Pith. sign in

REVIEW 4 major objections 5 minor 50 references

Investigation of the neutron-proton effective mass splitting via heavy ion collisions: Constraints and Implications

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read In tin-on-tin collisions, the kinetic-energy slope of the neutron-to-proton yield ratio is dominated by the neutron-proton effective mass splitting, and the data favor $m_n^*>m_p^*$ below 60 MeV but $m_n^*<m_p^*$ above 60 MeV.

desk verdict Useful sensitivity study, but the headline opposite-sign Δm*_np claim is not established: it rests on hand-picked energy windows and a model that misses the full spectrum. read the letter →

arxiv 2506.17973 v1 pith:FECULOZE submitted 2025-06-22 nucl-th nucl-ex

Junping Yang , Meiqi Sun , Ying Cui , Yangyang Liu , Zhuxia Li , Kai Zhao , Yingxun Zhang This is my paper · ORCID
classification nucl-thnucl-ex PACS 21.65.Ef25.70.-z24.10.Cn21.30.Fe
keywords neutron-protoneffectivemasssplittingheavy-ioncollisionssymmetryenergyneutron-to-protonyieldratioSkyrmeinteractionsquantummoleculardynamicsisospinasymmetrytransportmodel
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

This paper tries to pin down the neutron-proton effective mass splitting—how differently neutrons and protons effectively respond to moving through dense nuclear matter—by simulating $^{112,124}$Sn+$^{112,124}$Sn collisions at 120 MeV/u with the improved quantum molecular dynamics model and comparing them with published yield-ratio data. The authors find that the slope of the neutron-to-proton yield ratio with respect to kinetic energy, $S_{n/p}$, is almost linearly controlled by the splitting, with correlation coefficients up to $r=0.928$ for $^{124}$Sn+$^{124}$Sn. The same data favor $m_n^*>m_p^*$ for nucleons emitted below 60 MeV, matching nucleon-nucleus scattering analyses, and $m_n^*

What carries the argument

The load-bearing quantity is $S_{n/p}$, the two-point slope of the logarithm of the neutron-to-proton yield ratio across a kinetic-energy window. The paper uses the proportionality $S_{n/p} \propto -(m/m_s^*)^2 \Delta m^*_{np}$, feeds the model with the inverse-effective-mass difference $f_I = (1/2\delta)(m/m_n^* - m/m_p^*)$ rather than $\Delta m^*_{np}$ directly, and samples 189 parameter sets in the four-dimensional space $S_0$, $L$, $m_s^*$, $f_I$ using Latin hypercube sampling. The transport model is the improved quantum molecular dynamics (ImQMD) model with standard and extended Skyrme momentum-dependent interactions; extended interactions are fit to optical-potential data. The observable is computed for two kinetic windows, 45–60 MeV and 60–95 MeV, chosen from the available data points.

What would settle it

Measure $R_{n/p}$ for $^{124}$Sn+$^{124}$Sn at 120 MeV/u with fine kinetic-energy bins from 40 to 100 MeV; if the slope $S_{n/p}$ does not change sign near 60 MeV when the bins and errors are handled consistently, the central claim of a sign-flipping constraint is refuted.

Watch

Extended reading notes

Core claim

The central claim is that the kinetic-energy slope of the logarithm of the neutron-to-proton yield ratio, $S_{n/p} = \partial \ln R_{n/p}/\partial E_k$, is a direct and nearly linear observable for the neutron-proton effective mass splitting, and that comparing it with existing data from $^{112,124}$Sn+$^{112,124}$Sn at 120 MeV/u yields two different signs depending on the nucleon kinetic energy. With 189 parameter sets covering $S_0$, $L$, $m_s^*$, and $f_I$, the authors obtain $\Delta m^*_{np}/\delta \approx 0.28$–$0.41$ from the 45–60 MeV window and $\Delta m^*_{np}/\delta \approx -0.33$ to $-0.12$ from the 60–95 MeV window. They interpret the sign flip as evidence that the isovector potential is non-monotonic in momentum, a behavior standard Skyrme interactions cannot produce but finite-range Gogny forces already predict. The paper also notes that the model does not exactly reproduce the measured $R_{n/p}$ spectrum, and that a high-momentum tail from short-range correlations in the initial nucleus could compete with the high-energy interpretation.

