Analysis of precision data on inclusive neutron scattering from liquid He

We report on an analysis of the response of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ for medium q at temperatures below and just above ${\mathit{T}}_{\mathit{c}}$. It is shown that inclusion of a previously omitted final-state-interaction (FSI) term of order m/q brings about approximate agreement between different predictions and with data for q=10 Å ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$. We make predictions for some new, very fine instrumental-resolution precision data at q=13 and 18 Å ${}_{}{}^{\mathrm{-}1}{}_{}{}^{}$, T=4.2 K. Agreement with those data will prove that the dynamics of the dominant FSI is understood. Very high resolution in T${\mathit{T}}_{\mathit{c}}$ data gravely complicates the otherwise clear picture, and a critical discussion shows that, unless artificially broadened, there is at present no way to describe those data. We discuss remaining possible sources of uncertainties in the input, yet argue already at this stage that the study of the response in the discussed q range may have reached its limits.