Interpreting Difference Compton Profiles in Zirconium Hydride: Reference States, Normalization, and Uncertainty

Compton profiles probe projected electron momentum density and can constrain the electronic changes accompanying hydrogen incorporation in zirconium. This focused critical methodological review examines how reference states, normalization, and experimental response affect the interpretation of zirconium-hydride difference profiles. The published Zr/ZrH₂ experiment provides the historical starting point, considered alongside subsequent electronic-structure and spectroscopic evidence. Electron-count conservation distinguishes absolute hydride-minus-metal differences, neutral-hydrogen reference differences, and equal-electron-count shape differences. These constructions answer different questions, and their integrals do not uniquely separate added-electron contributions from host-state rearrangement or determine atom-centered charges. Reproducible analytical examples demonstrate that equal electron counts permit different profile shapes. For an illustrative 40-electron host, metal-reference overscaling of 0.5% reduces the absolute difference integral from 2.0 to 1.8 electrons. Gaussian broadening preserves full-line integrals while attenuating the central feature of the selected redistribution function. An explicit first-order covariance model describes the correlations introduced by uncertain relative normalization. The resulting framework identifies requirements for future comparisons of phase-specific theoretical profiles with composition-controlled measurements, including response matching, finite-window treatment, and joint uncertainty propagation. No historical spectra are refitted, and the analytical examples are neither experimental reconstructions nor first-principles predictions for ZrH₂.