A Compton profile representation for some second period elements

Abstract

Compton profiles for the elements C, N and O, which are important both in medical science and security screening, are represented here as weighted sums of three Gaussians. Simple scaling relationships describe the dependence on atomic number ( Z) of the amplitudes and standard deviations of the component Gaussians, which are identified with the Compton profiles of the 1s, 2s and 2p orbitals. This representation of the Compton profile agrees with tabulated values for C, N and O to a rms deviation of the order of 1% of the mean profile amplitude over the momentum range 0≤ q≤4, where q is expressed in units of the hydrogen ground state momentum. This representation allows a “mean atomic number” for mixtures and compounds dominated by second period elements to be assigned on the basis of experimental measurements of the Doppler broadening of back-scattered X-ray K characteristic lines. Processed spectra of water and ethanol from a Compton spectrometer equipped with a room-temperature semiconductor detector are compared with the Compton profiles synthesized as suggested here, and a satisfactory agreement between the measured and theoretical mean atomic numbers and the profile shapes is found.