Pith. sign in

REVIEW 2 major objections 3 minor 72 references

The hyperfine anomaly in mercury and test of the Moskowitz-Lombardi rule

T0 review · 2 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper determines the Bohr-Weisskopf hyperfine correction in mercury isotopes and shows that the additive constant in the Moskowitz-Lombardi rule is much smaller than the standard theory value.

desk verdict Valuable new absolute BW values for mercury, but the claimed significant ML-vs-FA deviation does not survive the common-mode muonic anchor error. read the letter →

arxiv 2411.09912 v2 pith:VY5AC4NY submitted 2024-11-15 physics.atom-ph nucl-exnucl-th

J. Vandeleur , G. Sanamyan , B. M. Roberts , J. S. M. Ginges This is my paper · ORCID
classification physics.atom-phnucl-exnucl-th
keywords Bohr-WeisskopfeffecthyperfineanomalyMoskowitz-Lombardirulemercuryisotopesmuonicatomsstructureatomicmany-bodycalculationsnuclearmagneticmoments
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

The paper establishes empirical values for the Bohr-Weisskopf (BW) effect, the correction to hyperfine structure from the finite radial distribution of the nuclear magnetic moment, in ten mercury isotopes and isomers. It tests the Moskowitz-Lombardi rule, which relates the relative BW effect $\epsilon$ to $1/|\mu|$ plus an additive constant; for mercury this constant had never been measured. From the measured hyperfine splitting in muonic $^{199}$Hg, translated to electronic systems with screening factors, the paper finds $\epsilon = -2.34(44)\%$ for neutral $^{199}$Hg and $-2.59(49)\%$ for $^{199}$Hg$^{+}$. Fitting the rule to all isotopes gives $c_{\mathrm{exp}} = -3.6(8)\times10^{-3}$ and $\alpha_{\mathrm{exp}} = 0.98(5)\times10^{-2}\,\mu_N$, so the additive constant is significantly smaller in magnitude than the widely used Fujita-Arima value $c=-0.01$. If the result holds, precision atomic calculations for mercury can correct for the finite nuclear magnetization with an empirical anchor instead of a model spread.

What carries the argument

The central identity is the split $A = A_0 + A_{\mathrm{BW}} + A_{\mathrm{QED}}$, where $A_0$ is the point-nucleus hyperfine constant, $A_{\mathrm{BW}}$ is the Bohr-Weisskopf correction, and $A_{\mathrm{QED}}$ is the QED correction; subtracting well-calculated $A_0$ and $A_{\mathrm{QED}}$ from the measured $A$ isolates $A_{\mathrm{BW}}$. The second load-bearing mechanism is the two-step translation of the muonic-atom BW effect to a H-like ion and then to many-electron mercury through electronic screening factors $x_{\mathrm{scr}} = \epsilon_{\mathrm{atom}}/\epsilon_{\mathrm{H-like}}$, computed at the random-phase-approximation-with-exchange level. The third is the use of measured differential anomalies between isotopes, with the ratio in Eq. (4) relating neutral and singly-ionized mercury, which spreads the absolute $^{199}$Hg value to other isotopes and isomers. These pieces work together because only $s$ and $p_{1/2}$ orbitals penetrate the nucleus and they are proportional there, so the H-like result carries all the BW information.

What would settle it

Calculate the differential Breit-Rosenthal contribution $^{199}\delta^{201}$ for the $6s6p\,{}^3P_1$ state of neutral Hg with a relativistic many-body method; if it is comparable to the 0.4% uncertainty in the ratio 0.902(4), the neutral-atom BW values and the fitted constant $c_{\mathrm{exp}}$ shift by more than their quoted errors. Alternatively, a new measurement of the muonic $^{199}$Hg 1s hyperfine splitting with uncertainty well below 0.12 keV would directly test the seed value $-68(8)\%$.

