Various approaches to the linear response in the near-asymptotic regime

We demonstrate to O(${\mathit{q}}^{\mathrm{-}2}$) the correspondence between the response in the Gersch and the multiple-scattering approach. In the course we establish a rigorous requirement for the preference of one scaling variable over another. We also show that the reduced response, when computed by means of a particle-hole (spectral function) approach, does not lead to a systematic 1/q expansion. For liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and nuclear matter we calculate components of the dominant final-state interaction. The asymptotic region for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is reached, for not too large y, when q≥10 A${\mathrm{̊}}^{\mathrm{-}1}$. Results for nuclear matter obtained by means of spectral functions indicate that even for momentum transfers as high as q∼9 ${\mathrm{fm}}^{\mathrm{-}1}$ the convergence is slow, except for the smallest y values.