Predictions for the ($n,2n$) reaction cross section based on a Bayesian neural network approach

Nuclear $(n,2n)$ reaction cross sections are studied based on the Bayesian neural network (BNN) approach. Three physical quantities besides the proton and neutron numbers are proposed to improve the performance of the BNN approach. These three physical quantities are the incident neutron energy with respect to the reaction threshold, the physical quantity related to the odd-even effect, and the theoretical $(n,2n)$ reaction cross section, and they are included as the inputs to the neural network. The BNN approach has better performance in the description of the $(n,2n)$ reaction cross sections than the theoretical library TENDL-2021 calculated by the talys code based on the Hauser-Feshbach statistical model, especially for heavy nuclei. The root-mean-square deviation of the BNN approach with respect to the evaluation data is reduced to 0.10 barns compared to 0.25 barns of TENDL-2021. The extrapolation ability of the BNN approach is verified with the $(n,2n)$ cross section data that are not used to train the neural network. Furthermore, it is found that the BNN approach still well describes the trend of the $(n,2n)$ cross sections with the incident neutron energy predicted by TENDL-2021 even when extrapolated to the unknown region.

Figure 1

The $(n,2n)$ reaction cross sections of Te isotopes from ENDF/B-VIII.0 [18] as a function of (a) $E$ and (b) $\mathrm{\Delta }E$.

Figure 2

The integral $S_{\sigma }$ of the cross sections with respect to $E$ for Ag and Sn isotopes.

Figure 3

The rms deviations ${\sigma }_{\mathrm{rms}}$(Cross Section) of different BNN predictions with respect to the evaluation data [18] of $(n,2n)$ reaction cross sections for the total set, learning set, validation set, and testing set. The corresponding ${\sigma }_{\mathrm{rms}}$(Cross Section) of TENDL-2021 [66] are shown for comparison.

Figure 4

Scatter distribution of the $(n,2n)$ reaction cross sections predicted by the BNN-I5 approach and TENDL-2021 [66] as a function of the evaluation data.

Figure 5

The rms deviations ${\sigma }_{\mathrm{rms}}$(Cross Section) of cross section predictions by BNN-I5 and TENDL-2021 [66] with respect to the evaluation data in different nuclear regions. The dashed line shows the corresponding rms deviations of the total set.

Figure 6

The $(n,2n)$ reaction cross sections predicted by the BNN-I5 approach for ${}^{61}\mathrm{Ni}, {}^{88}\mathrm{Sr}, {}^{100}\mathrm{Mo}, {}^{135}\mathrm{I}, {}^{145}\mathrm{Pm}$, and ${}^{184}\mathrm{Os}$. The evaluation data in the learning and validation sets are indicated by the filled squares and open squares, respectively. The BNN-I5 predictions and their uncertainties are shown as the solid lines and green hatched regions. The theoretical results from TENDL-2021 [66] are shown by the dotted lines for comparison.

Figure 7

Same as Fig. 6, but for ${}^{115}\mathrm{Ag}, {}^{139}\mathrm{Ba}, {}^{178}\mathrm{Hf}$, and ${}^{248}\mathrm{Cm}$.

Figure 8

Comparison of the $(n,2n)$ reaction cross sections from BNN-I5 predictions and TENDL-2021 [66] for various nuclei.

Figure 9

Comparison of the $(n,2n)$ reaction cross sections from BNN-I5 predictions with the original experimental data in Refs. [67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91] for ${}^{66}\mathrm{Zn}, {}^{144}\mathrm{Sm}$, and ${}^{192}\mathrm{Pt}$.

Figure 10

The rms deviations between the $(n,2n)$ reaction cross sections predicted by the BNN-I5 approach and evaluation data for various nuclei.