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REVIEW 4 minor 93 references

Ab initio calculations show no shell closure at neutron number 90 in 140Sn: the first 2+ excitation energy is small, contradicting the closed-subshell assumption.

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2026-07-14 14:44 UTC pith:4CDR75J2

load-bearing objection Solid ab-initio reductio that cleanly kills the proposed N=90 shell closure in 140Sn; the result is robust across methods and the soft spots are already quantified.

arxiv 2607.09897 v1 pith:4CDR75J2 submitted 2026-07-10 nucl-th nucl-ex

Absence of a shell closure in ¹⁴⁰Sn

Francesca Bonaiti , Bingcheng He , Gaute Hagen , Thomas Papenbrock This is my paper
classification nucl-th nucl-ex
keywords shell closure140Snab initio nuclear structurechiral effective field theorycoupled-cluster theoryIMSRGneutron-rich tin isotopesN=90
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 settles a long-running disagreement about whether the neutron-rich tin isotope 140Sn has a shell closure at neutron number 90. Using a chiral nuclear interaction already known to reproduce shell closures in lighter magic nuclei, the authors first check that it correctly describes the low-lying spectrum of 133Sn. They then assume that 140Sn has a closed 7/2- neutron subshell and compute the energy of its first excited 2+ state with two independent many-body methods. The calculated excitation energy is low—below about 1.5 MeV and still falling as the model space is enlarged—which is incompatible with a robust shell gap. The result removes the expectation of a new magic number at N=90 and aligns with earlier shell-model trends and with mass and radius systematics that show no kink at that point.

Core claim

If 140Sn is assumed to possess a closed 7/2- neutron subshell beyond 132Sn, first-principles calculations with the 1.8/2.0 (EM) interaction yield a first 2+ excitation energy that is small (under 1.5 MeV and still decreasing with model-space size). That low energy contradicts the closed-subshell premise and therefore rules out a shell closure at N=90 for this interaction.

What carries the argument

The equation-of-motion coupled-cluster and valence-space in-medium similarity-renormalization-group methods applied to the 1.8/2.0 (EM) chiral Hamiltonian; both methods start from a closed-shell reference and extract the 2+ excitation energy, whose smallness falsifies the reference assumption.

Load-bearing premise

That a nuclear force whose constants were fixed only on the lightest nuclei remains accurate enough to decide shell structure in the neutron-rich tin region around mass 140.

What would settle it

A direct experimental measurement of the first 2+ excitation energy in 140Sn itself; a value above roughly 2–3 MeV would restore the possibility of a shell closure, while a value near or below 1 MeV would confirm the calculation.

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

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If this is right

  • No new magic number is expected at N=90 in the tin isotopic chain.
  • Shell-model calculations that already predicted a soft 2+ energy of 0.5–1 MeV are consistent with the ab initio result.
  • Astrophysical r-process abundance patterns near A≈130 need not incorporate a pronounced N=90 shell gap.
  • Future mass and radius measurements of even tin isotopes beyond 138Sn should show smooth trends rather than a kink at N=90.

Where Pith is reading between the lines

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

  • The same interaction and methods can now be used to map the entire tin chain from the proton dripline to the neutron dripline without assuming artificial shell closures.
  • If continuum effects lower the unbound 13/2+ state in 133Sn, similar continuum corrections may further soften the 2+ energy already found in 140Sn.
  • A systematic survey of other N=90 isotones with the same force would test whether the absence of a shell gap is specific to tin or generic.

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

0 major / 4 minor

Summary. The manuscript addresses the disputed existence of an N=90 subshell closure in 140Sn by ab initio calculations with the chiral 1.8/2.0(EM) interaction. After validating the Hamiltonian on the low-lying single-particle spectrum of 133Sn (PA-EOM-CCSD and VS-IMSRG), the authors adopt a spherical Hartree–Fock reference that assumes a filled 1f7/2 neutron subshell and compute the first 2+ excitation energy of 140Sn with EOM-CCSD/T-1, VS-IMSRG(2/3f2) and EOM-IMSRG(2). All methods yield a small excitation energy (below ~1.5 MeV and still decreasing with model-space size), which is inconsistent with a robust shell closure and with the much larger 2+ energies of known doubly-magic nuclei. Ground-state energies are also reported and found consistent with mass-model estimates.

