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 studie d by means of quantum Monte Carlo methods. Accurate ground state energies a nd structural properties are obtained using accurate trial wave functions a nd 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 cl uster containing He-3 is He-4(2) He-3 with a nonrigid structure having a ma rked 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 o dd feature of having five out of six unbound pairs. In general, the substit ution 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 remainin g He-4 atoms, which retain the high floppiness already found in the pure cl usters. As the number of atoms increases the isotopic impurity has the mark ed tendency to stay on the surface of the cluster. This behavior is consist ent with the formation of the so-called "Andreev states" of a single He-3 i n liquid He-4 helium and droplets, where the impurity tends to form single- particle states on the surface of the pure He-4. (C) 2000 American Institut e of Physics. [S0021-9606(00)30802-9].