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REVIEW 4 major objections 5 minor 81 references

Radii of light nuclei from the Jacobi No-Core Shell Model

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

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Pith's one-line read The paper shows that fitting an exponential tail to the intermediate-range part of no-core shell model densities makes matter and charge radii of helium and lithium isotopes converge and agree with experiment.

desk verdict A plausible tail-repair method that produces reasonable radii, but the key decay constant is never validated against the physical separation energy, leaving the central claim in 'deduced' territory. read the letter →

arxiv 2502.03989 v1 pith:QJF5IQVF submitted 2025-02-06 nucl-th

Xiang-Xiang Sun , Hoai Le , Ulf-G. Mei{ss}ner , Andreas Nogga This is my paper · ORCID
classification nucl-th MSC 81V35 PACS 21.60.Cs21.10.Ft21.10.Gv
keywords no-coreshellmodelnuclearradiitwo-bodyrelativedensitiesdensitytailcorrectionharmonicoscillatorbasischiralforceslightnucleicoordinates
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 addresses a known breakdown in the no-core shell model: with a harmonic oscillator basis, binding energies converge while radii do not, because the long-range part of the density falls as $e^{-\beta r^2}$ instead of the physical $e^{-\kappa r}$. Its claim is that the correct exponential tail can be recovered from limited-basis densities by fitting $\alpha e^{-\kappa r}$ in an intermediate range of distances and choosing $\alpha$ and $\kappa$ so that repaired densities from different basis sizes agree far out. Splicing that tail onto the relative-coordinate NCSM density makes the matter and charge radii of 4,6,8He and 6,7,8Li converge rapidly in the basis size and agree with experiment, with the SRG evolution of the interaction shifting radii only slightly. The practical significance is that reliable long-range observables might be extracted from existing calculations without pushing to much larger model spaces.

What carries the argument

The load-bearing object is the two-body relative density $\rho_{m_t}(r)$ for each isospin channel of a nucleon pair, constructed from the no-core shell model wave function through the two-nucleon transition densities and normalized so that summing channels and integrating $r^2\rho(r)$ gives one. The repair mechanism is Eq. (14): keep the NCSM density up to a radius $r_2$, and replace the tail by $\alpha e^{-\kappa r}$ beyond it. The two parameters are not free: $\alpha$ and $\kappa$ are chosen by a consistency criterion in which the repaired densities from different basis sizes $N_{\rm HO}$ are required to agree at a large distance (about 7 fm) within a tolerance that is tightened until the extracted radius stabilizes. That criterion is what turns the fit into a physical asymptotic rather than a merely numerical one.

What would settle it

Take the fitted $\alpha e^{-\kappa r}$ tail for a nucleus, read off $\kappa$ from the repair, and compare it with $\sqrt{2\mu S_2}/\hbar$, the binding momentum from the two-nucleon separation energy of that nucleus; if the two disagree beyond numerical uncertainty for several isotopes, the repaired tail is not the physical asymptote and the method is only imposing self-consistency. A complementary check is to run the same repair for a light nucleus whose exact radius is known from a converged calculation using radial functions with exponential asymptotics and see whether the repaired value reproduces that radius.

Watch

Extended reading notes

Core claim

The central claim is that the asymptotic behavior of the two-body relative density can be deduced from NCSM densities computed in a limited basis, even though the harmonic-oscillator basis gives those densities a Gaussian falloff. In an intermediate window of $r$ — roughly 2 to 5 fm depending on the oscillator frequency — the densities from different basis sizes nearly agree, and the paper treats this window as carrying the physical short- and intermediate-range information. Fitting $\alpha e^{-\kappa r}$ there, and selecting the fit so that the tails for different $N_{\rm HO}$ coincide at large $r$ (Appendix B), produces an 'improved' density that is kept up to a matching radius and replaced by the exponential beyond it. With this density, the rms matter radii of 4,6,8He and 6,7,8Li converge over basis size and frequency and match measured values; for 6Li at $\omega=16$ MeV the largest-basis result moves from 2.181 fm before repair to 2.350 fm after repair. The paper also reports charge radii from the repaired point-proton densities, which agree with experiment within the spread across oscillator frequencies.

Load-bearing premise

The load-bearing premise is that requiring the repaired densities from different basis sizes to agree far from the center picks out the true physical tail, rather than merely making all calculations agree with each other; the paper never checks the fitted decay rate against the rate expected from the two-nucleon separation energy.

