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arxiv: 2607.02126 · v1 · pith:AHO3ITSZnew · submitted 2026-07-02 · ⚛️ nucl-th

Scaling Laws for Three-Body Nuclear Contacts

Raz Yankovich , Ehoud Pazy , Nir Barnea This is my paper

Pith reviewed 2026-07-03 03:55 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords three-body contactsshort-range correlationsscaling lawsgeneralized contact formalismisospin symmetry breakingsemi-empirical mass formulanucleon triplets
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The pith

Three-body nuclear contacts follow universal scaling patterns with nuclear mass and composition, analogous to two-body contacts.

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

The paper computes three-body nuclear contacts using the generalized contact formalism with a mean-field description for the long-range part of the wave function. It finds significant isospin-symmetry breaking in the contacts for 3He and 3H, similar to earlier two-body results. Motivated by the semi-empirical mass formula, the authors derive a simple scaling relation and demonstrate that it reproduces the computed contact values for medium-mass and heavy nuclei. The work shows a systematic dependence of three-nucleon short-range correlations on nuclear mass and composition. This matters because it suggests three-body contacts obey universal scaling laws much like those already established for short-range-correlated nucleon pairs.

Core claim

Using the generalized contact formalism and a mean-field description of the long-range component of the nuclear wave function, we compute three-body contacts and derive a simple scaling relation based on the semi-empirical mass formula that accurately reproduces the calculated values across medium-mass and heavy nuclei. The 3He and 3H contacts exhibit significant isospin-symmetry breaking, analogous to that observed previously for two-body contacts. Our results reveal a systematic dependence of 3N-SRCs on nuclear mass and composition, suggesting that three-body contacts obey universal scaling patterns closely analogous to those governing short-range-correlated nucleon pairs.

What carries the argument

Three-body nuclear contacts, which quantify the probability of finding correlated nucleon triplets at short distances, computed in the generalized contact formalism with mean-field long-range wave functions and extended by a scaling relation derived from the semi-empirical mass formula.

If this is right

  • Three-body contacts for 3He and 3H exhibit isospin-symmetry breaking analogous to two-body contacts.
  • The scaling relation accurately reproduces three-body contact values for medium-mass and heavy nuclei.
  • Three-nucleon short-range correlations depend systematically on nuclear mass and composition.
  • Three-body contacts obey universal scaling patterns closely analogous to those for short-range-correlated nucleon pairs.

Where Pith is reading between the lines

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

  • The scaling relation may allow estimates of three-body contacts in nuclei too large for direct computation.
  • Similar mass-dependent patterns could appear in other short-range nuclear observables.
  • Electron-scattering experiments on a sequence of nuclei could directly test the predicted mass and composition dependence.

Load-bearing premise

The mean-field description of the long-range component of the nuclear wave function is accurate enough to compute reliable three-body contacts when combined with the generalized contact formalism.

What would settle it

A set of measurements of three-nucleon short-range correlation probabilities across nuclei of varying mass and composition that deviate from the predicted scaling relation.

Figures

Figures reproduced from arXiv: 2607.02126 by Ehoud Pazy, Nir Barnea, Raz Yankovich.

Figure 1
Figure 1. Figure 1: FIG. 1. The two 3N-SRC contacts, corresponding to [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The ratios [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Mass-number dependence of the normalized [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Mass-number dependence of the normalized [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Mass-number dependence of the normalized [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

Three-nucleon short-range correlations (3N-SRCs) represent one of the least understood manifestations of short-range nuclear dynamics. We investigate these correlations within the generalized contact formalism and compute three-body nuclear contacts using a mean-field description of the long-range component of the nuclear wave function. These contacts quantify the probability of finding correlated nucleon triplets at short distances and provide a natural extension of the contact formalism beyond nucleon pairs. We find that the $^{3}$He and $^{3}$H contacts exhibit significant isospin-symmetry breaking, analogous to that observed previously for two-body contacts. Motivated by the semi-empirical mass formula, we derive a simple scaling relation for three-body contacts and show that it accurately reproduces the calculated values across medium-mass and heavy nuclei. Our results reveal a systematic dependence of 3N-SRCs on nuclear mass and composition, suggesting that three-body contacts obey universal scaling patterns closely analogous to those governing short-range-correlated nucleon pairs.

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

2 major / 1 minor

Summary. The manuscript computes three-body nuclear contacts for light, medium-mass, and heavy nuclei within the generalized contact formalism, employing a mean-field description of the long-range wave-function component. It reports significant isospin-symmetry breaking between the 3H and 3He contacts, derives a scaling relation motivated by the semi-empirical mass formula, and demonstrates that this relation reproduces the computed contact values across the mass range, thereby claiming universal scaling patterns for 3N-SRCs analogous to those established for 2N-SRCs.

Significance. If the scaling relation proves robust beyond the specific computational framework, the work would furnish a compact parametrization for three-body contacts that extends the practical reach of the contact formalism in nuclear structure and reaction theory. The explicit treatment of isospin breaking in the A=3 systems supplies a concrete point of contact with existing two-body contact studies.

major comments (2)
  1. [Methods] Methods section (generalized contact formalism with mean-field long-range component): the reliability of the extracted three-body contacts rests on the mean-field approximation for the long-range wave function being sufficiently accurate at the relevant short-distance scales; no benchmark against ab initio wave functions or experimental observables is supplied, rendering this assumption load-bearing for all subsequent claims.
  2. [Scaling relation] Scaling-relation derivation: the coefficients in the proposed scaling law are fixed by matching to the same set of mean-field-based contact values that the law is then shown to reproduce; this renders the agreement an internal consistency check rather than an independent test of universality against external data or alternative theoretical approaches.
minor comments (1)
  1. [Figures and results] Figure captions and text should explicitly state the numerical values or error estimates attached to the computed contacts so that the quality of the scaling fit can be assessed quantitatively.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below.

read point-by-point responses

  1. Referee: [Methods] Methods section (generalized contact formalism with mean-field long-range component): the reliability of the extracted three-body contacts rests on the mean-field approximation for the long-range wave function being sufficiently accurate at the relevant short-distance scales; no benchmark against ab initio wave functions or experimental observables is supplied, rendering this assumption load-bearing for all subsequent claims.

    Authors: We agree that the mean-field treatment of the long-range wave-function component is a central assumption whose validity at short distances is essential to the extracted contacts. Although the generalized contact formalism has been applied with analogous approximations in earlier two-body studies, the present work does not contain direct benchmarks against ab initio wave functions for the three-body case. In the revised manuscript we will add an explicit discussion of this limitation in the Methods section, together with references to existing validations of the long-range mean-field component at short distances. revision: yes

  2. Referee: [Scaling relation] Scaling-relation derivation: the coefficients in the proposed scaling law are fixed by matching to the same set of mean-field-based contact values that the law is then shown to reproduce; this renders the agreement an internal consistency check rather than an independent test of universality against external data or alternative theoretical approaches.

    Authors: The functional form of the scaling law is taken directly from the structure of the semi-empirical mass formula (volume, surface, and Coulomb terms), which supplies an independent physical motivation. The numerical coefficients are subsequently determined by fitting to the computed contacts in order to quantify how well this form reproduces the mass and isospin dependence. We acknowledge that the resulting agreement therefore constitutes an internal consistency check within our mean-field framework rather than a test against external data or alternative calculations. We will revise the text to state this distinction explicitly and to avoid implying an independent validation of universality. revision: partial

Circularity Check

1 steps flagged

Scaling relation parameters fixed by fit to paper's own mean-field contact values; reproduction is internal consistency

specific steps
  1. fitted input called prediction [Abstract]
    "Motivated by the semi-empirical mass formula, we derive a simple scaling relation for three-body contacts and show that it accurately reproduces the calculated values across medium-mass and heavy nuclei."

    The scaling relation is presented as derived from the external SEMF, yet its ability to 'accurately reproduce' the contacts is demonstrated on the exact set of contacts computed in the paper (via mean-field + GCF). If the relation's free parameters are fixed by fitting those contacts, the reproduction is tautological and does not provide independent confirmation of the claimed universal scaling.

full rationale

The paper computes three-body contacts exclusively via generalized contact formalism + mean-field long-range wave functions, then motivates a scaling form from the semi-empirical mass formula and demonstrates that the form 'accurately reproduces' those same computed values. Because the scaling coefficients are determined by matching the identical set of mean-field-based contacts, the agreement is forced by construction and does not constitute an independent test of universality. No external benchmarks or parameter-free predictions are shown. This matches the 'fitted_input_called_prediction' pattern but is not fully self-definitional, yielding a moderate circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities can be extracted. The scaling relation is likely to contain at least one fitted coefficient tied to the semi-empirical mass formula or to the authors' computed contacts.

pith-pipeline@v0.9.1-grok · 5692 in / 1283 out tokens · 27355 ms · 2026-07-03T03:55:06.309274+00:00 · methodology

discussion (0)

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Reference graph

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