Bayesian evaluation of photofission product yields of Th isotopic chains

Exploring the Systematic Evolution of Photofission in Thorium Isotopes

A joint research team from Henan Normal University, and the Shanghai Advanced Research Institute has made progress in predicting fragment yields from photofission reactions of thorium isotopes. Photofission is a process where high-energy photons interact with a heavy atomic nucleus, causing it to split into two or more lighter fragments. Since the interaction between the photon and the nucleus is purely electromagnetic, this process provides a unique "clean probe" for studying nuclear structure and reaction mechanisms. However, relevant experimental fission data are often incomplete and subject to large uncertainties.

From Theoretical Models to Observable Yields: The Introduction of Bayesian Neural Networks

To overcome the limitations of traditional theoretical methods in describing photofission fragment yields, the research team systematically applied Bayesian Neural Network (BNN) technology to thorium photofission reactions for the first time. BNNs assign prior probability distributions to model parameters and update them using observed data via Bayes' theorem. This approach effectively avoids overfitting, quantifies predictive uncertainty, and captures complex non-linear relationships inherent in the data.

The team developed two independent BNN models: the BNN-CY model to predict the charge yields of photofission fragments for thorium isotopes (²¹⁶⁻²³²Th), and the BNN-MY model to predict the mass yields for ²³²Th at various incident gamma-ray energies.

Unveiling Nuclear Fission Mechanisms with Advanced Techniques

The input parameters for the BNN-CY model include the charge number of the fission fragment, the proton and neutron numbers of the fissioning nucleus, the excitation energy of the compound nucleus, and a parameter (δ) representing the odd-even effect. By incorporating this odd-even parameter, the model successfully reproduces the characteristic "odd-even staggering" phenomenon, where fragments with an even number of protons are produced with significantly enhanced yields.

The model predictions are in excellent agreement with experimental data from the GSI Helmholtz Centre for Heavy Ion Research (the Schmidt team, 2000, and the Chatillon team, 2019), successfully revealing the systematic evolution of the fission mechanism in thorium isotopes as a function of neutron number:

1. For neutron-deficient, light thorium isotopes (e.g., ²¹⁷Th), symmetric fission dominates, and the charge yield distribution exhibits a single peak.
2. As the neutron number increases, intermediate-mass thorium isotopes display a triple-peak structure, indicating the coexistence of symmetric and asymmetric fission modes.
3. For heavy thorium isotopes (e.g., ²³²Th), asymmetric fission becomes dominant, and the yield distribution shows the characteristic double-peak structure.

The research team further noted: "This systematic evolution clearly demonstrates the strong dependence of the fission mechanism on the neutron number in the thorium isotopic chain."

Implications for Science and Technology

The study analyzed the excitation functions for fission fragments ⁹¹Kr (located in the light-fragment peak region) and ¹⁴⁰Xe (in the heavy-fragment peak region), revealing an evolution where yields first increase and then decrease with energy. Furthermore, predictions for untrained energy points (7.64 MeV and 17.5 MeV) agreed well with independent experimental data, validating the model's extrapolation capabilities.

Advancing Nuclear Physics Research

"Bayesian Neural Network models provide a powerful and reliable tool for predicting photofission fragment yields," stated the principal investigator. "They successfully reveal the evolution of fission mechanisms and the associated odd-even effects, offering critical theoretical support for nuclear data library development, advanced reactor design, and rare isotope production applications."

Currently, several large-scale scientific facilities worldwide are conducting photofission research, including the High-Intensity Gamma-ray Source (HIγS) at Duke University (USA), GSI (Germany), and the Extreme Light Infrastructure – Nuclear Physics (ELI-NP) facility. The research team notes that the Shanghai Laser Electron Gamma Source (SLEGS) at the Shanghai Synchrotron Radiation Facility can provide quasi-monochromatic gamma-ray beams from 0.25 MeV to 21.7 MeV, offering a promising platform for future experimental validation of the theoretical predictions from this study.

The complete study is via by DOI: https://doi.org/10.1007/s41365-026-01951-0