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Clustered Nature of Hot and Dense Nuclear Matter: Signatures from Heavy-Ion Collisions

Rui Wang1,2,3,*,**, Zhen Zhang4,†, Yu-Gang Ma1,5,6,‡, Lie-Wen Chen7,§, Che Ming Ko8,∥, and Kai-Jia Sun1,5,¶

  • *Contact author: rui.wang@lns.infn.it
  • †Contact author: zhangzh275@mail.sysu.edu.cn
  • ‡Contact author: mayugang@fudan.edu.cn
  • §Contact author: lwchen@sjtu.edu.cn
  • ∥Contact author: ko@comp.tamu.edu
  • Contact author: kjsun@fudan.edu.cn
  • **Present address: INFN, Laboratori Nazionali del Sud, I-95123 Catania, Italy.
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Phys. Rev. Lett. 136, 172301 – Published 1 May, 2026

DOI: https://doi.org/10.1103/ffxr-mmlg

Abstract

Although light nuclear clusters are known to form abundantly in warm and dilute nuclear matter, their role in hot and dense nuclear matter remains unclear due to the lack of experimental indication for their modifications by the Mott effect under such conditions. To address this issue, we resort to intermediate-energy heavy-ion collisions, where light clusters are mainly produced in the transiently formed hot and dense matter. A kinetic approach, which includes dynamically the formation and dissociation of light clusters, is employed to deduce the strength of the Mott effect and the α-particle fraction in hot and dense nuclear matter from the light-nuclei yields measured by the FOPI Collaboration in central Au+Au collisions at energies of 0.25A to 0.6A  GeV. We find an unexpectedly abundant α clustering in this environment, which will have profound implications for modeling the nuclear equation of state and describing supernovae and neutron star mergers.

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References (53)

