Robust linear correlations related to neutron skin thickness

C. L. Bai; X. Lian; Y. Lei

REVIEW 3 major objections 7 minor 1 cited by

Robust linear correlations related to neutron skin thickness

T0 review · 3 major / 7 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read Mirror-radius and neutron-skin slopes put the nuclear symmetry energy at 28–36 MeV.

desk verdict New empirical C–L correlations are useful; the L constraint is prior-dependent and needs sensitivity checks. read the letter →

arxiv 2502.05820 v2 pith:EDWZRTKZ submitted 2025-02-09 nucl-th

Y. Lei , X. Lian , C. L. Bai This is my paper · ORCID

classification nucl-th

keywords neutronskinthicknessmirrorchargeradiisymmetryenergysloperandomSkyrmeensemblequasi-particleshapecoexistencenuclearequationofstateisospinasymmetry

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 shows that two simple nuclear-radius observables, the neutron skin thickness $\Delta R_{\rm np}$ and the charge-radius difference of mirror nuclei (nuclei with proton and neutron numbers interchanged), grow linearly with isospin asymmetry $I=(N-Z)/A$, and that this linearity becomes more pronounced as the model space grows, both in shell-model calculations with random interactions and in a newly built random Skyrme ensemble. The slopes of those lines, $C_{\rm np}$ and $C_{\rm mirr}$, are in turn linearly correlated with the symmetry-energy slope $L$, the quantity that controls the softness of the nuclear equation of state and the size of neutron stars. The paper uses this two-step linearity to turn measured radius trends into a $1\sigma$ constraint $L=28\pm8$ MeV (about 20–36 MeV), and narrows it to about 28–36 MeV by attributing the outlier mirror pair 18O/Ne to shape coexistence. If the claim holds, neutron-skin and mirror-charge-radius measurements become a practical, mostly proton-based ruler for the equation of state.

What carries the argument

The machinery is the pair of slopes $C_{\rm np}$ and $C_{\rm mirr}$ obtained by fitting $\Delta R_{\rm np}$ and $\Delta R_{\rm mirr}$ against the isospin asymmetry $I$ across a set of even-even nuclei, used as composite observables that average over nuclear-structure details. The explanation for why $C_{\rm np}$ tracks $L$ runs through the relation $C_{\rm np}=\frac{3}{2}r_0 J/Q^*$, with the effective surface stiffness $Q^*$ treated as roughly constant, and through the observation that $L$ and $J$ are nearly linearly related because both are linear combinations of the same four contributions $J_1,\dots,J_4$. The random Skyrme ensemble supplies the sampling distribution over which the experimental slope constraints are filtered.

What would settle it

A well-calibrated energy-density functional with $L$ inside the claimed 28–36 MeV band that, in a large model space, gives correlation coefficient $r<0.85$ for $\Delta R_{\rm np}$–$I$ or slopes far from $C_{\rm np}=0.9(1)$ and $C_{\rm mirr}=1.31(4)$ would break the claimed universality; alternatively, a precision measurement showing 18O/Ne lies on the $\Delta R_{\rm mirr}=1.31I$ line without a coexisting shape would remove the basis for the narrower band.

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Extended reading notes

Core claim

On the paper's own terms, the central claim is that the experimentally observed linear trends—$\Delta R_{\rm np}=0.9(1)I-0.04(2)$ and $\Delta R_{\rm mirr}=1.31(4)I$—are not accidents of particular interactions. In the random quasi-particle ensemble the probability of correlation coefficient $|r|>0.95$ for both correlations grows with model-space size, and in the random Skyrme ensemble (built from the mean and covariance of 160 fitted parametrizations) strong linearity appears in more than half of the samples for $\Delta R_{\rm np}$ and in roughly 89% for $\Delta R_{\rm mirr}$. The slopes $C_{\rm np}$ and $C_{\rm mirr}$ extracted from these fits are themselves linearly correlated with $L$, a connection the paper traces to the structural similarity between the formulas for $L$ and the symmetry-energy coefficient $J$. Filtering the ensemble to reproduce the experimental slopes gives a $1\sigma$ constraint $L=28\pm8$ MeV; requiring additionally that the $\Delta R_{\rm mirr}$ of 18O/Ne be reproduced, with shape coexistence supplying the extra radius value, narrows the range to $32\pm4$ MeV, roughly 28–36 MeV, pointing to a relatively soft symmetry energy.

