Dynamics of³He impurities in⁴He films

Using a microscopic variational theory we calculate the binding energy of³He impurities in films of⁴He absorbed to a graphite substrate. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the³He impurity. To calculate excited states, we then introduce a time-dependent variational wave function. In that way, the impurity acquires a hydrodynamic effective mass for its motion parallel to the surface due to hydrodynamic backflow. Excited states have a finite lifetime. When these effects are included, both the energy of the first excited state of the impurity, and the effective mass of the ground state, also agree well with experimental data.