Theory of the temperature dependence of the roton energy

The temperature dependence of the roton energy is examined considering its collision with another thermally excited roton and the interaction between one excitation and two rotons. The strong final state interaction strongly modifies the two-roton density of states, and therefore the Hartree-Fock approximation is not valid for the roton-roton scattering. Using the point interaction model for the roton-roton coupling and examining only the self-energy processes for the one-particle Green function linear in the number of rotons, it is shown that the amplitude of this temperature dependence changes sign as the roton-roton coupling strength is increased and an upper bound is obtained for the temperature dependence of the roton energy. As this upper bound is only one-seventh of the experimental result, they can be interpreted only by assuming more than seven independent channels with different angular dependence.This work is based on part of the author's Ph.D. thesis (Roland Eötvös University, Budapest). The support of the Central Research Institute for Physics is acknowledged.