Theory and Data Analysis for the High Momentum End of $^4$He spectrum

Abstract

The hybridization of the single-excitation branch with the two-excitation continuum is reconsidered from the theoretical point of view by including the effect of the interference term between one and two excitations. The phenomenological theory presented is used to reproduce the experimental data over a wide region of momentum (2.3-3.6 A^{-1}) and energy (0-12 meV). It is thus possible to extract the final part of $^4$He spectrum with higher accuracy. It is found that data agree with a dispersion relation always below twice the roton energy. This is consistent with the negative value of the roton-roton interaction found.