Influence of inelastic collisions with hydrogen atoms on the non-LTE line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars

Andrey K. Belyaev; Lyudmila Mashonkina; Svetlana A. Yakovleva; Tatyana Sitnova

REVIEW 3 major objections 5 minor 53 references

Influence of inelastic collisions with hydrogen atoms on the non-LTE line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Quantum-mechanical hydrogen-collision rates reconcile Fe I and Fe II abundances in metal-poor stars.

desk verdict Careful, well-tested stellar NLTE paper that makes a solid case for dropping the empirical Drawin scaling factor and treating Fe II in LTE at [Fe/H] > -3; the main residual risk is the external accuracy of the QM H I collision rates, which the authors themselves flag. read the letter →

arxiv 1908.02478 v1 pith:KBLLWDBY submitted 2019-08-07 astro-ph.SR

Lyudmila Mashonkina , Tatyana Sitnova , Svetlana A. Yakovleva , Andrey K. Belyaev This is my paper · ORCID

classification astro-ph.SR

keywords non-LTElineformationironabundanceshydrogenatomcollisionslate-typestarsmetal-poorionisationequilibriumquantum-mechanicalratecoefficientsstellaratmospheres

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

For decades, iron abundances derived from neutral (Fe I) and singly ionised (Fe II) lines disagreed in metal-poor stars, and the standard fix was to scale the classical Drawin hydrogen-collision rates by an empirical factor. This paper replaces those rates with quantum-mechanical rate coefficients for inelastic Fe I+H I and Fe II+H I collisions and shows that the Fe I/Fe II ionisation equilibrium is restored in stars down to $[\mathrm{Fe/H}] \approx -3.5$. The key quantitative finding is that hydrogen collisions thermalise Fe II so efficiently that Fe II lines behave as if they were in LTE: their NLTE abundance corrections are below 0.02 dex at $[\mathrm{Fe/H}] > -3$, and only about +0.06 dex near $[\mathrm{Fe/H}] \approx -4$. A sympathetic reader would care because this removes the main uncontrolled atomic-physics input in iron abundance measurements of old stars.

What carries the argument

The load-bearing object is a set of quantum-mechanical inelastic collision rate coefficients for iron with neutral hydrogen: the B18 and YBK18 data sets for Fe I+H I (which include charge-exchange processes such as Fe I + H I → Fe II + H−) and the YBK19 data set for Fe II+H I. These rates replace the Drawin approximation, whose strength in previous work was adjusted by a free scaling factor $S_H$. In the statistical-equilibrium equations, H I collisions couple the excited Fe II levels to the Fe II ground state and couple Fe I to the Fe II continuum, suppressing the strong departures from LTE that appear when only electron collisions are included.

What would settle it

A next-generation ab initio calculation of Fe I+H I and Fe II+H I collisions that includes short-range non-adiabatic coupling would settle the bracket; if its rates move the Fe I NLTE corrections by more than about 0.1 dex in HD 122563, the apparent Fe I/Fe II agreement would not be robust. A purely observational check is to redo the dwarf-galaxy analysis with asteroseismic surface gravities and interferometric effective temperatures; the residual Fe I–Fe II differences at $[\mathrm{Fe/H}] \lesssim -3.7$ should disappear if the collision rates are the right fix.

Watch

Extended reading notes

Core claim

The paper's central claim is that inelastic collisions with neutral hydrogen atoms, treated quantum mechanically, resolve the long-standing Fe I/Fe II abundance discrepancy in cool metal-poor stars. In the authors' calculations, the mean NLTE abundances from Fe I and Fe II agree within 0.10 dex for the halo benchmarks when the YBK18 rates are used and within 0.13 dex with B18, and the average difference is $-0.01 \pm 0.10$ dex for the 32 dwarf-galaxy giants at $[\mathrm{Fe/H}] > -3.5$. The same calculations show that Fe II is efficiently coupled to LTE by H I collisions, so its NLTE corrections stay at or below 0.02 dex in absolute value down to $[\mathrm{Fe/H}] \approx -3$. The paper concludes that the empirically tuned scaling factor can be replaced by a fixed set of ab initio rates.

