Density dependence of the roton spectrum in liquidHe4

The density dependence of the roton spectrum in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is calculated using Brillouin-Wigner perturbation theory. The trial ground-state wave function is an extended Jastrow function, including three-body factors. The three-body factors produce an improved density dependence over the pure Jastrow trial function. We note, however, that the amount of improvement depends upon the particular approximation chosen for the three-particle structure function, $S^{\mathrm{}\left(3\right)\mathrm{}}({\overrightarrow{\mathrm{k}}}_1,{\overrightarrow{\mathrm{k}}}_2,{\overrightarrow{\mathrm{k}}}_3)$. Specifically, better agreement with experiment is obtained by using an approximation for $S^{\mathrm{}\left(3\right)\mathrm{}}$ which has been obtained recently in the density-phase variable theory of the weakly interacting Bose gas, when compared to the convolution approximation for $S^{\mathrm{}\left(3\right)\mathrm{}}$.