Intuitive dimensional analyses of the energy and atomic number dependences of the cross sections for radiation interaction with matter

Abstract

Scattering cross sections of radiation interactions with matter form the foundation for diagnostic x-ray imaging, nuclear medicine, and radiotherapy. These cross sections are typically presented as numerical charts in medical physics literature or complicated formulas in quantum electrodynamics literature. There seems to be a lack of comprehensible explanations for these cross section coefficients. Intuitive dimensional estimations of the dependences on photon energy and atomic number for radiation matter interaction cross sections are provided using elementary concepts of classical and quantum physics for Compton scattering, Rayleigh scattering, photoelectric effects, and pair production. This easy-to-understand approach is found to yield dimensional relations similar to that derived from quantum electrodynamics.