The structure of approximate two electron wavefunctions in intense laser driven ionization dynamics

TL;DR

This paper investigates the structure of approximate two-electron wavefunctions in intense laser-driven ionization, comparing methods like TD-EHF, TDHF, and natural orbitals, revealing their strengths and limitations in modeling ionization dynamics.

Contribution

It clarifies the equivalence of TD-EHF and multiconfiguration methods, and assesses their effectiveness in describing ionization processes in a one-dimensional helium model.

Findings

TDHF fails to describe tunneling ionization.

TD-EHF provides insightful interpretation of electron correlation.

Natural orbitals enable direct propagation and improved analysis.

Abstract

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.