The average β and γ energies data of the β——decay nuclei plays an important role in many fields of nuclear technology and scientific research, Such as the decay heat and antineutrino spectrum calculation of different kinds of reactors. However, for many nuclei, the reliable experimental measurements of their average energy are lacking, and the theoretical calculation needs to be improved to meet the accuracy requirements of the technical applications.
In this study, the average β, γ and neutrino energies of the β—decay nuclei were investigated by the neural network approach based on the newly evaluated experimental data of 543 nuclei from a total of 1136 β—decay nuclei. For the neural network approach, three different feature groups are used for model training. Each feature group contains a characteristic feature value (one of the T_1/2, (1/T_1/2)^1/5, and 1/3Q), along with five identical feature values (Z, N, parity of Z, parity of N, and ΔZ).
The three characteristics feature values were selected based on the physical mechanism below:1. the average energy is obviously related with Q value and approximately taken as 1/3Q in the reactor industry. Hence the 1/3Q was selected as one characteristics feature value; 2. the half-live is relative with the Q value of β—decay, and T_1/2 was considered; 3. considering the Sargent' s law, (1/T_1/2)^1/5 ∝ Q, a more accurate (1/T_1/2)^1/5 value were selected.
As a result, for the feature group of T_1/2, the training results for all three types of average energy were unsatisfactory. For the other groups, for the average β energy data, the relative errors are 19.32% and 28.11% for(1/T_1/2)^1/5 and 1/3Q feature groups in the training set and 82% and 56.9% in the validation set; for the average γ energy, the relative errors were 28.9% and 76.9% for (1/T_1/2)^1/5 and 1/3Q feature groups and >100% and >100% in the validation set; for the average neutrino energy, the relative errors in the training set were 27.82% and 35.33% for (1/T_1/2)^1/5 and 1/3Q feature group and 76.32% and 37.76% in the validation set.
Considering the accuracy comparison of the three groups, 1/3Q feature group were selected to predict the average energy data of nuclei in the fission product region (mass numbers ranging from 66 to 172) for which miss reliable experimental data. As a result, we supplemented the average energy data with predicted values for 291 nuclei. Besides, a comparison were performed between the calculated data and the evaluated experimental data through the nuclide chart. It is found that the neural network provides good prediction of the experimental data for the average β and neutrino energies which exhibit relatively strong regularity. However, it shows significant deviations in predictions for average γ energy (relative error in the training set was 76.9%). Large deviation also emerges in the odd-odd nuclei and nuclei near magic numbers. This study confirms that incorporating empirical relationships and physical principles can effectively enhance the performance of the neural network, and simultaneously reveals the relationship between data regularity and model generalization capability. These findings provide a basis for future integration of physical mechanisms to optimize machine learning models.