Pinning of Quantized Vortices in Helium Drops by Dopant Atoms and Molecules

Using a density functional method, we investigate the properties of liquid ${}^4\mathrm{He}$ droplets doped with atoms (Ne and Xe) and molecules ( ${\mathrm{SF}}_6$ and hydrogen cyanide). We consider the case of droplets having a quantized vortex pinned to the dopant. A liquid-drop formula is proposed that accurately describes the total energy of the complex and allows one to extrapolate the density functional results to large $N$. For a given impurity, we find that the formation of a $\mathrm{dopant}+\mathrm{vortex}{+}^4{\mathrm{He}}_N$ complex is energetically favored below a critical size $N_{\mathrm{cr}}$. Our results support the possibility to observe quantized vortices in helium droplets by means of spectroscopic techniques.