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REVIEW 3 major objections 6 minor 72 references

Microscopic analysis of the giant monopole resonance excitation energy

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Using Skyrme HF+BCS densities and the coherent density fluctuation model, this paper argues that the BCPM functional with a two-term radius formula reproduces the measured ISGMR excitation energies of nuclei from 40Ca to 208Pb, while the…

desk verdict Useful systematic tables and a transparent method, but the fitted r0(A) curve does not actually reproduce the anchor points, so the headline agreement is overstated. read the letter →

arxiv 2506.08736 v1 pith:KQEJ5I76 submitted 2025-06-10 nucl-th

M.K. Gaidarov , M.V. Ivanov , Y.I. Katsarov , A.N. Antonov , I.C. Danchev This is my paper
classification nucl-th PACS 24.30.Cz21.10.Gv21.60.-n21.65.+f
keywords isoscalargiantmonopoleresonancenuclearincompressibilitycoherentdensityfluctuationmodelSkyrmeHF+BCSBCPMenergyfunctionalneutronskinthicknessequationofstate
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 sets out to show that the energy of the isoscalar giant monopole resonance—the collective 'breathing' mode in which the nucleus expands and contracts—can be obtained across the whole mass range from calcium to lead by combining the incompressibility of infinite nuclear matter with each nucleus's own density profile. The tool is the coherent density fluctuation model, which turns a nuclear-matter incompressibility into a finite-nucleus value by averaging over density-weighted fluctuations. The central claim is that, using the BCPM energy functional for nuclear matter and writing the monopole energy with the radius $R=[1+2.40/A^{2/3}]A^{1/3}$, the predicted centroid energies agree with experimental data for all of the considered nuclei. The Brueckner functional, tested the same way, falls systematically low. If the claim is right, it offers a practical, semi-empirical way to estimate breathing-mode energies in nuclei whose neutron radii are not well known.

What carries the argument

The load-bearing device is the coherent density fluctuation model (CDFM), which represents a nucleus as a superposition of uniform-density pieces ('fluctons') and constructs a weight function $|F(x)|^2$ from the density gradient of the Skyrme HF+BCS ground state. This weight function converts the nuclear-matter incompressibility $K(\rho_0(x))$, including its symmetry and Coulomb components, into the finite-nucleus incompressibility $K_A$ by averaging. The second load-bearing object is the semi-empirical radius $R=[1+2.40/A^{2/3}]A^{1/3}$ appearing in the monopole-energy formula; its $A^{-2/3}$ term is the paper's way of encoding surface diffuseness. Together they turn a bulk-matter property into a predicted excitation energy for each specific nucleus.

What would settle it

Compile empirical half-density radii $R_{1/2}$ for the nuclei from 40Ca to 208Pb and check whether $R_{1/2}/A^{1/3}$ follows $1+2.40/A^{2/3}$; a systematic deviation beyond the few-percent level would falsify the radius formula and with it the reported BCPM(v) agreement.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a microscopic bridge from nuclear matter to finite-nucleus breathing modes can be made to work quantitatively. The incompressibility of infinite nuclear matter is computed from two energy-density functionals, then averaged with the CDFM weight function built from Skyrme HF+BCS ground-state densities to give the incompressibility $K_A$ of each finite nucleus. Inserting that $K_A$ into the standard monopole relation $E_{\mathrm{ISGMR}} = (\hbar/R)\sqrt{K_A/m}$ with the semi-empirical radius $R=[1+2.40/A^{2/3}]A^{1/3}$ yields centroid energies in good agreement with experiment for all nuclei from $^{40}$Ca to $^{208}$Pb, provided the BCPM(v) functional is used. The radius formula is fixed by requiring agreement for $^{40}$Ca and $^{208}$Pb; with the same formula the BCPM(v) energies are reported to agree with the experimental values across the table, while the Brueckner functional gives energies roughly 1–3 MeV too low. A second route using the ground-state mean-square radius and measured neutron skin thicknesses gives consistent energies for the Sn isotopes, $^{48}$Ca, and $^{208}$Pb.

Load-bearing premise

The load-bearing premise is that the effective radius $R=[1+2.40/A^{2/3}]A^{1/3}$ represents the size scale for every nucleus from calcium to lead, a two-constant form fixed only by 40Ca and 208Pb, and the reported BCPM(v) agreement stands or falls with it.

