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No chiral nuclear interaction passes the tin charge-radius test

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2026-08-02 20:49 UTC pith:YF5BCUZU

load-bearing objection A solid, honest benchmark showing chiral Hamiltonians fail the Sn radius test at BCCSD level, but the 'wrong reason' claim for EM7.5 rests on an unquantified many-body error budget. the 4 major comments →

arxiv 2602.22030 v2 pith:YF5BCUZU submitted 2026-02-25 nucl-th nucl-ex

Ab initio calculations of nuclear charge radii across and beyond {}¹³²Sn: Putting chiral EFT nuclear interactions to the test

Pepijn Demol , Urban Vernik , Thomas Duguet , Alexander Tichai This is my paper
classification nucl-th nucl-ex PACS 21.10.Ft21.60.De
keywords nuclear charge radiitin isotopeschiral effective field theoryBogoliubov coupled clusterisotope shiftsshell orderingkinkab initio
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper computes charge radii for the even-mass tin chain from 96Sn to 150Sn with ab initio Bogoliubov coupled cluster at the singles-doubles level, using three chiral effective field theory (χEFT) interactions. It finds that no single interaction reproduces all measured features: the overall trend, the parabolic isotope shifts between N=50 and N=82, and the kink at 132Sn. The interaction that matches the 132Sn kink only does so because it places the added neutrons in the spatially extended 1h9/2 orbital, contradicting the known 2f7/2 ground state of 133Sn; the same mis-ordering creates a spurious inverted kink at 142Sn. The authors argue that the tin chain, particularly beyond 132Sn, offers a stringent differential test that current fine-tuned χEFT interactions fail.

Core claim

On the authors' terms, the central discovery is that the charge-radius kink through 132Sn — the sharp rise in mean-square radius between 132Sn and 134Sn — is not reproduced for the right physical reason by any of the three Hamiltonians. The 1.8/2.0 (EM7.5) interaction alone gives the measured rise of 0.22 fm², but it attributes the effect to neutron occupancy of the spatially extended 1h9/2 shell beyond N=82; the other two interactions, which fill the experimentally established 2f7/2 shell, account for only about half of the rise. The paper traces this to the HFB valence-shell angular momentum and shows the EM7.5 prediction is further compromised by a correlated, dubious inverted kink at 142

What carries the argument

The central mechanism is the single-particle shell ordering of neutrons beyond the N=50, N=82, and N=92 closures, extracted from Hartree-Fock-Bogoliubov (HFB) calculations. The paper identifies the angular momentum j of the neutron valence shell as the quantity that controls whether extra neutrons pull the proton density outward (large j, spatially extended orbitals such as 1h9/2) or not (compact orbitals such as 2f7/2). The calculation itself is Bogoliubov coupled cluster at the singles and doubles level (BCCSD), with the radius operator treated at one-body level and isotopic shifts used as differential observables; two-neutron separation energies serve as auxiliary diagnostics for the cred

Load-bearing premise

The comparison assumes that the omitted many-body and operator corrections — triples excitations, two-body charge-density contributions, and collective correlations — are smaller than the differences between the three Hamiltonians; the paper notes these omissions are on the order of the very kink it analyzes.

