Analysis of the strengths of the contact potential at N4LO through nuclear and neutron matter

Francesca Sammarruca; Tomiwa Ajagbonna

REVIEW 5 major objections 5 minor 16 references

Analysis of the strengths of the contact potential at N4LO through nuclear and neutron matter

T0 review · 5 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Contact three-nucleon-force couplings fitted to nd scattering give nuclear-matter energy shifts far too large to be compatible with empirical binding.

desk verdict A careful, honestly hedged plug-in calculation shows the N4LO contact LECs from nd scattering give absurdly large nuclear-matter energies; the qualitative caution is worth taking seriously, but the missing E_i table and regulator discussion keep it from being a quantitative result. read the letter →

arxiv 2608.06610 v1 pith:D5DQLWXB submitted 2026-08-06 nucl-th

Francesca Sammarruca , Tomiwa Ajagbonna This is my paper · ORCID

classification nucl-th PACS 21.30.Fe21.65.Mn

keywords three-nucleonforceN4LOcontactinteractionsnuclearmatterneutronchiraleffectivefieldtheorydensity-dependentpotentiallow-energyconstants

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 argues that the 13 contact couplings of the N4LO (fifth-order chiral) three-nucleon force, as extracted from fits to elastic nucleon-deuteron scattering, cannot simply be transferred to infinite nuclear matter. Evaluated through density-dependent in-medium potentials in first-order Born approximation, these couplings produce positive energy shifts in symmetric nuclear matter and neutron matter that are far larger than the empirical binding energy per nucleon. The same incompatibility appears for the leading-order $c_D,c_E$ contact couplings when $c_E$ is taken from the three-nucleon continuum rather than from triton-plus-saturation fits. If the claim holds, any practical use of these contact terms in nuclei requires additional constraints beyond the three-nucleon continuum, and the system-dependence of the low-energy constants must be understood rather than ignored.

What carries the argument

The load-bearing object is the density-dependent in-medium nucleon-nucleon potential obtained by averaging the three-nucleon force over the filled Fermi sea. For the N4LO contact force this potential (Eq. (2)) is a quadratic polynomial in the relative momentum $p$, the momentum transfer $q$, and the Fermi momentum $k_F$, with 13 couplings $E_1,\ldots,E_{13}$. Its first-order expectation value in symmetric nuclear matter collapses to the single combination $2E_1+2E_2+2E_3+6E_4-E_9-3E_{10}-E_{11}-3E_{12}+E_{13}$ multiplying $k_F^8/(10\pi^4)$ (Eq. (3)); neutron matter gives the analogous combination in Eq. (5). These closed-form expressions are what turn the scattering-fitted contact strengths into a direct prediction for the equation of state.

What would settle it

Recompute the energy per nucleon with the same contact strengths but including the omitted N3LO three-nucleon force and regulator-consistent density-dependent potentials; if the resulting $E/A$ at $\rho\approx0.16$ fm$^{-3}$ comes within a few MeV of the empirical $-16$ MeV, the claimed incompatibility would not survive. Alternatively, refit the 13 $E_i$ to simultaneously reproduce nd scattering, the triton binding energy, and nuclear-matter saturation and check whether the nd-scattering observables remain equally well described.

Watch

Extended reading notes

Core claim

Using the density-dependent potentials derived from subleading chiral three-nucleon forces, the authors compute the first-order contribution to the energy per particle from the N4LO contact interaction. With the 13 strengths $E_i$ taken from the nucleon-deuteron scattering fit of Ref. [1], the resulting energy shift in symmetric nuclear matter and neutron matter is incompatible with the empirical equation of state: the magnitude is far too large, and the sign is wrong for binding. The authors also show that the leading-order contact contribution changes from $-0.72$ MeV to $+7.05$ MeV at normal density when $c_E=0.13$ (triton/saturation constrained) is replaced by $c_E=-1.27$ (continuum fitted), illustrating how strongly the short-range couplings depend on the system used to fix them. They then use a mass-formula estimate to show that moving the equation of state toward more attraction at densities around $0.07$--$0.12$ fm$^{-3}$ improves the binding energies of $^{16}$O, $^{40}$Ca, and $^{208}$Pb, suggesting where the missing attraction would need to come from.

Load-bearing premise

The calculation assumes the 13 contact strengths fitted to nucleon-deuteron scattering can be inserted directly into the density-dependent in-medium potentials and evaluated at first order, with the regularization used in the scattering fit matching the one used for matter and with no compensating contribution from the omitted N3LO three-nucleon force.