Editorial extensions

If this is right

  • Matter radii of 4,6,8He and 6,7,8Li extracted from repaired densities converge with basis size and agree with experimental values, whereas the raw NCSM radii do not converge in the accessible basis.
  • For 6Li the corrected radii across four oscillator frequencies lie in a 2.33–2.39 fm band at $N_{\rm HO}=12$, compared with a much wider spread before correction.
  • Including the SRG transformation of the two-body density changes the 4He matter radius by about 0.02 fm, so the long-range tail, not the short-range unitary evolution, controls the extracted size.
  • Charge radii obtained from the repaired point-proton densities are consistent with experiment for the helium and lithium isotopes studied, with the Li charge radii slightly larger than earlier theoretical results.
  • The same density repair can be applied to other long-range observables, and the corrected densities could be combined with neural-network extrapolation to add uncertainty estimates.

Reading between the lines

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

  • The fitted $\kappa$ is never compared with the binding momentum $\sqrt{2\mu S_2}/\hbar$ fixed by the two-nucleon separation energy; checking that would test whether the repaired tail is the physical asymptotic or just a common convergence curve.
  • The consistency criterion could be turned into a controlled extrapolation: varying the fit window $[r_1,r_2]$ and the tolerance, and studying how the radius and $\kappa$ respond, would quantify the systematic uncertainty of the method.
  • A decisive extension would be to apply the same repair to a nucleus for which an exact radius is available from a converged calculation with non-Gaussian radial functions; agreement there would validate the method independently of the shell-model basis.
  • The systematically larger Li radii compared with neural-network extrapolations on the same interaction suggest the repair changes more than convergence; whether the difference is missing three-nucleon physics or an artifact of the tail assumption is a question the paper leaves open.
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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 presents a method to extract rms matter and charge radii of light nuclei from Jacobi no-core shell model (J-NCSM) calculations using chiral SMS N4LO+ + N2LO interactions. The two-body relative densities obtained in finite harmonic-oscillator spaces are modified by fitting an exponential tail α exp(−κr) to the density in an intermediate-distance window and replacing the density beyond r2 by this exponential. The parameters α and κ are selected by requiring that the repaired densities from different basis sizes (NHO) agree at r = 7 fm, with the tolerance tightened until the extracted radii collapse. The procedure is applied to 4,6,8He and 6,7,8Li; the corrected matter and charge radii converge in NHO and, for most cases, agree with experiment, whereas the raw NCSM radii are not converged.

Significance. If the method is valid, it offers a practical alternative to extrapolation or specialized bases for computing long-range observables from HO-based ab initio calculations, and it provides concrete radius predictions for p-shell nuclei with a modern chiral interaction. The paper is careful in using two-body transition densities, in checking the effect of SRG evolution on densities, and in documenting the fitting procedure. The main weakness is that the physical content of the fitted exponential tail is not independently validated; the only fully converged benchmark (4He) is also the case where the correction is nearly negligible. Establishing the method therefore requires an external check of the fitted decay constant or an equivalent validation, and a more honest treatment of the 8He case.