Watch

Extended reading notes

Core claim

On its own terms, the paper claims that the absolute BW effect in $^{199}$Hg can be extracted from experiment rather than left to nuclear models. The extraction starts from the measured 1s hyperfine constant of muonic $^{199}$Hg, where the muon is essentially unscreened, giving $\epsilon = -68(8)\%$ in the muonic atom. This is translated to the H-like ion and then to many-electron Hg through electronic screening factors, yielding $-2.59(49)\%$ for the $6s$ state of $^{199}$Hg$^{+}$ and $-2.34(44)\%$ for the $6s6p\,{}^3P_1$ state of neutral $^{199}$Hg. An independent direct extraction from the measured $^{199}$Hg$^{+}$ hyperfine constant using all-orders atomic many-body calculations gives $-3.4(10)\%$, consistent with the muonic route. Combining the $^{199}$Hg anchor with measured differential anomalies gives BW effects for ten isotopes and isomers, and fitting $\epsilon = c - \alpha/|\mu|$ to these data yields $c_{\mathrm{exp}} = -3.6(8)\times10^{-3}$ and $\alpha_{\mathrm{exp}} = 0.98(5)\times10^{-2}\,\mu_N$ for neutral mercury. The paper concludes that the additive constant is much smaller than the Fujita-Arima value $c_{\mathrm{FA}}=-0.01$, and that the discrepancy points to omitted many-body nuclear effects in the older theory.

Load-bearing premise

The load-bearing premise is that the measured ratio of differential anomalies between isotopes 199 and 201 in neutral mercury and in the ion equals the ratio of the Bohr-Weisskopf effects alone, with the small difference in how the finite nuclear charge distribution shifts the electron wave functions (the differential Breit-Rosenthal effect) neglected; the paper says it checked this numerically but does not show the check.

Editorial extensions

If this is right

  • The absolute BW correction for $^{199}$Hg is now anchored empirically at the percent level, so hyperfine-structure calculations can use $-2.34(44)\%$ (neutral) or $-2.59(49)\%$ (ion) instead of a spread of nuclear-model predictions.
  • The fitted coefficients give a concrete empirical rule for neutral mercury, $\epsilon(\%) = -0.36 - 0.98/|\mu(\mu_N)|$, which predicts both absolute anomalies and isotopic trends.
  • Using the old Fujita-Arima constant $c=-0.01$ would make the predicted absolute anomaly for $^{199}$Hg about 45% larger in magnitude than the empirical value.
  • The ten isotope and isomer BW values provide direct benchmarks that microscopic nuclear-magnetization models must reproduce, which is relevant to Schiff-moment and electric-dipole-moment interpretations in mercury.

Reading between the lines

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

  • Beyond the paper's claims, the agreement between the muonic and direct routes suggests that the same two-step translation could be applied to muonic-atom data for other heavy nuclei to test whether the Moskowitz-Lombardi rule's constants are universal or nucleus-specific.
  • A published numerical value for the differential Breit-Rosenthal factor $^{199}\delta^{201}$ in the $6s6p\,{}^3P_1$ state would close the only unshown check in the neutral-mercury chain; until then, the neutral screening factor carries a hidden systematic absent from the ion-only extraction.
  • If $c_{\mathrm{exp}}$ is genuinely near zero, the Fujita-Arima factorization misses substantial many-body nuclear effects, which implies that absolute-anomaly measurements near other shell closures, not just isotopic differential anomalies, are the right way to map where the rule holds.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper extracts the Bohr-Weisskopf (BW) effect for neutral and singly-ionized mercury isotopes from the measured hyperfine splitting of muonic 199Hg, using a two-step translation through H-like mercury with five nuclear wavefunction shapes, then applies electronic screening factors to obtain values for Hg+ and neutral Hg. The authors also perform an all-orders atomic many-body calculation for 199Hg+ and extract the BW effect directly from the experimental hyperfine constant. From the isotope-dependent BW values, they fit the Moskowitz-Lombardi rule epsilon = c - alpha/|mu| and report c_exp = -3.6(8) x 10^-3 and alpha_exp = 0.98(5) x 10^-2 muN for neutral Hg, concluding that the additive constant differs significantly from the Fujita-Arima value c_FA = -0.01.