  1. N. F. Mott, Metal-insulator transition, Rev. Mod. Phys. 40, 677 (1968).
  2. G. Röpke, L. Münchow, and H. Schulz, Particle clustering and Mott transitions in nuclear matter at finite temperature: (I). Method and general aspects, Nucl. Phys. A379, 536 (1982).
  3. G. Röpke, M. Schmidt, L. Münchow, and H. Schulz, Particle clustering and Mott transition in nuclear matter at finite temperature (II): Self-consistent ladder Hartree-Fock approximation and model calculations for cluster abundances and the phase diagram, Nucl. Phys. A399, 587 (1983).
  4. M. Schmidt, G. Röpke, and H. Schulz, Generalized Beth-Uhlenbeck approach for hot nuclear matter, Ann. Phys. (N.Y.) 202, 57 (1990).
  5. 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).
  6. G. Röpke, Nuclear matter equation of state including two-, three-, and four-nucleon correlations, Phys. Rev. C 92, 054001 (2015).
  7. F. Gulminelli and A. R. Raduta, Unified treatment of subsaturation stellar matter at zero and finite temperature, Phys. Rev. C 92, 055803 (2015).
  8. Z.-W. Zhang and L.-W. Chen, Low density nuclear matter with light clusters in a generalized nonlinear relativistic mean-field model, Phys. Rev. C 95, 064330 (2017).
  9. G. Röpke, Light nuclei quasiparticle energy shifts in hot and dense nuclear matter, Phys. Rev. C 79, 014002 (2009).
  10. R. Bougault et al. (INDRA Collaboration), Light charged clusters emitted in 32  MeV/nucleon Xe136,124+124,112Sn reactions: Chemical equilibrium and production of He3 and He6, Phys. Rev. C 97, 024612 (2018).
  11. K. Hagel et al., Experimental determination of in-medium cluster binding energies and Mott points in nuclear matter, Phys. Rev. Lett. 108, 062702 (2012).
  12. L. Qin et al., Laboratory tests of low density astrophysical nuclear equations of state, Phys. Rev. Lett. 108, 172701 (2012).
  13. H. Pais, R. Bougault, F. Gulminelli, C. Providência, E. Bonnet, B. Borderie, A. Chbihi, J. D. Frankland, E. Galichet, D. Gruyer, M. Henri, N. Le Neindre, O. Lopez, L. Manduci, M. Parlôg, and G. Verde, Low density in-medium effects on light clusters from heavy-ion data, Phys. Rev. Lett. 125, 012701 (2020).
  14. 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).
  15. G. F. Bertsch and S. Das Gupta, A guide to microscopic models for intermediate energy heavy ion collisions, Phys. Rep. 160, 189 (1988).
  16. B.-A. Li, High density behaviour of nuclear symmetry energy and high energy heavy-ion collisions, Nucl. Phys. A708, 365 (2002).
  17. 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).
  18. W. Reisdorf et al. (FOPI Collaboration), Systematics of central heavy ion collisions in the 1A  GeV regime, Nucl. Phys. A848, 366 (2010).
  19. A. Ono, Dynamics of clusters and fragments in heavy-ion collisions, Prog. Part. Nucl. Phys. 105, 139 (2019).
  20. R. Bougault, B. Borderie, A. Chbihi, Q. Fable, J. D. Frankland, E. Galichet, T. Genard, D. Gruyer, M. Henri, M. La Commara, N. Le Neindre, I. Lombardo, O. Lopez, M. Pârlog, P. Pawłowski, G. Verde, E. Vient, and M. Vigilante, Light cluster production in central symmetric heavy-ion reactions from fermi to Gev energies, Symmetry 13, 1406 (2021).
  21. M. Oertel, M. Hempel, T. Klähn, and S. Typel, Equations of state for supernovae and compact stars, Rev. Mod. Phys. 89, 015007 (2017).
  22. K. Sumiyoshi, T. Kojo, and S. Furusawa, Equation of state in neutron stars and supernovae, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, Singapore, 2020), pp. 1–51, 10.1007/978-981-15-8818-1_104-1.
  23. J. A. Pons, S. Reddy, M. Prakash, J. M. Lattimer, and J. A. Miralles, Evolution of proto-neutron stars, Astrophys. J. 513, 780 (1999).
  24. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  25. 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).
  26. F. Rami et al. (FOPI Collaboration), Isospin tracing: A probe of nonequilibrium in central heavy-ion collisions, Phys. Rev. Lett. 84, 1120 (2000).
  27. W. Reisdorf et al. (FOPI Collaboration), Nuclear stopping from 0.09A to 1.93A  GeV and its correlation to flow, Phys. Rev. Lett. 92, 232301 (2004).
  28. A. Andronic, J. Łukasik, W. Reisdorf, and W. Trautmann, Systematics of stopping and flow in Au+Au collisions, Eur. Phys. J. A 30, 31 (2006).
  29. 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).
  30. P. Danielewicz and G. F. Bertsch, Production of deuterons and pions in a transport model of energetic heavy-ion reactions, Nucl. Phys. A533, 712 (1991).
  31. J. Rammer, Quantam Field Theory of Non-Equilibrium States (Cambridge University Press, New York, 2007).
  32. B. G. Carlsson, J. Dobaczewski, and M. Kortelainen, Local nuclear energy density functional at next-to-next-to-next-to-leading order, Phys. Rev. C 78, 044326 (2008).
  33. R. Wang, L.-W. Chen, and Y. Zhou, Extended Skyrme interactions for transport model simulations of heavy-ion collisions, Phys. Rev. C 98, 054618 (2018).
  34. S.-P. Wang, R. Wang, J.-T. Ye, and L.-W. Chen, Extended Skyrme effective interactions for transport models and neutron stars, Phys. Rev. C 109, 054623 (2024).
  35. S.-P. Wang, X. Li, R. Wang, J.-T. Ye, and L.-W. Chen, Extended Skyrme effective interactions with higher-order momentum dependence for transport models and neutron stars, Phys. Rev. C 111, 054605 (2025).
  36. C.-Y. Wong, Dynamics of nuclear fluid. VIII. Time-dependent Hartree-Fock approximation from a classical point of view, Phys. Rev. C 25, 1460 (1982).
  37. R. J. Lenk and V. R. Pandharipande, Nuclear mean field dynamics in the lattice Hamiltonian Vlasov method, Phys. Rev. C 39, 2242 (1989).
  38. R. Wang, Lie-Wen Chen, and Z. Zhang, Nuclear collective dynamics in the lattice Hamiltonian Vlasov method, Phys. Rev. C 99, 044609 (2019).
  39. R. Wang, Z. Zhang, L.-W. Chen, C. M. Ko, and Y.-G. Ma, Constraining the in-medium nucleon-nucleon cross section from the width of nuclear giant dipole resonance, Phys. Lett. B 807, 135532 (2020).
  40. R. Wang, Z. Zhang, L.-W. Chen, and Y.-G. Ma, Nuclear collective dynamics in transport model with the lattice Hamiltonian method, Front. Phys. 8, 330 (2020).
  41. R. Wang, Z. Zhang, S. Burrello, M. Colonna, and E. G. Lanza, Phase-space excluded-volume approach for light clusters in a nuclear medium, Phys. Rev. C 113, 034624 (2026).
  42. 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).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ffxr-mmlg for box calculations of nuclear matter with the kinetic approach and details of the Bayesian inference, which includes Refs. [9,18,41,44].
  44. M. Plumlee, Ö. Sürer, and S. M. Wild, surmise Users Manual (2021), version 0.1.0, NAISE.
  45. D. Oliinychenko, L.-G. Pang, H. Elfner, and V. Koch, Microscopic study of deuteron production in PbPb collisions at s=2.76  TeV via hydrodynamics and a hadronic afterburner, Phys. Rev. C 99, 044907 (2019).
  46. G. Coci, S. Gläßel, V. Kireyeu, J. Aichelin, C. Blume, E. Bratkovskaya, V. Kolesnikov, and V. Voronyuk, Dynamical mechanisms for deuteron production at mid-rapidity in relativistic heavy-ion collisions from energies available at the GSI Schwerionensynchrotron to those at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 108, 014902 (2023).
  47. K.-J. Sun, R. Wang, C. M. Ko, Y.-G. Ma, and C. Shen, Unveiling the dynamics of little-bang nucleosynthesis, Nat. Commun. 15, 1074 (2024).
  48. A. Andronic, P. Braun-Munzinger, K. Redlich, and J. Stachel, Decoding the phase structure of QCD via particle production at high energy, Nature (London) 561, 321 (2018).
  49. H. Shen, H. Toki, K. Oyamatsu, and K. Sumiyoshi, Relativistic equation of state of nuclear matter for supernova and neutron star, Nucl. Phys. A637, 435 (1998).
  50. S. Burrello and S. Typel, Embedding short-range correlations in relativistic density functionals through quasi-deuterons, Eur. Phys. J. A 58, 120 (2022).
  51. 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).
  52. M. Colonna, M. Di Toro, A. Guarnera, S. Maccarone, M. Zielinska-Pfabé, and H. H. Wolter, Fluctuations and dynamical instabilities in heavy-ion reactions, Nucl. Phys. A642, 449 (1998).
  53. G. Batko, J. Randrup, and T. Vetter, N-body collisions in high-energy nuclear reactions, Nucl. Phys. A536, 786 (1992).

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Phys. Rev. Lett. 136, 172301– Published 1 May, 2026
  • Received 22 July 2025
  • Revised 8 March 2026
  • Accepted 31 March 2026
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