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Equation of state and Fermi liquid properties of dense matter based on chiral effective field theory interactions

F. Alp1,2,3,*, Y. Dietz1,2,†, K. Hebeler1,2,3,‡, and A. Schwenk1,2,3,§

  • *Contact author: faruk_musa.alp@tu-darmstadt.de
  • †Contact author: yannick.dietz@tu-darmstadt.de
  • ‡Contact author: kai.hebeler@physik.tu-darmstadt.de
  • §Contact author: schwenk@physik.tu-darmstadt.de

Phys. Rev. C 112, 055802 – Published 19 November, 2025

DOI: https://doi.org/10.1103/ls3l-dn1y

Abstract

We present results for the equation of state of symmetric nuclear matter and pure neutron matter obtained in many-body-perturbation theory (MBPT) up to third order, based on various chiral two- and three-nucleon interactions used in ab initio calculations of nuclei. We extract equation of state properties, such as the incompressibility and the symmetry energy, and discuss estimates of the theoretical uncertainties due to neglected higher-order contributions in the MBPT expansion as well as the chiral effective field theory expansion. In addition, we discuss the Fermi liquid approach to nuclear matter. We calculate all two- and three-nucleon contributions to the quasiparticle interaction up to second order in MBPT and present results for the Landau parameters, effective mass, and speed of sound for pure neutron matter.

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References (63)

