Thwaites D E, Watt D E
Phys Med Biol. 1978 May;23(3):426-37. doi: 10.1088/0031-9155/23/3/006.
Bragg's additivity rule is the basis for calculating stopping powers of compounds from data on their constituent elements. Major assumptions in applying it are that chemical binding and the physical state of the stopping material have negligible influence on the slowing down process. The fragmentary and, at times conflicting evidence for phase effects for low energy heavy charged particles is summarised. A detailed survey of published stopping powers has been made and the information grouped according to target medium and phase. Each group has been fitted to universal curves of Lindhard type with the object of separating phase contributions to stopping. Least square fits have been made to each set of data. From these a quantitative measure of the effect is obtained and presented as stopping power ratios (vapour/condensed phase). From the experimental evidence available, it is concluded that phase effects do occur, decreasing the stopping power in solids and liquids as compared to the corresponding vapours, and are thought to be due largely to changes in electronic excitation levels as the phase is changed, combined with a physical-state dependence of the effective ion change at low energies. Magnitudes of the stopping power ratio deviate from unity by up to approximately 25%, but have significant associated errors, pointing to need for more accurate stopping power measurements.
布拉格加和规则是根据化合物组成元素的数据计算其阻止本领的基础。应用该规则的主要假设是化学结合和阻止材料的物理状态对减速过程的影响可忽略不计。总结了关于低能重带电粒子相效应的零碎且有时相互矛盾的证据。已对已发表的阻止本领进行了详细调查，并根据靶介质和相将信息进行了分组。为了区分相贡献对阻止的影响，每组数据都拟合到了林哈德类型的通用曲线上。对每组数据进行了最小二乘法拟合。由此获得了该效应的定量度量，并以阻止本领比（气相/凝聚相）的形式呈现。根据现有实验证据得出结论，相效应确实存在，与相应的气相相比，固体和液体中的阻止本领降低，并且认为这主要是由于相变化时电子激发水平的变化，以及低能时有效离子电荷对物理状态的依赖性。阻止本领比的大小与1的偏差高达约25%，但存在显著的相关误差，这表明需要进行更精确的阻止本领测量。
