  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. For cold and dense
(solid-state density) plasmas, our results show that quantum effects can
enhance the plasma screening for thermonuclear reactions up to one order of
magnitude compared to the classical case. This result can have impact on
nuclear astrophysics predictions, and also may play a role for fusion energy
gain prospects. Our simulations allow us to identify the laser-generated plasma
experimental setting in which the quantum effects on plasma screening could be
confirmed at existing high-intensity laser facilities.
