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We have studied the atomic density of a cloud confined in an isotropicharmonic trap at the vicinity of the Bose-Einstein transition temperature. Weshow that, for a non-interacting gas and near this temperature, theground-state density has the same order of magnitude as the excited statesdensity at the centre of the trap. This holds in a range of temperatures wherethe ground-state population is negligible compared to the total atom number. Wecompare the exact calculations, available in a harmonic trap, to semi-classicalapproximations. We show that these latter should include the ground-statecontribution to be accurate.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Atomic density of a harmonically trapped ideal gas near Bose-Einstein transition temperature