Radial distribution function within the framework of the Tsallis statistical mechanics

This study is conducted to obtain the radial distribution function (RDF) within the Tsallis statistical mechanics. To this end, probability distribution functions are applied in the first and fourth versions of the Tsallis statistics. Moreover, a closed formula is proposed for RDF. The power nature of the probability distribution in the Tsallis statistics makes it difficult to separate kinetic energy and configurational potential parts. By using the Taylor expansion around q=1 of the power distribution, it is possible to show the independency of momenta and coordinates through integrating over the phase space variables. In addition, at low densities, numerical calculations have been performed for the RDF. Our results show that the correlation increases as q values increase.