Pith. sign in

REVIEW 4 major objections 5 minor 49 references

General Radial-Composition Correlations in Two-Component Many-Body Systems

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read This paper sets out to show that the linear correlation between RMS radius difference and composition asymmetry, seen in nuclei, bimetallic nanoalloys, and self-interacting dark matter, is not a symmetry artifact but is produced by the shor

desk verdict Useful random-ensemble diagnostic for the neutron-skin linearity, but the 'short-range attraction' claim leans on a cutoff fit to the same data, so the confirmation isn't as clean as advertised. read the letter →

arxiv 2602.00529 v2 pith:FM4T4HAB submitted 2026-01-31 nucl-th

Y. Lei This is my paper · ORCID
classification nucl-th
keywords neutronskinthicknessrandom-interactionensemblesharmonic-oscillatormeanfieldMoshinskytransformationvirialtheoremshort-rangecentralforcecompositionasymmetryRMSradiusdifference
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 tries to establish that the nearly universal linear relation between a two-component system's radius difference and its composition asymmetry—the neutron skin versus isospin asymmetry in nuclei, and analogous trends in gold–silver clusters—is generated by one physical ingredient: the short-range attractive central force. Using random-interaction ensembles inside a Hartree-Fock model, it finds that random central forces, unlike random tensor, spin-orbit, or fully random interactions, reproduce the correlation, and that the successful samples have harmonic-oscillator-like single-particle spectra. The proposed mechanism is that a short-range attractive well behaves, at low energy, like a global harmonic oscillator; through the virial theorem, each particle's energy is then tied to its mean squared radius, so adding particles of one species systematically expands its radius. If correct, the linearity is a structural fingerprint of the nuclear force itself, and extrapolations toward neutron-rich matter and other two-component systems are more reliable than they would be if the trend were a modeling artifact.

What carries the argument

The key machinery is the random-interaction ensemble within Hartree-Fock theory, which statistically filters which force components can produce the correlation: only central-force samples do. The explanatory mechanism then rests on two standard results: the Moshinsky transformation (a coordinate transformation that maps a harmonic-oscillator two-body interaction into independent particles moving in a global HO mean field) and the virial theorem, which in an HO field makes single-particle energy proportional to mean squared radius. The named 'short-range' criterion in Eq. (2), r<1.5√(ℏ/mω) with an attractive interior and noise outside, is the operational definition used to build the direct ra

What would settle it

Repeat the random central-force ensemble with the radial matrix elements taken from a purely long-range attractive interaction (e.g., a 1/r potential) across the full model space. If the nine reference nuclei still yield a high rate of strong ΔRnp–I correlation (P(ρ>0.9) ≥ 0.5), then short-range attraction is not the essential ingredient. Alternatively, sweep the cutoff in Eq. (2) upward: if P(ρ>0.9) remains high for r_c > 3.0√(ℏ/mω), the short-range attribution fails.

Watch

Extended reading notes

Core claim

The central discovery is that the ΔRnp–I correlation, long seen across experimental data and many nuclear models, originates specifically from the short-range attractive component of the central nucleon-nucleon interaction. The evidence comes from statistical ensembles: random interactions respecting only symmetries yield essentially no correlation (P(ρ>0.9)<1%); random tensor and spin-orbit components also fail; but random central-force interactions produce a pronounced peak near ρ≈0.95, and the samples that succeed show shell closures at harmonic-oscillator magic numbers 2, 8, 28. A direct test with a potential V(r)=V0(r−r0)² gives ρ≈1 only when the well minimum sits within r0<1.5√(ℏ/mω),

Load-bearing premise

The argument hinges on the cutoff r < 1.5√(ℏ/mω) defining "short-range" in the direct ensemble test; the paper obtains that value from the same central-force samples that already exhibited the correlation, so if it is a fitted threshold rather than an independently derived scale, the 78.7% success rate is not a clean confirmation.

Editorial extensions

If this is right

  • The neutron skin–isospin linearity can be trusted as a structural fingerprint of the nuclear force, making empirical fits and extrapolations toward neutron-rich nuclei more reliable.
  • Because the correlation is insensitive to the sharpness of the attractive potential, mean-field, droplet, and ab initio models that share short-range attraction will all reproduce the trend, explaining the convergence among frameworks.
  • The slope of the ΔRnp–I correlation can serve as a route to quantify the symmetry-energy slope L, as proposed in the paper's companion work and supported by this mechanism.
  • Two-component systems beyond nuclei—such as bimetallic nanoalloys and dark-matter halos with self-interactions—should exhibit the same correlation whenever their pair interaction is short-range and attractive.
  • Tensor and spin-orbit forces are not responsible for the correlation; random ensembles show that without the central force, the linear trend does not emerge.

