- Physical Review Journals
All JournalsPhysics Magazine

Physical Review C

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Nuclear-matter saturation and symmetry energy within Δ-full chiral effective field theory

W. G. Jiang1,2, C. Forssén1, T. Djärv1,3, and G. Hagen3,4

PDF

Phys. Rev. C 109, L061302 – Published 12 June, 2024

DOI: https://doi.org/10.1103/PhysRevC.109.L061302

Abstract

Nuclear saturation and the symmetry energy are key properties of low-energy nuclear physics that depend on fine details of the nuclear interaction. The equation of state around saturation is also an important anchor for extrapolations to higher densities and studies of neutron stars. Here we develop a unified statistical framework that uses realistic nuclear forces to link the theoretical modeling of finite nuclei and infinite nuclear matter. We construct fast and accurate emulators for nuclear-matter observables and employ an iterative history-matching approach to explore and reduce the enormous parameter domain of Δ-full chiral interactions. We perform rigorous uncertainty quantification and find that model calibration including O16 observables gives saturation predictions that are more precise than those that only use few-body data.

View figure in article

Physics Subject Headings (PhySH)

See Also

Emulating ab initio computations of infinite nucleonic matter

W. G. Jiang, C. Forssén, T. Djärv, and G. Hagen
Phys. Rev. C 109, 064314 (2024)

Article Text

Supplemental Material

References (77)

