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Ab initio nuclear theory can now supply the radiative and recoil corrections that make precision beta decay a sharp probe of beyond-Standard-Model physics.

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2026-08-04 00:33 UTC pith:A4JH3AEA

load-bearing objection Useful, readable review of ab initio corrections in beta decay, but the flagship '10^-4 precision' claim rests on EFT LECs set to arbitrary values and an unpublished matching relation. the 3 major comments →

arxiv 2602.00341 v3 pith:A4JH3AEA submitted 2026-01-30 nucl-th

The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model

Grigor H. Sargsyan , Garrett B. King , Ayala Glick-Magid , Chien-Yeah Seng This is my paper
classification nucl-th PACS 23.40.-s12.15.Hh21.60.Cs
keywords beta decaybeyond Standard Modelab initio nuclear many-body methodsradiative correctionsrecoil-order correctionsVud extractionCKM unitarityeffective field theory
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.

This review sets out to establish that ab initio many-body nuclear theory—built on realistic nucleon-nucleon interactions and systematically improvable approximations—has reached the precision needed to compute the radiative and recoil-order corrections on which beta-decay experiments depend. Its central claim is that for superallowed beta decays (10C→10B, 14O→14N) and allowed Gamow-Teller transitions (6He→6Li, 8Li→8Be, 8B→8Be), these corrections can now be evaluated with quantified uncertainties of order 10^-4, where older estimates carried uncontrolled systematics. If that claim holds, precision measurements of beta-decay lifetimes, spectra, and angular correlations can be converted into sharper extractions of the CKM matrix element Vud and tighter constraints on exotic scalar and tensor weak currents, reaching effective new-physics scales of order 10 TeV. A concrete path is proposed: an effective-field-theory evaluation of the corrections as ground-state matrix elements of two-body potentials, calibrated by a matching identity to the full current-algebra calculation, which would extend first-principles precision to heavier nuclei and additional decay modes.

Core claim

The paper's core claim is that the nuclear-structure-dependent radiative correction δ_NS—historically the largest theory uncertainty in Vud from superallowed decays—can now be computed ab initio by two routes: a current-algebra/dispersive evaluation that sums over all intermediate nuclear states, and an effective-field-theory evaluation using two-body potentials whose matrix elements can be evaluated with quantum Monte Carlo and no-core shell-model methods. The two routes are connected by the identity δ_NS = (2/M_F^(0))⟨V0^mag + V0^{rec,1} + V0^CT⟩, which is intended to fix the two unknown low-energy constants of the EFT approach. Representative results include δ_NS(10C→10B) = -0.422(29)% fr

What carries the argument

The central object is the nuclear γW-box diagram, whose nucleus-dependent part is the correction δ_NS. The argument is carried by the matching identity δ_NS = (2/M_F^(0))⟨V0^mag + V0^{rec,1} + V0^CT⟩, which equates the full current-algebra evaluation (a sum over all intermediate nuclear states) with the effective-field-theory evaluation (ground-state matrix elements of two-body magnetic, recoil, and counterterm potentials). This identity is what would allow the two unknown low-energy constants to be pinned down from one pair of transitions and then reused for other decays. For recoil corrections, the central mechanism is the multipole expansion of the weak current, with subleading multipoles

Load-bearing premise

The load-bearing premise is that the two counterterm low-energy constants of the EFT approach are fixed or bounded by the quoted matching relation δ_NS = (2/M_F^(0))⟨V0^mag + V0^{rec,1} + V0^CT⟩, which the review cites to an unpublished source; if that matching is incomplete, or if the constants differ from the arbitrary ±1/(m_N(2F_π)^2) values used in the table, the central 10^-4 uncertainty claims for Vud are not established.

What would settle it

A lattice QCD calculation of the two-nucleon matrix elements of the counterterm operators would settle whether the assumed natural size of the low-energy constants is correct; if the extracted constants lie outside ±1/(m_N(2F_π)^2), the EFT-based Vud uncertainties of 38–43×10^-5 are underestimates. A complementary direct test: compute δ_NS for 14O by both the current-algebra and EFT methods and require agreement within combined uncertainties.