Editorial extensions

If this is right

Contact strengths fixed by 3N scattering data alone cannot be used reliably in nuclear-matter or finite-nucleus calculations; a refit that includes matter observables is needed.
The $c_D,c_E$ couplings of the leading three-nucleon force depend strongly on the system used to determine them, so constraints from the triton and from saturation must be combined with continuum data in any consistent chiral EFT application.
The N4LO contact contribution is not naturally small at normal density; the first-order Born estimate is large enough that regulator and convergence questions cannot be ignored.
A softer two-nucleon force plus extra attraction in the density region $0.07$--$0.12$ fm$^{-3}$ would bring mass-formula binding energies for $^{16}$O, $^{40}$Ca, and $^{208}$Pb closer to experiment.
Neutron matter shows the same incompatibility, which matters for neutron-star equations of state because the $c_D,c_E$ terms vanish there and the N4LO contacts carry the entire short-range 3N contribution.

Reading between the lines

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

Because Eq. (3) is a single linear combination of the 13 couplings, nuclear and neutron matter data constrain only one direction in the $E_i$ parameter space; the remaining 12 combinations could be adjusted to restore agreement with nd scattering without changing this energy shift.
The paper's suggestion that off-shell components matter is testable: refitting the $E_i$ with matter saturation included should move the couplings along the combination that leaves on-shell nd-scattering observables unchanged.
A direct extension is to compute the N4LO contact contribution to the symmetry energy and neutron-skin thickness; those observables are sensitive to the same linear combinations and could discriminate between alternative $E_i$ sets.
If the omitted N3LO three-nucleon force turns out to be repulsive at saturation, it would cancel part of the large contact contribution reported here; checking that cancellation is a clear target for the next generation of chiral potentials.

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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

Short version: this is a small, honestly hedged phenomenology note that does one genuinely new thing. It takes the 13 N4LO contact couplings that Witala et al. fitted to nd scattering and plugs them into Kaiser's density-dependent in-medium potentials. In first-order Born approximation the resulting energy per nucleon in symmetric nuclear matter and neutron matter is tens to hundreds of MeV—orders of magnitude above the empirical binding. That qualitative incompatibility is almost certainly correct, and it is worth saying out loud. The paper says it clearly and does not oversell.

What it does well: the authors are upfront about what is missing. They state that the N3LO 3NF is not included, that the complete N4LO 3NF is unavailable, and that the finite-nuclei exercise is exploratory. The leading-order comparison with cE sets a useful scale, and the figures are easy to read. The arithmetic in Eqs. (3) and (5) is simple and transparent.

The soft spots are real but not fatal to the qualitative claim. The E_i values from Ref. [1] are not listed in the paper, so a reader cannot reproduce Eq. (3) or see which coupling drives the huge repulsion. More importantly, the regulator/scheme compatibility between the nd-scattering fit and Kaiser's local density-dependent potentials is not discussed. Chiral LECs are scheme-dependent; without a cutoff check or a matching argument, the large k_F^8 contribution could be partly an artifact. The paper also gives no uncertainty estimate. And the omitted N3LO 3NF could, in principle, bring compensating attraction, though that is speculation. All of these are acknowledged or at least consistent with the paper's cautious tone.

The finite-nuclei section is the weakest part. Choosing cD=6.0, cE=0.50 to mimic extra attraction and then rejoining the other EoS is a post hoc exercise. It is labeled exploratory, so I do not count it heavily, but it does not add much beyond what is already known about cD,cE systematics.

Bottom line: this is a cautionary note for anyone who wants to use the N4LO contact LECs from nd scattering in nuclear matter or nuclear structure. It deserves peer review. I would ask the authors to include a table of the E_i values, run a quick cutoff-dependence check, and be explicit about the scheme-matching limitation. With those additions it would be a solid, useful short paper.

Referee Report

5 major / 5 minor

Summary. The paper computes the first-order (Born) contribution of the N4LO three-nucleon contact interaction to the energy per particle of symmetric nuclear matter and neutron matter, using the density-dependent in-medium potentials of Kaiser (Eqs. (2) and (4)) together with the 13 contact couplings E_i extracted from elastic nucleon-deuteron scattering in Ref. [1]. Using Eq. (3) and Eq. (5), the authors find contributions that are orders of magnitude larger than the empirical binding energy (blue curve in Fig. 3 and Table III) and conclude that the contact strengths obtained from the three-nucleon continuum are incompatible with nuclear and neutron matter. The paper also revisits the c_D,c_E couplings of the leading three-nucleon force and performs an explicitly exploratory finite-nuclei study in which a modified equation of state is used to improve binding energies of 16O, 40Ca, and 208Pb.