Load-bearing premise

The load-bearing assumption is that the random Skyrme ensemble, generated from the mean and covariance of 160 previously fitted parametrizations, fairly spans the realistic space of nuclear interactions—and, within the analytical explanation, that the effective surface stiffness $Q^*$ stays nearly constant while $J$ varies.

Editorial extensions

If this is right

The $\Delta R_{\rm np}$–$I$ and $\Delta R_{\rm mirr}$–$I$ trends become more pronounced in larger model spaces, so the correlations should be treated as a generic property of finite nuclear matter rather than a feature of one interaction.
Because $C_{\rm np}$ and $C_{\rm mirr}$ are slopes built from all available radius data, they can constrain $L$ without relying on a single high-precision neutron-radius measurement.
With the experimental slopes, the $1\sigma$ band is $L=28\pm8$ MeV; after including the shape-coexistence reading of 18O/Ne, the band shrinks to about 28–36 MeV, implying a relatively soft equation of state and smaller neutron-star radii.
The shape-coexistence interpretation predicts that odd-$A$ mirror pairs, where an unpaired nucleon can alter the nuclear shape, will scatter more strongly around the $\Delta R_{\rm mirr}$–$I$ line than even-even pairs.

Reading between the lines

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

If the Gaussian prior over Skyrme parameters fairly spans realistic functionals, the same slope-matching procedure could be applied to other composite observables, and the near-linearity of $J$ with $L$ suggests the $L$ constraint may be relatively insensitive to which functional family is used.
The model-space trend implies that future radius measurements of heavier mirror pairs should show even cleaner $\Delta R_{\rm mirr}$–$I$ linearity, providing a direct test of the universality claim.
The 18O/Ne correction is testable: a measurement or ab initio calculation that resolves two coexisting charge radii for 18O/Ne would confirm the shape-coexistence picture, while a single-shape result on the $1.31I$ line would shift the final $L$ band by several MeV.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The genuinely new result here is the random Skyrme ensemble and the observation that the slopes Cnp and Cmirr of the ΔRnp–I and ΔRmirr–I linear relations track L linearly across a wide spread of parametrizations. That is a genuinely useful organizing fact, and the paper earns credit for it. The RQE and RSE calculations are extensive, the counting statistics are clear, and the finding that ΔRnp–I and ΔRmirr–I linearity strengthens as the model space grows is solid and interesting. The J–L explanation via shared linear-combination structure is plausible and supported by a simple random-variable test.

The soft spot is the L constraint in Sec. IV. It is an ensemble-filtering exercise: the RSE is built from a multivariate Gaussian fit to 160 existing Skyrme parametrizations, then stratified to uniform L bins, filtered by Pearson r thresholds and experimental slopes, and the surviving L distribution is fit with a Gaussian to quote 28±8 MeV. Each of those steps is a prior choice, and no sensitivity test is given. The uniform-L stratification in particular is doing real work; if the true distribution of realistic functionals is not uniform in L, the quoted interval inherits that assumption. The abstract's 20–36 MeV range vs the text's 28±8 MeV (and 32±4 with the shape-coexistence cut) also needs reconciliation. The Q*≈const assumption in Eq. (3) is secondary because the empirical C–L linearity stands on its own, but it is unverified.

The shape-coexistence discussion for 18O/Ne is reasonable but post hoc, and it narrows the constraint using a subset of the same prior. I would not treat the L interval as a measurement; I would treat it as a conditional illustration.

Who is this for? Nuclear structure people working on neutron skins and mirror charge radii will find the correlation results useful and will want to cite the RSE construction. The L constraint should be read as preliminary. The paper deserves a serious referee because the empirical correlations are solid and the method can be strengthened with a prior-sensitivity analysis. My recommendation: engage with it, but push for the sensitivity checks and a consistent statement of the quoted interval.

