Pith. sign in

REVIEW 2 major objections 7 minor 89 references

Machine learning the impact parameter in heavy-ion collisions at $\sqrt{s_{\rm NN}}$ = 4 and 11 GeV: a cross-check study with UrQMD, AMPT, and JAM

T0 review · 2 major / 7 minor · reviewed 2026-07-09 · glm-5.2

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read ML pins collision geometry to 0.3 fm across rival models

desk verdict Solid cross-model ML study for impact parameter, but the read the letter →

arxiv 2607.06897 v1 pith:FETX3MPL submitted 2026-07-08 nucl-th

Xiaoqing Yue , Guojun Wei , Yongjia Wang , Zhilong Li , Pengcheng Li , Haojie Xu , Xiangrong Zhu , Qingfeng Li
show 2 more authors
Fuhu Liu Yasushi Nara
This is my paper · ORCID
classification nucl-th PACS 25.75.-q25.75.Ag25.75.Gz24.10.Lx
keywords heavy-ioncollisionsimpactparametermachinelearningLightGBMtransportmodelscentralitydeterminationUrQMDAMPT
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether a machine-learning model trained on simulated heavy-ion collision data from one transport model can reliably predict the impact parameter (the transverse separation of the two colliding nuclei) when tested on data from a different transport model. This matters because the impact parameter is not directly measurable in experiment and is conventionally inferred through model-dependent fits that fail when the simulation model changes. The authors train a gradient-boosted-tree algorithm (LightGBM) on six pion-related observables — charged pion yields, mid-rapidity yields, and total transverse momenta — generated by three independent transport models (UrQMD, AMPT, and JAM) at collision energies of 4 and 11 GeV. They find that the mean absolute error in reconstructing the impact parameter stays between 0.2 and 0.4 femtometers even in cross-model tests, where the training model differs from the testing model. By contrast, the standard polynomial-fit method relating pion multiplicity to impact parameter collapses entirely in cross-model application. In a classification task, the ML method assigns events to six centrality classes with roughly one-percent-level accuracy across models. An unsupervised K-means clustering on the same observables, given no impact-parameter labels at all, autonomously separates events into six clusters that correspond to physically meaningful centrality ranges. The central claim is that the ML algorithm learns a model-independent mapping from pion observables to collision geometry, and that this mapping is robust enough to eventually be applied to real experimental data.

What carries the argument

LightGBM (gradient-boosted decision trees) for supervised regression and classification; K-means for unsupervised clustering; six input features: charged pion yields, mid-rapidity charged pion yields, and total transverse momenta of charged pions; three transport models (UrQMD, AMPT, JAM) with different initialization and mean-field configurations; mean absolute error (MAE) and signed mean error as evaluation metrics.

What would settle it

Train the ML algorithm on data from two of the three transport models and test on the third, then repeat with a fourth transport model (e.g., SMASH or GiBUU) that uses substantially different hadronic physics. If the MAE jumps well above 0.4 fm, the claimed robustness is an artifact of the tested model space rather than a model-independent physical mapping.

Watch

Extended reading notes

Core claim

A gradient-boosted-tree ML algorithm trained on six pion-related observables from one transport model predicts the impact parameter of heavy-ion collisions at 4 and 11 GeV with 0.2–0.4 fm accuracy even when tested on data from different transport models, while the conventional polynomial-fit method fails in this cross-model setting. Unsupervised K-means clustering on the same observables recovers six centrality classes without any model-based binning.

Load-bearing premise

The paper assumes that six pion-related observables contain enough information for the ML algorithm to learn a genuinely model-independent mapping to the impact parameter, rather than learning model-specific patterns that happen to correlate with the impact parameter across the three models tested. The cross-model robustness is demonstrated only within a limited family of transport models that may share hidden commonalities.

