Determination of the effective atomic number: A theoretical justification

In this paper, we have tried to seek a theoretical justification for the effective atomic number $(Z_{\text{eff}})$ for Compton scattering studies by computing it from free atom Hartree-Fock wave function based Compton profiles compiled by Biggs et al. Typical experimental examples have been provided which show a good agreement with that of theory justifying the validity of the mixture rule. This envisages $Z_{\text{eff}}$ as a reliable mixture parameter that can quantify the understanding of photon interaction properties of complex media. The paper also provides details of how the theoretical Compton profiles can be used to calculate $Z_{\text{eff}}$ for Compton scattering of any sample at any energy or angle (momentum transfer)