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REVIEW 3 major objections 6 minor 51 references

Study of thorium in hypersonic gas jets: Ionization potentials of Th and Th$^+$

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Thorium's first two ionization potentials are pinned down to record precision

desk verdict Clean, significantly improved IP1 from a first in-gas-jet Rydberg series; IP2 is plausible but the threshold method's missing systematic error keeps it from being equally secure. read the letter →

arxiv 2507.21946 v1 pith:KHIBTW7V submitted 2025-07-29 physics.atom-ph nucl-ex

A. Claessens , F. Ivandikov , M. Brasseur , A. Dragoun , Ch. E. Düllmann , R. Ferrer , Yu. Kudryavtsev , P. Palmeri
show 5 more authors
P. Quinet S. Raeder D. Renisch P. Van den Bergh P. Van Duppen
This is my paper · ORCID
classification physics.atom-phnucl-ex PACS 32.10.-f32.30.-r32.80.Fb32.80.Rm
keywords thoriumionizationpotentialRydbergserieshypersonicgasjetlaserspectroscopyautoionizingstatesfieldnuclearclockisomerMCDHFcalculations
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 reports the most precise values yet for the first and second ionization potentials of thorium: IP1 = 50 868.41(11) $cm^{-1}$ and IP2 = 99 207(73) $cm^{-1}$, improving on previous measurements by factors of 9 and 22. The key advance is performing resonance ionization spectroscopy in a hypersonic argon gas jet, where collision-induced quenching is suppressed and a clean Rydberg series converging to IP1 becomes visible. The same gas-cell data yield an efficient laser ionization scheme for Th+ based on an autoionizing state at 99 766.87 $cm^{-1}$, intended for future study of the 229mTh nuclear-clock isomer. The authors also validate their threshold-fitting method for IP2 by showing it reproduces the Rydberg-derived IP1 with a 21 $cm^{-1}$ offset.

What carries the argument

The central objects are the Rydberg series of neutral thorium observed in the hypersonic jet, described by the Rydberg-Ritz formula $E_n = E_{\mathrm{IP}} - R_\mu/(n-\delta)^2$ with a constant quantum defect $\delta = 0.56(1)$, and the empirical S-curve threshold $E_{\mathrm{IP2}} = 2\beta + x_0$ applied to the ion. The hypersonic argon jet, with Mach number above 8, is the enabling mechanism: it reduces the collision rate by about four orders of magnitude relative to the gas cell, suppressing quenching so that the Rydberg series becomes resolvable, and the electric field of the RFQ ion guide subsequently field-ionizes the Rydberg atoms in a localized region, as confirmed by time-of-flight measurements.

What would settle it

A future high-resolution measurement of a different Rydberg series of neutral Th, or of the Th+ Rydberg series in a gas jet, that fits a series limit incompatible with 50 868.41(11) $cm^{-1}$ beyond the combined uncertainties would falsify the IP1 claim; for IP2, a direct Rydberg-series limit for Th+ differing from 99 207(73) $cm^{-1}$ by more than the 21 $cm^{-1}$ calibration offset would falsify the threshold extrapolation.

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Extended reading notes

Core claim

We determine the first ionization potential of thorium to be 50 868.41(2)_stat(11)_sys $cm^{-1}$, or 6.306 879(14) eV, from a Rydberg-Ritz fit to 17 unperturbed members of a single Rydberg series observed in a hypersonic gas jet, and the second ionization potential to be 99 207(73) $cm^{-1}$, or 12.300(9) eV, from an S-curve threshold fit to photoionization data in a gas cell. The gas jet suppresses collisional quenching and delivers a spectral resolution of 240(30) MHz, and time-of-flight measurements show that the Rydberg atoms are ionized by field ionization in the RFQ region. Multiconfigurational Dirac-Hartree-Fock calculations reproduce the experimental values within 0.06% (IP1) and 0.19% (IP2). A laser ionization scheme for Th+ based on the autoionizing state at 99 766.87(22) $cm^{-1}$ reaches an efficiency of at least 1.2%, but attempts to observe laser photoionization of 229Th+ from a 233U recoil source were unsuccessful.

Load-bearing premise

The IP1 value assumes the 17 selected peaks form a single Rydberg series with a constant quantum defect $\delta = 0.56(1)$ and that the three excluded members (n = 56, 57, 58) are genuinely perturbed; the IP2 value additionally assumes the empirical S-curve threshold offset, calibrated on neutral thorium with a 21 $cm^{-1}$ deviation, applies to Th+.

