Prediction of $$2^{+}$$ energies in even–even nuclei of the Terra incognita with Bayesian neural network

Abstract A reliable Bayesian neural network (BNN) approach is employed to model a large dataset of the first excited $$2^+$$ 2 + state energies in even–even nuclei. The BNN is trained and validated using existing experimental data, achieving excellent agreement and a minimal root-mean-square error, which demonstrates its high predictive accuracy. In addition to reproducing known values, the BNN is used to perform boundary extrapolations of $$E(2^{+}_{1})$$ E ( 2 1 + ) along isotopic and isotonic chains toward heavier nuclei (Z $$\ge $$ ≥ 60). The effects of the proposed, but not yet established, magic numbers Z = 126 and N = 184 are examined, with distinct prediction outcomes observed depending on whether these values are included as input features. Our results, if taken not too far from present limits, might serve as an indication for planning of future experiments reaching out for the Terra incognita of the nuclear chart.