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arxiv: 2607.00806 · v1 · pith:IC6SI4DInew · submitted 2026-07-01 · ⚛️ physics.chem-ph

Inelastic electron scattering induced quantum coherence: isotope effect

Akshay Kumar , Vaibhav S. Prabhudesai This is my paper

Pith reviewed 2026-07-02 04:33 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords electron-induced coherenceisotope effectdipolar dissociationHD isotopologueD2angular distributionsFranck-Condon regionquantum superposition
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The pith

HD behaves as a homonuclear molecule in the Franck-Condon region during electron-impact excitation, producing identical angular asymmetry for H− and D− ions.

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

The paper examines how non-resonant electron scattering creates quantum coherence through a superposition of opposite-parity states, which produces measurable asymmetry in the angular distributions of fragment ions during dipolar dissociation. It measures this asymmetry in D2 at multiple electron energies and finds that heavier isotopes display reduced asymmetry because their slower dissociation allows more time for coherence loss. For the heteronuclear isotopologue HD, the authors show that the mass asymmetry between H and D does not change the observed asymmetry pattern, which remains the same for both H− and D− ions. This result is attributed to HD exhibiting homonuclear-like properties specifically within the Franck-Condon region where the excitation occurs. A reader would care because the finding isolates the excitation step as the origin of coherence, separating it from later dissociation dynamics governed by reduced mass.

Core claim

In non-resonant inelastic electron scattering, excitation creates a coherent superposition of opposite-parity states that survives to produce asymmetry in the angle-differential cross sections of dipolar dissociation. Measurements on D2 across electron energies confirm an isotope effect in which heavier isotopes exhibit diminished asymmetry due to longer dissociation times. In HD the asymmetric masses do not alter the excitation outcome, so the angular distributions of H− and D− ions show the same asymmetry; this occurs because HD displays homonuclear-like behavior inside the Franck-Condon region.

What carries the argument

coherent superposition of opposite-parity states created by electron-impact excitation, whose persistence until dissociation determines the observed left-right asymmetry in fragment angular distributions

If this is right

  • The isotope effect on asymmetry in D2 holds across a range of electron energies rather than only at 50 eV.
  • Coherence established at excitation is independent of the subsequent fragment masses in HD.
  • The Franck-Condon region fixes the effective symmetry of the excited HD molecule before dissociation begins.
  • Asymmetry magnitude scales inversely with dissociation time set by reduced mass.
  • Coherence signatures can be compared directly between homonuclear and heteronuclear isotopologues without mass correction in the initial step.

Where Pith is reading between the lines

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

  • If the Franck-Condon region dominates, similar coherence measurements on other heteronuclear molecules should also erase mass-asymmetry effects at the excitation stage.
  • The result suggests that varying the initial internuclear separation (for example via vibrational excitation before scattering) could test whether the homonuclear-like behavior persists outside the equilibrium geometry.
  • The same coherence mechanism may appear in other non-resonant scattering channels whose final states also involve opposite-parity mixing.

Load-bearing premise

The measured asymmetry in angular distributions is produced by a coherent superposition whose survival time is set by the dissociation timescale, which in turn is controlled by isotope mass.

What would settle it

Direct measurement of different angular asymmetries for H− versus D− ions from HD at an electron energy where dissociation timescales differ substantially from those already reported would contradict the claim that mass asymmetry has no influence on the excitation step.

Figures

Figures reproduced from arXiv: 2607.00806 by Akshay Kumar, Vaibhav S. Prabhudesai.

Figure 1
Figure 1. Figure 1: (a) Momentum image of D− from D2 formed by the DD at the electron energy 50eV and the corresponding normalized angular distributions (b) obtained for the KE range 3 to 9 eV, the arrow indicates the direction of the electron beam. The corresponding �it of the angular distribution is shown by the red line obtained using Equation 2. Similar to the H2 case, the angular distribution shows unexpected forward-bac… view at source ↗
Figure 2
Figure 2. Figure 2: (a) The energy-integrated asymmetry parameter obtained from the model for D2 as a function of incoming electron energy for various impact parameters. (b) Experimentally obtained energy-integrated asymmetry parameters for D2. The corresponding values of asymmetry parameters are compared with H2 (shown in blue), from ref. 12. Using equation (2), the expected asymmetry can be calculated. We have measured the … view at source ↗
Figure 3
Figure 3. Figure 3: Experimentally obtained energy-integrated asymmetry parameters for D− from HD as a function of electron energy. To examine the DD dynamics, we obtained the VSIs of D− from HD and H− from HD. Due to the asymmetric mass of HD, after dissociation, H− will have 2/3 of the KER, while D− will have 1/3 based on the momentum conservation. As a result, H− from HD has a KE of 5-12 eV. In our current experimental set… view at source ↗
Figure 4
Figure 4. Figure 4: Momentum images of (a) D− and (b) H− from HD obtained at 35eV electron energy. The arrow indicates the direction of the incident electron beam [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

Recent discoveries of electron-induced coherence in both resonant and non-resonant interactions have introduced new perspectives in the field. In non-resonant processes, coherence has been observed in dipolar dissociation, where electron-induced excitation forms a coherent superposition of states of opposite parities, resulting in asymmetry in the angle-differential cross-section of the process relative to the incident electron beam. Notably, an isotope effect has been observed in $D_2$ at 50 eV, where heavier isotopes exhibit diminished asymmetry due to their longer dissociation times. Here, we report the isotope effect on quantum coherence in $D_2$ across different electron energies. Additionally, we investigate the role of coherence in the isotopologue HD. Our findings reveal that the asymmetric masses in HD do not influence electron-impact excitation, leading to similar asymmetry in the angular distributions of $H^-$ and $D^-$ ions. This observation is explained by the homonuclear-like behavior of HD within the Franck-Condon region.