Significance. If the incompatibility claim is robust, it is a significant result: it would show that N4LO three-nucleon contact couplings fitted to the continuum cannot be transferred directly to infinite matter, with consequences for nuclear-structure calculations and for the interpretation of the N4LO contact force. The paper's first-order derivation is transparent and easy to follow, and the authors are appropriately cautious in describing the finite-nuclei part as exploratory. However, the central numerical claim is not reproducible from the manuscript as written, and its validity depends on regulator and scheme consistency between Ref. [1] and Kaiser's density-dependent potentials, which is not established. The concern raised in the stress-test note is genuine and lands: without the E_i values and a cutoff/scheme check, the huge k_F^8-weighted energies in Eq. (3) could be artifacts of mixing regularized scattering-fit couplings with unregularized local Born expressions.

major comments (5)

[Section II.B, Eq. (3) and Fig. 3] The central quantitative claim is that Eq. (3) gives contributions of tens of MeV per nucleon, but the 13 input values E_i from Ref. [1] are not listed anywhere in the manuscript. Without these numbers, the blue curve in Fig. 3 and the entire incompatibility statement cannot be reproduced or checked. A table of the E_i values (including the two that relate to c_D and c_E) is essential and is the first thing a reader needs.
[Sections II.B and III, Eqs. (2)-(5)] The manuscript does not establish that the E_i couplings from the regularized nd-scattering fit of Ref. [1] can be inserted directly into Kaiser's density-dependent potentials, which are derived for local contact operators without the same regulator. Chiral low-energy constants are scheme- and regulator-dependent; the k_F^8 scaling of Eq. (3) amplifies any mismatch. The authors should either provide a matching calculation, a cutoff-sensitivity study with the regulator of Ref. [1], or at minimum a clear statement of the scheme used in each input and a quantitative estimate of the resulting uncertainty. As written, the huge values in Fig. 3 could be artifacts of using the couplings outside their fitted Hilbert space.
[Introduction and Sections II.B-V] The paper's abstract and main conclusion state that the N4LO contact strengths are 'incompatible' with nuclear and neutron matter, yet the calculation omits the N3LO 3NF (acknowledged in the introduction as 'presently not on stable grounds') and the complete N4LO 3NF. The first-order N4LO contact contribution alone does not exclude a compensating contribution of opposite sign from the omitted terms. The authors should soften the claim to a statement about the N4LO contact contribution in isolation, or perform a complete equation-of-state calculation including the known 2NF and 3NF pieces to demonstrate that compensation cannot occur.
[Section IV, Fig. 5 and Table IV] The finite-nuclei test is transparently exploratory, but as presented it is partly post hoc: the blue EoS is constructed by selecting c_D=6.0 and c_E=0.50 and then artificially rejoining the red EoS at rho~0.12 fm^-3 to preserve saturation. The resulting improvement in binding energies in Table IV is therefore built into the construction rather than being a prediction. This does not invalidate the section, but the authors should clearly state that the blue-curve agreement is not evidence for the N4LO contact strengths or for a particular c_D,c_E pair; it is only a sensitivity study of the mass formula to low-density attraction.
[Tables I-III] No uncertainties are given for any of the computed energies. Since the main claim is that the N4LO contact contribution is orders of magnitude too large, the authors should at least indicate the sensitivity of Eqs. (3) and (5) to the E_i values, for example by providing the individual E_i contributions or a range from the fit covariance of Ref. [1] if available. Without any uncertainty estimate, the reader cannot distinguish a robust incompatibility from a large but poorly constrained number.

minor comments (5)

