Inelastic electron scattering: Tests of many-electron threshold theory

A test of the many-electron threshold theory is suggested: for transitions from $d$ or $f$ core levels to conduction bands, the inelastic electron scattering spectral shape $S(\overrightarrow{\mathrm{q}}, \omega )$ should be dramatically enhanced as the momentum transfer $\hslash \overrightarrow{\mathrm{q}}$ is increased from zero. Using the Doniach, Platzman, and Yue theory, experimental threshold exponents, and calculations of matrix elements, we evaluate both this effect and the effect currently being sought experimentally by Gibbons, Schnatterly, Moog, and Slusky: the flattening with increasing $\overrightarrow{\mathrm{q}}$ of the $L_{2,3}$ edges ($2p$ to Fermi level) of Na, Mg, and Al.