Thermodynamic properties of a condensed 39K Bose gas in a harmonic trap

In this paper, the thermodynamic behavior of a 39K Bose gas with a finite number of atoms confined in a harmonic potential is investigated. By taking into account the conservation of the total number of particles N and using a modified semiclassical approximation, we derive analytically the simple explicit expression for the thermal atoms number in the excited state. This modification assures to include, finite size and indirectly the interatomic interaction effects simultaneously. Various experimental, the critical atoms number and its corresponding temperature are predicted via the graphical representation. The calculated results show that the thermodynamical parameters depend critically on the size, shape, and harmonic nature of the potential. The calculated critical atoms number are coincide with the measured experimental results for 39K, as reported in Tammuz et al. [3] and Smith et al. [4].