Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory

D. R. Entem; R. Machleidt (Universities of Idaho; Salamanca)

REVIEW

Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory

D. R. Entem, R. Machleidt (Universities of Idaho, Salamanca)

Nuclear Theory · Submitted 5 Apr 2003 · 40 references

Pith's verdict: The paper that made chiral EFT quantitatively competitive with phenomenological NN potentials, though its abstract's 'necessary and sufficient' claim outruns what a single-cutoff in-sample fit can establish.

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CitationD. R. Entem, R. Machleidt (Universities of Idaho, Salamanca). "Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory." arXiv:nucl-th/0304018 (2003). https://pith.science/paper/4YEK6V5E

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Worth your time, with one caveat about the abstract's wording rather than the physics. What is new: this is the first nucleon-nucleon potential carried to fourth order (N3LO) in chiral EFT, combining Kaiser's full N3LO two-pion exchange with the 24 contact terms through Q4 plus two charge-dependent contacts, and charge dependence handled at NLØ of the isospin-violation scheme. The authors' own earlier potential (their Ref. [27]) had the Q4 contacts but only NNLO TPE; Epelbaum et al. stopped at NNLO. The combination is genuinely first. What it does well: the order-by-order table is the real evidence, and it is clean. np chi-squared per datum goes 36.2 at NLO to 10.1 at NNLO to 1.10 at N3LO; pp goes 80.1 to 35.4 to 1.50, against AV18's 1.04 and 1.38. That demonstrates the fourth-order contacts matter. Fig. 1 against the Nijmegen multi-energy and VPI SM99 analyses is an honest comparison, and the pp numbers are worse than AV18 in every bin, so 'comparable' is the right word and they use it. Soft spots: the abstract's 'necessary and sufficient' [abstract:s3] outruns the paper. Necessity is supported by the table. Sufficiency is not: everything runs at one cutoff, Lambda = 0.5 GeV, with no variation and no truncation-error estimate, so a chi-squared near 1 cannot be separated from the contacts absorbing higher-order physics. The visible symptom is c4 = 5.40 against 3.40 +/- 0.04 from pi-N, with c3 also pushed below its pi-N value. The text acknowledges both ('substantially above', 'slightly more than one standard deviation below') but never costs out what that tension does to the error budget. Minor by comparison: the 26 contact constants are not tabulated and the code is available only on request, so reproduction means re-fitting from scratch. With 29 parameters against 2402 np points the flexibility worry is bounded, not fatal. Who it is for: anyone building few-body or structure calculations on a chiral two-nucleon input, and anyone who wants the reference point for the modern N3LO/N4LO family. It deserves referees; the questions to press are cutoff variation and a truncation-error estimate, not the central result.

Referee report

Significance

If the result holds, this is an important paper: it is the first demonstration that a systematically derived chiral NN potential, with its accompanying many-body forces fixed by the same expansion, reaches the accuracy threshold that exact few-body and microscopic nuclear-structure calculations require. The order-by-order comparison in Tables II and III is a genuinely informative piece of evidence, and the inclusion of charge dependence up to NLO of the isospin-violation scheme is a real technical advance over earlier chiral potentials. The construction is also falsifiable in a useful sense: the peripheral partial waves with L >= 3 are parameter-free predictions of OPE plus TPE, and the three 1S0 scattering lengths are fixed by two charge-dependent contacts. The paper is candid about the c3 and c4 tensions with the piN determinations, which is to its credit.

