Parametrizations and dynamical analysis of angle-integrated cross sections for double photoionization including nondipole effects

Abstract

Similarly to differential cross sections for one-electron photoionization, the doubly differential cross section for double photoionization (DPI) may be conveniently described by four parameters: the singly differential (with respect to energy sharing) cross section $({\ensuremath{\sigma}}_{0})$, the dipole asymmetry parameter $(\ensuremath{\beta})$, and two nondipole asymmetry parameters ($\ensuremath{\gamma}$ and $\ensuremath{\delta}$). Here we derive two model-independent representations for these parameters for DPI from a $^{1}S_{0}$ atomic bound state: (i) in terms of one-dimensional integrals of the polarization-invariant DPI amplitudes and (ii) in terms of the exact two-electron reduced matrix elements. For DPI of He at excess energies, ${E}_{\mathrm{exc}}$, of 100 eV, 450 eV, and 1 keV, we present numerical results for the asymmetry parameters within the framework of the convergent close-coupling theory and compare them with results of lowest-order (in the interelectron interaction) perturbation theory (LOPT). The results for ${E}_{\mathrm{exc}}=1\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ exhibit a nondipole asymmetry that is large enough to be easily measured experimentally. We find excellent agreement between our LOPT results and other theoretical predictions and experimental data for total cross sections and ratios of double to single ionization cross sections for $K$-shell DPI from several multielectron atoms.