Future perspective of muons; a quantum particle measuring quantum processes

Adam Berlie; Alex Louat; John Wilkinson; Rhea Stewart; Sayani Biswas

Future perspective of muons; a quantum particle measuring quantum processes

T0 review · 0 major / 9 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This perspective argues that muon spin spectroscopy is best understood, and best advanced, by treating the implanted muon as a quantum particle embedded in the quantum system it measures, so the measured signal is the time evolution of a…

desk verdict A clearly-written, honest perspective on treating the muon as a quantum probe; the physics is sound and the roadmap is plausible, though the computational scaling premise remains unproven. read the letter →

arxiv 2608.10856 v1 pith:LJKEL47O submitted 2026-08-11 cond-mat.other quant-ph

Adam Berlie , Sayani Biswas , Alex Louat , Rhea Stewart , John Wilkinson This is my paper · ORCID

classification cond-mat.otherquant-ph

keywords muonspinspectroscopymuSRquantumprobeHamiltonianentanglementmuoniumRF-munegativeanalysis

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This perspective argues that muon spin spectroscopy (µSR) should be understood, and pushed forward, by embracing the muon as a quantum particle embedded in the quantum mechanical environment it measures. On this view the measured signal is not a classical precession in a local field but the time evolution of a coupled muon–matter Hamiltonian, a distinction that matters whenever dipolar, hyperfine, or quadrupolar couplings entangle the muon with surrounding spins. The authors propose that the field's future lies in moving from phenomenological relaxation functions toward Hamiltonian-based interpretation, in actively manipulating the muon spin with radio-frequency, microwave, and optical excitation, and in exploiting negative muons for bulk elemental analysis. If this direction is right, µSR becomes a way to read off local microscopic interactions directly from a bulk signal.

What carries the argument

The central object is the local muonic Hamiltonian $H_0$, with the measured polarisation given by $P_z^\mu(t) = \operatorname{Tr}(e^{iH_0 t}\rho_0 e^{-iH_0 t}\sigma_z^\mu)$, where $\rho_0$ is the initial density matrix of the muon and its environment. The load-bearing example is the F–µ coupled spin cluster, where the quantum spin-$1/2$ treatment of dipolar interactions yields energy levels and a polarisation function that a classical vector-spin model cannot reproduce; this is what motivates interpreting spectra through Hamiltonians rather than relaxation functions. Active manipulation adds a drive term $H_{\mathrm{drive}}(t)$ to $H_0$, turning the muon into a handle for local quantum-state control.

What would settle it

A concrete test would be to take a well-characterised material such as a spin liquid or battery cathode and show either that a Hamiltonian-derived polarisation function cannot be computed within practical computational resources, or that a classical vector-spin model reproduces the measured µSR spectrum just as well, eliminating the predictive advantage the quantum treatment claims.

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Extended reading notes

Core claim

The central claim is that the muon is a quantum particle embedded within a quantum mechanical environment, so the µSR asymmetry is a direct time-domain readout of the quantum evolution under the local Hamiltonian $H_0$. The paper's worked example is the fluorine–muon spin cluster: a quantum spin-$1/2$ calculation of the zero-field polarisation function differs substantially from a classical vector-spin description, showing that experiments rarely measure a field in isolation but rather the consequence of quantum evolution under the local Hamiltonian. The authors therefore argue that future progress comes from treating the muon as an infinitely dilute quantum defect whose spin evolution reports how that defect couples to the material, and from adding time-dependent drive terms to actively manipulate the coupled system. The same reframing extends to muonium as a light hydrogen isotope and to negative-muon X-ray and lifetime studies of chemical composition.

Load-bearing premise

The forward-looking roadmap assumes that computing a muon polarisation function from a microscopic Hamiltonian will become computationally practical for realistic materials; if electronic-structure, quantum-spin, and data-analysis tools cannot reach that point, the recommended shift from fitting relaxation functions to first-principles simulation remains out of reach for most systems.