Load-bearing premise

The load-bearing premise is that the two-point slopes $S_{n/p}$ computed from the published data in the selected 45–60 MeV and 60–95 MeV windows are unbiased probes of $\Delta m^*_{np}$, even though the model does not exactly reproduce the measured neutron-to-proton spectrum and the high-energy window could also be explained by the unmodeled high-momentum tail of the initial nucleon distribution.

Editorial extensions

If this is right

  • Low-energy heavy-ion data and nucleon-nucleus scattering now point the same way, $m_n^*>m_p^*$, which removes one longstanding source of disagreement.
  • Constraints on the effective mass splitting must be quoted per kinetic-energy window rather than as a single number, because the same Skyrme-type interaction cannot describe both windows.
  • The sign reversal at about 60 MeV implies the symmetry (isovector) potential is non-monotonic in nucleon momentum, a qualitative feature that standard Skyrme forces do not contain.
  • The strong, stable correlation between $S_{n/p}$ and $\Delta m^*_{np}$ (up to $r=0.928$) makes the yield-ratio slope a practical observable for future heavy-ion experiments aimed at the effective mass splitting.

Reading between the lines

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

  • If the energy-window dependence is genuine, average constraints on $\Delta m^*_{np}$ obtained from the full spectrum will tend to cancel two opposite signs and could look artificially close to zero; separate bin-by-bin constraints would be the safer route.
  • The correlation analysis suggests that single ratios are far more informative than double ratios for this question, since $S_{DR}$ correlates only weakly with $f_I$; future analyses could therefore prioritize single-ratio measurements.
  • A decisive separation of the two explanations the paper leaves open—non-monotonic mean-field momentum dependence versus short-range-correlation high-momentum tails—would come from a transport calculation that adds high-momentum tails to the initial nucleus while holding $\Delta m^*_{np}$ fixed and checking whether both windows can then be reproduced without a sign flip.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript uses the ImQMD transport model with standard and extended Skyrme momentum-dependent interactions to study the neutron-proton effective mass splitting (Δm*_np). A Latin-hypercube sample of 189 parameter sets is generated in the space (S0, L, m*_s/m, f_I), and the slope S_n/p of the neutron-to-proton yield ratio with respect to kinetic energy is computed in two selected windows, 45–60 MeV and 60–95 MeV, via the two-point formula in Eq. (9). The authors report a strong linear correlation between S_n/p and Δm*_np/δ, with correlation coefficients up to 0.928 for 124Sn+124Sn, and compare the model slopes with data from Ref. [31]. They find that the low-energy window favors m*_n > m*_p with Δm*_np/δ between +0.28 and +0.41, while the high-energy window favors m*_n < m*_p with values between -0.33 and -0.12. The paper concludes that a fixed-Δm*_np Skyrme interaction cannot describe both windows, that the momentum-dependent symmetry potential may be non-monotonic, and that the high-momentum tail of the initial momentum distribution could also affect the high-energy part of the spectrum.

Significance. If the central claim is correct, the analysis would provide a path toward reconciling heavy-ion collision constraints on Δm*_np with nucleon-nucleus scattering analyses, and it would motivate momentum-dependent symmetry potentials beyond the standard Skyrme form. The paper has several genuine strengths: it carries out a multi-parameter sensitivity study rather than varying only L and Δm*_np; it tests both standard and extended Skyrme MDI; it demonstrates with correlation coefficients that S_n/p is much more sensitive to f_I than to S0, L, or m*_s/m in the model; and it applies the correlation to an external dataset rather than only to model-generated data. These features make the correlation analysis useful regardless of the final constraint values. However, the quantitative constraints are only as reliable as the slope extraction from a spectrum that the model itself does not reproduce, and the sign-flip claim is currently sensitive to window choices and to the error prescription used. The paper is therefore significant but not yet conclusive.

