Pith. sign in

REVIEW 3 major objections 4 minor 34 references

Depth profiling the elemental composition with negative muons: Monte Carlo based tools for improved data analysis

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that coupling muonic X-ray depth profiles with Monte Carlo stopping simulations determines the thickness of a surface gold layer on copper alloys to about ±1 µm, in agreement with SEM measurements.

desk verdict A useful proof-of-concept for muonic depth profiling of gold layers, but the EM2 discrepancy and tuned parameters mean the ±1 µm claim needs a stronger uncertainty treatment. read the letter →

arxiv 2505.04679 v1 pith:3DPIGNW7 submitted 2025-05-07 physics.chem-ph physics.app-ph

M.Cataldo , A.D Hillier , O.Cremonesi , F.Grazzi , S.Porcinai , M.Clemenza This is my paper · ORCID
classification physics.chem-phphysics.app-ph
keywords muonspectroscopydepthprofilingelementalanalysisarchaeometrymuonicX-rayMonteCarlosimulationgildingthickness
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

Muonic atom X-ray emission spectroscopy (µ-XES) can see tens of microns to centimetres into a material, but turning its depth scans into a layer thickness has been mostly qualitative. The paper proposes a quantitative route: simulate where negative muons stop in a layered sample with two Monte Carlo codes, GEANT4/ARBY and SRIM/TRIM, and compare the simulated depth profile with the measured muonic X-ray profile by reduced chi-square. Applied to standard gilded copper-alloy foils, the method recovers the gold layer thickness to about ±1 µm, matching SEM measurements. If it works, restorers and curators could measure gildings, patinas, and corrosion crusts without cutting or sampling the object.

What carries the argument

The load-bearing object is the momentum-scan depth profile: a series of muonic X-ray spectra taken at increasing beam momenta, in which each element's fitted peak area is plotted against momentum. The comparison engine is the reduced chi-square between measured and simulated profiles, computed over all momentum runs including zero-intensity runs. The simulation chain uses GEANT4/ARBY, a detailed-geometry Monte Carlo transport code, and SRIM/TRIM, a layered stopping-and-range code run with a hydrogen ion of one-ninth the muon mass, to output the number of stopped muons per layer; the paper assumes this number is proportional to the measured X-ray intensity. The muon itself is the physical enabler: at 207 times the electron mass, its cascade X-rays reach hundreds of keV to MeV, escaping from deep inside metals and giving the technique its non-destructive penetration.

What would settle it

Measure a multilayer standard of known composition (for example gold on nickel on copper) with a precisely machined gold thickness, run the full momentum scan, and fit it. If the best-fit simulated thickness disagrees with the known thickness by more than the claimed ±1 µm, or if switching to a substrate with very different muon capture properties shifts the fitted thickness while SEM confirms a constant gold thickness, the proportionality assumption is wrong. A more targeted check is to measure the actual beam momentum spread at the sample position; if it is 4% while simulations require 5%, the method is compensating for an unmodelled effect rather than measuring thickness cleanly.

Watch

Extended reading notes

Core claim

The paper's central claim is that a layer's thickness can be recovered by matching a simulated muon-stopping depth profile to a measured one. Because a negative muon stopped in a layer produces that layer's characteristic muonic X-rays, the authors assume the full-energy peak intensity from a layer is proportional to the number of muons stopped there. They scan the muon beam momentum so that muons stop at increasing depths, build momentum-dependent profiles for gold, nickel, copper, aluminium, and nitrogen, then vary the simulated gold thickness until the reduced chi-square between simulated and measured profiles is minimized. For electroplated samples, the best-fit gold thicknesses are 3.5±1, 4.5±1, and 7.5±1 µm against SEM values of 3.3±0.2, 4.6±0.6, and 7.3±0.8 µm; for the amalgam-gilded brass sample the best fit is 11±1 µm versus 11±1 µm by SEM, and for the bronze sample the best fit is 5±1 µm with a 20% reduced gold density to mimic surface unevenness and air pockets. Both simulation codes agree, with GEANT4/ARBY handling thin layers better than SRIM/TRIM.

Load-bearing premise

The whole method assumes that the intensity of a layer's muonic X-ray peak is directly proportional to the number of muons stopped in that layer; if capture probabilities, cascade yields, or muon transfer between layers vary, the fitted thickness will be biased.