[Abstract and Introduction] There are several typos, including 'fi?ts' in the abstract, 'strucure' in the introduction, 'a a wide range' in the introduction, and 'conributions' in Section II.A. The manuscript should be carefully proofread.
[Fig. 3 caption and text] In the paragraph after Eq. (3), the green curve is said to use c_E=0.13 with reference [1], but the correct source for c_E=0.13 appears to be Ref. [6] (Drischler et al.), as stated earlier in Section II.A. Please check and correct the citation.
[Eq. (6)] Equation (6) contains '=≈' and should be either '=' or '≈'. Also, the expansion in alpha is standard, but the definition of e_sym(rho) is not given explicitly; a one-line definition would improve clarity.
[Section IV] The statement 'the saturation properties of SNM ... should be naturally related to the energy and density distributions of nucleons in nuclei' is repeated twice (once in the Introduction and once at the start of Section IV). One occurrence should be removed.
[General] The notation for the Fermi momentum k_f and k_f,n is introduced inconsistently: in Eq. (2) and Eq. (4) the symbols are used without a clear definition in the text. Since the paper is short, a brief definitions sentence in Section II or III would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the N4LO contact couplings are external fitted inputs and the nuclear/neutron-matter energies are independent computed consequences.

full rationale

The paper's derivation chain is self-contained and non-circular. The 13 E_i couplings and the c_D, c_E values are taken from external fits (Ref. [1] for the nd-scattering E_i, Ref. [6] for the triton-constrained c_D, c_E trajectory), and the nuclear/neutron-matter energy per particle is then obtained by inserting those fixed numbers into Kaiser's density-dependent in-medium potentials and evaluating the first-order Born integrals, Eqs. (3) and (5). Nothing in this calculation is fitted to the quantity being tested: the SNM and NM energies are not used to determine any LEC, and the claimed incompatibility with empirical saturation is a cross-system comparison of externally fixed inputs. The finite-nuclei exercise is explicitly labeled 'an exploratory test to probe the sensitivity of the binding energy per nucleon', and the c_D = 6.0, c_E = 0.50 pair is selected from the triton trajectory to illustrate sensitivity; the paper does not present the resulting BE/A values as an independent prediction, so no fitted-input-as-prediction step is present. The acknowledged omission of the N3LO 3NF ('presently not on stable grounds') and the possible regulator/scheme mismatch between the nd-scattering fit and the unregularized potentials are validity caveats, not self-referential reductions; they affect the strength of the incompatibility claim but do not make the derivation equivalent to its inputs. The one self-citation (Ref. [4]) is contextual and not load-bearing. No equation is defined in terms of the target result, and no fitted parameter is renamed as a prediction; therefore the circularity score is 0.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central numbers rest on externally fitted LEC values, on Kaiser's density-dependent potential formulae, and on first-order many-body truncation. The paper lists the E_i from Ref [1] only by reference, not by value, and selects the blue EoS couplings post hoc.

free parameters (6)

E_i (i=1,...,13) from Ref [1] = not listed in the paper
The 13 N4LO contact couplings extracted from nd scattering are used without listing their values; Fig. 3 and Table III depend on them.
c_D (blue EoS) = 6.0
Selected from the c_D,c_E trajectory of Ref [6] as the 'largest pair of positive values' to add attraction in the 0.07-0.12 fm^-3 region.
c_E (blue EoS) = 0.50
Selected together with c_D=6.0 for the same purpose.
c_D (red EoS) = 2.75
Taken from Ref [6] as a standard point on the triton-fitting trajectory.
c_E (red EoS) = 0.13
Taken from Ref [6]; the paper also compares with c_E=-1.27 from the 3N continuum in Table I.
Blue EoS rejoin density = rho ~ 0.12 fm^-3
The blue EoS is joined to the red EoS above this density; ad hoc.

assumptions (6)

domain assumption The density-dependent in-medium contact potentials of Kaiser (Refs [5], [8], [9]) correctly represent the N2LO and N4LO 3NF contact interactions in nuclear matter
Invoked in Section II A Eq. (1) and II B Eq. (2) without derivation; standard chiral EFT results.
domain assumption First-order (Born/Hartree-Fock) approximation is sufficient to estimate the size of the contact 3NF contribution to the energy per particle
Eqs. (3) and (5) are first-order only; the conclusions about incompatibility rely on the size of this leading contribution.
ad hoc to paper The omitted N3LO 3NF does not cancel the large N4LO contact contribution
The paper states the calculation is 'unavoidably incomplete' (Section I) but still concludes the contact strengths are incompatible; this assumes no compensating large opposite-sign contribution from the missing N3LO 3NF.
ad hoc to paper The E_i LECs from Ref [1] can be used with Kaiser's density-dependent potentials without regulator or scheme adjustment
No cutoff or regularization of the E_i values is specified in the paper, yet they are entered into Eqs. (2)-(5).
domain assumption The mass formula with quadratic isospin expansion (Eq. (6)) is a valid tool for estimating binding energies from the EoS
Used in Section IV; approximate but established in the literature.
ad hoc to paper Rejoining the blue EoS to the red EoS at rho ~ 0.12 fm^-3 is a legitimate way to preserve saturation while adding attraction at lower densities
The 'hybrid' EoS in Fig. 5 is constructed by an arbitrary match point.

