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

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 $\left({\sigma }_0\right)$, the dipole asymmetry parameter $\left(\beta \right)$, and two nondipole asymmetry parameters ($\gamma$ and $\delta$). 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 $E_{\mathrm{exc}}=1\mathrm{keV}$ 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.

Figure 1

DDCS for DPI of He for an excess energy of 100 eV, linear polarization, and coplanar geometry. Directions of the photon wave vector $\widehat{\mathbf{k}}$ and polarization $\widehat{\mathbf{ϵ}}$ are as shown in (a). The angular distributions for the electron having energy $E_1$ are shown. Full and dashed curves in bold: CCC; full and dashed curves of regular thickness: LOPT. Full curves: dipole-quadrupole results; dashed curves: dipole results. Experimental results [27] are normalized to the CCC results.

Figure 2

DDCS for DPI of He for an excess energy of 450 eV, linear polarization, and coplanar geometry. Directions of the photon wave vector $\widehat{\mathbf{k}}$ and polarization $\widehat{\mathbf{ϵ}}$ are as shown in (a). The angular distributions for the electron having energy $E_1$ are shown. Curves are defined as in Fig. 1. Experimental results [29] are normalized to the CCC results.

Figure 3

DDCS for DPI of He for an excess energy of 1 keV, linear polarization, and coplanar geometry. Directions of the photon wave vector $\widehat{\mathbf{k}}$ and polarization $\widehat{\mathbf{ϵ}}$ are as shown in (a). Angular distributions for the electron having energy $E_1$ are shown. Curves are defined as in Fig. 1.

Figure 4

SDCS for DPI of He at an excess energy of 450 eV. Full curve: present LOPT results; dashed curve: CCC results from Ref. 29; the experimental data (from Ref. 29) are normalized to the CCC results.