Editorial extensions

If this is right

µSR analysis should shift from fitting static or dynamic Kubo–Toyabe relaxation functions to calculating polarisation functions from microscopic Hamiltonians, tying spectra to stopping sites, bonding, nuclear-spin networks, and charge density.
RF, microwave, and optical excitation become first-class tools: RF can drive or decouple muon–nuclear transitions, microwave can coherently control muonium states, and laser–µSR acts as a pump–probe of photoinduced material changes.
Muonium, as a light hydrogen isotope with enhanced zero-point motion and tunnelling, can expose nuclear quantum effects in chemical reactions and probe transient radical intermediates, including in catalysis.
Negative-muon X-ray and lifetime measurements give depth-selective, non-destructive elemental composition maps, with muonic X-rays penetrating millimetres into samples where X-ray fluorescence only reaches micrometres.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If Hamiltonian-based interpretation becomes routine, µSR spectra could serve as benchmark data for quantum simulation methods, with small entangled clusters like F–µ providing controlled testbeds for decoherence models.
Treating the muon as a deliberately introduced quantum defect suggests a design principle: choose stopping-site chemistry to engineer specific couplings, in effect using the muon as a tunable local quantum sensor rather than a probe to be corrected for.
A testable extension would be to compare Hamiltonian-predicted polarisation functions against classical-vector predictions for a series of ionic conductors, to see empirically where the quantum treatment changes the inferred diffusion parameters.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a perspective from the ISIS muon group, not a research paper. It makes a decent, well-written case for treating the muon as a quantum probe and shifting muSR analysis from phenomenological relaxation functions toward Hamiltonian-based interpretation. The physics is sound and the citations are appropriate, but the forward-looking roadmap leans on a computational-feasibility assumption that the paper itself only frames as a hope.

What is genuinely useful: the paper does a good job explaining, for a non-specialist, why the classical picture of muSR is incomplete, with the fluorine-muon example (Figure 3) nicely showing the quantum vs classical discrepancy. It also bundles together a clean survey of active control directions: RF-µSR, microwave control of muonium, laser pump-probe, and THz-pump speculation, plus a solid overview of negative-muon elemental analysis. The writing is clear and honestly cites Celio-Meier and later work as the origin of the quantum treatment. As a perspective, it is a fair map of the field.

Soft spots: first, novelty is essentially zero in the sense that no new equations, data, or derivations appear; that is fine for a perspective, but it means the value is in the framing. Second, the central recommendation—that the field move from Kubo-Toyabe fitting to Hamiltonian-based simulation—rests on the premise that this can scale to realistic materials with many nuclear and electronic degrees of freedom. The cited proof-of-principle works (refs 38-42) are mostly small clusters or DFT site calculations, not end-to-end accuracy checks. The authors acknowledge this indirectly with 'as computational methods... improve,' so it is not a hidden flaw, but it does mean the roadmap is aspirational rather than demonstrated. Third, minor blemishes: Table 2's quadrupolar form looks misprinted (S indices instead of I), and a few typo-level errors. None of this undermines the central message.

Who is this for? New graduate students and scientists wanting an accessible entry point to muSR's quantum perspective, and possibly funders or strategists thinking about future facility capabilities. Established practitioners will not learn much new physics. It deserves a serious referee because it is a well-crafted perspective from a major facility group that could shape community priorities; it should be published with minor revisions, not desk-rejected. My verdict: send it to review, just do not expect a groundbreaking result.

Referee Report

0 major / 9 minor

Summary. This paper is a perspective on muon spin rotation, relaxation, and resonance (muSR). The authors argue that the positive muon is not merely a classical local magnetometer but a quantum spin-1/2 particle embedded in a quantum environment, so that the measured polarization is generated by coherent time evolution under the local Hamiltonian of the coupled muon-matter system (Eq. 2). They advocate a shift from phenomenological relaxation-function fits toward Hamiltonian-based interpretation, the active manipulation of muon spin states with RF, microwave, and optical fields, and the use of muonium as a light hydrogen isotope. The paper also reviews negative-muon X-ray and lifetime techniques for elemental analysis. The manuscript is a perspective rather than a research article and contains no new derivations; its contribution is a unifying viewpoint and a roadmap for future work.

