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arxiv: 2606.19287 · v1 · pith:RM2ZCR24new · submitted 2026-06-17 · ⚛️ physics.atom-ph

Suppression of ionization stabilization in a driven Morse-Soft-Coulomb system

Murilo D. Forlevesi , Emanuel Fernandes de Lima , Gabriel Albertin Amici This is my paper

Pith reviewed 2026-06-26 18:42 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords ionization stabilizationMorse-Soft-Coulomb potentialKramers-Henneberger potentialstrong-field ionizationbroken symmetryphase-space transportatomic modelsescape dynamics
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The pith

Adding a repulsive Morse branch to the Soft-Coulomb potential suppresses the ionization stabilization window by breaking left-right symmetry.

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

The paper compares ionization in a driven Soft-Coulomb model, which shows a stabilization window where ionization probability falls at high field strengths, to a Morse-Soft-Coulomb variant that adds a repulsive Morse barrier. Systematic scans of ionization probabilities, escape-time maps on the field-free energy shell, and sample trajectories show that the stabilization window is strongly suppressed in the Morse-Soft-Coulomb case. The authors trace the difference to the time-averaged Kramers-Henneberger potential: the symmetric Soft-Coulomb version forms two equivalent trapping wells, while the Morse version produces only a single minimum because the Morse branch destroys left-right symmetry and shrinks the effective trapping region.

Core claim

The stabilization window observed in the Soft-Coulomb model is strongly suppressed in the Morse-Soft-Coulomb system as a consequence of the broken left-right symmetry introduced by the Morse branch, which converts the Kramers-Henneberger effective potential from a symmetric double-well into a single-minimum structure and thereby reduces the effective trapping region.

What carries the argument

The Kramers-Henneberger effective potential (the cycle-averaged potential experienced by the driven electron), which forms two symmetric trapping wells in the Soft-Coulomb model but only a single minimum in the Morse-Soft-Coulomb model due to the broken left-right symmetry from the Morse branch.

If this is right

  • Ionization probabilities stay high across a broad range of field amplitudes once the Morse barrier is present.
  • Escape-time maps on the energy shell show shorter residence times near the nucleus in the Morse-Soft-Coulomb system.
  • Representative trajectories exhibit less long-term trapping once the double-well structure is lost.
  • The suppression persists across the range of softening parameters examined.

Where Pith is reading between the lines

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

  • The same symmetry-breaking approach could be applied to other one-dimensional atomic models to test whether stabilization requires symmetric wells.
  • In experiments, adding an asymmetric barrier might provide a way to maintain high ionization rates even at very strong fields.
  • Extending the comparison to two-dimensional or three-dimensional versions of the potential would check whether the single-minimum effect survives in higher dimensions.

Load-bearing premise

The reduction from two trapping wells to one in the effective potential is the direct cause of the lost stabilization rather than other changes in the driven dynamics.

What would settle it

Numerical integration of the Morse-Soft-Coulomb equations of motion that recovers a clear decrease in ionization probability with rising field amplitude, for the same softening parameters used in the paper, would falsify the suppression result.

Figures

Figures reproduced from arXiv: 2606.19287 by Emanuel Fernandes de Lima, Gabriel Albertin Amici, Murilo D. Forlevesi.

Figure 1
Figure 1. Figure 1: FIG. 1: Ionization probability as a function of the field amplitude for the Soft-Coulomb [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Ionization probability as a function of the field amplitude for the Soft-Coulomb [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Escape-time maps with the energy shell [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Escape-time maps with the energy shell [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Gradient of the forward Lagrangian descriptor, [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Gradient of the forward Lagrangian descriptor, [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Representative trajectories selected from the energy shell [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Representative ionizing trajectory of the Morse-Soft-Coulomb model with [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Comparison between the Kramers-Henneberger effective potentials of the [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

