The Non-thermal Energy Window for Laser-Driven Nuclear Reactions

Astrophysical nuclear reaction rates in stellar environments are governed by the Gamow window, where Maxwell-Boltzmann distributions and quantum tunneling probabilities combine to produce effective reactivity. However, this conventional formulation is inadequate for the non-thermal ion distributions generated in ultra-intense laser-plasma interactions. Here, we introduce an analytical framework, based on a Target Normal Sheath Acceleration (TNSA) mechanism, to evaluate nuclear reaction rates under these non-equilibrium conditions. We identify a new effective energy window and analytical expression of the fusion reactivity distinct from the conventional Gamow window, providing a predictive tool for laboratory astrophysics experiments designed to replicate astrophysical nuclear processes using laser-driven nuclear reactions.