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

As for one-electron ionization cross sections, the doubly and singly-differential cross sections (DDCSs and SDCSs) for double photoionization (DPI) may be conveniently described by four dipole and quadrupole asymmetry parameters, $\sigma_0$, $\beta$, $\gamma$, and $\delta$. Here we derive two {\it ab initio} parametrizations for these parameters: (i)~in terms of one- dimensional integrals of the polarization-invariant DPI amplitudes and (ii)~in terms of the exact two-electron matrix elements. The dynamical parameters are calculated including electron correlations to lowest order. Our results for SDCSs and DDCSs of He for excess energies of 100~eV and 450~eV are in reasonable agreement with experimental measurements and other theoretical calculations. Agreement with results of others for ratios of double to single ionization cross sections for K-shell DPI from multi-electron atoms is excellent in most cases.