Ionization stabilization is a well-known phenomenon in strongly driven Soft-Coulomb atomic models, where the ionization probability decrease as the field amplitude increases. In this work, we investigate how this mechanism is affected by introducing a repulsive Morse barrier into the binding potential, leading to a Morse-Soft-Coulomb (MsC) model. A systematic comparison between the Soft-Coulomb and Morse-Soft-Coulomb systems is performed for different values of the softening parameter. Ionization probabilities, escape-time maps computed on the field-free energy shell and representative trajectories reveal that the stabilization window observed in the Soft-Coulomb model is strongly suppressed in the Morse-Soft-Coulomb system. To elucidate the origin of this behavior, we analyze the corresponding Kramers-Henneberger effective potentials. While the Soft-Coulomb model develops a symmetric double-well structure supporting two equivalent trapping regions, the Morse-Soft-Coulomb potential exhibits a single effective minimum as a consequence of the broken left-right symmetry introduced by the Morse branch. The combined analysis of ionization probabilities, escape dynamics, representative trajectories, and Kramers-Henneberger potentials indicates that the suppression of stabilization is closely associated with the modification of the phase-space transport structures and the reduction of the effective trapping region induced by the Morse

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 / 1 minor

Summary. The manuscript claims that ionization stabilization in strongly driven Soft-Coulomb (SC) models is strongly suppressed upon introduction of a repulsive Morse branch, yielding a Morse-Soft-Coulomb (MsC) potential. Systematic comparisons for varying softening parameters show this via ionization probabilities, escape-time maps on the field-free energy shell, representative trajectories, and Kramers-Henneberger (KH) effective potentials. The suppression is attributed to broken left-right symmetry producing a single KH minimum (versus the symmetric double-well in SC), which reduces the effective trapping region and modifies phase-space transport.

Significance. If the numerical results hold, the work demonstrates how asymmetry and repulsive cores in model potentials can suppress stabilization, providing a phase-space perspective via KH structures and escape maps that complements probability data. The multi-diagnostic approach and parameter variation add value for understanding driven ionization beyond symmetric models.

major comments (1)
  1. [KH potential analysis and escape dynamics] The central attribution of suppression 'as a consequence of the broken left-right symmetry' (KH analysis paragraph) is not isolated from other Morse-induced effects. The escape-time maps and trajectories correlate with the single-minimum KH structure, but the Morse branch also introduces a repulsive core whose range and shape differ from pure asymmetry; no control comparison (e.g., an asymmetric potential lacking the Morse core) is described to test whether symmetry breaking dominates over altered transport or escape pathways.
minor comments (1)
  1. [Abstract] The final sentence of the abstract is truncated mid-phrase ('induced by the Morse'); ensure the submitted manuscript completes all sentences and conclusions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [KH potential analysis and escape dynamics] The central attribution of suppression 'as a consequence of the broken left-right symmetry' (KH analysis paragraph) is not isolated from other Morse-induced effects. The escape-time maps and trajectories correlate with the single-minimum KH structure, but the Morse branch also introduces a repulsive core whose range and shape differ from pure asymmetry; no control comparison (e.g., an asymmetric potential lacking the Morse core) is described to test whether symmetry breaking dominates over altered transport or escape pathways.

    Authors: We agree that the Morse branch simultaneously breaks left-right symmetry and introduces a repulsive core, so the two effects are not fully decoupled in the MsC model. Our attribution rests on the Kramers-Henneberger analysis, which shows that the resulting effective potential changes from a symmetric double well (SC) to a single minimum (MsC) precisely because of the asymmetry; the escape-time maps and sample trajectories are then shown to be consistent with the reduced trapping region of that single-minimum structure. While an auxiliary asymmetric potential lacking the Morse core would allow a stricter separation, the present work is deliberately focused on the concrete MsC potential that arises when a repulsive Morse branch is added to the Soft-Coulomb form. We will revise the KH-analysis paragraph and the concluding discussion to state this limitation explicitly and to emphasize that the observed suppression is tied to the modified KH landscape produced by the full Morse-Soft-Coulomb interaction. revision: partial

Circularity Check

0 steps flagged

No circularity; numerical model comparison is self-contained

full rationale

The paper conducts direct numerical comparisons of ionization probabilities, escape-time maps, trajectories, and Kramers-Henneberger potentials between the Soft-Coulomb and Morse-Soft-Coulomb systems. The central claim associates stabilization suppression with the single-minimum KH structure arising from Morse-induced asymmetry. No equations or steps reduce a derived quantity to a fitted input by construction, no predictions are statistically forced from the same data, and no load-bearing self-citations or uniqueness theorems are invoked. The analysis rests on independent simulations and potential computations that can be reproduced externally without reference to the target result.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

pith-pipeline@v0.9.1-grok · 5767 in / 1024 out tokens · 25719 ms · 2026-06-26T18:42:08.794202+00:00 · methodology

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Reference graph

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