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REVIEW 4 major objections 5 minor 38 references

Does strange meson condensation reduce the moment of inertia of massive proto neutron stars? insights at S = 1 and YL = 0.4

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

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Pith's one-line read Including strange mesons in a proto-neutron-star model lowers the moment of inertia of stars near 2.7 solar masses by about 0.6%, while leaving stars below 2.1 solar masses unchanged.

desk verdict A standard RMF plus Hartle-Thorne parameter scan with a plausible but under-specified composition solver; the claimed ~0.6% shift in the moment of inertia is not yet established. read the letter →

arxiv 2608.03022 v1 pith:OE753VBZ submitted 2026-08-04 nucl-th

Nie-Cheng Jian , Xian-Feng Zhao This is my paper · ORCID
classification nucl-th PACS 26.60.Kp21.65.Mn
keywords proto-neutronstarsstrangemesonsrelativisticmean-fieldtheorymomentofinertiaequationstatehyperonsHartle-ThorneapproximationTW99parametrization
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 the strange mesons $\sigma^*$ and $\phi$, included as mediators of hyperon-hyperon interactions, change the rotation of massive proto-neutron stars. Working with the TW99 relativistic mean-field parametrization at fixed entropy per baryon $S=1$ and lepton fraction $Y_L=0.4$, the paper solves the TOV equations and computes the moment of inertia in the Hartle-Thorne slow-rotation approximation. It finds that the strange mesons soften the equation of state at high densities, slightly lower the maximum mass and radius, shift the peak of the moment-of-inertia curve toward higher central density, and reduce $I$ by about 0.6\% at $2.7\,M_\odot$. For stars below $2.1\,M_\odot$ the effect is essentially zero. The point of the calculation is that strangeness is not a global correction but a mass-threshold effect that matters only for the most compact proto-neutron stars, with consequences for spin-down and gravitational-wave signals.

What carries the argument

The load-bearing machinery is the finite-temperature relativistic mean-field Lagrangian for proto-neutron-star matter: baryons (nucleons plus the hyperon octet) coupled to $\sigma$, $\omega$, $\rho$, and the strange mesons $\sigma^*$ (the $f_0(975)$) and $\phi$ (the $\phi(1020)$), with TW99 nucleonic couplings and hyperon couplings fixed by SU(6) symmetry and hyperon potential depths. From this Lagrangian the paper builds the equation of state, integrates the Tolman-Oppenheimer-Volkoff equations for the mass-radius sequence, and computes the moment of inertia with the Hartle-Thorne slow-rotation formula, which requires solving for the frame-dragging function $\bar\omega(r)$. The diagnostic that carries the argument is the density-dependent pressure change $\delta p$: the strange mesons lower the pressure most near $\rho\sim0.37$ fm$^{-3}$, exactly where $I$ peaks, explaining why the peak shifts upward in density and slightly downward in magnitude.

What would settle it

An independent implementation with an explicit composition solver that enforces charge neutrality, lepton-number conservation, and weak-reaction balance (with a trapped-neutrino chemical potential) would settle the claim: if the hyperon onset density moves by more than a few percent, the predicted $-0.6\%$ at $2.7\,M_\odot$ and the $2.1\,M_\odot$ threshold would shift, and the specific numbers in Figure 6 would not survive.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that including $\sigma^*$ and $\phi$ mesons in the TW99 description of hot, lepton-rich proto-neutron-star matter at $S=1$, $Y_L=0.4$ softens the equation of state most strongly in the intermediate-density region where the moment of inertia peaks. Concretely, the maximum gravitational mass drops from $2.7358$ to $2.7339\,M_\odot$, the radius at that maximum from $13.799$ to $13.786$ km, and the peak moment of inertia from $3.8537\times10^{45}\,\mathrm{g\,cm}^2$ to $3.8489\times10^{45}\,\mathrm{g\,cm}^2$, while the central density of the peak rises from $0.3738$ to $0.3742$ fm$^{-3}$. The relative change $\delta I$ is essentially zero below $2.1\,M_\odot$ and grows to about $-0.6\%$ at $2.7\,M_\odot$. The paper attributes this to the attractive $\sigma^*$ and $\phi$ interactions among hyperons reducing pressure support, which contracts the star and pushes the turnover of $I\sim MR^2$ to higher densities.

