Energy and angular momentum densities of states of ripplons on the surfaces of helium nanodroplets and bubbles

We present an analytical evaluation of the statistical densities of states of surface excitations (“ripplons”) of (1) isolated liquid-drop helium nanoclusters and (2) large multielectron bubbles in bulk liquid helium [1]. For the former case, the calculation of the energy density of states, $\rho (E)$, can be accurately performed in a microcanonical ensemble formalism [2] and yields an expression which is extremely close both to the exact numerical calculation and to its fitted form [3]. For case (2) the canonical ensemble formulation is appropriate. For both systems, the calculation is then extended to yield the energy- and angular-momentum- resolved density of states $\rho (E,L)$ (c.f. [3]); in other words, the ripplon moment of inertia is described. \newline \newline [1] J.Tempere, I.F.Silvera, J.T.Devreese, Phys.Rev.Lett. {\bf 87}, 275301 (2001). \newline [2] J.U.Andersen, E.Bonderup, K.Hansen, J.Chem.Phys. {\bf 114}, 6518 (2001). \newline [3] K.K.Lehmann, J.Chem.Phys. {\bf 119}, 3336 (2003).