Significance. The perspective is timely and generally well grounded. It correctly identifies the quantum character of the muon probe and cites the key historical and recent work (Celio-Meier, Wilkinson-Blundell, muon-fluorine entanglement studies). The illustrative comparison between quantum and classical dipolar spin dynamics in Fig. 3 is effective, and the discussion of active manipulation (RF-muSR, microwave-muSR, laser-muSR, and possible THz-pump muSR) is an original and useful synthesis. If the proposed Hamiltonian-based interpretation is adopted, it could change analysis practice and experimental design across the field. The paper is honest about the continued value of Kubo-Toyabe models and about the need for computational improvements, which makes the roadmap plausible. The main caveat is that the forward-looking recommendation depends on computational feasibility that is not yet demonstrated for realistic materials, but this is a limitation of the perspective genre rather than an internal inconsistency.

minor comments (9)

[Table 2] In the Dipole-Dipole Hamiltonian, the anisotropic term is written with the same spin vector S_i in both factors; the second factor should involve S_j, specifically (S_j dot r_hat_ij). Please correct this typo, given the paper's emphasis on using these Hamiltonians.
[Table 1] The electron magnetic moment is listed as 647 mu_p, but the measured value is approximately 658 mu_p. Please verify and correct this value.
[Abstract and 'A Brief Introduction to Muon Spin Spectroscopy'] The mass statement '1/9 m_p or 207 m_e' should be phrased as 'about 1/9 m_p (207 m_e)' or '1/9 m_p ≈ 207 m_e' for consistency, since 207/1836 ≈ 1/8.87.
[Figure 1 caption] The label 'diamagnetic muonium' is not standard terminology; muonium denotes the paramagnetic muon-electron bound state, while the diamagnetic species is usually called a diamagnetic muon or diamagnetic muon state. Please rephrase the label and caption to avoid confusion.
[Advancing knowledge of chemical composition] The sentence 'The Li muonic X-rays, not visible in Fig. 5(a) are easily identified in Fig. 5(b)' is inconsistent with Fig. 5(b) being a lifetime spectrum. Please rephrase, for example, 'The Li component is easily identified in the lifetime spectrum in Fig. 5(b).'
[References] Reference 10 is missing the journal name; please complete the bibliographic details (journal, volume, article number, year).
[References] Reference 84 is listed as 'Forthcoming, To be Submitted'; this is not a citable reference. Please provide a preprint identifier, cite it as a personal communication, or remove the citation.
[The muon as a quantum probe embedded in a quantum system] In the paragraph after Table 2, the statement that it is 'increasingly realistic' to calculate the muon polarization from microscopic Hamiltonians is supported by refs 38-42, which are mostly proof-of-principle demonstrations on small clusters or idealized model systems. I suggest adding one or two sentences acknowledging the gap between these demonstrations and routine application to realistic materials, and identifying the main computational bottlenecks (e.g., size of the nuclear spin bath, stopping-site uncertainties, decoherence timescales). This would strengthen the roadmap's credibility.
[Throughout] Minor typos and formatting: 'larmor precession' should be 'Larmor precession'; 'M¨ ossbauer' should be 'Mössbauer'; the Fig. 2 caption lacks a period after 'spectroscopy'; and 'the dipole-dipole interactions was used' should be 'the dipole-dipole interaction was used'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a perspective making interpretive and programmatic claims; its central Eq. (2) is a definitional statement, not a prediction derived from fitted inputs.

full rationale

The manuscript is a forward-looking perspective, not a derivation. The central quantitative statement is Eq. (2), P_z^mu(t) = Tr(e^{iH0t} rho0 e^{-iH0t} sigma_z^mu), which defines the muon polarization as time evolution under a Hamiltonian; this is the standard quantum-mechanical definition and is not obtained by fitting a parameter and then predicting the same quantity. The recommendation to move from Kubo-Toyabe phenomenological relaxation functions to Hamiltonian-based interpretation is a research direction; its support [38-42] is cited as proof-of-principle computational demonstrations, and the text explicitly frames scalability as an improving prospect (“as computational methods… improve”), not as a demonstrated result. The frequent self-citations (e.g., refs 16, 30, 31, 45, 55, 84) support specific experimental/computational examples or ongoing work; none is invoked as a uniqueness theorem or as the sole justification of the central thesis. The skeptic concern that Hamiltonian-based analysis may not scale to realistic materials is a feasibility/aspiration risk, not a circularity: the roadmap does not define its conclusion into its premises. Therefore no circular step can be identified by the paper's equations or citations, and the honest finding is score 0.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The paper introduces no free parameters and no new entities. Its arguments rest on standard quantum mechanical formalism and established domain knowledge. The only 'fit' in the paper is the illustrative quantum calculation in Figure 3, which is not fitted to data but computed from a known Hamiltonian.

