Non-extensive resonant reaction rates in astrophysical plasmas

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 approximate analytical formulae in order to calculate thermonuclear resonant reaction rates inside very coupled and non-ideal astrophysical plasmas in which non-extensive effects are likely to arise. Our results are presented as simple first-order corrective factors that generalize the well-known classical rates obtained in the framework of Maxwell-Boltzmann statistical mechanics. As a possible application of our results, we calculate the dependence of the total corrective factor with respect to the energy at which the resonance is located, in an extremely dense and non-ideal carbon plasma.Received: 7 January 2004, Revised: 9 March 2004, Published online: 14 September 2004PACS: 24.30.-v Resonance reactions - 26.50. + x Nuclear physics aspects of novae, supernovae, and other explosive environments - 05.90. + m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems