Microscopic studies of collective spectra of quantum liquid clusters

Theoretical methods are developed for determining the collective vibrational excitation spectra of quantum clusters, and applied to clusters of 4He. A quantum liquid drop model gives excitation energies in terms of two-point ground state density correlations, which are evaluated from microscopic calculations of the ground state wave functions. An alternative approach based on a Bijl–Feynman ansatz for the excited states also yields excitation energies in terms of ground state correlations, without the imposition of a sharp liquid surface. These methods are applied to the calculation of the excitation spectra of 4HeN , N=20, 70, and 240 clusters. The relationship between the collective spectra of these clusters and that of bulk fluid He II, and the significance of an observed roton minimum in the spectrum for N≥70 are discussed.