Reading between the lines

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

  • Because the short-range cutoff is chosen from the same data it is used to explain, an independent test should derive it from a physically defined scale (scattering length or effective range). If P(ρ>0.9) stays high for cutoffs well beyond 1.5√(ℏ/mω), the claim that attraction must be short-range would weaken.
  • The shell-filling mechanism implies that isotope chains crossing a major shell closure should show kinks in the ΔR–I line, mirroring the piecewise segments in Au–Ag clusters; parity-violating electron scattering on such isotope chains could look for these breaks.
  • A direct realization could be made in an ultracold two-component Fermi gas with tunable Feshbach resonances: as the interaction is tuned from short-range attractive to repulsive, the predicted radius–asymmetry correlation should switch on and off, providing a controlled test of universality.
  • The paper's argument ties the slope of the correlation to the effective oscillator frequency of the mean field; a natural extension is to predict that systems with a deeper, longer-ranged attraction will show a steeper slope, which the nanoalloy data or dark-matter simulations could check.
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

4 major / 5 minor

Summary. The paper uses random-interaction ensembles in a Hartree-Fock framework over nine reference nuclei to identify the interaction ingredients required for the robust linear correlation between neutron-proton RMS radius difference, ΔRnp, and isospin asymmetry, I. It reports that random quasi-particle, tensor, and spin-orbit ensembles fail to produce strong correlations, while a random central-force ensemble produces a peak near ρ≈0.95. Analyzing the successful central-force samples, the paper finds HO-like radial matrix elements and single-particle spectra. It then tests a parameterized harmonic-oscillator potential V(r)=V0(r−r0)^2, finding strong positive correlation only for an attractive potential with minimum r0<1.5√(ℏ/mω). This threshold is then used in Eq. (2) to define a random short-range attractive ensemble, which yields P(ρ>0.9)≈78.7% for V0=1 and near 100% for V0≥2. The authors conclude that short-range attraction of the central force is the essential ingredient, with a proposed mechanism based on Moshinsky transformation and the virial theorem, and support this by citing a similar correlation in Au-Ag nano-alloy clusters.

Significance. If the central claim is correct, the paper offers a conceptually simple and potentially universal explanation for a correlation observed across nuclear experiments, mean-field and ab initio models, metallic nano-alloys, and possibly self-interacting dark matter. The ensemble-decomposition strategy is a useful stress test: the negative results for tensor and spin-orbit forces and the nontrivial peak for central forces are interesting and go beyond a pure symmetry argument. The proposed mechanism would also make falsifiable predictions about other two-component systems. However, the load-bearing evidence is weakened by a cutoff in Eq. (2) that is calibrated using the same data and correlation metric, and by a mechanism that is presented qualitatively rather than derived. The paper is therefore a promising contribution that needs substantial additional verification before its strong conclusions can be accepted.