Significance. The result is a clean, falsifiable reductio that resolves a long-standing controversy with a single, well-validated Hamiltonian and two independent many-body frameworks. The same interaction has previously reproduced or predicted shell closures in oxygen, calcium, nickel, 78Ni, 100Sn and 208Pb; the 133Sn benchmark further anchors the calculation near the region of interest. Explicit model-space trends and approximate triples corrections are shown, so residual incompleteness is quantified rather than hidden. The conclusion that 140Sn is not doubly magic is therefore robust and of direct interest for r-process modeling and for the interpretation of ongoing spectroscopic campaigns beyond 132Sn.

minor comments (4)
  1. In Sec. V the statement that EOM-CCSD(T) yields negative excitation energies is useful but terse; a short clause clarifying that this signals reference-state breakdown (rather than a numerical artifact) would help non-specialist readers.
  2. Fig. 3 caption and surrounding text could note more explicitly that the EOM-CCSDT-1 points are restricted to ẽpqr < 100 MeV; the truncation is mentioned in Sec. III but is easy to miss when reading the figure alone.
  3. The 13/2+ discrepancy in 133Sn (Sec. IV) is acknowledged; a one-sentence remark on whether continuum effects or Hamiltonian dependence is the more likely culprit would strengthen the discussion without requiring new calculations.
  4. Minor typographical inconsistencies appear (e.g., “HAMIL TONIAN”, “V ALIDA TION”, occasional missing spaces around math mode); a light copy-edit pass would remove them.

Circularity Check

0 steps flagged

No circularity: the 2+ energy is a genuine ab initio prediction under an assumption the calculation itself falsifies.

full rationale

The derivation is a clean reductio. The chiral interaction 1.8/2.0(EM) has LECs fixed solely on A=3,4 nuclei (Sec. II) and is not retuned to any Sn data. The 133Sn spectrum (Sec. IV) is an independent experimental benchmark that the same Hamiltonian and methods reproduce for the low-lying single-particle states. The 140Sn calculation (Sec. V) starts from an explicit closed 7/2- neutron subshell reference, computes the first 2+ excitation energy with EOM-CCSD/EOM-CCSDT-1 and VS-IMSRG/EOM-IMSRG, and finds a small value that continues to fall with Nmax; this contradicts the closed-shell premise. No parameter is fitted to the target 2+ energy, no uniqueness theorem is imported from the authors' prior work to force the result, and the self-citations (e.g., earlier benchmarks of the same interaction on known magic nuclei) are external validations, not load-bearing definitions of the present observable. Residual model-space incompleteness is quantified by the authors and does not reverse the qualitative conclusion. Score 0 is therefore required.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The central claim rests on a previously published chiral interaction (LECs fixed on light nuclei) and on standard many-body truncations; no new free parameters are introduced for 140Sn itself. The closed-subshell reference is an explicit working assumption that the calculation is designed to test and ultimately reject.

axioms (4)
  • domain assumption The 1.8/2.0(EM) chiral NN+3N interaction accurately describes low-lying states of medium- and heavy-mass closed-shell nuclei.
    Stated in Sec. II and used as the sole Hamiltonian throughout; previously validated on O, Ca, Ni, Sn, Pb but not guaranteed a priori for N=90 tin.
  • domain assumption Normal-ordered two-body approximation of the three-nucleon force plus E3max=28 ħΩ cut-off is sufficient for the observables of interest.
    Sec. III.C; standard practice but an uncontrolled approximation for absolute energies at the 1 % level.
  • domain assumption EOM-CCSD (and limited EOM-CCSDT-1) and VS-IMSRG(2/3f2) truncations capture the dominant correlations for the 2+ state once a closed-shell reference is assumed.
    Secs. III.A–B; the paper itself shows that higher excitations lower the 2+ energy, confirming the truncation direction.
  • ad hoc to paper A spherical Hartree–Fock reference with filled 1f7/2 neutron subshell is a legitimate starting point for testing the existence of that subshell closure.
    Explicit working hypothesis of Sec. V; the calculation is constructed precisely to falsify it if the resulting 2+ energy is small.

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Cite this review

Pith. "Pith review of Absence of a shell closure in $^{140}$Sn." pith.science (2026). https://pith.science/paper/4CDR75J2

@misc{pith2026260709897,
  author       = {Pith},
  title        = {Pith review of: Absence of a shell closure in $^140$Sn},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4CDR75J2}},
  note         = {Machine review of arXiv:2607.09897}
}
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read the original abstract

There are conflicting theoretical results about the presence of a shell closure in the neutron-rich nucleus $^{140}$Sn. We address this controversy by performing ab initio computations, using a nuclear interaction from chiral effective field theory that accurately reproduced and predicted low-lying states in doubly magic nuclei. We verify that this interaction accurately reproduces low-lying states in $^{133}$Sn. We assume that $^{140}$Sn exhibits a closed $7/2^-$ neutron subshell beyond $^{132}$Sn and compute its first excited $2^+$ state. The resulting energy is small and this contradicts the assumption.

Figures

Figures reproduced from arXiv: 2607.09897 by Bingcheng He, Francesca Bonaiti, Gaute Hagen, Thomas Papenbrock.

Figure 1
Figure 1. Figure 1: FIG. 1. Model space convergence of the excited states of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Model space convergence of the total ground-state [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Convergence of the first [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

discussion (0)

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