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. (c) 2007 Elsevier B.V. All rights reserved.