major comments (4)
  1. [Eq. (2) and preceding HO test] The short-range ensemble success is not an independent confirmation. The cutoff r_c=1.5√(ℏ/mω) in Eq. (2) is explicitly described as 'informed by our earlier finding' from the V0(r−r0)^2 test on the same nine nuclei and the same Pearson-ρ metric. Thus the 78.7% P(ρ>0.9) is conditioned on a threshold optimized on this same dataset. The paper should provide a sensitivity scan of P(ρ>0.9) versus r_c, and ideally a derivation of the cutoff from the interaction scale or a training/validation split. Without this, the claim that short-range attraction is the essential ingredient is overstated.
  2. [Random central-force ensemble and 'essential ingredient'] The text says the central force is 'unambiguously' the primary driver and later that short-range attraction is 'the essential ingredient.' However, the random central-force ensemble yields only about 20% of samples with ρ>0.8, and the short-range ensemble with V0=1 gives 78.7% with ρ>0.9. These numbers establish sufficiency under the chosen ensemble definitions, but not necessity. The paper does not show that successful central-force samples are exclusively short-range attractive, nor that long-range attractive central forces fail. A classification of central-force samples by range and sign of the potential is needed to support 'essential.'
  3. [Mechanism (Moshinsky/virial)] The proposed mechanism is presented in prose: in an HO mean field, energy and mean-square radius are proportional by the virial theorem, so sequential filling correlates radius with particle number. No equation or toy model shows how this yields linearity of ΔRnp in I. The proportionality is per single-particle level, but the total RMS radii of neutrons and protons depend on occupation numbers, shell degeneracies, and level spacing. Linearity in I is not automatic from per-level proportionality. This is a load-bearing gap in the argument and should be filled with a derivation or a quantitative minimal model.
  4. [Low-energy HO expansion and universality] The statement that 'any short-range potential with an attractive well near r=0 can be expanded as an HO potential in the low-energy limit' is an unsupported assumption. It conflates a two-body potential with the many-body mean field, and no derivation or reference is given. This assumption is the bridge between the random short-range result and the universal mechanism. The paper also extends the claim to dark matter and all two-component systems, but only one nano-alloy system is tested. A many-body derivation or a demonstration within the HF ensemble that short-range samples systematically produce HO-like single-particle spectra is needed.
minor comments (5)
  1. [Eq. (2) and model space] The oscillator parameter ω entering the cutoff 1.5√(ℏ/mω) is not specified. Since the model space is defined in HO basis, the numerical value of the cutoff depends on this choice. Please state ω (or the corresponding oscillator length b) and check sensitivity.
  2. [Thresholds] The paper uses ρ>0.85 for identifying 'successful' samples in Figs. 3 and 4, but quotes success rates with ρ>0.9 in Fig. 2 and the text. These thresholds should be made consistent or the choice should be justified.
  3. [Fig. 3] The figure shows ensemble-averaged radial matrix elements. The text acknowledges that individual samples only capture a few HO-like features. This caveat weakens the inference from the ensemble average to 'successful samples are HO-like.' A distribution or representative examples would strengthen the claim.
  4. [Abstract and scope] The abstract mentions self-interacting dark matter, but no dark-matter calculation or model is presented in the paper. Either add a test in a simple self-interacting dark-matter halo model or temper the claim about universality.
  5. [Eq. (2)] The notation V_S(r)∼N(−V0,1) is ambiguous: are values of V_S(r) sampled independently at each radial point, or is the potential a random function with some smoothness? Please clarify the construction of the random short-range ensemble.

Circularity Check

1 steps flagged · score 6.0 of 10

Short-range confirmation is calibrated: the 1.5√(ℏ/mω) cutoff in Eq. (2) is read off the same correlation test, so the reported 78.7% success rate is not an independent confirmation.

  1. fitted input called prediction [Eq. (2) and preceding explicit HO test paragraph (V(r)=V0(r−r0)^2)]
    "where a positive V0 ensures attraction and the critical distance 1.5√ℏ/mω is informed by our earlier finding regarding the localization of the potential minimum for strong ΔRnp−I correlation."

    The cutoff 1.5√ℏ/mω is not derived from the interaction or from an independent scale; it is exactly the boundary identified in the same paper's V0(r−r0)^2 test: 'Strong positive correlations (ρ≈1) only emerge when the minimum is localized within r0<1.5√ℏ/mω.' That test was performed on the same nine reference nuclei and evaluated with the same ΔRnp−I Pearson correlation. Reusing this calibrated boundary as the definition of 'short-range' in Eq. (2) means the short-range ensemble has been constructed to include the already-known-good region and exclude the already-known-bad region. The resulting P(ρ>0.9)≈78.7% therefore quantifies the earlier calibration rather than independently confirming that short-range attraction is the essential ingredient.

full rationale

Most of the paper's derivation is self-contained and non-circular. The RQE benchmark shows that symmetry alone does not force the ΔRnp–I correlation; the random central, tensor, and spin-orbit ensembles are independently sampled, and the central-force success (~20% with ρ>0.8) is a genuine ensemble result. The Fig. 3 comparison of successful samples with HO matrix elements is a post-hoc diagnostic, not used as evidence in itself. The explicit V0(r−r0)^2 scan is also a direct model test. The central circularity concern is localized to Eq. (2). The critical distance is not derived from the interaction; the paper states it is 'informed by our earlier finding' that strong positive correlations arise only when the HO-potential minimum r0<1.5√ℏ/mω. That earlier finding is obtained by scanning the same nine nuclei with the same Pearson metric, i.e., the threshold is calibrated on the very correlation under study. Reusing the same threshold as the definition of the 'short-range' ensemble means the 78.7% P(ρ>0.9) rate, and the claim that this 'directly identify[ies] short-range attraction as the essential ingredient,' quantifies a condition that was already known to produce the correlation. This is partial circularity, not complete: the random short-range ensemble still samples many non-HO radial shapes and is not literally the same as the V0(r−r0)^2 fit, and the central-force/random-ensemble part does not depend on the calibrated cutoff. The Au–Ag cluster analysis is external (Ref [46]) and provides independent qualitative support. There is also a self-citation to Ref [24] for the Skyrme-randomness observation, but it is motivational rather than load-bearing for the central derivation.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the random-ensemble sampling choices (model space, selected nuclei, sampling variance, success threshold) and on the HO/virial mapping. The most consequential input is the post-hoc cutoff in Eq. (2), which limits independence. No new entities such as particles or forces are introduced.

