Excluded-volume conditions and Raman scattering in He II

Abstract

We consider the dynamic correlation function $H(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}, {\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}, \ensuremath{\omega})$ appearing in the theory of Raman scattering in liquid helium. The simple fact that two atoms cannot overlap each other leads to an "excluded-volume condition" on the Fourier transform of $H$ with respect to ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}$ (or $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$) for all $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ (or ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}$) and $\ensuremath{\omega}$. It is demonstrated explicity that none of the available calculations of $H$ satisfy this condition. Hence, none of the existing direct quantitative interpretations of the Raman experiments is reliable. In particular, serious doubt is cast on the conclusiveness of the evidence for a two-roton bound state. Some related matters concerning the light-helium coupling function $t$ are also discussed. It is argued that previous quantitative agreement between theory and experiment is due to compensating errors in $H$ and $t$. An important "off-diagonal" property of $H$ is also demonstrated.