  1. K. Hebeler and A. Schwenk, Chiral three-nucleon forces and neutron matter, Phys. Rev. C 82, 014314 (2010).
  2. I. Tews, T. Krüger, K. Hebeler, and A. Schwenk, Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory, Phys. Rev. Lett. 110, 032504 (2013).
  3. J. W. Holt, N. Kaiser, and W. Weise, Nuclear chiral dynamics and thermodynamics, Prog. Part. Nucl. Phys. 73, 35 (2013).
  4. A. Carbone, A. Polls, and A. Rios, Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach, Phys. Rev. C 88, 044302 (2013).
  5. 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).
  6. 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).
  7. C. Wellenhofer, J. W. Holt, N. Kaiser, and W. Weise, Nuclear thermodynamics from chiral low-momentum interactions, Phys. Rev. C 89, 064009 (2014).
  8. C. Wellenhofer, J. W. Holt, and N. Kaiser, Thermodynamics of isospin-asymmetric nuclear matter from chiral effective field theory, Phys. Rev. C 92, 015801 (2015).
  9. J. E. Lynn, I. Tews, J. Carlson, S. Gandolfi, A. Gezerlis, K. E. Schmidt, and A. Schwenk, Chiral three-nucleon interactions in light nuclei, Neutron-α scattering, and neutron matter, Phys. Rev. Lett. 116, 062501 (2016).
  10. C. Drischler, K. Hebeler, and A. Schwenk, Asymmetric nuclear matter based on chiral two- and three-nucleon interactions, Phys. Rev. C 93, 054314 (2016).
  11. A. Ekström, G. Hagen, T. D. Morris, T. Papenbrock, and P. D. Schwartz, Δ isobars and nuclear saturation, Phys. Rev. C 97, 024332 (2018).
  12. 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).
  13. A. Carbone and A. Schwenk, Ab initio constraints on thermal effects of the nuclear equation of state, Phys. Rev. C 100, 025805 (2019).
  14. B.-N. Lu, N. Li, S. Elhatisari, D. Lee, J. E. Drut, T. A. Lähde, E. Epelbaum, and Ulf-G. Meißner, Ab initio nuclear thermodynamics, Phys. Rev. Lett. 125, 192502 (2020).
  15. J. Keller, C. Wellenhofer, K. Hebeler, and A. Schwenk, Neutron matter at finite temperature based on chiral effective field theory interactions, Phys. Rev. C 103, 055806 (2021).
  16. J. Keller, K. Hebeler, and A. Schwenk, Nuclear equation of state for arbitrary proton fraction and temperature based on chiral effective field theory and a Gaussian process emulator, Phys. Rev. Lett. 130, 072701 (2023).
  17. F. Marino, W. G. Jiang, and S. J. Novario, Diagrammatic ab initio methods for infinite nuclear matter with modern chiral interactions, Phys. Rev. C 110, 054322 (2024).
  18. E. Epelbaum, H.-W. Hammer, and Ulf-G. Meißner, Modern theory of nuclear forces, Rev. Mod. Phys. 81, 1773 (2009).
  19. R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011).
  20. H.-W. Hammer, S. König, and U. van Kolck, Nuclear effective field theory: Status and perspectives, Rev. Mod. Phys. 92, 025004 (2020).
  21. K. Hebeler, J. D. Holt, J. Menéndez, and A. Schwenk, Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter, Annu. Rev. Nucl. Part. Sci. 65, 457 (2015).
  22. J. E. Lynn, I. Tews, S. Gandolfi, and A. Lovato, Quantum Monte Carlo methods in nuclear physics: Recent advances, Annu. Rev. Nucl. Part. Sci. 69, 279 (2019).
  23. C. Drischler, J. W. Holt, and C. Wellenhofer, Chiral effective field theory and the high-density nuclear equation of state, Annu. Rev. Nucl. Part. Sci. 71, 403 (2021).
  24. H. Yasin, S. Schäfer, A. Arcones, and A. Schwenk, Equation of state effects in core-collapse supernovae, Phys. Rev. Lett. 124, 092701 (2020).
  25. A. S. Schneider, L. F. Roberts, C. D. Ott, and E. O'Connor, Equation of state effects in the core collapse of a 20M⊙ star, Phys. Rev. C 100, 055802 (2019).
  26. J. M. Lattimer, Neutron stars and the nuclear matter equation of state, Annu. Rev. Nucl. Part. Sci. 71, 433 (2021).
  27. M. Jacobi, F. M. Guercilena, S. Huth, G. Ricigliano, A. Arcones, and A. Schwenk, Effects of nuclear matter properties in neutron star mergers, Mon. Not. R. Astron. Soc. 527, 8812 (2023).
  28. L. D. Landau, The theory of a Fermi liquid, Sov. Phys. JETP 3, 920 (1956).
  29. L. D. Landau, Oscillations in a Fermi liquid, Sov. Phys. JETP 5, 101 (1957).
  30. L. D. Landau, On the theory of the Fermi liquid, Sov. Phys. JETP 8, 70 (1959).
  31. G. Baym and C. Pethick, Landau Fermi-Liquid Theory: Concepts and Applications (John Wiley & Sons, New York, 2008).
  32. B. Friman, K. Hebeler, and A. Schwenk, Renormalization group and Fermi liquid theory for many-nucleon systems, in Renormalization Group and Effective Field Theory Approaches to Many-Body Systems, Lecture Notes in Physics (Springer, Berlin, 2012), Vol. 852, p. 245.
