Theory of neutron scattering from superfluidHe4at finite temperatures

The dynamic structure factor $S(\overrightarrow{\mathrm{Q}},\omega )$ for a Bose-condensed system is calculated microscopically at temperatures where there are a significant number of thermally excited quasiparticles present. Our work is based on the one-loop diagrammatic approximation, which has been used by Wong and Gould to discuss the low-temperature limit. In our numerical calculations (for $Q=0.35\mathrm{} \mathrm{and} 0.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$) of proper, irreducible quantities, we use the Bogoliubov approximation for the coherence factors in conjunction with the experimentally determined quasiparticle spectrum. We find that at high temperatures, the collisionless phonon resonance exhibited by $S(\overrightarrow{\mathrm{Q}},\omega )$ has a width which increases with the number of thermally excited rotons, in rough agreement with the neutron scattering data of Cowley and Woods as well as those of Woods and Svensson. Our results are compared with those based on a phenomenological treatment of the phonon-roton coupling.