Pith. sign in

REVIEW 2 major objections 5 minor 18 references

Energies of $I^{8+}$ through $I^{12+}$ low-lying levels

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read High-accuracy MCDHF-CI calculations give reliable level energies and M1 transition rates for the low-lying $[\mathrm{Kr}]4d^n$ states in I8+ through I12+, and the I10+ through I12+ results fill a gap in the literature.

desk verdict Solid, useful reference data for iodine ions; the 3% accuracy-class claim for unmeasured ions is a fair extrapolation but needs to be flagged as such. read the letter →

arxiv 2412.04044 v1 pith:XHMTKJ4J submitted 2024-12-05 physics.atom-ph

Karol Kozio{l} , Jacek Rzadkiewicz This is my paper · ORCID
classification physics.atom-ph PACS 32.30.-r31.15.Ar32.70.Cs
keywords iodineionshighlychargedenergylevelsM1transitionratesMCDHF-CIatomicdata4dopen-shellconfigurationsforbiddentransitions
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 reports high-accuracy Multi-Configuration Dirac–Hartree–Fock with Configuration Interaction (MCDHF-CI) calculations of the low-lying energy levels and magnetic-dipole transition rates of the five iodine ions I8+ through I12+, whose valence configurations are $[\mathrm{Kr}]4d^n$ for $n=5$–$9$. For I10+ through I12+, the authors argue, these tables fill a genuine gap in the published data, since no detailed analysis of the I XI, I XII, and I XIII spectra exists in the literature. The results are argued to be converged at the AS3 active-space stage, with level energies for I9+ through I12+ assigned roughly 3% (A accuracy class) uncertainties and the strongest M1 rates assigned B or C+ classes. The evidence is convergence between successive active spaces, agreement with measured I8+ and I9+ spectra to within 2.6%, and cross-checks of the strongest transitions against an independent relativistic code.

What carries the argument

The machinery is the MCDHF-CI expansion of atomic state functions as linear combinations of configuration state functions, with virtual orbitals included through principal quantum number $n=7$ and orbital angular momentum $l=5$. The calculation steps through four active spaces, AS0 through AS3, with AS3 containing up to about $2\times10^6$ CSFs for the heavier ions; the Breit interaction is added perturbatively and QED self-energy and vacuum-polarization corrections are included. The difference between the AS3 and AS2 energies serves as the estimated level-energy uncertainty, transition-rate uncertainties follow the Kramida procedure, and the independent FAC code provides a cross-check on the strongest M1 rates. This machinery is what supports the claim that the AS3 results are converged and that the I10+ through I12+ tables can stand as reference data.

What would settle it

A clean test would be an electron-beam ion trap or beam-foil measurement of a predicted M1 line in I10+, I11+, or I12+: for example, an I10+ M1 transition predicted at 295.20 nm (level 12 to level 2) or the I12+ line predicted at 265.87 nm (level 2 to level 1). A measured wavelength that differs from the predicted value by more than the assigned 3% would show that the uncertainty estimate underestimates the true error, while agreement within the stated class would validate the tables as reference data.

Watch

Extended reading notes

Core claim

The central claim is that a consistent set of MCDHF-CI calculations, carried out with the GRASP 2018 code, gives reliable level energies and M1 transition rates for the $[\mathrm{Kr}]4d^n$ ($n=5$–$9$) configurations of I8+ through I12+. For the two lowest-charge ions the computed levels reproduce experimentally deduced spectra within 2.6%, while for I10+, I11+, and I12+ the present results are offered as the missing reference data. The authors assign an A accuracy class (roughly 3% uncertainties) to the I9+ through I12+ level energies and B or C+ classes to the tabulated M1 transition rates, based on active-space convergence and on differences between the GRASP 2018 and FAC calculations.

Load-bearing premise

To assign 3% uncertainties to the unmeasured I10+ through I12+ levels, the paper assumes that the difference between the AS3 and AS2 active-space results bounds the true computational error, and that the accuracy measured for I8+ and I9+ against experiment carries over to the ions for which no measured spectra exist.