Editorial extensions

If this is right

  • If the cross-model robustness holds, the method could replace Glauber-model-based centrality determination at intermediate energies where the eikonal approximation underlying the Glauber model is questionable.
  • The unsupervised K-means result suggests that centrality structure is encoded in pion observables in a way that does not require a model to define bin boundaries, which could make centrality calibration less model-dependent in future experiments at FAIR/CBM, NICA/MPD, and STAR-FXT.
  • The approach could be extended to additional observables (light charged particle yields, correlations) and additional transport models to further test whether the learned mapping is genuinely model-independent or an artifact of the limited model space tested.
  • If the method generalizes to real experimental data, it would reduce one of the dominant systematic uncertainties in extracting nuclear equation-of-state properties from heavy-ion collision measurements.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The claim of model-independence rests on three transport models that share underlying physics assumptions; a truly model-independent mapping would need to be validated against models with more divergent physics, such as those incorporating different baryon transport or resonance dynamics.
  • The six pion observables may contain model-specific correlations that happen to be consistent across the tested models but could break when applied to experimental data where detector effects, acceptance cuts, and background processes introduce correlations absent from the simulations.
  • If the ML algorithm is learning a physical relationship rather than model noise, one would expect the learned feature importances to reflect known physics — for instance, that multiplicity and transverse momentum carry complementary geometric information — which could be tested by examining the learned decision-tree splits.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 7 minor

Summary. This manuscript applies supervised (LightGBM regression and classification) and unsupervised (K-means clustering) machine-learning methods to reconstruct the impact parameter in Au+Au collisions at sqrt(s_NN) = 4 and 11 GeV. The central result is that LightGBM achieves MAE of 0.2–0.4 fm even when trained on data from one transport model (UrQMD, AMPT, or JAM) and tested on another, whereas a conventional polynomial fit to charged-pion multiplicity fails in cross-model application. The K-means algorithm is also shown to autonomously partition events into six centrality classes. The methodology is clearly described, the cross-model validation is a well-designed test of robustness, and the comparison with a traditional baseline is appropriate. The paper represents a useful contribution to the growing literature on ML-based centrality determination at low-to-intermediate energies.

Significance. The cross-model validation across three mainstream transport models (UrQMD, AMPT, JAM) with different initialization and propagation modes is a genuine strength and goes beyond single-model ML studies. The finding that ML generalizes across models where polynomial fitting does not is the key novel result. The unsupervised K-means analysis provides an additional, model-independent cross-check. The six input features (charged-pion yields, mid-rapidity yields, and total transverse momenta) are experimentally accessible, enhancing practical relevance for STAR-FXT, NICA/MPD, and FAIR/CBM.

major comments (2)
  1. Section III.A, Figs. 4–5: The central claim of cross-model robustness rests on the observation that LightGBM achieves low MAE even when trained on one model and tested on another, despite the fact that the six input features are absolute quantities whose distributions differ by up to ~60% across models (Fig. 1, Sec. II.A). The polynomial-fit baseline fails precisely because of these scale differences, yet ML with the same absolute features succeeds. The paper does not investigate the mechanism behind this success. A feature-importance analysis (e.g., SHAP or gain-based importance from LightGBM) would help clarify whether the algorithm is exploiting inter-feature correlations that reflect genuine physics or shared model artifacts. Without this, it is difficult to assess whether the cross-model MAE reflects genuine model independence or the narrowness of the tested model space, which is a載
  2. Section III.C, Fig. 10: The K-means clustering results are presented only for UrQMD/CH data. Since the paper's central theme is cross-model robustness, the absence of K-means results for AMPT and JAM is a gap. Showing that the unsupervised clustering produces comparable centrality partitions across at least one additional model would strengthen the claim that the method is model-independent. At minimum, the authors should discuss whether the cluster centroids and b-distributions are expected to be stable across models given the known yield differences shown in Fig. 1.
minor comments (7)
  1. Section II.A: The selection of six pion-related features is motivated, but the statement that observables like large-fragment yields and charged-particle multiplicity are 'highly model-dependent' and therefore excluded could be strengthened by briefly quantifying or citing the model dependence.
  2. Section II.B: The statement that varying LightGBM hyperparameters 'did not significantly alter the results' should be supported with at least one quantitative example (e.g., MAE change for a specific parameter variation) in a footnote or supplementary table.
  3. Section III.B, Figs. 6–9: The claim that deviations in centrality-class fractions are 'controlled at around 1%' is stated in the text but not tabulated. A small table comparing predicted vs. true fractions for each class and model pair would make this claim verifiable.
  4. The abstract states the method 'has the potential to be generalized to handle real experimental data.' Given that no detector effects, acceptance cuts, or efficiency corrections are included in the present study, this claim should be softened to acknowledge these missing elements explicitly.
  5. Section I: The phrase 'the classical picture is no longer valid' regarding the de Broglie wavelength at low energies is somewhat imprecise; a brief clarification of the energy scale at which this concern applies versus the energies studied here (4 and 11 GeV) would be appropriate.
  6. Figures 4 and 5: The panel labels (a)–(l) are small and the distinction between solid (ML) and dashed (polynomial) lines is difficult to read in the peripheral region where statistics are low. Enlarging the legend or using thicker lines would improve readability.
  7. Reference [21] is cited with a 2026 publication date and arXiv number 2601.20491; the editor should verify the publication status.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: cross-model ML validation is independently grounded, with only minor methodological self-citation.