Significance. If the central claim were fully supported, the paper would provide the first empirical determination of the absolute BW effect in mercury isotopes and a direct test of the additive constant in the Moskowitz-Lombardi rule, with implications for precision atomic clock measurements and nuclear structure studies. The extraction chain is explicit, the nuclear-model dependence is honestly assessed with five single-particle wavefunction shapes, and the independent all-orders atomic calculation serves as a valuable cross-check. However, the significance of the headline result is undermined by the common-mode uncertainty in the 199Hg anchor, as detailed below.

major comments (2)
  1. [Table III, Eq. (10), surrounding text] The quoted uncertainty on c_exp omits the fully correlated contribution from the common 199Hg anchor. All ten epsilons in Table III are derived by adding a differential anomaly to the 199Hg value epsilon_199 = -2.34(44)%, so a common shift of epsilon_199 shifts every point in the fit of Eq. (6) and therefore changes c by exactly the same amount. This 0.0044 absolute uncertainty is not reduced by the number of isotopes; the correct uncertainty on c is at least this large, and the quoted c_exp = -3.6(8) x 10^-3 uses an uncertainty of only 0.0008, which treats the ten values as independent. With the common-mode error included, the difference between c_exp and c_FA = -0.01 is only about 1.5 standard deviations, so the claim that the additive constant 'differs significantly' from the Fujita-Arima value is not supported. Please redo the fit with a covariance matrix that includes the fully correlated anchor error, and revise the abstract, title, and conclusions accordingly if the significance disappears.
  2. [Eq. (4) and following sentence] The assertion 'We have checked numerically that 199Delta201 is very small and may be omitted in the ratio (4)' is not backed by any numerical result or citation. Because Eq. (4) is the basis for translating the ion BW values to the neutral atom and therefore for all neutral-Hg entries in Table III, please provide the actual magnitude of 199Delta201 (or its ratio to the differential BW effect) so the reader can assess the size of the omitted Breit-Rosenthal term relative to the 0.4% uncertainty on the right-hand side of Eq. (4). Without this number, the systematic error on the neutral-atom BW values is not fully documented.
minor comments (3)
  1. [Table II] The two values listed for 199Hg+ (-2.59(49)% and -3.4(10)%) are visually confusing; consider using two explicitly labeled rows (e.g., 'muonic-deduced' and 'direct extraction') or a footnote that clearly separates the two determinations.
  2. [Eq. (5)] The convention for the isotope ordering in the differential anomaly 1Delta2 should be stated explicitly (i.e., whether it corresponds to epsilon(1) - epsilon(2) or the reverse), to avoid sign ambiguity when the definition is used with data from Ref. [60].
  3. [Paragraph after Eq. (10)] The statement 'The deviations arise from omitted many-body nuclear effects in the theory analysis of Ref. [32]' is a causal claim that goes beyond the data presented; consider softening it to 'may arise' unless a specific calculation supporting this attribution is included.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Moskowitz-Lombardi additive constant is a fitted output anchored to independent muonic and atomic data, not an input to the derivation.

