Prediction of the 1st excitation energy of odd–odd nuclei with the Bayesian neural network approach

Abstract

A Bayesian neural network (BNN) is developed to predict the 1st excitation energy of odd–odd nuclei. Aside from the proton number and neutron number, we introduce two empirical physical quantities into the input layer. δ=[−1N+−1Z]/2 is introduced to distinguish even–even, odd–odd and odd-A nuclei; and the so-called Casten factor P≡vpvnvp+vn is introduced to stand for collectivity. The BNN is trained with an experimental dataset of the 1st excitation energy for 434 odd–odd, 649 even–even and 1050 odd-A nuclei. After training, the BNN predicts the 1st excitation energy of odd–odd nuclei with a rms of 0.21 MeV. Examples of Dy, Gd, Eu and Cs isotopes are also shown. The BNN results show moderate predictive ability, in comparison with results from the projected Hartree–Fock method.