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REVIEW 2 major objections 6 minor 122 references

This review argues that a soft momentum-dependent equation of state, not a purely soft or uniquely hard one, is what fits the directed and elliptic flow of protons and light clusters in few-GeV heavy-ion collisions.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review

2026-08-04 19:44 UTC pith:JEHGQRKW

load-bearing objection An openly labeled review by PHQMD insiders; useful as a synthesis and caveat catalog, but its few-GeV conclusion leans on an unconstrained U_opt extrapolation and on self-cited preprints. the 2 major comments →

arxiv 2509.09061 v1 pith:JEHGQRKW submitted 2025-09-10 nucl-th

Study on the equation-of-state with light clusters and hypernuclei

Elena Bratkovskaya , J\"org Aichelin This is my paper
classification nucl-th PACS 25.75.-q25.75.Ld21.65.Mn
keywords equation of statecollective flowheavy-ion collisionsmomentum-dependent potentialoptical potentiallight clustershypernucleicompressibility
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Heavy-ion collisions in the few-GeV range compress nuclear matter to about three times saturation density, and the flow pattern of the outgoing particles is one of the few observables sensitive to the equation of state. Comparing transport-model calculations with HADES, FOPI, and STAR data, this review finds that a purely soft static potential is ruled out, while a soft potential with momentum dependence describes both directed (v1) and elliptic (v2) flow at lower beam energies. A hard static potential often reproduces the same flow observables, especially for light clusters, making the two nearly degenerate. The paper concludes that including the momentum dependence of the nucleon-nucleon interaction reconciles the compressibility extracted from early Plastic Ball flow data (about 380 MeV) with the value from giant monopole vibrations (about 200 MeV). If this holds, flow data no longer pick a unique stiffness, but they do establish momentum dependence as an essential ingredient.

Core claim

The central claim is that the momentum dependence of the nuclear mean-field potential is not a correction but a necessary part of any successful description of collective flow at SIS to 3 GeV beam energies. Within the PHQMD transport model, a soft momentum-dependent (SM) equation of state reproduces the HADES and FOPI v1 and v2 data for protons, deuterons, and tritons, whereas the same soft static potential systematically underestimates them. A hard static potential also gives acceptable flow, particularly for clusters, which is why the compressibility modulus K is not uniquely determined by flow alone. The reconciliation mechanism is that in a collision, a soft potential plus momentum depen

What carries the argument

The load-bearing element is the Schrödinger-equivalent optical potential U_opt(p), reconstructed from elastic proton-nucleus scattering up to 1.04 GeV and extrapolated to higher momenta. In PHQMD this is converted into a two-body momentum-dependent potential V(p,p1) whose parameters are fixed so the zero-temperature EoS gives E/A(rho0) = -16 MeV with a chosen compressibility K. Because a soft static and a soft momentum-dependent parametrization share the same energy per nucleon E/A(rho), the extra momentum-dependent pressure generated during a collision is what brings the soft equation of state into agreement with data and mimics a hard static EoS. Cluster flow is extracted by identifying de

Load-bearing premise

The load-bearing assumption is that the momentum-dependent potential, which is measured only up to a proton kinetic energy of about 1 GeV, can be safely extrapolated to the higher momenta probed at sqrt(s_NN)=3 and 5.4 GeV; the paper's own Fig. 8 shows that this extrapolation changes cluster flow at the higher energy.

What would settle it

Measure the optical potential in elastic pA scattering for proton kinetic energies above 1 GeV up to a few GeV. If the measured U_opt(p) disagrees with parametrization I, the PHQMD flow predictions at sqrt(s_NN)=3 and especially 5.4 GeV shift; a high-precision measurement of deuteron v1(pT) or v2(pT) at high pT at sqrt(s_NN)=5.4 GeV would also settle which extrapolation is correct.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • A purely soft static EoS is incompatible with SIS and sqrt(s_NN)=3 GeV flow data for protons and light clusters, so any future EoS extraction that ignores momentum dependence will be biased.
  • A soft momentum-dependent EoS describes v1 and v2 of protons, deuterons, and tritons to within about 10% at SIS energies, establishing momentum dependence as a required ingredient.
  • A hard static EoS produces nearly the same flow, particularly for clusters, so flow observables alone do not fix the compressibility modulus K.
  • Including momentum dependence reconciles the K about 380 MeV inferred from Plastic Ball flow with the K about 200 MeV from giant monopole vibrations, suggesting the two measurements constrain the same underlying EoS.
  • At sqrt(s_NN)=5.4 GeV, high-pT deuteron flow becomes sensitive to how U_opt(p) is extrapolated, making precision flow data and new elastic pA measurements a discriminating test.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A testable extension: if the optical potential is measured above 1 GeV and deviates from the parametrizations used here, the soft-momentum-dependent agreement may degrade, shifting the implied K back toward the hard side.
  • The static-hard/soft-momentum-dependent degeneracy suggests that discriminating observables should target early-time pressure gradients—for example, subthreshold kaon yields, baryon stopping, or pT-differential ratios of cluster-to-proton flow—rather than v1/v2 alone.
  • Hypernucleus flow carries a separate probe: because the Lambda hyperon feels a different potential than protons, flow of hypertritons and Lambda could test whether the momentum-dependence mechanism extends to the strangeness sector.
  • A multi-model Bayesian comparison of the same data sets, as sketched at the end of the review, could quantify how much of the spread in extracted K comes from different implementations of momentum dependence rather than from the EoS itself.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This manuscript is a review of transport-model constraints on the nuclear equation of state (EoS) extracted from collective flow of nucleons, light clusters, and hypernuclei in the few-GeV energy range. The authors present PHQMD results for Au+Au collisions at SIS energies (Ekin = 1.23 A GeV) and at sqrt(s_NN) = 3 and 5.4 GeV, compare them with HADES, FOPI, and STAR data, and contrast these results with pBUU, RBUU, IQMD, dcQMD, UrQMD, and SMASH. The central thesis is that a purely soft static EoS is disfavored, while a soft momentum-dependent (SM) EoS reproduces v1 and v2; a hard static EoS is often degenerate with SM, particularly for light clusters. The authors argue that momentum dependence reconciles the K about 380 MeV (Plastic Ball) and K about 200 MeV (giant monopole vibrations) compressibility values. The limitations are explicitly acknowledged: the optical potential U_opt is constrained only up to 1.04 GeV, model implementations of momentum dependence differ, and the EoS is defined for infinite cold matter while heavy-ion collisions probe hot, off-equilibrium systems.

