We present a diffusion Monte Carlo study of a vortex line excitation attached to the center of a ${}^4\mathrm{He}$ droplet at zero temperature. The vortex energy is estimated for droplets of increasing number of atoms, from $N=70$ up to 300, showing a monotonous increase with $N$. The evolution of the core radius and its associated energy, the core energy, is also studied as a function of $N$. The core radius is $\sim 1\mathrm{\AA }$ in the center and increases when approaching the droplet surface; the core energy per unit volume stabilizes at a value $2.8\mathrm{K}{\sigma }^{-3}$ $(\sigma =2.556\mathrm{\AA })$ for $N\ge 200$.

• Received 27 July 2007

DOI:https://doi.org/10.1103/PhysRevB.76.052507