Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Migdal effect in solid crystals and the role of nonadiabaticity

Angelo Esposito1,2,* and Andrea Rocchi1

  • *Contact author: angelo.esposito@uniroma1.it

Phys. Rev. D 112, 075034 – Published 17 October, 2025

DOI: https://doi.org/10.1103/198q-nv94

Abstract

We systematically apply the Born-Oppenheimer approximation to show that the Migdal effect in a solid crystal is entirely due to nonadiabatic effects, namely the deviation of the wave function from exact factorization of the electronic and nuclear contributions. The matrix element obtained this way matches exactly the result found by means of a previously derived low energy effective theory.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. Yue Meng et al. (PandaX-4T Collaboration), Dark matter search results from the PandaX-4T commissioning run, Phys. Rev. Lett. 127, 261802 (2021).
  2. P. Agnes et al. (DarkSide-50 Collaboration), Search for low-mass dark matter WIMPs with 12 ton-day exposure of DarkSide-50, Phys. Rev. D 107, 063001 (2023).
  3. J. Aalbers et al. (LZ Collaboration), Dark matter search results from 4.2  tonne−years of exposure of the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 135, 011802 (2025).
  4. E. Aprile et al. (XENON Collaboration), WIMP dark matter search using a 3.1  tonne×year exposure of the XENONnT experiment, arXiv:2502.18005.
  5. I. Alkhatib et al. (SuperCDMS Collaboration), Light dark matter search with a high-resolution athermal phonon detector operated above ground, Phys. Rev. Lett. 127, 061801 (2021).
  6. G. Angloher et al. (CRESST Collaboration), First observation of single photons in a CRESST detector and new dark matter exclusion limits, Phys. Rev. D 110, 083038 (2024).
  7. Rouven Essig, Jeremy Mardon, and Tomer Volansky, Direct detection of sub-GeV dark matter, Phys. Rev. D 85, 076007 (2012).
  8. Chris Kouvaris and Josef Pradler, Probing sub-GeV dark matter with conventional detectors, Phys. Rev. Lett. 118, 031803 (2017).
  9. A. B. Migdal, Ionizatsiya atomov pri yadernykh reaktsiyakh, Sov. Phys. JETP 9, 1163 (1939).
  10. A. Migdal, Ionizatsiya atomov pri yadernykh reaktsiyakh, Zh. Eksp. Teor. Fiz. 9, 1163 (1939).
  11. Masahiro Ibe, Wakutaka Nakano, Yutaro Shoji, and Kazumine Suzuki, Migdal effect in dark matter direct detection experiments, J. High Energy Phys. 03 (2018) 194.
  12. Lev Davidovich Landau and E. M. Lifshits, Quantum Mechanics: Non-Relativistic Theory, Course of Theoretical Physics Vol. 3 (Butterworth-Heinemann, Oxford, 1991).
  13. J. D. Vergados and H. Ejiri, The role of ionization electrons in direct neutralino detection, Phys. Lett. B 606, 313 (2005).
  14. Ch. C. Moustakidis, J. D. Vergados, and H. Ejiri, Direct dark matter detection by observing electrons produced in neutralino-nucleus collisions, Nucl. Phys. B727, 406 (2005).
  15. R. Bernabei et al., On electromagnetic contributions in WIMP quests, Int. J. Mod. Phys. A 22, 3155 (2007).
  16. Rouven Essig, Josef Pradler, Mukul Sholapurkar, and Tien-Tien Yu, Relation between the Migdal effect and dark matter-electron scattering in isolated atoms and semiconductors, Phys. Rev. Lett. 124, 021801 (2020).
  17. Peter Cox, Matthew J. Dolan, Christopher McCabe, and Harry M. Quiney, Precise predictions and new insights for atomic ionization from the Migdal effect, Phys. Rev. D 107, 035032 (2023).
  18. Matthew J. Dolan, Felix Kahlhoefer, and Christopher McCabe, Directly detecting sub-GeV dark matter with electrons from nuclear scattering, Phys. Rev. Lett. 121, 101801 (2018).
  19. Nicole F. Bell, James B. Dent, Jayden L. Newstead, Subir Sabharwal, and Thomas J. Weiler, Migdal effect and photon bremsstrahlung in effective field theories of dark matter direct detection and coherent elastic neutrino-nucleus scattering, Phys. Rev. D 101, 015012 (2020).
  20. Daniel Baxter, Yonatan Kahn, and Gordan Krnjaic, Electron ionization via dark matter-electron scattering and the Migdal effect, Phys. Rev. D 101, 076014 (2020).
  21. Zheng-Liang Liang, Lin Zhang, Fawei Zheng, and Ping Zhang, Describing Migdal effects in diamond crystal with atom-centered localized Wannier functions, Phys. Rev. D 102, 043007 (2020).
  22. C. P. Liu, Chih-Pan Wu, Hsin-Chang Chi, and Jiunn-Wei Chen, Model-independent determination of the Migdal effect via photoabsorption, Phys. Rev. D 102, 121303 (2020).
