Charged-Particle Thermonuclear Reaction Rates: II. Tables and Graphs of Reaction Rates and Probability Density Functions

TL;DR

This paper provides detailed tables, graphs, and statistical descriptions of thermonuclear reaction rates for nuclei with mass numbers 14 to 40, derived using Monte Carlo methods, to improve stellar modeling accuracy.

Contribution

It introduces a comprehensive Monte Carlo-based method for calculating and representing reaction rate probability densities, including lognormal approximations and reliability measures.

Findings

Reaction rates are provided as median, low, and high quantiles.

Lognormal distribution parameters are tabulated for each temperature.

Graphical and statistical tools are included to assess approximation reliability.

Abstract

Numerical values of charged-particle thermonuclear reaction rates for nuclei in the A=14 to 40 region are tabulated. The results are obtained using a method, based on Monte Carlo techniques, that has been described in the preceding paper of this series (Paper I). We present a low rate, median rate and high rate which correspond to the 0.16, 0.50 and 0.84 quantiles, respectively, of the cumulative reaction rate distribution. The meaning of these quantities is in general different from the commonly reported, but statistically meaningless expressions, "lower limit", "nominal value" and "upper limit" of the total reaction rate. In addition, we approximate the Monte Carlo probability density function of the total reaction rate by a lognormal distribution and tabulate the lognormal parameters {\mu} and {\sigma} at each temperature. We also provide a quantitative measure (Anderson-Darling test statistic) for the reliability of the lognormal approximation. The user can implement the approximate lognormal reaction rate probability density functions directly in a stellar model code for studies of stellar energy generation and nucleosynthesis. For each reaction, the Monte Carlo reaction rate probability density functions, together with their lognormal approximations, are displayed graphically for selected temperatures in order to provide a visual impression. Our new reaction rates are appropriate for bare nuclei in the laboratory. The nuclear physics input used to derive our reaction rates is presented in the subsequent paper of this series (Paper III). In the fourth paper of this series (Paper IV) we compare our new reaction rates to previous results.