Load-bearing premise

The results depend on an unstated step: the mixture of particles at each density must come from enforcing electric neutrality, conservation of lepton number, and the balance of weak reactions, but the paper never writes down those equations or includes the trapped neutrino fields it mentions, so the hyperon and strange-meson abundances that drive the effect are fixed by a solver the reader never sees.

Editorial extensions

If this is right

  • If the claim is correct, the moment of inertia of a proto-neutron star is not a monotonic function of central density: it peaks at a lower density than the maximum mass, so spin-down begins while the star can still accrete mass.
  • The strange-meson correction is confined to stars above about $2.1\,M_\odot$ and reaches only $-0.6\%$ at $2.7\,M_\odot$, so models of canonical-mass neutron stars can safely ignore $\sigma^*$ and $\phi$, while models of the most massive remnants cannot.
  • The maximum mass and radius are reduced by less than a tenth of a percent, so the existence of $\sim2.3\,M_\odot$ pulsars does not by itself constrain the strange-meson sector.
  • Because the peak of $I$ sits at lower density than the mass limit, rotational and gravitational-wave observations of massive proto-neutron stars probe intermediate-density matter, not just the extreme core, making the strange-meson softening directly visible in spin evolution.

Reading between the lines

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

  • If the paper's picture holds, the mass threshold near $2.1\,M_\odot$ is a prediction that can be sharpened: varying $S$ and $Y_L$ away from 1 and 0.4 should move the threshold, since hotter or more lepton-rich matter has different hyperon fractions, so mapping $\delta I$ across the $(S,Y_L)$ plane would show where the strange-meson effect becomes observable.
  • An independent reimplementation that explicitly enforces charge neutrality, lepton-number conservation, and weak-reaction balance with trapped neutrinos would test the robustness of the effect; the main uncertainty is likely the hyperon onset density rather than the Hartle-Thorne integration.
  • If the density offset between the $I$ peak and the mass peak ($\Delta\rho_c\approx0.25$ fm$^{-3}$) is generic across parametrizations, then a combined mass-radius-inertia measurement of one massive proto-neutron star could constrain the intermediate-density equation of state more tightly than any single observable, because mass and inertia weight different radial regions.
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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 paper investigates whether including the strange mesons σ* and φ in a relativistic mean-field (RMF) description of proto-neutron-star matter, at entropy per baryon S=1 and lepton fraction YL=0.4, affects the maximum mass, radius, and moment of inertia. Using the TW99 parametrization, the authors solve the TOV equations and the Hartle–Thorne slow-rotation equations, comparing models with and without σ* and φ. They report that the strange mesons soften the high-density equation of state, reduce the maximum mass by about 0.07%, reduce the peak moment of inertia by about 0.12%, shift the peak of I to slightly higher central density, and produce a relative decrease of about 0.6% in I at 2.7 solar masses, with negligible effect below about 2.1 solar masses.

Significance. The question addressed is relevant: strangeness degrees of freedom and their effect on the rotational properties of massive proto-neutron stars are of current interest for gravitational-wave and pulsar-spin-down studies. If the calculation were fully specified and robust, the main conclusion — that σ* and φ have only a sub-percent effect on the moment of inertia except near the maximum mass — would be a useful, if modest, quantitative result. The paper has the virtue of comparing with and without strange mesons within the same framework, which is a direct and non-circular comparison. However, the manuscript as written omits essential pieces of the PNS composition problem, so the reported numbers are not yet uniquely determined. The strength of the conclusion is also limited by the absence of any numerical convergence or uncertainty analysis for sub-percent effects, and by the lack of a clearly defined and justified composition solver.

