- 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
  • Open Access

Spinodal instability in nuclear matter with light cluster degrees of freedom

Stefano Burrello1,*, Carmelo Piazza1,2,†, Rui Wang1,‡, and Maria Colonna1,§

  • 1INFN, Laboratori Nazionali del Sud, I-95123 Catania, Italy
  • 2Department of Physics and Astronomy “Ettore Majorana,” University of Catania, Via Santa Sofia 64, I-95123 Catania, Italy

  • *Contact author: burrello@lns.infn.it
  • †Contact author: carmelo.piazza@phd.unict.it
  • ‡Contact author: rui.wang@ct.infn.it
  • §Contact author: colonna@lns.infn.it
PDF

Phys. Rev. C 113, 064617 – Published 18 June, 2026

DOI: https://doi.org/10.1103/7548-pwbt

Abstract

We investigate the thermodynamical stability of low-density isospin-symmetric nuclear matter at finite temperature, explicitly including light clusters as degrees of freedom. Within a generalized mean-field framework, we compute the curvature matrix of the free-energy density and determine the spinodal region, identifying the conditions under which mechanically unstable modes may develop in the presence of clustering. Particular attention is devoted to the formal consequences of introducing an infrared momentum cutoff in the density and current moments, which effectively accounts for Pauli-blocking effects and the associated reduction of low-momentum quasiparticle states in the medium. We show that when the cutoff is density dependent, thermodynamic consistency requires additional contributions to the chemical potentials, and extra terms also appear in the first hydrodynamic moment, influencing both the stability analysis and the location of the spinodal boundary. We further examine the character of the unstable modes and find that a sufficiently stiff density dependence of the cutoff may drive clusters to fluctuate out of phase with nucleons, pushing them toward low-density regions while nucleonic instabilities grow, in contrast with the in-phase pattern obtained when the density derivatives of the cutoff are neglected in the stability analysis. Our results shed new light on the role of light clusters in the phase dynamics of warm, dilute nuclear matter, with implications for heavy-ion collisions and for the physics of neutron-star crusts.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (68)

