The $S_{E1}$ factor of radiative $\alpha$ capture on $^{12}$C in cluster effective field theory

TL;DR

This paper applies effective field theory to calculate the $S_{E1}$ factor of radiative alpha capture on carbon-12, providing a refined estimate at the Gamow-peak energy with quantified uncertainties.

Contribution

It introduces a modified counting rule in effective field theory and fits two key parameters to experimental data, improving the theoretical prediction of the $S_{E1}$ factor.

Findings

Calculated $S_{E1}$ factor at Gamow-peak: 59 ± 3 keV·b

Result is about 30% smaller than recent estimates

Discussed uncertainties in the theoretical prediction

Abstract

The $S_{E1}$-factor of radiative $\alpha$-capture on $^{12}$C is studied in effective field theory up to next-to-leading order. A modification of the counting rules for the radiative capture amplitudes is discussed. We find that only two unfixed parameters remain in the amplitudes, and those two parameters are fitted to the experimental $S_{E1}$ data. An $S_{E1}$ factor is calculated at the Gamow-peak energy as $S_{E1}=59\pm 3$ keV$\cdot$b, and the result is found to be about 30% smaller than the estimates reported recently. An uncertainty of the estimate in the present work is also discussed.