Compton scattering beyond the impulse approximation

TL;DR

This paper develops a new theoretical framework for non-relativistic Compton scattering that goes beyond the impulse approximation and independent particle model, enabling better analysis of correlated electron systems in inelastic x-ray scattering.

Contribution

It introduces a formalism expressing the scattering cross section in terms of Dyson orbitals, allowing analysis beyond traditional approximations.

Findings

Derives an expression for the triple differential scattering cross section using Dyson orbitals.

Shows how to recover the impulse approximation formula in the high energy transfer regime.

Enables analysis of electronic transitions in correlated systems via inelastic x-ray scattering.

Abstract

We treat the non-relativistic 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 (N-1) 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 (EMD) of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering (IXS) spectroscopy beyond the constraints of the IA and the IPM.