Variational study of a 3He impurity near a 4He vortex core

We have carried out variational calculations of the properties of a quantum vortex line He-4 using a shadow wave-function, which generates a distributed vorticity. Based on these calculations we present a microscopic of study the binding of a single He-3 to the vortex using both the Lekner-Feynman formalism and a correlated variational wave-function. Both approaches predict that the impurity should be bound. Lekner-Feynman model, however; does not appear to describe correctly some of the correlation effects within the vortex core. To remedy this defect, we propose a variational wave-function, and a preliminary calculation based on it predicts a binding energy in agreement with experiment. PACS numbers: 67.40. Vs, 02.70.Lq.