Astrophysical thermonuclear functions for Boltzmann-Gibbs statistics and Tsallis statistics

One of the first applications of Gamow’s theory of quantum mechanical potential barrier penetration to other than his analysis of alpha radioactivity was in the field of thermonuclear astrophysics [1,2]. Atkinson and Houtermans proposed that the source of energy released by stars lay in thermonuclear reactions taking place near their centres where the motion of nuclei was supposed to be in thermal equilibrium. The state of hot stellar plasmas is such that only the lightest chemical elements could contribute because of the Coulomb repulsion between nuclei. In effect, the rate of energy production is goverend by the average of the Gamow penetration factor over the MaxwellBoltzmann velocity distribution [3]. The thermonuclear reaction rate is the coefficient in the rate equation that is used to describe the change of chemical composition of hot plasmas. Similarly fundamental, the inverse of this coefficient is the characteristic time scale for the respective thermonuclear