Editorial extensions

If this is right

  • If the BCPM(v) result is correct, the ISGMR centroid energy of a medium-heavy nucleus can be estimated from its mass number and the nuclear-matter functional without a separate neutron-radius measurement, using the parametrized radius formula.
  • The contrast between the BCPM(v) and Brueckner functionals shows that monopole centroid energies are sensitive enough to the isovector and density dependence of the functional to distinguish between them.
  • When neutron-skin data such as PREX-II and CREX are available, the mean-square-radius route yields ISGMR energies for 48Ca and 208Pb that are close to the HF+BCS values, so those results are robust against skin-measurement differences.
  • The same CDFM scheme yields symmetry energies, slope parameters, and skewnesses for each nucleus, with BCPM(v) values for 208Pb close to chiral-effective-field-theory estimates, connecting the monopole study to the broader equation-of-state program.
  • The two-parameter radius formula could plausibly be applied to nuclei outside the fitted range, though the paper does not itself test that extrapolation.

Reading between the lines

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

  • Because the radius formula is pinned to only 40Ca and 208Pb, the sharpest independent test would be a precise ISGMR measurement on an un-fitted neutron-rich nucleus such as 100Sn or 132Sn, for which the paper currently lists no data.
  • The near-insensitivity of the Eq. (2) energies to the choice of neutron-skin measurement in Sn isotopes suggests that monopole centroid energies by themselves are not a sharp skin observable for stable tin; the full strength distribution would likely be needed.
  • A microscopic derivation of the 2.40/A^{2/3} surface term from computed density profiles would turn the fitted radius into a genuine prediction; until then, its use for exotic nuclei rests on an assumption about how the diffuse surface scales.
  • If the BCPM(v) pattern persists in heavier or more neutron-rich systems, monopole energies could become a low-cost constraint on the isospin dependence of the nuclear equation of state, complementing neutron-star observations.
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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

3 major / 6 minor

Summary. The manuscript applies the coherent density fluctuation model (CDFM) together with Brueckner and BCPM(v) energy density functionals to compute the nuclear incompressibility K_A and isoscalar giant monopole resonance (ISGMR) centroid energies for a range of even-even nuclei from 40Ca to 208Pb. Two definitions of the ISGMR energy are used: Eq. (1), which depends on a radius parameter r0, and Eq. (2), which uses the ground-state mean-square radius. The authors introduce a semi-empirical mass dependence r0(A) = 1 + 2.40/A^{2/3} fm, which they state is obtained by matching Eq. (1) to the experimental ISGMR energies of 40Ca and 208Pb, and report good overall agreement for the BCPM(v) functional in Table IV. They also examine the sensitivity of the results to measured neutron skin thicknesses for Sn isotopes, 48Ca, and 208Pb, and conclude that Eq. (1) with the parametrized radius is preferable to the parameter-free Eq. (2).

Significance. If the central claim were established, the paper would provide a simple semi-empirical relation linking ISGMR energies across A=40-208 to the nuclear-matter incompressibility within the CDFM, and a practical way to use measured neutron skins in monopole-energy estimates. The CDFM formalism in Section II is clearly presented, and the parameter-free Eq. (2) results are useful reference calculations that expose the behavior of the two functionals. However, the agreement that carries the paper's main conclusion is tied to an unvalidated radius parameterization, and the fit claim is internally inconsistent with the numerical tables. The paper is therefore more valuable for its transparent methodology and systematic tabulations than as an established predictive result.

