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We perform a systematic analysis of how nonsequential double ionization inintense, linearly polarized laser fields is influenced by the initial states inwhich both electrons are bound, and by the residual ionic potential. We assumethat the second electron is released by electron-impact ionization of the firstelectron with its parent ion, using an S-Matrix approach. We work within theStrong-Field Approximation, and compute differential electron momentumdistributions using saddle-point methods. Specifically, we consider electronsin $1s$, $2p$, $3p$ and localized states, which are released by either acontact or a Coulomb-type interaction. We also perform an adequate treatment ofthe bound-state singularity which is present in this framework. We show thatthe momentum distributions are very sensitive with respect to spatiallyextended or localized wave functions, but are not considerably influenced bytheir shape. Furthermore, the modifications performed in order to overcome thebound-state singularity do not significantly alter the momentum distributions,apart from a minor suppression in the region of small momenta. The only radicalchanges occur if one employs effective form factors, which take into accountthe presence of the residual ion upon rescattering. If the ionic potential isof contact type, it outweighs the spreading caused by a long-rangeelectron-electron interaction, or by spatially extended bound states. Thisleads to momentum distributions which exhibit a very good agreement with theexisting experiments.Comment: 13 pages revtex, 11 figures (eps files

Bound-state corrections in laser-induced nonsequential double ionization