Significance. If the conclusions hold, the review provides a useful consolidated statement: momentum dependence is indispensable, and few-GeV flow data are compatible with a soft EoS plus momentum dependence, with K not uniquely fixed. The paper's strengths are its explicit comparison across many transport codes, transparent reporting of model disagreements (e.g., SMASH hardening versus IQMD/PHQMD soft MD, Section 3.7), internally consistent parameter tables (Table 1), and a clear statement of limitations in Section 4. It is a synthetic review rather than a new measurement, and it is one of the few works placing PHQMD results in the broader transport-model context. The authors deserve credit for explicitly flagging the U_opt extrapolation problem and the model-dependent treatment of momentum dependence.

major comments (2)
  1. [Sec. 3.1.2, Figs. 8–10] The STAR comparison in Figs. 9 and 10 is performed only with Parametrization I of U_opt, as noted in Sec. 3.1.1 and 3.1.2. However, Fig. 8 demonstrates that v1(pT) and v2(pT) of deuterons at sqrt(s_NN) = 3 GeV already show visible splitting among Parametrizations I, II, and III at high pT, and the splitting grows at 5.4 GeV. Since the STAR data in Figs. 9–10 extend to several GeV/c, the conclusion that a soft momentum-dependent EoS provides a consistent description of STAR data is not yet shown to be robust against the documented lack of empirical constraints above 1.04 GeV (Sec. 2.2). The manuscript is transparent about this limitation, but the limitation is load-bearing because it sits exactly on the energy range used to extend the EoS constraint beyond SIS. Please either include the II/III variants in the STAR comparison, or explicitly restrict the STAR claim to the pT range where I/I
  2. [Sec. 4, Summary] The statement that 'the introduction of the momentum dependent potential reconciles the compressibility of both data sets' (K≈380 from Plastic Ball, K≈200 from GMR) is stronger than what the review demonstrates. The models are constructed with K=200 (S, SM) and K=380 (H) as inputs (Table 1), and the flow comparisons in Sec. 3 are qualitative; no single parametrization is shown to simultaneously reproduce both the Plastic Ball-era and GMR constraints in a quantitative fit. Given the paper's own caveats about model dependence and the extrapolated U_opt, the sentence should be softened to state that a soft MD EoS is compatible with both constraints within current uncertainties, unless a closure test is added. This is central to the summary and should be made precise.
minor comments (6)
  1. [Sec. 3.1.2] Typo: 'high precession data' should be 'high-precision data'.
  2. [Sec. 3.1.1, Fig. 5] The text refers to 'bottom right panel' of Fig. 5, but the figure appears to have only three panels (p, d, t). Update the reference or add the fourth panel.
  3. [Sec. 3.3] Typo: 'PHQMD framefork' should be 'PHQMD framework'.
  4. [Sec. 3.5] The sentence 'For cluster production a MST coalescence algorithm applied at the local freeze-out time (rather than during the entire simulation, as in PHQMD); and threshold effects for elastic scattering' is grammatically incomplete and should be revised.
  5. [References] References [54] and [56] are the same STAR paper and should be merged. References [76] and [77] are arXiv preprints; in a review they should be clearly labeled as such, and claims based on them should be distinguished from peer-reviewed literature.
  6. [Sec. 2.2, Fig. 1] The normalization U_opt(p=0)=0 and the relation between the proton kinetic energy epsilon in Eq. (12) and the total momentum p used in Fig. 1 should be stated explicitly.

