Symmetry Method for the Absolute Determination of Energy-Band DispersionsE(k)Using Angle-Resolved Photoelectron Spectroscopy

Angle-resolved spectra for emission in a mirror plane as a function of emission angle and photon energy $h\nu$ show critical-point behavior in interband intensities for transitions on zone boundaries. For such transitions, the absolute energies $E$ and crystal momentum $\overrightarrow{\mathrm{k}}$ for both the initial and final states are given by $h\nu$ and the emission angle. $E\left(\overrightarrow{\mathrm{k}}\right)$ dispersions have been determined for several $d$ bands and conduction bands along the $\Delta$, $\Lambda$, and $\Sigma$ axes of copper.