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 alpha/lambda(c)A, where a is the scattering length for s wave and A, is lambda(c) Broglie wavelength at critical temperature. As alpha/lambda(c)<<1/(2 pi)(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 Rb-87 bose gas trapped in a harmonic well.