Major objections (4)

[Abstract, sentence 3] The sentence 'the fourth order is necessary and sufficient for a reliable NN potential' is the strongest claim in the paper, and only the 'necessary' half is supported by the evidence presented. Necessity is well supported by the order-by-order comparison in Tables II and III (NNLO chi-squared/datum of 10.1 versus 1.10 at N3LO for np). Sufficiency is not: the entire construction uses one regulator scale, 'We use Lambda = 0.5 GeV throughout' (text following Eq. 1), and no cutoff variation, no truncation-error estimate, and no residual-order analysis is given. At a single cutoff, a chi-squared per datum near 1.1 cannot distinguish genuine fourth-order convergence from the 26 contact parameters absorbing physics that belongs at higher orders or in the regulator. The concrete test is a refit at two or three nearby cutoffs (e.g. 0.45, 0.5, 0.6 GeV) with the resulting variation in chi-squared and in the phase parameters reported as an error band. If that study is not feasible within the scope of this Letter, the abstract sentence should be softened to a statement about necessity plus demonstrated accuracy at this cutoff.
[Table I and the text following it] Table I lists c4 = 5.40 against the piN determination 3.40 +/- 0.04, a displacement of roughly fifty standard deviations, and the text acknowledges it ('substantially above the value determined in piN ... necessary to bring the 3F2 phase shift down'). The authors are to be credited for stating the tension openly, but the cost is never quantified. Since c4 enters the dimension-two piN Lagrangian, a fit that reaches chi-squared per datum near 1 only by moving it this far outside its piN range weakens the 'systematically derived' character of the accuracy, and the reader cannot judge whether the displacement is compensating for omitted higher-order two-pion exchange or for the regulator. A short quantitative statement is needed: what happens to the overall chi-squared and to the 3F2 and 3P2 phase shifts if c4 is held at its piN value, and how much of the residual is recovered by the O(Q4) contacts? The same, though milder, question applies to c3 = -3.20 versus -4.69 +/- 1.34.
[Tables II and III, and footnote [39]] The order-by-order evidence in Tables II and III is not a clean scan within one scheme. The NLO and NNLO entries in Table II are taken from Epelbaum et al. (Ref. [35]), which uses a different cutoff and regulator, while footnote [39] states that the pp versions of the NLO and NNLO potentials were constructed by the present authors by 'incorporating charge-dependence and minimizing the pp chi-squared'. The dramatic improvement from NNLO to N3LO therefore mixes the order of the calculation with the choice of cutoff, regulator, and fitting procedure. This matters because the improvement is the sole support for the 'necessary' half of the abstract claim. A comparison at fixed cutoff and fixed fitting procedure, truncating the present potential at each order, would make the argument airtight; failing that, the text should state explicitly that the lower-order entries come from a different implementation and that the comparison is indicative rather than controlled.
[Tables II and III] The abstract's 'comparable to the one of phenomenological high-precision potentials' is defensible for np (1.10 versus 1.04) but is a stretch for pp: Table III gives 1.50 overall versus 1.38 for AV18, and in the 190-290 MeV bin the N3LO value (1.93) is worse than AV18 (1.82). The text should say this plainly rather than resting on the overall parity of the two numbers. Relatedly, the chi-squared values in Tables II and III are in-sample fit residuals: the same 1999 database below 290 MeV is used to fix the 26 contact parameters and to refine the three piN LECs. With 2402 np data points and 29 parameters this is not a severe over-fitting concern, but the paper should describe the chi-squared as a fit quality rather than as a reproduction of independent data, and should state whether any data were held out.

Minor objections (6)

