Compton scattering beyond the impulse approximation

We treat the nonrelativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation ~IA! or the independent particle model ~IPM!. An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the (N21) electron singly ionized quantum states of the target. We show how in the high-energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground-state electron momentum density of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering spectroscopy beyond the constraints of the IA and the IPM.