Phy-X/ZeXTRa: a software for robust calculation of effective atomic numbers for photon, electron, proton, alpha particle, and carbon ion interactions

The purpose of the present work is robust calculation of effective atomic numbers ($${Z}_{\text{eff}}$$s) for photon, electron, proton, alpha particle and carbon ion interactions through the newly developed software, Phy-X/ZeXTRa (Zeff of materials for X-Type Radiation attenuation). A pool of total mass attenuation and energy absorption coefficients (for photons) and total mass stopping powers (for charged particles) for elements was constructed first. Then, a matrix of interaction cross sections for elements Z = 1–92 was constructed. Finally, effective atomic numbers were calculated for any material by interpolating adjacent cross sections through a linear logarithmic interpolation formula. The results for $${Z}_{\text{eff}}$$ for photon interaction were compared with those calculated through Mayneord’s formula, which suggests a single-valued $${Z}_{\text{eff}}$$ for any material for low-energy photons for which photoelectric absorption is the dominant interaction process. The single-valued $${Z}_{\text{eff}}$$ was found to agree well with that obtained by other methods, in the low-energy region. In addition, $${Z}_{\text{eff}}$$ values of various materials of biological interest were compared with those obtained experimentally at 59.54 keV. In general, the agreement between values calculated with Phy-X/ZeXTRa and Auto-Zeff and those measured were satisfactory. A comparison of $${Z}_{\text{eff}}$$ values for photon energy absorption calculated with Phy-X/ZeXTRa and literature values for a nucleotide base, adenine, was made, and the relative difference (RD) in $${Z}_{\text{eff}}$$ between Phy-X/ZeXTRa and literature values was found to be 2% < RD < 11%, at low photon energies (1–100 keV), while it was less than 1% at energies higher than 100 keV. Highest $${Z}_{\text{eff}}$$ values were observed at low photon energies, where photoelectric absorption dominates photon interaction. For electrons, corresponding RD(%) values in $${Z}_{\text{eff}}$$ were found to be in the range 0.4 ≤ RD(%) ≤ 1.7, while for heavy charged particle interactions it was 2.4 ≤ RD(%) ≤ 4.2 for total proton interaction and 0 ≤ RD(%) ≤ 8 for total alpha particle interaction. In view of the importance of $${Z}_{\text{eff}}$$ for identifying and differentiating tissues in diagnostic imaging as well as for estimating accurate dose in radiotherapy and particle-beam therapy, Phy-X/ZeXTRa could be used for fast and accurate calculation of $${Z}_{\text{eff}}$$ in a wide energy range for both photon and charged particle (electrons, protons, alpha particles and C ions) interactions.