Zero-temperature properties of a trapped Bose-condensed gas: Beyond the Thomas-Fermi approximation

We consider the leading corrections to the Thomas-Fermi approach to the description of the properties of a magnetically trapped, Bose-condensed cloud of atoms. Simple analytical expressions are derived for the kinetic energy in terms of an effective cutoff length, which we calculate numerically by considering the one-dimensional problem for a linear-ramp potential. We also determine the lowest angular velocity at which it is energetically favorable for a vortex to enter the cloud, For large clouds, our results are in excellent agreement with available numerical calculations.