  We formulate a three-dimensional semi-classical model to address triple and
double ionization in three-electron atoms driven by intense infrared laser
pulses. During time propagation, our model fully accounts for the Coulomb
singularities, the magnetic field of the laser pulse and for the motion of the
nucleus at the same time as for the motion of the three electrons. The
framework we develop is general and can account for multi-electron ionization
in strongly-driven atoms with more than three electrons. To avoid unphysical
autoionization arising in classical models of three or more electrons, we
replace the Coulomb potential between pairs of bound electrons with effective
Coulomb potentials. The Coulomb forces between electrons that are not both
bound are fully accounted for. We develop a set of criteria to determine when
electrons become bound during time propagation. We compare ionization spectra
obtained with the model developed here and with the Heisenberg model that
includes a potential term restricting an electron from closely approaching the
core. Such spectra include the sum of the electron momenta along the direction
of the laser field as well as the correlated electron momenta. We also compare
these results with experimental ones.
