It has been shown by Galitskii and Yakimets that in a dense plasma, like th
e stellar core, the tunneling particles undergo simultaneous collisions wit
h other particles and, due to quantum uncertainty effects, the particles di
stribution function over momenta acquires a non-Maxwellian power-like tail
even under thermodynamic equilibrium. We show that these many-body effects
imply a strongly modification of the nuclear CNO reaction rates which are,
however, strongly modulated by taking into account the correct non-extensiv
e thermostatistical framework when memory effects and long range force are
not negligible. These statistical features match the plasma characteristic
of weak non-ideal stellar plasma like solar interior.