Editorial extensions

If this is right

  • The first ionization potential of thorium is now known to 0.11 cm^-1, a 9-fold improvement, providing a precise anchor for Rydberg extrapolations and atomic-structure calculations across the actinides.
  • The second ionization potential at 99 207(73) cm^-1 constrains the energies of autoionizing states and the electronic-bridge decay estimates relevant to the 229mTh isomer in Th+.
  • The demonstrated combination of in-gas-jet Rydberg spectroscopy with subsequent field ionization establishes a route to high-resolution ionization-potential measurements for short-lived actinides at on-line laser-spectroscopy facilities.
  • The laser ionization scheme using the 99 766.87 cm^-1 autoionizing state offers a practical basis for efficient gas-cell laser ion sources producing thorium beams.
  • The observed 21 cm^-1 offset between the threshold method and the Rydberg-Ritz fit provides a species-specific calibration point for the threshold approach.

Reading between the lines

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

  • If the in-gas-jet Rydberg method can be extended to Th+, the IP2 uncertainty, currently 73 cm^-1, could shrink by roughly two orders of magnitude to match the IP1 precision; the paper's inability to observe a Th+ Rydberg series in the gas jet makes that the direct next test.
  • The unsuccessful 229Th+ photoionization suggests that a substantial fraction of recoiling ions occupy long-lived metastable 'dark' states; if so, isomer studies may need either an ionization scheme targeting those states or a neutralization-reionization strategy.
  • The constant quantum defect $\delta = 0.56(1)$ over the range n = 44 to 63 is consistent with a single 6d7s np Rydberg series; identifying its spectator configuration could tie the measured limit to a specific LS term and test the present level assignments.
  • If the threshold S-curve offset of 21 cm^-1 is found to be similar for other elements, the threshold method could serve as a semi-empirical predictor of ionization potentials for species where Rydberg series are experimentally inaccessible.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript reports laser ionization spectroscopy of 232Th and 232Th+ in an argon gas cell and in a hypersonic gas jet. The authors identify a 17-member Rydberg series in neutral Th, fit it with the Rydberg-Ritz formula, and obtain IP1(Th) = 50868.41(2)_stat(11)_sys cm^-1, a large improvement over the literature value. For Th+, they extract a photoionization threshold by fitting a sigmoid to selected background regions of a congested spectrum and quote IP2(Th+) = 99207(73) cm^-1 = 12.300(9) eV. The paper also reports autoionizing states with laser ionization efficiencies up to a few percent, MCDHF and HFR+CPOL atomic structure calculations, an in-gas-jet hyperfine spectrum of 229Th, and an unsuccessful search for laser ionization of 229Th+ from 233U recoil sources.

Significance. If the two ionization potentials are correct, the paper delivers the most precise first ionization potential of thorium and a substantially improved second ionization potential, together with the first in-gas-jet Rydberg series detected via field ionization. The strengths of the paper are concrete: the Rydberg-Ritz analysis uses 17 unperturbed members with a constant quantum defect and a clearly stated step-size systematic uncertainty; the field-ionization mechanism is supported by time-of-flight measurements; and the gas-jet performance is demonstrated by a 238(30) MHz hyperfine line. The IP2 result is, however, less secure because it relies on an empirical threshold convention whose only in-paper validation is a single species with a 21 cm^-1 offset. The paper would be an important experimental contribution after that systematic issue is addressed quantitatively.