Circularity Check

0 steps flagged

No significant circularity: PHQMD flow results are model predictions compared against external data, with EoS and optical-potential inputs fixed independently of the flow observables.

full rationale

The paper's derivation chain is: (i) the momentum-dependent optical potential U_opt is fitted to elastic pA scattering data (Section 2.2, Eq. 12 and Fig. 1); (ii) the static EoS parameters are fixed by nuclear matter saturation properties with K as a free parameter (Section 2.3, Eqs. 18-21 and Table 1); (iii) PHQMD transport then generates v1 and v2 for protons and clusters; (iv) these are compared to HADES, FOPI, and STAR data. No flow observable is used to fit the PHQMD parameters shown in the review, and the paper explicitly stresses that the soft and soft momentum-dependent EoS have identical E/A(ρ) by construction, so the flow differences between S and SM are genuine dynamical predictions rather than definitions. The two anchor studies [76,77] are self-citations from the same collaboration, but they are confronted with external experimental data and are complemented by independent models (IQMD, dcQMD, UrQMD, pBUU, RBUU, SMASH), so the central claim does not reduce to a self-citation chain. The limitation noted in Section 4 that high-momentum U_opt extrapolations 'rely on extrapolations constrained by comparisons with heavy-ion observables' is a stated uncertainty, and the paper actually shows sensitivity among three parametrizations (Fig. 8) and restricts its SIS conclusions to p<1 GeV/c where U_opt is data-constrained. This is a robustness caveat, not evidence that the flow predictions were fitted to the same data they are claimed to describe. Overall, the review is a self-contained model-data comparison with explicit and load-bearing caveats, but no circular step is exhibited.

Axiom & Free-Parameter Ledger

7 free parameters · 4 axioms · 0 invented entities

The review's claims inherit free parameters of the underlying transport models: the Skyrme coefficients alpha, beta, gamma fixed to saturation with free K; the momentum-dependent potential parameters a, b, c (and d, e, f for the third parametrization) fitted to optical potential data; model choices L, C, and cluster thresholds; plus SMASH's C, Lambda from Ref. [35]. The domain assumptions are QMD's factorization ansatz, the transfer of U_opt from pA scattering into in-medium potentials, the premise that flow can discriminate the EoS despite other model ingredients, and the use of cluster flow as a proxy for nucleon flow. No new particles or fields are introduced.

free parameters (7)
  • Skyrme parameters alpha, beta, gamma for S/H/SM EoS = S: -0.3835, 0.3295, 1.15; H: -0.1253, 0.071, 2.0; SM: -0.478, 0.4137, 1.1
    Fixed to E/A(rho0) = -16 MeV with compressibility K chosen as 200 MeV (S, SM) or 380 MeV (H); K is a free parameter of the EoS (Section 2.3, Table 1).
  • Momentum-dependent potential parameters a, b, c = a=236.326 GeV^-1, b=-20.730 GeV^-3, c=0.901 GeV^-1
    Fit to the Schrodinger-equivalent optical potential U_opt from pA scattering data (Section 2.2, Fig. 1, Table 1).
  • High-momentum extrapolation parameters d, e, f (parametrization III) = d=72.237 GeV, e=27.085, f=-1.722 GeV^-1
    Continuation of U_opt beyond 1.7 GeV/c; the choice of parametrization (I, II, III) affects v1, v2 at sqrt(s_NN) = 5.4 GeV (Section 3.1.2, Fig. 8).
  • Gaussian width L = 4.33 fm^2
    Time-independent width of single-particle Wigner densities in QMD propagation (Eq. 4), a chosen model parameter.
  • Density correction factor C = adjusted numerically
    Compensates for lower density in QMD vs mean-field approaches (Eq. 11); 'adjusted numerically to achieve equality of the two densities' (Section 2.1).
  • Cluster recognition and coalescence thresholds = r_clus = 4 fm; 3.575 fm, 285 MeV/c
    MST bound criterion (Eq. 22) and coalescence phase-space cuts (Section 2.4); these choices affect which nucleons are counted as clusters and therefore the computed cluster flow.
  • SMASH momentum-dependent potential parameters C, Lambda (Eq. 27) = see Table 1 of Ref. [35]
    Adjusted to reproduce nuclear ground state properties and U_opt; the review's comparative claims about SMASH depend on them (Section 3.7).
axioms (4)
  • domain assumption N-body wave function factorizes as a direct product of single-particle Gaussian wave functions without antisymmetrization (Eq. 2, Section 2.1)
    This is the QMD approximation underlying all PHQMD results; the Pauli principle is only approximately accounted for.
  • domain assumption The Schrodinger-equivalent optical potential U_opt (Eq. 12) extracted from elastic pA scattering below 1.04 GeV describes the in-medium two-body NN potential at the densities and momenta of heavy-ion collisions, also in the extrapolated region.
    The paper itself notes extrapolation is needed for sqrt(s_NN) > 2.32 GeV and introduces uncertainties (Section 2.2); the parametrization choice affects flow at 5.4 GeV (Section 3.1.2).
  • domain assumption Transport-model flow observables at few-GeV energies are governed by the mean-field potential (EoS input) to a degree that permits EoS discrimination despite other ingredients (collision parametrization, initial state).
    This is the entire review's premise; the paper itself lists 'flow observables are sensitive to other ingredients' (Section 4).
  • domain assumption Cluster flow reflects the flow of the constituent nucleons, so clusters can be used as EoS probes (mass-number scaling of v1).
    Used in Sections 3.1.1-3.1.2 and 3.6; the review notes a 'small subset of nucleons identified as deuterons by coalescence and by MST coincide' (Section 3.1.1).

