Surface Excitations of Helium Droplets

We apply an optimized variational theory to the study of high angular vibrational modes of helium droplets. Collective excitation energies for angular modes $\ell >2\mathrm{}$ are computed for cluster sizes $N=20\mathrm{}$ to $N=1000\mathrm{}$ on the basis of Feynman's ansatz. We show that the resulting spectrum, when plotted as a function of an effective wave number $k=\frac{\sqrt{\ell (\ell +1)}}{R}$, forms a universal excitation curve insensitive to the size of the droplet and in excellent agreement with theoretical and experimental excitation energies determined for plane liquid surfaces and films. This agreement, in turn, allows us to use experimental film and surface data to infer about the excitations of helium droplets.