major comments (4)
  1. [Appendix B, Eq. (14)] The selection criterion for α and κ is internal consistency, not physical correctness: the authors require that repaired densities from different NHO agree at r = 7 fm and then lower the tolerance until the extracted radii converge. As the text itself states, 'the range of the extracted radii goes towards a single value by construction when decreasing the tolerance.' Because the radius is an r^4-weighted integral of the density, forcing all repaired tails to pass through a common point at large r largely fixes the tail contribution and therefore tends to collapse the radii regardless of whether κ is the true decay constant. To support the claim that the repaired density carries the physical long-range behavior, the fitted κ should be compared with the decay constant determined by the relevant two-body separation energy (e.g., the α-d threshold for 6Li, accounting for the factor two between wavefunction and density decay constants), or the method should be tested against an independent converged calculation for a p-shell nucleus. Without such a check, the agreement with experiment for 6,7Li and 6,8He is not an independent confirmation of the method.
  2. [§III, Fig. 4] The 8He charge radius is not converged after the correction: the paper reports 2.10 fm for ω = 12 MeV versus 1.96–2.02 fm for ω = 16, 20, 24 MeV at the largest basis sizes, and the binding energy is underbound by about 4 MeV. Including 8He in the headline claim that radii 'can be accurately obtained' is therefore not supported by the presented results. The authors should either exclude 8He from the central claim or provide a quantitative convergence criterion and explain why the method fails for this nucleus.
  3. [§III, Fig. 1 and Appendix B] The 4He benchmark cannot validate the tail-repair procedure in the regime where it matters. For 4He the raw radii are already converged (1.447 fm with SRG, 1.466 fm without), and the repair changes the result by only about 0.02 fm. In the p-shell nuclei the correction shifts the radius by 0.1–0.2 fm, so the entire predictive content for those nuclei rests on the fitted exponential tail whose physical validity is not independently established. A validation on a case where the raw radius is genuinely non-converged but a converged reference exists (for example 6Li in a much larger model space, or an exactly solvable few-body model) is needed.
  4. [Appendix B and Figs. A1–A2] The procedure contains several choices whose influence on the final radius is not quantified: the fitting window (r1, r2), the matching point (7 fm), and the tolerance. Appendix B shows that the extracted radius for NHO = 6 changes from 2.318–2.343 fm at tolerance 5×10^-5 to 2.334 fm at 3×10^-6, and the tolerance adopted varies strongly with ω (from 9.5×10^-7 to 2×10^-4). The error bars in Fig. 4 are only the spread over four ω values at the largest NHO; they do not include the uncertainty from the fitting choices or from the neglect of induced three-body currents in the SRG evolution of the density operator. The paper should provide a systematic study of these choices and a more complete uncertainty budget before claiming 0.01–0.05 fm accuracy.
minor comments (5)
  1. [Appendix A] The sentence 'the deviation without SRG transformation to the bare result for the radius is 0.032 fm^-1' should read '0.032 fm'; the inverse-length unit is incorrect.
  2. [§II, Eq. (14)] The asymptotic form in Eq. (14) is a single exponential for the total two-body density. For halo nuclei such as 6He and 8He one expects different decay scales for the halo neutrons and the core, and the total density is a sum of contributions from pp, nn, and np pairs with different thresholds. The paper does not discuss whether this single-exponential ansatz is adequate for those cases.
  3. [§IV] There are typographical errors, for example 'otherab initio' in Sec. IV and 'contribitions' in Appendix A; the manuscript should be proofread.
  4. [Fig. 3] In the 7Li panel of Fig. 3(a) the legend entry 'w srg' should be 'w. srg' for consistency with the other panels.
  5. [§III, after Eq. (15)] The neglect of two-body current contributions to the charge radius is mentioned, but the expected size of this effect for the Li isotopes is not estimated; a brief quantitative statement (or a reference with an estimate) would help the reader judge the significance of the agreement with experiment in Fig. 4.

Circularity Check

1 steps flagged · score 6.0 of 10

Tail-repair selection enforces the reported convergence; the physical decay constant κ is never independently validated.

  1. fitted input called prediction [Appendix B ('Determination of radius of 6Li'), selection procedure and Fig. A1 caption]
    "To ensure the same long-range behavior for different values of NHO, we select from these 4 × 77 cases groups of 4 with different NHO, for which the densities at r = 7.0 fm are the same within a given tolerance. ... The range of the extracted radii goes towards a single value by construction when decreasing the tolerance."

    The fit parameters (α, κ) in Eq. (14) are accepted only when the exponential tails agree at r = 7 fm across basis sizes, and the tolerance is then lowered until the resulting radii coincide. Since the radius is the r^4-weighted integral of these densities (Eq. 13), forcing the large-r densities to agree forces the tail contribution to the radius to agree across NHO; the improved convergence of the corrected radii is therefore an input to the fit selection, not an independent output of the physics. The paper itself states the collapse is 'by construction.' The procedure never checks that the selected κ equals the decay constant set by the two-body separation energy, so the claim that the 'correct' large-distance asymptotic has been deduced is not independently established.

full rationale

The only clearly circular step is the selection rule in Appendix B. The paper fits α and κ in Eq. (14) and accepts fits for which densities from different NHO agree at r = 7 fm; it then tightens the tolerance until the extracted radii are the same. Because the matter radius is the r^4-weighted integral of these densities (Eq. 13), this procedure imposes the convergence of the corrected radii by construction, as the paper itself concedes. This is a genuine fitted-input-called-prediction step: the 'nice convergence' after repair is largely a property of the fitting criterion rather than an independent test of the method. The 4He validation is weak on this point because 4He is already nearly converged without repair (raw radii converge by NHO = 12–18 and the correction changes the radius by only about 0.02 fm), so it does not test the tail repair in the p-shell regime where the shift is 0.1–0.2 fm. The final radii are nevertheless compared with experimental data and with ANN extrapolations from Ref. [43], giving the reported values independent empirical content; and the underlying J-NCSM densities, SRG evolution, and two-body radius formulas are technical inputs from prior work rather than load-bearing self-citations. Hence the circularity is partial, not total: the convergence claim is built into the selection, but the numerical radius values and their experimental comparison are not.

