Analytical dependence of effective atomic number on the elemental composition of matter and radiation energy in the range 10-1000 keV

In the present paper, a universal analytical dependence of effective atomic number on the composition of matter and radiation energy is proposed. This enables one to consider the case of a strong difference in the elemental composition with respect to their atomic numbers over a wide energy range. The contribution of photoelectric absorption and incoherent and coherent scattering during the interaction between radiation and matter is considered. For energy values over 40 keV, the contribution of coherent scattering does not exceed approximately 10% that can be neglected at a further consideration. The effective atomic numbers calculated on the basis of the proposed relationships are compared to the results of calculations based on other methods considered by different authors on the basis of experimental and tabulated data on mass and atomic attenuation coefficients. The examination is carried out for both single-element (e.g., 6C, 14Si, 28Cu, 56Ba, and 82Pb) and multi-element materials. Calculations are performed for W1−xCux alloys (x = 0.35; x = 0.4), PbO, ther moluminescent dosimetry compounds (56Ba, 48Cd, 41Sr, 20Ca, 12Mg, and 11Na), and SO4 in a wide energy range. A case with radiation energy between the K- and L1-absorption edges is considered for 82Pb, 74W, 56Ba, 48Cd, and 38Sr. This enables to substantially simplify the calculation of the atomic number and will be useful in technical and scientific fields related to the interaction between X-ray/gamma radiation and matter.