What would settle it

Measure the charge radius of 142Sn (or the 140-142Sn isotope shift); the EM7.5 interaction predicts an inverted kink that contradicts a monotonic rise. Alternatively, recompute 134Sn with triples and the two-body charge-density operator: if the 132-134Sn shift becomes smaller than about 0.1 fm², the paper's attribution of the kink to EM7.5 collapses.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • The tin chain from N=50 to N=100 is a more discriminating testbed for χEFT interactions than doubly-magic nuclei alone, because differential radii amplify disagreements in shell ordering.
  • The predicted kink at 100Sn is robust across all three interactions; upcoming isotope-shift measurements towards 100Sn can confirm whether that shared mechanism is correct.
  • The EM7.5 interaction's agreement at 132Sn should not be interpreted as a success: it is tied to an incorrect 1h9/2 occupancy that also generates an inverted kink at 142Sn.
  • Quantitative conclusions about which interaction is best for radii cannot be drawn until triples corrections and two-body charge-density operators are included; the authors estimate these contributions are not negligible on the scale of the 132Sn kink.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A single measurement of the 140-142Sn isotope shift could settle the EM7.5 question: the paper's analysis implies a rise would contradict the inverted-kink prediction and further disfavor that interaction.
  • The paper's shell-ordering diagnostic could be applied to other heavy isotopic chains (lead, nickel) to test whether 'right kink for the wrong reason' is a generic failure mode of chiral interactions.
  • Since the three interactions differ mainly in the three-nucleon force, the results suggest that differential charge radii encode information about the three-nucleon interaction that absolute radii in doubly-magic nuclei do not, motivating sensitivity analyses of the low-energy constants.
  • If subsequent BCCSDT calculations with two-body charge density shift the 132-134Sn value for EM7.5 downward, the only interaction currently matching the kink would lose that status, leaving the field without any reproducing Hamiltonian.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 3 minor

Summary. The paper reports Bogoliubov coupled-cluster singles-and-doubles (BCCSD) calculations of charge radii for even-mass 96–150Sn using three chiral-EFT Hamiltonians (1.8/2.0 (EM), ΔNNLOGO, and 1.8/2.0 (EM7.5)). It compares absolute radii and isotopic shifts with experiment and with VS-IMSRG(2) results, decomposes the 100–132Sn shifts into linear and quasi-parabolic parts, and analyzes kinks at N=50, 82, and 92 in terms of the angular momentum of the neutron valence shell. The central claim is that none of the three Hamiltonians captures all key charge-radius characteristics: 1.8/2.0 (EM) underpredicts radii, ΔNNLOGO does best on isotopic shifts but misses the 132Sn kink, and 1.8/2.0 (EM7.5) reproduces the 132Sn kink only because it places neutrons in the spatially extended 1h9/2 shell, leading to a dubious inverted kink at 142Sn.

Significance. If the conclusion holds, this is a stringent differential test showing that current fine-tuned χEFT Hamiltonians fail in heavy open-shell nuclei, and it provides a concrete motivation for new isotope-shift measurements and for higher-order many-body/operator corrections. The paper's strengths are the broad systematic scan across a long isotopic chain, the external benchmarking of two Hamiltonians against VS-IMSRG(2), the explicit model-space uncertainty bands, and the unusually frank discussion of missing triples, two-body charge operators, and collective correlations. However, the central negative verdict is load-bearing on truncation-error estimates that are quoted but not propagated to the differential quantities being compared, so the conclusion is not yet established at the claimed level of confidence.

major comments (4)
  1. [Footnote 1 / Conclusions] The 132→134Sn kink is δ⟨R²⟩≈0.22 fm² (Fig. 2, right panel). Footnote 1 reports that triples contribute ~0.7% of the radius in ⁴⁸Ca, and the Conclusions quote a two-body charge-density correction of ~0.04 fm in p-shell nuclei. For R≈4.7 fm these translate to changes in ⟨R²⟩ of roughly 0.3 fm² and 0.38 fm² if they do not cancel between 132Sn and 134Sn. The manuscript gives no argument or estimate for cancellation in the Sn differential shifts. Without bounding these omitted contributions, the central statement that 'none of the employed fine-tuned interactions can capture all key characteristics' is not yet supported.
  2. [Theoretical framework, Eq. (3)] The left ground state is evaluated with Λ approximated by T† at first order. This is a non-trivial approximation for a general operator, and its error for charge radii in heavy open-shell nuclei is never benchmarked. The kink analysis is built on the one-body density entering Eqs. (6)–(7), so the differential conclusions inherit this unquantified error. The authors should provide at least a perturbative estimate of the Λ correction, or a comparison against a method with a properly solved Λ, before drawing conclusions at the 0.2 fm² level.
  3. [Fig. 1 / §3.1] The VS-IMSRG(2) comparison is reassuring for 1.8/2.0 (EM) and ΔNNLOGO in 100–132Sn, but it does not cover the 1.8/2.0 (EM7.5) Hamiltonian, nor the N>82 region where the shell-ordering mechanism and the 142Sn inverted kink are claimed. Thus the cross-check does not constrain the truncation error in exactly the cases that carry the negative conclusion. A benchmark or explicit error estimate is needed there, not only in the 100–132 region.
  4. [Fig. 4 / Kinks section] The argument that 1.8/2.0 (EM7.5) reproduces the 132Sn kink 'for the wrong reason' relies on identifying the valence shell by a 'naive filling of canonical single-particle states' of HFB (footnote 3). This is an indirect and mean-field-based inference. The actual occupation of the correlated BCCSD wave function, for example from natural orbitals of the one-body density matrix, would directly test whether 1h9/2 dominates and 2f7/2 is empty beyond N=82. Without such a demonstration, the causal mechanism remains an interpretation, although a plausible one.
minor comments (3)
  1. [Fig. 1 caption] Typo: 'Valence-space IMSGR(2)' should read 'Valence-space IMSRG(2)'.
  2. [Conclusions] 'truly collective collective correlations' contains a duplicated word; delete one 'collective'.
  3. [Fig. 5 caption] 'commun to the three Hamiltonians' should read 'common to the three Hamiltonians'.