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

The central result rests on the fitted exponential tail (alpha, kappa), the choice of fitting window (r1, r2), and the consistency tolerance. The physical justification for these choices is an assumption that the intermediate-distance density already shows the true exponential decay. All final radii inherit these fitting choices.

free parameters (4)
  • alpha (exponential tail amplitude) = not reported
    Amplitude of the exponential tail in Eq. (14), fitted to the J-NCSM density in the interval [r1, r2] for each NHO and omega.
  • kappa (exponential decay constant) = not reported
    Decay constant of the tail, fitted from the densities rather than derived from the separation energy. It determines the long-range part of the radius integral.
  • r1, r2 (fitting window) = r2 ~ 4.2-4.8 fm, r1 ~ 2.5-3.5 fm for 6Li; varies by nucleus
    The interval over which the exponential is fitted is chosen from density crossing points and varied in steps of 0.1 fm, with fits selected by tolerance.
  • tolerance (cross-NHO consistency) = e.g., 3e-6 for 6Li at omega=16 MeV; varies
    Threshold on the difference of repaired densities at r = 7 fm across basis sizes. Lowering it forces the extracted radii to a single value by construction.
assumptions (4)
  • domain assumption The two-body relative density at large distance decays as alpha e^(-kappa r).
    Used to define the repaired density in Eq. (14). The physical asymptotic is exponential, but the decay constant is fitted, not derived.
  • domain assumption The intermediate-distance region (r between r1 and r2) of the J-NCSM density already contains the correct asymptotic behavior.
    Invoked in Sec. III and Appendix B when fitting the exponential to the crossing interval and using it to fix the tail.
  • domain assumption The SRG transformation of the radius operator can be truncated at the two-body level, neglecting induced three-nucleon contributions.
    Used in Sec. II and Appendix A. The missing 3N contribution is estimated at about 0.013 fm for 4He but is not propagated to other nuclei.
  • standard math The repaired density remains normalized according to Eq. (12).
    The renormalization after replacing the tail ensures the density integrates to the correct total pair number, as stated in Sec. II.

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Cite this review

Pith. "Pith review of Radii of light nuclei from the Jacobi No-Core Shell Model." pith.science (2026). https://pith.science/paper/QJF5IQVF

@misc{pith2026250203989,
  author       = {Pith},
  title        = {Pith review of: Radii of light nuclei from the Jacobi No-Core Shell Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QJF5IQVF}},
  note         = {Machine review of arXiv:2502.03989}
}
abstract

Accurately determining the size of the atomic nucleus with realistic nuclear forces is a long outstanding issue of nuclear physics. The no-core shell model (NCSM), one of the powerful ab initio methods for nuclear structure, can achieve accurate energies of light nuclei. The extraction of converged radii is more difficult. In this work, we present a novel method to effectively extract the radius of light nuclei by restoring the long-range behavior of densities from NCSM calculations. The correct large distance asymptotic of two-body relative densities are deduced based on the NCSM densities in limited basis size. The resulting radii using the corrected densities show a nice convergence. The root-mean-square matter and charge radii of $^{4,6,8}$He and $^{6,7,8}$Li can be accurately obtained based on Jacobi-NCSM calculations with the high-precision chiral two-nucleon and three-nucleon forces combined with this new method. Our method can be straightforwardly extended to other ab initio calculations, potentially providing a better description of nuclear sizes with realistic nuclear forces.

Figures

Figures reproduced from arXiv: 2502.03989 by the authors.

Figure 1
Figure 1. FIG. 1. Ground state rms matter radii (a) and energies (b) of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Ground state rms matter radii (a) before correction [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Ground state rms matter radii before correction (a) [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Calculated charge radii of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Works this paper leans on

81 extracted references · 45 canonical work pages

  1. [1]

    Epelbaum, H.-W

    E. Epelbaum, H.-W. Hammer, and U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009), arXiv:0811.1338 [nucl-th]

    arXiv 2009

  2. [2]

    Machleidt and D

    R. Machleidt and D. R. Entem, Phys. Rept. 503, 1 (2011), arXiv:1105.2919 [nucl-th]

    arXiv 2011

  3. [3]

