Neutron Compton scattering — critical analysis of some basic theoretical assumptions

Abstract

A detailed overview of the conventional (van Hove) neutron scattering theory and its specification to the Impulse Approximation (IA) are given. The IA constitutes the basis of all interpretations of results from neutron scattering experiments in the Compton regime, in which is widely believed that single-particle properties are probed. Here the validity of this approximation is carefully scrutinized and it is shown that there are several different steps in the derivation, whose validity can be questioned: (1) the scattering system is a closed system (in the quantum mechanical sense); (2) all entanglement in the scattering system is absent (N-body operators are replaced by single particle operators); (3) consequently the one-body momentum distribution n(p) is introduced ad hoc; (4) the δ-function in energy assumed in the derivation is not valid when the interaction times underlying the IA are so short that the uncertainty relation allows a noticeable spread in the energy balance. Additionally, (5) the entanglement due to the direct interaction of the neutron with a nucleus is completely absent in the general formalism. The concrete experimental context of recent neutron Compton scattering (NCS) experiments at the ISIS neutron spallation source is considered and emphasis is put on the ultrafast (attosecond) scattering time for the neutron-proton scattering. Recent modern theoretical developments are shortly mentioned in the discussion, which take into account the neutron's coherence length being larger than the de Broglie wavelength, or decoherence phenomena during the short but finite scattering time.