[Eq. (1) and the surrounding text] The regulator exponent 2n is described only as 'chosen to be sufficiently large so that the regulator generates powers which are beyond the order (nu = 4) at which our calculation is conducted'. The numerical value of n is never given, which prevents reproduction of the calculation. Please state n explicitly and, in one sentence, justify why the chosen value leaves terms up to Q4 unaffected.
[Text on charge dependence, paragraph beginning 'For an accurate fit'] The paper states that the two charge-dependent contacts 'make possible an accurate fit of the three different 1S0 scattering lengths, app, ann, and anp', but the resulting values are never reported. A short table or a sentence in the text giving the fitted app, ann, and anp against the empirical values would substantiate a claim that is currently unsupported by any number.
[Text on the deuteron, paragraph beginning 'The contact terms plus irreducible'] The homogeneous Lippmann-Schwinger equation is said to determine the properties of the two-nucleon bound state, but no deuteron numbers (binding energy, D-state probability, asymptotic D/S ratio, quadrupole moment) are given. For a potential intended as input to few-body and nuclear-structure calculations, the deuteron binding energy in particular is a cheap and informative check, and its absence is noticeable.
[Fig. 1] Fig. 1 shows only partial waves with J <= 2, i.e. exactly the waves governed by the fitted contacts. The peripheral waves with L >= 3 are the parameter-free predictions of OPE plus TPE and would be the cleanest test of the chiral amplitude; the text refers the reader to Ref. [29] for these, but including at least one such wave (for instance 3F3 or 3G3) in Fig. 1 would make the Letter self-contained on precisely the point where no fitting is involved.
[Footnote [27] and the abstract's 'first'] Footnote [27] discloses that the 24 N3LO contacts were already included in the authors' earlier potential (Phys. Lett. B524, 93 (2002)), which however had two-pion exchange only to NNLO. The abstract's claim to be the first N3LO potential is therefore correct but needs the qualifier to be visible in the body of the Letter rather than only in a footnote, so that the incremental advance (full N3LO two-pion exchange plus charge dependence) is clear to the reader.
[General] The potential is iterated in the Lippmann-Schwinger equation, i.e. Weinberg power counting is assumed for the amplitude. A single sentence acknowledging that the nonperturbative treatment of the potential is a scheme choice, and that the accuracy reported is conditional on it, would help the reader place the result relative to subsequent discussions of power counting in this system.

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The paper

The paper claims

A fourth-order chiral nucleon-nucleon potential reproduces low-energy data about as accurately as the best phenomenological potentials.

The reading

The paper sets out to show that a nucleon-nucleon potential built systematically from chiral effective field theory, carried to fourth order (next-to-next-to-next-to-leading order, N$^3$LO), can reproduce low-energy two-nucleon data about as well as the best phenomenological potentials. That matters because a chiral potential comes with a matching prescription for three-nucleon and many-nucleon forces at the same order, which is what exact few-body and microscopic nuclear-structure calculations need. The authors report a steep order-by-order improvement: below 290 MeV lab energy the $�chi^2$ per datum falls from 36.2 at NLO and 10.1 at NNLO to 1.10 at N$^3$LO for np, and from 80.1 and 35.4 to 1.50 for pp. They conclude that fourth order is both necessary and sufficient for a reliable chiral nucleon-nucleon potential, and that the result is ready to serve as input for few-body and nuclear-structure theory.

What carries the argument

The organizing device is the chiral expansion of the nucleon-nucleon amplitude in powers of $Q/�Lambda_�chi$, with $�Lambda_�chi�approx 1$ GeV, where at each order the potential separates into contact terms and irreducible pion exchanges. At N$^3$LO there are two contacts of order $Q^0$, seven of order $Q^2$, and fifteen of order $Q^4$, giving 24 contact parameters for partial waves with $L�le 2$; two more charge-dependent contacts of order $Q^0$ bring the contact count to 26. The pion sector uses static one-pion exchange at leading order and two-pion exchange through N$^3$LO, with three-pion exchange omitted because it was found negligible at this order. A regulator $�exp[-(p/�Lambda)^{2n}-(p'/�Lambda)^{2n}]$ with $�Lambda=0.5$ GeV suppresses high momenta without altering terms through $Q^4$, and the potential is inserted into a Lippmann-Schwinger equation to obtain phase shifts and observables. Three of the eight $�pi N$ low-energy constants, $c_2$, $c_3$, and $c_4$, are varied in the fit, making 29 parameters in total.

