Reaction rate by the non-extensive thermostatistics
M. Assunção 1*, F. E. M. Silveira 2, A. S. Lima 3
1 Departamento de Ciências Exatas e da Terra, Universidade Federal de São Paulo, Brazil
2 Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, SãoPaulo, Brazil
3 Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, São Paulo, Brazil
The problem of to determine the energy generation mechanism in stars was firstly attacked by Gamow in the framework of his quantum mechanical theory of potential barrier penetration [1-3]. In this work, the potential barrier penetration approach to stellar nuclear reactions rate has been rediscussed with basis on non-extensive statistics. This extended formulation, Tsallis distribution is written as a function of the q parameter. The investigation has been performed to non-resonant reactions, for which the S-factor can be regarded as a constant. The q-Gamow peak has been derived and, in connection with the usual Gaussian approximation, the corresponding half q-width has been also estimated. Plots of the q-Gamow peak shows that a small variation of the parameter results in different values of q-energy and half-width q-width for as reactions non-resonant. The results show that the Gamow window is changed as compared to the Maxwell-Boltzmann for small variations of the extensive q parameter. In this sense, our study indicates that the residence time of a star on the main sequence is changed depending on the approach considered. The calculation for the resonant reactions (still preliminary) complement this work.
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