Short-Range Correlations in He-4 Liquid and Small He-4 Droplets described by the Unitary Correlation Operator Method

The Unitary Correlation Operator Method (UCOM) is employed to treat short-range correlations in both, homogeneous liquid and small droplets of bosonic He-4 atoms. The dominating short-range correlations in these systems are described by an unitary transformation in the two-body relative coordinate, applied either to the many-body state or to the Hamiltonian and other operators. It is shown that the two-body correlated interaction can describe the binding energy of clusters of up to 6 atoms very well, the numerical effort consisting only in calculating one two-body matrix element with Gaussian single-particle states. The increasing density of bigger droplets requires the inclusion of correlation effects beyond the two-body order, which are successfully implemented by a density-dependent two-body correlator. With only one adjusted parameter the binding energies and radii of larger droplets and the equation of state of the homogeneous He-4 liquid can be described quantitatively in a physically intuitive and numerically simple way.