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The factorisation approximation in electron-atom ionisation

The distorted-wave impulse approximation for ionisation in a three-body model treats the two-body subsystems to all orders in the relevant potentials. It can only be calculated by making the approximation of factorising out the electron-electron T matrix. In the distorted-wave Born approximation the factorised and unfactorised amplitudes can both be calculated. They are compared for different kinematic ranges, to provide some insights into the validity of factorisation. The bound states used for illustration are the 2s and 2p Hartree-Fock orbitals of neon. It is concluded that factorisation is a good approximation near the bound-electron Bethe ridge, expect for very small momentum transfer.