major comments (3)
  1. [Sec. III C and Eq. (1), with Sec. V B] The quoted IP2 uncertainty of 73 cm^-1 is presented as a statistical fit error, but no systematic uncertainty is assigned for the threshold method or for the manual selection of background points. The single-species validation in Sec. V B yields a 21 cm^-1 offset between the threshold result and the Rydberg-Ritz IP1; the authors state that this is within the 73 cm^-1 statistical uncertainty, but that does not bound the offset for Th+, where the spectrum is much more congested and no independent Rydberg-series anchor exists. Because the abstract and conclusion claim a 22-fold improvement on IP2, an explicit systematic error budget and a discussion of the transferability of the calibration to Th+ are required before this claim is established.
  2. [Sec. III C, Fig. 4, Eq. (1)] The threshold fit depends on choices that are not reflected in the stated statistical error: the 0.5 cm^-1 averaging regions, the selection of 'valleys' at high energy, and the empirical definition E_IP2 = 2*beta + x0. I request a sensitivity analysis showing how the extracted IP2 changes when these choices are varied, and ideally a Monte Carlo over the point-selection procedure. Without such an analysis, the reader cannot distinguish the quoted 73 cm^-1 from a fitting artifact.
  3. [Sec. V B, Table II, Fig. 9] The 17-member Rydberg series is identified by constancy of the quantum defect, with n = 56, 57, 58 excluded as perturbed. Please provide a quantitative membership criterion: residuals of the Rydberg-Ritz fit in units of the line-position uncertainties, and the variation of the fitted IP and delta when individual members are included or excluded. The current result is plausible, but the statistical uncertainty of 0.02 cm^-1 is likely dominated by the choice of series membership, which is not quantified.
minor comments (6)
  1. [Sec. I] The sentence 'These investigations, led to the extraction' should read 'These investigations led to the extraction'.
  2. [Sec. III C] The phrase 'The raise in count rate' should be 'The rise in count rate'.
  3. [Table II] In the row beginning '51 50825.28(1)', the leading '51' appears to be a formatting artifact; the row should be labeled as n = 51.
  4. [Sec. VII] The phrase 'an 22-fold improvement' should read 'a 22-fold improvement', and 'in forseseen cases' should be 'in foreseen cases'.
  5. [References] The reference list contains several formatting problems, notably Ref. [29] ('A. Kramida, Yu. Ralchenko, J. Reader, and and NIST ASD Team') and Ref. [39], which has an embedded URL in the title; these should be cleaned.
  6. [Fig. 4 caption] The phrase 'The found IP2' should be 'The fitted IP2' or 'The determined IP2'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the IP values are data-extracted with an independent theoretical comparison.

full rationale

The derivation chain is not circular. The first ionization potential is obtained from a free Rydberg-Ritz fit (Eq. 2) to 17 unperturbed line positions; the literature IP1 is used only as an initial guess to assign principal quantum numbers, and the fitted limit 50868.41(11) cm^-1 is determined by the measured line energies, not by that guess. The second ionization potential is extracted using the explicitly defined sigmoid threshold E_IP2 = 2β + x0 (Eq. 1), an empirical estimator based on prior astatine work and checked here on atomic Th. This is a measurement convention, not a fitted parameter renamed as a prediction. The paper even quantifies the convention's offset for Th (21 cm^-1 lower than the Rydberg-Ritz value) and states that this is within the 73 cm^-1 statistical uncertainty of the Th+ threshold fit, so the limitation is disclosed rather than hidden. The MCDHF ionization potentials are computed from active-space expansions and then compared with the experimental values, so they serve as independent checks rather than inputs. Self-citations in the paper concern instrumentation, nozzle characterization, and prior source development; none carries the logical weight of the ionization-potential determination. The only substantive concern, namely that IP2 lacks an independent Rydberg-series anchor, is a systematic-accuracy risk and not a circularity.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central IP measurements rest on standard Rydberg theory and on two fitting models: the Rydberg-Ritz formula for IP1 and an empirical S-curve for IP2. The MCDHF and HFR+CPOL calculations are supporting, and their parameters are adjusted to known levels. No new particles, forces, or conserved quantities are introduced. The main imported assumptions are the constant quantum defect, the field-free jet region, and the threshold-method definition.

