Excess energy partition between the electrons in the double electron escape processes

The processes with two electrons in the final continuum state are considered for small energy excess E above the threshold. The distribution of the total energy E between the electrons is calculated within the quantum Wannier theory where the quadratic approximation for the Hamiltonian is employed in the vicinity of the Wannier ridge. The problem is cast in terms of the wavepacket propagation. The Green function formulation is employed and its physical implications are analysed. The final distribution is shown to be uniform and essentially independent of the boundary condition at the border of the inner Wannier zone. The extended model is developed which does not resort to the quadratic approximation but accounts for the attractive Coulomb singularities of the potential. It is solved numerically using the grid method. The manifestations of the competing process are discussed (single ionization with the other electron in a high Rydberg state).