Pith. sign in

REVIEW 3 major objections 5 minor 88 references

Relativistic configuration-interaction and coupled-cluster calculations of Ir$^{17+}$ transition energies and properties for optical clock applications

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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

Pith's one-line read Two forbidden transitions in the Ir17+ ion are predicted to serve as optical clock references, at 346 nm and 833 nm.

desk verdict A broadly useful property set for Ir17+ clock candidates, but the abstract swaps the two clock-transition wavelengths, which flips the sign of the magic-trap claim and needs correction before the paper is reliable. read the letter →

arxiv 2502.01112 v2 pith:ISSNTP3W submitted 2025-02-03 physics.atom-ph

H. X. Liu , Y. M. Yu , B. B. Suo , Y. F. Ge , Y. Liu This is my paper · ORCID
classification physics.atom-ph
keywords Ir17+highlychargedionopticalclockforbiddentransitionsrelativisticconfigurationinteractionFock-spacecoupledclusterfine-structureconstantvariationmagicradiofrequencytrapatomicpolarizability
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 paper predicts that the highly charged ion Ir$^{17+}$ offers two forbidden optical transitions suitable as clock references: from the $4f^{13}5s$ ground state to the $4f^{14} {}^1S_0$ state at about 346 nm, and to the $4f^{12}5s^2 {}^3H_6$ state at about 833 nm. The predictions come from two independent relativistic many-body methods, configuration interaction and Fock-space coupled cluster, whose results agree once basis-set and triple-excitation corrections are applied. If correct, Ir$^{17+}$ would provide narrow, long-lived clock lines whose negative differential polarizability allows a magic radiofrequency trap and whose opposite sensitivity coefficients make their frequency ratio a sensitive probe of variation in the fine-structure constant. The paper also supplies the supporting atomic properties—lifetimes, polarizabilities, quadrupole moments, hyperfine constants, isotope-shift factors, and Lorentz-invariance matrix elements—needed to plan experiments.

What carries the argument

The machinery is the relativistic many-body calculation under the Dirac-Coulomb-Gaunt Hamiltonian. Two independent methods carry the argument: a Kramers-restricted configuration-interaction (KRCI) calculation with single and double excitations of 32 electrons, and a Fock-space coupled-cluster (FSCC) calculation with single, double, and estimated triple excitations, both taken to increasingly large correlation-consistent basis sets. The argument is carried by the convergence pattern: basis-set enlargement and triple-excitation corrections move the two methods into agreement, and the same two methods are used for finite-field calculations of polarizabilities, quadrupole moments, hyperfine constants, and isotope-shift factors. The finite-field technique, which fits energies against applied electric-field or field-gradient perturbations, is what produces the differential polarizability and the 'magic' trap-frequency estimate.

What would settle it

A spectroscopic search in an electron-beam ion trap for the two forbidden lines would settle the claim: if no transitions appear near the predicted 346 nm and 833 nm positions, or if the $4f^{14} {}^1S_0$ level is found far outside the quoted $12006 \pm 1392$ cm$^{-1}$ window, then the two clock-candidate transitions are refuted.

Watch

Extended reading notes

Core claim

The central claim is that Ir$^{17+}$, with a ground configuration $4f^{13}5s$ and near-degenerate $4f^{14}$ and $4f^{12}5s^2$ excited configurations, has two strongly forbidden optical transitions with clock-grade properties. The KRCI calculation places the $4f^{14} {}^1S_0$ level at 12006 cm$^{-1}$ and the $4f^{12}5s^2 {}^3H_6$ level at 28848 cm$^{-1}$, corresponding to transitions at roughly 346 nm and 833 nm from the ground state; the paper quotes uncertainties of about 30 nm and 100 nm on these wavelengths. The first transition has a negative differential scalar polarizability of $-0.203$ a.u., which supports cancellation of the trap-induced Stark and micromotion shifts at a 'magic' radiofrequency near $500 \times 2\pi$ MHz, and the two transitions have opposite relativistic sensitivity coefficients ($K_\alpha \approx 68.7$ and $-35.5$), so their frequency ratio would be unusually sensitive to variation of the fine-structure constant. Long lifetimes, including 610 ms for the lowest excited state and states with lifetimes exceeding 100 ms, and small electric quadrupole moments for the ground and ${}^3H_6$ states are presented as additional clock advantages.