    B. R. Barrett, P. Navratil, and J. P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)

    2013

  4. [4]

    Hebeler, J

    K. Hebeler, J. D. Holt, J. Menendez, and A. Schwenk, Ann. Rev. Nucl. Part. Sci. 65, 457 (2015), arXiv:1508.06893 [nucl-th]

    arXiv 2015

  5. [5]

    Hergert, S

    H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama, Phys. Rept. 621, 165 (2016), arXiv:1512.06956 [nucl-th]

    arXiv 2016

  6. [6]

    T. A. L¨ ahde and U.-G. Meißner,Nuclear Lattice Effective Field Theory: An introduction , Vol. 957 (Springer, 2019)

    2019

  7. [7]

    Lee, Front

    D. Lee, Front. in Phys. 8, 174 (2020)

    work page 2020

  8. [8]

    Hammer, A

    H.-W. Hammer, A. Nogga, and A. Schwenk, Rev. Mod. Phys. 85, 197 (2013), arXiv:1210.4273 [nucl-th]

    arXiv 2013

Show all 81 references
  1. [9]

    Carlson, S

    J. Carlson, S. Gandolfi, F. Pederiva, S. C. Pieper, R. Schi- avilla, K. E. Schmidt, and R. B. Wiringa, Rev. Mod. Phys. 87, 1067 (2015), arXiv:1412.3081 [nucl-th]

    2015 arXiv

  2. [10]

    Hagen, T

    G. Hagen, T. Papenbrock, M. Hjorth-Jensen, and D. J. Dean, Rept. Prog. Phys. 77, 096302 (2014), arXiv:1312.7872 [nucl-th]

    2014 arXiv

  3. [11]

    Machleidt and F

    R. Machleidt and F. Sammarruca, Prog. Part. Nucl. Phys. 137, 104117 (2024), arXiv:2402.14032 [nucl-th]

    2024 arXiv

  4. [12]

    Elhatisari et al

    S. Elhatisari et al. , Nature 630, 59 (2024), arXiv:2210.17488 [nucl-th]

    2024 arXiv

  5. [13]

    Maris et al

    P. Maris et al. , Phys. Rev. C 103, 054001 (2021), arXiv:2012.12396 [nucl-th]

    2021 arXiv

  6. [14]

    Maris et al

    P. Maris et al. (LENPIC), Phys. Rev. C 106, 064002 (2022), arXiv:2206.13303 [nucl-th]

    2022 arXiv

  7. [15]

    S. K. Bogner, T. T. S. Kuo, and A. Schwenk, Phys. Rept. 386, 1 (2003), arXiv:nucl-th/0305035

    2003 arXiv

  8. [16]

    R. Roth, T. Neff, and H. Feldmeier, Prog. Part. Nucl. Phys. 65, 50 (2010), arXiv:1003.3624 [nucl-th]

    2010 arXiv

  9. [17]

    S. K. Bogner, R. J. Furnstahl, and R. J. Perry, Phys. Rev. C 75, 061001 (2007), arXiv:nucl-th/0611045

    2007 arXiv

  10. [18]

    E. D. Jurgenson, P. Navratil, and R. J. Furnstahl, Phys. Rev. Lett. 103, 082501 (2009), arXiv:0905.1873 [nucl-th]

    2009 arXiv

  11. [19]

    Hergert, Phys

    H. Hergert, Phys. Scripta 92, 023002 (2017), arXiv:1607.06882 [nucl-th]

    2017 arXiv

  12. [20]

    M. L. Bissell et al. , Phys. Rev. C 93, 064318 (2016)

    2016

  13. [21]

    Lapoux, V

    V. Lapoux, V. Som` a, C. Barbieri, H. Hergert, J. D. Holt, and S. R. Stroberg, Phys. Rev. Lett. 117, 052501 (2016), arXiv:1605.07885 [nucl-ex]

    2016 arXiv

  14. [22]

    R. F. Garcia Ruiz et al. , Nature Phys. 12, 594 (2016), arXiv:1602.07906 [nucl-ex]

    2016 arXiv

  15. [23]

    Koszor´ uset al

    A. Koszor´ uset al. , Nature Phys. 17, 439 (2021), [Er- ratum: Nature Phys. 17, 539 (2021)], arXiv:2012.01864 [nucl-ex]

    2021 arXiv

  16. [24]

    Kaur et al

    S. Kaur et al. , Phys. Rev. Lett. 129, 142502 (2022), arXiv:2209.00722 [nucl-ex]

    2022 arXiv

  17. [25]

