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  • Letter
  • Open Access

Constraining nuclear mass models using r-process observables with multiobjective optimization

Mengke Li1,2,*, Matthew Mumpower3,4, Nicole Vassh5, William Samuel Porter2, and Rebecca Surman2

  • *Contact author: mengkel@berkeley.edu
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Phys. Rev. Research 7, L032057 – Published 11 September, 2025

DOI: https://doi.org/10.1103/3x9p-64w7

Abstract

Modeling nuclear masses, particularly for nuclei far from stability, remains a key objective in nuclear physics. One contemporary approach is machine learning (ML), which trains on experimental data, but can suffer large errors when extrapolating toward neutron-rich species. In nature, such masses shape observables for the rapid neutron capture process (r process), which in principle could inform ML models. Here, we introduce a multiobjective optimization approach using the Pareto front algorithm. We show that this technique, capable of identifying models that generate r-process abundances aligning with both solar and stellar data, is a promising method to select ML models with reliable extrapolation power.

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References (35)

  1. C. Aidala, A. Aprahamian, S. Bacca, P. Bedaque, L. Bernstein, J. Carlson, M. Carpenter, K. Chipps, V. Cirigliano, I. Cloët et al., A new era of discovery: The 2023 long-range plan for nuclear science (V.1.2), Tech. Rep. LLNL–TR-857241; 1086788, Lawrence Livermore National Laboratory, Livermore, CA, 2023.
  2. M. Madurga et al., New half-lives of r-process Zn and Ga isotopes measured with electromagnetic separation, Phys. Rev. Lett. 109, 112501 (2012).
  3. G. Lorusso et al., β-decay half-lives of 110 neutron-rich nuclei across the n=82 shell gap: Implications for the mechanism and universality of the astrophysical r process, Phys. Rev. Lett. 114, 192501 (2015).
  4. D. Atanasov et al., Precision mass measurements of Cd131−129 and their impact on stellar nucleosynthesis via the rapid neutron capture process, Phys. Rev. Lett. 115, 232501 (2015).
  5. M. Vilen, J. M. Kelly, A. Kankainen, M. Brodeur, A. Aprahamian, L. Canete, T. Eronen, A. Jokinen, T. Kuta, I. D. Moore, M. R. Mumpower, D. A. Nesterenko, H. Penttilä, I. Pohjalainen, W. S. Porter, S. Rinta-Antila, R. Surman, A. Voss, and J. Äystö, Precision mass measurements on neutron-rich rare-earth isotopes at JYFLTRAP: Reduced neutron pairing and implications for r-process calculations, Phys. Rev. Lett. 120, 262701 (2018).
  6. D. Lunney, J. M. Pearson, and C. Thibault, Recent trends in the determination of nuclear masses, Rev. Mod. Phys. 75, 1021 (2003).
  7. J. Duflo and A. Zuker, Microscopic mass formulas, Phys. Rev. C 52, R23 (1995).
  8. H. Koura, T. Tachibana, M. Uno, and M. Yamada, Nuclidic mass formula on a spherical basis with an improved even-odd term, Prog. Theor. Phys. 113, 305 (2005).
  9. P. Möller, W. D. Myers, H. Sagawa, and S. Yoshida, New finite-range droplet mass model and equation-of-state parameters, Phys. Rev. Lett. 108, 052501 (2012).
  10. S. Goriely, N. Chamel, and J. M. Pearson, Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XVI. Inclusion of self-energy effects in pairing, Phys. Rev. C 93, 034337 (2016).
  11. A. E. Lovell, A. T. Mohan, and P. Talou, Quantifying uncertainties on fission fragment mass yields with mixture density networks, J. Phys. G: Nucl. Part. Phys. 47, 114001 (2020).
  12. Z.-P. Gao, Y.-J. Wang, H.-L. Lü, Q.-F. Li, C.-W. Shen, and L. Liu, Machine learning the nuclear mass, Nucl. Sci. Tech. 32, 109 (2021).
  13. Z. M. Niu and H. Z. Liang, Nuclear mass predictions with machine learning reaching the accuracy required by r-process studies, Phys. Rev. C 106, L021303 (2022).
  14. M. Mumpower, M. Li, T. M. Sprouse, B. S. Meyer, A. E. Lovell, and A. T. Mohan, Bayesian averaging for ground state masses of atomic nuclei in a machine learning approach, Front. Phys. 11, 1198572 (2023).
