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Pathway parameter and thermonuclear functions

Author

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  • Mathai, A.M.
  • Haubold, H.J.

Abstract

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 [A.M. Mathai, H.J. Haubold, Modern Problems in Nuclear and Neutrino Astrophysics, Akademie-Verlag, Berlin, 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. Non-extensive statistical mechanics, as developed by Tsallis [C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D 193 (2004) 3–34], provides the physical basis for the generalized thermonuclear functions considered in this paper.

Suggested Citation

  • Mathai, A.M. & Haubold, H.J., 2008. "Pathway parameter and thermonuclear functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2462-2470.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:11:p:2462-2470
    DOI: 10.1016/j.physa.2008.01.031
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    References listed on IDEAS

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    1. Mathai, A.M. & Haubold, H.J., 2007. "Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(1), pages 110-122.
    2. Saxena, R.K. & Mathai, A.M. & Haubold, H.J., 2004. "Astrophysical thermonuclear functions for Boltzmann–Gibbs statistics and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(3), pages 649-656.
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