Related papers: On extended thermonuclear functions through pathwa…
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…
Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar…
Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the…
The method for the evaluation of the non-resonant thermonuclear function in the Maxwell-Boltzmann case with depleted tail is discussed. Closed forms of the analytical results are obtained in computational format, and written in terms of the…
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…
The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai [Mathai A.M.:2005, A pathway to matrix-variate gamma and normal densities, Linear…
An analytic study of the reaction probability integrals corresponding to the various forms of the slowly varying cross-section factor $S(E)$ is attempted. Exact expressions for reaction probability integrals are expressed in terms of the…
We provide the most stringent constraint to date on possible deviations from the usually-assumed Maxwell-Boltzmann (MB) velocity distribution for nuclei in the Big-Bang plasma. The impact of non-extensive Tsallis statistics on thermonuclear…
Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three distinct velocity distributions,…
We study two different physical scenarios of thermonuclear reactions in stellar plasmas proceeding through a narrow resonance at low energy or through the low energy wing of a wide resonance at high energy. Correspondingly, we derive two…
The distribution function of the relative velocity in a two-body reaction of nonrelativistic uncorrelated particles is derived for general cases of given distribution functions of single particle velocities. The distribution function is…
Rigorous statistical methods for estimating thermonuclear reaction rates and nucleosynthesis are becoming increasingly established in nuclear astrophysics. The main challenge being faced is that experimental reaction rates are highly…
This work describes the formalism for estimating thermonuclear reaction rates for astrophysical applications, emphasizing modern statistical approaches such as Monte-Carlo sampling and Bayesian models. We discuss related topics including…
We present an analytic proof of the integrals for astrophysical thermonuclear functions which are derived on the basis of Boltzmann-Gibbs statistical mechanics. Among the four different cases of astrophysical thermonuclear functions, those…
The current Big-Bang Nucleosynthesis (BBN) model has been constructed based on a nuclear reaction network operating with thermal reactivities of Maxwell-Boltzmann (MB) distribution plasma. However, does the classical MB distribution still…
As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. In this paper mathematical/statistical techniques for deriving…
A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have…
Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The…