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arxiv: 2604.14748 · v1 · submitted 2026-04-16 · ⚛️ physics.atom-ph

Bound-state Compton scattering of linearly polarized photons

Jonas Sommerfeldt , Nick M. Mayer , Anna Maiorova , Wilko Middents , Stephan Fritzsche , Thomas St\"ohlker , Andrey Surzhykov This is my paper

Pith reviewed 2026-05-10 08:50 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords scatteringphotonsincidents-matrixcalculationscomptonelectronimpulse
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The pith

S-matrix calculations for bound-state Compton scattering of linearly polarized photons reveal kinematic regimes where the impulse approximation matches the full relativistic results reasonably well for Ne9+ and Pb81+ ions.

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

Compton scattering occurs when a photon collides with an electron and loses some energy while changing direction. In atoms, the electron is bound to the nucleus, which affects the scattering compared to a free electron. This work focuses on K-shell electrons, the innermost ones, in highly charged ions like neon and lead stripped to one electron. The authors use the scattering matrix approach based on relativistic Green's functions to calculate how the scattered photon's energy and direction depend on the incoming photon's energy, angle, and linear polarization. They also look at the polarization of the outgoing photon. By comparing to simpler models like treating the electron as free or using the impulse approximation, they identify conditions where the simpler models work okay and where binding effects matter more. Calculations cover a wide range of photon energies and scattering angles, including the sensitive 90-degree case. The study also considers slightly depolarized incident light.

Core claim

The calculations reveal kinematic regimes in which the impulse approximation agrees reasonably well with the S-matrix results. We also explore the polarization of scattered photons for slightly depolarized incident radiation, including the highly sensitive case of scattering at 90°.

Load-bearing premise

The S-matrix approach based on relativistic Green's functions fully captures the binding effects for K-shell electrons without needing higher-order QED corrections or more complex many-body effects.

Figures

Figures reproduced from arXiv: 2604.14748 by Andrey Surzhykov, Anna Maiorova, Jonas Sommerfeldt, Nick M. Mayer, Stephan Fritzsche, Thomas St\"ohlker, Wilko Middents.

Figure 1
Figure 1. Figure 1: FIG. 1: Geometry of the bound-state Compton scattering. The quan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The Feynman diagrams that describe the Compton scattering. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Double-differential Compton cross section [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Double-differential Compton cross section [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Double-differential Compton cross section [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Double-differential Compton cross section [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We present a theoretical study of Compton scattering of X- and $\gamma$-rays by a $K$-shell electron. Special attention is paid to the double-differential cross section and polarization of the scattered photons for linearly polarized incident photons. To investigate these observables, we employ the scattering matrix (S-matrix) approach based on relativistic Green's functions. The S-matrix results are moreover compared with predictions of the free-electron and impulse approximations, allowing us to assess the role of electron binding effects. Detailed calculations are carried out for hydrogen-like Ne$^{9+}$ and Pb$^{81+}$ targets over a wide range of incident photon energies and scattering angles. The calculations reveal kinematic regimes in which the impulse approximation agrees reasonably well with the S-matrix results. We also explore the polarization of scattered photons for slightly depolarized incident radiation, including the highly sensitive case of scattering at $90^\circ$.

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.

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper performs direct numerical evaluation of the S-matrix for bound-state Compton scattering using relativistic Green's functions on hydrogen-like ions, with explicit comparisons to the impulse and free-electron approximations. These are independent calculations under standard relativistic quantum mechanics; no parameters are fitted to the target observables, no predictions reduce to input definitions by construction, and no load-bearing uniqueness or ansatz is imported via self-citation. The reported kinematic regimes of agreement and polarization results follow from the stated equations without circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard relativistic atomic physics without introducing new free parameters, axioms beyond domain assumptions, or invented entities.

axioms (1)
  • domain assumption Relativistic quantum mechanics and the S-matrix formalism with Green's functions accurately describe photon scattering from bound K-shell electrons.
    Invoked throughout the theoretical framework for the scattering calculations.

pith-pipeline@v0.9.0 · 5466 in / 1261 out tokens · 40443 ms · 2026-05-10T08:50:16.448413+00:00 · methodology

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