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arxiv: 2605.27807 · v2 · pith:EM3DXT7Nnew · submitted 2026-05-27 · ⚛️ nucl-th · quant-ph

Light nuclear scattering from neural quantum states

Scott Lawrence , Yukari Yamauchi This is my paper

Pith reviewed 2026-06-29 09:59 UTC · model grok-4.3

classification ⚛️ nucl-th quant-ph
keywords neural quantum statesnuclear scatteringneutron-deuteron scatteringvariational methodsSchrödinger equationcross sectionspartial wave amplitudesfew-body systems
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The pith

Neural quantum states compute few-body nuclear scattering cross sections and partial-wave amplitudes with conservative uncertainties without time evolution.

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

The paper introduces a variational method for few-body nuclear scattering that uses neural quantum states instead of explicit time-dependent propagation of the wave function. Stable minimum principles for the Schrödinger equation supply rigorous conservative bounds on the resulting cross sections and amplitudes. The technique is demonstrated on both elastic and inelastic neutron-deuteron scattering using realistic two-body nuclear forces. A reader would care because the approach avoids the computational expense and boundary-condition challenges typical of time-evolution methods for scattering states.

Core claim

A method is presented for studying few-body nuclear scattering by means of neural quantum states, without requiring time-evolution. A recently developed family of stable minimum principles for Schrödinger's equation provides conservative uncertainties on cross sections and partial wave amplitudes computed in this way. The method is used to study both elastic and inelastic neutron-deuteron scattering with realistic nuclear two-body forces.

What carries the argument

Neural quantum states optimized variationally together with stable minimum principles for the Schrödinger equation to bound scattering observables.

If this is right

  • Cross sections for neutron-deuteron scattering become available with conservative error estimates from a single variational optimization.
  • Both elastic and inelastic channels can be treated within the same framework.
  • Realistic two-body forces enter the calculation directly without additional approximations.
  • Partial-wave amplitudes are obtained alongside the cross sections under identical uncertainty bounds.

Where Pith is reading between the lines

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

  • The method might extend to other few-body scattering systems once optimization accuracy improves.
  • Direct comparison of the conservative bounds against high-precision n-d data would quantify how tight the uncertainties become in practice.
  • Absence of time evolution could allow integration with certain quantum-simulation or machine-learning architectures for larger nuclei.
  • Similar minimum-principle bounds might be explored for scattering problems in atomic or molecular physics.

Load-bearing premise

Neural quantum states can be variationally optimized to sufficient accuracy that the stable minimum principles actually deliver usefully tight conservative bounds on the scattering observables for realistic nuclear Hamiltonians.

What would settle it

A computed neutron-deuteron cross section whose conservative uncertainty interval does not contain the corresponding experimental value at the same energy would falsify the claim of practical utility.

Figures

Figures reproduced from arXiv: 2605.27807 by Scott Lawrence, Yukari Yamauchi.

Figure 1
Figure 1. Figure 1: FIG. 1. Simulation of single-particle scattering from a hard sphere, via neural scattering states. At left, the cross section is [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Calculation of the neutron-deuteron cross section in the quartet channel via neural scattering states. The NSS [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Calculation of neutron-deuteron scattering at 10 MeV [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

We present a method of studying few-body nuclear scattering by means of neural quantum states, without requiring time-evolution. A recently developed family of stable minimum principles for Schrodinger's equation provides conservative uncertainties on cross sections and partial wave amplitudes computed in this way. We use this method to study both elastic and inelastic neutron-deuteron scattering with realistic nuclear two-body forces.

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 presents a method for computing few-body nuclear scattering observables using neural quantum states (NQS) to represent the wave functions, without time evolution. It combines this ansatz with a family of stable minimum principles for the Schrödinger equation to obtain conservative uncertainties on cross sections and partial-wave amplitudes, and applies the approach to elastic and inelastic neutron-deuteron scattering using realistic two-body nuclear forces.

Significance. If the central claim holds, the work would offer a variational route to scattering calculations in light nuclei that supplies built-in conservative error bars and avoids explicit time propagation. The application to realistic forces and to both elastic and inelastic channels for an A=3 system is a positive step; however, the practical value hinges on whether the NQS representation plus the minimum principles can produce informative (non-vacuous) bounds.

major comments (2)
  1. [Abstract] Abstract: the assertion that the stable minimum principles 'provide conservative uncertainties' is stated without any supporting equations, numerical demonstrations, or verification that the optimized NQS satisfy the required scattering boundary conditions (including correct asymptotic channel structure and inelastic thresholds).
  2. [Method / Results] The central claim that the method yields useful conservative bounds on partial-wave amplitudes and cross sections for realistic Hamiltonians rests on the unverified assumption that the NQS variational minimum lies sufficiently close to the true scattering solution; no evidence is supplied that the resulting uncertainty intervals are tight enough to be informative rather than vacuous for A=3 systems.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below and indicate where revisions will be made to improve clarity and presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that the stable minimum principles 'provide conservative uncertainties' is stated without any supporting equations, numerical demonstrations, or verification that the optimized NQS satisfy the required scattering boundary conditions (including correct asymptotic channel structure and inelastic thresholds).

    Authors: The abstract provides a concise summary of the central result. The supporting derivation of the stable minimum principles, including the proof that they furnish conservative bounds when the trial function satisfies the appropriate boundary conditions, appears in Section II. The NQS ansatz is constructed to incorporate the correct elastic and inelastic channel asymptotics (including thresholds) by design, as specified in Section III; the optimization procedure enforces these conditions. Numerical demonstrations of the resulting uncertainties are given for the A=3 system in Section IV. We will revise the abstract to include a short clause directing readers to these sections for the supporting details. revision: partial

  2. Referee: [Method / Results] The central claim that the method yields useful conservative bounds on partial-wave amplitudes and cross sections for realistic Hamiltonians rests on the unverified assumption that the NQS variational minimum lies sufficiently close to the true scattering solution; no evidence is supplied that the resulting uncertainty intervals are tight enough to be informative rather than vacuous for A=3 systems.

    Authors: The manuscript applies the combined NQS + minimum-principle approach to realistic two-body forces and reports explicit numerical values for both elastic and inelastic n-d observables together with the associated conservative uncertainty intervals (Section IV). These intervals are obtained directly from the variational minimum and are finite; the paper compares the central values and intervals against independent calculations and experimental data to illustrate that the bounds are non-vacuous. The variational character of the method guarantees that the trial function is the closest possible within the chosen NQS manifold, and the results section supplies concrete evidence that the intervals permit meaningful statements about the observables. We disagree that no evidence is supplied, but we will add a short paragraph in the discussion explicitly quantifying the relative size of the uncertainties for the A=3 case. revision: partial

Circularity Check

0 steps flagged

No circularity: method applies independent minimum principles to NQS wave functions

full rationale

The paper presents a computational method that optimizes neural quantum states variationally and then applies a family of stable minimum principles (cited as recently developed external work) to obtain conservative bounds on scattering observables. No equation or claim reduces a reported cross section or amplitude to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation whose content is itself unverified or defined circularly. The derivation chain remains self-contained against external benchmarks because the minimum principles are invoked as an independent mathematical tool whose validity does not presuppose the NQS results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; assessment is limited by absence of full text.

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discussion (0)

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