full rationale

The derivation chain is not circular. The absolute Bohr-Weisskopf anchor for 199Hg is obtained by subtracting calculated point-nucleus and QED hyperfine contributions from the measured muonic-199Hg hyperfine constant (Table I), using experimental data and atomic calculations that do not assume the Moskowitz-Lombardi rule. The H-like value is obtained by calibrating single-particle magnetization distributions to that muonic anchor (the paper says the magnetic radius is varied until the empirical BW effect is reproduced in muonic Hg), which is a model-calibration and extrapolation rather than a first-principles prediction, and it is independently checked by direct extraction from the measured 199Hg+ hyperfine constant (Table I, second row). The BW values for the other isotopes in Table III are propagated from this anchor using measured differential anomalies and the screening relation in Eq. (4); the fit of Eq. (6) then produces c_exp and alpha_exp as fitted outputs that are compared with the ML and FA values as external benchmarks. Self-citations appear for the screening-factor convergence (Refs. [21,23]) and QED interpolation (Ref. [15]), but these support methodological details and uncertainty estimates rather than importing the ML additive constant. The skeptical concern about common-mode uncertainty in epsilon_199 affecting the significance of c_exp is a statistical-covariance issue, not a circularity: it does not make the fitted c_exp equal to an input by construction.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced. The analysis uses existing measured quantities and established atomic-structure methods; the main new calculation outputs are not shipped as code or data.

free parameters (2)
  • Effective magnetic radius r_m in the single-particle nuclear model = Varied for each of five wavefunction shapes; individual values not tabulated.
    Adjusted to reproduce the muonic 199Hg BW effect before computing the H-like BW effect; the spread over the five shapes is used as the nuclear model uncertainty.
  • Moskowitz-Lombardi coefficients c and alpha = c = -3.6(8)e-3, alpha = 0.98(5)e-2 muN (neutral Hg); c = -4.0(9)e-3, alpha = 1.09(6)e-2 muN (Hg+).
    Fitted to the extracted BW values in Table III via Eq. (6). These are the reported empirical results, not hidden inputs, but their stated uncertainties depend on the covariance treatment, which is not described.
assumptions (3)
  • domain assumption The muonic 1s state can be treated as a hydrogenlike ion with a Fermi nuclear charge distribution, with vacuum polarization as the dominant QED correction.
    Standard muonic-atom treatment, cited to Borie and Rinker, used to compute A0 and AQED for muonic 199Hg. Invoked in the section following Eq. (1).
  • domain assumption The BW effect is determined by the s and p1/2 orbitals that penetrate the nucleus, and these orbitals are proportional inside the nucleus, so an electronic screening factor transfers the H-like BW effect to many-electron atoms.
    Used in the electronic screening factor section, citing Refs. [22,23,59]. Without this proportionality, the screening factor x_scr would not be isotope- and state-transferable.
  • domain assumption The ratio of measured differential anomalies in Eq. (4), 199Delta201(6s6p 3P1) / 199Delta201(6s 2S1/2), equals the ratio of BW effects, with negligible differential Breit-Rosenthal contribution 199delta201.
    The authors state they checked numerically that 199delta201 is very small, but the check is not shown. This assumption underlies the neutral-mercury screening factor and therefore the neutral-Hg c fit.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The hyperfine anomaly in mercury and test of the Moskowitz-Lombardi rule." pith.science (2026). https://pith.science/paper/VY5AC4NY

@misc{pith2026241109912,
  author       = {Pith},
  title        = {Pith review of: The hyperfine anomaly in mercury and test of the Moskowitz-Lombardi rule},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VY5AC4NY}},
  note         = {Machine review of arXiv:2411.09912}
}
read the original abstract

The Moskowitz-Lombardi rule gives a simple relation between the magnetic moment of an atomic nucleus and the effect of its radial distribution on the hyperfine structure - the magnetic hyperfine anomaly or "Bohr-Weisskopf" effect. It was originally formulated for mercury, for which experimental data for nuclear magnetic moments and hyperfine constants were available for a number of isotopes. While the relation for the differential effect between isotopes may be completely determined experimentally, the value for the additive constant that is needed to give the Bohr-Weisskopf (BW) effect for a single isotope has remained untested. In this work, we determine the BW effect in singly-ionized and neutral mercury from experimental muonic Hg-199 data together with our atomic calculations. We check this result by directly extracting the BW effect from the hyperfine constant for singly-ionized Hg-199 using state-of-the-art atomic many-body calculations. From this we deduce an empirical value for the additive constant in the Moskowitz-Lombardi rule, which differs significantly from the values advocated previously.