Editorial extensions

If this is right

  • Artworks with metal gildings, patinas, or corrosion crusts of ten to a few tens of microns can be measured non-destructively, recovering the thickness of each identifiable layer with about a micrometre of uncertainty.
  • The same profile-matching protocol applies to any layered material in which each layer has a distinct muonic X-ray line, including buried layers beneath thick outer shells that XRF and PIXE cannot see.
  • A quick open-source simulation route (SRIM/TRIM) gives usable thickness estimates, while a detailed-geometry code (GEANT4/ARBY) improves accuracy for thin or irregular layers.
  • Because the method reads the full layer sequence in one momentum scan, it yields not just the coating thickness but also information about the substrate and intermediate layers, such as nickel under gold.
  • For irregular or porous layers, the fit can absorb thickness variations as an effective density reduction, allowing the method to flag uneven gilding even when the nominal thickness is unknown.

Reading between the lines

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

  • If the stopped-muon-to-X-ray proportionality is verified layer by layer, the method could be extended from thickness fitting to quantitative per-layer composition, because the same machinery would then connect absolute peak intensities to elemental concentrations.
  • The reported ±1 µm uncertainty is set by the momentum spread and by the chi-square step size; a direct measurement of the beam's momentum distribution at the sample would likely tighten the error and remove the need to tune spread and source distance by hand.
  • The effective-density trick used for the uneven amalgam-gilded bronze suggests a testable extension: porosity of a gilding could be estimated from the density reduction needed to reach a best fit, giving conservators a quantitative measure of layer quality.
  • The same reduced-chi-square matching could be transferred to other depth-sensitive probes, but the muon's centimetre reach makes it uniquely suited to layered metal artefacts, where competing surface techniques lose signal.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a data-analysis protocol for muonic atom X-ray emission spectroscopy (μ-XES) in which Monte Carlo simulations (GEANT4/ARBY and SRIM/TRIM) are matched to measured muon stopping depth profiles to determine the thickness of a superficial gold layer. The method is demonstrated on two sets of gilded copper-alloy standards: three electroplated foils (EPA, EPB, EPC) and two amalgam-gilded foils (SM3, EM2). The simulated depth profiles are compared with measured normalised peak areas via reduced chi-square, with the gold thickness as the fitted parameter. The authors report best-fit thicknesses of 3.5±1, 4.5±1, and 7.5±1 µm for EPA, EPB, and EPC (SEM: 3.3±0.2, 4.6±0.6, 7.3±0.8 µm), 11±1 µm for SM3 (SEM: 11±1 µm), and 5±1 µm for EM2, the last with no SEM value listed in Table 2. The central claim is that the two simulation tools, despite their different approaches, yield consistent thickness estimates that agree with the SEM characterisation to within about ±1 µm.

Significance. If the ±1 µm accuracy claim holds, the protocol would be a valuable non-destructive depth-profiling tool for heritage science, where gilding and alteration layers of tens of microns are otherwise difficult to assess. The paper's strengths include the use of two independent simulation codes, a straightforward reduced-chi-square comparison criterion, open data links for the ISIS beamtime, and a clear validation design against SEM on multiple standard samples. The approach is falsifiable in principle: each sample's fitted thickness can be checked against an independent reference. However, the significance is substantially reduced by the incomplete validation record for EM2 and by the post-hoc adjustment of several physical inputs, which means the reported ±1 µm uncertainty is not yet established as a general systematic error budget.

major comments (3)
  1. [§2.2 and Table 2]
  2. [§2.1 and Discussion]
  3. [§1.1 and §1.4]
minor comments (4)
  1. [Figure 4 and Figure 5]
  2. [§2.2]
  3. [Figure 4d]
  4. [§2.1]

Circularity Check

2 steps flagged · score 6.0 of 10

Validation is partially circular: the gold-thickness search range is centered on the SEM values later used as the reference, so the claimed agreement is partly built into the scan.

  1. fitted input called prediction [Section 2.1, first paragraph (Electroplated samples)]
    "For each sample, simulations with different gold layer sizes were performed, in a range of ±0.5 µm from the SEM average value."

    The fitted thickness is not searched freely; it is confined to a 1 µm window centered on the SEM thickness that is then invoked as the independent validation. Because the paper states that the reduced chi-square is almost equal for 0.5 µm differences, any best fit inside this window is automatically consistent with SEM at the reported level. Thus the agreement between the simulated thickness and the SEM thickness is guaranteed by the choice of search range, not demonstrated by the simulation. This is a fitted input presented as an independent confirmation.