major comments (3)
  1. [Section III, Eqs. (34)-(35) and Table IV] The claim that x=2.40 and y=2/3 were obtained by fitting Eq. (1) to the experimental ISGMR energies of 40Ca and 208Pb is not borne out by the tables. Using the BCPM(v) K_A values from Table II (172.53 MeV for 40Ca and 165.85 MeV for 208Pb) and Eq. (1), the experimental centroid energies of 19.18 MeV and 13.96 MeV require r0 approximately 1.29 fm and 1.00 fm, respectively, whereas Eq. (35) gives 1.205 fm and 1.068 fm. The energies produced at the anchor points are 20.54 MeV for 40Ca and 13.11 MeV for 208Pb, which are not in agreement with the experimental values used to justify the fit. Thus the constants are not fixed by the data they are said to fit, and the apparent overall agreement in Table IV is a property of an ad hoc radius curve rather than an independent validation of the BCPM(v) functional. The manuscript should either derive r0(A) from a physical criterion, refit it with proper error propagation, or explicitly present Eq. (35) as a two-parameter phenomenological input and soften the conclusions accordingly.
  2. [Section IV and Table IV] The statement that a good overall agreement with experimental data for all considered nuclei is achieved with the BCPM(v) functional is too strong even if Eq. (35) is accepted. Table IV shows deviations of +9.8% for 60Ni (19.35 vs 17.62 MeV), +11.1% for 68Zn (18.44 vs 16.6 MeV), and -13.1% for 68Ni (18.33 vs 21.1 MeV), in addition to the anchor-point discrepancies noted above. The conclusion should be rephrased to state the actual level of agreement, including typical deviations and the specific nuclei that are not well reproduced, rather than claiming unqualified overall agreement.
  3. [Section III, Table II and surrounding discussion] The parameter-free Eq. (2) results show substantial disagreement with experiment for most nuclei when the BCPM(v) functional is used (for example 40Ca: 24.92 vs 19.18 MeV; 112Sn: 18.78 vs 16.2 MeV; 208Pb: 14.93 vs 13.96 MeV), while the Brueckner results systematically underestimate Pb by about 2.6 MeV. The manuscript does not quantify these discrepancies nor explain why the fitted radius of Eq. (1) should be preferred over a self-consistent mean-field radius. The preference for Eq. (1) is therefore not supported by a demonstrated failure analysis; the authors should provide a quantitative comparison of both definitions and justify the choice of an externally parameterized radius over the self-consistent one.
minor comments (6)
  1. [Section II, after Eq. (1)] The sentence 'r0 is a radius parameter deduced from the equilibrium density' is not operational; the authors should clarify whether r0 is a half-density radius, an equivalent radius, or a purely fitted parameter.
  2. [Section III, near Eq. (35)] The text says 'the second term in the right-hand side of Eq. (35) 2.40/A^{1/3}' but Eq. (35) contains 2.40/A^{2/3}; this should be corrected.
  3. [Throughout] Several occurrences of 'BCMP(v)' should read 'BCPM(v)' (for example in Tables II and IV and in the text).
  4. [Section IV] There are typos in the summary section: 'due the the lack of precise data' should be 'due to the lack of precise data', and 'we preformed calculations' should be 'we performed calculations'.
  5. [References] Reference [11] lists the journal as 'Phys. Rec. C111'; this should be 'Phys. Rev. C111'.
  6. [Section III, Fig. 2] The caption of Fig. 2 lists the nuclei in a compressed format (for example '40Ca-48Ca54Fe64,68Zn90,92Zr...'); a more readable notation or a supplementary table would help.

Circularity Check

1 steps flagged · score 6.0 of 10

The claimed BCPM(v) agreement for E_ISGMR rests on a two-parameter radius law (Eq. 35) fit to the experimental monopole energies of 40Ca and 208Pb; the Table IV comparison is therefore a fit evaluation rather than an independent prediction.

  1. fitted input called prediction [Section III, Eqs. (34)-(35) and Table IV; Section IV conclusions]
    "Using the comparison of E_ISGMR with the experimental data, we performed a more detailed semi-empirical analysis of the parameter r0. We parameterized it in a form: r0 = (1 + x/A^y) (34) and obtained values of x and y from the fit of E_ISGMR with the data for two nuclei in both limits of the considered nuclear range, namely for 40Ca and 208Pb. In the case of 40Ca r0=1.205 fm and in 208Pb r0=1.068 fm. These two conditions lead to the approximated values of x=2.40 fm and y=2/3. Thus, we obtained the following expression for the radius in the denominator of Eq."

    The central prediction channel is Eq. (1), which contains the radius parameter r0. Rather than deriving r0 from first principles or from independent density measurements, the paper fixes the two constants in r0 = 1 + x/A^y by fitting E_ISGMR to the experimental values for 40Ca and 208Pb. The same fitted r0(A) is then inserted into Eq. (1) for every nucleus, and the resulting Table IV agreement is presented as validation of the BCPM(v) functional. Thus the two anchor nuclei are inputs to the fit, so they cannot serve as independent confirmation, and the 'predicted' energies for all other nuclei are outputs of the same two-parameter empirical curve adjusted to the very observable being tested. The parameter-free Eq.

