Chargedparticle thermonuclear reaction rates: I. Monte Carlo method and statistical distributions
Abstract
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 chisquared 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 μ and σ. 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 issue (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.
 Publication:

Nuclear Physics A
 Pub Date:
 October 2010
 DOI:
 10.1016/j.nuclphysa.2010.04.008
 arXiv:
 arXiv:1004.4136
 Bibcode:
 2010NuPhA.841....1L
 Keywords:

 Thermonuclear reaction rates;
 Astrophysics  Solar and Stellar Astrophysics;
 Nuclear Theory
 EPrint:
 31 pages, 5 figures, 1 color