  We investigate the impact of magnetic fields on the potential barrier between
two interacting nuclei. We addressed this by solving the Boltzmann equation and
Maxwell's theory in the presence of a magnetic field, resulting in the
determination of magnetized permittivity. Additionally, we derived the
magnetized Debye potential, which combines the conventional Debye potential
with an additional magnetic component. We then compared the Boltzmann approach
with the Debye method. Both methods consistently demonstrate that magnetic
fields increase permittivity. This enhanced permittivity leads to a reduction
in the potential barrier, consequently increasing the reaction rate for
nucleosynthesis. Furthermore, the dependence on temperature and electron
density in each approach is consistent. Our findings suggest that magnetized
plasmas, which have existed since the Big Bang, have played a crucial role in
nucleosynthesis.
