Galitskii and Yakimets showed that in dense or low temperature plasma, due to quantum uncertainty effect, the particle distribution function over momenta acquires a power-like tail even under conditions of thermodynamic equilibrium. We show that in weakly non-ideal plasmas, like the solar interior, both non-extensivity and quantum uncertainty should be taken into account to derive equilibrium ion distribution functions and to estimate nuclear reaction rates and solar neutrino fluxes. The order of magnitude of the deviation from the standard Maxwell-Boltzmann distribution can be derived microscopically by considering the presence of random electrical microfield in the stellar plasma. We show that such a nonextensive statistical effect can be very relevant in many nuclear astrophysical problems.