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If this is right

  • If the quoted 10^-4 uncertainties hold, δ_NS ceases to be the dominant theory error in Vud, and CKM-unitarity tests from superallowed decays become limited by other sources, including experiment.
  • The predicted Standard Model Fierz-like term in 6He (δb ≈ -1.5×10^-3) means future spectrum-shape measurements must subtract this nuclear-structure baseline before attributing any residual distortion to tensor currents.
  • The state-dependent recoil form factors for 8Li/8B show near order-of-magnitude differences between the lowest 2+ state and higher-lying states, so angular-correlation experiments that restrict to the lowest state gain a substantial reduction in systematic uncertainty.
  • Once the two EFT low-energy constants are fixed through matching, the EFT method can be applied to superallowed transitions where the full intermediate-state sum is computationally prohibitive, extending precision Vud extraction to heavier nuclei.
  • The same ab initio machinery is being extended to unique first-forbidden decays, giving complementary sensitivity to right-handed and tensor currents inaccessible in allowed decays.

Where Pith is reading between the lines

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

  • If the matching identity proves complete, the calibrated EFT approach could compute δ_NS for medium-mass superallowed emitters with essentially no additional many-body cost, potentially moving the Vud frontier from A≈14 to the full set of measured superallowed transitions.
  • The no-core shell-model result for the induced-tensor form factor in 6He is roughly four times larger than an older shell-model estimate; if confirmed, previous beta-neutrino correlation analyses that used the older value would need revision, and existing tensor-current limits could shift by more than their quoted errors.
  • The correlation between recoil form factors and measured quadrupole moments suggests a general strategy for other slowly converging nuclear observables: use precisely measured ground-state properties as anchors to reduce ab initio extrapolation uncertainties.
  • A dedicated measurement of the 6He spectrum shape at the target 0.1% precision would test the predicted recoil-induced Fierz term directly; because the predicted value is negative and of order 10^-3, it should appear as a distinct energy dependence rather than a constant shift.

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

3 major / 6 minor

Summary. The paper is a review of recent ab initio calculations of radiative and recoil-order corrections to beta decay, covering NCSM, SA-NCSM, and QMC methods and focusing on their implications for precision determinations of V_ud and for searches for BSM tensor and scalar currents. It presents the current-algebra and EFT formalisms for the nuclear-structure-dependent radiative correction delta_NS, reports results for 10C->10B and 14O->14N, and reviews recoil-correction calculations for 6He, 8Li, and 8B decays. The central claim is that ab initio calculations have achieved 'unprecedented precision' and reduced theoretical uncertainties to the order of 10^-4, thereby sharpening tests of the Standard Model.

Significance. If the reported corrections and uncertainties are reliable, the review would document a genuinely important milestone: quantified ab initio control of the nuclear-structure corrections that currently dominate V_ud extractions, plus high-precision recoil corrections for BSM-sensitive observables. The paper is useful as a pedagogical survey of the many-body methods (NCSM, SA-NCSM, GFMC, AFDMC) and of the two theoretical frameworks for delta_NS. It is also honest in several places, e.g., in Eq. (3.30) it explicitly breaks down the NCSM uncertainty sources, and in Table 3.1 it labels the LEC values as 'arbitrary'. However, the review's headline precision claims for the EFT-based V_ud results are conditional on unconstrained LECs and on an unpublished matching relation, and some numerical results are traceable only to private communications. These issues are load-bearing because the abstract and Section 5 promote the precision without those caveats. The recoil-order sections (6He, 8Li, 8B) are on firmer ground, being based on published data with concrete uncertainty estimates, though the 8Li/8B correlation plots rely on linear regressions whose parametric dependence is not fully discuss