Extended reading notes

Core claim

The central claim is that the fourth-order chiral potential is the first derived from chiral perturbation theory to reach the accuracy threshold of high-precision phenomenology. With 24 contact terms through order $Q^4$ plus two charge-dependent contacts, and with pion-exchange contributions through N$^3$LO, the fit gives $�chi^2$/datum of 1.10 for np and 1.50 for pp below 290 MeV, against 1.04 and 1.38 for Argonne V18. The same tables show that lower-order chiral potentials are not quantitatively viable: 10.1 (np) and 35.4 (pp) at NNLO, and 36.2 and 80.1 at NLO. Charge dependence is included up to next-to-leading order of the isospin-violation scheme, with the pion-mass difference in one-pion exchange, the Coulomb potential in pp, pion-mass difference in the NLO two-pion exchange, $�pi�gamma$ exchange, and two charge-dependent contacts that allow the three $^1S_0$ scattering lengths to be fitted.

Load-bearing premise

The load-bearing premise is that a $�chi^2$ per datum near 1.1 for np and 1.5 for pp, obtained with 29 fitted parameters at a single cutoff of 0.5 GeV, demonstrates genuine fourth-order accuracy rather than fit flexibility, since the paper reports no cutoff variation and no estimate of the truncation error from omitted higher orders.

Original abstract

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,318 input tokens.

What the abstract itself states, as probabilities: claims first 0.96 · states limitation 0.32 · human participants 0.01 · controlled comparison 0.30 · randomized assignment 0.01 · states quantitative result 0.84 · compares with prior results 0.96 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians. The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory.	contribution 1.00	0.96	0.17	asserted 1.00
s1	Charge-dependence is included up to next-to-leading order of the isospin-violation scheme.	contribution 0.74	0.87	0.04	asserted 1.00
s2	The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials.	result 0.99	0.88	0.18	asserted 1.00
s3	Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians.	interpretation 0.93	0.49	0.78	asserted 1.00
s4	The new potential provides a promising starting point for exact few-body calculations and microscopic nuclear structure theory (including chiral many-body forces derived on the same footing).	interpretation 0.57	0.47	0.09	hedged possibility 0.91

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from simulation or computation 0.76.

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sources read

arXiv listing abstract v1

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full text
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relations to other papers

levels run

P abstract

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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Semilocally regularized chiral EFT nucleon-nucleon potentials now fit low-energy scattering data at phenomenological-potential precision, but consistent regularization of three-nucleon forces remains the main obstacle...
Relativistic chiral nuclear forces: status and prospects
nucl-th 2025-01 conditional novelty 2.0 of 10

A review of the relativistic chiral nuclear force, presenting the Beihang group's own NNLO results for nucleon-nucleon scattering and promising faster convergence than the standard Weinberg approach.
Deep learning for exploring hadron-hadron interactions
nucl-th 2024-12 conditional novelty 2.0 of 10

Deep neural networks can recover hadron interaction potentials from simulated femtoscopy and lattice QCD correlation data, with validation currently limited to synthetic tests and a toy model.

How later papers used it

330 later papers cite it

Evidence: substantial. 325 of the citing papers share no author with it, and 92 of those carry a confident label from Pith's citation classifier.

Pith read 39 of the 542 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

15 later papers by other authors are listed below: 9 used its method or tool, 4 used its data or values and 2 compared their own results with it.

Uses its method or tool 9 of 49 papers with this label

Used the potential developed by Entem and Machleidt within chiral effective field theory at N3LO.

Charged-current reactions in the supernova neutrino-sphere (2014) · 0.99 · paraphrased: the licence does not allow quoting
Computed no-core shell-model wave functions with the Entem-Machleidt N3LO chiral interaction evolved by the similarity renormalization group to a resolution of 2.0 fm^-1.

Uncertainties in tellurium-based dark matter searches stemming from nuclear structure uncertainties (2025) · 0.98 · paraphrased: the licence does not allow quoting
The , , and Hamiltonians are constructed from the 3 NN potential developed by Entem and Machleidt (EM) in Ref. [ref] unitarily transformed to the resolution scales $λ= 1.8, 2.0$, and $2.2 ħ$, respectively, via the similarity renormalization group [ref] and 3N potentials at 2 with a regulator cutoff of $2.0 ħ$ [ref] .

