Double photoionization of helium: Analysis of photoelectrons with respect to energies and angles

The basic sixfold differential cross section ${\mathit{d}}^6$ ${\mathrm{\sigma }}^{2+}$/${\mathit{d}}^3$ k ${\mathit{d}}^3$ k ’ (SDCS) of the double photoionization process is derived within a ‘‘wave-function approach’’ (WFA) using a highly correlated ground-state wave function and a double-continuum final state approximated by a symmetrized product of one-electron Coulomb waves with k and k ’ asymptotic momenta. Relevant integrations of the SDCS are shown to provide a complete description of the (γ,2e) process. The theory is illustrated by calculations for helium targets: total cross sections, kinetic energy spectra, and angular plots of photoelectrons are presented. Considering the total cross section, it is found first that the agreement between the length and velocity result is worse than expected from the previous studies. In addition, the present model provides kinetic energy distributions of photoelectrons having the symmetry required by the Pauli principle. This is in contrast with earlier formulations of the WFA. For the SDCS, calculations have been done with final states where Coulomb waves were provided with either fixed charge (Z=2: unscreened nucleus) or variable effective charges. In the former case, it is found that the event where electrons escape with the same energy, along the polarization direction, has a significant probability. This deficiency is removed by use of angle-dependent effective charges since final-state correlation is partly accounted for in this way.