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

Article type: Research Article

Authors: Wang, Yi

Affiliations: Departments of Radiology and Biomedical Engineering Cornell University, New York, USA

Note: [] Corresponding author: Yi Wang, PhD, Radiology and Biomedical Engineering, Cornell University, 575 Lexington Ave, 3rd floor, New York, NY 10022, USA. Tel.: +1 646 253 2809; E-mail: [email protected]

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.

Keywords: Dimensional analysis, interaction between radiation and matter, interaction cross sections, compton scattering, rayleigh scattering, photoelectric effects, pair production

Journal: Journal of X-Ray Science and Technology, vol. 15, no. 3, pp. 169-175, 2007