Vortex Rings in a Bose Fluid

Vortex rings are considered as flow patterns of a phenomenological Hartree-type fluid with parameters fitted to the observed phonon-roton spectrum. The basis of the calculations is variational, and density patterns which are constant except in vortex cores are employed. The energy of vortex lines and rings is expressed in terms of a core radius $c$, defined as the distance from the singular line of the vortex to the point of half the asymptotic density. The core size is determined by minimizing the energy and is found to be independent of the ring radius when the latter is larger than ten times the core radius. Comparing the results with the data of Rayfield and Reif, one finds $c=1.7\mathrm{}$ Å, while the phenomenological model yields half this value. The critical velocity associated with ring formation in a channel is considered following the lines of Fetter's earlier calculation. In the present calculation it is possible to incorporate the Fineman-Chase analysis of channel wall effects. Agreement with experiment is considerably improved.