  Electron-core interactions play a key role in strong-field ionization and the
formation of photoelectron spectra. We analyse the temporal dynamics of strong
field ionization associated with these interactions using the time-dependent
analytical R-matrix (ARM) method, developed in our previous work [J. Kaushal
and O. Smirnova, Phys. Rev. A 88, 013421 (2013)]. The approach is fully quantum
but includes the concept of trajectories. However, the trajectories are not
classical in the sense that they have both real and imaginary components all
the way to the detector. We show that the imaginary parts of these
trajectories, which are usually ignored, have a clear physical meaning and are
crucial for the correct description of electron-core interactions after
ionization. In particular, they give rise to electron deceleration, as well as
dynamics associated with electron recapture and release. Our approach is
analytical and time-dependent, and allows one to gain access to the electron
energy distribution and ionization yield as a function of time. Thus we can
also rigorously answer the question: when is ionization completed?