    Maris, H

    P. Maris, H. Le, A. Nogga, R. Roth, and J. P. Vary, Front. in Phys. 11, 1098262 (2023), arXiv:2305.19648 [nucl-th]

    2023 arXiv

  18. [26]

    E. R. Anderson, S. K. Bogner, R. J. Furnstahl, and R. J. Perry, Phys. Rev. C 82, 054001 (2010), arXiv:1008.1569 [nucl-th]

    2010 arXiv

  19. [27]

    M. D. Schuster, S. Quaglioni, C. W. Johnson, E. D. Jur- genson, and P. Navratil, Phys. Rev. C 90, 011301 (2014), arXiv:1402.7106 [nucl-th]

    2014 arXiv

  20. [28]

    Miyagi, T

    T. Miyagi, T. Abe, M. Kohno, P. Navratil, R. Okamoto, T. Otsuka, N. Shimizu, and S. R. Stroberg, Phys. Rev. C 100, 034310 (2019), arXiv:1901.11106 [nucl-th]

    2019 arXiv

  21. [29]

    T. Neff, H. Feldmeier, and W. Horiuchi, Phys. Rev. C 92, 024003 (2015), arXiv:1506.02237 [nucl-th]

    2015 arXiv

  22. [30]

    S. K. Bogner, R. J. Furnstahl, P. Maris, R. J. Perry, A. Schwenk, and J. P. Vary, Nucl. Phys. A801, 21 (2008), arXiv:0708.3754 [nucl-th]

    2008 arXiv

  23. [31]

    Cockrell, J

    C. Cockrell, J. P. Vary, and P. Maris, Phys. Rev. C 86, 034325 (2012), arXiv:1201.0724 [nucl-th]

    2012 arXiv

  24. [32]

    Maris and J

    P. Maris and J. P. Vary, Int. J. Mod. Phys. E22, 1330016 (2013)

    2013

  25. [33]

    T. Heng, J. P. Vary, and P. Maris, Phys. Rev. C 95, 014306 (2017), arXiv:1602.00156 [nucl-th]

    2017 arXiv

  26. [34]

    I. J. Shin, Y. Kim, P. Maris, J. P. Vary, C. Forss´ en, J. Ro- tureau, and N. Michel, J. Phys. G 44, 075103 (2017), arXiv:1605.02819 [nucl-th]

    2017 arXiv

  27. [35]

    Choudhary, P

    P. Choudhary, P. C. Srivastava, and P. Navr´ atil, Phys. Rev. C 102, 044309 (2020), arXiv:2009.10257 [nucl-th]

    2020 arXiv

  28. [36]

    M. A. Caprio, P. J. Fasano, P. Maris, and A. E. Mc- Coy, Phys. Rev. C 104, 034319 (2021), arXiv:2106.12128 [nucl-th]

    2021 arXiv

  29. [37]

    earlier, a direct comparison to results using other in- teractions has to be taken with care

    using the Daejeon16 interaction. earlier, a direct comparison to results using other in- teractions has to be taken with care. However, the re- sults of Refs. [37] and [38] using the JISP16 interaction of 2 .342(7) fm and 2 .32 fm are consistent with our val- ues. However, our...

  30. [38]

    M. A. Caprio, P. Maris, and J. P. Vary, Phys. Rev. C 90, 034305 (2014), arXiv:1409.0877 [nucl-th]

    2014 arXiv

  31. [39]

    D. M. Rodkin and Y. M. Tchuvil’sky, Phys. Rev. C 106, 034305 (2022), arXiv:2205.13798 [nucl-th]

    2022 arXiv

  32. [40]

    R. J. Furnstahl, G. Hagen, and T. Papenbrock, Phys. Rev. C 86, 031301 (2012), arXiv:1207.6100 [nucl-th]

    2012 arXiv

  33. [41]

    R. J. Furnstahl, T. Papenbrock, and S. N. More, Phys. Rev. C 89, 044301 (2014), arXiv:1312.6876 [nucl-th]. 9 0 2 4 6 8 r (fm) 10 4 10 3 10 2 10 1 100 NN(r) (fm 3) =16 MeV, NHO = 06 before: 2.053 fm after: 2.318~2.343 fm tol.=5.0×10 5 0 2 4 6 8 r (fm) =16 MeV, NHO = 08 before: ...

