A Comparative Analysis of R-Matrix Fitting: ${}^{12}$C$(p,\gamma)$${}^{13}$N as Test Case

TL;DR

This paper compares frequentist and Bayesian R-matrix fitting methods to improve the accuracy and reliability of nuclear reaction cross section estimates, focusing on the $^{12}$C($p,\, ext{γ}$)$^{13}$N reaction relevant to stellar nucleosynthesis.

Contribution

It provides a systematic comparison of statistical techniques for R-matrix fitting, emphasizing uncertainty treatment and covariance estimation in nuclear astrophysics.

Findings

Bayesian methods offer more consistent uncertainty estimates.

Systematic uncertainty treatment improves fit reliability.

Covariance matrix estimation is crucial for reproducibility.

Abstract

In nuclear astrophysics, the accurate determination of nuclear reaction cross sections at astrophysical energies is critical for understanding stellar evolution and nucleosynthesis. This study focuses on the $^{12}$C($p, \gamma$)$^{13}$N reaction, which takes part in the CNO cycle and is significant for determining the $^{12}$C/$^{13}$C ratio in stellar interiors. Data from various studies, including recent LUNA measurements, reveal high discrepancies in cross section values, underscoring the need for robust fitting approaches. Utilizing the R-matrix theory, we compare different frequentist and Bayesian methodologies for estimating reaction cross sections and their uncertainties. The analysis evaluates the strengths and weaknesses of different statistical techniques, highlighting the importance of systematic uncertainty treatment and the estimate of covariance matrix estimation to enhance the reliability and reproducibility of uncertainty estimates in nuclear astrophysics.