Overview
This research investigates the applicability of ab initio symmetries, specifically Wigner's SU(4) and Elliott's SU(3), in governing nuclear binding across the entire nuclear chart. The study employs interpretable neural networks (NNs) to construct mass models that incorporate these symmetries. The models were trained on the AME2016 dataset and validated using nuclei new to AME2020. The objective extends beyond high-precision prediction to gaining physical insight through symmetry-based modeling.
Research Context
Ab initio modeling has established Wigner's SU(4) and Elliott's SU(3) as dominant symmetries influencing the nuclear force in light and intermediate-mass nuclei. The research explores whether these established symmetries maintain their governing role in nuclear binding properties across the full spectrum of the nuclear chart. The approach focuses on leveraging these symmetries for physical insight, rather than solely for predictive accuracy.
Approach
The researchers constructed three neural-network mass models using the SU(3) and SU(4) Casimir operators as foundational elements:
- Feature-Informed NN (FINN): Designed for point predictions of nuclear masses.
- Gaussian-Informed NN (GINN): Extends FINN by incorporating uncertainty quantification into its predictions.
- Wigner-Informed NN (WINN): Configured as a mass formula that utilizes the SU(3) and SU(4) Casimirs as an operator basis.
These models were trained using data from the AME2016 atomic mass evaluation. Validation was conducted on nuclei that were newly introduced in AME2020, ensuring the evaluation of their predictive and interpretive capabilities on unseen data.
Findings
- The inclusion of SU(4) operators alone reduced the root-mean-square error (RMSE) by nearly half on both training and test datasets when compared to a liquid-drop baseline. For extrapolation, the RMSE was reduced by approximately one-fifth. This indicates that Wigner's symmetry provides predictive information beyond what can be explained by bulk nuclear properties.
- Despite its compact form, the WINN model achieved a validation RMSE of 0.430 MeV. This RMSE is competitive with state-of-the-art mass models. The researchers interpret this performance as evidence that the symmetry basis within WINN captures significant underlying physics.
- WINN revealed an enhancement of the quadratic SU(4) Casimir operator near the neutron dripline. This enhancement is interpreted as a signal of the restoration of Wigner's symmetry in this region.
- The model also indicated an unexpected gain of the quartic operator in the superheavy region of the nuclear chart.
These findings collectively suggest that emergent symmetries, specifically Wigner's SU(4) and Elliott's SU(3), function as a governing principle across the entire nuclear chart, extending their role from localized order within individual nuclei.
Why This Matters
This research elevates emergent symmetries from internal features of nuclei to a comprehensive principle governing the nuclear chart. The development of interpretable neural networks that incorporate established physical symmetries offers a methodology for gaining physical insight into fundamental nuclear properties rather than solely focusing on predictive accuracy.