full rationale

The paper's central claim is that LightGBM achieves MAE 0.2-0.4 fm for impact-parameter reconstruction even when trained on one transport model (e.g., UrQMD/CH) and tested on data from a different model (e.g., AMPT, JAM). This claim is tested against genuinely external benchmarks: the test data are generated by independent transport models with different physics implementations, and the ML algorithm is never trained on the test data. The polynomial-fit baseline (Eq. 2) is a fair, non-circular comparison that fails across models as expected. The self-citations (Refs. 68, 69) are to prior methodological work by some of the same authors, but they establish the use of LightGBM for impact-parameter determination—they do not constitute a load-bearing argument that forces the present result by construction. The K-means clustering result (Sec. III.C) is an unsupervised analysis that does not rely on predefined model-based binning, further supporting independence. No step in the derivation chain reduces to its own inputs by definition or by fitted-parameter renaming. The paper's limitations (lack of mechanistic explanation for cross-model success, narrowness of tested model space) are correctness and generalization concerns, not circularity.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper does not invent new physical entities or forces. It uses existing ML algorithms (LightGBM, K-means) and existing transport models. The free parameters are standard ML configuration choices and predefined centrality bins.

free parameters (3)
  • LightGBM hyperparameters (num_boost_round, num_leaves, max_depth) = default values
    The paper states these are set to default values and that varying them did not significantly alter results, but they are still free choices in the pipeline.
  • Number of K-means clusters (k) = 6
    Chosen to match the six centrality classes defined in Table I. This is a parameter choice aligned with experimental convention rather than derived from data.
  • Centrality class boundaries (b_min, b_max) = See Table I
    The impact parameter intervals for the six classes are predefined based on geometric considerations, not derived from the data.
assumptions (3)
  • domain assumption The true impact parameter b in transport model simulations is a well-defined ground truth label.
    The supervised learning approach relies entirely on the transport model's generated b being the correct target to predict.
  • domain assumption Pion observables (yield, mid-rapidity yield, total transverse momentum) are measurable on an event-by-event basis in experiments.
    Stated in Sec II.A as the reason for selecting these features, bridging the gap between simulation and experimental applicability.
  • ad hoc to paper The three transport models used (UrQMD, AMPT, JAM) span a sufficiently large model space to claim 'robustness'.
    The claim of strong robustness depends on these models being representative of the diversity of possible physics, yet they share underlying assumptions (e.g., Woods-Saxon distributions).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Machine learning the impact parameter in heavy-ion collisions at $\sqrt{s_{\rm NN}}$ = 4 and 11 GeV: a cross-check study with UrQMD, AMPT, and JAM." pith.science (2026). https://pith.science/paper/FETX3MPL

@misc{pith2026260706897,
  author       = {Pith},
  title        = {Pith review of: Machine learning the impact parameter in heavy-ion collisions at $\sqrts_\rm NN$ = 4 and 11 GeV: a cross-check study with UrQMD, AMPT, and JAM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FETX3MPL}},
  note         = {Machine review of arXiv:2607.06897}
}
abstract

