Quantized Vortex Rings in Superfluid Helium

Abstract

Evidence is presented to show that charged particles in superfluid helium at low temperatures can be accelerated to create freely moving charge-carrying vortex rings in the liquid. The circulation of these vortex rings can be determined by measuring their energy and velocity; it is found to be equal to one quantum $\frac{h}{m}$, where $h$ is Planck's constant and $m$ is the mass of a helium atom. The core radius of the vortex is approximately 1 \AA{}. The dynamical properties of such a vortex ring moving under the influence of external forces can be described by a dispersion relation $E\ensuremath{\propto}{p}^{\frac{1}{2}}$ connecting its energy $E$ and momentum $p$; it can also be understood in detail in terms of the hydrodynamic Magnus force. Experiments are described which verify the essential validity of this dynamical analysis. Vortex rings can interact with various quasiparticles in the liquid, i.e., with rotons, phonons, and ${\mathrm{He}}^{3}$ impurities. The scattering of these quasiparticles by vortex rings can be investigated by experiments designed to study the temperature dependence of the rate of energy loss of such rings moving through the liquid. In this way it is possible to measure the effective momentum-transfer cross sections for scattering of the various quasiparticles by vortex lines. The cross section thus deduced is 9.5 \AA{} for scattering of rotons and 18.3 \AA{} for scattering of ${\mathrm{He}}^{3}$ atoms. The experiments yield only scant information about scattering of phonons, but are not inconsistent with the magnitude of the phonon scattering cross section expected on theoretical grounds.