Load-bearing premise

Everything rests on the quantum-mechanical H I rate coefficients being roughly right; the paper itself notes that both the B18 and YBK18 calculations omit short-range non-adiabatic regions, which could raise the rates by up to several orders of magnitude.

Editorial extensions

If this is right

Fe II lines can be used as LTE abundance indicators in metal-poor stars down to $[\mathrm{Fe/H}] \approx -3$, with no NLTE correction exceeding 0.02 dex.
The Fe I/Fe II ionisation equilibrium can be computed from first principles rather than tuned; the same recipe works across a metallicity range from $[\mathrm{Fe/H}] \approx -3.5$ to solar-like values.
The gap between the B18 and YBK18 rate sets provides a systematic error bar for the collision treatment, while the remaining 0.10–0.13 dex Fe I–Fe II residual in the warmer benchmarks is attributed to line data and 3D effects rather than H I collisions.
At the lowest metallicities, $[\mathrm{Fe/H}] \lesssim -3.7$, the ionisation equilibrium is less secure, and both Fe I and Fe II corrections grow, so ultra-metal-poor stars still need a full NLTE treatment.

Reading between the lines

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

If the B18/YBK18 bracket is confirmed by future short-range calculations, the residual Fe I–Fe II offset in HD 84937 and HD 140283 becomes a direct probe of Fe II transition probabilities; laboratory gf-measurements of the UV Fe II lines would then sharpen the solar iron scale.
The same thermalising role of H I collisions should apply to other minority neutral species with similar ionisation structure, such as Mn I and Cr I; a testable prediction is that their apparent NLTE abundance trends with excitation energy will flatten once quantum-mechanical H I rates are used.
Because Fe II corrections grow only near $[\mathrm{Fe/H}] \approx -4$, iron abundances of the most metal-poor stars rest on Fe I, which means the remaining systematic risk moves to the Fe I photoionisation cross-sections and the thermal structure of the model atmospheres.

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.

Desk Editor's Note

read the letter

Bottom line: this is a genuine advance in stellar abundance modelling, and the main result survives a close read. It is the first paper to apply the YBK19 quantum-mechanical Fe II + H I collision rates in stellar NLTE calculations, and it shows that those rates thermalise Fe II so effectively that LTE is a safe assumption for Fe II lines at [Fe/H] > -3. It also demonstrates that the empirical scaling factor SH that people have been applying to Drawin rates is no longer needed when the QM rates are used; the Fe I/Fe II ionisation equilibrium comes out right for a wide metallicity range.

The analysis is careful. The authors compare pure electronic collisions, B18, YBK18, YBK19, and scaled Drawin rates, and they tabulate how Teff, log g, xi_t, gf-values, and photoionisation data shift the ionisation equilibrium. The B18 and YBK18 treatments of Fe I + H I give mean abundances that agree to within 0.03 dex, which is a good external cross-check because the two calculations are independent. The visible-UV comparison for HD 84937 and HD 140283 is a nice addition, and the discussion against ALA16, S16, and R18 is honest.

The soft spots are two, and they are both minor to moderate. First, the UV Fe I line list was partly selected to be consistent with a reference LTE abundance, which could flatter the visible-UV agreement. The authors state this openly, but the selection is still a mild bias in that sub-argument. It does not affect the visible-line Fe I/Fe II equilibrium. Second, and more fundamentally, the whole result inherits the accuracy of the QM collision rates. The authors themselves note in Sect. 2.1 that both B18 and YBK18 omit short-range non-adiabatic regions, which could increase rate coefficients by several orders of magnitude. The B18/YBK18 pair brackets the core-changing matrix elements, but not that missing physics. If the true Fe I + H I rates are higher than YBK18, the Fe I NLTE corrections shrink, and the already negative Fe I - Fe II difference in HD 122563 (-0.07 to -0.09 dex) would get more negative. For Fe II, the paper uses only YBK19, with no lower-limit bracket. That said, the Fe II corrections are so small at [Fe/H] > -3 that even a factor of a few in the rates would not overturn the LTE approximation there; the thermalisation conclusion is robust. The Fe I/Fe II equilibrium claim is more sensitive, but the authors' uncertainty table shows the total systematic budget, and the rates are the largest external unknown.

