Nuclear level scheme

A nuclear level scheme represents nuclear energy levels and transitions among them. Gamma ray energies constrain pairwise differences; emission counts and coincidence measurements help resolve different schemes having the same difference multiset.

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.