Purpose: The most appropriate method of evaluating the effective atomic number necessitates consideration of energy-dependent behavior. Previously, this required quite laborious calculation, which is why many scientists revert to over-simplistic power-law methods. The purpose of this work is to develop user-friendly software for the robust, energy-dependent computation of effective atomic numbers relevant within the context of medical physics, superseding the commonly employed simplistic power law approaches. Method : Visual Basic was used to develop a GUI allowing the straightforward calculation of effective atomic numbers. Photon interaction cross section matrices are constructed for energies spanning 10 keV to 10 GeV and elementsZ = 1–100. Coefficients for composite media are constructed via linear additivity of the fractional constituents and contrasted against the precalculated matrices at each energy, thereby associating an effective atomic number through interpolation of adjacent cross section data. Uncertainties are of the order of 1–2%. Results : Auto-Zeff allows rapid (∼0.6 s) calculation of effective atomic numbers for a range of predefined or user-specified media, allowing estimation of radiological properties and comparison of different media (for instance assessment of water equivalence). The accuracy of Auto-Zeff has been validated against numerous published theoretical and experimental predictions, demonstrating good agreement. The results also show that commonly employed power-law approaches are inaccurate, even in their intended regime of applicability (i.e., photoelectric regime). Furthermore, comparing the effective atomic numbers of composite materials using power-law approaches even in a relative fashion is shown to be inappropriate. Conclusion : Auto-Zeff facilitates easy computation of effective atomic numbers as a function of energy, as well as average and spectral-weighted means. The results are significantly more accurate than normal power-law predictions. The software is freely available to interested readers, who are encouraged to contact the authors.

Robust calculation of effective atomic numbers: The Auto-Zeff software

The effective atomic number, Z(eff), the effective electron density, N(el), and kerma have been calculated for some fatty acids and carbohydrates for photon interaction in the extended energy range from 1 keV to 100 GeV using an accurate database of photon-interaction cross sections and the WinXCom program. The significant variation of Z(eff) and N(el) is due to the variations in the dominance of different interaction processes in different energy regions. The maximum values of Z(eff) and N(el) are found in the low-energy range, where photoelectric absorption is the main interaction process. The minimum values of Z(eff) and N(el) are found at intermediate energies, typically 0.05 MeV < E < 5 MeV, where Compton scattering is dominant. In this case, Z(eff) is equal to the mean atomic number of the bio-molecule. Wherever possible, the calculations are compared with experimental results. A comparison is also made with the single values of the Z(eff) and N(el) provided by the program XMuDat. It is also observed that carbohydrates have a larger kerma than fatty acids in the low-energy region, where photoelectric absorption dominates. In contrast, fatty acids have a larger kerma than carbohydrates in the MeV range, where Compton scattering is the main interaction process.

https://iopscience.iop.org/article/10.1088/0031-9155/53/20/N01/pdf

Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates.

In this study, the total mass attenuation coefficients (μ(m)) for some homo- and hetero-chain polymers, namely polyamide-6 (PA-6), poly-methyl methacrylate (PMMA), low-density polyethylene (LDPE), polypropylene (PP) and polystyrene (PS) were measured at 59.5, 511, 661.6, 1173.2, 1274.5 and 1332.5 keV photon energies. The samples were separately irradiated with (241)Am, (22)Na, (137)Cs and (60)Co (638 kBq) radioactive gamma sources. The measurements were made by performing transmission experiments with a 2″×2″ NaI(Tl) scintillation detector having an energy resolution of 7 % at 662 keV gamma ray from the decay of (137)Cs. The effective atomic numbers (Z(eff)) and the effective electron densities (N(eff)) were determined experimentally and theoretically using the obtained μ(m) values for the investigated samples. Furthermore, Z(eff) and N(eff) of each polymer were computed for total photon interaction cross-sections using theoretical data over a wide energy region from 1 keV to 10 MeV. The experimental values of the selected polymers were found to be in good agreement with the theoretical values.

Mass attenuation coefficients, effective atomic numbers and effective electron densities for some polymers

Effective atomic numbers for photon energy absorption, ZPEA,eff, and for photon interaction, ZPI,eff, have been calculated by a direct method in the photon-energy region from 1 keV to 20 MeV for biological molecules, such as fatty acids (lauric, myristic, palmitic, stearic, oleic, linoleic, linolenic, arachidonic, and arachidic acids), nucleotide bases (adenine, guanine, cytosine, uracil, and thymine), and carbohydrates (glucose, sucrose, raffinose, and starch). The ZPEA,eff and ZPI,eff values have been found to change with energy and composition of the biological molecules. The energy dependence of the mass attenuation coefficient, ZPEA,eff, and the mass energy-absorption coefficient, ZPI,eff, is shown graphically and in tabular form. Significant differences of 17%−38% between ZPI,eff and ZPEA,eff occur in the energy region 5–100 keV. The reasons for these differences, and for using ZPEA,eff rather than ZPI,eff in calculations of the absorbed dose, are discussed.

Energy dependence of effective atomic numbers for photon energy absorption and photon interaction: studies of some biological molecules in the energy range 1 keV-20 MeV.

gamma-rays from the decay of 137 Cs. The effective atomic numbers (Zeff) and the effective electron densities (Neff) were determined experimentally and theoretically using the obtained μs values for the soil samples. Furthermore, the Zeff and Neff values of the soil samples were computed for the total photon interaction cross-sections using theoretical data over a wide energy region ranging from 1 keV to 15 MeV. The experimental values of the soils were found to be in good agreement with the theoretical values. Sandy loam and sandy clay loam soils demonstrated poor photon energy absorption characteristics. However, clay loam and clay soils had good photon energy absorption characteristics.

Ishtiaq Ahmed

Papers

Determination of effective atomic number and electron density of some fatty acids by gamma-ray attenuation