Roton interactions in superfluid helium

Based on a hard-sphere model for superfluid helium we derive a microscopic theory for quasiparticle interactions in this liquid. A satisfactory upper bound for the roton-roton collision frequency is obtained from this model. This theory also leads to an attractive coupling of two rotons with opposite momenta but the coupling strength is an order of magnitude larger than the phenomenological estimates based on experiments. However, as our analysis reveals, this large coupling strength is compatible with other physical considerations presented in this paper and does not contradict experimental data.