Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

The critical temperature of Bose-Einstein condensation at minimum momentum state for weakly interacting Bose gases in a power-law potential and the deviation of the critical temperature from ideal bose gas are studied. The effect of interaction on the critical temperature is ascribed to the ratiao α/λc, where α is the scattering length for s wave and λc is de Broglie wavelength at critical temperature. As α/λc<<1/(2π )2, the interaction is negligible. The presented deviation of the critical temperature for three dimensional harmonic potential is well in agreement with recent measurement of critical temperature for 87Rb bose gas trapped in a harmonic well.