major comments (3)
  1. [Section 3.4, Eqs. (3.37)-(3.43), Table 3.1] The EFT-based V_ud extractions carry uncertainties of 23-43x10^-5 from the two undetermined LECs g_NN_V1 and g_NN_V2. Table 3.1 states these LECs are set to 'arbitrary values' +/-1/(m_N(2F_pi)^2). Because the contact matrix elements enter delta_NS linearly, a sign or factor-of-two change in the true LECs would shift V_ud by an amount comparable to or larger than the quoted total uncertainty. The abstract's 'unprecedented precision' and Section 5's 'uncertainties to the order of 10^-4' therefore overstate what is established for these EFT results. The claims should be qualified as conditional on the assumed LEC values, or the EFT numbers should be presented with an explicit statement that they are not yet a verified precision determination.
  2. [Section 3.2.3, Eq. (3.26)] The proposed strategy to pin down the LECs rests on the matching relation delta_NS = 2/M_F^(0) <V0^mag + V0^rec,1 + V0^CT>, which is cited to unpublished Ref. [107]. This is the key step that would turn the EFT approach into a predictive tool. Because the derivation is not publicly available, the reader cannot verify that the current-algebra delta_NS indeed contains exactly the counterterm physics encoded in V_CT^0, nor that the operator normalizations in the two approaches match. The review should either outline the derivation or explicitly state that this step is not yet publicly checkable. As written, the conclusion on p. 17 that 'the physics in the counterterms can indeed be obtained explicitly in the current algebra approach' is not verifiable.
  3. [Section 3.4, footnote 4] The 14O results, including delta^(0)_NS = -2.84(88)x10^-3 and the V_ud value in Eq. (3.42), are said to be 'corrected for the re-evaluation of V_rec^0 matrix element' via private communication with E. Mereghetti and W. Dekens. This makes a central numerical result of the review nontraceable. For a review intended to inform precision experiments and to establish the state of the art, all reported numbers should be traceable to public, citable sources or be explicitly flagged as new/unpublished results supplied by the authors. Otherwise the community cannot independently assess or use these values.
minor comments (6)
  1. [Abstract and Section 5] Both the abstract and the Section 5 summary refer to '14O->14C', but 14O beta decays to 14N. The correct final nucleus is 14N, as used in Section 3.4. Please correct.
  2. [Section 3.2.3, final paragraph] Typographical/grammatical issue: 'their connections' should be 'the connection between them'.
  3. [Eq. (3.2)] The placement of 's' in '2984.431(3)s / (Ft(...))' is visually confusing; consider writing the formula with an explicit 'sec' or 's' in the denominator as in the original literature.
  4. [Section 4.1, end of first paragraph and Fig. 4 caption] Typo: 'Theresultedcalculations' should be 'The resulting calculations'.
  5. [Section 4.2, last paragraph] Typo: 'psuedoscalar' should be 'pseudoscalar'.
  6. [Section 4.3, text after Eq. (4.15)] The sentence 'making our predictions parameters and model (interaction) independent' is ambiguous; it should read 'parameter- and model-(interaction-)independent'.

Circularity Check

1 steps flagged

No constructed circularity in the reviewed results; one minor self-citation (Eq. 3.26 to unpublished [107]) is load-bearing only for the proposed LEC-fixing strategy, while Table 3.1's arbitrary LECs are an explicit caveat rather than a circular input.

specific steps
  1. self citation load bearing [Section 3.2.3, Eq. (3.26); Ref. [107]]
    "As a result, we have the following matching [107]: δNS = 2/M_F^(0) ⟨V0^mag + V0^rec,1 + V0^CT⟩f i. ... So, a useful way to make progress is to first choose a pair of superallowed transitions that can be easily handled in both methods. One then computes the LHS of Eq.(3.26) using the current algebra approach, and the RHS using the EFT approach. With that, we are able to extract the values of the two unknown LECs by the above matching relation."

