Characterizing dissociative motion in time-resolved x-ray scattering from gas-phase diatomic molecules

Abstract

Time-resolved x-ray scattering (TRXS) measures internuclear separations in a molecule following laser-induced photoexcitation. The molecular dynamics induced by the excitation laser may lie on one or several bound or dissociative electronic states. Time-resolved x-ray scattering from these states can be difficult to isolate because they generally overlap in the angle-resolved x-ray scattering pattern $I(x,y,\ensuremath{\tau})$, where $\ensuremath{\tau}$ is the pump-probe delay and $(x,y)$ are the physical pixel positions. Here we show how standard transform methods can isolate the dynamics from individual states. We form the temporal Fourier transform $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{I}(x,y,\ensuremath{\omega})={\ensuremath{\int}}_{\ensuremath{-}\ensuremath{\infty}}^{+\ensuremath{\infty}}d\ensuremath{\tau}\phantom{\rule{0.16em}{0ex}}{e}^{\ensuremath{-}i\ensuremath{\omega}\ensuremath{\tau}}I(x,y,\ensuremath{\tau})$. This frequency-resolved x-ray scattering (FRXS) signal segregates the bound states according to their vibrational frequencies ${\ensuremath{\omega}}_{i}$ and also displays dissociative states along straight lines $\ensuremath{\omega}=vQ$, where the slope $v$ is the rate of increase of the internuclear distance and $Q$ is the momentum transfer between the incident and scattered x-ray photon. We derive this relation and use FRXS to extract state-specific dynamics from experimental TRXS from molecular iodine following a 520-nm pump. Dynamics observed include one- and two-photon dissociation of the ${}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$ and ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ excited states and vibrational wave packets on the $B{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Pi}}}_{0u}{}^{+}$ state.