major comments (4)
  1. [Section 2, Eq. (9) and Fig. 3] The two-point slopes S_n/p are computed in windows E1=45/E2=60 MeV and E1=60/E2=95 MeV that appear to be selected after inspecting the data, and the two windows share the same 60 MeV boundary, so the low- and high-energy constraints are not independent. Because the model does not exactly reproduce the measured R_n/p spectrum, as the paper itself states in Section 2 and as is visible in Fig. 2, the extracted slopes can be dominated by the model-data mismatch rather than by f_I sensitivity. Please provide a varying-window scan (for example, moving E1 and E2 over the available energy range) or a full-spectrum fit, and show that the sign of the extracted Δm*_np/δ does not depend on the chosen binning.
  2. [Table II and Fig. 4] The two error prescriptions for the data S_n/p lead to constraints that are not mutually consistent. With the error-propagation method, the low-energy Δm*_np/δ values are 0.28±0.27 (standard MDI) and 0.31±0.22 (extended MDI), while the high-energy values are -0.12±0.22 and -0.21±0.23; under this error treatment the low- and high-energy constraints are statistically compatible with each other at roughly the 1σ level. With the alternative hatched-area method the separation is larger. Because the choice of error method changes the conclusion from a clear sign flip to at most a marginal one, the paper should justify one error prescription over the other and report the significance of the observed sign change under both methods.
  3. [Section 2, Fig. 2] The authors state that a χ2 analysis was performed to obtain the optimal parameter sets shown as blue curves in Fig. 2, but the minimized reduced χ2 values are never reported. Since the model visibly fails to reproduce the full R_n/p spectrum, the reader cannot assess whether the remaining model-data discrepancy is small compared with the S_n/p sensitivity to f_I. Please report the χ2 values and residuals, and quantify how much of the two-point slope in each window is attributable to the systematic model deficiency rather than to the f_I dependence.
  4. [Discussion (final paragraphs)] The paper acknowledges that the high-momentum tail of the nucleon momentum distribution in the initial nucleus can influence R_n/p at high kinetic energies and thereby affect the interpretation of the data. Since the high-energy window is precisely where the claim m*_n < m*_p is made, this alternative explanation is load-bearing and needs a quantitative test. Concretely, the authors should vary the initial momentum distribution or remove the highest-energy bins and show that the extracted high-energy Δm*_np/δ remains negative; otherwise the non-monotonic symmetry potential conclusion is not yet supported.
minor comments (5)
  1. [Eq. (6)] The notation f_I = (1/(2δ))(m/m*_n - m/m*_p) = m/m*_s - m/m*_v is surprising because the first expression depends on δ while the second does not; the equivalence should be stated explicitly or the definitions of m*_s and m*_v should be given in the text.
  2. [Fig. 3 caption and text] The text says the high-energy S_H_n/p results are presented in panels (e)-(f), but the Fig. 3 caption indicates panels (a)-(h) are for S_L,H_n/p; please correct the panel reference.
  3. [Section 2, text near Eq. (9)] There is a typo: 'subjec to large uncertainties' should be 'subject to large uncertainties', and 'wealky correlated' should be 'weakly correlated'.
  4. [Fig. 4 and Fig. 5] The correlation coefficient quoted in the text changes between f_I and Δm*_np/δ (r=0.798/0.904 for f_I versus 0.80/0.928 for Δm*_np/δ); since the two quantities are linearly related in the model, this should be clarified so the reader does not perceive an inconsistency.
  5. [Table II] The column headings D_L^Ext, D_L^Stand, D_H^Ext, D_H^Stand are not defined in the caption; please add a sentence explaining that D denotes the data window and Ext/Stand the two MDI forms.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the Δm*_np/δ constraints are read from external R_n/p data and optical-potential calibration; self-citations are not load-bearing, though the two-window slope extraction carries acknowledged model-data caveats.