  1. R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011).
  2. K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Improved nuclear matter calculations from chiral low-momentum interactions, Phys. Rev. C 83, 031301(R) (2011).
  3. A. Ekström, G. Baardsen, C. Forssén, G. Hagen, M. Hjorth-Jensen, G. R. Jansen, R. Machleidt, W. Nazarewicz, T. Papenbrock, J. Sarich, and S. M. Wild, Optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order, Phys. Rev. Lett. 110, 192502 (2013).
  4. A. Ekström, G. R. Jansen, K. A. Wendt, G. Hagen, T. Papenbrock, B. D. Carlsson, C. Forssén, M. Hjorth-Jensen, P. Navrátil, and W. Nazarewicz, Accurate nuclear radii and binding energies from a chiral interaction, Phys. Rev. C 91, 051301(R) (2015).
  5. W. G. Jiang, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Accurate bulk properties of nuclei from A=2 to ∞ from potentials with Δ isobars, Phys. Rev. C 102, 054301 (2020).
  6. V. Somà, P. Navrátil, F. Raimondi, C. Barbieri, and T. Duguet, Novel chiral Hamiltonian and observables in light and medium-mass nuclei, Phys. Rev. C 101, 014318 (2020).
  7. B. S. Hu, W. G. Jiang, T. Miyagi, Z. H. Sun, A. Ekström, C. Forssén, G. Hagen, J. D. Holt, T. Papenbrock, S. R. Stroberg, and I. Vernon, Ab initio predictions link the neutron skin of Pb208 to nuclear forces, Nat. Phys. 18, 1196 (2022).
  8. P. Maris et al. (LENPIC Collaboration), Nuclear properties with semilocal momentum-space regularized chiral interactions beyond NLO2, Phys. Rev. C 106, 064002 (2022).
  9. S. Elhatisari, L. Bovermann, E. Epelbaum, D. Frame, F. Hildenbrand, H. Krebs, T. A. Lähde, D. Lee, N. Li, B.-N. Lu, M. Kim, Y. Kim, Y. Ma, U.-G. Meißner, G. Rupak, S. Shen, Y.-H. Song, and G. Stellin, Wavefunction matching for solving quantum many-body problems, Nature 630, 59 (2024).
  10. T. Dietrich, M. W. Coughlin, P. T. H. Pang, M. Bulla, J. Heinzel, L. Issa, I. Tews, and S. Antier, Multimessenger constraints on the neutron-star equation of state and the Hubble constant, Science 370, 1450 (2020).
  11. S. Huth et al., Constraining neutron-star matter with microscopic and macroscopic collisions, Nature (London) 606, 276 (2022).
  12. J. M. Lattimer, Constraints on nuclear symmetry energy parameters, Particles 6, 30 (2023).
  13. E. Khan, J. Margueron, and I. Vidaña, Constraining the nuclear equation of state at subsaturation densities, Phys. Rev. Lett. 109, 092501 (2012).
  14. G. Hagen, A. Ekström, C. Forssén, G. R. Jansen, W. Nazarewicz, T. Papenbrock, K. A. Wendt, S. Bacca, N. Barnea, B. Carlsson, C. Drischler, K. Hebeler, M. Hjorth-Jensen, M. Miorelli, G. Orlandini, A. Schwenk, and J. Simonis, Neutron and weak-charge distributions of the Ca48 nucleus, Nat. Phys. 12, 186 (2016).
  15. A. Kievsky, M. Viviani, D. Logoteta, I. Bombaci, and L. Girlanda, Correlations imposed by the unitary limit between few-nucleon systems, nuclear matter and neutron stars, Phys. Rev. Lett. 121, 072701 (2018).
  16. C. Drischler, K. Hebeler, and A. Schwenk, Chiral interactions up to next-to-next-to-next-to-leading order and nuclear saturation, Phys. Rev. Lett. 122, 042501 (2019).
  17. P. G. Reinhard and W. Nazarewicz, Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach, Phys. Rev. C 93, 051303(R) (2016).
  18. Z. Carson, A. W. Steiner, and K. Yagi, Constraining nuclear matter parameters with GW170817, Phys. Rev. D 99, 043010 (2019).
  19. C. Drischler, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties, Phys. Rev. Lett. 125, 202702 (2020).
  20. C. Drischler, J. A. Melendez, R. J. Furnstahl, and D. R. Phillips, Quantifying uncertainties and correlations in the nuclear-matter equation of state, Phys. Rev. C 102, 054315 (2020).
  21. U. von Toussaint, Bayesian inference in physics, Rev. Mod. Phys. 83, 943 (2011).
  22. I. Vernon, M. Goldstein, and R. G. Bower, Galaxy formation: A Bayesian uncertainty analysis, Bayesian Anal. 5, 619 (2010).
  23. I. Vernon, M. Goldstein, and R. Bower, Galaxy formation: Bayesian history matching for the observable universe, Stat. Sci. 29, 81 (2014).
  24. I. Vernon, J. Liu, M. Goldstein, J. Rowe, J. Topping, and K. Lindsey, Bayesian uncertainty analysis for complex systems biology models: Emulation, global parameter searches and evaluation of gene functions, BMC Syst. Biol. 12, 1 (2018).