Editorial extensions

If this is right

  • The tables give the first computed energy-level and M1 transition-rate data for I10+, I11+, and I12+ in the $[\mathrm{Kr}]4d^n$ configurations, filling the gap noted in the NIST Atomic Spectra Database.
  • The I8+ and I9+ comparisons against measured spectra provide a benchmark for using the same method on neighbouring ions where experimental data are missing.
  • The listed M1 transitions, especially the strongest lines, give plasma diagnosticians and astrophysical modelers direct input for line identifications in iodine spectra.
  • The I11+ ($4d^6$, Mo-like) and I12+ ($4d^5$, Nb-like) data connect to the search for forbidden transitions suitable as optical-clock frequency references, a direction the introduction explicitly raises.

Reading between the lines

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

  • Applying the same AS2/AS3 convergence procedure to neighbouring tellurium and xenon ions would likely show similar accuracy, since the open-$d$-shell correlation structure varies smoothly along isoelectronic sequences; this is an inference, not a claim in the paper.
  • A systematic GRASP-versus-FAC comparison across all tabulated transitions, rather than only the strongest ones, would turn the overall B/C+ rate classification into a per-transition reliability map, which the paper does not provide.
  • Extending the active space beyond $n=7$ would indicate how much of the residual level-energy uncertainty comes from basis-set truncation rather than from physical effects such as higher-order QED or core-valence correlation.
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

2 major / 5 minor

Summary. The paper reports GRASP2018-based Multi-Configuration Dirac-Hartree-Fock with Configuration Interaction (MCDHF-CI) calculations of energy levels and M1 transition rates for the [Kr]4d^n (n=5-9) valence configurations of I8+ through I12+, with the explicit goal of providing reference data for I10+ through I12+, for which no measured spectra are available. The authors document active-space convergence (AS0 through AS3), estimate theoretical uncertainties from the AS2-to-AS3 difference, benchmark the I8+ and I9+ level energies against published experimental values, and compare selected M1 rates with FAC calculations. The main advertised result is a set of level-energy tables and transition-rate tables for the five iodine ions, with an A accuracy class (about 3%) claimed for the unmeasured ions I9+-I12+.

Significance. If the accuracy claims hold, the tables would be a useful reference for plasma spectroscopy, astrophysical modeling, and studies of forbidden transitions in open-d-shell highly charged ions, filling a genuine gap in the literature for I10+-I12+. The paper's strengths are that the calculations follow a systematic active-space protocol, the convergence pattern is reported for every ion, the I8+ and I9+ comparisons are genuine external benchmarks, and no parameter is fitted to the target data. The data tables are extensive and clearly organized. The main weakness is that the uncertainty classification for the unmeasured ions rests on an extrapolation that the paper's own benchmark data do not fully support; this weakens the central 'high-accuracy' claim unless it is corrected or recast.

major comments (2)
  1. [§3.3 and Table D] The assignment of a 3% (A accuracy class) uncertainty to I9+-I12+ level energies is not supported by the paper's internal evidence. The convergence-based uncertainty in §3.2 is up to 0.3% for I9+, yet Table D shows theory-experiment deviations for the same ion ranging from 0.1% to 2.6%, with all theoretical values systematically above the experimental ones (e.g., level 5 at 30638.93 cm^-1 vs 29860 cm^-1 and level 9 at 83632.17 cm^-1 vs 81670 cm^-1). Thus the AS2/AS3 convergence metric underestimates the true error by roughly an order of magnitude and does not capture the systematic offset. Taking the maximum observed I8+/I9+ deviation as the uncertainty for I10+, I11+, and I12+ is an extrapolation that needs either an explicit physical justification (e.g., why the error envelope should not grow with open-shell complexity or charge state) or a substantially more conservative accuracy statement. This is load-bearing because the abstract and conclusions advertise high-accuracy data for exactly the ions with no measured spectra.
  2. [§3.2-§3.3] The error budget is incomplete in a way that matters for the stated accuracy class. The paper accounts for active-space convergence (AS2 vs AS3) and, for transition rates, a GRASP-FAC comparison, but it does not quantify the combined contribution of the Breit interaction treatment, the QED model (screened hydrogenic self-energy and Fullerton-Rinker vacuum polarization), or the effect of restricting substitutions to 4s, 4p, and 4d subshells while keeping the n=1-3 core frozen. Because the I9+ benchmark shows a systematic offset much larger than the convergence estimate, one or more of these omitted terms likely dominate the error. I request a transparent discussion of these contributions, a level- or term-dependent error estimate, or a downgrade of the accuracy class for the unmeasured ions to a more defensible statement such as 'estimated to be within a few percent based on the I8+/I9+ envelope, but with an unquantified systematic component.'
minor comments (5)
  1. [Tables 6-10] The column header 'Upper level No. Upper level No.' appears in each transition table; the second column should be labeled 'Lower level No.' or 'Lower level' for clarity.
  2. [§3.3] The phrase 'Basing on this finding' should read 'Based on this finding'.
  3. [§1] The sentence 'Recent study suggested that HCIs with d(4−6) configurations might host suitable forbidden transitions' has a number and tense error ('Recent study suggested'); it should be 'A recent study suggested' or 'Recent studies have suggested'.
  4. [§3.2] The definition of the transition-rate uncertainty (selecting transitions with intensity above 10% of the strongest and extending that uncertainty to all transitions) should be justified for weak transitions, because the fractional uncertainty of a weak M1 rate can be much larger than that of the strong transitions used for calibration.
  5. [Table B] The notation |∆| = |AGRASP − AFAC|/AGRASP should be defined in the table caption, and the values are reported without explicit signs; specifying the sign would help identify systematic biases in the FAC comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: ab initio MCDHF-CI level energies and transition rates are computed from first principles with no fit to the target data, and the experimental comparisons used are external benchmarks.