Circularity Check

0 steps flagged

No circular derivation: Sn radii are external predictions; remaining self-references are non-load-bearing.

full rationale

The paper's central comparison is an external benchmark. The three Hamiltonians were tuned on scattering, saturation, or 16O data, not on Sn radii: the 1.8/2.0 (EM7.5) interaction uses a refitted cD = 7.5 'to match the ground-state energy and charge radius of 16O'. The Sn isotopic shifts and kinks are not inputs to these fits, so reproducing the 132Sn kink (0.22 fm2) or failing to do so is a genuine predictive test. The paper's mechanistic explanation of the EM7.5 kink through the occupation of the spatially extended 1h9/2 shell is a diagnostic that is compared against experimental ground-state spins in odd-even Sn isotopes, not a self-consistency loop; the paper even states that 'the reproduction of the experimental kink of the charge radius at 132Sn by the 1.8/2.0 (EM7.5) Hamiltonian is obtained for the wrong reason.' The only self-references are methodological (BCC framework, e.g., Ref. [32]) or future-prospect (Ref. [56], in preparation; private communication Ref. [64]); none carries the main verdict. The manuscript honestly flags truncation limitations: footnote 1 notes 'the next order contribution to charge radii from triples excitations (0.7%) is only mildly suppressed in 48Ca', and the Conclusions mention 'the two-body charge density correction that has been shown to contribute to about 0.04fm in p-shell nuclei'. These uncorrected contributions could affect the differential shifts, but they are not fitted to Sn data and are presented as open issues rather than as predictions. This is a robustness caveat, not circularity. Score 2 reflects only the minor, non-load-bearing reliance on the authors' own in-preparation triples reference.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The calculation uses three pre-existing Hamiltonians as inputs; the paper contributes the BCCSD benchmark and its interpretation. No new particle, force, or conserved quantity is introduced. The main ledger entries are the fitted LECs of the Hamiltonians (including EM7.5's cD tuned to the 16O charge radius) and the many-body/operator truncations that are acknowledged but not fully propagated.