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Cite this review

Pith. "Pith review of Analysis of the strengths of the contact potential at N4LO through nuclear and neutron matter." pith.science (2026). https://pith.science/paper/D5DQLWXB

@misc{pith2026260806610,
  author       = {Pith},
  title        = {Pith review of: Analysis of the strengths of the contact potential at N4LO through nuclear and neutron matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D5DQLWXB}},
  note         = {Machine review of arXiv:2608.06610}
}

read the original abstract

We examine the contact three-nucleon force at N4LO expressed as a density dependent potential. In Ref. [1], the necessary couplings (13, including two that appear in the leading three-nucleon force), were extracted from nd scattering observables. The contact strengths obtained through the three- nucleon continuum, without fi?ts to the triton, seem incompatible with the energy of nuclear and neutron matter. We take the opportunity to revisit the role of the cD, cE couplings of the leading three-nucleon force in nuclear matter and nuclei.

Figures

Figures reproduced from arXiv: 2608.06610 by the authors.

**Figure 1.** FIG. 1: Figure reproduced from Fig. 13 of Ref. [1]. The black diamond marks the experimental values of the triton binding [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** FIG. 2: Matrix elements of Eq. (1) in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3: Blue: Contribution to the energy per particle in Born approximation from the contact terms at N [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4: First two frames from the left: Matrix elements of the potential in Eq. (4) for J=0 at normal density as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: FIG. 5: Red: Our standard EoS at N [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 12 canonical work pages

[1]

It underbinds the nuclei in Table IV due to insufficient attraction at the appropriate density

The red curve saturates the EoS with energy of -16 MeV at a larger density than the phenomenological parametrization (green). It underbinds the nuclei in Table IV due to insufficient attraction at the appropriate density

work page
[2]

The shift of the minimum to lower densities as compared to the red EoS amounts to extra attraction in the region where it’s needed to enhance the binding of nuclei

The green curve demonstrates what could be an ideal saturation point, at 0.155 fm −3 and E/A = -16 MeV. The shift of the minimum to lower densities as compared to the red EoS amounts to extra attraction in the region where it’s needed to enhance the binding of nuclei

work page
[3]

With a bold change in the short-range couplings (while still binding the triton), the blue EoS simulates the attraction needed to get close to the experimental BE/A values, especially Calcium. V. T AKEA W A YS Our main takeaways and open questions can be summarized as follows. The values ofc D,c E andE i depend dramatically on the system from which they a...

work page
[4]

Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

H. Wita la, J. Golak, R. Skibi´ nski, Significance of chiral three-nucleon force contact terms for understanding of elas- tic nucleon-deuteron scattering, Phys. Rev. C 105 (5) (2022) 054004.\path{arXiv:2203.08499},\path{doi:10.1103/ PhysRevC.105.054004}

work page Pith review arXiv 2022
[5]

D. R. Entem, R. Machleidt, H. Witala, Chiral NN model and A(y) puzzle, Phys. Rev. C 65 (2002) 064005.\path{arXiv: nucl-th/0111033},\path{doi:10.1103/PhysRevC.65.064005}

work page Pith review arXiv 2002
[6]

Reinert, H

P. Reinert, H. Krebs, E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J. A 54 (5) (2018) 86.\path{arXiv:1711.08821},\path{doi:10.1140/epja/i2018-12516-4}

arXiv 2018
[7]

Sammarruca, R

F. Sammarruca, R. Millerson, Exploring the relationship between nuclear matter and finite nuclei with chiral two- and three-nucleon forces, Phys. Rev. C 102 (3) (2020) 034313.\path{arXiv:2005.01958},\path{doi:10.1103/PhysRevC. 102.034313}

arXiv 2020
[8]

J. W. Holt, N. Kaiser, W. Weise, Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces, Phys. Rev. C 81 (2010) 024002.\path{arXiv:0910.1249},\path{doi:10.1103/PhysRevC.81.024002}

work page Pith review arXiv 2010

Show all 16 references

[9]

Drischler, K

C. Drischler, K. Hebeler, A. Schwenk, Chiral interactions up to next-to-next-to-next-to-leading order and nuclear satura- tion, Phys. Rev. Lett. 122 (4) (2019) 042501.\path{arXiv:1710.08220},\path{doi:10.1103/PhysRevLett.122.042501}

