Vortices in Doped 4He Clusters

We investigate the properties of liquid ⁴ He_N clusters hosting a quantized vortex pinned to a dopant atom (Ne or Xe) or molecule (SF ₆ or HCN). A density functional theory is used to calculate the stationary configurations of pure and doped clusters, with and without vortex, up to N=1000. A liquid drop formula is then proposed that accurately describes the total energy of the complex and allows one to extrapolate the results to larger N values. We find that forming a dopant+vortex+ ⁴ He_N complex is energetically favored below a critical size N _cr , which strongly depends on the type of dopant.