This is a careful paper with a real result. It deserves a serious referee and, after a revision that addresses the UV selection and adds an explicit sensitivity test on the Fe II rate scale, it should be publishable. The audience is stellar abundance practitioners and atomic physicists working on H I collisions. I would cite it.

Referee Report

3 major / 5 minor

Summary. The paper investigates how quantum-mechanical (QM) rate coefficients for inelastic collisions between iron and hydrogen atoms affect non-LTE line formation of Fe I and Fe II in 1D model atmospheres. The authors update the Fe I-II model atom of Mashonkina et al. (2011) by adding Fe I + H I rates from Barklem (2018, B18) and Yakovleva et al. (2018, YBK18), Fe II + H I rates from Yakovleva et al. (2019, YBK19), and Kaulakys-type rates for missing transitions. They apply the resulting line-formation scenarios to three Galactic halo benchmarks (HD 122563, HD 84937, HD 140283) using visible and UV spectra, and to 38 very metal-poor giants in dwarf spheroidal galaxies. The main findings are that collisions with H I thermalise Fe II so strongly that Fe II NLTE abundance corrections are below 0.02 dex at [Fe/H] > -3 and reach only about +0.06 dex at [Fe/H] ~ -4, and that the Fe I/Fe II ionisation equilibrium is restored for stars with [Fe/H] > -3.5 when QM rates are used together with Gaia-based surface gravities. The paper concludes that the empirical scaling factor applied to Drawin rates is no longer needed for iron, and that LTE is a safe approximation for Fe II lines in all but the most metal-poor stars.

Significance. If the results are robust, the paper provides a practical replacement for the ad hoc Drawin scaling-factor approach in iron abundance analyses, with direct consequences for stellar parameter determinations and for chemical-evolution studies of metal-poor stars. The authors deserve credit for comparing several collisional recipes, for checking UV and visible lines separately, for tabulating systematic shifts from Teff, log g, microturbulence, gf-values, and photoionisation data in Table 3, and for publishing machine-readable line-by-line abundances. The Fe II thermalisation result is tested across a metallicity range and is important because it supports the common practice of treating Fe II in LTE. However, the central claims inherit the accuracy of the external QM rate coefficients, and the paper explicitly acknowledges that the adopted rate sets may not bracket the missing short-range non-adiabatic contributions. The overall conclusion is therefore plausible and well documented, but it is conditional on an atomic-physics premise that is not fully quantified within this manuscript.

major comments (3)

[Sect. 2.1] The paper presents B18 and YBK18 as lower-limit and upper-limit estimates for the Fe I + H I inelastic rate coefficients, but the bracketing argument covers only the treatment of core-changing transitions. The text itself states that both methods 'do not take short-range non-adiabatic regions into account' and that including these regions 'may increase rate coefficients by up to several orders of magnitude.' This means the true Fe I + H I rates could lie outside the B18-YBK18 bracket, and the resulting Fe I NLTE abundance corrections could shift toward LTE or away from it. Because the Fe I/Fe II ionisation equilibrium for HD 122563 and the dSph sample is the central observational claim, the paper should quantify this sensitivity, for example by recalculating Fe I abundances with a uniformly scaled-up or scaled-down version of the adopted rates, or by clearly stating what rate range would be needed to destroy the equilibrium. As written, the conclusion rests on a bracket that the authors themselves indicate may not contain the physical rates.
[Sect. 2.1 and Sect. 3.4] The headline result that Fe II is strongly thermalised by H I collisions and that Fe II lines can be used under LTE is derived using only the single YBK19 rate set. No alternative lower-limit or upper-limit estimate for Fe II + H I collisions is considered, whereas the Fe I analysis benefits from the B18/YBK18 comparison. The text notes that the YBK19 rates lie at the upper boundary of the Drawinian rate set, which is a warning sign: if the true Fe II + H I rates are lower than YBK19, the Fe II NLTE corrections at low metallicity could become larger than the quoted 0.02 dex at [Fe/H] > -3, and the +0.06 to +0.12 dex corrections at [Fe/H] ~ -4 could grow. Since the paper explicitly claims that Fe II NLTE corrections are negligible, it should provide at least a bounded test of the dependence on the Fe II collisional rates, e.g. by scaling YBK19 down by a factor of a few.
[Sect. 3.4 and Fig. 9] The paper states that 'the Fe I/Fe II ionisation equilibrium is achieved for each [Fe/H] > -3.5 star of our dwarf galaxy sample', but the supporting analysis is based on literature Teff, log g, and microturbulent velocities from Mashonkina et al. (2017a) and Pakhomov et al. (2019), and no equivalent of Table 3 is provided for the dSph sample. At the lowest metallicities, five of six stars show Fe I abundances higher than Fe II by up to 0.35 dex, and the authors attribute this to overestimated Teff without performing a quantitative test. Because the boundary at [Fe/H] > -3.5 is a key part of the conclusion, the manuscript should either propagate the parameter uncertainties for the dSph stars or explicitly state that the equilibrium claim is conditional on the adopted parameters rather than demonstrated for every star.