major comments (4)
  1. [§2, Eqs. (2)–(3)] The energy density and pressure expressions contain only meson and baryon contributions; there are no lepton kinetic terms, and no neutrino terms, despite the Introduction stating that the PNS is lepton-rich with trapped neutrinos. For YL=0.4, electrons and muons contribute non-negligibly to the EoS, and if YL includes neutrinos then neutrino chemical potentials and neutrino distribution functions must appear. As written, Eqs. (2)–(3) do not define the EoS of the matter that the paper claims to study. This is a load-bearing omission because the EoS directly determines the TOV solutions and the moment of inertia.
  2. [§2–§3 (composition equations)] Nowhere in the paper are the equations that determine the PNS composition written down: there is no charge-neutrality condition, no lepton-number conservation condition, and no beta-equilibrium condition (with or without trapped neutrinos). The baryon fractions of Λ, Σ, and Ξ — which control when σ* and φ become active — depend on these constraints. Without them the strange-meson effect is not uniquely defined, and the comparison in Fig. 6 and Table 1 is conditional on an unspecified composition solver. The authors should provide the full set of constraints and show the resulting particle fractions, including the neutrino chemical potential if trapped neutrinos are included.
  3. [§4, Fig. 2 and surrounding text] The text states that the softening originates from 'attractive interactions mediated by the σ* and φ mesons among hyperons.' This is physically misleading: in the Lagrangian (1), φ enters as a vector meson like ω and its contribution is repulsive at finite baryon density, while σ* is the attractive scalar field. The net softening may come from σ*, but attributing attraction to φ is incorrect. This matters because the physical interpretation of the central result is part of the paper's claim. The authors should clarify the separate roles of σ* and φ and, if possible, decompose their contributions to the pressure change.
  4. [§5, Fig. 6 and Table 1] The key quantitative results are changes at the 0.07%–0.6% level, but no numerical convergence test or estimate of the tolerance of the TOV and Hartle–Thorne solvers is provided. Without such a test, it is not possible to rule out that the reported shifts in the peak density and the small reductions in Imax are within the numerical noise of the integration. The authors should demonstrate convergence with respect to radial grid resolution, EoS tabulation density, and any iterative tolerance used in solving the field equations.
minor comments (5)
  1. [Title and Abstract] The title refers to 'strange meson condensation,' but the paper does not treat a condensation transition; σ* and φ are ordinary mean fields included in the RMF Lagrangian. The title should be reworded to avoid implying kaon-like condensation.
  2. [Abstract] The abstract says the relative change 'decreases to about -0.6 at 2.7 solar mass'; the percent sign is missing. The text correctly uses '-0.6%'.
  3. [§4] The sentence 'The pressure increase in the high-density regime leads to a more compact star for a given central density' appears immediately after a discussion of softening and lower pressure; it is confusing and should be rephrased to distinguish the density range where the pressure is reduced from the range where it recovers.
  4. [§3] The hyperon–vector coupling ratio x_ωh is chosen as 0.9 'to maximize the mass,' but no sensitivity study is presented. Since the central effect depends on hyperon abundances, a brief variation of x_ωh (e.g., 0.7–1.0) would strengthen the robustness of the conclusion.
  5. [§2] The meson field equations and the effective chemical potentials for baryons are not written down, so the reader cannot reproduce the calculation of the EoS from Eq. (1). Adding these equations would improve the completeness of the theoretical framework.

Circularity Check

1 steps flagged · score 2.0 of 10

Central strange-meson comparison is a direct RMF/TOV computation, not a fit; a minor self-citation justifies the xωh=0.9 hyperon-vector choice.

  1. self citation load bearing [Section 3 (Parameters), hyperon coupling constants paragraph]
    "The values of xρh are fixed according to the SU(6) quark-model symmetry [32, 33]. Since previous studies have shown that the PNS mass increases with both xσh and xωh [34], we choose a relatively large value xωh=0.9 to maximize the mass."

    Reference [34] is Zhao X F 2019, a paper by the present co-author. The only cited justification for the hyperon-vector coupling ratio xωh=0.9 is this self-citation, and the value is explicitly chosen to maximize the mass. This input controls the hyperon onset and the density window where σ* and φ act, so the quantitative regime (masses up to 2.7 M⊙ and the reported δI ≈ -0.6%) inherits a parameter fixed by the authors' own prior work rather than derived in this paper. However, the comparison with versus without strange mesons is then solved directly from the Lagrangian, so the central claim does not reduce to the self-citation.

