Theoretical studies of the dynamic structure function of liquidHe4

The dynamic structure factor S(k,ω) for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is studied with the use of perturbation theory in a correlated basis generated by the Feynman-Cohen (FC) excitation operator acting on the interacting ground state. We consider the coupling of one FC excitation to two FC excitations and sum the important contributions to all orders in perturbation theory. S(k,ω) is calculated for many values of k in the interval (0.8 A${̊}^{\mathrm{-}1}$, 4.5 A${̊}^{\mathrm{-}1}$). We find a low-energy δ-function peak which corresponds to the phonon-maxon-roton spectrum and report its energy e(k) and Z(k) as a function of k. ‘‘Two-quasiparticle’’ peaks are also found and they may be identified as roton-roton, maxon-maxon, and maxon-roton contributions. At high k, most of the strength of S(k,ω) is distributed in the neighborhood of quasifree scattering energy ω≃${ħ}^2$ $k^2$/2m, and the results are comparable with results of the impulse approximation. Semiquantitative agreement is found between the calculated S(k,ω) and that inferred from neutron inelastic scattering experiments.