Sum Rules and Inelastic Neutron Scattering in Paramagnetic Intermediate-Valence Compounds

Exact evaluation of low-order moments of the imaginary part of the dynamic susceptibility is used to analyze inelastic neutron scattering in a paramagnetic intermediate-valence system. It is shown that (i) the second moment of $\frac{{\chi }^{\prime \prime }(\overrightarrow{\mathrm{q}},\omega )}{\omega }$ measures the mixing energy, (ii) only a weak $\overrightarrow{\mathrm{q}}$ dependence of ${\chi }^{\prime \prime }(\overrightarrow{\mathrm{q}},\omega )$ is expected even in "coherent" systems, and (iii) there are no diffusive modes in the hydrodynamic regime.