    The matching relation Eq. (3.26) is cited to Ref. [107], an unpublished manuscript by the lead author, and no derivation is given in this review. The text immediately uses it as the basis for the proposed strategy to determine the two LECs g_NN_V1,V2 that dominate the EFT Vud uncertainty (Sec. 3.4). Thus the validity of that proposed LEC-determination path is supported only by a non-public self-citation. However, this affects a future extension, not the central reviewed results (10C/14O δNS, 6He/8Li/8B recoil terms), which are published and benchmarked; hence it is a minor self-citation rather than a fully circular derivation.

full rationale

This paper is a review rather than a new derivation, so most of its quantitative content is reported from published literature (Refs. [13]–[20]) rather than constructed in the text. The central results are benchmarked: the 10C δNS value (Eq. 3.30) is an NCSM calculation with an explicit error budget; the EFT Vud numbers (Eqs. 3.37–3.43) are explicitly conditioned on LECs that Table 3.1 labels 'arbitrary values' and whose contribution is included as the dominant uncertainty, so the precision claim is a caveat or overstatement risk, not a fitted input disguised as a prediction. The 8Li/8B recoil-term 'predictions' are obtained by regression against the experimental quadrupole moment, an independent observable, not against the target recoil form factors. The only self-citation with load-bearing weight for a stated strategy is Eq. (3.26), which cites the corresponding author's unpublished work [107] to justify the matching procedure proposed for pinning down the LECs; this affects a future direction, not the main reviewed results, and is best treated as a verification concern rather than circularity. Overall, no significant circularity is present.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The review itself introduces no new entities and no new fitted numbers beyond the schemes summarized; the entries above are the load-bearing numbers from the underlying calculations that the review adopts as its evidence. The two LECs are the main not-yet-determined inputs; the 20% shadowing factor and the quadrupole-moment regression are calibration choices in the reviewed results.

free parameters (3)
  • g_NN_V1, g_NN_V2 (EFT counterterm LECs) = +/- 1/(m_N (2F_pi)^2) (arbitrary values, Table 3.1)
    Two undetermined low-energy constants in the EFT potential V_CT^0 (Eq. 3.24). The review says their values 'must be determined by other means' and Table 3.1 sets them to arbitrary values; the Vud uncertainties in Eqs. 3.37-3.43 are dominated by these.
  • Shadowing scale factor for delta(Box^inel_n)^shad = 0.20
    In Section 3.3 the nuclear modification to the nucleon inelastic box diagram below Q^2=2 GeV^2 is estimated by multiplying by 20%, based on the maximum deviation of the F2 ratio R from 1 for A~10. This is an ad hoc error-estimate parameter, not a computed quantity; it enters the 'sh' error (24) in Eq. 3.30.
  • Linear-regression slope/intercept for j_K/A^2c vs Q(2+) = Implied by Fig. 4.5 (not tabulated)
    In Section 4.3, SA-NCSM predictions for j2/A^2c, j3/A^2c and d/A^2c are obtained by linear regression of calculated points on the quadrupole moment, then evaluated at the experimental Q(2+). The regression parameters are fitted to the ab initio points, so the 'prediction' is a calibrated interpolation.
axioms (4)
  • domain assumption The nuclear Hamiltonian contains at most two- and three-nucleon forces (Eq. 2.1); four-nucleon and higher forces are neglected.
    Used in all the many-body calculations reviewed (Section 2). The truncation is standard in chiral EFT but is an assumption; the paper notes the ongoing debate on power counting (Section 2, Refs. [30,31]).
  • domain assumption The weak charge/current operators are dominated by one-body terms; two-body currents enter only in some calculations (e.g., 6He with GFMC, Section 4.2).
    Section 4.1 uses impulse-approximation one-body operators for 6He NCSM and estimates the missing two-body current contribution from EFT power counting (epsilon_EFT <= 0.15). The correctness of the recoil corrections depends on this two-body-current assumption.
  • domain assumption The single-nucleon inelastic box diagram is unmodified for Q^2 > 2 GeV^2 and modified by at most 20% below (Section 3.3, after Eq. 3.29).
    The 10C delta_NS error budget uses this to set the 'sh' uncertainty. It is an empirical estimate based on the F2 shadowing/EMC ratio, not a derived bound.
  • ad hoc to paper The matching relation Eq. 3.26 equates the current-algebra delta_NS to the sum of EFT two-body potential matrix elements, including the counterterm potential V_CT^0.
    This is the key link in the proposed LEC-pinning strategy (Section 3.2.3). It is not derived in this review; it is cited to the unpublished Ref. [107]. If the matching is incomplete, the proposed program cannot fix the LECs.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model." pith.science (2026). https://pith.science/paper/A4JH3AEA

