Binding Of Impurities To A He-4 Superfluid Vortex

We calculate the binding energies of a He-3 impurity and a fictitious He-4 impurity to a superfluid He-4 vortex. Within the accuracy of the calculation, there is no difference between the mass-3 and mass-4 binding energies, suggesting that the binding is due to the displacement of atoms from the core. Comparing the results between Onsager-Feynman (Psi(OF)) and "shadow" (Psi(D)) variational functions, the energy is dependent on the density for Psi(OF), but independent for Psi(D). The binding of 2.3 K for Psi(D) at zero pressure is smaller than the experimental estimate. We also estimate the binding energies of charged ions.