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

TL;DR

This paper develops a phenomenological theory to analyze the high momentum end of the $^4$He spectrum, incorporating interference effects, and successfully reproduces experimental data to refine the spectrum and understand roton interactions.

Contribution

It introduces a theoretical approach that includes interference effects between excitations, improving the accuracy of the $^4$He spectrum analysis at high momentum.

Findings

Data agree with a dispersion relation below twice the roton energy.

Negative roton-roton interaction is supported by the analysis.

Enhanced accuracy in the $^4$He spectrum extraction.

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.