SYSTEMATICS OF PURE AND DOPED HE-4 CLUSTERS

Optimized variational calculations have been carried out for pure and doped clusters of He-4 atoms up to a cluster size of N=1000 particles. For small cluster sizes with less than or equal to 112 particles, whe re comparisons with existing diffusion Monte Carlo results are possibl e, we find excellent agreement for the ground-state energy, correlatio n, and structure functions. For larger clusters, our ground-state ener gies extrapolate smoothly toward a bulk limit of -7.2 K with a surface energy of 0.272 K Angstrom(-2). The resulting ground-state densities show unmistakable oscillations, confirming our earlier conclusions bas ed on diffusion Monte Carlo studies. The present study of large cluste rs allows us to bridge the gap between finite systems and the bulk lim it. Specifically, we show how the bulk limit of collective energies is reached as well as how the bulk Feynman spectrum is reproduced in the S-wave component of the dynamic structure function in large droplets. By plotting the collective excitation energy of higher multiple modes as a function of an effective wave number K = root l(l+1)/R, we show that the resulting spectrum can be directly compared with experimental excitation energies determined for plane liquid surfaces and films. B y summing up to l = 50 partial wave components, we show that the full dynamic structure function simultaneously displays the phonon-roton an d the ripplon excitation spectrum. In the case of helium droplets dope d with impurities such as rare gas atoms or the SF6 molecule, we show that the dipole collective mode becomes unstable with increased drople t size, strongly indicating that these impurities are delocalizled ins ide large droplets. The microscopic character of the instability is re vealed in the excitation functions and transition densities of the dip ole mode. The introduction of impurities also profoundly alters the dy namic structure function, severely ''fragments'' the Feynman spectrum, and obliterates landmark structures such as the maxon and the roton.