Department of Physics, Faculty of Science, Atatürk University, 25240, Erzurum, Turkey.
Department of Electricity and Energy, Technical Scientific Vocational School, Bayburt University, 69000, Bayburt, Turkey.
Radiat Environ Biophys. 2020 May;59(2):321-329. doi: 10.1007/s00411-019-00829-7. Epub 2020 Jan 20.
The purpose of the present work is robust calculation of effective atomic numbers ([Formula: see text]s) for photon, electron, proton, alpha particle and carbon ion interactions through the newly developed software, Phy-X/ZeXTRa (Z 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 [Formula: see text] for photon interaction were compared with those calculated through Mayneord's formula, which suggests a single-valued [Formula: see text] for any material for low-energy photons for which photoelectric absorption is the dominant interaction process. The single-valued [Formula: see text] was found to agree well with that obtained by other methods, in the low-energy region. In addition, [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] values were observed at low photon energies, where photoelectric absorption dominates photon interaction. For electrons, corresponding RD(%) values in [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] in a wide energy range for both photon and charged particle (electrons, protons, alpha particles and C ions) interactions.
本工作的目的是通过新开发的软件 Phy-X/ZeXTRa（用于 X 型辐射衰减的材料 Z）稳健地计算光子、电子、质子、α 粒子和碳离子相互作用的有效原子数 ([Formula: see text])。首先构建了元素的总质量衰减和能量吸收系数（光子）和总质量阻止本领（带电粒子）的数据库。然后，构建了 Z=1-92 元素的相互作用截面矩阵。最后，通过线性对数插值公式对相邻截面进行插值，计算出任何材料的有效原子数。光子相互作用的 [Formula: see text] 与 Mayneord 公式计算的结果进行了比较，该公式表明对于光电吸收是主要相互作用过程的低能光子，任何材料的单一 [Formula: see text]。在低能区，发现单一的 [Formula: see text] 与其他方法获得的值吻合较好。此外，还将各种生物感兴趣材料的 [Formula: see text] 值与在 59.54 keV 处获得的实验值进行了比较。一般来说，用 Phy-X/ZeXTRa 计算的 [Formula: see text] 值与 Auto-Zeff 和实验测量值之间的一致性令人满意。对 Phy-X/ZeXTRa 和文献中核苷酸碱基腺嘌呤的光子能量吸收计算的 [Formula: see text] 值进行了比较，发现 Phy-X/ZeXTRa 和文献值之间的 [Formula: see text] 相对差异 (RD) 在低能光子 (1-100 keV) 时为 2%<RD<11%，而在高于 100 keV 时则小于 1%。在低光子能量下，光电吸收主导光子相互作用时，观察到最高的 [Formula: see text] 值。对于电子，在 [Formula: see text] 中对应的 RD(%) 值在 0.4≤RD(%)≤1.7 范围内，而对于重带电粒子相互作用，总质子相互作用的 RD(%) 值为 2.4≤RD(%)≤4.2，总α 粒子相互作用的 RD(%) 值为 0≤RD(%)≤8。鉴于有效原子数对于在诊断成像中识别和区分组织以及在放射治疗和粒子束治疗中估计准确剂量的重要性，Phy-X/ZeXTRa 可用于快速准确地计算光子和带电粒子（电子、质子、α 粒子和 C 离子）相互作用的宽能范围内的 [Formula: see text]。