free parameters (4)
  • short-range cutoff r_c in Eq. (2) = 1.5 sqrt(ℏ/mω)
    Chosen after inspecting which random-central-force samples produced ρ > 0.85; the high success rate of the short-range ensemble depends on this value, so it is not an independent prediction.
  • potential-minimum threshold r0 = r0 < 1.5 sqrt(ℏ/mω)
    In the explicit V(r)=V0(r−r0)^2 test, strong correlation appears only below this threshold; the threshold is read off the same data and used to justify the cutoff in Eq. (2).
  • attractive strength V0 in short-range ensemble = V0=1 gives P(ρ>0.9)≈78.7%; V0≥2 gives ≈100%
    Varied as a control to show saturation, but not derived from theory; it demonstrates robustness to strength, not a prediction.
  • successful-sample threshold ρ > 0.85 = 0.85
    Defines which random-central-force samples are averaged to infer HO-likeness and matrix-element fingerprints; different thresholds could change the inferred structural feature.
assumptions (6)
  • standard math Virial theorem for harmonic-oscillator single-particle states: energy proportional to mean square radius.
    Invoked in the mechanism section to link sequential energy-level filling to increasing spatial extent.
  • standard math Moshinsky transformation maps a two-body HO interaction into a global HO mean field.
    Cited via Ref. [45] and used to justify the independent-particle HO description of the short-range interacting system.
  • domain assumption Random-interaction ensembles in a 0s1/2 to pf model space over nine chosen nuclei represent generic many-body behavior relevant to the ΔRnp–I correlation.
    The statistical conclusions about which force components produce linearity depend on this model space and the selected nuclei.
  • domain assumption Decomposing the nuclear force into central, tensor, and spin-orbit components and randomizing their radial matrix elements isolates the physical ingredients.
    Used in the central ensemble analysis; assumes no important ingredient is left out of the decomposition.
  • ad hoc to paper Any short-range potential with an attractive well near r=0 can be expanded as an HO potential in the low-energy limit.
    This is the pivot from HO-like matrix elements to real nuclear forces; the paper gives no rigorous derivation and uses it to generalize the mechanism.
  • ad hoc to paper The critical distance 1.5 sqrt(ℏ/mω) is the correct operational definition of 'short-range' for the interaction.
    Not derived from first principles; it is introduced after inspecting which HO-like samples produce strong correlations and is reused as the Eq. (2) cutoff.

how reviews work

0 comments
Cite this review

Pith. "Pith review of General Radial-Composition Correlations in Two-Component Many-Body Systems." pith.science (2026). https://pith.science/paper/FM4T4HAB

@misc{pith2026260200529,
  author       = {Pith},
  title        = {Pith review of: General Radial-Composition Correlations in Two-Component Many-Body Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FM4T4HAB}},
  note         = {Machine review of arXiv:2602.00529}
}
read the original abstract

The linear correlation between RMS radius difference and composition asymmetry in two-component many-body systems is a robust feature observed across nuclear experiments, diverse nuclear structural models, molecular dynamic simulations for bimetallic clusters, and galactic modeling with self-interacting dark matter. We identify the short-range attractive central force as the key ingredient for its emergence, a mechanism underpinned by the coordinate transformation under low-energy harmonic-oscillator approximation, the virial theorem, and Pauli principle/hard core potential, in many-fermion system/classic many-body system.

Figures

Figures reproduced from arXiv: 2602.00529 by the authors.