full rationale

The paper has two branches. Eq. (2) is parameter-free and self-contained: both K_A and the rms radius are computed from the same HF+BCS densities, and this branch is honestly reported in Table II with mixed agreement; it is not circular. The headline claim, however, is made for the Eq. (1) branch. There the denominator radius is not derived; Eqs. (34)-(35) fix x and y by requiring Eq. (1) to match the experimental ISGMR energies of 40Ca and 208Pb. Using the same r0(A) to compute E_ISGMR for all nuclei and then reporting 'good overall agreement' as support for BCPM(v) is a fitted-input-called-prediction pattern: the two anchor data points enter the construction of the model, so their agreement is in-sample by intent, and the intermediate values are outputs of the same two-parameter empirical curve rather than independent tests. The paper itself labels the procedure 'semi-empirical'. Notably, the quoted constants do not actually reproduce the anchors with BCPM(v): Table IV gives 20.54 MeV for 40Ca versus 19.18±0.37 MeV experimental and 13.11 MeV for 208Pb versus 13.96±0.2 MeV experimental; this numerical inconsistency further weakens the claim, although it also means the agreement is not fully forced. The CDFM machinery, the SLy4 densities, and the BCPM(v) EDF are external and self-contained, and there is no load-bearing self-citation. The circularity is localized to the r0 parameterization used for the paper's central conclusion, so the score is 6 rather than higher.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The calculation rests on two imported nuclear matter EDFs, the CDFM mapping, two standard scaling formulas, and one ad hoc two-parameter radius fit. The only fitted constants are x and y in the r0(A) formula; all other parameters are inherited from prior EDFs (Brueckner, BCPM, SLy4). No new physical entities are introduced.

free parameters (1)
  • r0(A) parameterization constants x and y = x=2.40 fm, y=2/3
    Obtained by fitting Eq. (34) so that Eq. (1) reproduces experimental E_ISGMR for 40Ca and 208Pb; these constants set the effective radius denominator for all computed nuclei and are the main reason the BCPM(v) branch agrees with data.
assumptions (5)
  • domain assumption CDFM weight function |F(x)|^2 = -1/rho0(x) drho/dr is valid for all considered nuclei
    Requires drho/dr <= 0 for every r; HF+BCS densities can have shell fluctuations. The weight determines K_A through Eq. (15), so a violation changes all computed energies.
  • domain assumption Nuclear matter incompressibility K(rho) from Brueckner and BCPM(v) EDFs is reliable over the sampled densities
    K_A is a weighted average of K(rho0(x)); errors in the imported EDFs propagate directly into E_ISGMR. The paper does not benchmark K(rho) against independent constraints inside this work.
  • domain assumption Eqs. (1) and (2) connect ISGMR centroid energy to K_A and a radius
    These are standard scaling-model relations from Refs. [22,47], but they are macroscopic approximations; the paper does not compare with an RPA response calculation.
  • ad hoc to paper r0(A) = 1 + 2.40/A^{2/3} remains valid for all A from 40 to 208
    The constants are fitted to two experimental energies (40Ca and 208Pb) and no derivation is provided; the interpolation is assumed to hold for all intermediate nuclei and is the basis of the preferred BCPM(v) agreement.
  • domain assumption SLy4 HF+BCS densities and radii are realistic for all nuclei studied
    Both the CDFM weight function and the mean square radius in Eq. (2) come from these densities; no direct comparison with measured charge radii is shown in the paper.

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Pith. "Pith review of Microscopic analysis of the giant monopole resonance excitation energy." pith.science (2026). https://pith.science/paper/KQEJ5I76

@misc{pith2026250608736,
  author       = {Pith},
  title        = {Pith review of: Microscopic analysis of the giant monopole resonance excitation energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KQEJ5I76}},
  note         = {Machine review of arXiv:2506.08736}
}
read the original abstract

A systematic study of the isoscalar giant monopole resonance (ISGMR) in a wide range of nuclei from various isotopic chains is performed within the microscopic self-consistent Skyrme HF+BCS method and coherent density fluctuation model (CDFM). The calculations for the nuclear incompressibility are based on the Brueckner and Barcelona-Catania-Paris-Madrid (BCPM) energy density functionals for nuclear matter using the capability of the CDFM to make a transition to the corresponding incompressibility in finite nuclei. The results obtained by applying of different definitions of the ISGMR energy, as well as the two energy-density functionals, are analyzed and compared with the available experimental data. The consideration includes the peculiarities of the proton and neutron density distributions and their corresponding linear size characteristics. In general, a connection with the measured neutron skin thicknesses is proposed as a possible way for realistic estimations of the energy of ISGMR.