Referee Report

3 major / 7 minor

Summary. The paper reports the observation of robust linear correlations between neutron skin thickness (ΔRnp) or mirror-nucleus charge-radius difference (ΔRmirr) and isospin asymmetry I, using two random-interaction ensembles (the random quasi-particle ensemble RQE in shell-model spaces and the new random Skyrme ensemble RSE built from a Gaussian distribution of the 10 Skyrme parameters fitted to 160 published parametrizations). It finds that the linearity becomes more pronounced as the model space is enlarged, and that the slopes Cnp and Cmirr of these correlations are linearly correlated with the symmetry energy slope L in the Skyrme ensemble and RSE. Using these correlations as an inverse calibration, the authors filter the RSE by the experimental slopes and obtain L = 28 ± 8 MeV (1σ), which they further narrow to L = 32 ± 4 MeV when the 18O/Ne mirror pair is included via the shape-coexistence hypothesis, suggesting a relatively soft nuclear equation of state.

Significance. If the L constraint were robust, this would be a valuable new observable: unlike individual nuclei, the global slopes use many data points and could mitigate the influence of structural anomalies in specific nuclei. The paper's strengths are the large counting statistics, the transparent specification of the ensemble (Table I), and the demonstration that the linear ΔRnp-I and ΔRmirr-I correlations appear in multiple frameworks. However, the headline L constraint is currently conditional on the choice of the RSE prior, the arbitrary filtering thresholds, and the shape-coexistence interpretation, so its external validity is not yet established. With prior-sensitivity tests and clearer acceptance criteria, the approach could become a useful method for constraining L.

major comments (3)

[Sec. IV A, Fig. 6, Table I] The L constraint is an inverse-calibration result that inherits the prior built into the RSE. The authors sample 10 Skyrme parameters from a multivariate Gaussian fitted to 160 parametrizations, then stratify to ~4000 samples per ΔL=5 MeV bin over L=0–200 MeV. This uniform-L stratification is a prior choice, and the filtered L distribution in Fig. 6 is a posterior under that prior. No prior-sensitivity test is reported (e.g., varying the stratification scheme, scaling the covariance, or using a different functional class), so the quoted 1σ interval 20–36 MeV is conditional on that prior and cannot be presented as a robust measurement of L. This issue is load-bearing because the abstract's central claim is the L constraint. I recommend that the authors either (i) report how the filtered L distribution changes under reasonable prior variations, or (ii) reformulate the result as a conditional constraint with the prior stated explicitly and its influence quantified.
[Sec. IV A] The filtering criteria that select the surviving parametrizations are not fully specified and no stability test is shown. The authors require Pearson r > 0.85 for the ΔRnp-I correlation and r > 0.99 for the ΔRmirr-I correlation, and they accept parametrizations yielding Cnp and Cmirr 'within experimental uncertainties' (Cnp = 0.9(1) fm/MeV and Cmirr = 1.31(4) fm/MeV, from Fig. 1). It is not stated whether 'within experimental uncertainties' means 1σ, 2σ, or some other tolerance, and the two Pearson thresholds are arbitrary. The final L histogram in Fig. 6 depends on these choices, yet the paper does not scan over thresholds or tolerances. Without such a scan, the peak at L ≈ 28 MeV may be an artifact of the filter rather than a robust feature. Please specify the exact acceptance criteria and show the sensitivity of the resulting L distribution to them.
[Sec. IV B] The narrowing of the L constraint to 28–36 MeV via the 18O/Ne mirror pair is conditional on the shape-coexistence hypothesis, which is not independently validated. The authors find that ~200 of the ~2000 already-selected parametrizations can, when the initial deformation is varied over β ∈ [-0.2, 0.2], reproduce both the experimental ΔRmirr-I linearity and the experimental ΔRmirr of 18O/Ne. This establishes consistency with the shape-coexistence picture, but it does not demonstrate that shape coexistence is the correct explanation of the deviation, and it does not remove the prior-dependence of the underlying RSE. The 32 ± 4 MeV result is therefore a conditional estimate, not a more robust constraint. The abstract and Sec. V should either present this range as conditional on the shape-coexistence hypothesis or provide additional evidence before claiming a further narrowing.

