Pathway parameter and thermonuclear functions

TL;DR

This paper introduces a pathway parameter to generalize thermonuclear functions, allowing for a broader analysis of reaction rates and providing new interpretations for the parameter in different physical contexts.

Contribution

It extends previous models by incorporating a pathway parameter alpha, enabling a unified framework for thermonuclear functions with Maxwell-Boltzmann and non-standard distributions.

Findings

Generalized thermonuclear functions with pathway parameter alpha

Interpretations of alpha in cut-off and moment contexts

Recovery of Maxwell-Boltzmann case as alpha approaches 1

Abstract

In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell-Boltzmann distribution function were considered in a series of papers by Mathai and Haubold (1988). In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter alpha, so that when alpha --> 1 the thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will also give interpretations for the pathway parameter alpha in the case of cut-off and in terms of moments.