A Nonextensive Approach to Bose-Einstein Condensation of Trapped Interacting Boson Gas

Abstract

In the Bose-Einstein condensation of interacting atoms or molecules such as ⁸⁷Rb, ²³Na and ⁷Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy U _q and the particle number N _q of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature T _cq is derived versus T _c given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q≈0.1 for ⁸⁷Rb atomic gas, q≈0.95 for ⁷Li and q≈0.62 for ²³Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.