pith-pipeline@v1.3.0-alltime-deepseek · 27526 in / 17501 out tokens · 163085 ms · 2026-08-04T19:44:16.434180+00:00 · methodology

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read the original abstract

Heavy-ion collision experiments offer a unique opportunity to explore the early stages of the Universe by creating matter under extreme conditions of high temperature and baryon density. The properties of such matter are governed by the equation-of-state (EoS), which remains a central focus of investigation from both experimental and theoretical perspectives. Flow harmonics are among the most sensitive observables for probing the EoS, as they strongly reflect the underlying interactions and degrees of freedom of the system. In this article, we review the current status of our understanding of the EoS based on microscopic transport models, emphasizing comparisons with experimental data in the few GeV energy range.

Figures

Figures reproduced from arXiv: 2509.09061 by Elena Bratkovskaya, J\"org Aichelin.

Figure 1
Figure 1. Figure 1: Schrodinger equivalent optical potential ¨ Uopt versus total mo￾mentum p of the proton extracted from pA collisions [94, 95, 97]. The figure is adopted from Ref. [77]. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 -20 -10 0 10 20 30 ρ/ρ0 E / A (MeV ) EoS: S H SM [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Equation-of-state for T = 0 for the hard (green line), soft (blue line) and the soft momentum dependent potential (red line). The figure is adopted from Ref. [77]. kinetic energies of 1.04 GeV, no data are available, introducing uncertainties for heavy-ion collisions with √ sNN > 2.32 GeV. To study whether different parametrizations affect predic￾tions, we perform calculations with three parameterizations … view at source ↗
Figure 3
Figure 3. Figure 3: v1 of protons (left), deuterons (middle) and tritons (right) as a function of rapidity for 20-30% central Au+Au collisions at Ekin = 1.23 A GeV for 1.0 < pT < 1.5 GeV/c. The blue lines ”S” correspond to the PHQMD calculations with the ”soft” EoS, the green lines ”H” show the ”hard” EoS, the red lines the ”SM” represent the momentum dependent ”soft” EoS. The HADES experimental data are taken from Ref. [42].… view at source ↗
Figure 4
Figure 4. Figure 4: v1 of protons (left), deuterons (middle) and tritons (right) as a function of pT for 20-30% central Au+Au collisions at Ekin = 1.2 A GeV in the rapidity bin −0.25 < y < −0.15. The colour code is the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: v2 of protons (left), deuterons (middle) and tritons (right) as a function of rapidity for 20-30% central Au+Au collisions at Ekin = 1.23 A GeV for 1.0 < pT < 1.5 GeV/c. The colour code is the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: v2 of protons (left), deuterons (middle) and triton (right) as a function of pT for rapidity intervals |y| < 0.05 for 20-30% central Au+Au collisions at Ekin=1.23 A GeV. The colour code is the same as in [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Upper plot: Comparison of the v1(y) (left) and v2(y)(right) of deuterons produced by kinetic + MST mechanisms (solid lines) with the coalescence mechanism (dashed lines) for 20-30% central Au+Au collisions at Ekin = 1.23 A GeV for 1.0 < pT < 1.5 GeV/c. Lower plot: The comparison of v1(pT ) for −0.25 < y < −0.15 (left) and v2(pT ) for |y| < 0.05 (right) of deuterons produced by kinetic + MST mechanisms (sol… view at source ↗
Figure 8
Figure 8. Figure 8: The in-plane flow v1(pT ) near target rapidity (−1 < y < −0.5) (left) and elliptic flow v2(pT ) at mid-rapidity (−0.5 < y < 0) (right) of deuterons from PHQMD simulations of Au+Au collisions at √ sNN = 3 GeV (left column) and 5.4 GeV (right column) in the 10–40% centrality class. Results are shown for three different parameterizations of the nuclear optical potential (Parameterization I, II, and III). The … view at source ↗
Figure 9
Figure 9. Figure 9: The PHQMD results for the directed flow v1 of protons (left) and deuterons (right) calculated with S (blue lines), H (green lines), SM (red lines) EoS as a function of pT for 4 rapidity intervals in 10 − 40% mid-central Au+Au collisions at √ sNN = 3 GeV. The right plot shows the scaled v1/A for protons, deuterons, triton, 3He, and 4He versus pT for 4 rapidity intervals. The STAR data are taken from Ref. [4… view at source ↗
Figure 10