Load-bearing premise

The load-bearing premise is that the Dirac-Coulomb-Gaunt Hamiltonian without QED corrections (vacuum polarization and self-energy) and without the full Breit interaction describes the Ir$^{17+}$ spectrum accurately enough that the predicted clock-transition wavelengths and properties are trustworthy.

Editorial extensions

If this is right

  • If the central claim is correct, Ir$^{17+}$ becomes one of only a few highly charged ions with two viable optical clock transitions, one near-ultraviolet and one infrared.
  • A clock on the 346 nm transition could operate at a trap drive frequency near $500 \times 2\pi$ MHz where the DC Stark shift and the micromotion time-dilation shift cancel.
  • The frequency ratio of the two transitions would shift if the fine-structure constant changes, with the two lines moving in opposite directions, giving a self-calibrating $\alpha$-variation test.
  • The small quadrupole moments and low polarizabilities of the proposed clock states would suppress the dominant systematic shifts, while the large $T^{(2)}$ matrix elements would make Ir$^{17+}$ competitive in Lorentz-invariance searches.
  • The opposite-sign field-shift factors of the two transitions provide a path to isotope-shift and nuclear-structure studies of iridium.

Reading between the lines

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

  • A direct experimental target is electron-beam-ion-trap spectroscopy of Ir$^{17+}$ searching for the predicted 346 nm and 833 nm lines; confirmation would also settle whether the $4f^{14} {}^1S_0$ level sits near $12000$ cm$^{-1}$ rather than the $5000$-$7000$ cm$^{-1}$ range some earlier calculations suggested.
  • The same two-method convergence strategy could be transferred to neighboring charge states of iridium or to other $4f$-hole ions, where similar level crossings may hide clock-grade forbidden transitions.
  • A measurement of the differential polarizability of the 346 nm transition would test the magic-trap prediction more sharply than a frequency measurement alone, since a sign error in the computed $\Delta\alpha_d^S$ would eliminate the cancellation.
  • If omitted QED and full-Breit corrections shift the $4f^{14} {}^1S_0$ energy by thousands of cm$^{-1}$, the 833 nm transition may be the more robust candidate because its upper state's energy shows less scatter across the two methods and earlier calculations.
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 / 5 minor

Summary. The paper reports KRCI and FSCC calculations of Ir17+ excitation energies and properties under the Dirac-Coulomb-Gaunt Hamiltonian. It proposes two forbidden optical clock transitions from the 4f13 5s 3Fo4 ground state to the 4f14 1S0 and 4f12 5s2 3H6 states, with predicted wavelengths of about 346 nm and 833 nm, and claims that the negative differential polarizability of one transition enables a magic radio-frequency trap frequency while the two transitions have opposite Kα sensitivities. The manuscript also tabulates g-factors, lifetimes, polarizabilities, quadrupole moments, hyperfine constants, field-shift factors, and related properties for the low-lying states.

Significance. If the transition identification and properties are correct, Ir17+ would offer two long-lived forbidden optical transitions with useful features for HCI clocks and for searches of α-variation, including a possible magic RF trap frequency and opposite sensitivity coefficients. The paper's systematic use of multiple basis sets, explicit reference-state testing, and KRCI/FSCC cross-checks, together with the detailed supplementary tables, is a genuine strength. However, the headline identification is internally inconsistent, the two methods agree only at the one-sigma level for the clock states, and the error budget does not address omitted QED effects; these issues must be resolved before the claimed reliability can be accepted.

major comments (3)
  1. [Abstract; Sec. III A; Sec. III C; Table I; SM Table XV] The central clock-transition identification is internally inconsistent. The abstract assigns 346(30) nm to the 3Fo4 -> 4f14 1S0 transition and 833(100) nm to the 3Fo4 -> 4f12 5s2 3H6 transition, but Table I places 1S0 at 12006(1392) cm^-1 and 3H6 at 28848(2117) cm^-1, which by lambda = 10^7/E (cm^-1) corresponds to 833 nm and 347 nm, respectively. SM Table XV gives yet another set of values, 664 nm and 368 nm, for the same two transitions. Section III C then attributes the negative differential polarizability (which Table III gives only for 1S0) to the 346-nm transition and computes the magic RF frequency from it, even though Table III assigns the 346-nm transition to 3H6 with positive Delta-alpha. Until this assignment is corrected and the numerical sets are reconciled, the headline clock claims and the magic-frequency estimate cannot be evaluated.
  2. [Sec. III A; SM Table V] The claimed excellent agreement between KRCI and FSCC is overstated. For the two clock states, the FSCC final values are 10203(3563) cm^-1 for 4f14 1S0 and 27445(3007) cm^-1 for 4f12 5s2 3H6, while KRCI gives 12006(1392) cm^-1 and 28848(2117) cm^-1, respectively; the central values differ by about 1800 and 1400 cm^-1. The FSCC final values are obtained by adding Delta_T and Delta_basis corrections estimated at different truncation levels (SDT with the 2-zeta basis, SD with the 3-zeta/4-zeta bases), and the additivity of these separately estimated corrections is an assumption that is not tested. Given that the method differences are comparable to the quoted uncertainties, the robustness claim should either be demonstrated quantitatively or replaced by a more conservative statement.
  3. [Sec. II A, Eq. (1)] The Dirac-Coulomb-Gaunt Hamiltonian omits QED corrections (vacuum polarization and self-energy) and the frequency-dependent Breit interaction. For Z=77, these omitted contributions can be comparable to the 1000-3600 cm^-1 uncertainties quoted in Table I, and the manuscript provides no estimate of their size. A defensible error budget for candidate clock transitions needs at least a model estimate of these shifts or an explicit argument for their smallness, especially since the excited configurations differ in 4f/5s occupations and would not be expected to cancel.
minor comments (5)
  1. [Sec. III C] The formula for nu_magic is dimensionally unclear as written; please state whether nu_magic is a cyclic frequency or an angular frequency, give the SI conversions used for Delta-alpha, and show how the quoted 500 x 2pi MHz follows from the corrected transition frequency.
  2. [Table II] The columns for K_alpha and the LLI reduced matrix elements appear misaligned in the current rendering; please reformat the table and verify that the text's K_alpha values (0.7 and 1.9) are assigned to the intended states.
  3. [Sec. II D] The section heading 'The field-field calculation' should read 'The finite-field calculation'.
  4. [References] Reference [53] lists the year 2004, but the volume and page numbers (328, 109151) indicate the year should almost certainly be 2024.
  5. [Sec. III A] The statement that the dyall.aae3z basis set 'tends to underestimate energy values' is based on a limited 3-zeta/4-zeta comparison; please clarify whether this is intended as a general observation or is specific to the present calculations.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the central energies and properties come from independent ab initio KRCI and FSCC calculations; the abstract's swapped 346/833 nm labels are an internal-consistency error, not a circular reduction.

full rationale

All load-bearing quantities in this paper—the 4f13 5s to 4f14 and 4f12 5s2 excitation energies (Table I), lifetimes, polarizabilities, hyperfine constants, and Kalpha coefficients—are produced by ab initio KRCI and FSCC calculations under the DCG Hamiltonian. The excitation energies are not fitted to, or defined in terms of, the clock-transition wavelengths: the wavelengths reported in the abstract are simple c/Delta-E conversions of the independently computed KRCI energies. The KRCI/FSCC concordance is an internal cross-check between two independent many-body implementations, and the FSCC 'FINAL' values extrapolate from larger-basis CCSD plus small-basis SDT and basis-set corrections rather than tuning parameters to reproduce the KRCI or experimental data. No load-bearing step rests on a self-citation: the cited prior work by the same authors is methodological or contextual, not the source of the central predictions. The abstract's apparent inversion of the 346 nm and 833 nm assignments relative to Table I is an internal labeling inconsistency, but it does not feed back into the energy calculation and is therefore a correctness risk rather than a circular derivation.

