A moving ion in plasma creates a deformed electric potential depending on the ion velocity, which leads to the distinct screening effect compared to the standard static Salpeter formula. In this paper, adopting the test charge method, we explore the dynamical screening effects on big bang nucleosynthesis (BBN). We find that the high temperature in the early universe causes the ion velocity to be faster than the solar condition so that the electric potential is effectively polarized. However, the low density of background plasma components significantly suppresses the dynamical screening effects on thermonuclear reaction rates during the BBN epoch. We compare our results with several thermonuclear reaction rates for solar fusion considering the dynamical screening effects. Also, we discuss the additional plasma properties in other astrophysical sites for the possible expansion from the present calculation in the future.

This study provides an improved understanding of the penetration probabilities (PPs) in nuclear reactions of light nuclei by correcting the assumptions used in the conventional Gamow factor. The Gamow factor effectively describes the PP in nuclear reactions based on two assumptions: low particle energy than the Coulomb barrier and neglecting the dependence of nuclear interaction potential. However, we find that the assumptions are not valid for light nuclei. As a result of a calculation that excludes the assumptions, we obtain the PP that depends on the nuclear interaction potential depth for the light nuclei. For the potential depth fitted by the experimental fusion crosssection, we present that PPs of light nuclei (D+D, D+T, D+ 3 He, p+D, p+ 6 Li, and p+ 7 Li) become higher than the conventional one near the Coulomb barrier. We also discuss the implications of the modified PP, such as changes in the Gamow peak energy, which determine the measurement of energy range of the nuclear cross-section in experiments, and the electron screening effect.