Explaining critical angular velocities of the vortex formation in a stirred Bose-Einstein condensate

The problem of explanation of the critical angular velocity $\Omega_c$ when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible, is considered in the framework of the variational approach. The origin of smallness of the calculated $\Omega_c$ in comparison with the measured values which takes place for pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured $\Omega_c$ is achieved upon admitting a small admixture of the zero angular momentum state in the wave function of the one-vortex quantum state prepared after stirring. The portion of this admixture amounts to 10 - 13 % of the total condensed atoms. Possible test of this hypothesis is proposed.