Analytical Results Connecting Stellar Structure Parameters and Extended Reaction Rates

Possible modification in the velocity distribution in the nonresonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions is used to obtain the stellar luminosity and neutrino emission rates. The composite parameter that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduced by Mathai (2005). Simple analytic models considered by various authors are utilized for evaluating stellar luminosity and neutrino emission rates and are obtained in generalized special functions such as Meijer's G-function and Fox's H-function. The standard and extended nonresonant thermonuclear functions are compared by plotting them. Behaviour of the new energy distribution, which is more general than the Maxwell-Boltzmann, is also studied. 1. Introduction The mystery behind the distant universe is explored so far by the understanding of the sun, the star near to us. It is the only star whose mass, radius, and luminosity are fairly accurately known. The structural change in the sun is due to the central thermonuclear reactor in it. Solar nuclear energy generation and solar neutrino emission are governed by chains of nuclear reactions in the gravitationally stabilized solar fusion reactor [1, 2]. Qualitative calculations of specific reaction rates require a large amount of experimental inputs and theoretical assumptions. By using the theories from nuclear physics and kinetic theory of gases one can determine the reaction rate for low-energy nonresonant thermonuclear reactions in nondegenerate plasma [3]. The formalization of the calculation of the reaction rate of interacting articles under cosmological or stellar conditions was presented by many authors [4, 5]. For the most common case, a nuclear reaction in which a particle of type strikes a particle of type producing a nucleus and a new particle is symbolically represented as where is the energy release given by , where denote the masses of the particles and denotes the velocity of light. The reaction rate of the interacting particles and is obtained by averaging the reaction cross section over the normalized density function of the relative velocity of the particles [5–7]. Let and denote the number densities of the particles and , respectively, and let be the reaction cross section where is the relative velocity of the