A MORE ACCURATE ANALYSIS OF BOSE-EINSTEIN CONDENSATION IN HARMONIC TRAPS

Using the Euler-Maclaurin summation we calculate analytically the inte rnal energy for non-interacting bosons confined within a harmonic osci llator potential. The specific heat shows a sharp lambda-like peak ind icating a condensation into the ground state at a well-defined transit ion temperature. Full agreement is obtained with direct numerical calc ulation of the same quantities. When the number of trapped particles i s very large and at temperatures near and above the transition tempera ture, the results also agree with previous approximate calculations. A t extremely low temperatures both the specific heat and the number of particles excited from the condensate are exponentially suppressed.