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arxiv: 2104.05474 · v3 · submitted 2021-04-12 · ⚛️ nucl-th

Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory

M. S\'anchez S\'anchez , Dao Duy Duc , L. Bonneau This is my paper

Pith reviewed 2026-05-24 12:55 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords chiral effective field theoryleading orderHartree-Fockregularization cutoffspurious bound statesnuclear matterNogga-Timmermans-van Kolck power countingoxygen-16
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The pith

High cutoffs above the nucleon mass in leading-order chiral potentials prevent self-consistent Hartree-Fock mean fields free of spurious bound states for nuclei.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines what happens to nuclear ground-state calculations when a leading-order chiral effective field theory potential is regularized with a momentum cutoff larger than the nucleon mass. In the Hartree-Fock treatment of oxygen-16, these cutoffs produce strong sensitivity to low-energy constants in attractive singular channels and force large corrections for deeply bound spurious states. The central result is that no clean, self-consistent mean-field reference state can be obtained under the Nogga-Timmermans-van Kolck power counting once the cutoff exceeds the nucleon mass; any partial correction for spurious states must be moved into the residual interaction for beyond-mean-field work.

Core claim

When a leading-order chiral potential constructed in the Nogga-Timmermans-van Kolck power counting is regularized with a cutoff higher than the nucleon mass, the Hartree-Fock approximation cannot produce a self-consistent mean field free of spurious bound-state effects that could serve as a reference state for beyond-mean-field methods; for sufficiently high cutoffs that make the 3S1 contact attractive, only a partial spurious-state correction can be absorbed into the mean field, with the remainder required in the residual interaction.

What carries the argument

The spurious-state correction applied to the Hartree-Fock energy in singular partial waves (especially 3S1 and 3D2) when the regularization cutoff exceeds the nucleon mass, combined with the sign of the associated low-energy constants.

If this is right

  • For cutoffs high enough to make the 3S1 contact attractive, the mean-field solution can incorporate only a partial correction for spurious bound states.
  • The remaining spurious-state correction must be added to the residual interaction when going beyond Hartree-Fock.
  • A full correction in the 3D2 channel with energy shifts of order or larger than those in Phys. Rev. C 103, 054304 (2021) remains possible inside the mean-field step.
  • Nuclear bulk properties calculated at this order become sensitive to both the sign of low-energy constants in singular waves and the precise treatment of spurious states.

Where Pith is reading between the lines

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

  • If the spurious-state problem cannot be isolated at leading order, any subsequent many-body perturbation theory or coupled-cluster calculation built on that reference state will carry an uncontrolled starting-point dependence.
  • The result suggests that practical applications of this power counting to finite nuclei may require either lowering the cutoff below the nucleon mass or reformulating the mean-field step to absorb the full correction.
  • An explicit test would be to repeat the 16O calculation with the cutoff lowered just below the nucleon mass and check whether bound solutions reappear without additional spurious-state machinery.

Load-bearing premise

That the chosen power counting and regularization produce only controllable artifacts whose corrections can be cleanly separated into mean-field and residual-interaction pieces without changing the physical content of the leading-order potential.

What would settle it

A calculation that obtains a stable, bound Hartree-Fock ground state for 16O (or another light nucleus) using the same leading-order potential, the same cutoff above the nucleon mass, and the same power counting, while applying no or only the standard counter-term adjustments.

Figures

Figures reproduced from arXiv: 2104.05474 by Dao Duy Duc, L. Bonneau, M. S\'anchez S\'anchez.

Figure 1
Figure 1. Figure 1: FIG. 1. Momentum-space wavefunctions of the spurious [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Top panel: Diagonal matrix elements of the corrected [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as top panel of figure 2 in the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Ground-state energy [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Phaseshift in the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
read the original abstract