    2014 arXiv

  34. [42]

    G. A. Negoita et al. , Phys. Rev. C 99, 054308 (2019), arXiv:1810.04009 [nucl-th]

    2019 arXiv

  35. [43]

    Forss´ en, B

    C. Forss´ en, B. D. Carlsson, H. T. Johansson, D. S¨ a¨ af, A. Bansal, G. Hagen, and T. Papenbrock, Phys. Rev. C 97, 034328 (2018), arXiv:1712.09951 [nucl-th]

    2018 arXiv

  36. [44]

    Constantinou, M

    C. Constantinou, M. A. Caprio, J. P. Vary, and P. Maris, Nucl. Sci. Tech. 28, 179 (2017), arXiv:1605.04976 [nucl- th]

    2017 arXiv

  37. [45]

    Wolfgruber, M

    T. Wolfgruber, M. Kn¨ oll, and R. Roth, Phys. Rev. C110, 014327 (2024)

    2024

  38. [46]

    Tichai, J

    A. Tichai, J. M¨ uller, K. Vobig, and R. Roth, Phys. Rev. C 99, 034321 (2019), arXiv:1809.07571 [nucl-th]

    2019 arXiv

  39. [47]

    P. J. Fasano, C. Constantinou, M. A. Caprio, P. Maris, and J. P. Vary, Phys. Rev. C 105, 054301 (2022), arXiv:2112.04027 [nucl-th]

    2022 arXiv

  40. [48]

    Liebig, U.-G

    S. Liebig, U.-G. Meißner, and A. Nogga, Eur. Phys. J. A 52, 103 (2016), arXiv:1510.06070 [nucl-th]

    2016 arXiv

  41. [49]

    A. A. Filin, D. M¨ oller, V. Baru, E. Epelbaum, H. Krebs, and P. Reinert, Phys. Rev. C 103, 024313 (2021), arXiv:2009.08911 [nucl-th]

    2021 arXiv

  42. [50]

    H. Le, J. Haidenbauer, U.-G. Meißner, and A. Nogga, Phys. Rev. C 107, 024002 (2023), arXiv:2210.03387 [nucl-th]

    2023 arXiv

  43. [51]

    H. Le, J. Haidenbauer, U.-G. Meißner, and A. Nogga, Eur. Phys. J. A 56, 301 (2020), arXiv:2008.11565 [nucl- th]

    2020 arXiv

  44. [52]

    H. Le, J. Haidenbauer, U.-G. Meißner, and A. Nogga, 10 0 2 4 6 8 r (fm) 10 4 10 3 10 2 10 1 100 NN(r) (fm 3) =12 MeV, NHO = 06 before: 2.245 fm after: 2.402~2.402 fm tol.=9.5×10 7 0 2 4 6 8 r (fm) =12 MeV, NHO = 08 before: 2.231 fm after: 2.383~2.383 fm tol.=9.5×10 7 0 2 4 6 8...

    2024 arXiv

  45. [53]

    H. Le, J. Haidenbauer, U.-G. Meißner, and A. Nogga, Eur. Phys. J. A 57, 339 (2021), arXiv:2109.06648 [nucl- th]

    2021 arXiv

  46. [54]

    M. A. Caprio, P. Maris, and J. P. Vary, Phys. Rev. C 86, 034312 (2012), arXiv:1208.4156 [nucl-th]

    2012 arXiv

  47. [55]

    Bacca, N

    S. Bacca, N. Barnea, and A. Schwenk, Phys. Rev. C 86, 034321 (2012), arXiv:1202.0516 [nucl-th]

    2012 arXiv

  48. [56]

    Nogga et al

    A. Nogga et al. , NUCDENS: A package to ac- cess nuclear densities, https://jugit.fz-juelich.de/ a.nogga/nucdensity

  49. [57]

    H. W. Grießhammer, J. A. McGovern, A. Nogga, and D. R. Phillips, Few Body Syst. 61, 48 (2020), arXiv:2005.12207 [nucl-th]

    2020 arXiv

  50. [58]

    X.-X. Sun, H. Le, A. Nogga, and U.-G. Meißner, in prepa- ration (2025)

    2025

  51. [59]

    H. W. Griesshammer, J. Liao, J. A. McGovern, A. Nogga, and D. R. Phillips, Eur. Phys. J. A 60, 132 (2024), arXiv:2401.16995 [nucl-th]

    2024 arXiv

  52. [60]

    A. V. Dobrovolsky et al. , Nucl. Phys. A 766, 1 (2006)

    2006

  53. [61]