  2. fitted input called prediction [Section 2.2, amalgam samples, SM3 paragraph]
    "Here, only size was changed, in a range from 8 to 12 μm. The best fit was reached with a thickness of 11 ± 1 µm µm and standard gold density, in agreement with the SEM measurement"

    For SM3, the simulation search range is again centered on the SEM value of 11 ± 1 µm. The fitted result of 11 ± 1 µm is therefore not an independent determination; the allowed thickness interval was chosen around the reference value before fitting. The subsequent statement that the simulation 'is in agreement with SEM' is a consequence of the prior choice of the scan interval, making this validation step circular by construction.

full rationale

The core workflow is an inverse fit: measured muonic X-ray depth profiles are compared with simulated stopping profiles for assumed gold thicknesses, and the thickness is chosen by minimizing reduced chi-square. Inverse fitting is not itself circular. However, the paper's validation claim is significantly weakened because, for EPA, EPB, EPC, and SM3, the thickness search range is anchored to the SEM thickness that is later cited as the reference. Since chi-square is reported to be nearly flat over 0.5 µm steps, any fit value in the SEM-centered scan is within the stated ±1 µm uncertainty, so the 'agreement with SEM' is largely built into the search grid. Additional tuned inputs, including raising the momentum spread from 4% to 5% and adjusting source-to-sample distance for EP_C, are fit to the same measured profiles; the paper admits the spread 'was not extensively investigated' and that positioning represented a source of error. The ±1 µm thickness uncertainty is conditional on these tuned parameters and excludes their systematic effect. EM2 provides a further unaddressed inconsistency: the fitted thickness is 5 ± 1 µm while the SEM value is 11 ± 1 µm, and Table 2 omits the SEM entry for EM2, leaving the general claim of agreement unsupported. No load-bearing self-citation or imported uniqueness theorem is present; ARBY and TRIM are externally developed tools, and the cited prior uses are not used to justify the thickness result. The method has independent content, but the headline validation is partially circular because the reference values are used to define the fitting search space.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central result is produced by a chi-square fit of simulated depth profiles to measured ones. Four auxiliary parameters (thickness per sample, momentum spread, distance for one sample, density for one sample) are adjusted to improve agreement; only the thicknesses are cross-checked against SEM, and only for four of the five samples.

free parameters (4)
  • Gold layer thickness (per sample) = EPA 3.5, EPB 4.5, EPC 7.5, SM3 11, EM2 5 um
    The target of the fit, varied in simulations to minimize reduced chi-square against the measured depth profile.
  • Beam momentum spread (dp/p) = 5% (increased from nominal 4%)
    Adjusted in Section 2.1 because the simulated profile was narrower than measured; claimed plausible after facility refurbishment, but not independently measured.
  • Source-to-sample distance (EPC) = 9.7 cm (nominal 10 cm)
    Adjusted in Section 2.1 to improve fit for sample C; inferred from the aluminium profile shift, not measured directly.
  • Gold layer density (EM2) = 80% of nominal (15.46 g/cm3)
    Reduced in Section 2.2 to account for air bubbles/cracks in the handmade amalgam layer; no direct measurement.
assumptions (4)
  • domain assumption Muon stopping in matter is accurately modeled by GEANT4 and by TRIM using a hydrogen ion with one-ninth the proton mass (effectively muon mass).
    Section 1.1 states TRIM does not implement muons, so a scaled proton is used; stopping power differences are assumed negligible.
  • domain assumption The number of stopped muons in a layer is proportional to the emitted X-ray intensity.
    Section 1.1, underpinning the direct comparison of simulated stopping counts to measured peak areas.
  • domain assumption Detection efficiency is approximately constant over the 102-134 keV range, so no efficiency correction is applied.
    Section 1.4 states intensities were not corrected; a mild variation across the narrow energy range is assumed negligible.
  • domain assumption The samples consist of uniform, flat layers with sharp interfaces and the nominal compositions.
    The simulation geometry in Section 1.4 models Al, Au, Ni, and brass/bronze layers; for EM2, uniformity is relaxed by lowering density, but the layer structure remains ideal.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Depth profiling the elemental composition with negative muons: Monte Carlo based tools for improved data analysis." pith.science (2026). https://pith.science/paper/3DPIGNW7

@misc{pith2026250504679,
  author       = {Pith},
  title        = {Pith review of: Depth profiling the elemental composition with negative muons: Monte Carlo based tools for improved data analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3DPIGNW7}},
  note         = {Machine review of arXiv:2505.04679}
}
read the original abstract