Figures

Figures reproduced from arXiv: 2506.08736 by the authors.

Figure 1
Figure 1. FIG. 1: The centroid energies [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The dependence of the radius parameter [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

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Reference graph

Works this paper leans on

72 extracted references · 69 canonical work pages

  1. [1]

    G. F. Bertsch and S. Das Gupta, Phys. Rep.160, 189 (1988)

    work page 1988

  2. [2]

    H. A. Bethe, G. E. Brown, J. Applegate, and J. M. Lat- timer, Nucl. Phys. A324, 487 (1979)

    work page 1979

  3. [3]

    Oertel, M

    M. Oertel, M. Hempel, T. Kl¨ ahn, and S. Typel, Rev. Mod. Phys.89, 015007 (2017)

    2017

  4. [4]

    Lindblom, Astrophys

    L. Lindblom, Astrophys. J.398, 569 (1992)

    1992

  5. [5]

    Garg, Acta Physica Polonica B42, 659 (2011)

    U. Garg, Acta Physica Polonica B42, 659 (2011)

    work page 2011

  6. [6]

    S. K. Biswal and S. K. Patra, Cent. Eur. J. Phys.12, 582 (2014)

    work page 2014

  7. [7]

    Monrozeauet al., Phys

    C. Monrozeauet al., Phys. Rev. Lett100, 042501 (2008)

    work page 2008

  8. [8]

    Bagchiet al., Phys

    S. Bagchiet al., Phys. Lett. B751, 371 (2015)

    work page 2015

Show all 72 references
  1. [9]

    Vandebroucket al., Phys

    M. Vandebroucket al., Phys. Rev. Lett113, 032504 (2014)

    2014

  2. [10]

    Vandebroucket al., Phys

    M. Vandebroucket al., Phys. Rev. C92, 024316 (2015)

    2015

  3. [11]

    Arroyoet al., Phys

    J. Arroyoet al., Phys. Rec. C111, 014308 (2025)

    2025

  4. [12]

    Bohigas, A

    O. Bohigas, A. Lane, and J. Martorell, Phys. Rep.51, 267 (1979)

    1979

  5. [13]

    J. P. Blaizot, Phys. Rep.64, 171 (1980)

    1980

  6. [14]

    Garg and G

    U. Garg and G. Col` o, Prog. Part. Nucl. Phys.101, 55 (2018)

    2018

  7. [15]

    Liet al., Phys

    T. Liet al., Phys. Rev. C81, 034309 (2010)

    2010

  8. [16]

    Patel, U

    D. Patel, U. Garg, M. Fujiwara, H. Akimune, G. P. A. Berg, M. N. Harakeh, M. Itoh, T. Kawabata, K. Kawase, B. K. Nayak, T. Ohta, H. Ouchi, J. Piekarewicz, M. Uchida, H. P. Yoshida, M. Yosoi, Phys. Lett. B718, 447 (2012)

    2012

  9. [17]

    J. P. Blaizot, D. Gogny, and B. Grammaticos, Nucl. Phys. A265, 315 (1976)

    1976

  10. [18]

    Button, Y.-W

    J. Button, Y.-W. Lui, D. H. Youngblood, X. Chen, G. Bonasera, and S. Shlomo, Phys. Rev. C96, 054330 (2017)

    2017

  11. [19]

    K. B. Howard, U. Garg, Y. K. Gupta, and M. N. Harakeh, Eur. Phys. J. A55, 228 (2019)

    2019

  12. [20]

    K. B. Howardet al., Phys. Lett. B801, 135185 (2020)

    2020

  13. [21]

    K. B. Howardet al., Phys. Lett. B807, 135608 (2020)

    2020

  14. [22]

    K. A. Brueckner, M. J. Giannoni, and R. J. Lombard, Phys. Lett.31B, 97 (1970)

    1970

  15. [23]

    Shlomo, Pramana-J

    S. Shlomo, Pramana-J. Phys.57, 557 (2001)

    2001

  16. [24]

    Lie-Wen Chen and Jian-Zhong Gu, J. Phys. G39, 035104 (2012)

