  Due to screening effects, nuclear reactions in astrophysical plasmas may
behave differently than in the laboratory. The possibility to determine the
magnitude of these screening effects in colliding laser-generated plasmas is
investigated theoretically, having as a starting point a proposed experimental
setup with two laser beams at the Extreme Light Infrastructure facility. A
laser pulse interacting with a solid target produces a plasma through the
Target Normal Sheath Acceleration scheme, and this rapidly streaming plasma
(ion flow) impacts on a secondary plasma created by the interaction of a second
laser pulse on a gas jet target. We model this scenario here and calculate the
reaction events for the astrophysically relevant reaction $^{13}$C($^4$He,
$n$)$^{16}$O. We find that it should be experimentally possible to determine
the plasma screening enhancement factor for fusion reactions by detecting the
difference in reaction events between two scenarios of ion flow interacting
with the plasma target and a simple gas target. This provides a way to evaluate
nuclear reaction cross-sections in stellar environments and can significantly
advance the field of nuclear astrophysics.