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 / 0 minor

Summary. The manuscript reports experimental observations of an isotope effect in electron-induced quantum coherence during non-resonant dipolar dissociation. In D2, asymmetry in angle-differential cross sections diminishes for heavier isotopes at 50 eV due to longer dissociation timescales. The study extends this to other electron energies and examines the heteronuclear isotopologue HD, finding comparable angular asymmetries for H− and D− ions. This is interpreted as mass asymmetry not influencing the electron-impact excitation step, with HD exhibiting homonuclear-like behavior inside the Franck-Condon region that permits coherent superposition of opposite-parity states.

Significance. If the experimental interpretations are robustly supported, the results would extend prior observations of coherence in electron-molecule scattering and provide a test of how nuclear mass and molecular symmetry influence coherence survival during dissociation. The HD case is particularly notable as a potential probe of whether parity-based coherence mechanisms can persist in systems without inversion symmetry.

major comments (2)
  1. [Abstract] Abstract (HD results paragraph): The central interpretation that 'asymmetric masses in HD do not influence electron-impact excitation' and that HD behaves 'homonuclear-like' in the Franck-Condon region rests on the assumption that a coherent superposition of opposite-parity states can form. However, HD lacks inversion symmetry, so its electronic states carry no definite g/u parity. The selection rules and coherence mechanism invoked for homonuclear D2 therefore require explicit justification or supporting calculation showing how the asymmetry arises in HD; without this, the claim that mass asymmetry is irrelevant for excitation but relevant for dissociation is not yet load-bearing.
  2. [Abstract] Abstract (isotope-effect claims): The reported diminution of asymmetry with increasing mass in D2 is attributed to dissociation timescale, but the manuscript provides no quantitative comparison of observed asymmetries against predicted survival probabilities or dissociation times across the studied energies. This leaves the energy-dependent isotope effect vulnerable to alternative explanations (e.g., energy-dependent changes in the excited-state manifold) that are not addressed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments, which help clarify the presentation of our results on isotope effects in electron-induced quantum coherence. We address each major comment below and indicate where revisions will be made to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract (HD results paragraph): The central interpretation that 'asymmetric masses in HD do not influence electron-impact excitation' and that HD behaves 'homonuclear-like' in the Franck-Condon region rests on the assumption that a coherent superposition of opposite-parity states can form. However, HD lacks inversion symmetry, so its electronic states carry no definite g/u parity. The selection rules and coherence mechanism invoked for homonuclear D2 therefore require explicit justification or supporting calculation showing how the asymmetry arises in HD; without this, the claim that mass asymmetry is irrelevant for excitation but relevant for dissociation is not yet load-bearing.

    Authors: We acknowledge that HD lacks inversion symmetry and thus does not have strict g/u parity labels. However, in the Franck-Condon region the relevant excited-state potential energy curves of HD closely resemble those of D2, with the nuclear wave packet launched from a geometry where the center-of-mass frame still permits coherent excitation of states with opposite dipole character. The experimental observation that the angular asymmetries for H− and D− fragments are essentially identical directly supports that the excitation step itself is insensitive to the mass asymmetry. We will revise the abstract and add a short explanatory paragraph in the main text that explicitly addresses the coherence mechanism in the absence of inversion symmetry, referencing the similarity of the electronic surfaces near the vertical excitation region. revision: partial

  2. Referee: [Abstract] Abstract (isotope-effect claims): The reported diminution of asymmetry with increasing mass in D2 is attributed to dissociation timescale, but the manuscript provides no quantitative comparison of observed asymmetries against predicted survival probabilities or dissociation times across the studied energies. This leaves the energy-dependent isotope effect vulnerable to alternative explanations (e.g., energy-dependent changes in the excited-state manifold) that are not addressed.

    Authors: We agree that a quantitative comparison would strengthen the interpretation. While a full time-dependent calculation of coherence survival lies outside the scope of this primarily experimental work, the data show a clear, systematic reduction in asymmetry both with increasing nuclear mass at fixed energy and with increasing electron energy for a given isotope—trends that track the expected lengthening of the dissociation time. Alternative explanations based on energy-dependent changes in the excited-state manifold would affect all isotopologues similarly and cannot account for the observed mass dependence. We will add a brief discussion section that estimates dissociation timescales from the known repulsive curves and places the observed asymmetries in the context of these estimates. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations only

full rationale

The manuscript is a report of measured angular distributions for H-/D- ions from electron-impact dissociation of D2 and HD. No equations, fitted parameters, derivations, or model predictions appear in the provided text. Claims rest on direct experimental results (asymmetry, isotope dependence, HD similarity) interpreted via standard concepts (Franck-Condon region, dissociation timescale) without any reduction to self-defined quantities or self-citation chains. This is self-contained experimental work; the default non-circularity outcome applies.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no free parameters, axioms, or invented entities are described or required by the reported observations.

pith-pipeline@v0.9.1-grok · 5701 in / 1009 out tokens · 31953 ms · 2026-07-02T04:33:32.616368+00:00 · methodology

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