We present a Monte Carlo investigation of a vortex line in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ in a cylindrical container. We compute the excitation energy and the density profile for two different trial functions. The first is the standard Onsager-Feynman form for an excited vortex state. This gives a singular velocity on the axis of the vortex and a hollow core. In our second approach, a shadow wave function, is used to model the vortex state through the auxiliary, or shadow variables. As a consequence, the vorticity is distributed over a finite region and the density does not vanish at the vortex axis. This second wave function gives a substantially lower energy than the wave function of the Onsager-Feynman form. © 1996 The American Physical Society.

• Received 11 January 1996

DOI:https://doi.org/10.1103/PhysRevB.54.1205