  1. J. M. Lattimer and M. Prakash, The equation of state of hot, dense matter and neutron stars, Phys. Rep. 621, 127 (2016).
  2. M. Oertel, M. Hempel, T. Klähn, and S. Typel, Equations of state for supernovae and compact stars, Rev. Mod. Phys. 89, 015007 (2017).
  3. G. Burgio, H.-J. Schulze, I. Vidaña, and J.-B. Wei, Neutron stars and the nuclear equation of state, Prog. Part. Nucl. Phys. 120, 103879 (2021).
  4. C. Horowitz and A. Schwenk, Cluster formation and the virial equation of state of low-density nuclear matter, Nucl. Phys. A 776, 55 (2006).
  5. A. R. Raduta and F. Gulminelli, Statistical description of complex nuclear phases in supernovae and proto-neutron stars, Phys. Rev. C 82, 065801 (2010).
  6. S. Typel, G. Röpke, T. Klähn, D. Blaschke, and H. H. Wolter, Composition and thermodynamics of nuclear matter with light clusters, Phys. Rev. C 81, 015803 (2010).
  7. S. Burrello and M. Grasso, Finite-temperature infinite matter with effective-field-theory-inspired energy-density functionals, Eur. Phys. J. A 58, 22 (2022).
  8. 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).
  9. A. Rios, A. Polls, and W. H. Dickhoff, Density and isospin-asymmetry dependence of high-momentum components, Phys. Rev. C 89, 044303 (2014).
  10. O. Hen, G. A. Miller, E. Piasetzky, and L. B. Weinstein, Nucleon-nucleon correlations, short-lived excitations, and the quarks within, Rev. Mod. Phys. 89, 045002 (2017).
  11. S. Burrello and S. Typel, Embedding short-range correlations in relativistic density functionals through quasi-deuterons, Eur. Phys. J. A 58, 120 (2022).
  12. H. Pais, F. Gulminelli, C. Providência, and G. Röpke, Full distribution of clusters with universal couplings and in-medium effects, Phys. Rev. C 99, 055806 (2019).
  13. R. Wang, Z. Zhang, S. Burrello, M. Colonna, and E. G. Lanza, Phase-space excluded-volume approach for light clusters in nuclear medium, Phys. Rev. C 113, 034624 (2026).
  14. S. Burrello, F. Gulminelli, F. Aymard, M. Colonna, and A. R. Raduta, Heat capacity of the neutron star inner crust within an extended nuclear statistical equilibrium model, Phys. Rev. C 92, 055804 (2015).
  15. X.-H. Wu, S.-B. Wang, A. Sedrakian, and G. Röpke, Composition of nuclear matter with light clusters and Bose–Einstein condensation of α particles, J. Low Temp. Phys. 189, 133 (2017).
  16. G. Röpke, Light nuclei quasiparticle energy shifts in hot and dense nuclear matter, Phys. Rev. C 79, 014002 (2009).
  17. G. Röpke, Parametrization of light nuclei quasiparticle energy shifts and composition of warm and dense nuclear matter, Nucl. Phys. A 867, 66 (2011).
  18. V. Baran, M. Colonna, M. Di Toro, and A. Larionov, Spinodal decomposition of low-density asymmetric nuclear matter, Nucl. Phys. A 632, 287 (1998).
  19. P. Chomaz, M. Colonna, and J. Randrup, Nuclear spinodal fragmentation, Phys. Rep. 389, 263 (2004).
  20. V. Baran, M. Colonna, V. Greco, and M. Di Toro, Reaction dynamics with exotic nuclei, Phys. Rep. 410, 335 (2005).
  21. Y. Kanada-En'yo, M. Kimura, and A. Ono, Antisymmetrized molecular dynamics and its applications to cluster phenomena, Prog. Theor. Exp. Phys. 2012, 01A202 (2012).
  22. A. Ono, Dynamics of clusters and fragments in heavy-ion collisions, Prog. Part. Nucl. Phys. 105, 139 (2019).
  23. G. Röpke, Light p -shell nuclei with cluster structures (4≤A≤16) in nuclear matter, Phys. Rev. C 101, 064310 (2020).
  24. N. Alam, H. Pais, C. Providência, and B. K. Agrawal, Warm unstable asymmetric nuclear matter: Critical properties and the density dependence of the symmetry energy, Phys. Rev. C 95, 055808 (2017).
  25. O. Boukari, H. Pais, S. Antić, and C. Providência, Critical properties of calibrated relativistic mean-field models for the transition to warm, nonhomogeneous nuclear and stellar matter, Phys. Rev. C 103, 055804 (2021).