By generating heavy-ion collision data with the ultrarelativistic quantum molecular dynamics (UrQMD) model, a multiphase transport (AMPT) model, and the JAM model, the impact parameter ($b$) in Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 4 and 11 GeV is reconstructed using supervised learning and unsupervised learning in machine learning (ML). In supervised learning, the performance of ML algorithm is cross-checked by using data obtained from these three transport models. It is found that the typical mean absolute error (MAE) which measures the average magnitude of the absolute difference between the true and predicted $b$ is between 0.2-0.4 fm, even when training ML algorithm with data generated from one model but testing with data from others. While the conventional method (i.e., a polynomial fit to multiplicity as a function of $b$) only works for data generated from the same model. In the classification task, the present ML-based method also shows significantly superior results compared to the traditional approach. In unsupervised learning, the K-means clustering algorithm is used to partition collision events directly from experimental-style observables, showing that the algorithm autonomously identifies six clusters corresponding to different centrality classes without relying on predefined model-based binning. Our study demonstrates the strong robustness of using an ML algorithm trained on transport-model data for impact-parameter determination, and indicates that this method has the potential to be generalized to handle real experimental data.

Figures

Figures reproduced from arXiv: 2607.06897 by the authors.

Figure 1
Figure 1. The average number of charged π (⟨Nπ± ⟩) produced in Au + Au collisions at √ sNN=4 (upper panel) and 11 GeV (lower panel) is plotted as a function of impact parameter. The curves and shaded bands denote the mean value and the standard deviation, respectively. The standard deviation denotes variation from event to event. The inset plot shows the impact parameter dependence of the ratio between the standard deviation … view at source ↗
Figure 3
Figure 3. The MAE is plotted as a function of √ sNN. Panel (a) shows the results when the training and the test data are generated from the same model. Panel (b) and (c) are the results when the training data are generated from UrQMD/CH and AMPT, respectively. and that of JAM/C and JAM/M lie between these two groups. This ordering corresponds to the trend of the ratio σ observed in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Mean error of estimated impact parameter as a function of impact parameter at [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: Same as Fig. 4, but for the mean error of estimated impact parameter as a function of impact parameter in [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: The distributions of impact parameter for Au+Au collision at [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Same as Fig. 6, but at [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: The distribution of the impact parameter for Au+Au collision at [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Same as Fig. 8, but at [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: K-means clustering results for Au+Au collisions at [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

89 extracted references · 89 canonical work pages

  1. [1]

    1331 Project

    In the polynomial-fitting method, the charged-pion yield is used as a centrality-sensitive input feature, and its correlation with the true impact parameter obtained from transport-model simulations is parameterized by a third-order polynomial function, bfit =f(x) =gx 3 +hx 2 +ix+j,(2) wherexdenotes the charged-pion yield, andg,h,i, and jare the fitting p...

    work page

  2. [2]

    Determination of the Equation of State of Dense Matter

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

    work page Pith review arXiv 2002

  3. [3]

    The phase diagram of dense QCD

    K. Fukushima and T. Hatsuda, Rept. Prog. Phys.74, 014001 (2011), arXiv:1005.4814 [hep-ph]

    work page Pith review arXiv 2011

  4. [4]

    Dense Nuclear Matter Equation of State from Heavy-Ion Collisions

    A. Sorensenet al., Prog. Part. Nucl. Phys.134, 104080 (2024), arXiv:2301.13253 [nucl-th]

    work page Pith review arXiv 2024

  5. [5]

    Guoet al., Eur

    D. Guoet al., Eur. Phys. J. A60, 36 (2024)

    work page 2024

  6. [6]

    Klochkov, C

    V. Klochkov, C. Collaboration,et al., Nuclear Physics A 1005, 121945 (2021). 11

    work page 2021

  7. [7]

    Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program

    L. Adamczyket al.(STAR), Phys. Rev. C96, 044904 (2017), arXiv:1701.07065 [nucl-ex]

    work page Pith review arXiv 2017

  8. [8]

    Abgaryanet al.(MPD), Eur

    V. Abgaryanet al.(MPD), Eur. Phys. J. A58, 140 (2022), arXiv:2202.08970 [physics.ins-det]

    work page arXiv 2022

Show all 89 references
  1. [9]

    Syresinet al., Chin

    E. Syresinet al., Chin. Phys. C49, 074003 (2025)

    2025

  2. [10]