full rationale

The central derivation is a direct numerical computation: the RMF Lagrangian (Eq. 1), EoS (Eqs. 2-3), TOV equations (Eqs. 5-6), and Hartle-Thorne moment-of-inertia integral (Eq. 7) are solved with fixed couplings. The with/without strange-meson comparison is not fitted to the reported Mmax, Imax, or δI; the σ* and φ couplings are taken from published external sources (Ref. 16, hyperon potential depths), so those results are independent input. The model selection among eight parametrizations by largest maximum mass is a stated selection criterion, not a prediction fitted to the target. The only notable circularity-adjacent element is the self-citation [34] used to justify xωh=0.9, a load-bearing input for the quantitative mass scale but not for the logical derivation. Separately, the paper omits the charge-neutrality, lepton-number-conservation, and beta-equilibrium equations needed to fix the hyperon fractions, and Eq. (1) contains no neutrino fields despite the trapped-neutrino context; this is a reproducibility/correctness concern, but it is not a circular reduction of the kind defined here. Score 2 reflects one minor, partially load-bearing self-citation with otherwise self-contained computation.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The central claim is a model consequence computed from a specific RMF Lagrangian with hyperon-meson couplings drawn from prior literature and one hand-picked coupling ratio (x_omega h = 0.9). No new data or first-principles derivation is added, and the results inherit the uncertainties and choices of the model.

free parameters (4)
  • Hyperon-vector coupling ratio x_omega h = 0.9
    Chosen by hand to maximize the PNS mass, following the authors' earlier finding (Ref. [34]) that the mass increases with x_omega h. Directly sets the stiffness of the hyperonic EoS and therefore the size of the strange-meson effect on I.
  • Hyperon potential depths U_Lambda, U_Sigma, U_Xi = -30, 30, -14 MeV
    Empirical input from hypernuclear experiments, used in Eq. (14) to fix the scalar hyperon couplings x_sigma h. The onset density of hyperons, and hence of sigma* and phi effects, changes with these depths.
  • Strange meson coupling ratios g_sigma*B/g_sigma and g_phiB/g_omega = 0.69, 0.69, 1.25 and SU(6) relations
    Taken from Ref. [16] (Eqs. 15-17). They set the strength of the attractive sigma* and phi interactions that produce the central softening result; changing them would change both the sign and magnitude of the I shift.
  • TW99 nucleonic coupling set = standard TW99 parameters
    The nucleon-meson couplings are fitted to nuclear matter properties in Ref. [27]. The paper selects TW99 because it gives the largest maximum mass among eight sets, so all central numbers inherit this specific choice.
assumptions (7)
  • domain assumption The RMF approximation: meson fields are replaced by their classical expectation values.
    Invoked in Section 2 after Eq. (1). It ignores quantum fluctuations and is standard but not exact; the results inherit its limitations.
  • standard math Hartle-Thorne slow-rotation approximation is valid for the stars studied.
    Used in Eqs. (7)-(13). The approximation assumes slow rotation; massive PNSs, including the 709 Hz pulsar cited in the introduction, can rotate much faster, so the computed I may miss rapid-rotation corrections.
  • domain assumption The baryon octet is the complete set of baryonic degrees of freedom; no quarks, Delta resonances, or other exotic states appear.
    The Lagrangian sums over baryons B (Eq. 1) but the paper does not justify excluding other states. Hyperon fractions determine where sigma* and phi become active.
  • domain assumption Charge neutrality, lepton-number conservation, and chemical equilibrium are enforced by an unspecified composition solver.
    Not written down in Sections 2 or 3, yet required to evaluate the Fermi-Dirac distributions in Eqs. (2)-(4). The entire EoS depends on this unstated step.
  • ad hoc to paper Neutrinos are dynamically irrelevant or absent despite the trapped-neutrino description.
    Eq. (1) includes only electrons and muons; the introduction describes trapped-neutrino stars. The paper neither includes neutrino terms nor states why they are neglected, which can affect the EoS and hence I.
  • domain assumption Equation (14) maps laboratory hyperon potential depths to scalar couplings using the RMF relation.
    Standard in the RMF literature but model dependent; the resulting x_sigma h values are then used to determine the hyperon sector.
  • domain assumption SU(6) quark-model symmetry determines the rho-meson hyperon couplings.
    Used in Section 3 with Refs. [32,33] to fix x_rho h. This symmetry is an approximation and is not derived within the RMF model.