minor comments (7)

[Abstract; Sec. V] There are duplicate words in the phrase 'between between L and the symmetry energy coefficient' in both the abstract and the summary; in addition, 'Hatree-Fock' in Sec. V should be 'Hartree-Fock'.
[Fig. 6 caption] The caption states that the Gaussian fits provide 'L = 28 ± 8 MeV and 32 ± 4 MeV with and without including the ΔRmirr data for the 18O/Ne mirror pair, respectively,' but the black solid histogram corresponds to L=28±8 (without 18O/Ne) and the red dashed histogram to L=32±4 (with it), so 'with and without' should read 'without and with'.
[Sec. IV A] The two paragraphs that describe the sampling of the RSE and the resulting L=28±8 MeV constraint (beginning 'More precisely, we sample...' and 'To perform this constraint, we sampled...') are nearly identical and appear to be duplicated; please consolidate them.
[Sec. IV A, Fig. 6] The Gaussian fits to the histograms are reported with central values and widths, but no fit quality (e.g., χ², number of bins, or statistical uncertainty of the fitted parameters) is given; because the histograms are visibly skewed, the extracted 1σ ranges should be interpreted with caution and the fitting procedure should be documented.
[Sec. III B, Eq. (3)] The assumption that Q* is approximately constant compared to J is asserted without quantitative support; given that this assumption is used to connect the empirical Cnp-L linearity to the J-L linearity, it should be checked (for example by computing Q* from the SHF densities in the RSE) or the explanation should be labeled as heuristic.
[Sec. III A, Fig. 4(b)] The Cmirr-L correlation visibly weakens for L > 150 MeV, but the abstract and Sec. V state the correlation is 'robustly and linearly' without qualification; since the constraint region is below 150 MeV this does not affect the main result, but the wording should match the figure.
[Sec. II B] There are several typographical errors: 'dose not' should be 'does not', and the phrase 'prolately deformed initial basis' is unusual; please check the wording.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the L constraint is an ensemble rejection-sampling calibration, not a definitional reduction.

full rationale

The paper's central claim is that the experimental slopes Cnp and Cmirr can constrain the symmetry-energy slope L. In the derivation chain, Cnp and Cmirr are extracted from linear fits of SHF-computed neutron-skin and mirror-charge-radius differences against isospin asymmetry I, while L is computed from the same Skyrme parameters through the independent algebraic formula of Eq. (2). No step defines L in terms of Cnp or Cmirr, nor does any step fit a parameter to experimental Cnp/Cmirr values and then present that same fitted quantity as a prediction. The random Skyrme ensemble (RSE) is generated from the mean and covariance of 160 previously published parametrizations (Table I), with deliberate stratification to roughly 4000 samples per ΔL=5 MeV bin; the final constraint is obtained by rejection sampling: keep RSE parametrizations that satisfy the linearity thresholds and reproduce the experimental slope intervals, then histogram the resulting L values. This is a forward-model calibration whose posterior depends on the Gaussian prior and on the uniform-L stratification, but that dependence is a prior-sensitivity/robustness concern, not circularity. The explanation of Cnp-L linearity via Eq. (3) invokes Q* ≈ const as a simplifying assumption borrowed from an external reference (Ref. [44]), and the J-L linearity is supported by the algebraic similarity of Eqs. (5) and (6); neither reduces the target result to an input. Self-citations (Refs. [72,73,82]) support ancillary observations such as robust random-interaction correlations and the pervasiveness of shape coexistence; they are not load-bearing for the L constraint, and the 18O/Ne shape-coexistence argument is independently motivated by the known candidates (Ref. [81]) and by the SHF β-scan numerical results. No circular step can be exhibited with a specific equation or fitted-input renaming, so the derivation is self-contained in the circularity sense.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central constraint rests on the random Skyrme ensemble whose mean and covariance are fitted to 160 existing parametrizations, on arbitrary linearity thresholds, and on a post hoc shape coexistence assumption. No new physical entities are introduced.

