A unified approach to thermonuclear reaction rates

Thermonuclear fusion reactions within stellar interiors are primarily responsible for generating energy and synthesizing the elements that compose the universe. Calculating the reaction rates provides essential information about the lifespan and luminosity of Sun-like stars, eventually, it has siginificant role in big-bang nucleosynthesis. In this article, we consider the exact thermonuclear reaction rate functions in standard, cut-off, and depleted tail cases. Since 1984, analytic solution of these thermonuclear reaction rates were obtained by many authors and a number of possible generalizations and their closed form solutions are available in the literature. The present study unifies all such generalizations through a single thermonuclear rate function via the techniques in statistical mechanics. A novel velocity distribution function is developed for interacting particles, extending their applicability to the maximum. Since real stellar scenarios often deviate from strict hydrostatic equilibrium case, this improved distribution captures these deviations effectively. The paper gives more emphasis on non-resonant reaction rates in depleted tail case and obtain the closed-form solution in terms of Buschman H-function of two variables.