  The photoelectric effect is not truly instantaneous, but exhibits attosecond
delays that can reveal complex molecular dynamics. Sub-femtosecond duration
light pulses provide the requisite tools to resolve the dynamics of
photoionization. Accordingly, the past decade has produced a large volume of
work on photoionization delays following single photon absorption of an extreme
ultraviolet (XUV) photon. However, the measurement of time-resolved core-level
photoionization remained out of reach. The required x-ray photon energies
needed for core-level photoionization were not available with attosecond
tabletop sources. We have now measured the x-ray photoemission delay of
core-level electrons, and here report unexpectedly large delays, ranging up to
700 attoseconds in NO near the oxygen K-shell threshold. These measurements
exploit attosecond soft x-ray pulses from a free-electron laser (XFEL) to scan
across the entire region near the K-shell threshold. Furthermore, we find the
delay spectrum is richly modulated, suggesting several contributions including
transient trapping of the photoelectron due to shape resonances, collisions
with the Auger-Meitner electron that is emitted in the rapid non-radiative
relaxation of the molecule, and multi-electron scattering effects. The results
demonstrate how x-ray attosecond experiments, supported by comprehensive
theoretical modelling, can unravel the complex correlated dynamics of
core-level photoionization.