    2012

  17. [25]

    M. R. Anders and S. Shlomo, J. Phys.: Conf. Ser.420, 012051 (2013)

    2013

  18. [26]

    Jun Su, Long Zhu, and Chenchen Guo, Phys. Rev. C98, 024315 (2018)

    2018

  19. [27]

    Col` o, D

    G. Col` o, D. Gambacurta, W. Kleinig, J. Kvasil, V. O. Nesterenko, and A. Pastore, Phys. Lett. B811, 135940 (2020)

    2020

  20. [28]

    Bonasera, S

    G. Bonasera, S. Shlomo, D. H. Youngblood, Y.-W. Lui, J. Button, and X. Chen, Nucl. Phys. A1010, 122159 (2021)

    2021

  21. [29]

    K. A. Brueckner, J. R. Buchler, S. Jorna, and R. J. Lom- bard, Phys. Rev.171, 1188 (1968)

    1968

  22. [30]

    K. A. Brueckner, J. R. Buchler, R. C. Clark, and R. J. Lombard, Phys. Rev.181, 1543 (1969)

    1969

  23. [31]

    Baldo, L

    M. Baldo, L. M. Robledo, and X. Vi˜ nas, Eur. Phys. J. A 59, 156 (2023)

    2023

  24. [32]

    Baldo, L

    M. Baldo, L. M. Robledo, P. Schuck, and X. Vi˜ nas, Phys. Rev. C87, 064305 (2013)

    2013

  25. [33]

    Baldo, L.M

    M. Baldo, L.M. Robledo, P. Schuck, and X. Vi˜ nas, Phys. Rev. C95, 014318 (2017)

    2017

  26. [34]

    A. N. Antonov, V. A. Nikolaev, and I. Zh. Petkov, Bulg. 11 J. Phys.6, 151 (1979); Z. Phys. A297, 257 (1980);ibid 304, 239 (1982); Nuovo Cimento A86, 23 (1985); Bulg. J. Phys.18, 107 (1991); A. N. Antonovet al.,ibid102, 1701 (1989); A. N. Antonov, D. N. Kadrev, and P. E. Hodgso...

    1979

  27. [35]

    A. N. Antonov, P. E. Hodgson, and I. Zh. Petkov,Nu- cleon Momentum and Density Distributions in Nuclei (Clarendon Press, Oxford, 1988);Nucleon Correlations in Nuclei(Springer-Verlag, Berlin-Heidelberg-New York, 1993)

    1988

  28. [36]

    J. J. Griffin and J. A. Wheeler, Phys. Rev.108, 311 (1957)

    1957

  29. [37]

    M. K. Gaidarov, A. N. Antonov, P. Sarriguren, and E. Moya de Guerra, Phys. Rev. C84, 034316 (2011)

    2011

  30. [38]

    M. K. Gaidarov, A. N. Antonov, P. Sarriguren, and E. Moya de Guerra, Phys. Rev. C85, 064319 (2012)

    2012

  31. [39]

    M. K. Gaidarov, P. Sarriguren, A. N. Antonov, and E. Moya de Guerra, Phys. Rev. C89, 064301 (2014)

    2014

  32. [40]

    A. N. Antonov, M. K. Gaidarov, P. Sarriguren, and E. Moya de Guerra, Phys. Rev. C94, 014319 (2016)

    2016

  33. [41]

    A. N. Antonov, D. N. Kadrev, M. K. Gaidarov, P. Sarrig- uren, and E. Moya de Guerra, Phys. Rev. C98, 054315 (2018)

    2018

  34. [42]

    I. C. Danchev, A. N. Antonov, D. N. Kadrev, M. K. Gaidarov, P. Sarriguren, and E. Moya de Guerra, Phys. Rev. C101, 064315 (2020)

    2020

  35. [43]

    M. K. Gaidarov, I. Moumene, A. N. Antonov, D. N. Kadrev, P. Sarriguren, and E. Moya de Guerra, Nucl. Phys. A1004, 122061 (2020)

    2020

  36. [44]

    M. K. Gaidarov, A. N. Antonov, D. N. Kadrev, P. Sarrig- uren, and E. Moya de Guerra, Chapter inNuclear Struc- ture Physics, ed. by A. Shukla and S. K. Patra, (CRC Press, Taylor & Francis Group, 2020), pp.93–120 (2020)

