Critical Temperature and Condensate Fraction of the Trapped Interacting Bose Gas with Finite-size Effects

The critical temperature and condensate fraction of a trapped interacting Bose gas are investigated when both atom-atom interaction and finite-size effects are taken into account. Canonical ensemble is used to obtain the equations on the condensate fraction for the trapped interacting Bose gas near and below the critical temperature. In our approaches corrections due to atom-atom interaction and finite-size effects are obtained simultaneously for the critical temperature and condensate fraction of the system. Analytical high-order correction to the condensate fraction is given in this work.