Size of Quantized Vortex Rings in Liquid Helium II

The energy dependence of the size of quantized vortex rings in He II is measured by studying the transmission of charged vortex rings through grids with holes of the order of a micron. A maximum-energy ring which can be transmitted is found for each hole size. These cutoffs are interpreted geometrically and lead to a relationship between ring size and energy which supports the quantization of circulation and the applicability of classical hydrodynamics to this problem. The circulation $\kappa$ and core radius $a$ of the rings are determined to be $\kappa =(1.002\mathrm{}\pm 0.03)\times {10}^{-3}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ and $a=(0.90\mathrm{}\pm 0.50)\times {10}^{-8}$ cm.