2019 arXiv
[10]

D. R. Entem, R. Machleidt, Y. Nosyk, High-quality two-nucleon potentials up to fifth order of the chiral expansion, Phys. Rev. C 96 (2) (2017) 024004

2017
[11]

Kaiser, Energy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions, Phys

N. Kaiser, Energy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions, Phys. Rev. C 103 (2021) 054002

2021
[12]

Kaiser, Density-dependent nn-potential from subleading chiral three-neutron forces: Long-range terms

N. Kaiser, Density-dependent nn-potential from subleading chiral three-neutron forces: Long-range terms. (10 2020).\path{arXiv:2010.02739}

2020 arXiv
[13]

B. A. Brown, Constraints on the Skyrme Equations of State from Properties of Doubly Magic Nuclei, Phys. Rev. Lett. 111 (23) (2013) 232502.\path{arXiv:1308.3664},\path{doi:10.1103/PhysRevLett.111.232502}

2013 arXiv
[14]

Mondal, B

C. Mondal, B. K. Agrawal, J. N. De, S. K. Samaddar, Correlations among symmetry energy elements in Skyrme models, Int. J. Mod. Phys. E 27 (09) (2018) 1850078.\path{arXiv:1809.05354},\path{doi:10.1142/S0218301318500787}

2018 arXiv
[15]

Decharge, D

J. Decharge, D. Gogny, Hartree-Fock-Bogolyubov calculations with the D1 effective interactions on spherical nuclei, Phys. Rev. C 21 (1980) 1568–1593.\path{doi:10.1103/PhysRevC.21.1568}

1980 doi
[16]

Oyamatsu, K

K. Oyamatsu, K. Lida, H. Koura, Neutron dripline and the equation of state of nuclear matter, Phys. Rev. C 82 (2010) 027301

2010

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

It underbinds the nuclei in Table IV due to insufficient attraction at the appropriate density

The red curve saturates the EoS with energy of -16 MeV at a larger density than the phenomenological parametrization (green). It underbinds the nuclei in Table IV due to insufficient attraction at the appropriate density

work page

[2] [2]

The shift of the minimum to lower densities as compared to the red EoS amounts to extra attraction in the region where it’s needed to enhance the binding of nuclei

The green curve demonstrates what could be an ideal saturation point, at 0.155 fm −3 and E/A = -16 MeV. The shift of the minimum to lower densities as compared to the red EoS amounts to extra attraction in the region where it’s needed to enhance the binding of nuclei

work page

[3] [3]

With a bold change in the short-range couplings (while still binding the triton), the blue EoS simulates the attraction needed to get close to the experimental BE/A values, especially Calcium. V. T AKEA W A YS Our main takeaways and open questions can be summarized as follows. The values ofc D,c E andE i depend dramatically on the system from which they a...

work page

[4] [4]

Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

H. Wita la, J. Golak, R. Skibi´ nski, Significance of chiral three-nucleon force contact terms for understanding of elas- tic nucleon-deuteron scattering, Phys. Rev. C 105 (5) (2022) 054004.\path{arXiv:2203.08499},\path{doi:10.1103/ PhysRevC.105.054004}

work page Pith review arXiv 2022

[5] [5]

D. R. Entem, R. Machleidt, H. Witala, Chiral NN model and A(y) puzzle, Phys. Rev. C 65 (2002) 064005.\path{arXiv: nucl-th/0111033},\path{doi:10.1103/PhysRevC.65.064005}

work page Pith review arXiv 2002

[6] [6]

Reinert, H

P. Reinert, H. Krebs, E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order, Eur. Phys. J. A 54 (5) (2018) 86.\path{arXiv:1711.08821},\path{doi:10.1140/epja/i2018-12516-4}

arXiv 2018

[7] [7]

Sammarruca, R

F. Sammarruca, R. Millerson, Exploring the relationship between nuclear matter and finite nuclei with chiral two- and three-nucleon forces, Phys. Rev. C 102 (3) (2020) 034313.\path{arXiv:2005.01958},\path{doi:10.1103/PhysRevC. 102.034313}

arXiv 2020

[8] [8]

J. W. Holt, N. Kaiser, W. Weise, Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces, Phys. Rev. C 81 (2010) 024002.\path{arXiv:0910.1249},\path{doi:10.1103/PhysRevC.81.024002}

work page Pith review arXiv 2010