Dynamics of³He impurities in⁴He films

Using a microscopic theory we calculate the binding energy of³ He impurities in films of⁴ He absorbed to a graphite substrate. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the He impurity. By introducing a timedependent variational wave function, the impurity atom acquires a hydrodynamic effective mass for its motion parallel to the surface due to hydrodynamic backflow, and the 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, agree well with experimental data. A comparison with recent density functional results is carried out. It is shown that the substrate bound states on strong potentials are spurious and due to the inappropriate treatment of the effective mass within that theory.