  25. A. Ekström and G. Hagen, Global sensitivity analysis of bulk properties of an atomic nucleus, Phys. Rev. Lett. 123, 252501 (2019).
  26. S. König, A. Ekström, K. Hebeler, D. Lee, and A. Schwenk, Eigenvector continuation as an efficient and accurate emulator for uncertainty quantification, Phys. Lett. B 810, 135814 (2020).
  27. S. Wesolowski, I. Svensson, A. Ekström, C. Forssén, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, Rigorous constraints on three-nucleon forces in chiral effective field theory from fast and accurate calculations of few-body observables, Phys. Rev. C 104, 064001 (2021).
  28. T. Djärv, A. Ekström, C. Forssén, and H. T. Johansson, Bayesian predictions for A=6 nuclei using eigenvector continuation emulators, Phys. Rev. C 105, 014005 (2022).
  29. G. Baardsen, A. Ekström, G. Hagen, and M. Hjorth-Jensen, Coupled-cluster studies of infinite nuclear matter, Phys. Rev. C 88, 054312 (2013).
  30. G. Hagen, T. Papenbrock, A. Ekström, K. A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, and C. J. Horowitz, Coupled-cluster calculations of nucleonic matter, Phys. Rev. C 89, 014319 (2014).
  31. U. van Kolck, Few-nucleon forces from chiral Lagrangians, Phys. Rev. C 49, 2932 (1994).
  32. T. R. Hemmert, B. R. Holstein, and J. Kambor, Heavy baryon chiral perturbation theory with light deltas, J. Phys. G 24, 1831 (1998).
  33. N. Kaiser, S. Gerstendörfer, and W. Weise, Peripheral NN-scattering: Role of delta-excitation, correlated two-pion and vector meson exchange, Nucl. Phys. A 637, 395 (1998).
  34. H. Krebs, E. Epelbaum, and U. G. Meißner, Nuclear forces with Δ excitations up to next-to-next-to-leading order, part I: Peripheral nucleon-nucleon waves, Eur. Phys. J. A 32, 127 (2007).
  35. E. Epelbaum, H. Krebs, and U.-G. Meißner, Δ-excitations and the three-nucleon force, Nucl. Phys. A 806, 65 (2008).
  36. A. Ekström, G. Hagen, T. D. Morris, T. Papenbrock, and P. D. Schwartz, Δ isobars and nuclear saturation, Phys. Rev. C 97, 024332 (2018).
  37. W. G. Jiang, C. Forssén, T. Djärv, and G. Hagen, companion paper, Emulating ab initio computations of infinite nucleonic matter, Phys. Rev. C 109, 064314 (2024).
  38. I. Shavitt and R. J. Bartlett, Many-Body Methods in Chemistry and Physics (Cambridge University Press, Cambridge, 2009).
  39. A. F. M. Smith and A. E. Gelfand, Bayesian statistics without tears: A sampling-resampling perspective, Am. Stat. 46, 84 (1992).
  40. W. Jiang and C. Forssén, Bayesian probability updates using sampling/importance resampling: Applications in nuclear theory, Front. Phys. 10, 1058809 (2022).
  41. J. A. Melendez, C. Drischler, R. J. Furnstahl, A. J. Garcia, and X. Zhang, Model reduction methods for nuclear emulators, J. Phys. G 49, 102001 (2022).
  42. D. Frame, R. He, I. Ipsen, D. Lee, D. Lee, and E. Rrapaj, Eigenvector continuation with subspace learning, Phys. Rev. Lett. 121, 032501 (2018).
  43. A. Sarkar and D. Lee, Convergence of eigenvector continuation, Phys. Rev. Lett. 126, 032501 (2021).
  44. J. A. Melendez, C. Drischler, A. J. Garcia, R. J. Furnstahl, and X. Zhang, Fast & accurate emulation of two-body scattering observables without wave functions, Phys. Lett. B 821, 136608 (2021).
  45. X. Zhang and R. J. Furnstahl, Fast emulation of quantum three-body scattering, Phys. Rev. C 105, 064004 (2022).
  46. P. Demol, T. Duguet, A. Ekström, M. Frosini, K. Hebeler, S. König, D. Lee, A. Schwenk, V. Somà, and A. Tichai, Improved many-body expansions from eigenvector continuation, Phys. Rev. C 101, 041302(R) (2020).
  47. T. Djärv, JupiterNCSM: A Pantheon of Nuclear Physics, Ph.D. thesis, Chalmers University of Technology, 2021.
  48. F. Coester, Bound states of a many-particle system, Nucl. Phys. 7, 421 (1958).
  49. F. Coester and H. Kümmel, Short-range correlations in nuclear wave functions, Nucl. Phys. 17, 477 (1960).
  50. J. Čížek, On the correlation problem in atomic and molecular systems. Calculation of wavefunction components in Ursell-type expansion using quantum-field theoretical methods, J. Chem. Phys. 45, 4256 (1966).
  51. H. Kümmel, K. H. Lührmann, and J. G. Zabolitzky, Many-fermion theory in expS- (or coupled cluster) form, Phys. Rep. 36, 1 (1978).
  52. R. F. Bishop, An overview of coupled cluster theory and its applications in physics, Theor. Chim. Acta 80, 95 (1991).
