Astrophysical factors of ${}^{12}{\rm C}+{}^{12}{\rm C}$ fusion from Trojan horse method

TL;DR

This paper critically examines the Trojan horse method's application to ${}^{12}{ m C}+{}^{12}{ m C}$ fusion, revealing that previous results indicating a strong low-energy rise are artifacts of an invalid approximation, significantly revising the astrophysical factor.

Contribution

The study demonstrates that the previously reported rise in the astrophysical factor is due to an invalid plane-wave approximation, providing a corrected analysis that substantially reduces the factor at resonance energies.

Findings

The rise in astrophysical factor is an artifact of approximation.

Corrected calculations reduce the astrophysical factor by up to 10^3 times.

The invalid approximation led to overestimation of low-energy fusion rates.

Abstract

Carbon-carbon burning plays an important role in many stellar environments. Recently, using the indirect Trojan horse method A. Tumino {\em et al.} reported [Nature {\bf 557} 687 (2018)] a strong rise of the astrophysical factor for the carbon-carbon fusion at low resonance energies. In this paper, we demonstrate that this rise is the artifact of using an invalid plane-wave approximation. It is shown that the calculated renormalization factor decreases the astrophysical factor from [A. Tumino {\em et al.}, Nature {\bf 557} 687 (2018)] at the resonance energies of $E=0.8-0.9$ MeV by as much as $\approx 10^{3}$ times.