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

No experimental data were used to fit constants, so the ledger contains no fitted parameters in the usual sense. The listed items are modeling and convergence choices (reference state, virtual cutoff, correction additivity) plus the physical Hamiltonian assumption; together they set the numerical values that underpin the clock-transition claims.

free parameters (3)
  • DHF reference state choice (Case II, 14in7(4f)) = All 14 valence electrons in 4f orbitals
    Selected because other DHF references (14in8, 13in7+5s, 12in7+5s2) predict incorrect ground states, disordered levels, or missed states (SM Sec. I); the final KRCI energies depend on this choice.
  • Virtual orbital truncation at 20 a.u. = 20 a.u.
    Final e32-CISD and e60-CCSD calculations keep virtual orbitals with energy above 20 a.u.; uncertainty is estimated by comparing with a 300 a.u. cutoff (SM Table IV), so this is a convergence control rather than a fitted parameter.
  • FSCC triple-excitation correction Delta_T = e.g., -3441 cm^-1 for 4f14 1S0
    Computed as the difference between e32-CCSD and e32-CCSDT at the 2z basis and added to the 4z e60-CCSD result; the final FSCC energies are extrapolations, not direct large-basis SDT calculations (SM Table V).
assumptions (3)
  • domain assumption The Dirac-Coulomb-Gaunt Hamiltonian (Eq. 1) accurately models the relevant Ir17+ states, including neglect of QED.
    The Hamiltonian omits frequency-dependent Breit and radiative corrections; no numerical estimate of these effects is given, yet the paper assigns sub-4000 cm^-1 uncertainties to the energies.
  • ad hoc to paper The Case II DHF reference state provides a balanced representation of the 4f13 5s, 4f14, and 4f12 5s2 manifolds.
    The choice is justified by comparison to expected physical ordering but is not derived from a first-principles criterion: SM Sec. I shows other references fail.
  • ad hoc to paper Additivity of separately estimated basis-set, virtual-truncation, and triple-excitation corrections.
    The final KRCI and FSCC values are formed by adding Delta_basis, Delta_virt, and Delta_T computed under different model spaces; this assumes the corrections are independent and linear.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Relativistic configuration-interaction and coupled-cluster calculations of Ir$^{17+}$ transition energies and properties for optical clock applications." pith.science (2026). https://pith.science/paper/ISSNTP3W

@misc{pith2026250201112,
  author       = {Pith},
  title        = {Pith review of: Relativistic configuration-interaction and coupled-cluster calculations of Ir$^17+$ transition energies and properties for optical clock applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ISSNTP3W}},
  note         = {Machine review of arXiv:2502.01112}
}
abstract

The transition energies and properties of the Ir$^{17+}$ ion are calculated using the Kramers-restricted configuration-interaction (KRCI) and Fock-space coupled-cluster (FSCC) methods within the Dirac-Coulomb-Gaunt Hamiltonian framework. These calculations show several forbidden optical transitions between the $4f^{13}5s$ ground state and the $4f^{14}$ and $4f^{12}5s^2$ excited states, underscoring their potential as candidates for optical clock applications. Additionally, key properties of the ground and low-lying excited states are reported, including Lande $g_J$ factors, lifetimes, electric dipole polarizabilities, electric quadrupole moments, hyperfine structure constants, relativistic sensitivities, Lorentz-invariance coefficient tensor, and isotope shifts. The excellent agreement between the results from the KRCI and FSCC methods demonstrates the robustness of the calculations and confirms the reliability of the proposed clock transitions.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

88 extracted references · 70 canonical work pages

  1. [1]

    S. M. Brewer, J. -S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, Phys. Rev. Lett. 131, 059901 (2023)

    2023

  2. [2]

    Lange, A

    R. Lange, A. A. Peshkov, N. Huntemann, C. Tamm, A. Surzhykov, and E. Peik, Phys. Rev. Lett. 127, 213001 (2021)

    2021

  3. [3]

    Tofful, C

    A. Tofful, C. F. A. Baynham, E. A. Curtis, A. O. Parsons, B. I. Robertson, M. Schioppo, J. Tunesi, H. S. Margolis, R. J. Hendricks, J. Whale, R. C. Thompson, and R. M. Godun, Metrologia 61, 045001 (2024)

    2024

  4. [4]

    Aeppli, K

    A. Aeppli, K. Kim, W. Warfield, M. S. Safronova, and J. Ye, Phys. Rev. Lett. 113, 023401 (2024)

    2024

  5. [5]

    Takamoto, I

    M. Takamoto, I. Ushijima, N. Ohmae, T. Yahagi, K. Kokado, H. Shinkai, and H. Katori, Nat. Photon. 14, 411 (2020)

    2020

  6. [6]

    K. Kim, A. Aeppli, T. Bothwell, and J. Ye, Phys. Rev. Lett. 130, 113203 (2024)

    2024

  7. [7]