  15. E. Yüksel, D. Soydaner, and H. Bahtiyar, Nuclear mass predictions using machine learning models, Phys. Rev. C 109, 064322 (2024).
  16. M. Wang, W. Huang, F. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references, Chin. Phys. C 45, 030003 (2021).
  17. M. Li, T. M. Sprouse, B. S. Meyer, and M. R. Mumpower, Atomic masses with machine learning for the astrophysical r-process, Phys. Lett. B 848, 138385 (2024).
  18. P. Ngatchou, A. Zarei, and A. El-Sharkawi, Pareto multi objective optimization, in Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems, Arlington, VA, USA (IEEE, Piscataway, NJ, 2005), pp. 84–91.
  19. C. M. Bishop, Mixture density networks, Tech. Rep. NCRG/94/004, Neural Computing Research Group, Aston University, 1994.
  20. M. R. Mumpower, G. C. McLaughlin, R. Surman, and A. W. Steiner, Reverse engineering nuclear properties from rare earth abundances in the r process, J. Phys. G: Nucl. Part. Phys. 44, 034003 (2017).
  21. N. Vassh, G. C. McLaughlin, M. R. Mumpower, and R. Surman, Markov chain Monte Carlo predictions of neutron-rich lanthanide properties as a probe of r-process dynamics, Astrophys. J. 907, 98 (2021).
  22. T. Kajino, W. Aoki, A. Balantekin, R. Diehl, M. Famiano, and G. Mathews, Current status of r-process nucleosynthesis, Prog. Part. Nucl. Phys. 107, 109 (2019).
  23. M. Li and B. S. Meyer, Dependence of (n,γ)−(γ,n) equilibrium r-process abundances on nuclear physics properties, Phys. Rev. C 106, 035803 (2022).
  24. M. R. Mumpower, T. Kawano, T. M. Sprouse, N. Vassh, E. M. Holmbeck, R. Surman, and P. Möller, β-delayed fission in r-process nucleosynthesis, Astrophys. J. 869, 14 (2018).
  25. M. R. Mumpower, T. Kawano, and P. Möller, Neutron-γ competition for β-delayed neutron emission, Phys. Rev. C 94, 064317 (2016).
  26. P. Möller, M. Mumpower, T. Kawano, and W. Myers, Nuclear properties for astrophysical and radioactive-ion-beam applications (II), At. Data Nucl. Data Tables 125, 1 (2019).
  27. T. Kawano, R. Capote, S. Hilaire, and P. Chau Huu-Tai, Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies, Phys. Rev. C 94, 014612 (2016).
  28. N. Vassh, M. R. Mumpower, G. C. McLaughlin, T. M. Sprouse, and R. Surman, Coproduction of light and heavy r-process elements via fission deposition, Astrophys. J. 896, 28 (2020).
  29. H. Beer, F. Corvi, and P. Mutti, Neutron capture of the bottleneck isotopes Ba138 and Pb208, s-process studies, and the r-process abundance distribution, Astrophys. J. 474, 843 (1997).
  30. I. U. Roederer, J. E. Lawler, E. A. Den Hartog, V. M. Placco, R. Surman, T. C. Beers, R. Ezzeddine, A. Frebel, T. T. Hansen, K. Hattori, E. M. Holmbeck, and C. M. Sakari, The r-process alliance: A nearly complete r-process abundance template derived from ultraviolet spectroscopy of the r-process-enhanced metal-poor star HD 222925, Astrophys. J. Suppl. Ser. 260, 27 (2022).
  31. P. Möller, A. Sierk, T. Ichikawa, and H. Sagawa, Nuclear ground-state masses and deformations: FRDM(2012), At. Data Nucl. Data Tables 109–110, 1 (2016).
  32. S. Goriely, N. Chamel, and J. M. Pearson, Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. XIII. The 2012 atomic mass evaluation and the symmetry coefficient, Phys. Rev. C 88, 024308 (2013).
  33. Y. Zhu, R. T. Wollaeger, N. Vassh, R. Surman, T. M. Sprouse, M. R. Mumpower, P. Möller, G. C. McLaughlin, O. Korobkin, T. Kawano, P. J. Jaffke, E. M. Holmbeck, C. L. Fryer, W. P. Even, A. J. Couture, and J. Barnes, Californium-254 and kilonova light curves, Astrophys. J. Lett. 863, L23 (2018).
  34. O. Just, A. Bauswein, R. A. Pulpillo, S. Goriely, and H.-T. Janka, Comprehensive nucleosynthesis analysis for ejecta of compact binary mergers, Mon. Not. R. Astron. Soc. 448, 541 (2015).
  35. M. Li, M. Mumpower, N. Vassh, and R. Surman, PF_selections_3D (2025), https://osf.io/7v4qa.

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Phys. Rev. Research 7, L032057– Published 11 September, 2025
  • Received 27 April 2025
  • Accepted 24 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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