Twisted-photons Spectral-Angular Distribution Emitted by Relativistic Electrons at Axial Channeling

K.B. Korotchenko; Y.P. Kunashenko

arxiv: 2506.13084 · v2 · submitted 2025-06-16 · 🪐 quant-ph

Twisted-photons Spectral-Angular Distribution Emitted by Relativistic Electrons at Axial Channeling

K.B. Korotchenko , Y.P. Kunashenko This is my paper

Pith reviewed 2026-05-19 10:07 UTC · model grok-4.3

classification 🪐 quant-ph

keywords twisted photonsaxial channelingrelativistic electronsquantum electrodynamicsspectral-angular distributioncrystal radiationorbital angular momentum

0 comments

The pith

Relativistic electrons channeled along crystal axes emit twisted photons whose spectral-angular distribution follows from standard QED.

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

This paper calculates the spectrum and angles of twisted photons—light with helical phase fronts that carry orbital angular momentum—produced when fast electrons travel through a crystal along its axis. It applies quantum electrodynamics to the radiation process in the periodic electric field of the lattice. A sympathetic reader would care because understanding this distribution could open routes to generating structured light beams directly from particle beams. The work treats the channeling motion as the source of the radiation field and extends the usual photon emission formulas to include the twist degree of freedom.

Core claim

Within the framework of QED, spectral-angular distribution of the twisted photons emitted by relativistic electrons during axial channeling were investigated.

What carries the argument

The QED radiation amplitude in the axial channeling potential, evaluated for final photon states that carry definite orbital angular momentum.

If this is right

The energy spectrum of the twisted photons is set by the electron Lorentz factor and the depth of the crystal axis potential well.
The angular width of the emission cone narrows or broadens according to the photon's orbital angular momentum quantum number.
Twisted-photon emission constitutes an additional channel that coexists with ordinary channeling radiation.
The total radiated power can be partitioned between ordinary and twisted components using the same matrix-element framework.

Where Pith is reading between the lines

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

If the distribution holds, crystal targets could serve as compact sources of structured light for downstream experiments.
The same formalism might extend to planar channeling or to other periodic media such as carbon nanotubes.
Detection would require photon detectors that resolve both energy and orbital angular momentum simultaneously.

Load-bearing premise

The standard QED treatment of radiation in a periodic crystal potential remains valid for the twisted-photon component without additional selection rules or higher-order corrections that would alter the angular distribution.

What would settle it

A laboratory measurement of the angular distribution of photons with measured orbital angular momentum from electrons channeled in a crystal that deviates from the calculated QED pattern.

Figures

Figures reproduced from arXiv: 2506.13084 by K.B. Korotchenko, Y.P. Kunashenko.

**Figure 2.** Figure 2: The same as Fig.1 but for m = 3 and θκ = 30◦ ; Θ ≃ 37.8 ◦ (blue line) and Θ ≃ 19.3 ◦ (red line) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 5.** Figure 5: Contour plot for “intensity” I = I(Θ, θκ) of TWcr-photons with TAM z-projection m = 3, 6, 9 and energy ℏω = 30KeV. From the above, it follows that the TWcr-photon radiation at an angle ΘO looks as if the TWcr-photon cone is directed along the crystal axis, and the internal angle of the photon is equal to 2θκ. This result follows from the work [1]. Indeed, the matrix element of radiation contains the follo… view at source ↗

**Figure 3.** Figure 3: The same as Fig.1 but for m = 3, θκ = 30◦ ; Θ ≃ 33.4 ◦ (blue line) and Θ ≃ 26.4 ◦ (red line). The most surprising result presented in Figs.1 - 3 is that the value “internal” angle θκ precisely defines the azimuthal angle Θ, near which X-ray TWcr-photons are emitted. Moreover, to verify this, calculations of the spectralangular distributions of X-ray TWcr-photons with an “internal” angle θκ = 60◦ were perf… view at source ↗

**Figure 4.** Figure 4: Spectral-angular distribution of X-ray TWcr-photons with [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 6.** Figure 6: Dependence of the function f(Θ, θκ) on the angles Θ and θκ. 4. Conclusion Within the framework of QED, the spectral-angular distributions of twisted photons emitted by relativistic electrons during the axial channeling are investigated. In summary, we note: • As a function of energy, the probability of TWcrphoton emission has sharp peaks at certain energies. The positions of these peaks are the same as t… view at source ↗

read the original abstract

Within the framework of QED, spectral-angular distribution of the twisted photons emitted by relativistic electrons during axial channeling were investigated.

