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Many-body quantum muon effects and quadrupolar coupling in solids

Gomilšek, Matjaž; Pratt, Francis L.; Cottrell, Stephen P.; Clark, Stewart J.; Lancaster, Tom

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Matjaž Gomilšek

Francis L. Pratt

Stephen P. Cottrell

Stewart J. Clark


Strong quantum zero-point motion (ZPM) of light nuclei and other particles is a crucial aspect of many state-of-the-art quantum materials. However, it has only recently begun to be explored from an ab initio perspective, through several competing approximations. Here we develop a unified description of muon and light nucleus ZPM and establish the regimes of anharmonicity and positional quantum entanglement where different approximation schemes apply. Via density functional theory and path-integral molecular dynamics simulations we demonstrate that in solid nitrogen, α–N2, muon ZPM is both strongly anharmonic and many-body in character, with the muon forming an extended electric-dipole polaron around a central, quantum-entangled [N2–μ–N2]+ complex. By combining this quantitative description of quantum muon ZPM with precision muon quadrupolar level-crossing resonance experiments, we independently determine the static 14N nuclear quadrupolar coupling constant of pristine α–N2 to be –5.36(2) MHz, a significant improvement in accuracy over the previously-accepted value of –5.39(5) MHz, and a validation of our unified description of light-particle ZPM.


Gomilšek, M., Pratt, F. L., Cottrell, S. P., Clark, S. J., & Lancaster, T. (2023). Many-body quantum muon effects and quadrupolar coupling in solids. Communications Physics, 6(1),

Journal Article Type Article
Acceptance Date Jun 2, 2023
Online Publication Date Jun 16, 2023
Publication Date 2023
Deposit Date Jun 19, 2023
Publicly Available Date Aug 16, 2023
Journal Communications Physics.
Electronic ISSN 2399-3650
Publisher Nature Research
Volume 6
Issue 1
Public URL


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