@misc{pith2026260200341,
  author       = {Pith},
  title        = {Pith review of: The Role of Ab Initio Beta-Decay Calculations in Light Nuclei for Probes of Physics Beyond the Standard Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A4JH3AEA}},
  note         = {Machine review of arXiv:2602.00341}
}
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read the original abstract

Precision beta decay experiments serve as powerful probes of physics beyond the Standard Model, enabling stringent tests of fundamental symmetries of nature. In particular, these experiments primarily focus on precise determinations of the Cabibbo-Kobayashi-Maskawa matrix element Vud and the search for exotic weak currents, both of which depend critically on theoretical calculations of radiative, recoil-order, and isospin-breaking corrections with quantified uncertainties. In recent years, ab initio nuclear many-body methods--grounded in realistic nucleon-nucleon interactions and systematically improvable approximations--have advanced considerably in their ability to compute these higher-order corrections for various nuclei. This review provides a comprehensive overview of state-of-the-art ab initio calculations of beta-decay corrections, encompassing both radiative corrections and recoil-order terms, and examines their significance for precision tests of the Standard Model. We discuss the theoretical formalisms employed, including the integration of effective field theory frameworks with many-body approaches. Particular attention is given to recent results for superallowed Fermi decays (e.g., 10C -> 10B and 14O -> 14C) and allowed Gamow-Teller transitions (e.g., 6He -> 6Li, 8Li -> 8Be, 8B -> 8Be), where ab initio calculations have achieved unprecedented precision. We also highlight emerging calculations for unique forbidden decays, which offer complementary sensitivity to BSM physics. Finally, we outline future directions aimed at extending the reach of ab initio calculations to heavier nuclei and additional decay modes, thereby strengthening the synergy between theory and experiment in the ongoing search for new physics.

Figures

Figures reproduced from arXiv: 2602.00341 by Ayala Glick-Magid, Chien-Yeah Seng, Garrett B. King, Grigor H. Sargsyan.

