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

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.