  23. Yonatan Kahn, Gordan Krnjaic, and Bashi Mandava, Dark matter detection with bound nuclear targets: The Poisson phonon tail, Phys. Rev. Lett. 127, 081804 (2021).
  24. Victor V. Flambaum, Liangliang Su, Lei Wu, and Bin Zhu, New strong bounds on sub-GeV dark matter from boosted and Migdal effects, Sci. China Phys. Mech. Astron. 66, 271011 (2023).
  25. Nicole F. Bell, James B. Dent, Bhaskar Dutta, Sumit Ghosh, Jason Kumar, and Jayden L. Newstead, Low-mass inelastic dark matter direct detection via the Migdal effect, Phys. Rev. D 104, 076013 (2021).
  26. Javier F. Acevedo, Joseph Bramante, and Alan Goodman, Accelerating composite dark matter discovery with nuclear recoils and the Migdal effect, Phys. Rev. D 105, 023012 (2022).
  27. Wenyu Wang, Ke-Yun Wu, Lei Wu, and Bin Zhu, Direct detection of spin-dependent sub-GeV dark matter via Migdal effect, Nucl. Phys. B983, 115907 (2022).
  28. Carlos Blanco, Ian Harris, Yonatan Kahn, Benjamin Lillard, and Jesús Pérez-Ríos, Molecular Migdal effect, Phys. Rev. D 106, 115015 (2022).
  29. Zheng-Liang Liang, Chongjie Mo, Fawei Zheng, and Ping Zhang, Describing the Migdal effect with a bremsstrahlung-like process and many-body effects, Phys. Rev. D 104, 056009 (2021).
  30. Simon Knapen, Jonathan Kozaczuk, and Tongyan Lin, Migdal effect in semiconductors, Phys. Rev. Lett. 127, 081805 (2021).
  31. Zheng-Liang Liang, Chongjie Mo, Fawei Zheng, and Ping Zhang, Phonon-mediated Migdal effect in semiconductor detectors, Phys. Rev. D 106, 043004 (2022); 106, 109901(E) (2022).
  32. Kim V. Berghaus, Angelo Esposito, Rouven Essig, and Mukul Sholapurkar, The Migdal effect in semiconductors for dark matter with masses below ∼100  MeV, J. High Energy Phys. 01 (2023) 023.
  33. Jiwei Li, Liangliang Su, Lei Wu, and Bin Zhu, Spin-dependent sub-GeV inelastic dark matter-electron scattering and Migdal effect. Part I. Velocity independent operator, J. Cosmol. Astropart. Phys. 04 (2023) 020.
  34. Nicole F. Bell, Peter Cox, Matthew J. Dolan, Jayden L. Newstead, and Alexander C. Ritter, Exploring light dark matter with the Migdal effect in hydrogen-doped liquid xenon, Phys. Rev. D 109, L091902 (2024).
  35. Zai Yun, Junwei Sun, Bin Zhu, and Xuewen Liu, Probing inelastic signatures of dark matter detection via polarized nucleus*, Chin. Phys. C 48, 103106 (2024).
  36. Yuchao Gu, Jie Tang, Lei Wu, and Bin Zhu, Probing light DM via the Migdal effect with spherical proportional counter*, Chin. Phys. C 47, 125105 (2023).
  37. Gonzalo Herrera, A neutrino floor for the Migdal effect, J. High Energy Phys. 05 (2024) 288.
  38. Yu-Feng Li and Shuo-yu Xia, Migdal effect of phonon-mediated neutrino nucleus scattering in semiconductor detectors, Nucl. Phys. B1006, 116632 (2024).
  39. Wakutaka Nakano, Comparison of the Migdal transition probabilities in electron-atom inelastic cross sections, arXiv:2410.16911.
  40. Tarak Nath Maity, Neutrinos as background and signal in Migdal search, Phys. Rev. D 111, 123020 (2025).
  41. E. Aprile et al. (XENON Collaboration), Search for light dark matter interactions enhanced by the Migdal effect or bremsstrahlung in XENON1T, Phys. Rev. Lett. 123, 241803 (2019).
  42. P. Agnes et al. (DarkSide Collaboration), Search for dark-matter–nucleon interactions via Migdal effect with DarkSide-50, Phys. Rev. Lett. 130, 101001 (2023).
  43. Duncan Adams, Daniel Baxter, Hannah Day, Rouven Essig, and Yonatan Kahn, Measuring the Migdal effect in semiconductors for dark matter detection, Phys. Rev. D 107, L041303 (2023).
  44. Jingke Xu et al., Search for the Migdal effect in liquid xenon with keV-level nuclear recoils, Phys. Rev. D 109, L051101 (2024).
  45. Prakruth Adari et al. (SENSEI Collaboration), First direct-detection results on sub-GeV dark matter using the SENSEI detector at SNOLAB, Phys. Rev. Lett. 134, 011804 (2025).
  46. Yonatan Kahn and Jesús Pérez-Ríos, Measuring the molecular Migdal effect with neutron scattering on diatomic gases, Phys. Rev. D 110, 092012 (2024).
  47. Max Born and Kun Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, New York, 1996).
  48. Steven Weinberg, Lectures on Quantum Mechanics (Cambridge University Press, Cambridge, England, 2015).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation