Quantitative study of the Zawadowski-Ruvalds-Solana model of the dynamics of liquid helium

Abstract

We study the Zawadowski-Ruvalds-Solana (ZRS) model of quasiparticle interactions in liquid helium both quantitatively and theoretically. We find that the model cannot account quantitatively for the multiphonon peak in the neutron-scattering spectrum even if we vary the quasiparticle spectrum phenomenologically. We find that the model can account for the experimental light-scattering spectrum if the effective roton-roton coupling $g_4(\overrightarrow{\mathrm{k}},{\overrightarrow{\mathrm{k}}}^{\prime })$ is sharply peaked at the roton minimum ($k\cong k^{\prime }\cong k_0$). We suggest that the neutron-scattering results would be improved without changing the light-scattering prediction if the density operator contained nonlinear terms in the quasiparticle operator. We criticize the implicit assumption in the ZRS model that the zero-order ground state is nondegenerate. The relationship of this model to one devised by Jackson is discussed.