On the relativistic impulse approximation for the calculation of Compton scattering cross sections and photon interaction coefficients used in kV dosimetry

Abstract

<p>We calculate differential and integrated cross sections for the Compton interaction as well as mass</p><p>attenuation (μC/ρ), mass energy-transfer (μC</p><p>tr/ρ), and mass energy-absorption (μen/ρ)</p><p>coefficients, within the relativistic impulse approximation (RIA) using Compton profiles (CPs)</p><p>obtained from unrestricted Hartree–Fock electron densities. We investigate the impact of using</p><p>molecular as opposed to atomic CPs on dosimetric photon interaction coefficients for air, water</p><p>and graphite, and compare our cross sections to the simpler Waller–Hartree (WH) and</p><p>Klein–Nishina (KN) formalisms. We find that differences in μC/ρ and μC</p><p>tr/ρ resulting from the</p><p>choice of CPs within the RIA are small relative to the differences between the RIA, WH, and KN</p><p>calculations. Surprisingly, although the WH binding corrections seem accurate when considering</p><p>μC/ρ, there are significant discrepancies between the WH and RIA results when we look at μC</p><p>tr/ρ.</p><p>The WH theory can differ substantially from the predictions of KN and the RIA in the tens of keV</p><p>range (e.g. 6%–10% at 20 keV), when Compton scattering becomes the dominant interaction</p><p>mechanism. For lower energies, the disagreement further grows to about one order of magnitude</p><p>at 1 keV. However, since the photoelectric effect transfers more energy than the Compton</p><p>interaction in the tens of keV range and below, the differences in the total μen/ρ values resulting</p><p>from the choice of Compton models (KN, WH, or RIA) are not larger than 0.4%, and the</p><p>differences between WH and the other two theories are no longer prominent.</p>