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Charged-Particle Thermonuclear Reaction Rate Evaluation for A=12-40 Nuclei: I. Monte Carlo Method and Statistical Distributions



Ryan P. Fitzgerald, R Longland, C. Iliadis, E. Champagne, J.R. Newton, C. Ugalde


A new 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, log-normal and chi-square 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 log-normal distribution and present, at each temperature, the log-normal parameters m and s. 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 the reaction rates, together with a description of the Monte Carlo code RateErrorsMC, is presented in a third paper (Paper III).
Nuclear Physics A


Monte Carlo, nuclear astrophsics, reaction rate: thermonuclear, uncertainty


Fitzgerald, R. , Longland, R. , Iliadis, C. , Champagne, E. , Newton, J. and Ugalde, C. (2010), Charged-Particle Thermonuclear Reaction Rate Evaluation for A=12-40 Nuclei: I. Monte Carlo Method and Statistical Distributions, Nuclear Physics A, [online], (Accessed June 12, 2024)


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Created April 28, 2010, Updated February 17, 2017