Self-consistent Strong Screening Applied to Thermonuclear Reactions

Self-consistent strong plasma screening around light nuclei is implemented in the Big Bang nucleosynthesis (BBN) epoch to determine the short-range screening potential, e ϕ(r)/T ≥ 1, relevant for thermonuclear reactions. We numerically solve the nonlinear Poisson-Boltzmann equation incorporating Fermi-Dirac statistics, adopting a generalized screening mass to find the electric potential in the cosmic BBN electron-positron plasma for finite-sized α particles (⁴He⁺⁺) as an example. Although the plasma follows Boltzmann statistics at large distances, Fermi-Dirac statistics is necessary when work performed by ions on electrons is comparable to their rest-mass energy. While self-consistent strong screening effects are generally minor owing to the high BBN temperatures, they can enhance the fusion rates of high-Z (Z > 2) elements while leaving fusion rates of lower-Z (Z ≤ 2) elements relatively unaffected. Our results also reveal a pronounced spatial dependence of the self-consistent strong screening potential near the nuclear surface. These findings about the electron-positron plasma’s role refine BBN theory predictions and offer broader applications for studying weakly coupled plasmas in diverse cosmic and laboratory settings.