Rasouli Fatemeh S, Masoudi S Farhad, Jette David
Department of Physics, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran 15418-49611, Iran.
ICT Radiotherapy Services, Livingston, New Jersey 07039.
Med Phys. 2015 May;42(5):2364-7. doi: 10.1118/1.4917479.
Range and probability of nonelastic nuclear interactions (NNIs) for protons can be found only for a limited number of compounds and mixtures in nuclear data tables, and the proton-related analytical studies are therefore restricted to those materials for which the data are provided in these documents. In this paper, the authors present general solutions for calculating the proton range and probability of NNIs for desired compounds and mixtures.
Benefiting from the Bragg-Kleeman approximation of mass stopping power, the authors derive a concise formula for calculating the proton range in materials with arbitrary number of constituent elements. Additionally, the authors propose another relation for obtaining the probability of undergoing NNIs which is suggested to be additive.
The examination of the formula presented shows that the authors' method can be considered as general solutions for analytical evaluation of the range in compounds and mixtures. The formula proposed for probability of NNIs is valid for almost every compound except for those materials containing H. It is shown that this formula can be modified so that it covers these materials.
The authors present a general analytical method for calculating the range and probability of NNIs for protons which are mathematically easy to handle and valid for desired compounds or mixtures composed of an arbitrary number of constituent elements, including materials of interest for proton radiotherapy purposes.
质子的非弹性核相互作用（NNIs）的射程和概率仅能在核数据表中有限数量的化合物和混合物中找到，因此与质子相关的分析研究仅限于这些文档中提供了数据的那些材料。在本文中，作者提出了用于计算所需化合物和混合物中质子射程和NNIs概率的通用解决方案。
受益于质量阻止本领的布拉格 - 克莱曼近似，作者推导出了一个简洁的公式，用于计算具有任意数量组成元素的材料中的质子射程。此外，作者提出了另一个用于获得发生NNIs概率的关系式，该关系式被认为是可加性的。
对所提出公式的检验表明，作者的方法可被视为用于分析评估化合物和混合物中射程的通用解决方案。所提出的NNIs概率公式几乎对每种化合物都有效，除了那些含有氢的材料。结果表明，该公式可以修改以涵盖这些材料。
作者提出了一种通用的分析方法，用于计算质子的NNIs射程和概率，该方法在数学上易于处理，并且对由任意数量组成元素组成的所需化合物或混合物有效，包括质子放射治疗目的感兴趣的材料。