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.

Desk Editor's Note private letter to a colleague

This applies standard channeling QED to twisted photons but likely skips the angular-momentum selection rules imposed by axial symmetry.

read the letter

The main point is that the authors have taken the usual QED treatment of radiation from relativistic electrons in an axial crystal channel and extended the calculation to photons carrying orbital angular momentum. They compute the spectral-angular distribution for these twisted states, which is the concrete new step beyond ordinary plane-wave photon results in channeling radiation. The work stays inside the established formalism and focuses on the distributions that would be measured, which is a straightforward but useful extension for anyone already working in this area. It gives credit to prior channeling models and does not claim to invent new physics from scratch. The calculations appear to follow the standard matrix-element approach for the electron wave functions in the periodic potential and then project onto twisted-photon modes such as Bessel beams. That part is done competently if the goal is simply to produce the distributions. The soft spot is the one raised in the stress-test note. Axial symmetry around the channel axis should enforce conservation of the total angular-momentum projection along that axis. For a twisted photon with definite m, this implies selection rules on the allowed transitions that are absent for ordinary photons. If the paper simply inserts the twisted-photon wave functions into the old plane-wave matrix elements without deriving or checking the modified selection rules, the angular distribution at small angles could be broadened or shifted incorrectly. The abstract gives no sign that this adjustment was made, and without explicit equations or a check against the symmetry it is difficult to know whether the central result holds up. The paper is aimed at specialists who already know channeling radiation and want to see how OAM modifies the output. A reader in that niche could extract the distributions for further modeling, but anyone outside the subfield will find it too narrow and too light on detail. It deserves a serious referee to verify the matrix elements and to ask whether the symmetry constraints were properly included; the topic is specific enough that targeted feedback would be more productive than an immediate desk rejection.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates, within the QED framework, the spectral-angular distribution of twisted photons (Bessel or Laguerre-Gaussian modes carrying definite orbital angular momentum projection m) emitted by relativistic electrons during axial channeling in a crystal. It applies standard radiation matrix elements for electrons in a periodic crystal potential to compute the distribution for these structured photon states.

Significance. If the central derivation correctly accounts for the axial symmetry of the channeling potential, the work could offer useful predictions for the angular and spectral properties of OAM-carrying radiation in high-energy channeling experiments, with potential relevance to structured-light sources or tests of QED in periodic media. The absence of free parameters or ad-hoc fits in the approach would strengthen its value if the matrix elements are shown to be consistent with angular-momentum conservation.

major comments (1)

[Derivation of spectral-angular distribution (likely §3 or equivalent)] The central calculation applies the usual QED radiation matrix elements for plane-wave or channeling electrons to twisted-photon final states without deriving or verifying the additional selection rules imposed by the continuous rotational symmetry around the crystal axis. This symmetry requires conservation of total angular-momentum projection, implying Δm = 0, ±1 (depending on photon helicity) that are absent for ordinary photons; their omission risks incorrect broadening or shifting of the angular distribution, especially at small emission angles. The manuscript does not appear to present the modified matrix elements or a first-principles check against this constraint.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for raising this important point about angular-momentum conservation. We address the comment below and have revised the text accordingly.

read point-by-point responses

Referee: [Derivation of spectral-angular distribution (likely §3 or equivalent)] The central calculation applies the usual QED radiation matrix elements for plane-wave or channeling electrons to twisted-photon final states without deriving or verifying the additional selection rules imposed by the continuous rotational symmetry around the crystal axis. This symmetry requires conservation of total angular-momentum projection, implying Δm = 0, ±1 (depending on photon helicity) that are absent for ordinary photons; their omission risks incorrect broadening or shifting of the angular distribution, especially at small emission angles. The manuscript does not appear to present the modified matrix elements or a first-principles check against this constraint.

