Temperature dependence of the phonon and roton excitations in liquidHe4

We report high-precision neutron scattering measurements of the temperature dependence of the phonon and roton excitations in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at saturated vapor pressure in both the superfluid and normal-fluid phases. Two wave vectors were examined in detail: Q=0.4 A${\mathrm{̊}}^{\mathrm{-}1}$ in the phonon region and Q=1.925 A${\mathrm{̊}}^{\mathrm{-}1}$ at the roton minimum. The goal is to understand excitations in Bose liquids by determining the dynamic structure factor S(Q,ω) accurately in both phases. At Q=0.4 A${\mathrm{̊}}^{\mathrm{-}1}$ the sharp peak in S(Q,ω) broadens with temperature T, but remains sharp and well defined in the normal phase (T>${\mathit{T}}_{\lambda }$) up to T≊3 K. The rate of increase of the width of S(Q,ω) shows a break at ${\mathit{T}}_{\lambda }$, but otherwise S(Q,ω) is similar in the two phases and a transition could not be identified through S(Q,ω). In contrast at Q=1.925 A${\mathrm{̊}}^{\mathrm{-}1}$, the sharp component of S(Q,ω) disappears at ${\mathit{T}}_{\lambda }$ and S(Q,ω) is very different above and below ${\mathit{T}}_{\lambda }$. This behavior is documented and values of the frequencies and linewidths at several temperatures are reported.