Figure 1
Figure 1. FIG. 1. Experimental ∆ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (Color online) Distributions of Pearson’s [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (Color online) Hartree-Fock (HF) mean-field single [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. (Color online) Correlations between the RMS radial [PITH_FULL_IMAGE:figures/full_fig_p003_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

49 extracted references · 1 canonical work pages

  1. [1]

    Alex Brown, Neutron radii in nuclei and the neutron equation of state, Phys

    B. Alex Brown, Neutron radii in nuclei and the neutron equation of state, Phys. Rev. Lett. 85, 5296 (2000)

    2000

  2. [2]

    C. J. Horowitz and J. Piekarewicz, Neutron star structure and the neutron radius of208pb, Phys. Rev. Lett. 86, 5647 (2001)

    2001

  3. [3]

    M. B. Tsang, J. R. Stone, F. Camera, P. Danielewicz, S. Gandolfi, K. Hebeler, C. J. Horowitz, J. Lee, W. G. Lynch, Z. Kohley, R. Lemmon, P. M¨ oller, T. Murakami, S. Riordan, X. Roca-Maza, F. Sammarruca, A. W. Steiner, I. Vida˜ na, and S. J. Yennello, Constraints on the symmetry energy and neutron skins from experiments and theory, Phys. Rev. C 86, 015803 (2012)

    2012

  4. [4]

    Hagen, A

    G. Hagen, A. Ekstr¨ om, C. Forss´ en, G. R. Jansen, W. Nazarewicz, T. Papenbrock, K. A. Wendt, S. Bacca, N. Barnea, B. Carlsson, C. Drischler, K. Hebeler, M. Hjorth-Jensen, M. Miorelli, G. Orlandini, A. Schwenk, and J. Simonis, Neutron and weak-charge distributions of the 48ca nucleus, Nature Physics 12, 186 (2016)

    2016

  5. [5]

    2 of of Ref

    The observed piecewise linearity directly tracks the evolution of shell occupation already demonstrated in Fig. 2 of of Ref. [ 46]: the segments x = 30–110 and x = 111–180 cor- respond to the Au-atom filling of the 3rd and 4th shells, respectively, with a chaotic transition at x = 145 − 166 due to irregular 2nd-shell occupation; subsequent steady growth in...

  6. [6]

    B. A. Brown, Mirror charge radii and the neutron equa- tion of state, Phys. Rev. Lett. 119, 122502 (2017)

    2017

  7. [7]

    F. J. Fattoyev, J. Piekarewicz, and C. J. Horowitz, Neu- tron skins and neutron stars in the multimessenger era, Phys. Rev. Lett. 120, 172702 (2018)

    2018

  8. [8]

    C. A. Bertulani and J. Valencia, Neutron skins as labo- ratory constraints on properties of neutron stars and on what we can learn from heavy ion fragmentation reac- tions, Phys. Rev. C 100, 015802 (2019)

    2019

Show all 49 references
  1. [9]

    Roca-Maza, M

    X. Roca-Maza, M. Centelles, X. Vi˜ nas, and M. Warda, Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment, Phys. Rev. Lett. 106, 252501 (2011)

    2011

  2. [10]

    Reinhard and W

    P.-G. Reinhard and W. Nazarewicz, Nuclear charge and neutron radii and nuclear matter: Trend analysis in skyrme density-functional-theory approach, Phys. Rev. C 93, 051303 (2016)

    2016

  3. [11]

    Steiner, M

    A. Steiner, M. Prakash, J. Lattimer, and P. Ellis, Isospin asymmetry in nuclei and neutron stars, Physics Reports 411, 325 (2005)

    2005

  4. [12]

    Zenihiro, H

    J. Zenihiro, H. Sakaguchi, S. Terashima, T. Uesaka, G. Hagen, M. Itoh, T. Murakami, Y. Nakatsugawa, T. Ohnishi, H. Sagawa, H. Takeda, M. Uchida, H. P. Yoshida, S. Yoshida, and M. Yosoi, Direct determina- tion of the neutron skin thicknesses in 40,48ca from proton elastic scatt...

    2018 arXiv

  5. [13]

    JASTRZEBSKI, A

    J. JASTRZEBSKI, A. TRZCI ´NSKA, P. LUBI ´NSKI, B. K/suppress LOS, F. J. HARTMANN, T. von EGIDY, and S. WYCECH, Neutron density distributions from an- 5 tiprotonic atoms compared with hadron scattering data, International Journal of Modern Physics E 13, 343 (2004), https://doi....

