Gamma-cascade intensity balance ($\sum I_{\mathrm{feed}}=\sum I_{\mathrm{deexcite}}$)

For a prompt nuclear level fed in a steady decay cascade, incoming and outgoing transition populations balance. Quoted photon intensities must represent efficiency-corrected emission counts; internal conversion, alternative particle decays and unobserved feeds must either be included or explicitly excluded. Equal photon counts suggest a serial cascade, while a feed intensity equal to the sum of two branches suggests splitting. intensities alone do not determine the chronological order of equal-count lines.

Reconstructing a nuclear gamma scheme amounts to assigning measured photon energies to differences between ordered level energies. Cascade energy sums constrain the graph, while population-flow balances constrain its orientation and feeding. Experimental central energies need not close exactly; a weighted least-squares energy-network fit uses their uncertainties consistently. Multiple graphs can satisfy the same spectrum when coincidence or lifetime information is absent.