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

TL;DR

This paper extends thermonuclear reaction rate models to include Tsallis statistics and the pathway model, providing analytical representations that unify classical and generalized distributions for nuclear reaction analysis.

Contribution

It introduces a unified analytical framework for thermonuclear functions using the pathway model, encompassing Maxwell-Boltzmann and Tsallis distributions, with closed-form solutions.

Findings

Closed-form representations of thermonuclear functions using H- and G-functions.

Maxwell-Boltzmann functions are special cases of the extended model.

The pathway model generalizes existing distribution-based reaction rate theories.

Abstract

The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) 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 (2005), 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.