  33. A. Schwenk, B. Friman, and G. E. Brown, Renormalization group approach to neutron matter: Quasiparticle interactions, superfluid gaps and the equation of state, Nucl. Phys. A 713, 191 (2003).
  34. A. Schwenk and B. Friman, Polarization contributions to the spin dependence of the effective interaction in neutron matter, Phys. Rev. Lett. 92, 082501 (2004).
  35. J. W. Holt, N. Kaiser, and W. Weise, Second-order quasiparticle interaction in nuclear matter with chiral two-nucleon interactions, Nucl. Phys. A 870-871, 1 (2011).
  36. J. W. Holt, N. Kaiser, and W. Weise, Chiral Fermi liquid approach to neutron matter, Phys. Rev. C 87, 014338 (2013).
  37. J. Simonis, S. R. Stroberg, K. Hebeler, J. D. Holt, and A. Schwenk, Saturation with chiral interactions and consequences for finite nuclei, Phys. Rev. C 96, 014303 (2017).
  38. 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).
  39. P. Arthuis, K. Hebeler, and A. Schwenk, Neutron-rich nuclei and neutron skins from chiral low-resolution interactions, arXiv:2401.06675.
  40. 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).
  41. S. R. Stroberg, J. D. Holt, A. Schwenk, and J. Simonis, Ab initio limits of atomic nuclei, Phys. Rev. Lett. 126, 022501 (2021).
  42. K. Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter, Phys. Rep. 890, 1 (2021).
  43. T. Miyagi, S. R. Stroberg, P. Navrátil, K. Hebeler, and J. D. Holt, Converged ab initio calculations of heavy nuclei, Phys. Rev. C 105, 014302 (2022).
  44. K. Hebeler, V. Durant, J. Hoppe, M. Heinz, A. Schwenk, J. Simonis, and A. Tichai, Normal ordering of three-nucleon interactions for ab initio calculations of heavy nuclei, Phys. Rev. C 107, 024310 (2023).
  45. A. Tichai, P. Demol, and T. Duguet, Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory, Phys. Lett. B 851, 138571 (2024).
  46. J. A. Melendez, S. Wesolowski, and R. J. Furnstahl, Bayesian truncation errors in chiral effective field theory: Nucleon-nucleon observables, Phys. Rev. C 96, 024003 (2017).
  47. J. A. Melendez, R. J. Furnstahl, D. R. Phillips, M. T. Pratola, and S. Wesolowski, Quantifying correlated truncation errors in effective field theory, Phys. Rev. C 100, 044001 (2019).
  48. 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).
  49. 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).
  50. T. Hahn, CUBA—a library for multidimensional numerical integration, Comput. Phys. Commun. 168, 78 (2005).
  51. T. Hahn, Concurrent Cuba, Comput. Phys. Commun. 207, 341 (2016).
  52. D. R. Entem, R. Machleidt, and Y. Nosyk, High-quality two-nucleon potentials up to fifth order of the chiral expansion, Phys. Rev. C 96, 024004 (2017).
  53. 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).
  54. D. R. Entem and R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory, Phys. Rev. C 68, 041001(R) (2003).
  55. B. D. Carlsson, A. Ekström, C. Forssén, D. F. Strömberg, G. R. Jansen, O. Lilja, M. Lindby, B. A. Mattsson, and K. A. Wendt, Uncertainty analysis and order-by-order optimization of chiral nuclear interactions, Phys. Rev. X 6, 011019 (2016).
  56. M. J. H. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).
  57. I. Tews, J. M. Lattimer, A. Ohnishi, and E. E. Kolomeitsev, Symmetry parameter constraints from a lower bound on neutron-matter energy, Astrophys. J. 848, 105 (2017).
  58. M. Dutra, O. Lourenco, J. S. Sa Martins, A. Delfino, J. R. Stone, and P. D. Stevenson, Skyrme interaction and nuclear matter constraints, Phys. Rev. C 85, 035201 (2012).
  59. R. Essick, I. Tews, P. Landry, and A. Schwenk, Astrophysical constraints on the symmetry energy and the neutron skin of Pb208 with minimal modeling assumptions, Phys. Rev. Lett. 127, 192701 (2021).
  60. S. Huth, C. Wellenhofer, and A. Schwenk, New equations of state constrained by nuclear physics, observations, and QCD calculations of high-density nuclear matter, Phys. Rev. C 103, 025803 (2021).
  61. Y. Lim and A. Schwenk, Symmetry energy and neutron star properties constrained by chiral effective field theory calculations, Phys. Rev. C 109, 035801 (2024).
  62. I. Ia. Pomeranchuk, On the stability of a Fermi liquid, Sov. Phys. JETP 8, 361 (1959).
  63. F. Alp, Y. Dietz, K. Hebeler, and A. Schwenk, Data: Equation of state and Fermi liquid properties of dense matter based on chiral EFT interactions [Data set], Zenodo (2025), https://doi.org/10.5281/zenodo.17377267.

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