A quantum plasma screening model based on the density matrix formalism is used to investigate theoretically the thermonuclear reactions $^{13}$C($alpha$, $n$)$^{16}$O and $^2$H($d$, $n$)$^3$He in laser-generated plasmas over a large range of densities and temperatures. We find that for cold and dense (solid-state density) plasmas, the quantum model predicts plasma screening enhancement factors up to one order of magnitude larger than the ones from classical plasma models. Our results indicate that quantum effects can enhance the plasma screening for thermonuclear reactions, with potential also for industrial fusion energy gain. We put forward a possible experimental test of the screening theory in laser-generated plasmas which could also confirm predictions from nuclear astrophysics.
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