IX LASNPA, Quito 2011 |

Reaction rate by the non-extensive thermostatistics

M. Assunção ^{1}*, F. E. M. Silveira ^{2}, A. S. Lima ^{3}

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.

References

[1] Clayton, D. D. 1983, Principles of Stellar Evolution and Nucleosynthesis, second ed. (Chicago and London, The University of Chicago Press).

[2] Rolfs, C. E. and Rodney, W. S. 2005, Cauldrons in the Cosmos: Nuclear Astrophysics (Theoretical Astrophysics) (Chicago - London, The University of Chicago Press).

[3] Fowler, W. A. 1984, Rev. Mod. Phys., 56, 149.

References

[1] Clayton, D. D. 1983, Principles of Stellar Evolution and Nucleosynthesis, second ed. (Chicago and London, The University of Chicago Press).

[2] Rolfs, C. E. and Rodney, W. S. 2005, Cauldrons in the Cosmos: Nuclear Astrophysics (Theoretical Astrophysics) (Chicago - London, The University of Chicago Press).

[3] Fowler, W. A. 1984, Rev. Mod. Phys., 56, 149.

* Corresponding author - massuncao@unifesp.br | oral presentation |

22 |