The responses of the three photomultiplier tubes (PMTs) in a triple-to-double coincidence ratio (TDCR) liquid scintillation (LS) system are often not identical. Such asymmetries can have a significant influence on activity determinations. The problem is often solved by means of a minimization algorithm which can easily be applied when analytical methods are used for the efficiency calculation, as is usually done for pure beta emitters. However, for radionuclides with more complex decay schemes, the counting efficiencies are often calculated with stochastic methods and the computation of the required corrections becomes very challenging.

This paper presents a new numerical method to overcome the asymmetry problem for such complex decays and a comprehensive study on ⁵⁵Fe is described in detail. For the measurements, the asymmetry was varied by means of grey filter films which were placed in front of one of the photomultiplier tubes.

In the case of the pure electron-capture (EC) radionuclide ⁵⁵Fe, the asymmetry can also be taken into account with a very simple correction which is derived assuming monoenergetic emissions. This work is also of great importance for the planned extension of the International Reference System (SIR) at the BIPM which will be used for international comparisons in radionuclide metrology.

在三重对重合比率（TDCR）液体闪烁（LS）系统中，三个光电倍增管（PMT）的响应通常不相同。这样的不对称性可能对活动确定产生重大影响。通常使用最小化算法解决该问题，当使用分析方法进行效率计算时，可以很容易地应用该算法，就像通常对纯β发射体所做的那样。然而，对于具有更复杂衰变方案的放射性核素，通常使用随机方法来计算计数效率，并且所需校正的计算变得非常具有挑战性。

本文提出了一种克服此类复杂衰变不对称问题的新数值方法，并详细描述了⁵⁵ Fe的综合研究。对于测量，通过放置在光电倍增管之一前面的灰色滤光片来改变不对称性。

在纯电子捕获（EC）放射性核素⁵⁵ Fe的情况下，还可以通过非常简单的校正来考虑不对称性，该校正是在假设单能发射的情况下得出的。这项工作对于BIPM国际参考系统（SIR）的计划扩展也将具有重要意义，该系统将用于放射性核素计量学的国际比较。