    Zhu, X.-Y

    J. Zhu, X.-Y. Wu, and G.-Y. Qin, Chin. Phys. C49, 044103 (2025), arXiv:2401.15536 [hep-ph]

    2025 arXiv

  3. [11]

    Wolteret al.(TMEP), Prog

    H. Wolteret al.(TMEP), Prog. Part. Nucl. Phys.125, 103962 (2022), arXiv:2202.06672 [nucl-th]

    2022

  4. [12]

    Adamczyket al.(STAR), Phys

    L. Adamczyket al.(STAR), Phys. Rev. Lett.112, 032302 (2014), arXiv:1309.5681 [nucl-ex]

    2014 arXiv

  5. [13]

    Zhang, Y

    X. Zhang, Y. Zhang, X. Luo, and N. Xu, Chin. Phys. C 50, 011003 (2026), arXiv:2506.18832 [nucl-ex]

    2026

  6. [14]

    Cavata, M

    C. Cavata, M. Demoulins, J. Gosset, M. C. Lemaire, D. L’Hote, J. Poitou, and O. Valette, Phys. Rev. C42, 1760 (1990)

    1990

  7. [15]

    M. L. Miller, K. Reygers, S. J. Sanders, and P. Steinberg, Ann. Rev. Nucl. Part. Sci.57, 205 (2007), arXiv:nucl- ex/0701025

    2007

  8. [16]

    Adamczewski-Muschet al.(HADES), Eur

    J. Adamczewski-Muschet al.(HADES), Eur. Phys. J. A 54, 85 (2018), arXiv:1712.07993 [nucl-ex]

    2018 arXiv

  9. [17]

    B. I. Abelevet al.(STAR), Phys. Rev. C81, 024911 (2010), arXiv:0909.4131 [nucl-ex]

    2010 arXiv

  10. [18]

    Adamczyket al.(STAR), Phys

    L. Adamczyket al.(STAR), Phys. Rev. C86, 054908 (2012), arXiv:1206.5528 [nucl-ex]

    2012 arXiv

  11. [19]

    Adamet al.(STAR), Phys

    J. Adamet al.(STAR), Phys. Rev. C101, 024905 (2020), arXiv:1908.03585 [nucl-ex]

    2020

  12. [20]

    Adamet al.(STAR), Phys

    J. Adamet al.(STAR), Phys. Rev. C102, 034909 (2020), arXiv:1906.03732 [nucl-ex]

    2020

  13. [21]

    Abdallahet al.(STAR), Phys

    M. Abdallahet al.(STAR), Phys. Rev. C107, 024908 (2023), arXiv:2209.11940 [nucl-ex]

    2023

  14. [22]

    X. Yue, P. Li, Y. Wang, Q. Li, and F. Liu, Phys. Rev. C113, 024905 (2026), arXiv:2601.20491 [nucl-th]

    2026

  15. [23]

    Lukasiket al., Phys

    J. Lukasiket al., Phys. Rev. C55, 1906 (1997)

    1906

  16. [24]

    Lukasiket al., Phys

    J. Lukasiket al., Phys. Lett. B608, 223 (2005), arXiv:nucl-ex/0410030

    2005 arXiv

  17. [25]

    Schüttaufet al., Nucl

    A. Schüttaufet al., Nucl. Phys. A607, 457 (1996), arXiv:nucl-ex/9606001

    1996 arXiv

  18. [26]

    W.Reisdorfet al.(FOPI),Nucl.Phys.A612,493(1997), arXiv:nucl-ex/9610009

    1997 arXiv

  19. [27]

    Le Fèvre, Y

    A. Le Fèvre, Y. Leifels, W. Reisdorf, J. Aichelin, and C. Hartnack, Nucl. Phys. A945, 112 (2016), arXiv:1501.05246 [nucl-ex]

    2016 arXiv

  20. [28]

    Luo and N

    X. Luo and N. Xu, Nucl. Sci. Tech.28, 112 (2017), arXiv:1701.02105 [nucl-ex]

    2017 arXiv

  21. [29]

    Charged pion production in au+au collision at√sN N = 3.2-4.5 gev with the star detector,

    L. Chen, “Charged pion production in au+au collision at√sN N = 3.2-4.5 gev with the star detector,” Conference report

  22. [30]

