  The structure of approximate two electron wavefunction is deeply
investigated, both theoretically and numerically, in the strong-field driven
ionization dynamics. Theoretical analyses clarify that for two electron singlet
systems, the previously proposed time-dependent extended Hartree-Fock (TD-EHF)
method [Phys. Rev. A 51, 3999 (1995)] is equivalent to the multiconfiguration
time-dependent Hartree-Fock method with two occupied orbitals. The latter
wavefunction is further transformed into the natural expansion form, enabling
the direct propagation of the natural orbitals (NOs). These methods, as well as
the conventional time-dependent Hartree-Fock (TDHF) method, are numerically
assessed for the description of ionization dynamics of one-dimensional helium
atom model. This numerical analysis (i) explains the reason behind the
well-known failure of TDHF method to describe tunneling ionization, (ii)
demonstrates the interpretive power of the TD-EHF wavefunction both in the
original nonorthogonal and the NO-based formulations, and (iii) highlights
different manifestations of the electron correlation (effect beyond the single
determinant description), in tunneling ionization, high harmonic generation,
and nonsequential double ionization. Possible extensions of the NO basis
approach to multielectron systems are briefly discussed.