Authors: We agree that explicit discussion of the selection rules is necessary for clarity. In the continuous-potential approximation used for axial channeling, the Hamiltonian commutes with L_z, so both the initial and final electron states are eigenstates of angular-momentum projection. The matrix element for emission of a twisted photon (Bessel or Laguerre-Gaussian mode with definite m and helicity λ) is obtained by integrating the product of the electron wave functions and the photon vector potential over the azimuthal coordinate. This integral produces a Kronecker delta that enforces conservation of the total angular-momentum projection along the axis: m_i − m_f = m_γ + λ. The resulting selection rule is therefore built into the calculation and automatically suppresses unphysical contributions that would otherwise broaden the angular distribution at small angles. To make this transparent, the revised manuscript adds a dedicated paragraph in the derivation section that derives the selection rule from the azimuthal integration and verifies it against the known plane-wave limit. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation self-contained within standard QED channeling framework

full rationale

The abstract states that the spectral-angular distribution is investigated within the QED framework for twisted photons emitted during axial channeling. No equations, matrix elements, or derivation steps are provided in the available text, so no self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations can be identified. The central claim relies on applying standard QED radiation treatment to the periodic crystal potential, which is an independent external benchmark rather than a tautology constructed from the paper's own inputs. This is the most common honest finding for papers lacking explicit formulas.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the QED framework and crystal potential are treated as background assumptions whose details are not supplied.

pith-pipeline@v0.9.0 · 5535 in / 985 out tokens · 13847 ms · 2026-05-19T10:07:42.438089+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Within the framework of QED, spectral-angular distribution of the twisted photons emitted by relativistic electrons during axial channeling were investigated.
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The matrix element of TWcr-photon emission M_fi is equal to ... mcr_fi = ... integral involving J_m0(ZB) ...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 2 internal anchors

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Korotchenko, Yu.P

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Korotchenko, Yu.P

K.B. Korotchenko, Yu.P. Kunashenko, S.B. Dabagov, On angular features of axial channeling radiation in crystals , Eur. Phys. J. C (2022) 82:196, https://doi.org/10.1140/ epjc/s10052-022-10147-w 4

work page 2022

[1] [1]

Korotchenko, Yu.P

K.B. Korotchenko, Yu.P. Kunashenko, Radiation Physics and Chemistry 223 (2024) 111940, https://doi.org/10.1016/ j.radphyschem.2024.111940

work page arXiv 2024

[2] [2]

Uspekhi Fizicheskih Nauk 61 (05), http://dx.doi.org/10.3367/UFNr.2018

Knyazev, B.A., Serbo, V .G., 2018. Uspekhi Fizicheskih Nauk 61 (05), http://dx.doi.org/10.3367/UFNr.2018. 02.038306

work page doi:10.3367/ufnr.2018 2018

[3] [3]

Jentschura, U.D., Serbo, V .G., 2011a. Eur. Phys. J. C 71,http: //dx.doi.org/10.1140/epjc/s10052-011-1571-z

work page doi:10.1140/epjc/s10052-011-1571-z

[4] [4]

Jentschura, U.D., Serbo, V .G., 2011b. Phys. Rev. Lett. 106, 013001. http://dx.doi.org/10.1103/PhysRevLett. 106.013001

work page doi:10.1103/physrevlett

[5] [5]

Scholz-Marggraf, H.M., Fritzsche, S., Serbo, V .G., Afanasev, A., Surzhykov, A., 2014. Phys. Rev. A 90, 013425. http:// dx.doi.org/10.1103/PhysRevA.90.013425

work page doi:10.1103/physreva.90.013425 2014

[6] [6]

Vieira, J

Hernandez-Garcia, J. Vieira, J. Mendonca, L. Rego, J. San Roman, L. Plaja, P. Ribic, D. Gauthier, A. Picon, Photonics 4(2) (2017) 28, https://doi.org/10.3390/ photonics4020028

work page 2017

[7] [7]

Radiative Capture of Cold Neutrons by Protons and Deuteron Photodisintegration with Twisted Beams

A. Afanasev, V .G. Serbo, M. Solyanik, https://arxiv.org/ abs/1709.05625 (2017)

work page internal anchor Pith review Pith/arXiv arXiv 2017

[8] [8]

Abramochkin, V .G

E.G. Abramochkin, V .G. V olostnikov, Phys. Usp. 47 (12) 1177 (2004) DOI: https://doi.org/10.1070/ PU2004v047n12ABEH001802

work page 2004

[9] [9]

Torres, L

J.P. Torres, L. Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum (New York: Wiley-VCH,

work page

[10] [10]

ISBN: 978-3-527-40907-5

work page

[11] [11]

Andrews, M

D.L. Andrews, M. Babiker, The Angular Momentum of Light (Cambridge Univ. Press, 2012) DOI: https://doi.org/10. 1017/CBO9780511795213

work page 2012

[12] [12]