full rationale

The paper's central constraint on Δm*_np/δ is obtained by comparing ImQMD model calculations (189 parameter sets varying S0, L, m*_s/m, and fI) with the published R_n/p data of Morfouace et al. (Ref. [31]). The extended-MDI coefficients b_I are fitted to the Hama optical potential data (Ref. [38]), an external benchmark, and the prior ranges for the nuclear-matter parameters come from external compilations (Refs. [40–42]); neither source is the data being constrained. The strong correlation between S_n/p and Δm*_np/δ is recomputed in this paper from 189 transport simulations, so it does not simply import Eq. (1) from the authors' Ref. [35]; that earlier relation is presented as motivation, while the constraint itself is read off from the external data. The self-citations (Refs. [35], [39], [43], [47]) are methodological or contextual and are not load-bearing: the central claim would stand or fall with the comparison to Ref. [31] and the optical-potential calibration of Ref. [38]. No derivation step reduces to its own input by construction, and the extracted Δm*_np/δ values are not fitted parameters renamed as predictions. The paper explicitly acknowledges that its model does not exactly reproduce the R_n/p spectrum and that the high-momentum tail of the initial nucleon distribution could affect the high-energy interpretation; these are correctness caveats, not circularity. The score of 2 reflects only the presence of minor self-citations in the derivation chain.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The analysis varies four nuclear matter parameters plus the two energy window boundaries. The priors for S0, L, m*_s/m, and f_I come from earlier literature, while the energy windows are introduced ad hoc in this paper. The model itself (ImQMD with Skyrme interactions) is taken from prior work, and the MDI parameters are fitted to external optical potential data. No new entities are postulated. The central constraint is read from a correlation generated by the same model, which is a standard forward-model approach but depends on the adequacy of the model as an axiom.

free parameters (5)
  • S0 (symmetry energy coefficient) = constrained to 31.27 to 35.33 MeV in Table II
    Sampled uniformly in [28,41] MeV from priors in Refs [39-42]; the constrained average depends on the energy window and MDI form.
  • L (slope of symmetry energy) = constrained to 80.68 to 88.52 MeV in Table II
    Sampled in [30,134] MeV; weakly correlated with S_n/p per Figure 3.
  • m*_s/m (isoscalar effective mass ratio) = constrained to 0.78 to 0.84 in Table II
    Sampled in [0.6,1.0]; shows a mild correlation with the extracted Δm*_np in Figure 5.
  • f_I (input for Δm*_np/δ) = positive values 0.28-0.41 for low-E window, negative values -0.12 to -0.33 for high-E window
    The central model parameter controlling the isospin splitting of effective masses; sampled in [-0.5,0.4] and constrained by comparison of S_n/p with data.
  • Energy window boundaries E1, E2 = Low window: 45, 60 MeV; High window: 60, 95 MeV
    Chosen by hand in Eq. (9) and Figure 3; the sign of the extracted Δm*_np flips between the two windows, so the boundaries are load-bearing and appear post hoc.
assumptions (5)
  • domain assumption The ImQMD transport model accurately describes the collision dynamics and nucleon emission for these systems.
    Invoked throughout; the model is the authors' own code, not cross-validated against other transport codes in this paper.
  • domain assumption Skyrme energy density functionals with standard and extended MDI span the relevant momentum dependence of the symmetry potential.
    The paper uses only these two forms and later suggests non-monotonic momentum dependence may be needed, which standard Skyrme cannot produce.
  • domain assumption Prior ranges for S0, L, m*_s/m, and f_I taken from Refs [39-42] bracket the true nuclear matter values.
    Stated in the section on parameter sampling; the constrained values are drawn from these priors.
  • domain assumption The published R_n/p and DR(n/p) data from Ref [31] are reliable within the quoted errors.
    All constraints are derived by comparing model outputs to this single experimental dataset.
  • domain assumption The relationship between S_n/p and Δm*_np is approximately linear across the sampled parameter range, justifying linear fits and reading off constraints.
    The linear fits in Figure 4 are used to guide the eye and to map the data region onto Δm*_np values.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Investigation of the neutron-proton effective mass splitting via heavy ion collisions: Constraints and Implications." pith.science (2026). https://pith.science/paper/FECULOZE

