Statistical learning of nuclear masses: Implicit shell gaps and the breakdown of minimal models for light nuclei

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We present a minimalist Mixture Density Network (MDN) for nuclear mass predictions using only 12 bulk‑inspired features, excluding explicit shell corrections, Wigner terms, and deformation parameters. Trained on AME2016, the model achieves 0.38 MeV RMS for nuclei with A ≥ 60—surpassing FRDM2012 on the same subset—while failing systematically for A < 60 (RMS ≈ 2 MeV). This sharp transition identifies A ≈ 60 as the boundary between statistically learnable mean‑field behavior and quantum‑correlation‑dominated regimes. Major shell closures emerge implicitly from the data, whereas light N = Z nuclei reveal missing Wigner energy and clustering effects. The work provides a transparent, calibrated baseline for hybrid physics–machine‑learning approaches and defines the domain of validity for physics‑minimal models.

This Version 2 of “Statistical learning of nuclear masses: Implicit shell gaps and the breakdown of minimal models for light nuclei” presents a refined and extended analysis of the limits of purely statistical learning in nuclear mass prediction. The study employs a deliberately minimal Mixture Density Network (MDN) using only 12 bulk–valence features, excluding all explicit shell-gap energies, Wigner terms, pairing gaps, and deformation parameters.

The updated manuscript strengthens the discussion of existing machine‑learning approaches to nuclear masses and clarifies the physical interpretation of the model’s successes and failures. The central empirical result is a sharp transition at \(A \approx 60\): for heavy nuclei, the minimalist MDN achieves an RMS of 0.38 MeV—surpassing FRDM2012 on the same subset—while for light nuclei the error increases fivefold. This degradation is shown to be physically meaningful, directly reflecting irreducible contributions from Wigner energy, \(\alpha\)-clustering, and the breakdown of mean‑field behavior.

Version 2 includes improved narrative structure, expanded related‑work coverage, updated figures, and a clearer articulation of the model’s domain of validity. The work provides a transparent, calibrated baseline for future hybrid physics–machine‑learning approaches and a data‑driven map of the limits of physics‑minimal models.