Figures

Figures reproduced from arXiv: 2411.09912 by the authors.

Figure 1
Figure 1. FIG. 1. Fit of the Moskowitz-Lombardi rule to the relative [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

72 extracted references · 60 canonical work pages

  1. [1]

    J. S. M. Ginges and V. V. Flambaum, Phys. Rep. 397, 63 (2004)

    work page 2004

  2. [2]

    B. M. Roberts, V. A. Dzuba, and V. V. Flambaum, Annu. Rev. Nucl. Part. Sci. 65, 63 (2015)

    work page 2015

  3. [3]

    Safronova, D

    M. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Rev. of Mod. Phys. 90, 025008 (2018)

    work page 2018

  4. [4]

    Arrowsmith-Kron, M

    G. Arrowsmith-Kron, M. Athanasakis-Kaklamanakis, M. Au, J. Ballof, R. Berger, A. Borschevsky, A. A. Breier, F. Buchinger, D. Budker, L. Caldwell, C. Charles, N. Dattani, R. P. de Groote, D. DeMille, T. Dickel, J. Dobaczewski, C. E. D¨ ullmann, E. Eliav, J. Engel, M. Fan, V. Flambaum, K. T. Flanagan, A. N. Gaiser, R. F. G. Ruiz, K. Gaul, T. F. Giesen, J. S...

    work page 2024

  5. [5]

    I. B. Khriplovich, Parity Nonconservation in Atomic Phenomena (Gordon and Breach, Philadelphia, 1991)

    work page 1991

  6. [6]

    I. B. Khriplovich and S. K. Lamoureaux, CP Violation Without Strangenessa (Springer, Berlin, 1997)

    work page 1997

  7. [7]

    V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. Lett. 82, 888 (1999)

    1999

  8. [8]

    J. C. Berengut, D. Budker, C. Delaunay, V. V. Flam- baum, C. Frugiuele, E. Fuchs, C. Grojean, R. Harnik, R. Ozeri, G. Perez, and Y. Soreq, Phys. Rev. Lett. 120, 091801 (2018)

    2018

Show all 72 references
  1. [9]

    Counts, J

    I. Counts, J. Hur, D. P. L. Aude Craik, H. Jeon, C. Le- ung, J. C. Berengut, A. Geddes, A. Kawasaki, W. Jhe, and V. Vuleti´ c, Phys. Rev. Lett.125, 123002 (2020)

    2020

  2. [10]

    S. O. Allehabi, V. A. Dzuba, V. V. Flambaum, and A. V. Afanasjev, Phys. Rev. A 103, L030801 (2021)

    2021

  3. [11]

    V. V. Flambaum, Phys. Lett. B 320, 211 (1994)

    1994

  4. [12]

    Auerbach, V

    N. Auerbach, V. V. Flambaum, and V. Spevak, Phys. Rev. Lett. 76, 4316 (1996)

    1996

  5. [13]

    Engel, J

    J. Engel, J. L. Friar, and A. C. Hayes, Phys. Rev. C 61, 035502 (2000)

    2000

  6. [14]

    M ˚ artensson-Pendrill, Phys

    A.-M. M ˚ artensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)

    1995

  7. [15]

    J. S. M. Ginges, A. V. Volotka, and S. Fritzsche, Phys. Rev. A 96, 062502 (2017)

    2017

  8. [16]

    E. A. Konovalova, Y. A. Demidov, M. G. Kozlov, and A. E. Barzakh, Atoms 6, 39 (2018)

    2018

  9. [17]

    E. A. Konovalova, Y. A. Demidov, and M. G. Kozlov, Opt. Spectrosc. 128, 1530 (2020)

    2020

  10. [18]

    B. M. Roberts and J. S. M. Ginges, Phys. Rev. Lett. 125, 063002 (2020)

    2020

  11. [19]

    A. E. Barzakh, D. Atanasov, A. N. Andreyev, M. Al Mon- thery, N. A. Althubiti, B. Andel, S. Antalic, K. Blaum, T. E. Cocolios, J. G. Cubiss, P. Van Duppen, T. D. Goodacre, A. de Roubin, Y. A. Demidov, G. J. Farooq- Smith, D. V. Fedorov, V. N. Fedosseev, D. A. Fink, L. P. Gaffn...

