Classical and quantum non-extensive statistics effects in nuclear many-body problems

Recent progress in statistical mechanics indicates the Tsallis non-extensiv e thermostatistics as the natural generalization of the standard classical and quantum statistics, when memory effects and long-range forces are not n egligible. In this framework, we show that in weakly non-ideal plasma non-e xtensive and quantum uncertainty effects should be taken into account to de rive the equilibrium distribution functions, quantum fluctuations and corre lations between the particles. The strong influence of these effects is dis cussed in the context of the solar neutrino problem and in the high-energy nuclear-nuclear collision experiments. Although the deviation from the Bolt zmann-Gibbs statistics, in both cases, is very small, the nuclear reaction rates and quantum fluctuations are strongly influenced by the non-extensive feature of the solar plasma and the hadronic gas produced by a quark-gluon plasma. The discrepancies between the experimental data and theoretical pr evisions are sensibly reduced. (C) 2001 Elsevier Science Ltd. All rights re served.