Determination of the Hole Lifetime from Photoemission: Ti3dStates inTiTe2

The electron hole spectral width ${\Gamma }_h$ of Ti $3d$ states in layered ${\mathrm{TiTe}}_2$ and the inverse lifetime $V_i$ of the photoelectron final states are determined from experiment within the one-step theory of photoemission. The condition for the possibility of separating the effects of ${\Gamma }_h$ and $V_i$ is a strongly non-free-electron character of the final states. The resulting drastic changes of the line shape with photon energy are experimentally observed and explained by an ab initio theory. A nonmonotonic dependence of $V_i$ on the final-state energy is observed; it is shown to reveal the real space structure of the complex electron self-energy.