Gildings, patinas and alteration crusts are common features of many heritage artefacts, especially for metals. Their size depends on many factors, like the manufacturing method for gildings or the conservation state for alteration crusts: in some cases, it can be in the scale of the tens of microns. Such thickness would be difficult to investigate with classical non-destructive methods and would prevent getting information from the bulk of the sample. This work proposes an innovative approach for the study of multi-layered materials with the Muonic atom X-ray Emission Spectroscopy technique ({\mu}-XES). Based on the detection of the high-energy X-rays emitted after the muon capture by the atom, this method is characterised by a remarkable penetration depth (from microns to cm). From the surface to the bulk, this technique can evaluate the variation of the elemental composition as a function of depth. The paper focuses on providing an improved interpretation of {\mu}-XES data by coupling the analysis with the use of two Monte Carlo simulation software, GEANT4/ARBY and SRIM/TRIM. With these two software, it is possible to replicate the negative muon experiments and compare the experimental and simulated outputs to address the size of a given layer. To validate this approach, a set of standard gilded bronze and brass foils were measured at the ISIS Neutron and Muon source. From simulations, it was possible to evaluate the thickness of the superficial gold layer, with results in agreement with the preliminary SEM characterisation of the samples.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 26 canonical work pages

  1. [1]

    External Beam IBA Measurements for Cultural Heritage,

    M. Chiari, “External Beam IBA Measurements for Cultural Heritage,” Applied Sciences (Switzerland), vol. 13, no. 5, Mar. 2023, doi: 10.3390/app13053366

    work page doi:10.3390/app13053366 2023

  2. [2]

    Time-of-flight secondary ion mass spectrometry imaging in cultural heritage: A focus on old paintings,

    C. Bouvier, S. Van Nuffel, P. Walter, and A. Brunelle, “Time-of-flight secondary ion mass spectrometry imaging in cultural heritage: A focus on old paintings,” Journal of Mass Spectrometry, vol. 57, no. 1, p. e4803, 2022, doi: https://doi.org/10.1002/jms.4803

    work page doi:10.1002/jms.4803 2022

  3. [3]

    Towards nanometric resolution in multilayer depth profiling: A comparative study of RBS, SIMS, XPS and GDOES,

    R. Escobar Galindo, R. Gago, D. Duday, and C. Palacio, “Towards nanometric resolution in multilayer depth profiling: A comparative study of RBS, SIMS, XPS and GDOES,” 2010, Springer Verlag. doi: 10.1007/s00216-009-3339-y

    work page doi:10.1007/s00216-009-3339-y 2010

  4. [4]

    Comparison of depth profiling techniques using ion sputtering from the practical point of view,

    S. Oswald and S. Baunack, “Comparison of depth profiling techniques using ion sputtering from the practical point of view,” 2003

    work page 2003

  5. [5]

    A deep view in cultural heritage-confocal micro X-ray spectroscopy for depth resolved elemental analysis,

    B. Kanngießer, W. Malzer, I. Mantouvalou, D. Sokaras, and A. G. Karydas, “A deep view in cultural heritage-confocal micro X-ray spectroscopy for depth resolved elemental analysis,” Appl Phys A Mater Sci Process, vol. 106, no. 2, pp. 325–338, Feb. 2012, doi: 10.1007/s00339- 011-6698-0

    doi:10.1007/s00339- 2012

  6. [6]

    The Role of PIXE and XRF in Heritage Science: The INFN-CHNet LABEC Experience,

    L. Sottili et al., “The Role of PIXE and XRF in Heritage Science: The INFN-CHNet LABEC Experience,” Applied Sciences, vol. 12, no. 13, 2022, doi: 10.3390/app12136585

    work page doi:10.3390/app12136585 2022

  7. [7]

    Bezur, L

    A. Bezur, L. (Lynn F. Lee, M. Loubser, K. Trentelman, Getty Conservation Institute, and Institute for the Preservation of Cultural Heritage, Handheld XRF in cultural heritage : a practical workbook for conservators

    work page

  8. [8]

    Muon spin spectroscopy,

    A. D. Hillier et al., “Muon spin spectroscopy,” Nature Reviews Methods Primers, vol. 2, no. 1, p. 4, 2022, doi: 10.1038/s43586-021-00089-0

    doi:10.1038/s43586-021-00089-0 2022

Show all 34 references
  1. [9]

    S. J. Blundell, R. De Rienzi, T. Lancaster, and F. L. Pratt, Muon Spectroscopy: an Introduction. Oxford University press, 2021

    2021

  2. [10]