The nuclear charge radius of $^{13}\mathrm{C}$ (2025) · Methods · 0.97
Adopted a Hamiltonian based on the chiral N3LO NN interaction of this paper and an N2LO 3N force.

Unified description of $^6$Li structure and deuterium-$^4$He dynamics with chiral two- and three-nucleon forces (2014) · 0.85 · paraphrased: the licence does not allow quoting
Performed calculations using the Entem-Machleidt 2NF, a chiral two-body force based on terms up to fourth order in chiral EFT.

Symmetric nuclear matter with chiral three-nucleon forces in the self-consistent Green's functions approach (2013) · 0.88 · paraphrased: the licence does not allow quoting
Employed as an ingredient the chiral effective field theory potential with two-nucleon forces of this paper plus three-nucleon forces.

Nuclear structure corrections to the Lamb shift in $\mu^3$He$^+$ and $\mu^3$H (2015) · 0.82 · paraphrased: the licence does not allow quoting
Used a chiral nucleon-nucleon force derived at N3LO.

Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon-nucleon interactions (2014) · 0.94 · paraphrased: the licence does not allow quoting
Used the chiral EFT N3LO two-body interaction developed by Entem and Machleidt.

Nuclear multipole responses from chiral effective field theory interaction (2020) · 0.90 · paraphrased: the licence does not allow quoting
Started from the chiral N3LO NN potential of this paper, evolved through a similarity renormalization group transformation with evolution parameter 2.02 fm^-1.

${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction in the NCSM/RGM approach (2017) · 0.92 · paraphrased: the licence does not allow quoting

Uses its data or values 4 of 26 papers with this label

Used the constants c1 = -0.81 GeV^-1, c3 = -3.2 GeV^-1 and c4 = 5.4 GeV^-1 for Entem-Machleidt.

Correlated density-dependent chiral forces for infinite matter calculations within the Green's function approach (2014) · 1.00 · paraphrased: the licence does not allow quoting
Fixed its long-range constants to c1 = -0.81, c3 = -3.2 and c4 = 5.4.

Uncertainties with low-resolution nuclear forces (2025) · 1.00 · paraphrased: the licence does not allow quoting
Took its fit of parameters for the NN interaction, carried out at N3LO with a momentum cutoff of 500, from this paper.

Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian (2020) · 0.97 · paraphrased: the licence does not allow quoting
Took its fit of parameters for the two-nucleon interaction, carried out at N3LO with a momentum cutoff of 500 MeV/c, from Entem and Machleidt.

Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of $^{48}$Ca (2019) · 0.95 · paraphrased: the licence does not allow quoting

Compares with it 2 of 19 papers with this label

We benchmark the results against published cross section results for the traditional interaction [ref] and systematically compare and analyze different cross section observables at a variety of energies using the interactions [ref] and .

Neutron-deuteron scattering cross-sections with chiral $NN$ interactions using wave-packet continuum discretization (2022) · Introduction · 0.98
However, our value is slightly smaller than theoretical calculations with the NCSM in continuum $2.46(2)$ fm [ref] using the Idaho N$^3$LO interaction [ref] SRG-evolved without adding a 3NF.

Radii of light nuclei from the Jacobi No-Core Shell Model (2025) · Results and discussions · 0.98

How the literature uses it

79 arXiv papers cite this in 129 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Since NN potentials of order three or less of ChPT are known to be deficient in quantitative terms, the recent advances show that the fourth order of ChPT is necessary and sufficient for a reliable NN potential derived from chiral effective Lagrangians.

The nuclear force problem: Are we seeing the end of the tunnel? · 0.98

Papers citing it · 78 sentences without a confident label

Uses its method or tool 7 papers

For that, we use the chiral effective field theory ($χ$EFT) approach at N$^3$LO [ref] derived from the principles of quantum chromodynamics (QCD) to represent the nuclear force between two nucleons using chiral perturbation theory.