Figure 10. Figure 10: The PHQMD results for the elliptic flow v2 of protons (left) and deuterons (right) calculated with S (blue lines), H (green lines), SM (red lines) EoS as a function of pT for rapidity interval −0.1 < y < 0 in 10 − 40% mid-central Au+Au collisions at √ sNN = 3 GeV. The right plot shows the scaled v2/A for protons, deuterons, triton, 3He versus pT for −0.1 < y < 0. The STAR data are taken from Ref. [46] The… view at source ↗
Figure 11
Figure 11. Figure 11: EOS for symmetric nuclear matter at zero temperature. The shaded region corresponds to the region of pressures consistent with the experimental flow data. The various curves and lines show predic￾tions for different symmetric matter EOS. The figure is adopted from Ref. [80]. to the mean-field momentum dependence in midperipheral to peripheral collisions. Here we emphasize a key difference in the treatment… view at source ↗
Figure 13
Figure 13. Figure 13: shows the RBUU results for the sideward flow F = d [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Excitation function of the elliptic flow v2 of protons at mid￾rapidity. The experimental data (black circles) are from the FOPI Col￾laboration [44]. The data is measured in the impact parameter range 3.1 < b < 5.6 fm and a cut on ut0 > 0.8 is applied. IQMD model results are presented for two different nuclear EOS (HM with red lines and SM with black lines) for b = 4 fm and with an additional cut on ut0 > … view at source ↗
Figure 15
Figure 15. Figure 15: Elliptic flow v2 for protons, deuterons, tritons, 3He as func￾tion of incident beam energy from IQMD for different EoS: SM - soft momentum dependent (blue), HM - hard momentum dependent (red) in comparison to the FOPI data [44]. The figure is adopted from Ref. [98]. In [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The dcQMD predictions for transverse momentum dependent v2 of protons, deuterons and tritons are compared to the FOPI experi￾mental data [44] [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Left: Isoscalar optical potential at saturation density as a function of nucleon momentum from four sources: HIC (pcQMD), empirical Hama potential [97], microscopical DBHF [108] and χFT [109] calculations. Right: The same as in the left panel but for the symmetry (Lane) potential. The shown empirical Lane potential depicts a parametrization [110] of analyses of nucleon-nucleus scattering experiments at be… view at source ↗
Figure 18
Figure 18. Figure 18: The directed flow v1 as a function of rapidity of pro￾tons (upper left), deuterons (upper right), tritons and 3He (lower left) and 4He (lower right) from 10-40% central Au+Au collisions at √ sNN = 3 GeV from UrQMD with coalescence (solid lines) and from UrQMD combined with the statistical multi-fragmentation model (dashed lines). Experimental data points are taken from STAR [46, 48, 50]. The figure is ado… view at source ↗
Figure 19
Figure 19. Figure 19: The elliptic flow v1 as a function of rapidity of protons (up￾per left), deuterons (upper right), tritons and 3He (lower left) and 4He (lower right) from 10-40% central Au+Au collisions at √ sNN = 3 GeV from UrQMD with coalescence (solid lines) and from UrQMD combined with the statistical multi-fragmentation model (dashed lines). Experimental data points are taken from STAR [46, 48]. The figure is adopted… view at source ↗
Figure 20
Figure 20. Figure 20: SMASH results for the directed flow v1 for Z = 1 for different EoS as a function of normalized rapidity y 0 (left) and transverse momentum pT (right) compared to the FOPI data [119] for Au+Au collisions at Ekin = 0.4 AGeV. The figure is adopted from Ref. [35]. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 (0) T p −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 2 v H, κ=380 MeV HM, κ=380 MeV HMS , κ=380 MeV MM, κ=290 MeV SM, κ=215 Me… view at source ↗
Figure 21
Figure 21. Figure 21: SMASH results for the elliptic flow v2 for different EoS as a function of transverse momentum pT at Ekin = 0.4 AGeV (left) and Ekin = 1.0 AGeV (right) compared to FOPI data [120]. Here ”HMs” stands for Hard EoS with momentum dependent potentials and the stochastic collision criterion. Right plot: the elliptic flow coefficient for Z = 1 particles as a function of the beam kinetic energy for mid-central Au+… view at source ↗
Figure 22
Figure 22. Figure 22: Comparison of EoS - a pressure as a function of the baryon density - for symmetric nuclear matter at vanishing temperature recon￾structed via Bayesian analysis by SMASH (blue line) to the estimate from the BUU model by Danielewicz et al. [80] (aria bounded by or￾ange line) and the IQMD model by Huth et al. [122] (brown area). The figure is adopted from Ref. [36]. A similar trend has been found by the SMAS… view at source ↗

