  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.
