Density and quasiparticle excitations in liquidHe4

The recent interpretation of the phonon-roton excitations in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ as a density mode at low wave vector and a quasiparticle excitation at higher Q proposed by Glyde and Griffin is developed. When there is a condensate, ${\mathit{n}}_0$(T), the quasiparticle response of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, becomes a component of the observed density dynamic structure factor, S(Q,ω). The quasiparticle and density response functions also share a common denominator, due to a coupling via the condensate. At low Q, the observed S(Q,ω) is confined predominantly to a single peak. The peak broadens with temperature but remains well defined in normal ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, where ${\mathit{n}}_0$(T)=0. This peak is interpreted as a density mode. At the maxon and higher Q, S(Q,ω) has a sharp peak plus a broad component. The sharp peak is interpreted as the quasiparticle component of S(Q,ω). As T is increased and ${\mathit{n}}_0$(T) is decreased, the intensity in the sharp peak is reduced until it vanishes from S(Q,ω) at ${\mathit{T}}_{\lambda }$. A simple model based on uncoupled quasiparticle and density excitations with coupling via ${\mathit{n}}_0$(T) is proposed. For simplicity, all model parameters are held independent of T. By allowing only ${\mathit{n}}_0$(T) to vary with T, the temperature dependence of S(Q,ω) can be quite accurately reproduced.