    Werner, J

    K. Werner, J. Jahan, I. Karpenko, T. Pierog, M. Stefa- niak, and D. Vintache, Phys. Rev. C111, 014903 (2025), arXiv:2401.11275 [hep-ph]

    2025 arXiv

  23. [31]

    Qu, J.-Y

    S. Qu, J.-Y. Zhang, and M. Bao, Chin. Phys. C49, 104106 (2025)

    2025

  24. [32]

    M. R. Mumpower, T. M. Sprouse, A. E. Lovell, and A. T. Mohan, Phys. Rev. C106, L021301 (2022), arXiv:2203.10594 [nucl-th]

    2022 arXiv

  25. [33]

    Z. Gao, Y. Wang, H. Lü, Q. Li, C. Shen, and L. Liu, Nuclear Science and Techniques32, 109 (2021)

    2021

  26. [34]

    Yüksel, D

    E. Yüksel, D. Soydaner, and H. Bahtiyar, Phys. Rev. C 109, 064322 (2024), arXiv:2401.02824 [nucl-th]

    2024 arXiv

  27. [35]

    Kvasiuk, E

    Y. Kvasiuk, E. Zabrodin, L. Bravina, I. Didur, and M. Frolov, JHEP07, 133 (2020), arXiv:2004.14409 [nucl- th]

    2020 arXiv

  28. [36]

    Wang and Q

    Y. Wang and Q. Li, Front. Phys. (Beijing)18, 64402 (2023), arXiv:2305.16686 [nucl-th]

    2023 arXiv

  29. [37]

    N. K. Patra, T. Malik, H. Pais, K. Zhou, B. K. Agrawal, and C. Providência, Phys. Lett. B865, 139470 (2025), arXiv:2502.20226 [nucl-th]

    2025 arXiv

  30. [38]

    J. M. Wang, X. G. Deng, W. J. Xie, B. A. Li, and Y. G. Ma, Chin. Phys. C49, 124105 (2025), arXiv:2406.07051 [nucl-th]

    2025 arXiv

  31. [39]

    K. F. Pu, H. L. Li, H. L. Lu, and L. G. Pang, Chin. Phys. C47, 054104 (2023), arXiv:2303.03934 [nucl-th]

    2023 arXiv

  32. [40]

    Z. P. Gao, S. Y. Liu, P. W. Wen, Z. H. Liao, Y. Yang, J. Su, Y. J. Wang, and L. Zhu, Phys. Rev. C109, 024601 (2024), arXiv:2306.11236 [nucl-th]

    2024 arXiv

  33. [41]

    Y. Q. Wu, X. Liu, H. L. Li, and F. Q. Wang, (2025), arXiv:2505.24194 [physics.comp-ph]

    2025 arXiv

  34. [42]

    DONG and L

    X. DONG and L. GENG, Atomic Energy Science and Technology57, 679 (2023)

    2023

  35. [43]

    Z. Li, Y. Wang, Q. Li, and B.-f. Lv, Phys. Rev. C112, 014312 (2025)

    2025

  36. [44]

    X. Guo, Z. Chi, and J. Liu, Int. J. Mod. Phys. E35, 2650007 (2026)

    2026

  37. [45]

    W. Li, X. Zhang, and J. Fang, Phys. Scripta99, 045308 (2024)

    2024

  38. [46]

    Z. L. Li, B. F. Lv, Y. J. Wang, and C. Petrache, Chin. Phys. C50, 014107 (2026)

    2026

  39. [47]

    X.-K. Du, P. Guo, X.-H. Wu, and S.-Q. Zhang, Chin. Phys. C47, 074108 (2023)

    2023

  40. [48]

    Huang, K

    M. Huang, K. A. Wendt, N. F. Schunck, and E. M. Holmbeck, Phys. Rev. C112, 034317 (2025), arXiv:2504.09013 [nucl-th]

    2025

  41. [49]

    Bentley, J

    I. Bentley, J. Tedder, M. Gebran, and A. Paul, Phys. Rev. C111, 034305 (2025), arXiv:2412.09504 [nucl-th]

    2025 arXiv

  42. [50]

    Z.-Y. Yuan, D. Bai, Z. Wang, and Z.-Z. Ren, Nucl. Sci. Tech.35, 105 (2024)