    A Novel Non-Destructive Technique for Cultural Heritage: Depth Profiling and Elemental Analysis Underneath the Surface with Negative Muons,

    M. Cataldo, M. Clemenza, K. Ishida, and A. D. Hillier, “A Novel Non-Destructive Technique for Cultural Heritage: Depth Profiling and Elemental Analysis Underneath the Surface with Negative Muons,” May 01, 2022, MDPI. doi: 10.3390/app12094237

    2022 doi

  3. [11]

    Development of elemental analysis by muonic X-ray measurement in J- PARC,

    K. Ninomiya et al., “Development of elemental analysis by muonic X-ray measurement in J- PARC,” J Phys Conf Ser, vol. 225, pp. 1–3, 2010, doi: 10.1088/1742-6596/225/1/012040

    2010 doi

  4. [12]

    Elemental Analysis of Bronze Artifacts by Muonic X-ray Spectroscopy,

    K. Ninomiya et al., “Elemental Analysis of Bronze Artifacts by Muonic X-ray Spectroscopy,” Physical Society of Japan, Sep. 2015. doi: 10.7566/jpscp.8.033005

    2015 doi

  5. [13]

    Understanding Roman Gold Coinage Inside Out,

    G. A. Green, K. Ishida, B. V. Hampshire, K. Butcher, A. M. Pollard, and A. D. Hillier, “Understanding Roman Gold Coinage Inside Out,” J Archaeol Sci, vol. 134, Oct. 2021, doi: 10.1016/j.jas.2021.105470

    2021

  6. [14]

    The non-destructive investigation of a late antique knob bow fibula (Bügelknopffibel) from Kaiseraugst/CH using Muon Induced X-ray Emission (MIXE),

    S. Biswas et al., “The non-destructive investigation of a late antique knob bow fibula (Bügelknopffibel) from Kaiseraugst/CH using Muon Induced X-ray Emission (MIXE),” Herit Sci, vol. 11, no. 1, Dec. 2023, doi: 10.1186/s40494-023-00880-0. © 2025. This manuscript version is mad...

    2023 doi

  7. [15]

    Use of Muonic X Rays for Nondestructive Analysis of Bulk Samples for Low Z Constituents,

    J. J. Reidy, R. L. Hutson, H. Daniel1, and K. Springer, “Use of Muonic X Rays for Nondestructive Analysis of Bulk Samples for Low Z Constituents,” Anal Chem, vol. 50, no. 1, pp. 40–44, 1978, doi: 10.1021/ac50023a015

    1978 doi

  8. [16]

    Application of muonic X-ray techniques to the elemental analysis of archeological objects,

    E. Köhler, R. Bergmann, H. Daniel, P. Ehrhart, and F. J. Hartmann, “Application of muonic X-ray techniques to the elemental analysis of archeological objects,” Nuclear Instruments and Methods, vol. 187, no. 2–3, pp. 563–568, 1981, doi: 10.1016/0029-554X(81)90389-X

    1981 doi

  9. [17]

    FLUKA: A multi-particle transport code (Program version 2005),

    A. Ferrari, P. R. Sala, A. Fasso, and J. Ranft, “FLUKA: A multi-particle transport code (Program version 2005),” Jul. 2005, doi: 10.2172/877507

    2005 doi

  10. [18]

    GEANT4 - A simulation toolkit,

    S. Agostinelli et al., “GEANT4 - A simulation toolkit,” Nucl Instrum Methods Phys Res A, vol. 506, no. 3, pp. 250–303, 2003, doi: 10.1016/S0168-9002(03)01368-8

    2003 doi

  11. [19]

    MCNP User Manual . Code Versione 6.2,

    C. J. Werner, “MCNP User Manual . Code Versione 6.2,” Los Alamos National Laboratory, 2017

    2017

  12. [20]

    The projected background for the CUORE experiment,

    C. Alduino et al., “The projected background for the CUORE experiment,” The European Physical Journal C, vol. 77, no. 8, p. 543, 2017, doi: 10.1140/epjc/s10052-017-5080-6

    2017 doi

  13. [21]

    Measurement of the two-neutrino double-beta decay half-life of $$^{130}$$Te with the CUORE-0 experiment,

    C. Alduino et al., “Measurement of the two-neutrino double-beta decay half-life of $$^{130}$$Te with the CUORE-0 experiment,” The European Physical Journal C, vol. 77, no. 1, p. 13, 2017, doi: 10.1140/epjc/s10052-016-4498-6

    2017 doi

  14. [22]

