Nuclear astrophysical plasmas: ion distribution functions and fusion rates

This article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discuss several mechanisms that can cause such deviations. Fusion reactions are the fundamental energy source of stars and play important roles in most astrophysical contexts. Since the beginning of quantum mechanics, basic questions were addressed such as how nuclear reactions occur in stellar plasmas at temperatures of few keV (1 keV ≈ 11.6× 10 ◦K) against Coulomb barriers of several MeV and what reactions or reaction networks dominate the energy production. It was soon realized that detailed answers to such questions involved not only good measurements or quantum mechanical understanding of the relevant fusion cross sections, but also the use of statistical physics for describing energy and momentum distributions of the ions and their screening [1]. Gamow understood that reacting nuclei penetrate Coulomb barriers by means of the quantum tunnel effect and Bethe successfully proposed the CNO and then the pp cycle as candidates for the stellar energy production: this description has been directly confirmed by several terrestrial experiments that have detected neutrinos produced by pp and CNO reactions in the solar core [2]. In the past only few authors (e.g., d’E. Atkinson, Kacharov, Clayton, Haubold) examined critically the energy distribution and proposed that such distribution could deviate from the Maxwellian form. In fact, it is commonly accepted that main-sequence stars like the Sun have a core, i.e. an electron nuclear plasma, where the ion velocity distribution is Maxwellian. In the following, we first discuss why even tiny deviations from the Maxwellian distribution can have important consequences and then what can originate such deviations.