Abstract
We consider the effect of inter-atom interactions on the condensation temperature Tc of an atomic Bose-Einstein condensate. We find an analytic expression of the shift in Tc induced by interactions with respect the ideal non-interacting case, in the mean-field and semi-classical approximations. Such a shift is expressed in terms of the ratio a/λTc between the s-wave scattering length a and the thermal wavelength λTc. This result is used to discuss the tension between mean-field predictions and observations in strongly interacting K39 condensates. It is shown that such a tension is solved taking into account the details of the Feshbach resonance used to tune a in the experiments.
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