free parameters (4)

Mean vector of 10 Skyrme parameters = Table I, e.g., ⟨t0⟩=−2.03×10^3 MeV·fm^3, ⟨W0⟩=134 MeV·fm^5
The random Skyrme ensemble is centered on the mean of the 160 parametrizations; this choice shapes the distribution of L and hence the final constraint.
Covariance matrix of 10 Skyrme parameters = Table I, 10x10 matrix
Controls the spread and correlations of the random ensemble; the L constraint depends on this covariance.
Pearson r selection thresholds = 0.85 for ΔRnp−I, 0.99 for ΔRmirr−I
Ad hoc cuts to classify parametrizations as linear; changing them changes the sample of surviving parametrizations and the resulting L histogram.
Initial deformation β = 0.2 (prolate)
HFBTHO runs start from a prolate single-particle basis to favor prolate solutions; this choice can affect which local minima are found and thus the computed radii and slopes.

assumptions (5)

domain assumption Skyrme parametrizations with no positive root of the saturation condition Eq. (1) are unphysical and are excluded.
Exclusion shapes the RSE; the resulting ensemble is conditioned on the existence of symmetric nuclear matter at some positive density.
ad hoc to paper The effective surface stiffness Q* in Eq. (3) is approximately constant compared to the variation of J.
Used to convert Cnp = (3/2) r0 J/Q* into a direct proportionality Cnp ∝ J, which underlies the explanation of Cnp−L linearity; no independent evidence is given.
domain assumption ΔRmirr approximately equals ΔRnp under isospin conservation.
Standard argument from Refs [16,37] used to connect mirror charge radii to neutron skins; generally accepted but approximate.
domain assumption The 160 Skyrme parametrizations from Ref [77] are a representative sample of realistic interactions.
The mean and covariance of this set define the random ensemble; the paper provides no test of representativeness.
ad hoc to paper Shape coexistence in 18O and 18Ne can explain the experimental deviation of their ΔRmirr from the linear trend.
Invoked to reconcile the outlier and to narrow the L range; the SHF calculations produce multiple minima, but the interpretation is post hoc.

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Pith. "Pith review of Robust linear correlations related to neutron skin thickness." pith.science (2026). https://pith.science/paper/EDWZRTKZ

@misc{pith2026250205820,
  author       = {Pith},
  title        = {Pith review of: Robust linear correlations related to neutron skin thickness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EDWZRTKZ}},
  note         = {Machine review of arXiv:2502.05820}
}

abstract

We observe various robust linear correlations related to neutron skin thickness ($\Delta R_{\rm np}$) within different interaction ensembles, including newly proposed random Skyrme ensemble. The robust linear correlation between $\Delta R_{\rm np}$, or charge radius difference of mirror nuclei ($\Delta R_{\rm mirr}$), and the isospin asymmetry ($I=\frac{N-Z}{A}$) becomes apparent as the model space is enlarged. Shape coexistence, or shape effect on charge radius, is considered to explain the experimental deviation of ${}^{18}$O/Ne and some odd-$A$ $\Delta R_{\rm mirr}$s from the $\Delta R_{\rm mirr}-I$ linearity. The slopes of the linear $\Delta R_{\rm mirr}-I$ and $\Delta R_{\rm np}-I$ correlations ($C_{\rm np}$ and $C_{\rm mirr}$, respectively) are also robustly and linearly correlated to the slope of the symmetry energy ($L$). These linear correlations are further understood with the similar formulation between between $L$ and the symmetry energy coefficient ($J$). The linear correlations between $C_{\rm np}-L$ and $C_{\rm mirr}-L$ are also adopted to constrain $L$ to $20\sim36$ MeV with 1$\sigma$ confidence. Considering the deviation of ${}^{18}$O/Ne $\Delta R_{mirr}$ due to shape coexistence, the 1$\sigma$ range for $L$ is further narrowed to $28\sim36$ MeV, suggesting a relatively soft equation of state for nuclear matter.

