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arxiv: 2606.18735 · v1 · pith:LJT366ZHnew · submitted 2026-06-17 · ⚛️ nucl-th

Vortex Nucleons as Partial-Wave Filters in Nucleon--Nucleon Scattering

Jinniu Hu , Ying Zhang , Hong Shen This is my paper

Pith reviewed 2026-06-26 19:08 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords vortex nucleonspartial-wave filtersnucleon-nucleon scatteringangular momentum selectionon-axis scatteringS-matrix projectionphase shifts
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The pith

An on-axis vortex nucleon with fixed orbital projection m_L excludes low-L partial waves from nucleon-nucleon scattering.

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

The paper shows how vortex nucleons can serve as filters for specific partial waves in nucleon-nucleon scattering. By preparing an on-axis vortex state with a chosen orbital projection ℓ, only waves with total orbital angular momentum L at least |ℓ| enter the scattering. Consequently the S wave drops out for ℓ=1 and both S and P waves drop out for ℓ=2, without any change to the phase shifts themselves. The vortex merely changes which ordinary partial waves contribute to the observed amplitude. Off-axis cases relax this filtering through additional Bessel weights.

Core claim

Using the standard LSJ partial-wave S matrix as input, an on-axis vortex incident state with fixed m_L=ℓ imposes the direct selection rule L≥|ℓ| on the initial nucleon-nucleon partial waves. As a result the initial S wave is excluded for ℓ=1 while both the initial S and P waves are excluded for ℓ=2. The underlying phase shifts are not modified; instead the vortex external state changes how the ordinary partial waves are projected into the scattering amplitude. Off-axis scattering introduces Bessel-function weights that partially relax the on-axis selection rule.

What carries the argument

The on-axis vortex incident state with fixed orbital angular-momentum projection m_L=ℓ, which enforces the L≥|ℓ| selection rule on initial partial waves via projection into the scattering amplitude.

If this is right

  • The initial S wave is excluded for ℓ=1 vortex states.
  • Both initial S and P waves are excluded for ℓ=2 vortex states.
  • The phase shifts of the nucleon-nucleon interaction remain unmodified.
  • Off-axis scattering introduces Bessel-function weights and partially relaxes the on-axis selection rule.

Where Pith is reading between the lines

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

  • This approach could isolate higher partial-wave contributions in NN scattering experiments by preparing vortex states.
  • The same vortex filtering might extend to other two-body scattering systems that admit partial-wave descriptions.
  • Experimental realization would require verifying that the vortex structure does not introduce additional dynamical effects beyond the geometric projection.

Load-bearing premise

A vortex nucleon state with well-defined orbital angular momentum projection m_L can be prepared and the scattering remains fully described by the standard LSJ partial-wave S-matrix.

What would settle it

Observation of S-wave contributions to the scattering amplitude in an ℓ=1 on-axis vortex nucleon collision would contradict the claimed selection rule.

Figures

Figures reproduced from arXiv: 2606.18735 by Hong Shen, Jinniu Hu, Ying Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of on-axis and off-axis OAM-resolved vortex nucleon scattering. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Differential cross section and longitudinal beam analyzing power [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Off-axis differential cross sections for the fixed-OAM state with [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
read the original abstract

We propose vortex nucleon scattering as an angular-momentum-resolved probe of nucleon--nucleon partial waves. Using the standard $LSJ$ partial-wave $S$ matrix as input, we show that an on-axis vortex incident state with a fixed orbital angular-momentum projection $m_L=\ell$ imposes the direct selection rule $L\geq |\ell|$ on the initial nucleon--nucleon partial waves. As a result, the initial $S$ wave is excluded for $\ell=1$, while both the initial $S$ and $P$ waves are excluded for $\ell=2$. The underlying phase shifts are not modified. Instead, the vortex external state changes how the ordinary partial waves are projected into the scattering amplitude. We further analyze off-axis scattering, where the displacement of the target from the vortex axis introduces Bessel-function weights and partially relaxes the on-axis selection rule. These results suggest that vortex nucleons can provide a new experimental handle on the partial-wave content of the strong nucleon--nucleon interaction.

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

1 major / 0 minor

Summary. The paper proposes vortex nucleon scattering as an angular-momentum-resolved probe of nucleon-nucleon partial waves. Using the conventional LSJ partial-wave S-matrix as external input, it argues that an on-axis vortex incident state with fixed m_L = ℓ imposes the selection rule L ≥ |ℓ| on the initial partial waves (excluding the S-wave for ℓ=1 and both S- and P-waves for ℓ=2) while leaving the underlying phase shifts unmodified. The vortex structure only alters the projection of ordinary partial waves into the scattering amplitude. Off-axis scattering is analyzed via Bessel-function weights that partially relax the on-axis rule.

Significance. If the central claim holds, the work supplies a parameter-free, falsifiable prediction for how standard partial-wave amplitudes are filtered by a vortex incident state, grounded in angular-momentum addition. This could furnish a new experimental handle on the partial-wave content of the NN interaction without requiring any modification to on-shell phase shifts. The approach is internally consistent with the standard S-matrix framework and introduces no new free parameters or ad-hoc entities.

major comments (1)
  1. [Abstract] Abstract and main text: the claim that the selection rule L ≥ |ℓ| 'follows from the standard S-matrix input' is asserted without explicit derivation steps, projection formulas, or amplitude expressions showing how the Bessel-beam decomposition restricts the sum over L. This omission makes the central result difficult to verify beyond the conceptual level.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, the positive assessment of the work's internal consistency, and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and main text: the claim that the selection rule L ≥ |ℓ| 'follows from the standard S-matrix input' is asserted without explicit derivation steps, projection formulas, or amplitude expressions showing how the Bessel-beam decomposition restricts the sum over L. This omission makes the central result difficult to verify beyond the conceptual level.

    Authors: We agree that the derivation of the L ≥ |ℓ| selection rule from the fixed m_L = ℓ vortex state could be presented with greater explicitness. The manuscript already employs the standard LSJ S-matrix elements as external input and obtains the restriction solely from the angular-momentum projection in the Bessel-beam decomposition of the incident state; the phase shifts themselves remain unmodified. To make this transparent, the revised manuscript will insert the explicit projection formulas for the vortex incident state onto the partial-wave basis together with the resulting scattering amplitude expression. These additions will display how the sum over L is restricted by the fixed m_L without introducing new parameters or altering on-shell physics. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper explicitly takes the conventional LSJ partial-wave S-matrix as an external input and applies the standard angular-momentum addition rule |m_L| ≤ L to a vortex (Bessel) incident state. This produces the stated selection rule L ≥ |ℓ| without modifying or fitting any on-shell phase shifts. No self-citation chain, ansatz smuggling, or fitted-input-called-prediction is present; the derivation is self-contained against external benchmarks of angular-momentum algebra.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The proposal rests on the pre-existing LSJ partial-wave S-matrix from the literature; no free parameters are introduced, no new axioms beyond standard quantum mechanics are stated, and no new entities are postulated.

pith-pipeline@v0.9.1-grok · 5707 in / 1194 out tokens · 23584 ms · 2026-06-26T19:08:49.799908+00:00 · methodology

discussion (0)

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Reference graph

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