Cluster effective field theory and nuclear reactions

TL;DR

This paper develops an effective field theory (EFT) framework to analyze low-energy nuclear reactions, specifically focusing on the astrophysical S-factor for radiative alpha capture on carbon-12, with applications to various related reactions.

Contribution

The paper introduces a novel EFT approach to model low-energy nuclear reactions, providing a systematic way to estimate reaction rates relevant to astrophysics.

Findings

Estimated the S-factor for the alpha capture on carbon-12 at the Gamow peak.

Applied EFT to elastic scattering, radiative capture, and beta-delayed alpha emission reactions.

Discussed the broader applicability of EFTs to low-energy nuclear processes.

Abstract

An effective field theory (EFT) for a nuclear reaction at low energies is studied. The astrophysical $S$-factor of radiative $\alpha$ capture on $^{12}$C at the Gamow-peak energy, $T_G=0.3$ MeV, is a fundamental quantity in nuclear-astrophysics, and we construct an EFT for the reaction. To fix parameters appearing in the effective Lagrangian, the EFT is applied to the study for three reactions: elastic $\alpha$-$^{12}$C scattering at low energies, $E1$ transition of radiative $\alpha$ capture on $^{12}$C, and $\beta$ delayed $\alpha$ emission from $^{16}$N. We report an estimate of the $S_{E1}$-factor of the reaction through the $E1$ transition at $T_G$ by employing the EFT. We also discuss applications of EFTs to nuclear reactions at low energies.