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Works this paper leans on

122 extracted references · 82 linked inside Pith

  1. [1]

    Gustafsson et al., Phys

    H.A. Gustafsson et al., Phys. Rev. Lett.52, 1590 (1984)

    1984

  2. [2]

    Koehn et al

    H. Koehn et al. (2024),2402.04172

    Pith/arXiv arXiv 2024

  3. [3]

    F. Ozel, D. Psaltis, S. Ransom, P. Demorest, M. Alford, Astrophys. J. Lett.724, L199 (2010),1010.5790

    Pith/arXiv arXiv 2010

  4. [4]

    Lastowiecki, D

    R. Lastowiecki, D. Blaschke, H. Grigorian, S. Typel, Acta Phys. Polon. Supp.5, 535 (2012),1112.6430

    Pith/arXiv arXiv 2012

  5. [5]

    Bogdanov et al., Astrophys

    S. Bogdanov et al., Astrophys. J. Lett.914, L15 (2021), 2104.06928

    Pith/arXiv arXiv 2021

  6. [6]

    Bogdanov et al., Astrophys

    S. Bogdanov et al., Astrophys. J. Lett.887, L25 (2019), 1912.05706

    Pith/arXiv arXiv 2019

  7. [7]

    Bogdanov et al., Astrophys

    S. Bogdanov et al., Astrophys. J. Lett.887, L26 (2019), 1912.05707

    Pith/arXiv arXiv 2019

  8. [8]

    Raaijmakers et al., Astrophys

    G. Raaijmakers et al., Astrophys. J. Lett.887, L22 (2019), 1912.05703

    Pith/arXiv arXiv 2019

  9. [9]

    Bauswein, H.T

    A. Bauswein, H.T. Janka, K. Hebeler, A. Schwenk, Phys. Rev. D86, 063001 (2012),1204.1888

    Pith/arXiv arXiv 2012

  10. [10]

    E.R. Most, A. Motornenko, J. Steinheimer, V . Dexheimer, M. Hanauske, L. Rezzolla, H. Stoecker, Phys. Rev. D107, 043034 (2023),2201.13150

    Pith/arXiv arXiv 2023

  11. [11]

    Abbott et al

    B.P. Abbott et al. (LIGO Scientific, Virgo), Phys. Rev. Lett.121, 161101 (2018),1805.11581

    Pith/arXiv arXiv 2018

  12. [12]

    Abbott et al

    B.P. Abbott et al. (LIGO Scientific, Virgo), Astrophys. J. Lett.892, L3 (2020),2001.01761

    Pith/arXiv arXiv 2020

  13. [13]

    Botermans, R

    W. Botermans, R. Malfliet, Phys. Rept.198, 115 (1990)

    1990

  14. [14]

    Fuchs, T

    C. Fuchs, T. Waindzoch, A. Faessler, D.S. Kosov, Phys. Rev. C58, 2022 (1998)

    2022

  15. [15]

    J.W. Holt, N. Kaiser, Phys. Rev. C95, 034326 (2017), 1612.04309

    Pith/arXiv arXiv 2017

  16. [16]

    C. Gale, G. Bertsch, S. Das Gupta, Phys. Rev. C35, 1666 (1987)

    1987

  17. [17]

    Aichelin, A

    J. Aichelin, A. Rosenhauer, G. Peilert, H. Stoecker, W. Greiner, Phys. Rev. Lett.58, 1926 (1987)

    1926

  18. [18]

    C.M. Ko, Q. Li, R.C. Wang, Phys. Rev. Lett.59, 1084 (1987)

    1987

  19. [19]

    Aichelin, Phys

    J. Aichelin, Phys. Rept.202, 233 (1991)

    1991

  20. [20]

    Weber, B

    K. Weber, B. Blaettel, W. Cassing, H.C. Doenges, A. Lang, T. Maruyama, U. Mosel, Nucl. Phys. A552, 571 (1993)

    1993

  21. [21]

    P.K. Sahu, A. Hombach, W. Cassing, U. Mosel, Nucl. Phys. A640, 493 (1998),nucl-th/9801043

    Pith/arXiv arXiv 1998

  22. [22]

    Danielewicz, R.A

    P. Danielewicz, R.A. Lacey, P.B. Gossiaux, C. Pinken- burg, P. Chung, J.M. Alexander, R.L. McGrath, Phys. Rev. Lett.81, 2438 (1998),nucl-th/9803047

    Pith/arXiv arXiv 1998

  23. [23]

    Kuhrts, M

    C. Kuhrts, M. Beyer, P. Danielewicz, G. Ropke, Phys. Rev. C63, 034605 (2001),nucl-th/0009037

    Pith/arXiv arXiv 2001

  24. [24]

    P.K. Sahu, W. Cassing, U. Mosel, A. Ohnishi, Nucl. Phys. A672, 376 (2000),nucl-th/9907002

    Pith/arXiv arXiv 2000

  25. [25]

    Cassing, E.L

    W. Cassing, E.L. Bratkovskaya, S. Juchem, Nucl. Phys. A674, 249 (2000),nucl-th/0001024

    Pith/arXiv arXiv 2000

  26. [26]

    P.K. Sahu, W. Cassing, Nucl. Phys. A712, 357 (2002), nucl-th/0208002

    Pith/arXiv arXiv 2002

  27. [27]

    Y . Nara, T. Maruyama, H. Stoecker, Phys. Rev. C102, 024913 (2020),2004.05550

    Pith/arXiv arXiv 2020

  28. [28]

    Molitoris, D

    J.J. Molitoris, D. Hahn, H. Stoecker, Nucl. Phys. A447, 13C (1986)

    1986

  29. [29]

    Cooper, S

    E.D. Cooper, S. Hama, B.C. Clark, Phys. Rev. C80, 034605 (2009)

    2009

  30. [30]

    Le F `evre, Y

    A. Le F `evre, Y . Leifels, W. Reisdorf, J. Aichelin, C. Hart- nack, Nucl. Phys. A945, 112 (2016),1501.05246

    Pith/arXiv arXiv 2016

  31. [31]

    Hillmann, J

    P. Hillmann, J. Steinheimer, T. Reichert, V . Gaebel, M. Bleicher, S. Sombun, C. Herold, A. Limphirat, J. Phys. G47, 055101 (2020),1907.04571