@misc{pith2026250617973,
  author       = {Pith},
  title        = {Pith review of: Investigation of the neutron-proton effective mass splitting via heavy ion collisions: Constraints and Implications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FECULOZE}},
  note         = {Machine review of arXiv:2506.17973}
}
abstract

The neutron-proton effective mass splitting ($\Delta m^*_{np}$) is investigated through analyses of heavy-ion collisions using the improved quantum molecular dynamics (ImQMD) model with both standard and extended Skyrme interactions. By uncovering the strong correlation between the slope of the neutron-to-proton yield ratio with respect to the kinetic energy (i.e., $S_{n/p} $) and $\Delta m^*_{np}$, we reveal that the constraints of the neutron-proton effective mass splitting via heavy ion collisions depend on the kinetic energy region of the emitted nucleons. At low kinetic energies, the data favor $m_n^*>m_p^*$ which is consistent with the nucleon-nucleus scattering analysis, while at high kinetic energies, they favor $m_n^*<m_p^*$. Our findings partly resolve the longstanding discrepancy in the constraints of neutron-proton effective mass splitting with heavy ion collisions and nucleon-nucleus scattering, and significantly advance the understanding of nucleon effective mass splitting through heavy ion collisions.

Figures

Figures reproduced from arXiv: 2506.17973 by the authors.

Figure 1
Figure 1. FIG. 1. The constraints on the neutron-proton effective mass [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The calculated results on the coalescence invariant [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (Color online) Results of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (Color online) The [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 39 canonical work pages

  1. [31]

    Morfouace, C

    P. Morfouace, C. Tsang, Y. Zhang, W. Lynch, M. Tsang, D. Coupland, M. Youngs, Z. Chajecki, M. Famiano, T. Ghosh, G. Jhang, J. Lee, H. Liu, A. Sanetullaev, R. Showalter, and J. Winkelbauer, Physics Letters B799, 135045 (2019)

    work page 2019

  2. [1]

    Li, B.-J

    B.-A. Li, B.-J. Cai, L.-W. Chen, and J. Xu, Progress in Particle and Nuclear Physics99, 29 (2018)

    work page 2018

  3. [2]

    Nakazato and H

    K. Nakazato and H. Suzuki, The Astrophysical Journal 878, 25 (2019)

    work page 2019

  4. [3]

    Prakash, I

    M. Prakash, I. Bombaci, M. Prakash, P. J. Ellis, J. M. Lattimer, and R. Knorren, Physics Reports280, 1 (1997)

    work page 1997

  5. [4]

    C. A. Raithel, F. Ozel, and D. Psaltis, The Astrophysical Journal875, 12 (2019)

    work page 2019

  6. [5]

    Xu, L.-W

    J. Xu, L.-W. Chen, and B.-A. Li, Phys. Rev. C91, 014611 (2015)

    work page 2015

  7. [6]

    Xu, Phys

    J. Xu, Phys. Rev. C91, 037601 (2015)

    work page 2015

  8. [7]

    Persram and C

    D. Persram and C. Gale, Phys. Rev. C65, 064611 (2002)

    work page 2002

Show all 50 references
  1. [8]

    Li and L.-W

    B.-A. Li and L.-W. Chen, Phys. Rev. C72, 064611 (2005)

    2005

  2. [9]

    Y. Cui, Y. Zhang, and Z. Li, Phys. Rev. C98, 054605 (2018)

    2018

  3. [10]

    Zhang, M

    Y. Zhang, M. Tsang, Z. Li, and H. Liu, Physics Letters B732, 186 (2014)

    2014

  4. [11]

