The Maxwell — Boltzmannian Approach to the Nuclear Reaction Rate Theory

Haubold, H. J.; Mathai, A. M.

doi:10.1002/prop.2190331103

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…The following derivations are adapted from [9]. From the Mellin-Barnes representation of the G-function, G 3, 1 1,3 ( (α−1)x 2…”

Section: Extended Kinetic Equationsmentioning

confidence: 99%

Some Aspects of Extended Kinetic Equation

Kumar¹

2015

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Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317-328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.

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“…The following derivations are adapted from [9]. From the Mellin-Barnes representation of the G-function, G 3, 1 1,3 ( (α−1)x 2…”

Section: Extended Kinetic Equationsmentioning

confidence: 99%

Some Aspects of Extended Kinetic Equation

Kumar¹

2015

Axioms

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“…The standard thermonuclear function in the Maxwell-Boltzmann case in the theory of nuclear reactions, is given by the following (Critchfield, 1972;Haubold and Mathai, 1985;Mathai and Haubold, 1988):…”

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confidence: 99%

Pathway parameter and thermonuclear functions

Mathai,

Haubold

2007

Preprint

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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 considered in a series of papers by Mathai and Haubold (1988). In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter α, so that when α → 1 the thermonuclear functions in the Maxwell-Boltzmannian case are recovered. We will also give interpretations for the pathway parameter α in the case of cut-off and in terms of moments.

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“…The inner integral can be evaluated by using a result in HAUBOLD and MATHAI (1985). This will be stated here as a lemma.…”

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A note on the linear stellar model

1987

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For a purely gaseous self-gravitating stellar configuration with linear matter density distribution the total power generated by nuclear reactions is considered. The analytic connection between physical parameters of the macroscopic and microscopic levels of the stellar equilibrium configuration is revealed.Fur eine gasformige selbstgravitierende Konfiguration mit linearer Dichteverteilung der Materie wird die totale nukleare Energieerzeugung berechnet. Die Abhangigkeit der Parameter, die die stellare Gleichgewichtskonfiguration auf mikrophysikalischer und rnakrophysikalischer Ebene kennzeichnen, wird mit analytischen Methoden aufgedeckt.Key words: stellar structure ~ nuclear reactions -energy production -analytical modelThe theory of stellar structure and stellar evolution is based on two different building blocks of physics. On the microscopic leuel that is the physics of elementary processes described by constitutive relations such as nuclear energy generation rate, radiative opacity, and thermodynamic properties as well. They are local physics considering those processes as proceeding in a chemically homogeneous medium with fixed temperature and density. On the macroscopic level the elementary processes have to be integrated over the temperature and density distributions of a self-gravitating system to obtain a stellar configuration. Nuclear burning stages of a star, for example, can be approximated by evolving equilibrium models where time-independent equations have to be solved.Both levels have attracted considerable attention in recent years. The importance of the existence and uniqueness of stellar equilibrium models has been demonstrated extensively by PERDANG (1975). Although almost all types of constitutive relations can be sources of multiple solutions of the stellar structure equations he could show under broad mathematical assumptions on the local physics that global existence and uniqueness properties can be given (c.f. also KAHLER and WEIGERT 1974).On the other hand, by means of gravothermodynamics, much work is done on the question of what is the internal structure of a se[f-gratiitating stellar configuration in thermal equilibrium and how it evolves (ANTONOV 1962; LYNDEN-BELL and WOOD 1968). Surely, the main result of such considerations is that if the temperature distribution in the configuration is isothermal it will be in thermal equilibrium and, as far as the density goes the jump between the center and a point of a certain mass shell is less than the critical value for which the configuration is stable against gravothermal catastrophe.Despite the fruitful results obtained by global considerations of self-gravitating stellar configurations in thermal equilibrium including well defined constitutive relations the problem of branching points occurring during the evolution of equilibrium models is still open. Such branching points can be simply generated by certain approximations (better mathematics is needed) or even can be hidden in the input physics leading to statistical effects deciding on...

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The Maxwell — Boltzmannian Approach to the Nuclear Reaction Rate Theory

Cited by 9 publications

References 15 publications

Some Aspects of Extended Kinetic Equation

Some Aspects of Extended Kinetic Equation

Pathway parameter and thermonuclear functions

A note on the linear stellar model

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