Self-consistent quantum structure of diffuse helium atom clusters

Diffuse clusters of arbitrary numbers of helium atoms are treated in a mean-field theory of the many-body system. The nonlinear Hartree self-consistent-field equations are solved numerically to give their energy eigenvalues and eigenfunctions. Both isotopes He-4 and He-3 are treated according to their bosonic and fermionic statistics and symmetry requirements. Clusters of all sizes of He-4 atoms are stable, but there is a minimum threshold of similar to 70 atoms for the formation of He-3 clusters. All the excited states in addition to the ground state were found. The wave functions are seen to have interesting differences from electronic wave functions in atoms.