free parameters (5)
  • cD (three-nucleon LEC) of 1.8/2.0 (EM7.5) = 7.5
    Ref. [37] fits this LEC to 16O ground-state energy and charge radius; it affects all radii and the 132Sn kink.
  • NN/3N LECs of 1.8/2.0 (EM) = Ref. [58] fit set
    Input Hamiltonian; underbinds absolute radii by ~5%, driving the absolute-radius comparison.
  • LECs of ΔNNLOGO = Λ=394 MeV, saturation-adjusted
    Input Hamiltonian explicitly adjusted to nuclear matter saturation to improve radii; used for comparison.
  • Model-space truncation (emax, ℏω, E3max) = 12, 12 MeV, 24
    Chosen for numerical feasibility, not fitted to Sn data; uncertainty sampled over ℏω=10-14 and emax=14.
  • Experimental slope a for residual shifts = 0.068 fm² (experimental fit)
    Eq. (10) defines a from a fit to experimental shifts with the 100Sn value extrapolated; used for the parabolic decomposition only.
axioms (5)
  • standard math The many-body Schrödinger equation is solved via the BCCSD parametrization |Ψ0⟩=e^T|Φ⟩ with |Φ⟩ a J=0 HFB vacuum (Eqs. 1-2).
    Foundation of the method; standard many-body formalism.
  • domain assumption Chiral EFT Hamiltonians at the employed orders and cutoffs are valid, representative models of the nuclear interaction.
    The negative conclusion assumes these three fine-tuned interactions fairly sample current χEFT.
  • domain assumption BCCSD with Λ≈T† and without triples or the two-body charge-density operator is accurate enough for differential charge radii.
    The paper's own estimates (0.7% in 48Ca, 0.04 fm in p-shell) are not propagated; this is the main unquantified premise.
  • domain assumption The charge-radius formula Eq. (5) with fixed proton/neutron radii, spin-orbit, and Darwin-Foldy terms applies in these heavy open-shell nuclei.
    Used to convert point-proton radius to charge radius; two-body charge density omitted.
  • ad hoc to paper Naive filling of canonical HFB single-particle states identifies the neutron valence shell and supports the kink interpretation.
    The 'wrong reason' diagnosis at 132Sn and the inverted kink at 142Sn depend on this interpretation; Fig. 4 and the kinks section.

pith-pipeline@v1.3.0-alltime-deepseek · 13112 in / 12887 out tokens · 130403 ms · 2026-08-02T20:49:02.755277+00:00 · methodology

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Cite this review

Pith. "Pith review of Ab initio calculations of nuclear charge radii across and beyond ${}^{132}$Sn: Putting chiral EFT nuclear interactions to the test." pith.science (2026). https://pith.science/paper/YF5BCUZU

@misc{pith2026260222030,
  author       = {Pith},
  title        = {Pith review of: Ab initio calculations of nuclear charge radii across and beyond $^132$Sn: Putting chiral EFT nuclear interactions to the test},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YF5BCUZU}},
  note         = {Machine review of arXiv:2602.22030}
}
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read the original abstract

Charge radii are investigated along the Tin isotopic chain via ab initio Bogoliubov coupled cluster calculations at the singles and doubles level. In addition to the reproduction of absolute radii, the parabolic behavior of isotopic shifts between the N = 50 and N = 82 magic numbers and the kink through ${}^{132}$Sn are shown to provide stringent tests for state-of-the-art chiral effective field theory ($\chi$EFT) inter-nucleon interactions. Indeed, none of the employed fine-tuned interactions can capture all such key characteristics. Eventually, the pronounced sensitivity of the results to the employed Hamiltonian beyond ${}^{132}$Sn provides a unique playground to pin down critical attributes of $\chi$EFT inter-nucleon interactions in the future. This calls for measuring isotopic shifts both towards ${}^{100}$Sn and beyond ${}^{134}$Sn, as well as for performing high-accuracy ab initio calculations of mean-square radii in heavy open-shell nuclei by adding both triples corrections to the many-body wave function and the two-body charge density correction to the operator

Figures

Figures reproduced from arXiv: 2602.22030 by Alexander Tichai, Pepijn Demol, Thomas Duguet, Urban Vernik.

Figure 1
Figure 1. Figure 1: Theoretical and experimental charge radii. Hartree-Fock [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Theoretical and experimental isotopic shifts. The left panel shows BCCSD results in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Differential isotopic shift (top) and two-neutron separation energies (bottom) across [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left panel: angular momentum of the neutron HFB valence (canonical) shell computed for the 1.8/2.0 (EM), [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Experimental and theoretical (quasi) parabolic component [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

discussion (0)

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Reference graph

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