Asymptotic properties of the scattering function in neutron Compton scattering, I: Constant scattering angle vs. constant momentum transfer scan

The recent upsurge of interest in data treatment of neutron Compton scattering (NCS) experiments has been triggered by the observation of a striking anomaly of the scattering intensities from protons at high energy and momentum transfers. The anomalous NCS intensities are measured with an experimental setup where the neutron detectors are placed at fixed scattering angles. It was put forward that, in order to compare the experimental results with rigorous sum rules, the scattering function must be transformed from a constant scattering angle to a fictitious constant momentum transfer scan by means of a proper Jacobian. The Jacobian discussed in the literature was derived for the case of inelastic neutron scattering from single crystals. Here, we present for the first time a full analytical derivation of a new Jacobian that is much better suited for the NCS.