    D. D. S. Coupland, M. Youngs, Z. Chajecki, W. G. Lynch, M. B. Tsang, Y. X. Zhang, M. A. Famiano, T. K. Ghosh, B. Giacherio, M. A. Kilburn, J. Lee, H. Liu, F. Lu, P. Morfouace, P. Russotto, A. Sanetullaev, R. H. Showalter, G. Verde, and J. Winkelbauer, Phys. Rev. C 94, 011601 (2016)

    2016

  5. [12]

    Feng, Nuclear Physics A878, 3 (2012)

    Z.-Q. Feng, Nuclear Physics A878, 3 (2012)

    2012

  6. [13]

    J. Su, L. Zhu, C.-Y. Huang, W.-J. Xie, and F.-S. Zhang, Phys. Rev. C96, 024601 (2017)

    2017

  7. [14]

    J. Su, L. Zhu, and C. Guo, Phys. Rev. C101, 044606 (2020)

    2020

  8. [15]

    Zhang and J

    F. Zhang and J. Su, Nuclear Science and Techniques31, 77 (2020)

    2020

  9. [16]

    Wang, J.-P

    F.-Y. Wang, J.-P. Yang, X. Chen, Y. Cui, Y.-J. Wang, Z.-G. Xiao, Z.-X. Li, and Y.-X. Zhang, Nuclear Science and Techniques34, 94 (2023)

    2023

  10. [17]

    Xie and F.-S

    W.-J. Xie and F.-S. Zhang, Physics Letters B735, 250 (2014)

    2014

  11. [18]

    Shang, J.-M

    X.-L. Shang, J.-M. Dong, W. Zuo, P. Yin, and U. Lom- bardo, Phys. Rev. C103, 034316 (2021)

    2021

  12. [19]

    S. Wang, H. Tong, Q. Zhao, C. Wang, P. Ring, and J. Meng, Phys. Rev. C108, L031303 (2023). 7

    2023

  13. [20]

    W. Zuo, L. G. Cao, B. A. Li, U. Lombardo, and C. W. Shen, Phys. Rev. C72, 014005 (2005)

    2005

  14. [21]

    T. R. Whitehead, Y. Lim, and J. W. Holt, Phys. Rev. Lett.127, 182502 (2021)

    2021

  15. [22]

    Mansour, K

    H. Mansour, K. Gad, and K. S. A. Hassa- neen, Progress of Theoretical Physics123, 687 (2010), https://academic.oup.com/ptp/article- pdf/123/4/687/5185923/123-4-687.pdf

    2010

  16. [23]

    Margueron, R

    J. Margueron, R. Hoffmann Casali, and F. Gulminelli, Phys. Rev. C97, 025805 (2018)

    2018

  17. [24]

    Chamseddine, J

    M. Chamseddine, J. Margueron, G. Chanfray, H. Hansen, and R. Somasundaram, Eur. Phys. J. A59, 177 (2023), arXiv:2304.01817 [nucl-th]

    2023 arXiv

  18. [25]

    Xu, B.-A

    C. Xu, B.-A. Li, and L.-W. Chen, Phys. Rev. C82, 054607 (2010)

    2010

  19. [26]

    Li, W.-J

    X.-H. Li, W.-J. Guo, B.-A. Li, L.-W. Chen, F. J. Fat- toyev, and W. G. Newton, Physics Letters B743, 408 (2015)

    2015

  20. [27]

    Zhang and L.-W

    Z. Zhang and L.-W. Chen, Phys. Rev. C93, 034335 (2016)

    2016

  21. [28]

    H.-Y. Kong, J. Xu, L.-W. Chen, B.-A. Li, and Y.-G. Ma, Phys. Rev. C95, 034324 (2017)

    2017

  22. [29]

    Xu and W.-T

    J. Xu and W.-T. Qin, Phys. Rev. C102, 024306 (2020)

    2020

  23. [30]

    J. Xu, J. Zhou, Z. Zhang, W.-J. Xie, and B.-A. Li, Physics Letters B810, 135820 (2020)

    2020

  24. [32]

    C. Y. Tsanget al.(S$π$RIT), Phys. Lett. B853, 138661 (2024), arXiv:2312.06678 [nucl-ex]

    2024 arXiv

  25. [33]

