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 B ose gas are investigated when both atom-atom interaction and finite-size ef fects are taken into account. A canonical ensemble is used to obtain the eq uations on the condensate fraction for the trapped interacting Bose gas nea r and below the critical temperature. In our approaches corrections due to atom-atom interaction and finite-size effects are obtained simultaneously f or the critical temperature and condensate fraction of the system. An analy tical high-order correction to the condensate fraction is given.