  We investigate laser induced nonsequential multiple ionization using a simple
statistical model in which an electron recollides inelastically with its parent
ion. In this collision, it thermalizes with the remaining $N-1$ bound electrons
within a time interval $\Delta t$. Subsequently, all the $N$ electrons leave.
We address the question of how the above time delays influence the individual
contributions from the orbits in which the first electron, upon return, is
accelerated or decelerated by the field, respectively, to the ion momentum
distributions. In both cases, the time delays modify the drift momenta obtained
by the $N$ electrons when they reach the continuum at $t+\Delta t$, by moving
such times towards or away from a crossing of the electric field. The
contributions from both types of collisions are influenced in distinct ways,
and the interplay between such trends determines the widths and the peak
momenta of the distributions. Specifically in the few-cycle pulse case, we also
show that such time delays do not affect the shapes of the momentum
distributions in a radical fashion. Hence, even with a thermalization time
$\Delta t$, nonsequential multiple ionization could in principle be used for
absolute-phase diagnosis.