We explore the effects on nuclear bulk properties of using regularization cutoffs larger than the nucleon mass within the chiral effective field theory with a power counting that ensures order-by-order renormalization in the two-nucleon system. To do so we calculate ground-state properties of the $^{16}$O nucleus in the Hartree--Fock approach in a basis made up of plane waves confined in a cube. We find that regularization cutoff effects manifest themselves in two distinct ways: a strong sensitivity to the the counter-terms in attractive singular partial waves (related to the sign of the corresponding low-energy constant) and to the correction for spurious deeply bound states (for high enough cutoffs). In fact the latter happens to deprive the Hartree--Fock approximation of yielding bound solutions in nuclei. We conclude that, when using a leading-order chiral potential in the Nogga--Timmermans--van Kolck's power counting (with a regularization cutoff higher than the nucleon mass), one cannot produce a selfconsistent mean field free of spurious bound-state effects that can serve as a reference state for beyond-mean-field methods. For high regularization cutoffs which yield an attractive $^3S_1$ contact potential, one can at best incorporate in the mean-field solution a partial correction for spurious bound states. Then the remaining correction has to be added to the residual interaction in a treatment beyond the Hartree--Fock approximation. In fact a ``full'' correction in the $^3D_2$ channel, with energy shifts of the order of or somewhat larger than those recommended in Phys. Rev. C 103, 054304 (2021), is possible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 4 minor

Summary. The manuscript examines cutoff effects in Hartree-Fock calculations of 16O ground-state properties using leading-order chiral EFT potentials in the Nogga-Timmermans-van Kolck power counting, with regularization cutoffs larger than the nucleon mass. Computations are performed in a plane-wave basis confined to a cube. The central claim is that such potentials produce strong sensitivity to counter-terms in attractive singular partial waves (tied to the sign of the associated low-energy constants) and to spurious deeply bound-state corrections; for sufficiently high cutoffs these effects prevent a self-consistent mean field free of spurious states that could serve as a reference for beyond-mean-field methods. Partial corrections in channels such as 3D2 are discussed as a possible workaround, with the remainder shifted to the residual interaction.

Significance. If the numerical findings hold, the work supplies concrete evidence that high-cutoff LO chiral potentials under this power counting cannot furnish clean HF reference states for nuclei, thereby constraining their use in mean-field and post-mean-field nuclear-structure calculations. The explicit demonstration of cutoff sensitivity, counter-term dependence, and the quantitative impact of spurious-state corrections (including energy shifts comparable to or larger than those in the cited PRC 103, 054304) offers a practical diagnostic for regularization choices in chiral EFT applications to finite nuclei.

minor comments (4)
  1. Abstract: repeated definite article ('sensitivity to the the counter-terms').
  2. Abstract: the phrase 'the Nogga--Timmermans--van Kolck's power counting' should be rephrased for grammatical consistency with standard citation style.
  3. The manuscript should state the precise numerical values of the spurious-state energy shifts obtained in the 3D2 channel and compare them directly to the recommended values from Phys. Rev. C 103, 054304 (2021).
  4. Basis-size convergence and quantitative error estimates for the reported HF binding energies and spurious-state corrections are not mentioned in the abstract and should be summarized in the main text or a dedicated table.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. The referee's summary accurately captures the central findings of the manuscript regarding cutoff effects, spurious bound states, and limitations of high-cutoff LO chiral EFT potentials under the Nogga-Timmermans-van Kolck power counting for Hartree-Fock calculations in nuclei.

Circularity Check

0 steps flagged

Minor self-citation; central claim from explicit HF computations

full rationale

The paper derives its main conclusion—that a self-consistent mean field free of spurious bound-state effects cannot be obtained at LO with cutoffs > nucleon mass—directly from plane-wave HF calculations of 16O ground-state properties under varying regularization cutoffs and counter-terms. These are numerical outputs, not quantities defined in terms of the target claim. The sole self-citation (to Phys. Rev. C 103, 054304 (2021) for recommended energy shifts) is peripheral and does not bear the load of the primary finding or power-counting argument.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The work rests on the Nogga-Timmermans-van Kolck power counting and the plane-wave Hartree-Fock implementation as background assumptions; no new free parameters or invented entities are introduced beyond the cutoff value and low-energy constants already standard in the field.

free parameters (2)
  • regularization cutoff Lambda
    Chosen larger than nucleon mass to explore effects; value not numerically specified in abstract.
  • low-energy constants in singular partial waves
    Their signs determine sensitivity to counter-terms.
axioms (1)
  • domain assumption Nogga-Timmermans-van Kolck power counting ensures order-by-order renormalization in the two-nucleon system
    Explicitly adopted as the framework for the leading-order potential.

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