    2004 doi

  6. [14]

    W. R. Gibbs and J.-P. Dedonder, Neutron radii of the calcium isotopes, Phys. Rev. C 46, 1825 (1992)

    1992

  7. [15]

    Adhikari, H

    D. Adhikari, H. Albataineh, D. Androic, K. A. Aniol, D. S. Armstrong, T. Averett, C. Ayerbe Gayoso, S. K. Barcus, V. Bellini, R. S. Beminiwattha, J. F. Benesch, H. Bhatt, D. Bhatta Pathak, D. Bhetuwal, B. Blaikie, J. Boyd, Q. Campagna, A. Camsonne, G. D. Cates, Y. Chen, C. Cla...

    2022

  8. [16]

    Giacalone, G

    G. Giacalone, G. Nijs, and W. van der Schee, Determi- nation of the neutron skin of 208Pb from ultrarelativistic nuclear collisions, Phys. Rev. Lett. 131, 202302 (2023)

    2023

  9. [17]

    Karl, Vii

    P. Karl, Vii. note on regression and inheritance in the case of two parents, Proc. R. Soc. Lond. 58, 240 (1895)

  10. [18]

    T. Li, Y. Luo, and N. Wang, Compilation of recent nu- clear ground state charge radius measurements and tests for models, Atomic Data and Nuclear Data Tables 140, 101440 (2021)

    2021

  11. [19]

    Trzci´ nska, J

    A. Trzci´ nska, J. Jastrz¸ ebski, P. Lubi´ nski, F. J. Hart- mann, R. Schmidt, T. von Egidy, and B. K/suppress los, Neutron density distributions deduced from antiprotonic atoms, Phys. Rev. Lett. 87, 082501 (2001)

    2001

  12. [20]

    S. J. Novario, D. Lonardoni, S. Gandolfi, and G. Hagen, Trends of neutron skins and radii of mirror nuclei from first principles, Phys. Rev. Lett. 130, 032501 (2023)

    2023

  13. [21]

    W. D. Myers and W. Swiatecki, Average nuclear proper- ties, Annals of Physics 55, 395 (1969)

    1969

  14. [22]

    Myers and W

    W. Myers and W. Swiatecki, The nuclear droplet model for arbitrary shapes, Annals of Physics 84, 186 (1974)

    1974

  15. [23]

    Myers and W

    W. Myers and W. Swiatecki, Droplet-model theory of the neutron skin, Nuclear Physics A 336, 267 (1980)

    1980

  16. [24]

    Pethick and D

    C. Pethick and D. Ravenhall, The dependence of neutron skin thickness and surface tension on neutron excess, Nu- clear Physics A 606, 173 (1996)

    1996

  17. [25]

    Y. Lei, X. Lian, and C. L. Bai, Robust linear correlations related to neutron skin thickness (2025), Phys. Rev. C accepted, 2026, arXiv:2502.05820 [nucl-th]

    2025 arXiv

  18. [26]

    Kota, Embedded random matrix ensembles for com- plexity and chaos in finite interacting particle systems, Physics Reports 347, 223 (2001)

    V. Kota, Embedded random matrix ensembles for com- plexity and chaos in finite interacting particle systems, Physics Reports 347, 223 (2001)

    2001

  19. [27]

    Y. Zhao, A. Arima, and N. Yoshinaga, Regularities of many-body systems interacting by a two-body random ensemble, Physics Reports 400, 1 (2004)

    2004

  20. [28]

    Zelevinsky and A

    V. Zelevinsky and A. Volya, Nuclear structure, ran- dom interactions and mesoscopic physics, Physics Re- ports 391, 311 (2004) , from atoms to nuclei to quarks and gluons: the omnipresent manybody theory

    2004

  21. [29]

    H. A. Weidenm¨ uller and G. E. Mitchell, Random matri- ces and chaos in nuclear physics: Nuclear structure, Rev. Mod. Phys. 81, 539 (2009)

    2009

  22. [30]

    C. W. Johnson, G. F. Bertsch, and D. J. Dean, Orderly spectra from random interactions, Phys. Rev. Lett. 80, 2749 (1998)

    1998

  23. [31]

    Y. M. Zhao, A. Arima, N. Shimizu, K. Ogawa, N. Yoshi- naga, and O. Scholten, Patterns of the ground states in the presence of random interactions: Nucleon systems, Phys. Rev. C 70, 054322 (2004)

    2004

  24. [32]