full rationale

The paper's central results are MCDHF-CI level energies and M1 transition rates obtained directly from the GRASP 2018 implementation of the Dirac–Hartree–Fock equations with configuration interaction. No parameter is fitted to the I8+–I12+ level energies or to the transition rates that are then reported; the active-space convergence checks (AS0–AS3) are internal consistency measures, not constraints derived from the final data. The only comparisons to measurements are external: Joshi and van Kleef (1980) for I8+ and Churilov et al. (1998) for I9+, and these are used as benchmarks after the calculations are complete. The uncertainty estimate of 3% for I9+ through I12+ is an extrapolated accuracy class based on the maximum observed theory–experiment deviation for I8+ and I9+, not a quantity that is then relabeled as a prediction. This is a robustness concern—whether the 3% envelope transfers to unmeasured I10+–I12+ ions—rather than a circular derivation. The comparison between GRASP and FAC transition rates likewise provides independent cross-checks of two distinct methodologies and does not define the reported values by construction. No self-citation is load-bearing, no uniqueness claim is imported from the authors' prior work, and no known result is merely renamed. The derivation chain is therefore self-contained, and the paper warrants a circularity score of 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central numbers rest on the standard MCDHF-CI model and on two hand-chosen computational thresholds. There are no physical free parameters fitted to the target data, and no new entities are introduced.

free parameters (2)
  • MCDHF active space truncation (AS3) = n<=7, l<=5
    The CI space is limited to single and double substitutions from 4s, 4p, 4d into virtual orbitals up to n=7 and l=5; convergence is checked by comparing AS2 and AS3, but the truncation determines the reported energies.
  • Transition intensity threshold for uncertainty subset = 10% of strongest transition
    Transition-rate uncertainties are computed only for transitions stronger than 10% of the strongest M1 rate and then applied to all studied transitions, a selection that plausibly understates uncertainties for weaker lines.
assumptions (4)
  • domain assumption The GRASP2018 implementation of the Dirac-Coulomb-Breit Hamiltonian with perturbative Breit and QED corrections is accurate for open 4d shell ions.
    Invoked throughout Section 2; the paper relies on the code rather than proving the Hamiltonian approximation.
  • domain assumption The AS3 active space (n<=7, l<=5) with single and double substitutions from 4s, 4p, 4d is sufficient for converged level energies.
    Section 3.1 presents convergence plots for selected states of I8+ and I9+ and infers AS3 adequacy for all five ions.
  • domain assumption Screened hydrogenic self-energy and Fullerton-Rinker vacuum polarization approximations are adequate at this charge range.
    Section 2 states these QED corrections are included, with no independent test of their accuracy for iodine.
  • domain assumption The difference between AS2 and AS3 energies estimates a realistic uncertainty band.
    Section 3.2 defines deltaE as |E_AS3 - E_AS2| and uses it to quote uncertainties; this assumes monotonic convergence with active space size.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Energies of $I^{8+}$ through $I^{12+}$ low-lying levels." pith.science (2026). https://pith.science/paper/XHMTKJ4J

