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arxiv: 2512.20095 · v2 · submitted 2025-12-23 · ⚛️ nucl-th · nucl-ex

Glauber-theory calculations of high-energy nuclear scattering observables using variational Monte Carlo wave functions

W. Horiuchi , Y. Suzuki , R.B. Wiringa This is my paper

Pith reviewed 2026-05-16 20:39 UTC · model grok-4.3

classification ⚛️ nucl-th nucl-ex
keywords Glauber theoryvariational Monte Carlonuclear reactionsscattering cross sectionsab initio calculationscumulant expansionlight nuclei
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0 comments X

The pith

Glauber theory with variational Monte Carlo wave functions accurately describes high-energy scattering for light nuclei.

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

This paper carries out first-principles calculations of proton and nucleus scattering on carbon-12 and helium-6 using Glauber theory. The nuclear wave functions come from variational Monte Carlo methods that incorporate realistic nucleon interactions. The phase-shift function is evaluated by direct Monte Carlo sampling over all multiple-scattering orders. The results match selected experimental cross sections closely, and a simplified cumulant series for the phase shift converges after the second term. These findings support using the same framework for analyzing data from high-energy nuclear experiments.

Core claim

Glauber-theory calculations that employ variational Monte Carlo wave functions for 6He and 12C reproduce the measured elastic differential cross sections and total reaction cross sections for p+12C, 12C+12C, and 6He+12C collisions at intermediate to high energies. The full multiple-scattering phase-shift function is obtained by Monte Carlo integration, and its cumulant expansion is shown to converge rapidly already at second order.

What carries the argument

The Glauber phase-shift function evaluated by Monte Carlo integration over nucleon-nucleon multiple scatterings, built from variational Monte Carlo nuclear wave functions that include two- and three-body correlations.

Load-bearing premise

The Glauber multiple-scattering approximation itself remains valid for the chosen beam energies and target nuclei.

What would settle it

New high-precision experimental data showing significant deviations from the calculated differential cross sections for any of the three systems at comparable energies would indicate that the description fails.

Figures

Figures reproduced from arXiv: 2512.20095 by R.B. Wiringa, W. Horiuchi, Y. Suzuki.

Figure 2
Figure 2. Figure 2: FIG. 2. Energy dependence of the total reaction cross sectio [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: plots the 12C+12C elastic differential cross sections. The effect of the Coulomb breakup contribution is small. Agreement between theory and experiment in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Energy dependence of the total reaction cross sectio [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work well, no convincing calculation has so far been done. We perform ab initio Glauber theory calculations of both elastic differential cross sections and total reaction cross sections for p+12C, 12C+12C, and 6He+12C systems. The wave functions of both 6He and 12C are generated by variational Monte Carlo calculations with spatial and spin-isospin correlations induced by realistic two- and three-nucleon potentials. Glauber's phase-shift function is computed by Monte Carlo integration up to all orders of nucleon-nucleon multiple scatterings. We show an excellent performance of the Glauber description to the selected data on the above systems. We also find that the cumulant expansion of the phase-shift function converges rapidly up to the second order for the above systems. This finding will open up interesting applications for the analysis of high-energy nuclear experiments.

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 / 2 minor

Summary. The manuscript performs ab initio Glauber-theory calculations of elastic differential cross sections and total reaction cross sections for the p+12C, 12C+12C, and 6He+12C systems at intermediate-to-high energies. Variational Monte Carlo wave functions are generated from realistic two- and three-nucleon potentials; the Glauber phase-shift function is evaluated by direct Monte Carlo integration over all orders of nucleon-nucleon multiple scatterings. The central results are excellent agreement with selected experimental data and rapid convergence of the cumulant expansion of the phase-shift function up to second order.