assumptions (3)

standard math The muon is a spin-1/2 quantum particle whose spin evolution is governed by a local Hamiltonian, as expressed in Eq. (2).
This is the foundational premise of the quantum framing, invoked throughout the paper (e.g., 'The muon as a quantum probe' section). It is standard quantum mechanics and not introduced ad hoc.
domain assumption Muonium behaves as a light isotope of hydrogen with reduced mass approximately one ninth of the hydrogen atom.
Stated in the 'Quantum Chemistry' section and Table 3. This is an established approximation in muonium chemistry, supported by prior literature.
standard math The measured experimental asymmetry is directly proportional to the muon spin polarization expectation value defined by Eq. (2).
This is a standard result of muSR theory, referenced to a textbook (ref 6). It underpins the claim that the time-domain signal reads out the local Hamiltonian evolution.

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Cite this review

Pith. "Pith review of Future perspective of muons; a quantum particle measuring quantum processes." pith.science (2026). https://pith.science/paper/LJKEL47O

@misc{pith2026260810856,
  author       = {Pith},
  title        = {Pith review of: Future perspective of muons; a quantum particle measuring quantum processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LJKEL47O}},
  note         = {Machine review of arXiv:2608.10856}
}

abstract

Although considered a niche technique, muon spectroscopy provides a unique and complementary insight into a range of different materials from hard condensed matter to biological samples and everything in between. In matter, the muon has a mass of $\frac{1}{9}~m_p$ or $207~m_e$, and is a local probe of quantum states that can provide a focus on the bulk properties of materials. While often interpreted in a classical framework, the muon is itself a quantum particle and it is increasingly common for researchers to take account of this when thinking about muon spectroscopy experiments. In this perspective, we focus on the power of using this quantum treatment of muon spectroscopy, which is a key future direction for the technique.

Figures

Figures reproduced from arXiv: 2608.10856 by the authors.

**Figure 2.** Comparison of the dynamical ranges accessed by selected spectroscopic and scattering techniques.(a) Approximate characteristic energy scales , E = ¯hω, and, for scattering techniques, momentum transfer ranges. Local and bulk probes are shown on the right using an equivalent energy scale derived from their characteristic frequencies. (b) Approximate frequency and corresponding time-scale windows accessible to reman… view at source ↗

**Figure 3.** a) Energy levels of the F–µ pair as a function of the magnetic field Bz, with the F–µ bond oriented along the x-axis. Only the dipolar coupling and an external magnetic field applied along the z-axis are included. The inset shows the geometry considered. b) Zero-field (ZF) muon polarisation function for unpolarised initial fluorine spins, calculated using quantum spin-1/2 dipolar dynamics and classical vector-spin d… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Excitation frequency and energy scales from kHz to PHz, illustrating representative [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]

**Figure 5.** Figure 5: Pictorial representation of the different quantum processes that take place in a [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

[1]

(1) UK Government The UK’s Modern Industrial Strategy 2025.https://www.gov.uk/ government/collections/the-uks-modern-industrial-strategy-2025, 2025; Ac- cessed June 15,

work page 2025
[15]

(81) Yamazaki, T.; Nagamine, K.; Nagamiya, S.; Hashimoto, O.; Sugimoto, K.; Nakai, K.; Kobayashi, S

2026; p 011004. (81) Yamazaki, T.; Nagamine, K.; Nagamiya, S.; Hashimoto, O.; Sugimoto, K.; Nakai, K.; Kobayashi, S. Negative Moun Spin Rotation.Physica Scripta1975,11,

work page 2026
[142]

J.; Bonf` a, P.; De Renzi, R.; Monacelli, L.; Mauri, F.; Calandra, M.; Er- rea, I

(39) Onuorah, I. J.; Bonf` a, P.; De Renzi, R.; Monacelli, L.; Mauri, F.; Calandra, M.; Er- rea, I. Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation.Phys. Rev. Mater.2019,3, 073804. (40) Goli, M.; Shahbazian, S. Two-Component Density Functional Theory for Muonic Molecules: Inclusion of the Electron–Pos...

work page 2019
[150]

J.; Cottrell, S

(54) Billington, D.; Riordan, E.; Salman, M.; Margineda, D.; Gill, G. J.; Cottrell, S. P.; McKenzie, I.; Lancaster, T.; Graf, M. J.; Giblin, S. R. Radio-frequency manipulation of state populations in an entangled fluorine-muon-fluorine system.Physical Review Letters2022,129, 077201. 28 (55) Chatterjee, D.; Huddart, B. M.; Wu, H. C.; Prabhakaran, D.; Louat...

