Time-dependent screening in the electron gas

The transient screening response in real space and time of the electron gas to a suddenly created point charge is calculated in the linear approximation, in a way which allows the decomposition of the response into a part due to plasmons and a part due to electron-hole pairs. The results are expected to be qualitatively correct as a description of core-hole creation in simple metals in the limit of large photoelectron energies. We obtain a clear picture of an electronic ''shock wave'' which propagates outward from the core hole with some dispersion; the group velocities are centered at the Fermi velocity. Behind the shock wave is the static distribution plus a small ringing due to small-q plasmons. The results are examined in the light of experimental evidence for transient effects on core-hole decay