free parameters (5)
  • IP1 (Rydberg-Ritz convergence limit) = 50868.41(11) cm^-1
    Fitted together with the quantum defect to the positions of 17 selected Rydberg peaks in the gas-jet spectrum (Eq. 2). This is the headline measurement, not an externally imposed constant.
  • Quantum defect delta of the identified series = 0.56(1)
    Fitted in the same Rydberg-Ritz fit; the constant-delta assumption is central to the extrapolation to the ionization limit.
  • IP2 (photoionization threshold intercept) = 99207(73) cm^-1
    Obtained from the S-curve definition E_IP2 = 2*beta + x0 fitted to selected background points of the Th+ level search (Eq. 1).
  • Sigmoid threshold parameters x0 and beta = not stated individually
    These parameters define the IP2 via Eq. (1); their fitted values and uncertainties propagate into IP2 but are not tabulated separately.
  • HFR+CPOL radial parameter scale factors = e.g., F2(6d,6d) scaled to 0.59 of ab initio value
    Least-squares adjustment of radial parameters to known low-lying Th levels (Table III); used for the intermediate-state composition claim, not for the IP measurements.
assumptions (6)
  • standard math The Rydberg-Ritz formula E_n = E_IP - R_mu/(n-delta)^2 with constant delta describes the selected series.
    Invoked in Eq. (2) and the analysis in Sec. V B.
  • domain assumption The identified chain of 17 peaks is a single unperturbed series; interlopers at n=56-58 are excluded correctly.
    Sec. V B and Table II; if another series or a perturbing state contaminates the selected peaks, the fitted IP1 shifts.
  • ad hoc to paper The threshold S-curve intercept method defines the ionization potential as E_IP2 = 2*beta + x0.
    Eq. (1) and Sec. III C; this is an empirical analytic definition from astatine work, not a derivation from photoionization cross-section theory.
  • domain assumption The Rydberg excitation region in the gas jet is field-free enough that Stark shifts are negligible at the fitted level accuracy.
    Sec. V C; the wire grid shields the RFQ field and localizes field ionization, but residual fields are not measured directly.
  • domain assumption Field ionization of Rydberg states in the RFQ region does not alter the measured line positions.
    Sec. V C; Rydberg atoms travel about 110 microseconds before field ionization, so excitation and ionization are separated, but high-n states near the limit may be lost or biased.
  • standard math MCDHF method with the stated active spaces converged for IP1 and IP2.
    Sec. VI B and Table V; relies on the GRASP2018 implementation and the assumed core relaxation procedure.

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Cite this review

Pith. "Pith review of Study of thorium in hypersonic gas jets: Ionization potentials of Th and Th$^+$." pith.science (2026). https://pith.science/paper/KHIBTW7V

@misc{pith2026250721946,
  author       = {Pith},
  title        = {Pith review of: Study of thorium in hypersonic gas jets: Ionization potentials of Th and Th$^+$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KHIBTW7V}},
  note         = {Machine review of arXiv:2507.21946}
}
abstract

Laser ionization spectroscopy was performed on both neutral and singly ionized $^{232}$Th with the aim of identifying the nuclear-clock isomer in the singly charged ionic state of $^{229}$Th. A search for an efficient laser ionization scheme of $^{232}$Th$^+$ was conducted in an argon-filled gas cell. This revealed a congested spectrum due to collisional quenching effects and the presence of several auto-ionizing states, one of which has a laser ionization efficiency of at least $1.2 \%$. Using a threshold approach, the second ionization potential was determined to be $12.300(9)\,$eV. The subsequent study on atomic $^{232}$Th validated the threshold approach. Conducting spectroscopy in a hypersonic gas jet, suppressed the gas-collision-induced quenching, revealing a Rydberg series that converges to the first ionization potential, determined to be $6.306879(14)\,$eV. The gas jet also cools down the thorium, allowing for high-resolution laser spectroscopy with a resolution of $240(30)\,$MHz. Using the Multiconfigurational Dirac-Hartree-Fock (MCDHF) method, the ionization potentials were computed, showing a relative difference of 0.06\% and 0.19\% between theory and our experimental values for the ionization potentials of Th and Th$^+$ respectively. Further calculations using a pseudo-relativistic Hartree-Fock method reveal strong mixing in the used intermediate state at $26113.27\,$cm$^{-1}$ of Th. A dedicated fast-extraction gas cell with $^{233}$U recoil sources was used to study $^{229}$Th$^+$ but no photo-ionization signal could be observed.

Figures

Figures reproduced from arXiv: 2507.21946 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic representation of the IGLIS jet laboratory at KU Leuven. The thorium isotopes are produced in the argon [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Mass spectrum when ablating thorium with identified [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. ) indicate a change in ionization behavior, i.e. the crossing of the IP2. The states shown in Table I are sub￾stantially wider than the typical peaks found at lower energies which have a FWHM of 0.2 − 0.3 cm−1 . The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (11 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Left: Spectrum of the AI states with the best fits [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Top: Part of the normalized level search shown in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Mass spectrum of the recoil sources in optimal con [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Left: Schematic of the fast gas cell and the positions [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: The second-step laser was scanned just below the [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Top: Spectrum obtained by scanning the 2nd step with both steps transversely illuminating the gas cell. Bottom: [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Top: Convergence of the identified Rydberg series [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: The results reveal the existence of two time [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Top: Time profiles of the different photoions close [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Hyperfine spectrum of neutral [PITH_FULL_IMAGE:figures/full_fig_p011_12.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Four different identified processes in 100 cm [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

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