Since Poincaré, the three-body problem is known to be chaotic and is believed to lack a general deterministic solution. Instead, decades ago a statistical solution was marked as a goal. Yet, despite considerable progress, all extant approaches display two flaws. First, probability was equated with phase space volume, thereby ignoring the fact that significant regions of phase space describe regular motion, including post-decay motion. Secondly and relatedly, an adjustable parameter, the strong interaction region, which is a sort of cutoff, was a central ingredient of the theory. This paper introduces remedies and presents for the first time a statistical prediction of decay rates, in addition to outcomes. Based on an analogy with a particle moving within a leaky container, the statistical distribution is presented in an exactly factorized form. One factor is the flux of phase-space volume, rather than the volume itself, and it is given in a cutoff-independent closed form. The other factors are the chaotic absorptivity and the regularized phase space volume. The situation is analogous to Kirchhoff’s law of thermal radiation, also known as greybody radiation. In addition, an equation system for the time evolution of the statistical distribution is introduced; it describes the decay rate statistics while accounting for sub-escape excursions. Early numerical tests indicate a leap in accuracy.

自庞加莱以来，三体问题被认为是混乱的，并且据信缺乏一般的确定性解决方案。相反，几十年前，统计解决方案被标记为目标。然而，尽管取得了长足的进步，所有现有方法都显示出两个缺陷。首先，概率等于相空间量，从而忽略了相空间的重要区域描述规则运动（包括后衰减运动）的事实。其次，与此相关的是，一个可调整的参数，即强相互作用区域，是一种截止点，是该理论的重要组成部分。本文介绍了补救措施，并首次提出了除结果外的衰减率的统计预测。基于粒子在泄漏容器中移动的类比，统计分布以精确分解的形式表示。一个因素是相空间体积的通量，而不是体积本身的通量，它以与截止值无关的闭合形式给出。其他因素是混沌吸收率和正则相空间体积。这种情况类似于基尔霍夫的热辐射定律，也称为灰体辐射。另外，引入了一个用于统计分布的时间演化的方程组。它描述了衰减率统计信息，同时考虑了子逃逸偏移。早期的数值测试表明准确性有了飞跃。也称为灰体辐射。另外，引入了一个用于统计分布的时间演化的方程组。它描述了衰减率统计信息，同时考虑了子逃逸偏移。早期的数值测试表明准确性有了飞跃。也称为灰体辐射。另外，引入了一个用于统计分布的时间演化的方程组。它描述了衰减率统计信息，同时考虑了子逃逸偏移。早期的数值测试表明准确性有了飞跃。