    2024

  43. [51]

    Jyothish, G

    K. Jyothish, G. Manangode, and A. K. Rhine Kumar, Phys. Rev. C112, 064309 (2025)

    2025

  44. [52]

    B.-S.CaiandC.-X.Yuan,Nucl.Sci.Tech.34,204(2023), arXiv:2305.05209 [nucl-th]

    2023

  45. [53]

    N. N. Ma, T. L. Zhao, W. X. Wang, and H. F. Zhang, Phys. Rev. C107, 014310 (2023)

    2023

  46. [54]

    Tang and Z

    L. Tang and Z. H. Zhang, Nucl. Sci. Tech.35, 19 (2024), arXiv:2404.12609 [nucl-th]

    2024 arXiv

  47. [55]

    S. M. Shree and M. Balasubramaniam, Eur. Phys. J. A 61, 32 (2025)

    2025

  48. [56]

    Z. M. Niu, H. Z. Liang, B. H. Sun, W. H. Long, and Y. F. Niu, Phys. Rev. C99, 064307 (2019), arXiv:1810.03156 [nucl-th]

    2019 arXiv

  49. [57]

    Z. Li, Z. Gao, L. Liu, Y. Wang, L. Zhu, and Q. Li, Phys. Rev. C109, 024604 (2024), arXiv:2310.04700 [nucl-th]

    2024 arXiv

  50. [58]

    H. Choi, S. Mitra, J. Brodksy, R. Glatt, E. Holmbeck, S. Liu, N. Schunck, A. Sieverding, and K. Wendt, Phys. Rev. C112, 044601 (2025), arXiv:2404.02332 [nucl-th]

    2025

  51. [59]

    S. A. Bass, A. Bischoff, C. Hartnack, J. A. Maruhn, J. Reinhardt, H. Stoecker, and W. Greiner, J. Phys. G20, L21 (1994)

    1994

  52. [60]

    S. A. Bass, A. Bischoff, J. A. Maruhn, H. Stoecker, and W. Greiner, Phys. Rev. C53, 2358 (1996), arXiv:nucl- th/9601024

    1996

  53. [61]

    De Sanctis, M

    J. De Sanctis, M. Masotti, M. Bruno, M. D’Agostino, E. Geraci, G. Vannini, and A. Bonasera, J. Phys. G36, 015101 (2009)

    2009

  54. [62]

    David, M

    C. David, M. Freslier, and J. Aichelin, Phys. Rev. C51, 1453 (1995). 12

    1995

  55. [63]

    K. A. Galaktionov, V. A. Roudnev, and F. F. Valiev, Phys. Atom. Nucl.86, 1426 (2023)

    2023

  56. [64]

    Galaktionov, V

    K. Galaktionov, V. Rudnev, and F. Valiev, Phys. Part. Nucl.54, 446 (2023)

    2023

  57. [65]

    Zhanget al., Phys

    X. Zhanget al., Phys. Rev. C105, 034611 (2022), arXiv:2111.06597 [nucl-th]

    2022 arXiv

  58. [66]

    Xiang, Y.-S

    P. Xiang, Y.-S. Zhao, and X.-G. Huang, Chin. Phys. C 46, 074110 (2022), arXiv:2112.03824 [hep-ph]

    2022 arXiv

  59. [67]

    Mallick, S

    N. Mallick, S. Tripathy, A. N. Mishra, S. Deb, and R. Sahoo, Phys. Rev. D103, 094031 (2021), arXiv:2103.01736 [hep-ph]

    2021 arXiv

  60. [68]

    L. LI, Y. ZHANG, Y. CUI, and J. LIANG, Sci. Sin. Phys. Mech. Astro.52, 252014 (2022)

    2022

  61. [69]

    F. Li, Y. Wang, Z. Gao, P. Li, H. Lü, H. Lv, Q. Li, C. Y. Tsang, and M. B. Tsang, Phys. Rev. C104, 034608 (2021), arXiv:2105.08912 [nucl-th]

    2021 arXiv

  62. [70]

    F. Li, Y. Wang, H. Lü, P. Li, Q. Li, and F. Liu, J. Phys. G47, 115104 (2020), arXiv:2008.11540 [nucl-th]

    2020 arXiv

  63. [71]

