  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
cross-section, 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 the energy
range of the nuclear cross-section in experiments, and the electron screening
effect.