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Pith. "Pith review of Does strange meson condensation reduce the moment of inertia of massive proto neutron stars? insights at S = 1 and YL = 0.4." pith.science (2026). https://pith.science/paper/OE753VBZ

@misc{pith2026260803022,
  author       = {Pith},
  title        = {Pith review of: Does strange meson condensation reduce the moment of inertia of massive proto neutron stars? insights at S = 1 and YL = 0.4},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OE753VBZ}},
  note         = {Machine review of arXiv:2608.03022}
}
read the original abstract

We investigate the effects of strange mesons (sigma-star and phi) on the structural and rotational properties of massive proto neutron stars (PNSs) within the relativistic mean-field (RMF) framework. Using the TW99 parametrization with entropy per baryon S=1 and lepton fraction YL=0.4, we solve the TOV equations and compute the moment of inertia via the Hartle-Thorne approximation. Among eight parametrizations, TW99 is chosen as it gives the largest maximum mass. Our results show that strange mesons soften the equation of state at high densities, reducing both the maximum mass and radius. The moment of inertia peaks at a lower central density than the maximum mass, and strange mesons shift this peak toward higher densities while slightly lowering its value. The relative change in I is negligible for PNSs below 2.1 solar mass, but decreases to about -0.6 at 2.7 solar mass, indicating that strangeness effects are most relevant for the most massive stars. Our findings provide useful constraints on the rotational evolution of massive PNSs and their potential gravitational-wave signatures.

Figures

Figures reproduced from arXiv: 2608.03022 by the authors.

Figure 1
Figure 1. displays the gravitational mass as a function of the central baryon density for PNSs with entropy per baryon S=1 and lepton fraction YL=0.4 , calculated us￾ing eight representative nucleonic parametrizations within the RMF framework. Among these models, TW99 yields the highest maximum gravitational mass and is therefore adopted as the baseline EoS for describing massive PNSs in the present study, with the contributi… view at source ↗
Figure 2
Figure 2. Pressure as a function of baryon density for PNSs with the TW99 parametrization, entropy per baryon S=1 , and lep￾ton fraction YL=0.4. The red solid curve represents the case without strange mesons ( σ ∗ and ϕ ), while the green dashed curve corresponds to the case with strange mesons included. The red inverted triangle marks the point where the moment of inertia reaches its maximum in the absence of strange mesons,… view at source ↗
Figure 3
Figure 3. Relative percentage change of pressure as a function of baryon density. Positive values indicate that the pressure increases when strange mesons (σ ∗ and ϕ) are included, while negative values indicate a decrease. The results are obtained for PNSs with entropy per baryon S=1, lepton fraction YL=0.4, and the nucleonic parametrization TW99. of inertia (around ρ=0.37 fm−3 ). In this region, the pres￾sure reduction reac… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: displays the moment of inertia I as a func￾tion of the central baryon density ρc for PNSs with the TW99 parametrization, entropy per baryon S=1, and lep￾ton fraction YL=0.4. The left panel presents the overall behavior of I over a broad density range, while the right p…
Figure 5
Figure 5. Figure 5: quantifies the shifts in the maximum moment of inertia ( Imax) and its corresponding central density ( ρ Imax c ) induced by strange mesons. The vertical and hor￾izontal dashed lines mark the changes in Imax and ρ Imax c , respectively. The inclusion of σ ∗ and ϕ meson…
Figure 6
Figure 6. Figure 6: Relative change rate of the moment of inertia as a function of gravitational mass for PNSs with the TW99 parametrization, entropy per baryon S=1 , and lepton frac￾tion YL=0.4 . The relative change rate is defined as δI = (Iwith − Iwithout)/Iwithout × 100% , where Iwith…

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Works this paper leans on

38 extracted references · 38 canonical work pages

  1. [1]

    Ding W B, Cai M D and Chan A H 2022 International Journal of Modern Physics A 37 2250034

    work page 2022

  2. [2]

    Mu X L, Jia H Y and Zhou X 2017 The Astrophysical Journal 846 140

    work page 2017

  3. [3]

    Li Y X, Chen H Y, Wen D H and Zhang J 2021 The Eu- ropean Physical Journal A 57 31

    work page 2021

  4. [4]

    Gao Z F, Wang N, Shan H, Li X D and Wang W 2017 The Astrophysical Journal 849 19

    work page 2017

  5. [5]

    Hartle J B 1967 Astrophysical Journal 150 1005

    work page 1967

  6. [6]

    Hartle J B and Thorne K S 1968 Astrophysical Journal 153 807

    work page 1968

  7. [7]