    SRIM – The stopping and range of ions in matter (2010),

    J. F. Ziegler, M. D. Ziegler, and J. P. Biersack, “SRIM – The stopping and range of ions in matter (2010),” Nucl Instrum Methods Phys Res B, vol. 268, no. 11–12, pp. 1818–1823, Jun. 2010, doi: 10.1016/J.NIMB.2010.02.091

    2010 doi

  15. [23]

    Thickness determination of metal multilayers by ED-XRF multivariate analysis using Monte Carlo simulated standards,

    W. Giurlani, E. Berretti, A. Lavacchi, and M. Innocenti, “Thickness determination of metal multilayers by ED-XRF multivariate analysis using Monte Carlo simulated standards,” Anal Chim Acta, vol. 1130, pp. 72–79, 2020, doi: https://doi.org/10.1016/j.aca.2020.07.047

    2020 doi

  16. [24]

    Monte Carlo simulations of XRF intensities in non- homogeneous matrices,

    J. A. Helsen and B. A. R. Vrebos, “Monte Carlo simulations of XRF intensities in non- homogeneous matrices,” Spectrochim Acta Part B At Spectrosc, vol. 39, no. 6, pp. 751–759, 1984, doi: https://doi.org/10.1016/0584-8547(84)80083-X

    1984 doi

  17. [25]

    The Implementation of MuDirac in Geant4: A Preliminary Approach to the Improvement of the Simulation of the Muonic Atom Cascade Process,

    M. Cataldo et al., “The Implementation of MuDirac in Geant4: A Preliminary Approach to the Improvement of the Simulation of the Muonic Atom Cascade Process,” Condens Matter, vol. 8, no. 4, Dec. 2023, doi: 10.3390/condmat8040101

    2023 doi

  18. [26]

    The practice and characterization of historic fire gilding techniques,

    K. Anheuser, “The practice and characterization of historic fire gilding techniques,” JOM, vol. 49, no. 11, pp. 58–62, 1997, doi: 10.1007/s11837-997-0015-6

    1997 doi

  19. [27]

    Gilding through the ages,

    A. Oddy, “Gilding through the ages,” Gold Bull, vol. 14, no. 2, pp. 75–79, 1981, doi: 10.1007/BF03214601

    1981 doi

  20. [28]

    Plating and Surface Treatments on Ancient Metalwork,

    A. Giumlia-Mair, “Plating and Surface Treatments on Ancient Metalwork,” Advances in Archaeomaterials, vol. 1, no. 1, pp. 1–26, Dec. 2020, doi: 10.1016/j.aia.2020.10.001

    2020 doi

  21. [29]

    Electroplating for decorative applications: Recent trends in research and development,

    W. Giurlani et al., “Electroplating for decorative applications: Recent trends in research and development,” Aug. 01, 2018, MDPI AG. doi: 10.3390/coatings8080260

    2018 doi

  22. [30]

    Muons at ISIS,

    A. D. Hillier, J. S. Lord, K. Ishida, and C. Rogers, “Muons at ISIS,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 377, no. 2137, pp. 1–7, 2019, doi: 10.1098/rsta.2018.0064. © 2025. This manuscript version is made ava...

    2019

  23. [31]

    The RIKEN-RAL pulsed Muon Facility,

    T. Matsuzaki, K. Ishida, K. Nagamine, I. Watanabe, G. H. Eaton, and W. G. Williams, “The RIKEN-RAL pulsed Muon Facility,” 2001

    2001

  24. [32]

    Electronic catalogue of muonic X-rays,

    Zinatulina Daniya et al., “Electronic catalogue of muonic X-rays,” EPJ Web Conf., vol. 177, p. 3006, 2018, doi: 10.1051/epjconf/201817703006

    2018

  25. [33]

    Charge-distribution parameters, isotope shifts, isomer shifts, and magnetic hyperfine constanst from muonic atoms,

    R. Engfer, H. Schneuwly, J. L. Vuilleumier, H. K. Walter, and A. Zehnder, “Charge-distribution parameters, isotope shifts, isomer shifts, and magnetic hyperfine constanst from muonic atoms,” At Data Nucl Data Tables, vol. 14, pp. 509–597, 1974

    1974

  26. [34]

    Mudirac: A Dirac equation solver for elemental analysis with muonic X-rays,

    S. Sturniolo and A. Hillier, “Mudirac: A Dirac equation solver for elemental analysis with muonic X-rays,” X-Ray Spectrometry, no. June, pp. 1–17, 2020, doi: 10.1002/xrs.3212

    2020 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.