    2020

  37. [45]

    M. K. Gaidarov, E. Moya de Guerra, A. N. Antonov, I. C. Danchev, P. Sarriguren, and D. N. Kadrev, Phys. Rev. C104, 044312 (2021)

    2021

  38. [46]

    M. K. Gaidarov, M. V. Ivanov, Y. I. Katsarov, and A. N. Antonov, Astronomy2, 1 (2023)

    2023

  39. [47]

    Stringari, Phys

    S. Stringari, Phys. Lett. B108, 232 (1982)

    1982

  40. [48]

    A. E. L. Dieperink, Y. Dewulf, D. Van Neck, M. Waro- quier, and V. Rodin, Phys. Rev. C68, 064307 (2003)

    2003

  41. [49]

    Lie-Wen Chen, Phys. Rev. C83, 044308 (2011)

    2011

  42. [50]

    Col` o, U

    G. Col` o, U. Garg, H. Sagawa, Eur. Phys. J. A50, 26 (2014)

    2014

  43. [51]

    K. A. Brueckner, S. A. Coon, and J. Dabrowski, Phys. Rev.168, 1184 (1968)

    1968

  44. [52]

    Chabanat, P

    E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, Nucl. Phys. A635, 231 (1998)

    1998

  45. [53]

    Vautherin, Phys

    D. Vautherin, Phys. Rev. C7, 296 (1973)

    1973

  46. [54]

    Sarriguren, M

    P. Sarriguren, M. K. Gaidarov, E. Moya de Guerra, and A. N. Antonov, Phys. Rev. C76, 044322 (2007)

    2007

  47. [55]

    Sammarruca and R

    F. Sammarruca and R. Millerson, Universe8, 133 (2022)

    2022

  48. [56]

    Buttonet al., Phys

    J. Buttonet al., Phys. Rev. C100, 064318 (2019)

    2019

  49. [57]

    Luiet al., Phys

    Y.-W. Luiet al., Phys. Rev. C73, 014314 (2006)

    2006

  50. [58]

    Sagawa, and G

    Li-Gang Cao, H. Sagawa, and G. Col` o, Phys. Rev. C86, 054313 (2012)

    2012

  51. [59]

    Fujiwaraet al., AIP Conf

    M. Fujiwaraet al., AIP Conf. Proc.1377, 164 (2011)

    2011

  52. [60]

    D. H. Youngblood, Y.-W. Lui, H. L. Clark, B. John, Y. Tokimoto, and X. Chen, Phys. Rev. C69, 034315 (2004)

    2004

  53. [61]

    De Vries, C

    H. De Vries, C. W. De Jager, and C. De Vries, At. Data Nucl. Data Tables36, 495 (1987)

    1987

  54. [62]

    Ray, Phys

    L. Ray, Phys. Rev. C19, 1855 (1979)

    1979

  55. [63]

    G. W. Hoffmannet al., Phys. Rev. Lett.47, 1436 (1981)

    1981

  56. [64]

    Trzcinska, J

    A. Trzcinska, J. Jastrzebski, P. Lubinski, F. J. Hartmann, R. Schmidt, T. von Egidy, and B. Klos, Phys. Rev. Lett. 87, 082501 (2001)

    2001

  57. [65]

    Krasznahorkayet al., Nucl

    A. Krasznahorkayet al., Nucl. Phys. A567, 521 (1994)

    1994

  58. [66]

    Krasznahorkayet al., Phys

    A. Krasznahorkayet al., Phys. Rev. Lett.82, 3216 (1999)

    1999

  59. [67]

    Krasznahorkayet al., Nucl

    A. Krasznahorkayet al., Nucl. Phys. A731, 224 (2004)

    2004

  60. [68]

    J. D. Patterson and R. J. Peterson, Nucl. Phys. A717, 235 (2003)

    2003

  61. [69]

    Adhikariet al., Phys

    D. Adhikariet al., Phys. Rev. Lett.126, 172502 (2021)

    2021

  62. [70]

    The CREX Collaboration, Phys. Rev. Lett.129, 042501 (2022)

    2022

  63. [71]

    Machleidt and F

    R. Machleidt and F. Sammarruca, Progr. Part. Nucl. Phys.137, 104117 (2024)

    2024

  64. [72]

    Angeli and K.P

    I. Angeli and K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)

    2013

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