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arXiv:2604.00575

Universal features of high-energy scattering of Laguerre-Gaussian states

Yaoqi Yang, Igor P. Ivanov

hep-phquant-phSubmitted Apr 1, 2026• Announced Apr 2, 2026
v1 · Apr 1, 2026v2 · Jun 16, 2026
arXivHTMLPDF

Abstract

Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter $b$. Since the total final transverse momentum $P_\perp$ is no longer fixed, we focus on how the differential cross section depends on $P_\perp$. We emphasize that non-trivial $P_\perp$-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter $b$ plays a key role in many $P_\perp$-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.

Journal reference
Phys. Rev. D 113, 116020 (2026)
DOI
10.1103/h5bv-6sl5
Comments
23 pages, 8 figures

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Vortex states of photons, electrons, and other particles are wave packets that carry intrinsic orbital angular momentum (OAM) and exhibit other features unavailable for plane waves. Collisions of high-energy vortex states can become a promising tool for nuclear and particle physics, once experimental challenges are overcome. An extensive literature exists on scattering processes involving vortex states; however, most works rely on assumptions that will be challenging to achieve in experiment. In this work, we initiate a systematic re-analysis of vortex-state scattering processes using paraxial Laguerre-Gaussian (LG) wave packets colliding at a non-zero impact parameter bbb. Since the total final transverse momentum P⊥P_\perpP⊥​ is no longer fixed, we focus on how the differential cross section depends on P⊥P_\perpP⊥​. We emphasize that non-trivial P⊥P_\perpP⊥​-dependent features can originate either from the shape of the LG wave packets or from the dynamics of the scattering process under interest. Here, we focus on the former source and explore in detail these universal kinematic features, while the study of process-specific modifications, along with the novel insights they may bring, is delegated to a future work. Interestingly, the non-zero impact parameter bbb plays a key role in many P⊥P_\perpP⊥​-dependent effects, making it a useful probe of vortex states, not a nuisance factor as often assumed.
While a plane-wave approximation in high-energy physics works well in a majority of practical cases, it becomes inapplicable for scattering of the vortex particles carrying orbital angular momentum, of Airy beams, of the so-called Schrödinger cat states, and their generalizations. Such quantum states of photons, electrons and neutrons have been generated experimentally in recent years, opening up new perspectives in quantum optics, electron microscopy, particle physics, and so forth. Here we discuss the non-plane-wave effects in scattering brought about by the novel quantum numbers of these wave packets. For the well-focused electrons of intermediate energies, already available at electron microscopes, the corresponding contribution can surpass that of the radiative corrections. Moreover, collisions of the cat-like superpositions of such focused beams with atoms allow one to probe effects of the quantum interference, which have never played any role in particle scattering.
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We explore elastic scattering of non-relativistic electrons in the form of standard Laguerre-Gaussian (sLG) and elegant Laguerre - Gaussian (eLG) packets on atomic targets in the generalized Born approximation and compare these results to the reference with Bessel-Gaussian (BG) packets. Scattering by hydrogen-like, iron, silver, and golden targets is considered. The incident electron carries a nonzero orbital angular momentum, while sLG and eLG packets have a definite radial quantum number n as well. In scattering of sLG and eLG wave packets by a macroscopic target sensitivity of the average cross section to the orbital angular momentum is observed, which is absent for BG packets. We highlight the opportunity to employ the differences in the experimental scattering results for the revelation of the properties of incident twisted electron wave packets
The exchange of orbital angular momentum (OAM) between paraxial optical vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In this paper, we develop a theory for the microscopic interaction between matter and an optical vortex beyond paraxial approximation. We show how superposition of vortex states of BEC can be created with a focused optical vortex. Since the polarization or spin angular momentum (SAM) of the optical field is coupled with OAM of the field, in this case, these angular momenta can be transferred to the internal electronic and external center-of-mass motion of atoms provided both the motions are coupled. We propose a scheme for producing the superposition of matter-wave vortices using Gaussian and a focused Laguerre-Gaussian beam. We study how two-photon Rabi frequencies of stimulated Raman transitions vary with focusing angles for different combinations of OAM and SAM of optical states. We demonstrate the formation of vortex-antivortex structure and discuss interference of three vortex states in a BEC.
A traveling wave or wave packet may possess orbital angular momentum (OAM) in the form of a phase vortex about its propagation axis. These OAM states are a general wave property and exist in single‐particle wave packets, in a beam of unstructured wave packets of particles or in a mixture. OAM states of photons were first created almost 30 years ago. Recently work has been done to create these states with massive particles: electrons and neutrons. OAM waves can be generated by passing an unstructured wave through a vortex phase plate. This technique is reliant on each particle adequately sampling the area of the vortex plate. While laser sources provide sufficient transverse coherence, beams of massive particles are more challenging. If incident wave packets do not interrogate the discontinuity at the center of the vortex phase plate, the probability of detecting a single particle having a unit of OAM about the packet center decreases substantially and the expectation value of the OAM about that center vanishes. Herein, using laser light, we restrict the transverse size of a beam to either illuminate the discontinuity or not and consider the implications for producing OAM in individual neutrons.
We comment on Ref.[D. Karlovets, D. Grosman, and I. Pavlov, Phys. Rev. Lett. 136, 085002 (2026)], which proposes a BMT-like equation for the mean kinetic orbital angular momentum (OAM) of vortex particles in accelerator fields and draws spin-like conclusions about depolarization, resonances, and control. We show that the proposed closure is not generally valid even at the mean-value level. In the authors' own homogeneous-field model, Eq.(8) already makes ⟨Lz⟩\langle L_z\rangle⟨Lz​⟩ depend on the packet second moment ⟨ρ2⟩(τ)\langle ρ^2\rangle(τ)⟨ρ2⟩(τ); for an exact family of breathing Landau/LG packets this yields an explicit oscillation incompatible with Eq.(9) except in the nongeneric matched case. Moreover, the Appendix A assumption that mixed correlators are negligible suppresses the transverse kinetic-OAM components themselves, since those correlators are precisely the building blocks of LxL_xLx​ and LyL_yLy​. We also stress that, even if a closed equation for ⟨L^⟩\langle \hat{\mathbf L}\rangle⟨L^⟩ were available, it would still not constitute a transport equation for a vortex quantum state. Mean-OAM transport does not determine OAM spectra, inter-mode coherences, or fidelity. State-level claims therefore require a mode-resolved density-matrix treatment rather than an Ehrenfest equation for a low-order moment.