minor comments (5)

[Abstract and Sect. 3.4] The abstract states that 'the Fe I/Fe II ionisation equilibrium is achieved for each [Fe/H] > -3.5 star of our dwarf galaxy sample', while the text reports a mean difference of -0.01 +/- 0.10 dex for 32 stars; the abstract should clarify that this is a statistical statement about the sample, not a claim that every individual star satisfies equilibrium within its own error bars.
[Fig. 8] The caption contains the typo 'magenda' for 'magenta'.
[Sect. 3.3] The selection of Fe I UV lines is based partly on agreement with the LTE abundance from a first subset of lines, within 0.15 dex; this procedure risks introducing a selection bias and should be described more carefully, ideally with the full line list and the rejection criteria stated explicitly.
[Sect. 2.1] The phrase 'Treating upper-limit data compensates somehow not accounting for the short-range regions' is presented as a justification, but it is an assertion rather than a demonstrated property of the calculations; the paper should distinguish between a physical bracket and a heuristic compensation argument.
[Table 3] The row labels such as 'ph-ion (BLB2017 - B1997)' and 'no Kaulakys' collisions' are clear enough for specialists but would benefit from a one-sentence explanation in the table notes, especially because the sign convention of the shifts is crucial for interpreting the ionisation-equilibrium test.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: quantum-mechanical H I collision rates are independent inputs, and the Fe I/Fe II equilibrium is a computed outcome, not an input.

full rationale

The derivation chain is self-contained in the required sense: the stellar abundance claims are not used to construct the H I collision rates. The rates from B18, YBK18, and YBK19 are quantum-mechanical calculations external to the present stellar analysis; the paper applies them as fixed inputs. The central results—small Fe II NLTE corrections and Fe I/Fe II equilibrium for [Fe/H] > -3.5—are computed consequences of solving the statistical-equilibrium and radiative-transfer equations, not parameters fitted to those outcomes. The two Fe I + H I rate sets (B18 and YBK18) are treated as lower/upper estimates, and the paper shows the resulting average abundances differ by at most 0.03 dex, so the equilibrium conclusion does not reduce to a single tuned input. The authors' own caveat that short-range non-adiabatic regions are omitted (Sect. 2.1) is a legitimate external accuracy concern, but it does not make the argument circular. Self-citations to the authors' atomic data papers and to the model atom of Mashonkina et al. (2011) are normal reuse of prior independent calculations, not a self-citation chain that forces the result. No equation in the paper defines the predicted abundances in terms of the stellar Fe I/Fe II differences, and no fitted scaling factor is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the accuracy of external quantum-mechanical collision data and on standard 1D model atmosphere assumptions; no new physical entities are introduced. The only parameters fitted in this paper are microturbulent velocities for three benchmark stars.

free parameters (3)

Microturbulent velocity for HD 122563 = 1.6 km/s
Adopted to remove the slope in the log abundance versus observed equivalent width trend for Fe I lines (Sect. 3.1).
Microturbulent velocity for HD 84937 = 1.7 km/s
Revised from the requirement that Fe I lines of different strength yield consistent absolute abundances (Sect. 3.1).
Microturbulent velocity for HD 140283 = 1.3 km/s
Same requirement as for HD 84937 (Sect. 3.1).

