2010/04/23 by R. Longland, Richard Longland, Christian Iliadis +11 · 162 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Chemistry #Cumulative distribution function #Log-normal distribution #Mathematics #Monte Carlo method #Nuclear physics research studies #Physics #Probability density function #Quantum Chromodynamics and Particle Interactions #Reaction rate #Series (stratigraphy) #Statistical physics #Statistics #astro-ph.SR #nucl-th
paper · pdf · doi:10.1016/j.nuclphysa.2010.04.008
published in Nuclear Physics A 841(1-4), 1-30 (Elsevier BV) · 31 pages, 5 figures, 1 color
arxiv created 2010/04/23 · openalex publication_date 2010/04/29 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended "classical" rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the statistically meaningless "minimum" (or "lower limit") and "maximum" (or "upper limit") reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters miu and sigma. The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory, are tabulated in the second paper of this series (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this series (Paper III). In the fourth paper of this series (Paper IV) we compare our new reaction rates to previous results.