Vortex nucleation by collapsing bubbles in Bose-Einstein condensates

The nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be about 28 healing lengths. The time after which the nucleation becomes possible is determined as a function of bubble's radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion made them sufficiently oblate.