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Parametric Mössbauer radiation in the grazing-diffraction geometry: Specular diffraction and superradiant amplification

Ze-an Peng*, Christoph H. Keitel, and Jörg Evers†

  • *Contact author: zean.peng@mpi-hd.mpg.de
  • †Contact author: joerg.evers@mpi-hd.mpg.de
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Phys. Rev. A 114, 013115 – Published 15 July, 2026

DOI: https://doi.org/10.1103/s93l-3hr5

Abstract

Parametric x-ray radiation (PXR) is a tunable and versatile x-ray production mechanism that relies on relativistic electrons traversing through a crystal. When the crystal contains Mössbauer nuclei, they may also contribute to the x-ray generation, giving rise to spectrally narrow parametric Mössbauer radiation (PMR) as a promising alternative to undulator-based x-ray sources. It is well known that the x-ray generation strongly depends on the diffraction geometry. Motivated by this, here, we develop a framework for parametric x-ray generation in general diffraction geometries, encompassing the entire x-ray emission range from the conventional grazing extremely asymmetric diffraction (EAD) geometry with a large emission direction to the crystal surface up to the grazing specular diffraction (SD) geometry with emission near parallel to the surface. The framework further incorporates a range of physical effects arising from more realistic modeling of both the Mössbauer crystal and the electron beam. We show that the PMR generation in the grazing SD geometry qualitatively differs from the previously considered grazing EAD case, and explain the physical origins of these differences. We further apply our framework to analyze the geometry dependence of superradiant parametric Mössbauer radiation (SPMR) generated from microbunched electron beams provided by x-ray free-electron lasers. Our results set the stage for the exploration of PXR, PMR, superradiant amplification of parametric x-ray radiation, and SPMR beyond the established diffraction geometries.

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Superradiant Parametric Mössbauer Radiation Source

Ze-an Peng, Christoph H. Keitel, and Jörg Evers
Phys. Rev. Lett. 137, 035001 (2026)

Article Text

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Phys. Rev. A 114, 013115– Published 15 July, 2026
  • Received 12 December 2025
  • Accepted 11 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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