work page arXiv
[165]

V.; Butcher, K.; Ishida, K.; Green, G.; Paul, D

(75) Hampshire, B. V.; Butcher, K.; Ishida, K.; Green, G.; Paul, D. M.; Hillier, A. D. Using Negative Muons as a Probe for Depth Profiling Silver Roman Coinage.Heritage2019, 2, 400–407. (76) Ninomiya, K.; Kubo, M. K.; Strasser, P.; Nagatomo, T.; Kobayashi, Y.; Ishida, K.; Higemoto, W.; Kawamura, N.; Shimomura, K.; Miyake, Y.; others Elemental analysis of ...

work page 2015
[305]

J.; Bonf` a, P.; De Renzi, R

(19) Onuorah, I. J.; Bonf` a, P.; De Renzi, R. Muon contact hyperfine field in metals: A DFT calculation.Phys. Rev. B2018,97, 174414. (20) McClelland, I.; Johnston, B.; Baker, P. J.; Amores, M.; Cussen, E. J.; Corr, S. A. Muon Spectroscopy for Investigating Diffusion in Energy Storage Materials.Ann. Rev. Mater. Res.2020,50,

work page 2020
[371]

U.; Kadono, R

24 (21) Ito, T. U.; Kadono, R. Distinguishing Ion Dynamics from Muon Diffusion in Muon Spin Relaxation.J. Phys. Soc. Jpn.2024,93, 044602. (22) McMullen, T.; Zaremba, E. Positive-Muon Spin Depolarization in Solids.Physical Re- view B1978,18, 3026–3040. (23) Maeter, H.; Luetkens, H.; Pashkevich, Y. G.; Kwadrin, A.; Khasanov, R.; Amato, A.; Gusev, A. A.; Lam...

work page 2024
[701]

Muon hyperfine interactions in magnetic oxides.Hyperfine Interact.1984, 17,

(18) Boekema, C. Muon hyperfine interactions in magnetic oxides.Hyperfine Interact.1984, 17,

work page 1984

Show all 15 references

[785]

M.; Blundell, S

(16) Wilkinson, J. M.; Blundell, S. J. Information and Decoherence in a Muon-Fluorine Coupled System.Phys. Rev. Lett.2020,125, 087201. (17) Estle, T. L. Review of experimental studies of muonium centers in semiconductors. Hyperfine Interact.1985,25,

2020
[850]

(13) Celio, M.; Meier, P. F. Spin relaxation of positive muons due to dipolar interactions. Phys. Rev. B1983,27, 1908–1910. (14) Brewer, J. H.; Kreitzman, S. R.; Noakes, D. R.; Ansaldo, E. J.; Harshman, D. R.; Keitel, R. Observation of muon-fluorine ”hydrogen bonding” in ionic...

1908
[1336]

Light-induced collective pseudospin precession res- onating with Higgs mode in a superconductor.Science2014,345, 1145–1149

(62) Matsunaga, R.; Tsuji, N.; Fujita, H.; Sugioka, A.; Makise, K.; Uzawa, Y.; Terai, H.; Wang, Z.; Aoki, H.; Shimano, R. Light-induced collective pseudospin precession res- onating with Higgs mode in a superconductor.Science2014,345, 1145–1149. (63) Reidy, J. J.; Hutson, R. L...

2022
[2024]

L.; Lederman, L

(8) Garwin, R. L.; Lederman, L. M.; Weinrich, M. Observations of the Failure of Conser- vation of Parity and Charge Conjugation in Meson Decays: the Magnetic Moment of the Free Muon.Phys. Rev.1957,105, 1415–1417. (9) Sugiyama, J.; Umegaki, I.; Nozaki, H.; Higemoto, W.; Hamada,...

1957
[2026]

pdf, 2025; Accessed June 15,

(2) Executive Office of the President Fiscal Year 2027 Administration Re- search and Development Budget Priorities and Cross-Cutting Actions (M-25- 34, NSTM-2).https://www.whitehouse.gov/wp-content/uploads/2025/09/ 22 M-25-34-NSTM-2-Fiscal-Year-FY-2027-Administration-Research-...

2027
[2890]

P.; Giblin, S

(58) Cottrell, S. P.; Giblin, S. R. New capabilities at pulsed muon facilities with pulsed radio-frequency techniques. Proceedings of the 14th International Conference on Muon Spin Rotation, Relaxation and Resonance (µSR2017). 2018; p 011050. (59) Estle, T.; Vanderwater, D. Th...

