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/λ_c, where α is the scattering length for s wave and λ_c is de Broglie wavelength at critical temperature. As α/λ_c<<(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.