    Q. Li, C. Shen, C. Guo, Y. Wang, Z. Li, J. Lukasik, and W. Trautmann, Phys. Rev. C83, 044617 (2011)

    2011

  64. [72]

    Y. Wang, Z. Gao, and Q. Li, Symmetry13, 2172 (2021)

    2021

  65. [73]

    B. Gao, Y. Wang, Z. Gao, and Q. Li, Phys. Lett. B838, 137685 (2023)

    2023

  66. [74]

    Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, Phys. Rev. C72, 064901 (2005), arXiv:nucl-th/0411110

    2005 arXiv

  67. [75]

    Y. Nara, N. Otuka, A. Ohnishi, K. Niita, and S. Chiba, Phys. Rev. C61, 024901 (1999), arXiv:nucl-th/9904059

    1999 arXiv

  68. [76]

    M. Isse, A. Ohnishi, N. Otuka, P. K. Sahu, and Y. Nara, Phys. Rev. C72, 064908 (2005), arXiv:nucl-th/0502058

    2005 arXiv

  69. [77]

    Nara and A

    Y. Nara and A. Ohnishi, Phys. Rev. C105, 014911 (2022), arXiv:2109.07594 [nucl-th]

    2022 arXiv

  70. [78]

    X. Yue, Y. Wang, Q. Li, and F. Liu, Universe8, 491 (2022), arXiv:2209.10923 [nucl-th]

    2022 arXiv

  71. [79]

    J. Xu, T. Song, C. M. Ko, and F. Li, Phys. Rev. Lett. 112, 012301 (2014), arXiv:1308.1753 [nucl-th]

    2014 arXiv

  72. [80]

    Y. Nara, H. Niemi, J. Steinheimer, and H. Stöcker, Phys. Lett. B769, 543 (2017), arXiv:1611.08023 [nucl-th]

    2017 arXiv

  73. [81]

    P. Li, Y. Wang, Q. Li, C. Guo, and H. Zhang, Phys. Rev. C97, 044620 (2018), arXiv:1804.04288 [nucl-th]

    2018 arXiv

  74. [82]

    M. Nan, P. Li, W. Zuo, and Q. Li, Chin. Phys. C49, 094112 (2025), arXiv:2412.13497 [nucl-th]

    2025

  75. [83]

    Liu, J.-P

    Y.-Y. Liu, J.-P. Yang, Y.-J. Wang, Q.-F. Li, Z.-X. Li, C.- J. Xia, and Y.-X. Zhang, Nucl. Sci. Tech.36, 45 (2025)

    2025

  76. [84]

    Y. Liu, Y. Wang, Y. Cui, C.-J. Xia, Z. Li, Y. Chen, Q. Li, and Y. Zhang, Phys. Rev. C103, 014616 (2021), arXiv:2006.15861 [nucl-th]

    2021 arXiv

  77. [85]

    Y. Wang, Z. Gao, H. Lü, and Q. Li, Phys. Lett. B835, 137508 (2022), arXiv:2208.10681 [nucl-th]

    2022 arXiv

  78. [86]

    Omana Kuttan, J

    M. Omana Kuttan, J. Steinheimer, K. Zhou, A. Redel- bach, and H. Stoecker, Phys. Lett. B811, 135872 (2020), arXiv:2009.01584 [hep-ph]

    2020 arXiv

  79. [87]

    Oleksiyuk, J

    I. Oleksiyuk, J. A. Raine, M. Krämer, S. Voloshynovskiy, and T. Golling, JHEP06, 163 (2024), arXiv:2402.17714 [hep-ph]

    2024 arXiv

  80. [88]

    R. V. Lobato, E. V. Chimanski, and C. A. Bertulani, J. Phys. Conf. Ser.2340, 012014 (2022), arXiv:2204.01183 [astro-ph.HE]

    2022 arXiv

  81. [89]

    Zhang, S

    J.-Z. Zhang, S. Guo, L.-L. Zhu, L. Wang, and G.-L. Ma, (2025), arXiv:2510.06691 [nucl-th]

    2025

Pith tools

Reviewed July 9, 2026 · model on record in the stance chip above.