We consider the two-photon double ionization of atomic systems by
ultrashort pulses. We examine the role of the electron correlations in
three different regimes: the direct and the sequential regimes as well
as a transient regime where the time of interaction is so short that the
distinction between the direct and the sequential transitions becomes
meaningless. Our analysis is based on an ab initio computational
treatment that is time-dependent and based on a spectral method of
conﬁguration interaction type combined with Jacobi matrix calculations.
This approach treats correctly the electron correlation both in the
initial and ﬁnal states as well as during the time propagation.
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