    2020

  12. [20]

    Y. A. Demidov, E. A. Konovalova, R. T. Imanbaeva, M. G. Kozlov, and A. E. Barzakh, Phys. Rev. A 103, 032824 (2021)

    2021

  13. [21]

    B. M. Roberts and J. S. M. Ginges, Phys. Rev. A 104, 022823 (2021)

    2021

  14. [22]

    L. V. Skripnikov, J. Chem. Phys. 153, 114114 (2020)

    2020

  15. [23]

    B. M. Roberts, P. G. Ranclaud, and J. S. M. Ginges, Phys. Rev. A 105, 052802 (2022)

    2022

  16. [24]

    S. D. Prosnyak and L. V. Skripnikov, Phys. Rev. C 103, 034314 (2021)

    2021

  17. [25]

    L. V. Skripnikov and S. D. Prosnyak, Phys. Rev. C 106, 054303 (2022)

    2022

  18. [26]

    Sanamyan, B

    G. Sanamyan, B. M. Roberts, and J. S. M. Ginges, Phys. Rev. Lett. 130, 053001 (2023)

    2023

  19. [27]

    Lechner, T

    S. Lechner, T. Miyagi, Z. Y. Xu, M. L. Bissell, K. Blaum, B. Cheal, C. S. Devlin, R. F. Garcia Ruiz, J. S. M. Gin- ges, H. Heylen, J. D. Holt, P. Imgram, A. Kanellakopou- los, ´A. Koszor´ us, S. Malbrunot-Ettenauer, R. Neu- gart, G. Neyens, W. N¨ ortersh¨ auser, P. Plattner, L...

    2023

  20. [28]

    S. G. Wilkins, S. M. Udrescu, M. Athanasakis- Kaklamanakis, R. F. G. Ruiz, M. Au, I. Beloˇ sevi´ c, R. Berger, M. L. Bissell, A. A. Breier, A. J. Brinson, K. Chrysalidis, T. E. Cocolios, R. P. de Groote, A. Dorne, K. T. Flanagan, S. Franchoo, K. Gaul, S. Geldhof, 6 T. F. Giese...

    2023

  21. [29]

    Vandeleur, G

    J. Vandeleur, G. Sanamyan, O. R. Smits, I. A. Val- uev, N. S. Oreshkina, and J. S. M. Ginges, (2024), arXiv:2408.16516

    2024 arXiv

  22. [30]

    Bohr and V

    A. Bohr and V. F. Weisskopf, Phys. Rev. 77, 94 (1950)

    1950

  23. [31]

    Bohr, Phys

    A. Bohr, Phys. Rev. 81, 331 (1951)

    1951

  24. [32]

    Fujita and A

    T. Fujita and A. Arima, Nuc. Phys. A 254, 513 (1975)

    1975

  25. [33]

    B¨ uttgenbach, Hyperfine Interact.20, 1 (1984)

    S. B¨ uttgenbach, Hyperfine Interact.20, 1 (1984)

    1984

  26. [34]

    V. M. Shabaev, J. Phys. B 27, 5825 (1994)

    1994

  27. [35]

    R. A. Sen’kov and V. F. Dmitriev, Nucl. Phys. A 706, 351 (2002)

    2002

  28. [36]

    Tomaselli, T

    M. Tomaselli, T. K¨ uhl, W. N¨ ortersh¨ auser, S. Borneis, A. Dax, D. Marx, H. Wang, and S. Fritzsche, Phys. Rev. A 65, 022502 (2002)

    2002

  29. [37]

    P. A. Moskowitz and M. Lombardi, Phys. Lett. B 46, 334 (1973)

    1973

  30. [38]

    P. A. Moskowitz, Phys. Lett. B 118, 29 (1982)

    1982

  31. [39]

    More- over, the value of the additive constant is experimentally inaccessible in most systems, and has remained largely untested

    and for the lanthanides Nd, Eu, and Gd [40]. More- over, the value of the additive constant is experimentally inaccessible in most systems, and has remained largely untested. In particular, to our knowledge, until now there has been no empirical test of the constant for Hg. Me...

