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The dynamic structure factor of superfluid $^4$He has been investigated atvery low temperatures by inelastic neutron scattering. The measurements combinedifferent incoming energies resulting in an unprecedentedly large dynamic rangewith excellent energy resolution, covering wave vectors $Q$ up to 5 \AA$^{-1}$and energies $\omega$ up to 15 meV. A detailed description of the dynamics ofsuperfluid $^4$He is obtained from saturated vapor pressure up tosolidification. The single-excitation spectrum is substantially modified athigh pressures, as the maxon energy exceeds the roton-roton decay threshold. Ahighly structured multi-excitation spectrum is observed at low energies, whereclear thresholds and branches have been identified. Strong phonon emissionbranches are observed when the phonon or roton group velocities exceed thesound velocity. The spectrum is found to display strong multi-excitationswhenever the single-excitations face disintegration following Pitaevskii's typea or b criteria. At intermediate energies, an interesting pattern in thedynamic structure factor is observed in the vicinity of the recoil energy. Allthese features, which evolve significantly with pressure, are in very goodagreement with the Dynamic Many-body calculations, even at the highestdensities, where the correlations are strongest.

Microscopic dynamics of superfluid $^4$He: a comprehensive study by inelastic neutron scattering