Universal time delays in the inelastic core level photoemission of metals

Abstract

Proposing a theoretical model of the core level photoemission of metals, we investigate the plasmon-driven inelastic photoemission delays based on a nonperturbative treatment of many-electron responses due to the long-range Coulomb potential. Being irrelevant to the plasmon coupling strength as well as the plasmon frequency, the emission delays $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{n}$ of the $n\mathrm{th}$-order plasmon satellites ($n=1,2,3,...$) are found to be universal order by order among the metals in the core level photoemission where the recoil-less approximation would be valid. In particular, for a main line with its weight ${e}^{\ensuremath{-}\ensuremath{\gamma}}$, where $\ensuremath{\gamma}$ quantifies the plasmon coupling strength, the average inelastic photoemission delay $\ensuremath{\langle}\mathrm{\ensuremath{\Delta}}\ensuremath{\tau}\ensuremath{\rangle}$ is found to be $\ensuremath{\gamma}{(1\ensuremath{-}{e}^{\ensuremath{-}\ensuremath{\gamma}})}^{\ensuremath{-}1}\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$ and thus is simply scaled by a universal time delay $\mathrm{\ensuremath{\Delta}}{\ensuremath{\tau}}_{1}$. This finding is sharply contrasted with the emission delays under the localized potential, which indicates a fundamental difference in the emission process between extended and localized screenings.