Extension of thermonuclear functions through the pathway model including Maxwell–Boltzmann and Tsallis distributions

The Maxwell–Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics [C. Tsallis, Possible generalization of Boltzmann–Gibbs statistics, Journal of Statistical Physics 52 (1988) 479–487] and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being conducted with the help of statistical techniques. The pathway model, recently introduced by Mathai [A.M. Mathai, A Pathway to matrix-variate gamma and normal densities, Linear Algebra and its Applications 396 (2005) 317–328], is utilized for thermonuclear functions and closed-form representations are obtained in terms of H-functions and G-functions. Maxwell–Boltzmannian thermonuclear functions become particular cases of the extended thermonuclear functions. A brief review on the development of the theory of analytic representations of nuclear reaction rates is given.