Reinvestigating the Gamow Factor of Reactions on Light Nuclei

Abstract

We present a modified Gamow factor by reinvestigating the conventional assumptions used in its derivation. The conventional Gamow factor, factorized from the total cross section, effectively describes the penetration probabilities (PPs) in low-energy nuclear reactions under the assumption of particle energies significantly lower than the Coulomb barrier. However, we find that the assumption is invalid for light nuclei, resulting in PPs that depend on the nuclear potential depth for such nuclei. By adopting a potential depth fitted to experimental fusion cross sections, we demonstrate that PPs for light nuclei (D+D, D+T, D+3He, p+D, p+6Li, and p+7Li) become higher than those predicted by the conventional form near the Coulomb barrier. This reduces the Gamow peak energy by a factor of 5.3 maximally compared to the conventional form. Furthermore, we show that the enhancement factor due to the Debye screening effects in the solar core can be reduced by approximately 5%-10% due to the modified PP. Our findings hold implications for evaluating the available energy region in low-energy reaction experiments based on the Gamow peak energy region and for understanding electron screening effects in typical astrophysical environments.