= Nuclear level population balance
{title2=$F_i=\sum_{j<i}C_{i\to j}-\sum_{k>i}C_{k\to i}$}
For a complete ensemble of downward <nuclear de-excitation> cascades, let $F_i$ be the direct population of excited level $i$ and $C_{i\to j}$ the total number of transitions from $i$ to $j$. Conservation of population gives the displayed outward-minus-inward formula. A negative $F_i$ rules out a proposed scheme under the assumed complete transition inventory. <Gamma ray> counts equal transition counts only when unreported <internal conversion> and other competing paths can be neglected or corrected. Summing over all excited levels cancels internal transitions and leaves the transitions into the <ground state>.
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