Extraction of Double Photoionization Amplitudes from Full-Scattered Wave Functions

Although cross sections for double photoionization (DPI) are much smaller than single photoionization cross sections, DPI by a single photon is a sensitive means of probing correlated electron dynamics. We extend a rigorous method for computing double ionization amplitudes in both time-independent and time-dependent computational formalisms by eliminating the requirement that the one-electron testing functions used to extract DPI amplitudes are continuum eigenfunctions that are orthogonal to the singly ionized states of the target. It is demonstrated that simple Coulomb testing functions can be used in an integral for the DPI amplitude restricted to the interaction region if few low-energy bound states of the singly charged ion are projected out of the full-scattered wave solution, resulting in surprisingly accurate triply and singly differential cross sections. These findings will simplify calculations of DPI amplitudes in more complicated polyatomic molecular targets than the benchmark two-electron systems considered here.