    Zhang, Z

    A. Zhang, Z. X. Xiong, X. T. Chen, Y. Y. Jiang, J. Q. Wang, C. C. Tian, Q. Zhu, B. Wang, D. Z. Xiong, L. X. He, L. S. Ma, and B. L. Lyu, Metrologia 59, 065009 (2022)

    2022

  8. [8]

    L. M. Luo, H. Qiao, D. Ai, M. Zhou, S. Zhang, C. Y. Sun, Q. C. Qi, C. Q. Peng, T. Y. Jin, W. Fang, Z. Q. Yang, T. C. Li, K. Liang, and X. Y. Xu, Metrologia 57, 065017 (2020)

    2020

Show all 88 references
  1. [9]

    M. Y. Zeng, Y. Huang, B. L. Zhang, Y. M. Hao, Z. X. Ma, R. M. Hu, H. Q. Zhang, Z. Chen, M. Wang, H. Guan, and K. L. Gao, Phys. Rev. Applied 19, 064004 (2023)

    2023

  2. [10]

    H. N. Hausser, J. Keller, T. Nordmann, N. M. Bhatt, J. Kiethe, H. Liu, I. M. Richter, M. von Boehn, J. Rahm, S. Weyers, E. Benkler, B. Lipphardt, S. D¨ orscher, K. Stahl, J. Klose, C. Lisdat, M. Filzinger, N. Huntemann, E. Peik, T. E. Mehlst¨ aubler, Phys. Rev. Lett.134, 023201 (2025)

    2025

  3. [11]

    V. V. Flambaum, Int. J. Mod. Phys. A 22, 4937 (2007)

    2007

  4. [12]

    R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, Phys. Rev. Lett. 113, 210801 (2014)

    2014

  5. [13]

    Huntemann, B

    N. Huntemann, B. Lipphardt, C. Tamm, V. Gerginov, S. Weyers, and E. Peik, Phys. Rev. Lett. 113, 210802 (2014)

    2014

  6. [14]

    Lange, N

    R. Lange, N. Huntemann, J. M. Rahm, C. Sanner, H. Shao, B. Lipphardt, C. Tamm, S. Weyers, and E. Peik, Phys. Rev. Lett. 126, 011102 (2021)

    2021

  7. [15]

    Filzinger, S

    M. Filzinger, S. D¨ orscher, R. Lange, J. Klose, M. Steinel, E. Benkler, E. Peik, C. Lisdat, and N. Huntemann, Phys. Rev. Lett. 130, 253001 (2023)

    2023

  8. [16]

    C. W. Chou, D. B. Hume, T. Rosenband, and D. J. Wineland, Science 329, 1630 (2010)

    2010

  9. [17]

    Delva, N

    P. Delva, N. Puchades, E. Sch¨ onemann, F. Dilssner, C. Courde, S. Bertone, F. Gonzalez, A. Hees, C. L. Poncin- Lafitte, F. Meynadier, R. Prieto-Cerdeira, B. Sohet, J. Ventura-Traveset, and P. Wolf, Phys. Rev. Lett. 121, 231101 (2018)

    2018

  10. [18]

    Bothwell, C

    T. Bothwell, C. J. Kennedy, A. Aeppli, D. Kedar, J. M. Robinson, E. Oelker, A. Staron, and J. Ye, Nature 602, 420 (2022)

    2022

  11. [19]

    Megidish, J

    E. Megidish, J. Broz, N. Greene, and H. H¨ affner, Phys. Rev. Lett. 122, 123605 (2019)

    2019

  12. [20]

    Sanner, N

    C. Sanner, N. Huntemann, R. Lange, C. Tamm, E. Peik, M. S. Safronova, and S. G. Porsev, Nature 567, 204 (2019)

    2019

  13. [21]

    L. S. Dreissen, C. H. Yeh, H. A. F¨ urst, K. C. Grense- mann, and T. E. Mehlst¨ oubler, Nat. Commun.13, 7314 (2022)

    2022

  14. [22]

    W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Sch¨ affer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, Nature564, 87 (2018)

    2018

  15. [23]

    Beloy, M

    K. Beloy, M. I. Bodine, T. Bothwell, S. M. Brewer, S. L. Bromley, J. S. Chen, J. D. Deschˆ enes, S. A. Diddams, R. J. Fasano, T. M. Fortier, Y. S. Hassan, D. B. Hume, D. Kedar, C. J. Kennedy, I. Khader, A. Koepke, D. R. Leibrandt, H. Leopardi, A. D. Ludlow, W. F. McGrew, W. R....

