Collective excitations of helium clusters

The excitation spectra of compressional modes of $^{4}\mathrm{He}_{\mathit{N}}$, N=20, 70, and 240, clusters at 0 K are calculated by treating the cluster as a quantum liquid drop. The spectrum of N=240 strongly resembles that of liquid helium with a visible roton structure, while for N=20 no roton minimum is seen and N=70 shows a weak minimum. Implications of these findings for superfluidity in helium clusters are discussed.