Three-roton bound states

The existence and binding energy of three-roton bound states with a vanishing total momentum are investigated. In the presence of attractive roton-roton interaction, however weak it may be, three-roton bound states of s- and d-wave symmetry are necessarily formed. Those binding energies can be expected to be about 1 K. The observability in experiments such as Raman scattering is also discussed. Further, the effects of four- and five-excitation states on the Raman spectrum are briefly discussed