    2021

  16. [24]

    J. L. Ellis, M. I. Bodine, W. C. Swann, S. A. Stevenson, E. D. Caldwell, L. C. Sinclair, N. R. Newbury, and J. D. Deschˆenes, Phys. Rev. Applied 15, 034002 (2021)

    2021

  17. [25]

    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

  18. [26]

    Casini, E

    S. Casini, E. Turan, A. Cervone, B. Monna, and P. Visser, Sci. Rep. 13, 16253 (2023)

    2023

  19. [27]

    E. A. Burt, T. A. Ely, and R. L. Tjoelker, J. Phys. Conf. Ser. 2889, 012014 (2024)

    2024

  20. [28]

    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

  21. [29]

    J. C. Berengut, C. Delaunay, A. Geddes, and Y. Soreq, Phys. Rev. Research 2, 043444 (2020)

    2020

  22. [30]

    Brzeminski, Z

    D. Brzeminski, Z. Chacko, A. Dev, I. Flood, and A. Hook, Phys. Rev. D 106, 095031 (2022)

    2022

  23. [31]

    N. H. Rehbehn, M. K. Rosner, J. C. Berengut, P. O. Schmidt, T. Pfeifer, M. F. Gu, and J. R. Crespo L´ opez- Urrutia, Phys. Rev. Lett. 131, 161803 (2023)

    2023

  24. [32]

    V. A. Dzuba, V. V. Flambaum, and A. J. Mansour, Phys. Rev. D 110, 055022 (2024)

    2024

  25. [33]

    J. C. Berengut and C. Delaunay, Nat. Rev. Phys. 7, 119 (2025)

    2025

  26. [34]

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

    2018

  27. [35]

    M. G. Kozlov, M. S. Safronova, J. R. Crespo L´ opez- Urrutia, and P. O. Schmidt, Rev. Mod. Phys. 90, 045005 (2018)

    2018

  28. [36]

    Y. M. Yu, B. K. Sahoo, and B. B. Suo, Front. Phys. 11, 1104848 (2023)

    2023

  29. [37]

    J. C. Berengut, V. A. Dzuba, V. V. Flambaum, and A. Ong, Phys. Rev. Lett. 106, 210802 (2011)

    2011

  30. [38]

    M. S. Safronova, V. A. Dzuba, V. V. Flambaum, U. I. Safronova, S. G. Porsev, and M. G. Kozlov, Phys. Rev. Lett. 113, 030801 (2014)

    2014

  31. [39]

    V. I. Yudin, A. V. Taichenachev, and A. Derevianko, Phys. Rev. Lett. 113, 233003 (2014)

    2014

  32. [40]

    V. A. Dzuba, V. V. Flambaum, and H. Katori, Phys. Rev. A 91, 022119 (2015). 10

    2015

  33. [41]

    V. A. Dzuba and V. V. Flambaum, Hyperfine Interact. 79, 86 (2015)

    2015

  34. [42]

    V. A. Dzuba, M. S. Safronova, U. I. Safronova, and V. V. Flambaum, Phys. Rev. A 92, 060502 (2015)

    2015

  35. [43]

    Y. M. Yu and B. K. Sahoo, Phys. Rev. A 94, 062502 (2016)

    2016

  36. [44]

    Y. M. Yu and B. K. Sahoo, Phys. Rev. A 97, 041403 (2018)

    2018

  37. [45]

    Y. M. Yu and B. K. Sahoo, Phys. Rev. A 99, 022513 (2019)

    2019

  38. [46]

    Bekker, A

    H. Bekker, A. Borschevsky, Z. Harman, C. H. Keitel, T. Pfeifer, P. O. Schmidt, J. R. Crespo L´ opez-Urrutia, and J. C. Berengut, Nat. Commun. 10, 5651 (2019)

    2019

  39. [47]

    Beloy, Phys

    K. Beloy, Phys. Rev. Lett. 127, 013201 (2021)

    2021

  40. [48]