@misc{pith2026241204044,
  author       = {Pith},
  title        = {Pith review of: Energies of $I^8+$ through $I^12+$ low-lying levels},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHMTKJ4J}},
  note         = {Machine review of arXiv:2412.04044}
}
abstract

High-accuracy Multi-Configuration Dirac-Hartree-Fock with Configuration Interaction calculations of level energies and transition rates have been carried out for iodine $I^{8+}$ through $I^{12+}$ ions related to the [Kr]4d$^n$ ($n$ = 5-9) configurations. For $I^{10+}$ through $I^{12+}$ ions the present data fill up the lack of such data in the literature.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

18 extracted references · 16 canonical work pages

  1. [1]

    C. Lyu, C. H. Keitel, and Z. Harman, (2023), arXiv:2305.09603

    work page Pith review arXiv 2023

  2. [2]

    Yu and B

    Y .-M. Yu and B. K. Sahoo, Physical Review A109, 023106 (2024)

    work page 2024

  3. [3]

    A. E. Kramida, Y . Ralchenko, J. Reader, and N. A. Team, NIST Atomic Spectra Database, (version 5.12), [Online]. Available: https://physics.nist.gov/asd [Thu Dec 05 2024]. National Institute of Standards and Technology, Gaithersburg, MD (2024)

    work page 2024

  4. [4]

    Y . N. Joshi and T. A. M. van Kleef, Journal of the Optical Society of America70, 1344 (1980). 7 Table D Present MCDHF-CI calculated energy levels for 4d8 valence electronic configuration of I9+ ion compared to the ones deduced in Ref. [5] from experimental spectra. Relative difference between theoretical and experimental data, given as ∆ = (Theo. − Exp.)...

    work page 1980

  5. [5]

    S. S. Churilov, Y . N. Joshi, and R. R. Gayazov, Journal of the Optical Society of America B15, 1923 (1998)

    work page 1998

  6. [6]

    R. R. Gayasov, S. S. Churilov, Y . N. Joshi, A. N. Ryabtsev, and V . I. Azarov, Journal of the Optical Society of America B14, 1013 (1997)

    work page 1997

  7. [7]

    E. P. Ivanova, Atomic Data and Nuclear Data Tables 95, 786 (2009)

    work page 2009

  8. [8]

    Froese Fischer, G

    C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Biero ´n, Computer Physics Communications 237, 184 (2019)

    work page 2019

Show all 18 references
  1. [9]

    K. G. Dyall, I. P. Grant, C. Johnson, F. A. Parpia, and E. Plummer, Computer Physics Communications 55, 425 (1989)

    1989

  2. [10]

    I. P. Grant, Relativistic Quantum Theory of Atoms and Molecules, edited by I. P. Grant, Springer Series on Atomic, Optical, and Plasma Physics, V ol. 40 (Springer, New York, NY , 2007)

    2007

  3. [11]

    B. J. McKenzie, I. P. Grant, and P. H. Norrington, Computer Physics Communications 21, 233 (1980)

    1980

  4. [12]

    P. J. Mohr, Physical Review A 46, 4421 (1992)

    1992

  5. [13]

    L. W. Fullerton and G. A. Rinker, Physical Review A 13, 1283 (1976)

    1976

  6. [14]

    Froese Fischer, Atoms 2, 1 (2014)

    C. Froese Fischer, Atoms 2, 1 (2014)

    2014

  7. [15]

    Froese Fischer, M

    C. Froese Fischer, M. R. Godefroid, T. Brage, P. Jönsson, and G. Gaigalas, Journal of Physics B: Atomic, Molecular and Optical Physics 49, 182004 (2016)

    2016

  8. [16]

    A. E. Kramida, Fusion Science and Technology 63, 313 (2013)

    2013

  9. [17]

    M. F. Gu, Canadian Journal of Physics 86, 675 (2008)

    2008

  10. [18]

    Kimura and N

    N. Kimura and N. Nakamura, Journal of Physics B: Atomic, Molecular and Optical Physics 56, 225001 (2023) 8 Explanation of Tables Tables 1-5. J Total momentum of the state p Parity of the state E Energy of atomic level relative to the groundstate (cm-1/eV) Tables 6-10. λ Transi...

    2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.