assumptions (4)

domain assumption MARCS 1D plane-parallel model atmospheres with standard abundances represent the stellar atmospheres of the program stars.
All NLTE calculations are based on these models (Sect. 2).
domain assumption The quantum-mechanical Fe I + H I and Fe II + H I rate coefficients are accurate enough for the conclusions.
The central input; the authors note both B18 and YBK18 neglect short-range non-adiabatic regions, which may increase rates by orders of magnitude (Sect. 2.1).
domain assumption The adopted atomic data (gf-values, photoionisation cross-sections, electron-impact data) are reliable.
Abundance results depend on these data; the paper discusses sensitivity to gf-values in Sect. 3.3.
domain assumption Electron-impact ionisation cross-sections from the classical path approximation with mean Gaunt factors of 0.1 (Fe I) and 0.2 (Fe II) are adequate.
Used in the model atom (Sect. 2.1), following Seaton (1962).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Influence of inelastic collisions with hydrogen atoms on the non-LTE line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars." pith.science (2026). https://pith.science/paper/KBLLWDBY

@misc{pith2026190802478,
  author       = {Pith},
  title        = {Pith review of: Influence of inelastic collisions with hydrogen atoms on the non-LTE line formation for Fe I and Fe II in the 1D model atmospheres of late-type stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBLLWDBY}},
  note         = {Machine review of arXiv:1908.02478}
}

read the original abstract

Iron plays a crucial role in studies of late-type stars. In their atmospheres, Fe I is the minority species and its lines are subject to the departures from LTE. In contrast, one believes that LTE is a realistic approximation for Fe II lines. The main source of the uncertainties in the non-LTE (NLTE) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms. We investigate the effect of Fe I + H I and Fe II + H I collisions and their different treatment on the Fe I/Fe II ionisation equilibrium and Fe abundance determinations for Galactic halo benchmark stars HD84937, HD122563, and HD140283 and a sample of 38 very metal-poor giants in the dwarf galaxies with well known distances. We perform the NLTE calculations for Fe I-II with using quantum-mechanical (QM) rate coefficients for collisions with H I from Barklem (2018, B18), Yakovleva, Belyaev, and Kraemer (2018, YBK18), and Yakovleva, Belyaev, and Kraemer (2019). We find that collisions with H I serve as efficient thermalisation processes for Fe II and the NLTE abundance corrections for Fe II lines do not exceed 0.02 dex at [Fe/H] > -3 and reach +0.06~dex at [Fe/H] ~ -4. For given star, the B18 and YBK18 treatments of Fe I + H I collisions lead to similar average NLTE abundances from Fe I lines, although there exist discrepancies in the NLTE corrections for individual lines. With using QM collisional data and the Gaia based surface gravity, we obtain consistent abundances from Fe I and Fe II for a red giant HD122563. For HD84937 and HD140283, we study the Fe lines in the visible and the UV (1968-2990 A) range. For both Fe I and Fe II, abundances from the visible and UV lines are consistent. The abundances from Fe I and Fe II agree within 0.10 and 0.13 dex in the YBK18 and B18 cases. The Fe I/Fe II ionisation equilibrium is achieved for each [Fe/H] > -3.5 star of our dwarf galaxy sample.

Figures

Figures reproduced from arXiv: 1908.02478 by the authors.

**Figure 1.** Left panel: Fe i excitation rates (in s−1 ), log C, for electron impact (triangles) compared with the rates for H i collisions from calculations of YBK18 (filled circles) and B18 (rhombi) and compared with the scaled (SH = 0.5) Drawinian rates (open circles). Right panel: rates, log C, of the processes Fe i + e − → Fe ii + 2e− and Fe i + H i → Fe ii + H − using similar symbols. The calculations were made with T = 58… view at source ↗

**Figure 2.** Fe ii excitation rates (in s−1 ), log C, for electron impact (triangles) compared with the rates for H i collisions from calculations of YBK19 (filled circles) and compared with the scaled (SH = 0.5) Drawinian rates (open circles). The calculations were made with T = 5830 K, log Ne(cm−3 ) = 13, and log NH(cm−3 ) = 16.9. and B18. The data correspond to a kinetic temperature of T = 5830 K and an H i number density o… view at source ↗

