A deformed Doppler Broadening Function considering the Tsallis speed distribution

Abstract

The Doppler Broadening Phenomenon provides a good description for the effects of thermal agitation on the cross-section of the neutron-nucleus interaction and has its theoretical basis on Quantum Mechanics through the Single Level Breit-Wigner Formalism, as well as on Statistical Mechanics, with the Maxwell Boltzmann distribution. In this paper, the consequences of replacing the Maxwell Boltzmann speed distribution by the non-extensive Tsallis distribution in the evaluation of the absorption cross section in three-dimension is discussed. The Tsallis speed distribution introduces a deformation parameter q that measures the deviation from the Maxwellian speed distribution and, by taking the limit q→1, the deformation is removed. In this context, and considering the Tsallis distribution, an integral form is obtained for a deformed Doppler Broadening Function in the scope of the single-level Breit-Wigner formalism and Bethe-Placzek approximations. This deformed Doppler Broadening Function reproduces the well-established conventional Doppler Broadening Function at the limit when q→1 in which the deformation is removed. In order to study the range of values where the effect is significant, numerical tests were carried out considering several values for the q parameter.