MONTE-CARLO STUDY OF IMPURITIES IN QUANTUM CLUSTERS - (H2HEN)-HE-4, N=2-19

Variational Monte Carlo techniques are employed in studying He-4 clusters, with and without an H-2 impurity. We find that a novel, yet simple, analytic nuclear wave-function form, derived from a numerical H2He wave function, yields high accuracy in computed ground-state energies of (HeN)-He-4. For the clusters studied here, three to twenty atoms, energies range from 94% to 90% of the exact values. Density profiles and distributions of particle separation are also computed. For reasonable computational cost (e.g., < 20 Cray/X-MP14 minutes for the largest cluster), density profiles are determined for the first time to high statistical accuracy to within 0.5 angstrom or less of the cluster center. The density profile of He-3 is found to possess a uniquely pronounced peak at the cluster center resulting from contributions of near-collinear atomic arrangements. We also study the effect of substituting an He by H-2, using modified wave functions containing products of pairwise He-H-2 terms. For all cluster sizes studied, we find a lowering of the total energy upon exchanging an He for an H-2. The exchange energy increases in magnitude with increasing cluster size, yet is still well below bulk estimates at N = 20. Size comparisons with the pure helium clusters show very little change upon He/H-2 exchange, e.g., the rms radii differ by less-than-or-equal-to 2% for N > 3. Density profiles and bond distributions show noticeable differentiation between H-2 and He. For N greater-than-or-equal-to 4, the peak in the H-2 density profile is not at the cluster but does remain inside the cluster. This peak is most pronounced for H2He13 implying an enhanced resistance to H-2 penetration for He13.