**Figure 3.** Departure coefficients, b, for the levels of Fe i and Fe ii as a function of log τ5000 in the model atmosphere 4600/1.40/−2.60 from calculations using different treatment of H i collisions: pure electronic collisions (top panel); YBK18 + YBK19 (middle panel); B18 + YBK19 (bottom panel). Every fifth of the first 60 levels (Eexc ≤ 5.73 eV) of Fe i is shown. They are quoted in the bottom right part of each panel. Al… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: LTE (top left panel) and NLTE (other three panels) abundances from lines of Fe i (circles) and Fe ii (triangles) in HD 122563 as a function of observed equivalent width Wobs. The top right panel corresponds to the NLTE calculations with pure electronic collisions. In t…

**Figure 5.** Figure 5: NLTE abundance corrections for the lines of Fe i in the 4600/1.40/−2.60 model from calculations that use pure electronic collisions (squares) and include collisions with H i according to YBK18 (filled circles) and B18 (triangles). For comparison, the NLTE corrections…

**Figure 6.** Figure 6: NLTE abundances of HD 84937 (left panel) and HD 140283 (right panel) from lines of Fe i (circles) and Fe ii (triangles) in the YBK18+YBK19 scenario as a function of observed equivalent width Wobs. The filled and open symbols correspond to the visible and UV lines, resp…

**Figure 7.** Figure 7: NLTE abundance corrections for lines of Fe i in the 6350/4.09/−2.15 model from calculations that include collisions with H i according to YBK18 (circles) and B18 (triangles). The filled and open symbols correspond to the visible and UV lines, respectively. compared wit…

**Figure 8.** Figure 8: NLTE abundance corrections for Fe i 5216 Å (Eexc = 1.61 eV, red circles), 6191 Å (Eexc = 2.43 eV, blue squares), and 5615 Å (Eexc = 3.33 eV, magenda triangles) in the dSph stars from calculations with the YBK18 data. At the lowest metallicity of our sample, [Fe/H] ∼ −4…

**Figure 9.** Figure 9: LTE (top panel) and NLTE (YBK18+YBK19, bottom panel) abundance differences between Fe i and Fe ii, log εFeI – log εFeII, in the stars in Sculptor (red circles), Ursa Minor (red triangles), Fornax (red rhombi), Sextans (red squares), Boötes I (blue circles), UMa II (blu…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 43 canonical work pages

[1]

M., Lind, K., Asplund, M., Barklem, P

Amarsi, A. M., Lind, K., Asplund, M., Barklem, P . S., & Collet , R. 2016, MN- RAS, 463, 1518

work page 2016
[2]

2003, The Messenge r, 114, 10

Bagnulo, S., Jehin, E., Ledoux, C., et al. 2003, The Messenge r, 114, 10

work page 2003
[3]

Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantele t, G., & Andrae, R. 2018, AJ, 156, 58

2018
[4]

Barklem, P . S. 2016, Phys. Rev. A, 93, 042705

work page 2016
[5]

Barklem, P . S. 2017, KAULAKYS: Inelastic collisions between hydrogen atoms and Rydberg atoms

work page 2017
[6]

Barklem, P . S. 2018, A&A, 612, A90

work page 2018
[7]

Bautista, M. A. 1997, A&AS, 122, 167

work page 1997
[8]

A., Lind, K., & Bergemann, M

Bautista, M. A., Lind, K., & Bergemann, M. 2017, A&A, 606, A12 7

work page 2017

Show all 53 references

[9]

Bautista, M. A. & Pradhan, A. K. 1996, A&AS, 115, 551

1996
[10]

Bautista, M. A. & Pradhan, A. K. 1998, ApJ, 492, 650

1998
[11]

T., Pickering, J

Belmonte, M. T., Pickering, J. C., Ru ﬀoni, M. P ., et al. 2017, ApJ, 848, 125

2017
[12]

Bensby, T., Feltzing, S., & Oey, M. S. 2014, A&A, 562, A71

2014
[13]

J., Eitner, P ., et al

Bergemann, M., Gallagher, A. J., Eitner, P ., et al. 2019, arX iv e-prints, arXiv:1905.05200

2019 arXiv
[14]

2012, MNRAS, 427, 27

Bergemann, M., Lind, K., Collet, R., Magic, