The Lekner-Feynman theory, together with variational Monte Carlo calculations, was used to estimate the energy of a single 3He impurity in a 4He crystal at absolute zero. When applied to the case of a crystal which contained a vacancy, the same method furnished an energy for the vacancy that was comparable to the one that was obtained by using  ab initio  simulations. The 3He impurity was located at lattice sites, and exhibited a density distribution which was different to that of the 4He; but the effect was rather small. This observation was in agreement with the fact that low concentrations of 3He in 4He crystals did not significantly alter the thermodynamic properties of the system. In the case of the vacancy, the variational procedure yielded an improvement of 25% with respect to the estimate that was obtained by assuming that the solid was unrelaxed around the vacancy. However, this value was considerably higher than the experimental value. This was suggested to indicate that delocalization of a vacancy in the crystal, and modification of the variational amplitude of the neighboring atoms, played an important role in this system. The Lekner-Feynman theory, together with Monte Carlo results on solid-liquid coexistence, did not predict the occurrence of any significant binding of 3He at the interface. It was suggested that binding of the 3He atoms might arise from the heterogeneity which was present at the solid/liquid interface.

F.Pederiva, F.Dalfovo, S.Fantoni, L.Reatto, S.Stringari: Physical Review B, 1997, 55[5], 3122-7