论文标题
吉格·纳特尔法律在重群衰减中的局限性
Limitations of the Geiger-Nuttall Law in heavy cluster decay
论文作者
论文摘要
Geiger-Nuttall定律是有关半衰期和衰减能量的放射性衰减中最简单的关系。最初仅限于单个同位素的$α$衰减，随后实现了在一组恒定系数下统一不同同位素和衰减模式的概括。这激发了调查在多大程度上可能进行的概括。我们还检查了是否存在通用的Geiger-Nuttall定律，该定律可以同时描述包括重簇在内的所有衰减模式和核。我们表明，Geiger-Nuttall定律及其概括的有效性取决于假设可以将半衰期线性近似作为衰减能量与库仑屏障高度比率的平方根的函数。对于12种衰减模式的整个核图表的系统计算表明，它在整个范围内有所不同。因此，没有线性近似可以在一组系数下统一所有核和衰减模式，因此与先前的主张相比，没有普遍的Geiger-Nuttall定律。在群集衰减中，该比率在0.6-1之内变化，其中非线性变得显着，因此不可能对重簇的广义描述。在持续的统一尝试中，可能有必要超越Geiger-Nuttall法律，并结合与衰减能量和/或其平方根成正比的其他术语。
Geiger-Nuttall Law is the simplest relation in radioactive decay relating the half-life and the decay energy. Initially restricted to $α$ decay of individual isotopes, generalizations unifying different isotopes and decay modes under a single set of constant coefficients were subsequently achieved. This motivates investigating to what extent such generalizations are possible. We also examine whether there exists a universal Geiger-Nuttall Law that can simultaneously describe all decay modes and nuclei including heavy clusters. We show that the validity of Geiger-Nuttall Law and its generalizations hinges on the assumption that half-life can be approximated linearly as a function of the square root of the ratio of the decay energy to the Coulomb barrier height. Systematic calculation of the ratio across the nuclear chart for 12 decay modes reveals that it varies over its whole range between 0 and 1. Consequently, no linear approximation can unify all the nuclei and decay modes under a single set of coefficients, and thus no universal Geiger-Nuttall Law is possible in contrast to previous claims. In cluster decay, the ratio varies within 0.6-1 where non-linearity becomes significant such that no generalized Geiger-Nuttall description of heavy clusters is possible. In the ongoing attempts of unification, it might be necessary to go beyond the Geiger-Nuttall Law and incorporate additional terms proportional to the decay energy and/or its square root.
