Nonlinear polarization effects on plasma screening for thermonuclear reactions

We investigate two-center plasma screening effects on thermonuclear reactions of D-T, p-$^{11}$B, and $^{12}$C-$^{12}$C, spanning from classical to degenerate regimes. The two-center screening potential is obtained within a finite-temperature Thomas-Fermi-Dirac framework, capturing two-ion correlations as the leading-order many-body effect. Combining the resulting screened Coulomb potential with a complex Woods-Saxon nuclear potential, we solve the stationary Schr\"{o}dinger equation to obtain the fusion tunneling probabilities and the corresponding reaction rates. Compared to Debye-H\"{u}ckel results, the present screening potential is stronger in weakly coupled and weakly degenerate regimes but weaker in strongly coupled and strongly degenerate regimes. Consequently, the fusion enhancement factors are amplified in the former but suppressed in the latter. An underlying interplay between two mechanisms is identified: the nonlinear polarization of ions tends to reduce the screening effect, whereas the nonlinear polarization of electrons tends to enhance it. This subtle competition is governed by the plasma coupling strength and degeneracy. These findings highlight that a two-center treatment is important for predicting fusion rates in dense plasmas.