Approach on Tsallis statistical interpretation of hydrogen-atom by adopting the generalized radial distribution function

Abstract

This paper revisits the statistical interpretation of the hydrogen atom within the framework of Tsallis Statistical Mechanics in the Canonical Ensemble. The convergence of the partition function does not exhibit for all the temperatures, while the well-known T → T′ transformation method of Tsallis Statistics fails, since non-monotonicity is observed between the ordinary temperature, T, and the auxiliary one, T′. Here we re-examine the inconsistency of T → T′ transformation method, in the case where the partition function converges for all the temperatures, by considering the generalized radial distribution function. We find that both the transformation method inconsistency and the partition function divergence can be recovered for all the temperatures, if the hydrogen atom is restricted within a critical radius R _c  ≤ 4.832 bohr, while Tsallis entropic index values are given by ${q\left( {R_c}\right)\in \left[ {q_c \cong 0.664,q^{\ast}=\frac{7}{9}}\right]}$.