    Pith/arXiv arXiv 2020

  32. [32]

    Welke, M

    G.M. Welke, M. Prakash, T.T.S. Kuo, S. Das Gupta, C. Gale, Phys. Rev. C38, 2101 (1988)

    1988

  33. [33]

    Gale, G.M

    C. Gale, G.M. Welke, M. Prakash, S.J. Lee, S. Das Gupta, Phys. Rev. C41, 1545 (1990)

    1990

  34. [34]

    Zhang, S

    J.m. Zhang, S. Das Gupta, C. Gale, Phys. Rev. C50, 1617 (1994),nucl-th/9405006

    Pith/arXiv arXiv 1994

  35. [35]

    Tarasovi ˇcov´a, J

    L.A. Tarasovi ˇcov´a, J. Mohs, A. Andronic, H. Elfner, K.H. Kampert (2024),2405.09889

    Pith/arXiv arXiv 2024

  36. [36]

    J. Mohs, S. Spies, H. Elfner (2024),2409.16927

    Pith/arXiv arXiv 2024

  37. [37]

    Cassing, A

    W. Cassing, A. Lang, S. Teis, K. Weber, Nucl. Phys. A 545, 123C (1992)

    1992

  38. [38]

    Bleicher, E

    M. Bleicher, E. Bratkovskaya, Prog. Part. Nucl. Phys. 122, 103920 (2022)

    2022

  39. [39]

    Wolter et al

    H. Wolter et al. (TMEP), Prog. Part. Nucl. Phys.125, 103962 (2022),2202.06672

    arXiv 2022

  40. [40]

    Sorensen et al., Prog

    A. Sorensen et al., Prog. Part. Nucl. Phys.134, 104080 (2024),2301.13253

    Pith/arXiv arXiv 2024

  41. [41]

    Mekjian, L

    A.Z. Mekjian, L. Zamick, Phys. Rev. C85, 044318 (2012),1112.0457

    Pith/arXiv arXiv 2012

  42. [42]

    Adamczewski-Musch et al

    J. Adamczewski-Musch et al. (HADES), Phys. Rev. Lett. 125, 262301 (2020),2005.12217

    Pith/arXiv arXiv 2020

  43. [43]

    Adamczewski-Musch et al

    J. Adamczewski-Musch et al. (HADES), Eur. Phys. J. A 59, 80 (2023),2208.02740

    Pith/arXiv arXiv 2023

  44. [44]

    Reisdorf et al

    W. Reisdorf et al. (FOPI), Nucl. Phys. A876, 1 (2012), 1112.3180

    Pith/arXiv arXiv 2012

  45. [45]

    Abdulhamid et al

    M. Abdulhamid et al. (STAR), Phys. Rev. C110, 054911 (2024),2311.11020

    arXiv 2024

  46. [46]

    Abdallah et al

    M.S. Abdallah et al. (STAR), Phys. Lett. B827, 137003 (2022),2108.00908

    arXiv 2022

  47. [47]

    Abdulhamid et al

    M.I. Abdulhamid et al. (STAR), JHEP10, 139 (2024), 2407.10110

    Pith/arXiv arXiv 2024

  48. [48]

    Abdallah et al

    M.S. Abdallah et al. (STAR), Phys. Lett. B827, 136941 (2022),2112.04066

    arXiv 2022

  49. [49]

    Abdallah et al

    M. Abdallah et al. (STAR), Phys. Rev. Lett.128, 202301 (2022),2110.09513

    arXiv 2022

  50. [50]

    Aboona et al

    B. Aboona et al. (STAR), Phys. Rev. Lett.130, 212301 (2023),2211.16981

    arXiv 2023

  51. [51]

    Reisdorf et al

    W. Reisdorf et al. (FOPI), Nucl. Phys. A848, 366 (2010), 1005.3418

    Pith/arXiv arXiv 2010

  52. [52]

    Anticic et al

    T. Anticic et al. (NA49), Phys. Rev. C69, 024902 (2004)

    2004

  53. [53]

    Anticic et al

    T. Anticic et al. (NA49), Phys. Rev. C94, 044906 (2016), 1606.04234 18 E. Bratkovskaya and J. Aichelin: Study on equation-of-state with light clusters and hypernuclei

    Pith/arXiv arXiv 2016

  54. [55]

    Adam et al

    J. Adam et al. (ALICE), Phys. Rev. C93, 024917 (2016), 1506.08951

    Pith/arXiv arXiv 2016

  55. [56]

    Adam et al

    J. Adam et al. (STAR), Phys. Rev. C99, 064905 (2019), 1903.11778

    Pith/arXiv arXiv 2019

  56. [57]

    Adamczewski-Musch et al

    J. Adamczewski-Musch et al. (HADES), Eur. Phys. J. A 56, 259 (2020),2005.08774

    Pith/arXiv arXiv 2020

  57. [58]

    Abdulhamid et al

    M. Abdulhamid et al. (STAR), Phys. Rev. Lett.130, 202301 (2023),2209.08058

    arXiv 2023

  58. [59]

    Andronic, P

    A. Andronic, P. Braun-Munzinger, J. Stachel, H. Stocker, Phys. Lett. B697, 203 (2011),1010.2995

    Pith/arXiv arXiv 2011

  59. [60]