    Y. M. Yu, P. Duo, S. L. Chen, B. Arora, H. Guan, K. Gao, and J. Chen, Atoms 10, 123 (2022)

    2022

  41. [49]

    S. O. Allehabi, S. M. Brewer, V. A. Dzuba, V. V. Flam- baum, and K. Beloy, Phys. Rev. A 106, 043101 (2022)

    2022

  42. [50]

    S. G. Porsev, C. Cheung, M. S. Safronova, H. Bekker, N. H. Rehbehn, J. R. Crespo L´ opez-Urrutia, and S. M. Brewer, Phys. Rev. A 110, 042823 (2024)

    2024

  43. [51]

    V. A. Dzuba and V. V. Flambaum, Phys. Rev. A 110, 012801 (2024)

    2024

  44. [52]

    Y. M. Yu and B. K. Sahoo, Phys. Rev. A 109, 023106 (2024)

    2024

  45. [53]

    S. O. Allehabi, V. A. Dzuba, and V. V. Flambaum, J. Quant. Spectr. Rad. Transfer 328, 109151 (2004)

    2004

  46. [54]

    S. A. King, L. J. Spieß, P. Micke, A. Wilzewski, T. Leopold, E. Benkler, R. Lange, N. Huntemann, A. Surzhykov, V. A. Yerokhin, J. R. Crespo L´ opez-Urrutia, and P. O. Schmidt, Nature 611, 43 (2022)

    2022

  47. [55]

    J. C. Berengut, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. Lett. 105, 120801 (2010)

    2010

  48. [56]

    Windberger, J

    A. Windberger, J. R. Crespo L´ opez-Urrutia, H. Bekker, N. S. Oreshkina, J. C. Berengut, V. Bock, A. Borschevsky, V. A. Dzuba, E. Eliav, Z. Harman, U. Kaldor, S. Kaul, U. I. Safronova, V. V. Flambaum, C. H. Keitel, P. O. Schmidt, J. Ullrich, and O. O. Versolato, Phys. Rev. Let...

    2015

  49. [57]

    U. I. Safronova, V. V. Flambaum, and M. S. Safronova, Phys. Rev. A 92, 022501 (2015)

    2015

  50. [58]

    Cheung, M

    C. Cheung, M. S. Safronova, S. G. Porsev, M. G. Kozlov, I. I. Tupitsyn, and A. I. Bondarev, Phys. Rev. Lett. 124, 163001 (2020)

    2020

  51. [60]

    Olsen, P

    J. Olsen, P. Jørgensen, and J. Simons, Chem. Phys. Lett. 169, 463 (1990)

    1990

  52. [61]

    Olsen, J

    J. Olsen, J. Chem. Phys. 113, 7140 (2000)

    2000

  53. [62]

    Fleig, J

    T. Fleig, J. Olsen, and L. Visscher, J. Chem. Phys. 119, 2963 (2003)

    2003

  54. [63]

    Fleig, H

    T. Fleig, H. J. Aa. Jensen, J. Olsen, and L. Visscher, J. Chem. Phys. 124, 104106 (2006)

    2006

  55. [64]

    Thyssen, T

    J. Thyssen, T. Fleig, and H. J. Aa. Jensen, J. Chem. Phys. 129, 034109 (2008)

    2008

  56. [65]

    Knecht, H

    S. Knecht, H. J. Aa. Jensen, and T. Fleig, J. Chem. Phys. 132, 014108 (2010)

    2010

  57. [66]

    Kaldor, Theor

    U. Kaldor, Theor. Chim. Acta 80, 427 (1991)

    1991

  58. [67]

    Visscher, T

    L. Visscher, T. J. Lee and K. G. Dyall, J. Chem. Phys. 105 (1996) 8769

    1996

  59. [68]

    Visscher, E

    L. Visscher, E. Eliav and U. Kaldor, J. Chem. Phys. 115 (2002) 9720

    2002

  60. [69]

    Pernpointner and L

    M. Pernpointner and L. Visscher, J. Comp. Chem. 24 754 (2003)

    2003

  61. [70]

    A. V. Oleynichenko, A. Zaitsevskii, and E. Eliav, in Super-computing, edited by V. Voevodin and S. Sobolev (Springer, Cham, 2020), Vol. 1331, pp. 375–386

    2020

  62. [71]

