Nonlinear polarization effects on plasma screening for fusion reactions
Using a finite-temperature two-center Thomas-Fermi-Dirac model, we investigate nonlinear plasma screening effects on the fusion reactions D-T, $^{12}$C-$^{12}$C, and p-$^{11}$B. The effective interaction between a reacting ion pair is obtained self-consistently at the mean-field level. Combining this potential with a complex Woods-Saxon nuclear potential, we solve the stationary Schrödinger equation to evaluate tunneling probabilities and reaction rates. Compared with Debye-Hückel theory, the two-center screening potential can be stronger or weaker, and the resulting fusion enhancement correspondingly amplified or suppressed, depending on the plasma conditions and the internuclear separation. We identify the underlying mechanisms: relative to the single-center prediction, the nonlinear evacuation of background ions suppresses screening, whereas nonlinear electron accumulation enhances it. The two channels respond to different plasma state parameters: the ionic suppression deepens with increasing coupling strength, whereas the electronic enhancement peaks at intermediate degeneracy. The two-center correction therefore follows a factorized scaling law in the nuclear charges of the reacting pair and the plasma state parameters. These findings highlight the importance of a self-consistent two-center treatment for determining effective interactions and evaluating static screening corrections to fusion reaction rates.