Figures

Figures reproduced from arXiv: 2502.05820 by the authors.

**Figure 2.** FIG. 2. (Color online) Probabilities of Pearson’s [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (Color online) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. (Color online) Distributions of the symmetry energy [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: For 18O, we observe three peaks in the distribution, around ∆β ∼ 0, 0.2, and 0.3. These peaks may correspond to scenarios of no shape coexistence, sphericaldeformed coexistence (between β ≃ 0 and ±0.2), and prolate-oblate coexistence (between β ≃ 0.2 and −0.1, or β …

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Works this paper leans on

87 extracted references · 74 canonical work pages · cited by 1 Pith paper

[1]

995 for ∆ Rnp − I linearity is 5%, which is notably smaller than the 69% observed for ∆ Rmirr − I linearity

We also noticed that the probability of achieving r > 0. 995 for ∆ Rnp − I linearity is 5%, which is notably smaller than the 69% observed for ∆ Rmirr − I linearity. This suggests that, within the Skyrme ensem- ble, Pearson’s r values for the ∆ Rnp − I correlation are generally lower than those for the ∆ Rmirr − I correlation. This is in line with our RQE...
[2]

For realistic nuclear systems, nucleons move within an eﬀectively inﬁnite Hilbert space

The larger model space in the SHF calculations does indeed appear to strengthen the predominance of linear ∆ Rnp − I and ∆ Rmirr − I corre- lations. For realistic nuclear systems, nucleons move within an eﬀectively inﬁnite Hilbert space. Based on our observa- tions in Fig. 2, robust linear correlations of ∆ Rnp − I and ∆ Rmirr − I are reasonably expected,...
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Unlike the Cnp − L correlation, the linear trend in the Cmirr − L correla- tion appears to weaken at larger L values

Panel (b) presents the correlation between Cmirr and L. Unlike the Cnp − L correlation, the linear trend in the Cmirr − L correla- tion appears to weaken at larger L values. We also observe the linear correlation between Cnp and L, and between Cmirr and L in the RSE. For Skyrme parametrizations in the RSE that exhibit Pearson’s r values above 0.85, we per...
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In contrast, if ten {J, L } data pairs are independently sampled from normal distributions, this probability is only around 1.90(4)%

and ( 6), is approx- imately 49(2)%. In contrast, if ten {J, L } data pairs are independently sampled from normal distributions, this probability is only around 1.90(4)%. The similarity in the linear combination structure for J and L as shown in Eqs. (
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This formulation similarity may oﬀer a partial explanation for the observed robust linear correlations in Figs

and ( 6) likely enhances the linear correlation between them, and consequently, the linearity between L and Cnp. This formulation similarity may oﬀer a partial explanation for the observed robust linear correlations in Figs. 3 and 4. IV. L CONSTRAINT A. Cnp and Cmirr constraint We further emphasize that the linear correlations of Cnp − L and Cmirr − L are...

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The L distribution of these sampled parametrizations demonstrates a plausi- ble range for L. In Fig. 6, the black solid step histogram represents this distribution. The distribution exhibits a peak, which is well described by a Gaussian function. The Gaussian ﬁt is shown as a black solid curve in Fig. 6, with a peak center at 28 MeV and a width of 16 MeV....
[8]

Recent studies also indicate that shape coexistence might be a widespread phenomenon across the nuclide chart [ 82]

We recall that 18O and 18Ne are both candidates for shape coexistence [81]. Recent studies also indicate that shape coexistence might be a widespread phenomenon across the nuclide chart [ 82]. Diﬀerent nuclear shapes could naturally lead to diﬀerent charge radii. Thus, it is conceivable that shape coexistence in the 18O/Ne pair results in multi- ple ∆ Rmi...

