Quantized vortices inHe4droplets: A quantum Monte Carlo study

Abstract

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 $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ in the center and increases when approaching the droplet surface; the core energy per unit volume stabilizes at a value $2.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}{\ensuremath{\sigma}}^{\ensuremath{-}3}$ $(\ensuremath{\sigma}=2.556\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}})$ for $N\ensuremath{\ge}200$.