Thermal distributions in stellar plasmas, nuclear reactions and solar neutrinos

Coraddu, M.; Kaniadakis, Giorgio; Lavagno, Andrea; Lissia, M.; Mezzorani, G.; Quarati, Piero

doi:10.1590/s0103-97331999000100014

Cited by 57 publications

(69 citation statements)

References 36 publications

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“…As already shown in the recent past, very small deviations from Maxwellian momentum distribution do not modify the properties of stellar core and are in agreement with the helioseismology constraints [6], but may affect the evaluation of the nuclear fusion rates that may be enhanced or depleted, depending on the superdiffusion or subdiffusion properties of the particles [7].…”

Section: Thermonuclear Reaction In Plasmas and Distribution Tailssupporting

confidence: 82%

“…The situation is very different in the presence of a Coulomb barrier, when the reacting particles are charged, as in the fusion europhysics news NOVEMBER reactions that power stars [7]. The penetration of large Coulomb barriers (Zα/r is of the order of thousands in units of kT when r is a typical nuclear radius) is a classically forbidden quantum effect.…”

Section: Thermonuclear Reaction In Plasmas and Distribution Tailsmentioning

confidence: 99%

“…The presence of random fields (e.g., distributions of random electric micro-fields or, in general, of random forces) introduces in the kinetic equations factors whose effect is to enhance or to deplete the high-momentum tail of the distribution function [7].…”

Section: Deviations From Maxwellian Distributionmentioning

confidence: 99%

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Nuclear astrophysical plasmas: ion distribution functions and fusion rates

Lissia

Quarati

2005

Europhysics News

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T his article illustrates how very small deviations from the Maxwellian exponential tail, while leaving unchanged bulk quantities, can yield dramatic effects on fusion reaction rates and discusses several mechanisms that can cause such deviations.Fusion reactions are the fundamental energy source of stars and play important roles in most astrophysical contexts. Since the beginning of quantum mechanics, basic questions were addressed such as how nuclear reactions occur in stellar plasmas at temperatures of few keV (1 keV ≈ 11.6 x 10 6 K) against Coulomb barriers of several MeV and what reactions or reaction networks dominate the energy production. It was soon realized that detailed answers to such questions involved not only good measurements or quantum mechanical understanding of the relevant fusion cross sections, but also the use of statistical physics to describe the energy and momentum distributions of the ions and their screening [1].Gamow understood that reacting nuclei penetrate Coulomb barriers by means of the quantum tunnel effect and Bethe successfully proposed the CNO and then the pp cycle as candidates for the stellar energy production: this description has been directly confirmed by several terrestrial experiments that have detected neutrinos produced by pp and CNO reactions in the solar core [2].In the past only a few authors (e.g., d'E. Atkinson, Kacharov, Clayton, Haubold) have examined critically the energy distribution and proposed that such a distribution could deviate from the Maxwellian form. In fact, it is commonly accepted that main-sequence stars like the Sun have a core, i.e. an electron nuclear plasma, where the ion velocity distribution is Maxwellian. In the following, we first discuss why even tiny deviations from the Maxwellian distribution can have important consequences and then what can be the origin of such deviations. Thermonuclear reaction in plasmas and distribution tailsIn a gas with n1 (n2) particles of type 1 (2) per cubic centimeter and relative velocity v, the reaction rate r (the number of reactions per unit volume and unit time) is given by (1)where σ = σ(v) is the nuclear cross section of the reaction. The reaction rate per particle pair is defined as the thermal average Therefore, the reaction rate per particle pair < σv > is determined by the specific cross section and by the velocity distribution function of the reacting particles. When no energy barrier is present and far from resonances, cross sections do not depend strongly on the energy. Most of the contribution to < σv > comes from particles with energy of the order of kT, and the dependence on the specific form of f (v) is weak. The same is true for bulk properties that receive comparable contributions from all particles: e.g., the equation of state.The (EG = 45.09 MeV, blue). Correspondingly, the peaks become (much) lower; note that the three curves have been multiplied times 10 5 , 10 17 , and 10 26 , respectively, to make them visible on the same scale.

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Section: Thermonuclear Reaction In Plasmas and Distribution Tailssupporting

confidence: 82%

Section: Thermonuclear Reaction In Plasmas and Distribution Tailsmentioning

confidence: 99%

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Nuclear astrophysical plasmas: ion distribution functions and fusion rates

Lissia

Quarati

2005

Europhysics News

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“…As an application of the results (5), (13), and (14) we deduce the values of the following two thermonuclear functions I 1 [8] and I 2 ["cut-off", 8,13,14,17], in terms of which the astrophysical thermonuclear functions are expressed [8, see also 2,9]:…”

Section: M) (12)mentioning

confidence: 99%

Astrophysical thermonuclear functions for Boltzmann–Gibbs statistics and Tsallis statistics

Saxena

Mathai

Haubold

2004

Physica A: Statistical Mechanics and its Applications

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“…The reaction coefficient itself can be considered to be a statistical quantity subject to accommodating a distribution function based either on Boltzmann-Gibbs or Tsallis statistics (Haubold and Mathai, 1998;Coraddu at al., 1999;Saxena, Mathai, and Haubold 2004b). If some of the particles produced are also destroyed and if the destruction rate is b i for the i-th particle, and proportional to the number density, then…”

Section: Reaction Equation and Fractional Calculusmentioning

confidence: 99%

Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy

Mathai

Haubold

2007

Physica A: Statistical Mechanics and its Applications

146

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Abstract. The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order α, considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Rényi, Tsallis, and Havrda-Charvát entropies. The generalized entropy measure introduced here is also shown to have interesting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics (Tsallis, 1988) and superstatistics introduced by Beck and Cohen (2003). The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.

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Thermal distributions in stellar plasmas, nuclear reactions and solar neutrinos

Cited by 57 publications

References 36 publications

Nuclear astrophysical plasmas: ion distribution functions and fusion rates

Nuclear astrophysical plasmas: ion distribution functions and fusion rates

Astrophysical thermonuclear functions for Boltzmann–Gibbs statistics and Tsallis statistics

Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy

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