    W.-J. Xie, J. Su, L. Zhu, and F.-S. Zhang, Phys. Rev. C 88, 061601 (2013)

    2013

  26. [34]

    J. Su, L. Zhu, C.-Y. Huang, W.-J. Xie, and F.-S. Zhang, Phys. Rev. C94, 034619 (2016)

    2016

  27. [35]

    J. Yang, X. Chen, Y. Cui, Y. Liu, Z. Li, and Y. Zhang, Phys. Rev. C109, 054624 (2024)

    2024

  28. [36]

    Zhang and Z

    Y. Zhang and Z. Li, Phys. Rev. C74, 014602 (2006)

    2006

  29. [37]

    Zhang, N

    Y. Zhang, N. Wang, Q.-F. Li, L. Ou, J.-L. Tian, M. Liu, K. Zhao, X.-Z. Wu, and Z.-X. Li, Front. Phys.15, 54301 (2020)

    2020

  30. [38]

    S. Hama, B. C. Clark, E. D. Cooper, H. S. Sherif, and R. L. Mercer, Phys. Rev. C41, 2737 (1990)

    1990

  31. [39]

    Zhang, M

    Y. Zhang, M. Liu, C.-J. Xia, Z. Li, and S. K. Biswal, Phys. Rev. C101, 034303 (2020)

    2020

  32. [40]

    W. G. Lynch and M. B. Tsang, The nuclear symmetry en- ergy at sub-saturation densities (2018), arXiv:1805.10757 [nucl-ex]

    2018 arXiv

  33. [41]

    Burgio, H.-J

    G. Burgio, H.-J. Schulze, I. Vidana, and J.-B. Wei, Progress in Particle and Nuclear Physics120, 103879 (2021)

    2021

  34. [42]

    Kumar, V

    R. Kumar, V. Dexheimer, J. Jahan, J. Noronha, J. Noronha-Hostler, C. Ratti, N. Yunes, A. R. Nava Acuna, M. Alford, M. H. Anik, D. Chatterjee, K. Chatziioannou, H.-Y. Chen, A. Clevinger, C. Conde, N. Cruz-Camacho, T. Dore, C. Drischler, H. Elfner, R. Essick, D. Friedenberg, S. ...

    2024

  35. [43]

    Zhang, M

    Y. Zhang, M. Tsang, and Z. Li, Physics Letters B749, 262 (2015)

    2015

  36. [44]

    TheS max n/p andS min n/p are calculated from the upper limit and lower limit ofR n/p at the beginning and the end of kinetic energy region, i.e., atE 1 andE 2

    The error isσ= 1 2|Smax n/p−S min n/p|. TheS max n/p andS min n/p are calculated from the upper limit and lower limit ofR n/p at the beginning and the end of kinetic energy region, i.e., atE 1 andE 2

  37. [45]

    Sellahewa and A

    R. Sellahewa and A. Rios, Phys. Rev. C90, 054327 (2014)

    2014

  38. [46]

    Chen, B.-J

    R. Chen, B.-J. Cai, L.-W. Chen, B.-A. Li, X.-H. Li, and C. Xu, Phys. Rev. C85, 024305 (2012)

    2012

  39. [47]

    M. Sun, D. Niu, J. Yang, Y. Cui, Z. Li, Q. Zhao, K. Zhao, and Y. Zhang, Phys. Rev. C111, 064607 (2025)

    2025

  40. [48]

    Wada, Phys

    R. Wada, Phys. Rev. C96, 031601 (2017)

    2017

  41. [49]

    O. Hen, G. A. Miller, E. Piasetzky, and L. B. Weinstein, Rev. Mod. Phys.89, 045002 (2017)

    2017

  42. [50]

    Z. X. Yang, X. L. Shang, G. C. Yong, W. Zuo, and Y. Gao, Phys. Rev. C100, 054325 (2019), arXiv:1907.10977 [nucl-th]

    2019 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.