Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions

Details Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions

2010-04-23

arxiv.org/abs/1004.4136v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

31 pages, 5 figures, 1 color

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Charged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694526