A new way to unravel the \(^{12}\)C(\(\alpha \),\(\gamma \))\(^{16}\)O cross section components using neural networks

Abstract

The \(^{12}\)C(\(\alpha \),\(\gamma \))\(^{16}\)O reaction rate is crucial in determining the carbon-to-oxygen abundance ratio in stellar nucleosynthesis. Measuring this reaction’s cross section at stellar energies is challenging due to its extremely small value, approximately 10\(^{-17}\) barn at E\(_{\mathrm {c.m.}}\) = 300 keV. To address this, R-matrix calculations are employed to extrapolate data to lower energies, requiring a comprehensive understanding of each contribution to the cross section. The dominant contributions to the cross section at stellar energies arise from electric dipole (E1) and electric quadrupole (E2) transitions to the ground state of \(^{16}\)O, along with a significant cascade contribution. Traditionally, these contributions have been separated using the \(\gamma \)-ray angular distribution. In this work, we propose a novel technique using the energy distribution of the \(^{16}\)O recoils at the focal plane. This method involves a neural network trained on detailed Monte Carlo simulations of the energy distribution of recoils transported through the recoil mass separator ERNA. This approach enables the simultaneous determination of all three contributions with errors around 10% in the energy range E\(_{\mathrm {c.m.}}\) = 1.0–2.2 MeV. By employing this new technique, we aim to significantly improve the accuracy of determining the cross section of the \(^{12}\)C(\(\alpha \),\(\gamma \))\(^{16}\)O reaction at astrophysical energies.