The four main goals of our full-dimensionality integration of the Time-Dependent Schroedinger Equation (TDSE) have been to: 1. Enable the calculation of intense-field (two-electron) phenomena that no low-dimensionality or ad hoc theory can adequately model. 2. Support the design of simplified theoretical models of multi-electron, atom-laser interactions and assess their ranges of validity. 3. Support, interpret and guide laboratory experiment. 4. Provide a stepping stone towards a full-dimensional treatment of the 3-body and 4-body problems presented by laser-driven H_2~+ and H_2 which are of fundamental importance to femto-second Chemistry In this paper, attention is focussed on points 1 and 3 above. A description of the method and associated computer algorithms is given in section 2. Section 3 concentrates on recent results obtained at a laser wavelength of 390 nm which take the form of ratios of double- to single-ionization yields. A direct comparison with experimental work is presented. Section 4 gives details of an investigation into ionization dynamics at a laser wavelength of 20.6 nm. Momentum distributions for doubly-ionizing wavepackets are given and preliminary results on two-electron above threshold ionization are reported.
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