    2025 arXiv

  32. [40]

    Fr¨ ommgen, D

    N. Fr¨ ommgen, D. L. Balabanski, M. L. Bissell, J. Biero´ n, K. Blaum, B. Cheal, K. Flanagan, S. Fritzsche, C. Geppert, M. Hammen, M. Kowalska, K. Kreim, A. Krieger, R. Neugart, G. Neyens, M. M. Rajabali, W. N¨ ortersh¨ auser, J. Papuga, and D. T. Yordanov, Eur. Phys. J. D 69,...

    2015

  33. [41]

    J. R. Persson, Atoms 8, 5 (2020)

    2020

  34. [42]

    Graner, Y

    B. Graner, Y. Chen, E. Lindahl, and B. Heckel, Phys. Rev. Lett. 116, 161601 (2016)

    2016

  35. [43]

    Engel, M

    J. Engel, M. J. Ramsey-Musolf, and U. van Kolck, Progress in Particle and Nuclear Physics 71, 21 (2013)

    2013

  36. [44]

    D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. Lett. 80, 2089 (1998)

    1998

  37. [45]

    S. A. Diddams, Science 293, 825 (2001)

    2001

  38. [46]

    Hachisu, K

    H. Hachisu, K. Miyagishi, S. G. Porsev, A. Derevianko, V. D. Ovsiannikov, V. G. Pal’chikov, M. Takamoto, and H. Katori, Phys. Rev. Lett. 100, 053001 (2008)

    2008

  39. [47]

    Tyumenev, M

    R. Tyumenev, M. Favier, S. Bilicki, E. Bookjans, R. L. Targat, J. Lodewyck, D. Nicolodi, Y. L. Coq, M. Abgrall, J. Gu´ ena, L. D. Sarlo, and S. Bize, N. J. Phys.18, 113002 (2016)

    2016

  40. [48]

    J. S. Schelfhout and J. J. McFerran, Phys. Rev. A 105, 022805 (2022)

    2022

  41. [49]

    E. A. Burt, J. D. Prestage, R. L. Tjoelker, D. G. Enzer, D. Kuang, D. W. Murphy, D. E. Robison, J. M. Seubert, R. T. Wang, and T. A. Ely, Nature 595, 43 (2021)

    2021

  42. [50]

    S. Sels, T. Day Goodacre, B. A. Marsh, A. Pastore, W. Ryssens, Y. Tsunoda, N. Althubiti, B. Andel, A. N. Andreyev, D. Atanasov, A. E. Barzakh, M. Bender, J. Billowes, K. Blaum, T. E. Cocolios, J. G. Cu- biss, J. Dobaczewski, G. J. Farooq-Smith, D. V. Fe- dorov, V. N. Fedosseev...

    2019

  43. [51]

    B. A. Marsh, T. Day Goodacre, S. Sels, Y. Tsunoda, B. Andel, A. N. Andreyev, N. A. Althubiti, D. Atanasov, A. E. Barzakh, J. Billowes, K. Blaum, T. E. Cocol- ios, J. G. Cubiss, J. Dobaczewski, G. J. Farooq-Smith, D. V. Fedorov, V. N. Fedosseev, K. T. Flanagan, L. P. Gaffney, L...

