Nuclear level reconstruction from energy differences ($E_{\gamma ,i}=E_{u_i}-E_{l_i}$)

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.