Light clusters in nuclear matter: Excluded volume versus quantum many-body approaches

The formation of clusters in nuclear matter is investigated, which occurs e.g. in low energy heavy ion collisions or core-collapse supernovae. In astrophysical applications, the excluded volume concept is commonly used for the description of light clusters. Here we compare a phenomenological excluded volume approach to two quantum many-body models, the quantum statistical model and the generalized relativistic mean field model. All three models contain bound states of nuclei with mass number A <= 4. It is explored to which extent the complex medium effects can be mimicked by the simpler excluded volume model, regarding the chemical composition and thermodynamic variables. Furthermore, the role of heavy nuclei and excited states is investigated by use of the excluded volume model. At temperatures of a few MeV the excluded volume model gives a poor description of the medium effects on the light clusters, but there the composition is actually dominated by heavy nuclei. At larger temperatures there is a rather good agreement, whereas some smaller differences and model dependencies remain.

💡 Research Summary

The paper investigates the formation of light nuclear clusters (A ≤ 4) in nuclear matter, a phenomenon relevant for low‑energy heavy‑ion collisions and core‑collapse supernovae. In astrophysical simulations the excluded‑volume (ExV) approach is widely used because of its simplicity and computational efficiency. The authors compare this phenomenological model with two quantum many‑body frameworks: the quantum statistical (QS) model and the generalized relativistic mean‑field (gRMF) model, both of which incorporate medium effects such as self‑energy shifts and Pauli blocking in a microscopic way.

The ExV model treats nucleons and clusters as non‑relativistic classical particles occupying hard‑core volumes equal to the saturation density volume (V = A/n₀). The free nucleons are described by a density‑dependent relativistic mean‑field (RMF) with the DD2 parameter set, ensuring consistency with the QS and gRMF treatments of the unbound nucleons. Clusters are handled as ideal Maxwell‑Boltzmann gases with experimental masses; excited states are included via a temperature‑dependent internal partition function. The excluded‑volume correction is implemented through a free‑volume fraction κ = 1 − n_B/n₀, which diverges the free energy as the total baryon density approaches saturation, thereby forcing clusters to dissolve near n₀. Coulomb screening is approximated by placing each nucleus in a spherical Wigner‑Seitz cell filled with electrons.

In contrast, the QS model treats clusters as quasiparticles whose binding energies are modified by the surrounding medium. Pauli blocking of nucleon states and self‑energy shifts are calculated explicitly, leading to a density‑ and temperature‑dependent Mott transition where the cluster’s effective binding vanishes. The gRMF model extends this idea by coupling the cluster quasiparticle energies to the same RMF fields that act on the nucleons, so that clusters both feel and contribute to the mean fields. Consequently, the gRMF framework includes feedback between clusters and the meson fields, a feature absent in the ExV approach.

The authors perform systematic comparisons for symmetric nuclear matter (Yₚ = 0) at several fixed temperatures. At low temperatures (T ≈ 5 MeV) the ExV model fails to reproduce the strong medium suppression of light clusters predicted by QS and gRMF; it overestimates the abundances of deuterons, tritons, and ^3He. However, in this regime the composition is dominated by heavy nuclei (e.g., ^56Fe), so the impact of the inaccurate cluster description on bulk thermodynamic quantities is modest. At higher temperatures (T ≈ 10–20 MeV) the three models converge: cluster fractions, pressures, and chemical potentials differ by less than about 10 %. The ExV model, when equipped with an internal partition function that accounts for excited nuclear states, reproduces the heavy‑nucleus contribution at low temperature and yields a smooth transition to the high‑temperature regime where light clusters dominate.

The study also explores the role of heavy nuclei and excited states within the ExV framework. Including the full nuclear distribution (up to the drip line) and a simple temperature‑dependent degeneracy factor substantially increases the heavy‑nucleus fraction at low T, thereby improving agreement with the more microscopic models for the overall composition. The authors note that while the ExV approach captures the essential thermodynamic behavior at moderate to high temperatures, it lacks a microscopic description of the Mott effect and does not allow clusters to modify the mean‑field source terms, which can become important near saturation density.

In conclusion, the excluded‑volume model provides a computationally cheap and thermodynamically consistent EOS that can mimic the quantum many‑body results in the temperature range most relevant for supernova simulations (T ≳ 10 MeV). Nevertheless, for low‑temperature, low‑density conditions where Pauli blocking and self‑energy effects are pronounced, quantum statistical or generalized RMF treatments remain necessary. The paper suggests that future work should aim at hybrid schemes that retain the efficiency of the ExV model while incorporating microscopic medium corrections for light clusters, thereby delivering a unified EOS suitable across the entire density–temperature domain required in astrophysical modeling.