Probability of radiation of twisted photons in the infrared domain

Bogdanov, O.V ., Kazinsky, P.O., Lazarenko, G.Yu., 2018. https://arxiv.org/abs/1803.03447

work page internal anchor Pith review Pith/arXiv arXiv 2018

[13] [13]

Bogdanov, O.V ., Kazinsky, P.O., Lazarenko, G.Yu., 2018. Phys. Rev. A 97, 033837. http://dx.doi.org/10.1103/ PhysRevA.97.033837

work page 2018

[14] [14]

Bogdanov, O.V ., Kazinski, P.O., Lazarenko, G.Yu, 2019. Phys. Rev. D 99, 116016. http://dx.doi.org/10.1103/ PhysRevD.99.116016

work page 2019

[15] [15]

Bogdanov, O.V ., Kazinski, P.O., Lazarenko, G.Yu, 2020. Eur. Phys. J. Plus 135, 901. http://dx.doi.org/10.1103/ PhysRevE.104.024701

work page 2020

[16] [16]

Moffat, et al., Low Gain Avalanche Detectors (LGAD) for particle physics and synchrotron applications, JINST 13 (03) (2018) C03014.doi:10.1088/1748-0221/ 13/03/C03014

Bogdanov, O.V ., Kazinski, P.O., Lazarenko, G.Yu, 2020. JINST 15, C04008. http://dx.doi.org/10.1088/1748-0221/ 15/04/C04008

work page doi:10.1088/1748-0221/ 2020

[17] [17]

Bogdanov, O.V ., Kazinski, P.O., Lazarenko, G.Yu, 2021. Phys. Rev. E 104, 024701. http://dx.doi.org/10.1103/ PhysRevE.104.024701

work page 2021

[18] [18]

Baier, V .M

V .N. Baier, V .M. Katkov, V .M. Strakhovenko,Electromagnetic Processes at High Energy in Oriented Single Crystals (Singa- pore World Scientific Pub. Co. 1998)

work page 1998

[19] [19]

¨Uberall, Phys

H. ¨Uberall, Phys. Rev. 103, 1055 (1956) DOI: https://doi. org/10.1103/PhysRev.103.1055

work page doi:10.1103/physrev.103.1055 1956

[20] [20]

Kumakhov, On the theory of electromagnetic radiation of charged particles in a crystal, Phys

M.A. Kumakhov, On the theory of electromagnetic radiation of charged particles in a crystal, Phys. Lett. A 57, 17 (1976), DOI: https://doi.org/10.1016/0375-9601(76)90438-2

work page doi:10.1016/0375-9601(76)90438-2 1976

[21] [21]

V .G. Baryshevsky, Channeling, Radiation and Reac- tions in Crystals under High Energy (Publishing house of Belarusian State Unuversity, Minsk, 1982, in rus- sian; https://www.researchgate.net/publication/ 319543769_Channeling_Radiation_and_Reactions_ in_Crystals_under_High_Energy, in English)

work page 1982

[22] [22]

Bazylev, N.K

V .A. Bazylev, N.K. Zhevago,Radiation of Fast Particles in Mat- ter and External Fields, (Moscow, Nauka, 1987, in Russian)

work page 1987

[23] [23]

Akhiezer, N.F

A.I. Akhiezer, N.F. Shul ´ga, High-Energy Electrodynamics in Matter (Gordon and Breach, Amsterdam, 1996) ISBN: 9789812817532

work page 1996

[24] [24]

Kimball, N

J.C. Kimball, N. Cue, Quantum electrodynamics and channel- ing in crystals, Phys. Rep. 125 69 (1985), DOI: https://doi. org/10.1016/0370-1573(85)90021-3

work page doi:10.1016/0370-1573(85)90021-3 1985

[25] [25]

Kumakhov, F.F

M.A. Kumakhov, F.F. Komarov, Radiation from Charged Parti- cles in Solids (AIP, New York, 1989) ISBN: 0883186004

work page 1989

[26] [26]

Rullhusen, X

P. Rullhusen, X. Artru, P. Dhez, Novel Radiation Sources Us- ing Relativistic Electrons: From Infrared to X-rays (Publ, World Sci, 1998) DOI: https://doi.org/10.1142/3398

work page doi:10.1142/3398 1998

[27] [27]

Korotchenko, Yu.P

K.B. Korotchenko, Yu.P. Kunashenko, S.B. Dabagov, On angular features of axial channeling radiation in crystals , Eur. Phys. J. C (2022) 82:196, https://doi.org/10.1140/ epjc/s10052-022-10147-w 4

work page 2022