More accurate theory for Bose–Einstein condensation fraction

Bose–Einstein statistics is derived in the thermodynamic limit when the ratio of system size to thermal de Broglie wavelength goes to infinity. However, according to the experimental setup of Bose–Einstein condensation of harmonically trapped Bose gas of alkali atoms, the ratio near the condensation temperature (ToTo) is 30–50. And, at ultralow temperatures well below ToTo, this ratio becomes comparable to 1. We argue that finite size as well as the ultralow temperature induces corrections to Bose–Einstein statistics. From the corrected statistics we plot condensation fraction versus temperature graph. This theoretical plot satisfies well with the experimental plot [A. Griesmaier et al., Phys. Rev. Lett. 94 (2005) 160401].