2018
[7529]

P.; Lord, J

(32) McKenzie, I.; Scheuermann, R.; Cottrell, S. P.; Lord, J. S.; Tucker, I. M. Hyperfine cou- pling constants of the cyclohexadienyl radical in benzene and dilute aqueous solution. The Journal of Physical Chemistry B2013,117, 13614–13618. (33) Dehn, M. H.; Scheuermann, R.; Wa...

2021

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

(1) UK Government The UK’s Modern Industrial Strategy 2025.https://www.gov.uk/ government/collections/the-uks-modern-industrial-strategy-2025, 2025; Ac- cessed June 15,

work page 2025

[2] [15]

(81) Yamazaki, T.; Nagamine, K.; Nagamiya, S.; Hashimoto, O.; Sugimoto, K.; Nakai, K.; Kobayashi, S

2026; p 011004. (81) Yamazaki, T.; Nagamine, K.; Nagamiya, S.; Hashimoto, O.; Sugimoto, K.; Nakai, K.; Kobayashi, S. Negative Moun Spin Rotation.Physica Scripta1975,11,

work page 2026

[3] [142]

J.; Bonf` a, P.; De Renzi, R.; Monacelli, L.; Mauri, F.; Calandra, M.; Er- rea, I

(39) Onuorah, I. J.; Bonf` a, P.; De Renzi, R.; Monacelli, L.; Mauri, F.; Calandra, M.; Er- rea, I. Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation.Phys. Rev. Mater.2019,3, 073804. (40) Goli, M.; Shahbazian, S. Two-Component Density Functional Theory for Muonic Molecules: Inclusion of the Electron–Pos...

work page 2019

[4] [150]

J.; Cottrell, S

(54) Billington, D.; Riordan, E.; Salman, M.; Margineda, D.; Gill, G. J.; Cottrell, S. P.; McKenzie, I.; Lancaster, T.; Graf, M. J.; Giblin, S. R. Radio-frequency manipulation of state populations in an entangled fluorine-muon-fluorine system.Physical Review Letters2022,129, 077201. 28 (55) Chatterjee, D.; Huddart, B. M.; Wu, H. C.; Prabhakaran, D.; Louat...

work page arXiv

[5] [165]

V.; Butcher, K.; Ishida, K.; Green, G.; Paul, D

(75) Hampshire, B. V.; Butcher, K.; Ishida, K.; Green, G.; Paul, D. M.; Hillier, A. D. Using Negative Muons as a Probe for Depth Profiling Silver Roman Coinage.Heritage2019, 2, 400–407. (76) Ninomiya, K.; Kubo, M. K.; Strasser, P.; Nagatomo, T.; Kobayashi, Y.; Ishida, K.; Higemoto, W.; Kawamura, N.; Shimomura, K.; Miyake, Y.; others Elemental analysis of ...

work page 2015

[6] [305]

J.; Bonf` a, P.; De Renzi, R

(19) Onuorah, I. J.; Bonf` a, P.; De Renzi, R. Muon contact hyperfine field in metals: A DFT calculation.Phys. Rev. B2018,97, 174414. (20) McClelland, I.; Johnston, B.; Baker, P. J.; Amores, M.; Cussen, E. J.; Corr, S. A. Muon Spectroscopy for Investigating Diffusion in Energy Storage Materials.Ann. Rev. Mater. Res.2020,50,

work page 2020

[7] [371]

U.; Kadono, R

24 (21) Ito, T. U.; Kadono, R. Distinguishing Ion Dynamics from Muon Diffusion in Muon Spin Relaxation.J. Phys. Soc. Jpn.2024,93, 044602. (22) McMullen, T.; Zaremba, E. Positive-Muon Spin Depolarization in Solids.Physical Re- view B1978,18, 3026–3040. (23) Maeter, H.; Luetkens, H.; Pashkevich, Y. G.; Kwadrin, A.; Khasanov, R.; Amato, A.; Gusev, A. A.; Lam...

work page 2024

[8] [701]

Muon hyperfine interactions in magnetic oxides.Hyperfine Interact.1984, 17,

(18) Boekema, C. Muon hyperfine interactions in magnetic oxides.Hyperfine Interact.1984, 17,

work page 1984