Attosecond x-ray scattering from a particle-hole wave packet

We investigate the imaging of electron wave-packet dynamics by measuring the pattern of inelastically scattered photons. For this purpose, we develop a theory of time-resolved Compton scattering. We demonstrate that, by using a sufficiently short x-ray pulse, the scattering cross section directly reflects the instantaneous momentum density of the electron. Therefore, we propose time-resolved Compton scattering as a tool to image electron wave-packet dynamics in momentum space. To illustrate this, we simulate electron wave packets in argon by using the time-dependent configuration-interaction singles method. Specifically, we consider coherent particle-hole wave packets, where the hole is in either the $3p$ or the $3s$ shell, and the particle (the excited electron) is either in a Rydberg state or in the continuum. Our calculations confirm that the dynamics of electron wave packets can indeed be imaged by measuring the doubly differential Compton scattering cross section. When the x-ray detector has no energy resolution at all, the contribution of Compton scattering to the differential scattering cross section becomes stationary. In that case, the motion of the particle and the hole can no longer be inferred from the scattering pattern.