### 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 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 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.

Original language | English (US) |
---|---|

Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Nuclear Physics A |

Volume | 841 |

Issue number | 1-4 |

DOIs | |

State | Published - Oct 1 2010 |

### Fingerprint

### Keywords

- Thermonuclear reaction rates

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics A*,

*841*(1-4), 1-30. https://doi.org/10.1016/j.nuclphysa.2010.04.008

**Charged-particle thermonuclear reaction rates : I. Monte Carlo method and statistical distributions.** / Longland, R.; Iliadis, C.; Champagne, A. E.; Newton, J. R.; Ugalde, C.; Coc, A.; Fitzgerald, R.

Research output: Contribution to journal › Article

*Nuclear Physics A*, vol. 841, no. 1-4, pp. 1-30. https://doi.org/10.1016/j.nuclphysa.2010.04.008

}

TY - JOUR

T1 - Charged-particle thermonuclear reaction rates

T2 - I. Monte Carlo method and statistical distributions

AU - Longland, R.

AU - Iliadis, C.

AU - Champagne, A. E.

AU - Newton, J. R.

AU - Ugalde, C.

AU - Coc, A.

AU - Fitzgerald, R.

PY - 2010/10/1

Y1 - 2010/10/1

N2 - 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 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.

AB - 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 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.

KW - Thermonuclear reaction rates

UR - http://www.scopus.com/inward/record.url?scp=77953293420&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953293420&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysa.2010.04.008

DO - 10.1016/j.nuclphysa.2010.04.008

M3 - Article

AN - SCOPUS:77953293420

VL - 841

SP - 1

EP - 30

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

IS - 1-4

ER -