    Bijker and A

    R. Bijker and A. Frank, Band structure from random interactions, Phys. Rev. Lett. 84, 420 (2000)

    2000

  25. [33]

    Y. Lei, Z. Y. Xu, Y. M. Zhao, S. Pittel, and A. Arima, Emergence of generalized seniority in low-lying states with random interactions, Phys. Rev. C 83, 024302 (2011)

    2011

  26. [34]

    Y. Lu, Y. M. Zhao, N. Yoshida, and A. Arima, Correla- tions between low-lying yrast states for sd bosons with random interactions, Phys. Rev. C 90, 064313 (2014)

    2014

  27. [35]

    noncol- lective

    J. J. Shen, H. Jiang, and G. J. Fu, Robustness of “noncol- lective” rotational behavior for nuclei in the presence of random interactions, Phys. Rev. C 104, 054319 (2021)

    2021

  28. [36]

    White, A

    C. White, A. Volya, D. Mulhall, and V. Zelevinsky, Structured ground states of randomly interacting bosons, Phys. Rev. Res. 5, 013109 (2023)

    2023

  29. [37]

    G. J. Fu and C. Qi, Novel triaxiality-driven collective feature in atomic nuclei investigated via the two-body random ensemble, Phys. Rev. C 112, L061301 (2025)

    2025

  30. [38]

    G. J. Fu, J. J. Shen, Y. M. Zhao, and A. Arima, Regu- larities in low-lying states of atomic nuclei with random interactions, Phys. Rev. C 91, 054319 (2015)

    2015

  31. [39]

    Y. Lei, Y. M. Zhao, N. Yoshida, and A. Arima, Corre- lations of excited states for sd bosons in the presence of random interactions, Phys. Rev. C 83, 044302 (2011)

    2011

  32. [40]

    Lei, Robust correlations between quadrupole moments of low-lying 2 + states within random-interaction ensem- bles, Phys

    Y. Lei, Robust correlations between quadrupole moments of low-lying 2 + states within random-interaction ensem- bles, Phys. Rev. C 93, 024319 (2016)

    2016

  33. [41]

    Qin and Y

    Z.-Z. Qin and Y. Lei, Predominance of linear q andµ sys- tematics in random-interaction ensembles, Nuclear Sci- ence and Techniques 29, 163 (2018)

    2018

  34. [42]

    Stetcu and C

    I. Stetcu and C. W. Johnson, Random phase approxima- tion vs exact shell-model correlation energies, Phys. Rev. C 66, 034301 (2002)

    2002

  35. [43]

    Stetcu and C

    I. Stetcu and C. W. Johnson, Tests of the random phase approximation for transition strengths, Phys. Rev. C 67, 044315 (2003)

    2003

  36. [44]

    Stetcu and C

    I. Stetcu and C. W. Johnson, Gamow-teller transitions and deformation in the proton-neutron random phase ap- proximation, Phys. Rev. C 69, 024311 (2004)

    2004

  37. [45]

    Lawson, Theory of the Nuclear Shell Model , Oxford studies in nuclear physics (Clarendon Press, 1980)

    R. Lawson, Theory of the Nuclear Shell Model , Oxford studies in nuclear physics (Clarendon Press, 1980)

    1980

  38. [46]

    Moshinsky, Transformation brackets for harmonic os- cillator functions, Nuclear Physics 13, 104 (1959)

    M. Moshinsky, Transformation brackets for harmonic os- cillator functions, Nuclear Physics 13, 104 (1959)

    1959

  39. [47]

    P. M. Larsen, K. W. Jacobsen, and J. Schiøtz, Rich ground-state chemical ordering in nanoparticles: Exact solution of a model for ag-au clusters, Phys. Rev. Lett. 120, 256101 (2018)

    2018

  40. [48]

    Jacobsen, P

    K. Jacobsen, P. Stoltze, and J. Norskov, A semi-empirical 6 effective medium theory for metals and alloys, Surface Science 366, 394 (1996)

    1996

  41. [49]

    Guisbiers, R

    G. Guisbiers, R. Mendoza-Cruz, L. Baz´ an-D´ ıaz, J. J. Vel´ azquez-Salazar, R. Mendoza-Perez, J. A. Robledo- Torres, J.-L. Rodriguez-Lopez, J. M. Montejano- Carrizales, R. L. Whetten, and M. Jos´ e-Yacam´ an, Elec- trum, the gold–silver alloy, from the bulk scale to the nanos...

    2016

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.