    Butler, C.A

    S.T. Butler, C.A. Pearson, Phys. Rev.129, 836 (1963)

    1963

  60. [61]

    Zhu, C.M

    L. Zhu, C.M. Ko, X. Yin, Phys. Rev. C92, 064911 (2015), 1510.03568

    Pith/arXiv arXiv 2015

  61. [62]

    W. Zhao, C. Shen, C.M. Ko, Q. Liu, H. Song, Phys. Rev. C102, 044912 (2020),2009.06959

    Pith/arXiv arXiv 2020

  62. [63]

    K.J. Sun, R. Wang, C.M. Ko, Y .G. Ma, C. Shen (2021), 2106.12742

    Pith/arXiv arXiv 2021

  63. [64]

    Sombun, K

    S. Sombun, K. Tomuang, A. Limphirat, P. Hillmann, C. Herold, J. Steinheimer, Y . Yan, M. Bleicher, Phys. Rev. C99, 014901 (2019),1805.11509

    Pith/arXiv arXiv 2019

  64. [65]

    Kireyeu, J

    V . Kireyeu, J. Steinheimer, J. Aichelin, M. Bleicher, E. Bratkovskaya, Phys. Rev. C105, 044909 (2022), 2201.13374

    Pith/arXiv arXiv 2022

  65. [66]

    Aichelin, E

    J. Aichelin, E. Bratkovskaya, A. Le F `evre, V . Kireyeu, V . Kolesnikov, Y . Leifels, V . V oronyuk, G. Coci, Phys. Rev. C101, 044905 (2020),1907.03860

    Pith/arXiv arXiv 2020

  66. [67]

    Gl ¨aßel, V

    S. Gl ¨aßel, V . Kireyeu, V . V oronyuk, J. Aichelin, C. Blume, E. Bratkovskaya, G. Coci, V . Kolesnikov, M. Winn, Phys. Rev. C105, 014908 (2022), 2106.14839

    Pith/arXiv arXiv 2022

  67. [68]

    G. Coci, S. Gl ¨aßel, V . Kireyeu, J. Aichelin, C. Blume, E. Bratkovskaya, V . Kolesnikov, V . V oronyuk, Phys. Rev. C108, 014902 (2023),2303.02279

    Pith/arXiv arXiv 2023

  68. [69]

    Danielewicz, G.F

    P. Danielewicz, G.F. Bertsch, Nucl. Phys. A533, 712 (1991)

    1991

  69. [70]

    Danielewicz, Q.b

    P. Danielewicz, Q.b. Pan, Phys. Rev. C46, 2002 (1992)

    2002

  70. [71]

    Oliinychenko, C

    D. Oliinychenko, C. Shen, V . Koch, Phys. Rev. C103, 034913 (2021),2009.01915

    Pith/arXiv arXiv 2021

  71. [72]

    Staudenmaier, D

    J. Staudenmaier, D. Oliinychenko, J.M. Torres- Rincon, H. Elfner, Phys. Rev. C104, 034908 (2021), 2106.14287

    Pith/arXiv arXiv 2021

  72. [73]

    Wang, Y .G

    R. Wang, Y .G. Ma, L.W. Chen, C.M. Ko, K.J. Sun, Z. Zhang, Phys. Rev. C108, L031601 (2023), 2305.02988

    Pith/arXiv arXiv 2023

  73. [74]

    M. Ege, J. Mohs, J. Staudenmaier, H. Elfner (2024), 2409.04209

    Pith/arXiv arXiv 2024

  74. [75]

    Kireyeu, G

    V . Kireyeu, G. Coci, S. Gl ¨aßel, J. Aichelin, C. Blume, E. Bratkovskaya, Phys. Rev. C109, 044906 (2024)

    2024

  75. [76]

    Kireyeu, V

    V . Kireyeu, V . V oronyuk, M. Winn, S. Gl¨aßel, J. Aiche- lin, C. Blume, E. Bratkovskaya, G. Coci, J. Zhao (2024), 2411.04969

    Pith/arXiv arXiv 2024

  76. [77]

    Zhou et al

    Y . Zhou et al. (2025),2507.14255

    Pith/arXiv arXiv 2025

  77. [78]

    Steinheimer, T

    J. Steinheimer, T. Reichert, Y . Nara, M. Bleicher (2024), 2410.01742

    Pith/arXiv arXiv 2024

  78. [79]

    Danielewicz, Nucl

    P. Danielewicz, Nucl. Phys. A673, 375 (2000), nucl-th/9912027

    Pith/arXiv arXiv 2000

  79. [80]

    Danielewicz, R

    P. Danielewicz, R. Lacey, W.G. Lynch, Science298, 1592 (2002),nucl-th/0208016

    Pith/arXiv arXiv 2002

  80. [81]

    Hartnack, R.K

    C. Hartnack, R.K. Puri, J. Aichelin, J. Konopka, S.A. Bass, H. Stoecker, W. Greiner, Eur. Phys. J. A1, 151 (1998),nucl-th/9811015

    Pith/arXiv arXiv 1998

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 4, 2026.