Structure of vortices in helium at zero temperature

Abstract

A density-functional theory is used to investigate the structure of vortices in superfluid helium. The angular dependence of the many-body wave function is factorized following the Feynman-Onsager hypothesis. The density profile near the vortex axis is then calculated for different values of the external pressure. The profile shows damped stationary ripples with the roton wavelength, in agreement with the predictions of previous microscopic calculations. A critical negative pressure of 8 bars is found for the stability of a vortex line against a free expansion of the core. The application of the density-functional method to the problem of $^{3}\mathrm{He}$ impurities is also discussed.