Quantum Monte Carlo investigation of small He-4 clusters with a He-3 impurity

Small helium (He-4) clusters containing the lighter isotope He-3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang-Tonnies-Yiu (TTY) helium-helium pair potential. The dimer He-4-He-3 is not bound; as well as the trimer (HeHe2)-He-4-He-3. The smallest cluster containing He-3 is He-4(2) He-3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He-4(3) trimer, is able to bind another He-3 atom, forming the tetramer He-4(2) He-3(2), which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He-4 atom in a pure cluster with a He-3 atom leads to an energetic destabilization, as the pair He-4-He-3 is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He-4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called "Andreev states" of a single He-3 in liquid He-4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He-4.