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A Gaussian ﬁt to this distribution suggests a value of L = 32(4) MeV within the 1 σ conﬁ- dence. Given the considerable inﬂuence of nuclear shape on the ∆ Rmirr − I linearity, we propose that it may also con- tribute to the less systematic behavior observed for odd- A ∆ Rmirr ...
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The linear Cnp − L and Cmirr − L correlations have been used to constrain L to 20 ∼ 36 MeV, based on the sampling in the RSE

and ( 6). The linear Cnp − L and Cmirr − L correlations have been used to constrain L to 20 ∼ 36 MeV, based on the sampling in the RSE. Considering the deviation of 18O/Ne ∆ Rmirr, the 1 σ range of L is further reduced to 28 ∼ 36 MeV, tentatively suggesting a relatively soft EOS
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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

995 for ∆ Rnp − I linearity is 5%, which is notably smaller than the 69% observed for ∆ Rmirr − I linearity

We also noticed that the probability of achieving r > 0. 995 for ∆ Rnp − I linearity is 5%, which is notably smaller than the 69% observed for ∆ Rmirr − I linearity. This suggests that, within the Skyrme ensem- ble, Pearson’s r values for the ∆ Rnp − I correlation are generally lower than those for the ∆ Rmirr − I correlation. This is in line with our RQE...

[2] [2]

For realistic nuclear systems, nucleons move within an eﬀectively inﬁnite Hilbert space

The larger model space in the SHF calculations does indeed appear to strengthen the predominance of linear ∆ Rnp − I and ∆ Rmirr − I corre- lations. For realistic nuclear systems, nucleons move within an eﬀectively inﬁnite Hilbert space. Based on our observa- tions in Fig. 2, robust linear correlations of ∆ Rnp − I and ∆ Rmirr − I are reasonably expected,...

[3] [3]

Unlike the Cnp − L correlation, the linear trend in the Cmirr − L correla- tion appears to weaken at larger L values

Panel (b) presents the correlation between Cmirr and L. Unlike the Cnp − L correlation, the linear trend in the Cmirr − L correla- tion appears to weaken at larger L values. We also observe the linear correlation between Cnp and L, and between Cmirr and L in the RSE. For Skyrme parametrizations in the RSE that exhibit Pearson’s r values above 0.85, we per...

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S. Typel and B. A. Brown, Neutron radii and the neutron equation of state in relativistic models, Phys. Rev. C 64, 027302 (2001)

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In contrast, if ten {J, L } data pairs are independently sampled from normal distributions, this probability is only around 1.90(4)%

and ( 6), is approx- imately 49(2)%. In contrast, if ten {J, L } data pairs are independently sampled from normal distributions, this probability is only around 1.90(4)%. The similarity in the linear combination structure for J and L as shown in Eqs. (

[6] [6]

This formulation similarity may oﬀer a partial explanation for the observed robust linear correlations in Figs

and ( 6) likely enhances the linear correlation between them, and consequently, the linearity between L and Cnp. This formulation similarity may oﬀer a partial explanation for the observed robust linear correlations in Figs. 3 and 4. IV. L CONSTRAINT A. Cnp and Cmirr constraint We further emphasize that the linear correlations of Cnp − L and Cmirr − L are...

2000

[7] [7]

The L distribution of these sampled parametrizations demonstrates a plausi- ble range for L. In Fig. 6, the black solid step histogram represents this distribution. The distribution exhibits a peak, which is well described by a Gaussian function. The Gaussian ﬁt is shown as a black solid curve in Fig. 6, with a peak center at 28 MeV and a width of 16 MeV....

[8] [8]

Recent studies also indicate that shape coexistence might be a widespread phenomenon across the nuclide chart [ 82]

We recall that 18O and 18Ne are both candidates for shape coexistence [81]. Recent studies also indicate that shape coexistence might be a widespread phenomenon across the nuclide chart [ 82]. Diﬀerent nuclear shapes could naturally lead to diﬀerent charge radii. Thus, it is conceivable that shape coexistence in the 18O/Ne pair results in multi- ple ∆ Rmi...

2000