On extended thermonuclear functions through pathway model

TL;DR

This paper extends the thermonuclear reaction rate functions beyond Maxwell-Boltzmann statistics to include Tsallis statistics and other distributions, providing closed-form evaluations and comparisons.

Contribution

It introduces a generalized approach to thermonuclear functions using pathway models and evaluates these integrals in closed form for various parameters.

Findings

Closed-form expressions for extended reaction probability integrals.

Comparison between standard and extended reaction integrals.

Application of residue calculus for integral evaluation.

Abstract

The major problem in the cosmological nucleosynthesis is the evaluation of the reaction rate. The present scenario is that the standard thermonuclear function in the Maxwell-Boltzmann form is evaluated by using various techniques. The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. The main purpose of this paper is to investigate in some more detail the extended reaction probability integral in the equilibrium thermodynamic argument and in the cut-off case. The extended reaction probability integrals will be evaluated in closed form for all convenient values of the parameter by means of residue calculus. A comparison of the standard reaction probability integrals with the extended reaction probability integrals is also done.