Figure 2.1
Figure 2.1. Figure 2.1: Nmax= 0 and Nmax= 4 configurations in 10B in a standard particle-based NCSM (a single configuration is shown in each case). (ρ) and current (j) operators which are schematically given as, ρ = X i ρi + X ij ρij + . . . , (2.3) j = X i ji + X ij jij + . . . , (2.4) where the one-body terms represent an impulse approximation picture of single nucleon coupling to an external field, while two-body contributio… view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Ground-state energies of 6Li, 12C, and 16N obtained with the NN-N4LO + 3N∗ lnl interaction [34] with different HO frequencies. Data for the figure is taken from Ref. [35]. preservation of translational invariance of the nuclear self-bound system and provides solutions in terms of single-particle HO wavefunctions that are analytically known. With larger model spaces utilized in the no-core shell-model the… view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: (a) Convergence of the 8Li ground state quadrupole moment vs. Nmax calculated using SA-NCSM with different HO parameters (ℏΩ) and compared to the experimental value from [54]. The dashed horizontal line with a band shows the infinite-space extrapolated value. Figure adapted from Ref. [14] with permission. (b) Quadrupole moments of various nuclei divided by their proton numbers calculated using SA-NCSM an… view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: GFMC propagation of the 6He → 6Li Gamow-Teller β decay transition matrix element for the NV2+3-Ia nuclear Hamiltonian. The one-body matrix element is shown in blue in the top panel, and is compared with the matrix element retaining one- and two-body transition operators shown in green. The two-body contribution is isolated in the bottom panel and plotted in orange. The average GFMC estimate is shown by t… view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: First diagram: A generic γW-box diagram for β±-decay. Second and third diagram: the “traditional” picture for δNS. Vud can be extracted from beta decays of pion, free neutron, and nuclei. For pion which is theoretically the cleanest with recent lattice calculations of the electromagnetic radiative corrections (RC) [77, 78], the bottleneck is the large experimental uncertainty in the πe3 branching ratio [… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Lowest-order Feynman diagrams contributing to the effective two-body potentials. Figures courtesy of Wouter Dekens. [PITH_FULL_IMAGE:figures/full_fig_p015_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: RC diagram with the weak and electromagnetic vertices acting on the same nucleon. Figure courtesy of Wouter Dekens. [PITH_FULL_IMAGE:figures/full_fig_p017_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Main results of the δNS calculation for 10C→10B in Ref.[17] (see the text for explanation). other hand, as explained in Ref. [19], the same diagram in the EFT language probes only physics at the ultrasoft region, i.e. q ∼ 100 MeV. Therefore, the contribution from the quasielastic nucleons does not reside in Fig.3.3, but instead in the nuclear matrix element of the counterterm potentials. 3.3. 10C→ 10B wi… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Nuclear matrix element densities of various potentials contributing to [PITH_FULL_IMAGE:figures/full_fig_p020_3_5.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: (a) Calculated energy dependence of the spectrum of [PITH_FULL_IMAGE:figures/full_fig_p024_4_1.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Ratio of possible BSM-induced signals to SM nuclear-structure corrections for the [PITH_FULL_IMAGE:figures/full_fig_p026_4_2.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: The Standard Model (SM) spectrum for 6He β decay relative to the zero recoil approximation computed with GFMC (blue band), compared to results including BSM tensor (red band) and pseudoscalar (green band) contributions. The width of the band represents variations in the model Hamiltonian. Figure reprinted with permission from Ref. [15]. of the initial (final) state nucleus, and Ji is the angular momentum… view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Level diagram of the 8Li and 8B β decays to 8Be. All of 8Be states are above the α + α separation threshold. The dotted levels correspond to the states that have not been directly observed experimentally, but calculated in the SA-NCSM and proposed in earlier studies (see text for details). NN interactions, Nmax and ℏΩ parameters. In [PITH_FULL_IMAGE:figures/full_fig_p030_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Calculated j2/A2 c and j3/A2 c from SA-NCSM (squares and triangles, respectively) and their predicted values (upper and lower horizontal lines, respectively) for the 8Li β decay (left) and 8B β decay (right) to 2 + 1 in 8Be vs. the calculated quadrupole moments [Q(2+)] of the initial nuclei. Calculations use the NNLOopt, NNLOsat and N3LO chiral potentials, and the JISP16 NN, in Nmax=6-12 model spaces. Th… view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Calculated d/A2 c from SA-NCSM (blue dots) and their predicted values for the 8Li β decay (left) and 8B β decay (right) to 2 + 1 in 8Be vs. the calculated quadrupole moments [Q(2+)] of the initial nuclei. The vertical gray lines show the experimental values of 8Li and 8B Q(2+) with uncertainties [54, 172]. The horizontal blue bands are uncertainties solely from the Q(2+) experimental uncertainty while th… view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Calculated 8Li beta decay j3/A2 c vs. j2/A2 c values to the lowest 2 + state in 8Be with NNLOopt, NNLOsat, N3LO-EM and JISP16 interactions for the same model spaces as in [PITH_FULL_IMAGE:figures/full_fig_p033_4_7.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.