  As a step toward the full \emph{ab-initio} description of two-photon double
ionization processes, we present a finite-pulse version of the
virtual-sequential model for polyelectronic atoms. The model relies on the
\emph{ab initio} description of the single ionization scattering states of both
the neutral and ionized target system. As a proof of principle and a benchmark,
the model is applied to the helium atom using the {\tt NewStock} atomic
photoionization code. The results of angularly integrated observables, which
are in excellent agreement with existing TDSE (time-dependent Schr\"odinger
equation) simulations, show how the model is able to capture the role of
electron correlation in the non-sequential regime, and the influence of
autoionizing states in the sequential regime, at a comparatively modest
computational cost. The model also reproduces the two-particle interference
with ultrashort pulses, which is within reach of current experimental
technologies. Furthermore, the model shows the modulation of the joint energy
distribution in the vicinity of autoionizing states, which can be probed with
extreme-ultraviolet pulses of duration much longer than the characteristic
lifetime of the resonance. The formalism discussed here applies also to
polyelectronic atoms and molecules, thus opening a window on non-sequential and
sequential double ionization in these more complex systems.