    Oleynichenko, A

    A. Oleynichenko, A. Zaitsevskii, and E. Eliav, EXP-T, an extensible code for Fock space relativistic coupled cluster calculations (see http://www.qchem.pnpi.spb.ru/expt) (2020)

    2020

  63. [72]

    K. G. Dyall, P. Tecmer, and A. Sunaga, J. Chem. Theory Comput. 19, 198 (2023)

    2023

  64. [73]

    Visscher and K

    L. Visscher and K. G. Dyall, At. Data Nucl. Data Tables 67, 207 (1997)

    1997

  65. [74]

    Sikkema, L

    J. Sikkema, L. Visscher, T. Saue and M. Iliaˇ s, J. Chem. Phys. 131, 124116 (2009)

    2009

  66. [75]

    Knecht, M

    S. Knecht, M. Repisky, H. J. Aa. Jensen, and T. Saue, J. Chem. Phys. 157, 114106 (2022)

    2022

  67. [76]

    Fleig, J

    T. Fleig, J. Olsen, and C. M. Marian, J. Chem. Phys. 114, 4775 (2001)

    2001

  68. [77]

    Thyssen, Ph.D

    J. Thyssen, Ph.D. dissertation, Department of Chem- istry, University of Southern Denmark, Odense, Den- mark, 2001

    2001

  69. [78]

    Detailed investigation of DHF reference states, data o f the KRCI and FSCC calculations of energy and various properties for different basis sets and computational pa- rameters with comparison of data and uncertainty anal- ysis, the calculation of the lifetime of excited states

  70. [79]

    DIRAC, a relativistic ab initio electronic structure p ro- gram, Release DIRAC22 (2022), written by H. J. Aa. Jensen, R. Bast, A. S. P. Gomes, T. Saue and L. Viss- cher, with contributions from I. A. Aucar, V. Bakken, C. Chibueze, J. Creutzberg, K. G. Dyall, S. Dubillard, U. E...

    2022

  71. [80]

    T. Saue, R. Bast, A. S. P. Gomes, H. J. Aa. Jensen, L. Visscher, I. A. Aucar, R. Di Remigio, K. G. Dyall, E. Eliav, E. Faßhauer, T. Fleig, L. Halbert, E. D. Hedeg ˚ ard, B. Helmich-Paris, M. Iliaˇ s, C. R. Jacob, S. Knecht, J. K. Laerdahl, M. L. Vidal, M. K. Nayak, M. Olejnicz...

    2020

  72. [81]

    D. Peng, N. Middendorf, F. Weigend, M. Reiher, J. Chem. Phys. 138, 184105 (2013)

    2013

  73. [82]

    E. F. Archibong and A. J. Thakkar, Phys. Rev. A 44, 5478 (1991)

    1991

  74. [83]

    X. T. Guo, Y. M. Yu, Y. Liu, B. B. Suo, and B. K. Sahoo, Phys. Rev. A 103, 013109 (2021)

    2021

  75. [84]

    P. A. B. Haase, E. Eliav, M. Ilia´ s, and A. Borschevsky, J. Phys. Chem. A 124, 3157 (2020)

    2020

  76. [85]

    Denis, P

    M. Denis, P. A. B. Haase, M. C. Mooij, Phys. Rev. A 105, 052811 (2022). 11

    2022

  77. [86]

    Dub´ e, A

    P. Dub´ e, A. A. Madej, Z. Zhou, and J. E. Bernard, Phys. Rev. A 87, 023806 (2013)

    2013

  78. [87]

    14in8(4f5s)

    R. Shaniv, N. Akerman, T. Manovitz, Y. Shapira, N. Ozeri, and D. F. J. Kimball, Phys. Rev. Lett.120, 103202 (2018). arXiv:2502.01112v2 [physics.atom-ph] 10 Feb 2025 1 I. CHOICE OF REFERENCE STATE FOR DHF CALCULATION In this section, we conduct a detailed investigation into the...

    2018 arXiv

  79. [88]

    Cheung, M

    C. Cheung, M. S. Safronova, S. G. Porsev, M. G. Kozlov, I. I . Tupitsyn, and A. I. Bondarev, Phys. Rev. Lett. 124, 163001 (2020)

    2020

  80. [89]

    V. A. Dzuba and V. V. Flambaum, Phys. Rev. A 108, 053111 (2023)

    2023

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.