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

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 elements Z = 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-Z(eff) allows rapid (similar to 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-Z(eff) 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-Z(eff) 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. (C) 2012 American Association of Physicists in Medicine. [http://dx.doi.org/10.1118/1.3689810]