  26. H. Wolter et al. (TMEP Collaboration), Transport model comparison studies of intermediate-energy heavy-ion collisions, Prog. Part. Nucl. Phys. 125, 103962 (2022).
  27. J. Xu, Transport approaches for the description of intermediate-energy heavy-ion collisions, Prog. Part. Nucl. Phys. 106, 312 (2019).
  28. P. Napolitani and M. Colonna, Bifurcations in Boltzmann–Langevin one body dynamics for fermionic systems, Phys. Lett. B 726, 382 (2013).
  29. H. Lin and P. Danielewicz, One-body Langevin dynamics in heavy-ion collisions at intermediate energies, Phys. Rev. C 99, 024612 (2019).
  30. P. Danielewicz and G. F. Bertsch, Production of deuterons and pions in a transport model of energetic heavy-ion reactions, Nucl. Phys. A 533, 712 (1991).
  31. R. Wang, Y.-G. Ma, L.-W. Chen, C. M. Ko, K.-J. Sun, and Z. Zhang, Kinetic approach of light-nuclei production in intermediate-energy heavy-ion collisions, Phys. Rev. C 108, L031601 (2023).
  32. H.-G. Cheng and Z.-Q. Feng, Novel approach to light-cluster production in heavy-ion collisions, Phys. Rev. C 109, L021602 (2024).
  33. H. Pais, S. Chiacchiera, and C. Providência, Light clusters, pasta phases, and phase transitions in core-collapse supernova matter, Phys. Rev. C 91, 055801 (2015).
  34. B.-A. Li, L.-W. Chen, and C. M. Ko, Recent progress and new challenges in isospin physics with heavy-ion reactions, Phys. Rep. 464, 113 (2008).
  35. M. Colonna, Collision dynamics at medium and relativistic energies, Prog. Part. Nucl. Phys. 113, 103775 (2020).
  36. A. Sorensen et al., Dense nuclear matter equation of state from heavy-ion collisions, Prog. Part. Nucl. Phys. 134, 104080 (2024).
  37. C. Y. Tsang, M. B. Tsang, W. G. Lynch, R. Kumar, and C. J. Horowitz, Determination of the equation of state from nuclear experiments and neutron star observations, Nat. Astron. 8, 328 (2024).
  38. C. Frosin, S. Piantelli, G. Casini, A. Ono, A. Camaiani, L. Baldesi, S. Barlini, B. Borderie, R. Bougault, et al. (INDRA-FAZIA Collaboration), Examination of cluster production in excited light systems at Fermi energies from new experimental data and comparison with transport model calculations, Phys. Rev. C 107, 044614 (2023).
  39. Q. Fable, L. Baldesi, S. Barlini, E. Bonnet, B. Borderie, R. Bougault, A. Camaiani, G. Casini, A. Chbihi, et al. (INDRA and INDRA-FAZIA Collaborations), Isospin diffusion from Ca40,48+Ca40,48 experimental data at Fermi energies: Direct comparisons with transport model calculations, Phys. Rev. C 109, 064605 (2024).
  40. K. Sumiyoshi and G. Röpke, Appearance of light clusters in post-bounce evolution of core-collapse supernovae, Phys. Rev. C 77, 055804 (2008).
  41. A. Arcones, G. Martínez-Pinedo, E. O'Connor, A. Schwenk, H.-T. Janka, C. J. Horowitz, and K. Langanke, Influence of light nuclei on neutrino-driven supernova outflows, Phys. Rev. C 78, 015806 (2008).
  42. S. Burrello, M. Colonna, and F. Matera, Pairing effects on neutrino transport in low-density stellar matter, Phys. Rev. C 94, 012801(R) (2016).
  43. A. V. Yudin, M. Hempel, S. I. Blinnikov, D. K. Nadyozhin, and I. V. Panov, Asymmetric nuclear light clusters in supernova matter, Mon. Not. R. Astron. Soc. 483, 5426 (2019).
  44. T. Fischer, S. Typel, G. Röpke, N.-U. F. Bastian, and G. Martínez-Pinedo, Medium modifications for light and heavy nuclear clusters in simulations of core collapse supernovae: Impact on equation of state and weak interactions, Phys. Rev. C 102, 055807 (2020).
  45. P. J. Davis, H. Dinh Thi, A. F. Fantina, F. Gulminelli, M. Oertel, and L. Suleiman, Inference of neutron-star properties with unified crust-core equations of state for parameter estimation Astron. Astrophys. 687, A44 (2024).
  46. H. H.-Y. Ng, P. C.-K. Cheong, A. T.-L. Lam, and T. G. F. Li, General-relativistic radiation transport scheme in Gmunu. II. Implementation of novel microphysical library for neutrino radiation—Weakhub, Astrophys. J. Suppl. Ser. 272, 9 (2024).
