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

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. TRXS from these states can be difficult to isolate because they generally overlap in the angle-resolved x-ray scattering pattern $I(x,y,{\tau})$, where ${\tau}$ 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, $\tilde{I}(x,y,{\omega})$$=\int_{-\infty}^{\infty} d\tau e^{-i\omega\tau} I(x,y,\tau)$. This frequency-resolved x-ray scattering (FRXS) signal segregates the bound states according to their vibrational frequencies, ${\omega}_i$, and also displays dissociative states along straight lines ${\omega}=vQ$, 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 $^{1}{\Pi}_{u}$ and $^{1}{\Sigma}_{g}^{+}$ excited states, and vibrational wave packets on the B ($^{3}{\Pi}_{0u}^{+}$)state.