    Bejger M, Bulik T, and Haensel P 2005 Monthly Notices of the Royal Astronomical Society 364 635–639

    work page 2005

  8. [8]

    Raithel C A, ¨Ozel F and Psaltis D 2016 The Astrophysical Journal 831 44

    work page 2016

Show all 38 references
  1. [9]

    Demorest P B, Pennucci T, Ransom S M, Roberts M S E and Hessels J W T 2010 Nature 467 1081–1083

    2010

  2. [10]

    2016 The Astro- physical Journal 832 167

    Fonseca E, Pennucci T T, Ellis J A et al. 2016 The Astro- physical Journal 832 167

    2016

  3. [11]

    2013 Science 340 448

    Antoniadis J, Freire P C C et al. 2013 Science 340 448

    2013

  4. [12]

    Cromartie H T, Fonseca E and Ransom S M 2020 Nature Astronomy 4 72–76

    2020

  5. [13]

    2022 The Astrophysical Journal Letters 934 L17

    Romani R W, Kandel D, Filippenko A V et al. 2022 The Astrophysical Journal Letters 934 L17

    2022

  6. [14]

    Romani R W, Beleznay M, Filippenko A V, Brink T G and Zheng W K 2026 The Astrophysical Journal 996 101

    2026

  7. [15]

    Glendenning N 1985 Astrophysical Journal 293 470–493

    1985

  8. [16]

    1994 Annals of Physics 235 35–76

    Schaffner J, Dover C B, Gal A et al. 1994 Annals of Physics 235 35–76

    1994

  9. [17]

    1997 Physics Reports 280 1–77

    Prakash M, Bombaci I et al. 1997 Physics Reports 280 1–77

    1997

  10. [18]

    Burrows A and Lattier J M 1986 Astrophysical Journal 307 178

    1986

  11. [19]

    Glendenning N 1987 Physics Letters B 185 275–280

    1987

  12. [20]

    Glendenning N 1987 Nuclear Physics A 469 600–616

    1987

  13. [21]

    2024 Nuclear Physics B 1008 116697

    Ghosh S, Shaikh S, Kalita P J et al. 2024 Nuclear Physics B 1008 116697

    2024

  14. [22]

    Kunkel S, Wystub S and Schaffner-Bielich J 2025 Physical Review C 111 035807

    2025

  15. [23]

    Zhou S G 2016 Physica Scripta 91 063008

    2016

  16. [24]

    Glendenning N 1997 (New York, Inc.: Springer-Verlag)

    1997

  17. [25]

    Tolman R C 1939 Physical Review 55 364–373

    1939

  18. [26]

    Oppenheimer J R and Volkoff G M 1939 Physical Review 55 374–381

    1939

  19. [27]

    656 331–364

    Typel S and Wolter H H 1999 Nuclear Physics A. 656 331–364

    1999

  20. [28]

    Lee S J, Fink J and Balantekin A B 1986 Physical Review Letters 57 2916–2919 8 Cheng-Jian Nie 1, and Xian-Feng Zhao 2†: Title Suppressed Due to Excessive Length

    1986

  21. [29]

    Tolos L, Centelles M and Ramos A 2017 Publications of the Astronomical Society of Australia 34 e065

    2017

  22. [30]

    Todd-Rutel B G and Piekarewicz J 2005 Physical Review Letters 95 122501

    2005

  23. [31]

    Glendenning N and Moszkowski S A 1991 Physical Review Letters 67 2414–2417

    1991

  24. [32]

    Schaffner J and Mishustin I N 1996 Physical Review C 53 1416–1429

    1996

  25. [33]

    Schaffner-Bielich J and Gal A 2000 Physical Review C 62 034311

    2000

  26. [34]

    Zhao X F 2019 International Journal of Theoretical Physics 58 1060–1070

    2019

  27. [35]

    2012 Physical Review C 85 065802

    Weissenborn S, Chatterjee D, Schaffner-Bielich J et al. 2012 Physical Review C 85 065802

    2012

  28. [36]

    Gal A, Hungerford E V and Millener D J 2016 Reviews of Modern Physics 88 035004

    2016

  29. [37]

    Batty C J, Friedman E and Gal A 1997 Phys. Rep. 287 385–445

    1997

  30. [38]

    Harada T, Hirabayashi Y and Umeya A 2010 Physics Let- ters B 690 363–368

    2010

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