  53. C. Zeng, D. J. J. Farnell, and R. F. Bishop, An efficient implementation of high-order coupled-cluster techniques applied to quantum magnets, J. Stat. Phys. 90, 327 (1998).
  54. B. Mihaila and J. H. Heisenberg, Microscopic calculation of the inclusive electron scattering structure function in O16, Phys. Rev. Lett. 84, 1403 (2000).
  55. D. J. Dean and M. Hjorth-Jensen, Coupled-cluster approach to nuclear physics, Phys. Rev. C 69, 054320 (2004).
  56. R. J. Bartlett and M. Musiał, Coupled-cluster theory in quantum chemistry, Rev. Mod. Phys. 79, 291 (2007).
  57. G. Hagen, T. Papenbrock, D. J. Dean, and M. Hjorth-Jensen, Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions, Phys. Rev. C 82, 034330 (2010).
  58. S. Binder, P. Piecuch, A. Calci, J. Langhammer, P. Navrátil, and R. Roth, Extension of coupled-cluster theory with a noniterative treatment of connected triply excited clusters to three-body Hamiltonians, Phys. Rev. C 88, 054319 (2013).
  59. G. Hagen, T. Papenbrock, M. Hjorth-Jensen, and D. J. Dean, Coupled-cluster computations of atomic nuclei, Rep. Prog. Phys. 77, 096302 (2014).
  60. S. Gandolfi, A. Yu. Illarionov, K. E. Schmidt, F. Pederiva, and S. Fantoni, Quantum Monte Carlo calculation of the equation of state of neutron matter, Phys. Rev. C 79, 054005 (2009).
  61. G. Teschl, Mathematical methods in quantum mechanics, Vol. 157 (American Mathematical Soc., Providence, 2014).
  62. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (The MIT Press, Cambridge, Massachusetts, 2006).
  63. F. Coester, S. Cohen, B. Day, and C. M. Vincent, Variation in nuclear-matter binding energies with phase-shift-equivalent two-body potentials, Phys. Rev. C 1, 769 (1970).
  64. C. Ducoin, J. Margueron, C. Providência, and I. Vidana, Core-crust transition in neutron stars: Predictivity of density developments, Phys. Rev. C 83, 045810 (2011).
  65. B. M. Santos, M. Dutra, O. Lourenço, and A. Delfino, Correlations between the nuclear matter symmetry energy, its slope, and curvature from a nonrelativistic solvable approach and beyond, Phys. Rev. C 90, 035203 (2014).
  66. L. Coraggio, J. W. Holt, N. Itaco, R. Machleidt, L. E. Marcucci, and F. Sammarruca, Nuclear-matter equation of state with consistent two- and three-body perturbative chiral interactions, Phys. Rev. C 89, 044321 (2014).
  67. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevC.109.L061302 for numerical parameters of a Gaussian approximation to the PPD.
  68. J. M. Lattimer and Y. Lim, Constraining the symmetry parameters of the nuclear interaction, Astrophys. J. 771, 51 (2013).
  69. M. Bender, P.-H. Heenen, and P.-G. Reinhard, Self-consistent mean-field models for nuclear structure, Rev. Mod. Phys. 75, 121 (2003).
  70. S. Shlomo, V. M. Kolomietz, and G. Colo, Deducing the nuclear-matter incompressibility coefficient from data on isoscalar compression modes, Eur. Phys. J. A 30, 23 (2006).
  71. The prior for c1,2,3,4 is the multivariate Gaussian resulting from a Roy-Steiner analysis of πN scattering data [77].
  72. D. R. Tilley, C. M. Cheves, J. L. Godwin, G. M. Hale, H. M. Hofmann, J. H. Kelley, C. G. Sheu, and H. R. Weller, Energy levels of light nuclei A=5,6,7, Nucl. Phys. A 708, 3 (2002).
  73. J. Piekarewicz and M. Centelles, Incompressibility of neutron-rich matter, Phys. Rev. C 79, 054311 (2009).
  74. S. B. S. Miller, A. Ekström, and K. Hebeler, Neutron-deuteron scattering cross sections with chiral NN interactions using wave-packet continuum discretization, Phys. Rev. C 106, 024001 (2022).
  75. S. B. S. Miller, A. Ekström, and C. Forssén, Posterior predictive distributions of neutron-deuteron cross sections, Phys. Rev. C 107, 014002 (2023).
  76. T. Duguet, A. Ekström, R. J. Furnstahl, S. König, and D. Lee, Eigenvector continuation and projection-based emulators, arXiv:2310.19419.
  77. D. Siemens, J. Ruiz de Elvira, E. Epelbaum, M. Hoferichter, H. Krebs, B. Kubis, and U. G. Meißner, Reconciling threshold and subthreshold expansions for pion-nucleon scattering, Phys. Lett. B 770, 27 (2017).

Outline

Information

Phys. Rev. C 109, L061302– Published 12 June, 2024
  • Received 16 January 2023
  • Revised 19 March 2024
  • Accepted 3 June 2024
Crossmark - Check for updates button
Creative Commons Logo

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. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation