rates for the 50Fe(p,gamma)51Co reaction by utilizing the experimental Sp value. It shows that the statistical-model calculations are not ideally applicable for this reaction primarily because of the low density of low-lying excited states in 51Co. In this work, we recommend that a set of new reaction rate based on the mirror structure of 51Cr should be incorporated in the future astrophysical network calculations.
The propagation of uncertainties in reaction cross sections and rates of neutron-, proton-, and alpha-induced reactions into the final isotopic abundances obtained in nucleosynthesis models is an important issue in studies of nucleosynthesis and Galactic Chemical Evolution. We developed a Monte Carlo method to allow large-scale postprocessing studies of the impact of nuclear uncertainties on nucleosynthesis. Temperature-dependent rate uncertainties combining realistic experimental and theoretical uncertainties are used. From detailed statistical analyses uncertainties in the final abundances are derived as probability density distributions. Furthermore, based on rate and abundance correlations an automated procedure identifies the most important reactions in complex flow patterns from superposition of many zones or tracers. The method so far was already applied to a number of nucleosynthesis processes. Here we focus on the production of p-nuclei in white dwarfs exploding as thermonuclear (type Ia) supernovae. We find generally small uncertainties in the final abundances despite of the dominance of theoretical nuclear uncertainties. A separate analysis of low- and high-density regions indicates that the total uncertainties are dominated by the high-density regions.
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