  Ultrafast time-resolved x-ray scattering is an emerging approach to image the
dynamical evolution of the electronic charge distribution during complex
chemical and biological processes in real-space and real-time. Recently, the
differences between semiclassical and quantum-electrodynamical (QED) theory of
light-matter interaction for scattering of ultrashort x-ray pulses from the
electronic wavepacket were formally demonstrated and visually illustrated by
scattering patterns calculated for an electronic wavepacket in atomic hydrogen
[Proc. Natl. Acad. Sci. U.S.A., {\bf 109}, 11636 (2012)]. In this work, we
present a detailed analysis of time-resolved x-ray scattering from a sample
containing a mixture of non-stationary and stationary electrons within both the
theories. In a many-electron system, the role of scattering interference
between a non-stationary and several stationary electrons to the total
scattering signal is investigated. In general, QED and semiclassical theory
provide different results for the contribution from the scattering
interference, which depends on the energy resolution of the detector and the
x-ray pulse duration. The present findings are demonstrated by means of a
numerical example of x-ray TRI for an electronic wavepacket in helium. It is
shown that the time-dependent scattering interference vanishes within
semiclassical theory and the corresponding patterns are dominated by the
scattering contribution from the time-independent interference, whereas the
time-dependent scattering interference contribution does not vanish in the QED
theory and the patterns are dominated by the scattering contribution from the
non-stationary electron scattering.