Significance. If the numerical results hold, the work supplies the first fully ab initio, parameter-free Glauber calculations for these systems using realistic VMC wave functions, thereby strengthening the theoretical foundation for analyzing high-energy radioactive-beam experiments. The explicit Monte Carlo integration to all orders and the reported rapid cumulant convergence constitute concrete technical advances that could simplify future applications.

major comments (2)
  1. [Abstract] Abstract and results section: the claim of 'excellent performance' of the Glauber description rests exclusively on agreement with the chosen data sets; no independent benchmark against non-eikonal multiple-scattering calculations, exact few-body solutions, or prior calculations with different wave functions is provided to test the validity of the eikonal approximation itself for the selected energies and nuclei.
  2. [Results] Results section (Monte Carlo integration paragraph): quantitative details on statistical errors, number of samples, and convergence tests for the full phase-shift function (beyond the cumulant expansion) are not reported, making it impossible to assess whether the claimed all-order integration is numerically stable for the 6He+12C system.
minor comments (2)
  1. [Abstract] The beam energies for each reaction should be stated explicitly in the abstract and introduction rather than referred to only as 'the above systems'.
  2. [Figures] Figure captions should include the specific experimental references and the kinematic range shown so that the data-theory comparison can be reproduced without consulting external sources.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript to incorporate the suggestions where feasible.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results section: the claim of 'excellent performance' of the Glauber description rests exclusively on agreement with the chosen data sets; no independent benchmark against non-eikonal multiple-scattering calculations, exact few-body solutions, or prior calculations with different wave functions is provided to test the validity of the eikonal approximation itself for the selected energies and nuclei.

    Authors: We appreciate the referee's emphasis on validating the eikonal approximation independently. Our manuscript's central contribution is the first fully ab initio implementation of Glauber theory for these systems using realistic VMC wave functions, with the phase-shift function computed via direct Monte Carlo integration over all orders of multiple scattering. While we agree that additional benchmarks against non-eikonal or exact few-body calculations would be valuable, performing such new calculations lies outside the scope of the present work, which focuses on the integration of ab initio structure inputs with the standard Glauber framework. In the revised manuscript we have added a dedicated paragraph in the introduction and discussion sections referencing prior literature that has tested the eikonal approximation for light nuclei at comparable energies, thereby providing context for the applicability of our approach. revision: partial

  2. Referee: [Results] Results section (Monte Carlo integration paragraph): quantitative details on statistical errors, number of samples, and convergence tests for the full phase-shift function (beyond the cumulant expansion) are not reported, making it impossible to assess whether the claimed all-order integration is numerically stable for the 6He+12C system.

    Authors: We agree that explicit quantitative information on the Monte Carlo sampling procedure is essential for assessing numerical stability. In the revised manuscript we have expanded the relevant paragraph in the Results section to report the number of Monte Carlo samples used (10^6 configurations per nucleus), the estimated statistical uncertainties on the full phase-shift function (typically 1-3% for 6He+12C), and explicit convergence tests demonstrating that the all-order results stabilize with increasing sample size. These additions directly address the concern for the 6He+12C system. revision: yes

Circularity Check

0 steps flagged

No circularity: ab initio computation from established potentials and VMC wave functions

full rationale

The derivation begins with realistic two- and three-nucleon potentials and variational Monte Carlo wave functions for 6He and 12C. The Glauber phase-shift function is obtained by direct Monte Carlo integration over these wave functions up to all orders of multiple scattering. No parameters are adjusted to the p+12C, 12C+12C or 6He+12C scattering data under study; the reported agreement with experiment and the rapid convergence of the cumulant expansion to second order are presented as outcomes, not inputs. No self-citation chain or ansatz is invoked to force the central results. The calculation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the Glauber eikonal approximation at the chosen energies, the accuracy of the variational Monte Carlo wave functions generated from established two- and three-nucleon potentials, and the statistical convergence of the Monte Carlo sampling of the phase-shift function. No new parameters are fitted to the scattering data.

axioms (2)
  • domain assumption Glauber multiple-scattering series is a valid description of high-energy nucleon-nucleus and nucleus-nucleus collisions
    Invoked throughout the abstract as the framework whose performance is being tested
  • domain assumption Variational Monte Carlo with realistic two- and three-nucleon potentials produces sufficiently accurate ground-state wave functions for 6He and 12C
    Stated as the source of the input wave functions

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