    Tanihata, H

    I. Tanihata, H. Savajols, and R. Kanungo, Prog. Part. Nucl. Phys. 68, 215 (2013)

    2013

  54. [62]

    Caurier and P

    E. Caurier and P. Navratil, Phys. Rev. C 73, 021302 (2006), arXiv:nucl-th/0512015

    2006 arXiv

  55. [63]

    M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, Chin. Phys. C 45, 030003 (2021)

    2021

  56. [64]

    Forssen, E

    C. Forssen, E. Caurier, and P. Navratil, Phys. Rev. C 79, 021303 (2009), arXiv:0901.0453 [nucl-th]

    2009 arXiv

  57. [65]

    Nogga, P

    A. Nogga, P. Navratil, B. R. Barrett, and J. P. Vary, Phys. Rev. C 73, 064002 (2006), arXiv:nucl-th/0511082

    2006 arXiv

  58. [66]

    Maris, J

    P. Maris, J. P. Vary, and P. Navr´ atil, Phys. Rev. C 87, 014327 (2013), arXiv:1205.5686 [nucl-th]

    2013 arXiv

  59. [67]

    Papadimitriou, A

    G. Papadimitriou, A. T. Kruppa, N. Michel, W. Nazarewicz, M. Ploszajczak, and J. Rotureau, Phys. Rev. C 84, 051304 (2011), arXiv:1109.0223 [nucl-th]

    2011 arXiv

  60. [68]

    Gnech, M

    A. Gnech, M. Viviani, and L. E. Marcucci, Phys. Rev. C 102, 014001 (2020), arXiv:2004.05814 [nucl-th]

    2020 arXiv

  61. [69]

    Romero-Redondo, S

    C. Romero-Redondo, S. Quaglioni, P. Navratil, and G. Hupin, Phys. Rev. Lett. 117, 222501 (2016), arXiv:1606.00066 [nucl-th]. 11

    2016 arXiv

  62. [70]

    Symmetries and the Emergence of Structure in QCD

    using the Idaho N 3LO interaction [75] SRG-evolved without adding a 3NF. For 8He, the extrapolated ener- gies are smaller than the experimental results. This was already observed in Ref. [14]. In fact, using a lower or- der NN interaction [13], one obtains better agreement wit...

    2020

  63. [71]

    N¨ ortersh¨ auser, T

    W. N¨ ortersh¨ auser, T. Neff, R. Sanchez, and I. Sick, Phys. Rev. C 84, 024307 (2011)

    2011

  64. [72]

    Quaglioni, C

    S. Quaglioni, C. Romero-Redondo, P. Navr´ ati, and G. Hupin, Phys. Rev. C 97, 034332 (2018), arXiv:1710.07326 [nucl-th]

    2018 arXiv

  65. [73]

    X. Liu, P. Egelhof, O. Kiselev, and M. Mutterer, Phys. Rev. C 104, 034315 (2021)

    2021

  66. [74]

    G. D. Alkhazov et al. , Phys. Rev. Lett. 78, 2313 (1997)

    1997

  67. [75]

    L. X. Chung, O. A. Kiselev, D. T. Khoa, and P. Egelhof, Phys. Rev. C 92, 034608 (2015), arXiv:1508.07679 [nucl- ex]

    2015 arXiv

  68. [76]

    Tanihata, D

    I. Tanihata, D. Hirata, T. Kobayashi, S. Shimoura, K. Sugimoto, and H. Toki, Phys. Lett. B289, 261 (1992)

    1992

  69. [77]

    D. R. Entem and R. Machleidt, Phys. Rev. C 68, 041001 (2003), arXiv:nucl-th/0304018

    2003 arXiv

  70. [78]

    J. L. Friar and J. W. Negele, in Advances in Nuclear Physics: Volume 8 , edited by M. Baranger and E. Vogt (Springer US, Boston, MA, 1975) pp. 219–376

    1975

  71. [79]

    P. A. Zyla et al. (Particle Data Group), PTEP 2020, 083C01 (2020)

    2020

  72. [80]

    Lin, H.-W

    Y.-H. Lin, H.-W. Hammer, and U.-G. Meißner, Phys. Rev. Lett. 128, 052002 (2022), arXiv:2109.12961 [hep- ph]

    2022 arXiv

  73. [81]

    A. Ong, J. C. Berengut, and V. V. Flambaum, Phys. Rev. C 82, 014320 (2010), arXiv:1006.5508 [nucl-th]

    2010 arXiv

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