  47. A. R. Raduta and M. V. Beznogov, New ab initio constrained extended Skyrme equations of state for simulations of neutron stars, supernovae, and binary mergers, Astron. Astrophys. 701, A143 (2025).
  48. S. Burrello, F. Gulminelli, M. Antonelli, M. Colonna, and A. F. Fantina, Bayesian inference of neutron star crust properties using an ab-initio –benchmarked metamodel, Phys. Rev. C 112, 035802 (2025).
  49. G. Röpke, Nuclear matter equation of state including two-, three-, and four-nucleon correlations, Phys. Rev. C 92, 054001 (2015).
  50. R. Wang, S. Burrello, M. Colonna, and F. Matera, Dynamics of dilute nuclear matter with light clusters and in-medium effects, Phys. Rev. C 110, L031601 (2024).
  51. X. G. Deng, Y. G. Ma, and M. Veselský, Thermal and transport properties in central heavy-ion reactions around a few hundred MeV/nucleon, Phys. Rev. C 94, 044622 (2016).
  52. E. R. Most, A. Motornenko, J. Steinheimer, V. Dexheimer, M. Hanauske, L. Rezzolla, and H. Stoecker, Probing neutron-star matter in the lab: Similarities and differences between binary mergers and heavy-ion collisions, Phys. Rev. D 107, 043034 (2023).
  53. M. Colonna and F. Matera, Density dependence of isospin observables in spinodal decomposition, Phys. Rev. C 77, 064606 (2008).
  54. S. Burrello, M. Colonna, G. Colò, D. Lacroix, X. Roca-Maza, G. Scamps, and H. Zheng, Interplay between low-lying isoscalar and isovector dipole modes: A comparative analysis between semiclassical and quantum approaches, Phys. Rev. C 99, 054314 (2019).
  55. L. Shvedov, S. Burrello, M. Colonna, and H. Zheng, Probing nuclear structure and the equation of state through pre-equilibrium dipole emission in charge-asymmetric reactions, Phys. Rev. C 111, 014609 (2025).
  56. H. Zheng, S. Burrello, M. Colonna, and V. Baran, Pre-equilibrium effects in charge-asymmetric low-energy reactions, Phys. Lett. B 769, 424 (2017).
  57. V. Baran, M. Colonna, M. Di Toro, and V. Greco, Nuclear fragmentation: Sampling the instabilities of binary systems, Phys. Rev. Lett. 86, 4492 (2001).
  58. S. Burrello, M. Colonna, and F. Matera, Pairing effects on spinodal decomposition of asymmetric nuclear matter, Phys. Rev. C 89, 057604 (2014).
  59. H. Pais et al., Low density in-medium effects on light clusters from heavy-ion data, Phys. Rev. Lett. 125, 012701 (2020).
  60. L. Qin et al., Laboratory tests of low density astrophysical nuclear equations of state, Phys. Rev. Lett. 108, 172701 (2012).
  61. C. Kuhrts, M. Beyer, P. Danielewicz, and G. Röpke, Medium corrections in the formation of light charged particles in heavy ion reactions, Phys. Rev. C 63, 034605 (2001).
  62. G. Röpke, D. Voskresensky, I. Kryukov, and D. Blaschke, Fermi liquid, clustering, and structure factor in dilute warm nuclear matter, Nucl. Phys. A 970, 224 (2018).
  63. D. Voskresensky, Structure formation during phase transitions in strongly interacting matter, Prog. Part. Nucl. Phys. 130, 104030 (2023).
  64. C. Ducoin, P. Chomaz, and F. Gulminelli, Isospin-dependent clusterization of neutron-star matter, Nucl. Phys. A 789, 403 (2007).
  65. B. Borderie and J. Frankland, Liquid–gas phase transition in nuclei, Prog. Part. Nucl. Phys. 105, 82 (2019).
  66. P. Nieto Gallego, Master's thesis, University of Catania, 2025.
  67. R. Bougault et al., Equilibrium constants of hydrogen and helium isotopes at low nuclear densities, J. Phys. G 47, 025103 (2020).
  68. T. Custódio, A. Rebillard-Soulié, R. Bougault, D. Gruyer, F. Gulminelli, T. Malik, H. Pais, and C. Providência, Calibrating the medium effects of light clusters in heavy-ion collisions, Phys. Rev. Lett. 134, 082304 (2025).

Outline

Information

Phys. Rev. C 113, 064617– Published 18 June, 2026
  • Received 3 March 2026
  • Accepted 26 May 2026
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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation