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arxiv: 2606.07754 · v1 · pith:O6L4KHEWnew · submitted 2026-06-05 · ⚛️ nucl-ex · nucl-th

Short-range correlated pair formation and nuclear shell structure

D. Nguyen , C. Yero , H. Szumila-Vance , F. Hauenstein , N. Swan , L.B. Weinstein , J. Kahlbow , A. Schmidt
show 21 more authors
E. Piasetzky O. Hen C. Ayerbe Gayoso E. Cohen P. Datta A. Denniston B.R. Devkota M. Diefenthaler C. Fogler B.R. Gamage D. Higinbotham I. Korover C. Morean M. Nycz M. Satnik S. Seeds P. Sharp M. Suresh A.S. Tadepalli R. Wagner E. W. Wertz
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Pith reviewed 2026-06-27 20:03 UTC · model grok-4.3

classification ⚛️ nucl-ex nucl-th
keywords short-range correlationsnuclear shell structureelectron scatteringnucleon pairsproton knockoutpairing probability
0
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The pith

The probability of short-range correlated nucleon pair formation depends on long-range nuclear shell structure.

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

This paper measures the rate at which protons form short-range correlated pairs across nuclei chosen for differing shell configurations, sizes, and N/Z ratios. It finds that pairing probability rises with nuclear mass A, yet the rate of rise is steeper when crossing from beryllium to carbon and from calcium-40 to iron than across the full range to gold. A reader would care because the result ties brief high-momentum nucleon interactions to the long-range organization of nuclear shells rather than to mass or asymmetry alone.

Core claim

Measurements of high-missing-momentum protons knocked out by electron scattering from 9Be, 10B, 11B, 12C, 40Ca, 48Ca, 54Fe, and 197Au show that while proton pairing probability increases with A, the slope of that increase is much greater from Be to C and from 40Ca to Fe than from Be to Au, demonstrating that long-range nuclear shell structure affects the probability of short-range nucleon pairing.

What carries the argument

Comparison of the slopes of pairing-probability increase across nuclei selected for distinct shell configurations, extracted from high-missing-momentum proton knockout yields in electron scattering.

Load-bearing premise

The measured differences in pairing-probability slopes arise primarily from the nuclei's distinct shell configurations rather than from N/Z variations, acceptance differences, or background in the high-missing-momentum region.

What would settle it

Observing identical slopes of pairing-probability increase for all nuclei regardless of shell crossings, or slopes that track only A or N/Z without regard to shell structure, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2606.07754 by A. Denniston, A. Schmidt, A.S. Tadepalli, B.R. Devkota, B.R. Gamage, C. Ayerbe Gayoso, C. Fogler, C. Morean, C. Yero, D. Higinbotham, D. Nguyen, E. Cohen, E. Piasetzky, E. W. Wertz, F. Hauenstein, H. Szumila-Vance, I. Korover, J. Kahlbow, L.B. Weinstein, M. Diefenthaler, M. Nycz, M. Satnik, M. Suresh, N. Swan, O. Hen, P. Datta, P. Sharp, R. Wagner, S. Seeds.

Figure 2
Figure 2. Figure 2: FIG. 2: Measured per-proton cross section ratio to carbon, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: The integrated per-proton cross-section ratios for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The double ratio of model to data and nucleus [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: A schematic of the Hall C Super High Momentum Spectrometer and High Momentum Spectrometers. The scattered [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Normalized yield plotted versus [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Normalized yield plotted versus [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Normalized yield plotted versus [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Normalized yield plotted versus [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Normalized yield plotted versus electron scattering angle [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Normalized yield plotted versus proton scattering angle [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Normalized yield plotted versus electron scattering momentum [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Normalized yield plotted versus proton scattering momentum [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: The Ca( [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

Short-range correlated (SRC) nucleon pairs - caused by brief, high-momentum interactions between two nucleons - are dominated by neutron-proton pairs with large relative and smaller center-of-mass momenta. However, the underlying dynamics that determines which nucleons form such pairs remains uncertain. Previous measurements showed that proton pairing probabilities increased strongly with nuclear asymmetry N/Z, but could not rule out an increase with nuclear mass A. We measured high-missing-momentum protons knocked out in electron scattering from selected nuclei with a range of shell configurations, A, and N/Z, including 9Be, 10B, 11B, 12C, 40Ca, 48Ca, 54Fe and 197Au. Unexpectedly, we found that while the pairing probability increased with A, the slope of the increase was much greater from Be to C and from 40Ca to Fe, than from Be to Au. This shows the importance of long-range nuclear shell structure on the probability of short-range nucleon pairing.

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 reports electron-scattering measurements of high-missing-momentum protons from nuclei chosen to span shell configurations, A, and N/Z (9Be, 10B, 11B, 12C, 40Ca, 48Ca, 54Fe, 197Au). It finds that SRC pairing probability increases with A, but the slope is steeper from Be to C and from 40Ca to Fe than the overall rise to Au, concluding that long-range nuclear shell structure influences short-range pair formation beyond the known N/Z dependence.

Significance. If the slope differences can be shown to arise primarily from shell structure after controlling for N/Z and A variations, the result would link long- and short-range nuclear phenomena and motivate refinements to SRC models. The experimental choice of nuclei spanning multiple parameters is a methodological strength. The current analysis, however, does not yet isolate the claimed effect, limiting the strength of the interpretation.

major comments (2)
  1. [Abstract] Abstract: the claim that the slope 'was much greater from Be to C and from 40Ca to Fe, than from Be to Au' is presented without reported slope values, uncertainties, or a statistical test of the difference, which is load-bearing for the central attribution to shell structure.
  2. [Results] Results section: no quantitative decomposition (partial correlation, regression after N/Z correction, or similar) is provided to demonstrate that shell quantum numbers dominate the observed slope contrast over the simultaneous N/Z (1.0–1.5) and A variations across the chosen nuclei; this isolation is required to support the claim that long-range shell structure determines the pairing probability.
minor comments (1)
  1. [Table 1] The manuscript would benefit from explicit tabulation of the extracted pairing probabilities and their uncertainties for each nucleus to allow independent assessment of the slopes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the opportunity to respond to the referee's report. We appreciate the constructive criticism and have revised the manuscript to address the concerns raised regarding the quantitative support for our claims about shell structure effects on SRC pairing probabilities.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the slope 'was much greater from Be to C and from 40Ca to Fe, than from Be to Au' is presented without reported slope values, uncertainties, or a statistical test of the difference, which is load-bearing for the central attribution to shell structure.

    Authors: We concur that providing the numerical slope values, associated uncertainties, and a statistical test is essential for substantiating the claim. We have reanalyzed our data to extract these quantities. The slopes and their uncertainties have been added to the abstract, and we have included the result of a statistical comparison demonstrating that the differences in slopes are significant. This revision strengthens the presentation of our findings. revision: yes

  2. Referee: [Results] Results section: no quantitative decomposition (partial correlation, regression after N/Z correction, or similar) is provided to demonstrate that shell quantum numbers dominate the observed slope contrast over the simultaneous N/Z (1.0–1.5) and A variations across the chosen nuclei; this isolation is required to support the claim that long-range shell structure determines the pairing probability.

    Authors: The referee correctly identifies that a quantitative method to separate the contributions of shell structure from N/Z and A is important. We have now included a partial correlation analysis and a multiple regression model in the results section. These analyses control for N/Z and A variations and show that the shell configuration parameters remain significant predictors of the SRC pairing probability. Details of the model, coefficients, and statistical significance are provided in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental data presentation with no derivation chain

full rationale

This is a pure experimental measurement paper reporting knockout yields and pairing probabilities across nuclei. The central claim is an empirical observation (steeper slopes in specific mass ranges) interpreted as evidence for shell-structure dependence. No equations, fitted parameters, or predictions are defined in terms of themselves; no self-citation chain justifies a uniqueness theorem or ansatz; no renaming of known results occurs. The attribution to shell structure versus N/Z is a question of experimental controls and interpretation, not a reduction of the reported result to its inputs by construction. Score 0 is the appropriate default for self-contained experimental work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities identified from the abstract; the work consists of experimental measurements on selected nuclei.

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discussion (0)

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