Momentum-transfer dependence of theKabsorption edge of lithium

The lithium $K$ absorption edge has been studied as a function of momentum transfer in a high-resolution inelastic-electron-scattering experiment and found to exhibit no significant change with momentum transfer up to 1.2 ${\mathrm{\AA }}^{-1\mathrm{}}$. This result places severe restrictions on theories which interpret the shape of the threshold in terms of the final-state electron-hole interaction, and compatibility with this experiment could only be obtained in such theories by the utilization of a range ($\xi <0.01\mathrm{}$ eV) or an $s$-wave phase shift (${\delta }_0<0.5\mathrm{}$), values which differ from the presently accepted calculations. Our results are consistent with an edge shape determined by a simple step function in the one-electron transition probability convoluted with broadening due to phonon or lifetime effects.