    2018

  44. [52]

    Heyde and J

    K. Heyde and J. L. Wood, Rev. Mod. Phys. 83, 1467 (2011)

    2011

  45. [53]

    Borie and G

    E. Borie and G. A. Rinker, Rev. Mod. Phys. 54, 67 (1982)

    1982

  46. [54]

    Angeli and K

    I. Angeli and K. P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)

    2013

  47. [55]

    J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932)

    1932

  48. [56]

    M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949)

    1949

  49. [57]

    A. A. Elizarov, V. M. Shabaev, N. S. Oreshkina, I. I. Tupitsyn, and T. St¨ ohlker, Opt. Spectrosc. 100, 361 (2006)

    2006

  50. [58]

    E. A. Uehling, Phys. Rev. 48, 55 (1935)

    1935

  51. [59]

    A. V. Volotka, D. A. Glazov, I. I. Tupitsyn, N. S. Ore- shkina, G. Plunien, and V. M. Shabaev, Phys. Rev. A 78, 062507 (2008)

    2008

  52. [60]

    V. M. Shabaev, A. N. Artemyev, V. A. Yerokhin, O. M. Zherebtsov, and G. Soff, Phys. Rev. Lett. 86, 3959 (2001)

    2001

  53. [61]

    J. R. Persson, Atomic Data and Nuclear Data Tables 154, 101589 (2023)

    2023

  54. [62]

    R. J. Reimann and M. N. McDermott, Phys. Rev. C 7, 2065 (1973)

    1973

  55. [63]

    S. J. Grunefeld, B. M. Roberts, and J. S. M. Ginges, Phys. Rev. A 100, 042506 (2019)

    2019

  56. [64]

    B. M. Roberts, C. J. Fairhall, and J. S. M. Ginges, Phys. Rev. A 107, 052812 (2023)

    2023

  57. [65]

    V. A. Dzuba, V. V. Flambaum, P. G. Silvestrov, and O. P. Sushkov, Phys. Lett. A 131, 461 (1988)

    1988

  58. [66]

    N. J. Stone, Table of Recommended Nuclear Magnetic Dipole Moments (International Atomic Energy Agency (IAEA), 2019)

    2019

  59. [67]

    G. Ulm, S. K. Bhattacherjee, P. Dabkiewicz, G. Hu- ber, H. J. Kluge, T. K¨ uhl, H. Lochmann, E. W. Otten, K. Wendt, S. A. Ahmad, W. Klempt, and R. Neugart, Z. Phys. A 325, 247 (1986)

    1986

  60. [68]

    E. A. Burt, S. Taghavi-Larigani, and R. L. Tjoelker, Phys. Rev. A 79, 062506 (2009)

    2009

  61. [69]

    Antognini, N

    A. Antognini, N. Berger, T. E. Cocolios, R. Dressler, R. Eichler, A. Eggenberger, P. Indelicato, K. Jung- mann, C. H. Keitel, K. Kirch, A. Knecht, N. Michel, J. Nuber, N. S. Oreshkina, A. Ouf, A. Papa, R. Pohl, M. Pospelov, E. Rapisarda, N. Ritjoho, S. Roccia, N. Sev- erijns, ...

    2020

  62. [70]

    Wauters, A

    F. Wauters, A. Knecht, and muX collaboration, SciPost Phys. Proc. , 022 (2021)

    2021

  63. [71]

    Ullmann, Z

    J. Ullmann, Z. Andelkovic, C. Brandau, A. Dax, W. Gei- thner, C. Geppert, C. Gorges, M. Hammen, V. Hannen, S. Kaufmann, K. K¨ onig, Y. A. Litvinov, M. Lochmann, B. Maaß, J. Meisner, T. Murb¨ ock, R. S´ anchez, M. Schmidt, S. Schmidt, M. Steck, T. St¨ ohlker, R. C. Thompson, C....

    2017

  64. [72]

    Dickopf, B

    S. Dickopf, B. Sikora, A. Kaiser, M. M¨ uller, S. Ulmer, V. A. Yerokhin, Z. Harman, C. H. Keitel, A. Mooser, and K. Blaum, Nature 632, 757 (2024)

    2024

Pith tools

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