Solving two and three-body systems with deep neural networks · Study of the deuteron · 0.99
In the first [ref] , nucleons and pions are retained as explicit degrees of freedom and terms up to next-to-next-to-next-to-leading order (N3LO), in the standard Weinberg counting, are accounted for.

The X17 boson and the $^3$H$(p,e^+ e^-)^4$He and $^3$He$(n,e^+ e^-)^4$He processes: a theoretical analysis · Hamiltonians and wave functions · 0.83
We employ the formalism described in detail in Refs. [ref] , where the so-called continuous choice is taken for the intermediate states, and the N$^3$LO potential from [ref] is used for the NN interaction.

Constraining the p{\Lambda} interaction from a combined analysis of scattering data and correlation functions · Introduction · 1.00

Uses its data or values 5 papers

For the NN interaction we consider the next-to-next-to-next-to-leading order potential from the Idaho group with a regulator of $Λ_N = 500$ MeV (Idaho-N3LO(500)) [ref] , and the high-order semilocal momentum-space (SMS) potential regularized with $Λ_N = 450$ MeV (SMS N4LO+(450)) [ref] .

Jacobi no-core shell model for $p$-shell hypernuclei · Results · 0.81
They start from the NN potential with a cutoff of $500$ from Ref. [ref] , optimized to NN scattering data.

Ab initio calculations of parity-violating electron scattering off $^{48}$Ca and $^{208}$Pb · IMSRG calculations · 0.83
The initial ($λ= ∞$) NN potential used here is the 500 MeV N$^3$LO interaction from Ref. [ref] .

Applications of the Similarity Renormalization Group to the Nuclear Interaction · Convergence in the Oscillator Basis · 0.91

Compares with it 7 papers

We compare our findings with the neutron-matter calculations of Ref. [ref] using many-body perturbation theory () and nonlocal interactions from Refs. [ref] for reference.

Direct Astrophysical Tests of Chiral Effective Field Theory at Supranuclear Densities · Introduction · 1.00
We benchmark the results against published cross section results for the traditional interaction [ref] and systematically compare and analyze different cross section observables at a variety of energies using the interactions [ref] and .

Neutron-deuteron scattering cross-sections with chiral $NN$ interactions using wave-packet continuum discretization · Introduction · 0.98
However, our value is slightly smaller than theoretical calculations with the NCSM in continuum $2.46(2)$ fm [ref] using the Idaho N$^3$LO interaction [ref] SRG-evolved without adding a 3NF.

Radii of light nuclei from the Jacobi No-Core Shell Model · Results and discussions · 0.98

Cites it as support 1 paper

Recent progress in the accurate description of the two- [ref] and more-nucleon systems [ref] within the chiral EFT, see also [ref] and references therein, gives a strong motivation to apply this framework to the abovementioned processes.

Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation · Introduction · 0.96

Cites it as background 27 papers

Such potentials [ref] , now derived up to the fifth chiral order [ref] , have furnished a wide range of structure and reaction predictions across the nuclear chart [ref] , but at the same time they grapple with the renormalization challenge inherent to chiral nuclear forces [ref] .

Perturbative computations of neutron-proton scattering observables using renormalization-group invariant $\chi$EFT up to N$^3$LO · Introduction · 0.87
The potential is then inserted into the Schrödinger or Lippmann-Schwinger equation in order to obtain theoretical predictions [ref] .

Perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering · Introduction · 0.91
Precise two-nucleon potentials have been developed at next-to-next-to-next-to-leading order (N$^3$LO) in the chiral expansion, see Refs. [ref] . 3NFs first appear at N$^2$LO in the Weinberg counting scheme [ref] and have been analyzed and scrutinized in [ref] .

Subleading contributions to the chiral three-nucleon force I: long-range terms · Introduction · 0.89

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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A user-friendly computer code for the N 3LO potential is available from the authors upon request. 4

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