Isotopic ratios of radioactive xenons sampled in the subsurface and atmosphere can be used to detect underground nuclear explosions (UNEs) and civilian nuclear reactors. Disparities in the half-lives of the radioactive decay chains are principally responsible for time-dependent concentrations of xenon isotopes. Contrasting timescales, combined with modern detection capabilities, make the xenon isotopic family a desirable surrogate for UNE detection. However, without including the physical details of post-detonation cavity changes that affect radioxenon evolution and subsurface transport, a UNE is treated as an idealized system that is both closed and well mixed for estimating xenon isotopic ratios and their correlations so that the spatially dependent behavior of xenon production, cavity leakage, and transport are overlooked. In this paper, we developed a multi-compartment model with radioactive decay and interactions between compartments. The model does not require the detailed domain geometry and parameterization that is normally needed by high-fidelity computer simulations, but can represent nuclide evolution within a compartment and migration among compartments under certain conditions. The closed-form solution to all nuclides in the series 131–136 is derived using analytical singular-value decomposition. The solution is further used to express xenon ratios as functions of time and compartment position.

在地下和大气中采样的放射性氙的同位素比率可用于检测地下核爆炸 (UNE) 和民用核反应堆。放射性衰变链半衰期的差异是氙同位素浓度随时间变化的主要原因。对比时间尺度，结合现代检测能力，使氙同位素家族成为 UNE 检测的理想替代品。然而，在不包括影响放射性氙演化和地下传输的爆轰后空腔变化的物理细节的情况下，UNE 被视为一个理想化的系统，它既封闭又混合良好，用于估计氙同位素比率及其相关性，以便空间相关行为氙气的产生、空腔泄漏和传输被忽略了。在本文中，我们开发了一个多隔室模型，其中包含放射性衰变和隔室之间的相互作用。该模型不需要高保真计算机模拟通常需要的详细域几何形状和参数化，但可以表示特定条件下隔间内的核素演化和隔间之间的迁移。131-136 系列中所有核素的封闭形式解是使用解析奇异值分解推导出来的。该解决方案进一步用于将氙气比率表示为时间和隔室位置的函数。但可以表示在特定条件下隔室内的核素演化和隔室之间的迁移。131-136 系列中所有核素的封闭形式解是使用解析奇异值分解推导出来的。该解决方案进一步用于将氙气比率表示为时间和隔室位置的函数。但可以表示在特定条件下隔室内的核素演化和隔室之间的迁移。131-136 系列中所有核素的封闭形式解是使用解析奇异值分解推导出来的。该解决方案进一步用于将氙气比率表示为时间和隔室位置的函数。