Momentum Transfer Dependence of Inelastic X-Ray Scattering from the LiKEdge

Inelastic x-ray scattering from the $K$ edge of lithium metal at 30 K is measured at momentum transfers $q=8.8\mathrm{}$ and $97.3{\mathrm{nm}}^{-1\mathrm{}}$ with 80 meV energy resolution. The transition from dipolar ( $1s\to p$, $q=8.8\mathrm{}{\mathrm{nm}}^{-1\mathrm{}}$) to monopolar ( $1s\to s$, $q=97.3\mathrm{}{\mathrm{nm}}^{-1\mathrm{}}$) excitations is demonstrated by differences in the spectra reflecting either the $p$ or $s$ partial density of states above the Li Fermi level. The Mahan-Nozières-De Dominicis theory is utilized to determine both threshold exponents ${\alpha }_0$ and ${\alpha }_1$ from the present $K$-edge data.