Related papers: Analytical Study of Thermonuclear Reaction Probabi…
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…
Nuclear reactions govern major aspects of the chemical evolution od galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction…
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…
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…
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 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…
The problem of estimating non-resonant astrophysical S-factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many…
We have calculated astrophysical reaction cross-sections for $(\gamma,\alpha)$ reactions of some nuclei important for the calculation of $p$-process reaction-decay network. Reaction rates for $\alpha$-induced reactions are calculated with…
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…
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…
The quantum diffusion approach is extended to low energy fusion (capture) reactions of light- and medium-mass nuclei. The dependence of the friction parameter on bombarding energy is taken into account. A simple analytic expression is…
The cross sections for the deep sub-barrier fusion reaction of light nuclei are calculated within the theoretical framework of the selective resonant tunneling model. In this model, assumption of a complex square-well nuclear potential is…
We study the scaling properties of proton-nucleus total reaction cross sections for stable nuclei and propose an approximate expression in proportion to Z^{2/3}\sigma_{pp}^{total} + N^{2/3} \sigma_{pn}^{total}. Based on this expression, we…
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…
A recent article (D.A. Brown, et al., Phys. Rev. C98 024616 (2018)) rproposed a modification of the cross section formula used in practical calculations of compound nucleus reactions. We discuss the main concepts and approximations of…
An overview is presented on statistical techniques for the analytic evaluation of integrals for non-resonant, non-resonant depleted, non-resonant cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The techniques are…
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…
The cross-sections of proton-induced reactions on 184W at incident proton energy below 200MeV are calculated and analyzed including reaction cross-sections, elastic scattering angular distributions, energy spectra and double differential…
We present an approximate analytic expression for thermonuclear reaction rate of charged particles when the cross section contains a single narrow or wide resonance described by a Breit-Wigner shape. The resulting expression is uniformly…
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,…