Importance of vertex corrections for obtaining correct selection rules in the theory of photoemission

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Abstract
It is shown that the commonly used approximation for the no-loss angle-resolved photocurrent from solids in general violates the optical selection rules if the final-state inverse low-energy electron diffraction orbital is taken to be damped. The violations occur in the velocity formula, which is inconsistent with the corresponding and commonly used acceleration formula in which the matrix elements are evaluated with respect to the gradient of the one-electron potential. It has recently been shown that, in a correct description of the no-loss photocurrent, the bare matrix elements should be replaced by the appropriate vector-coupling vertex function. We demonstrate that this modification is needed in order to have correct selection rules and consistency between the velocity and acceleration formulas for photoemission and photoabsorption. Our formalism further allows us to interpret the commonly used acceleration formula in terms of a well-defined approximation which leaves out local-field effects, and to give approximations which obey the selection rules.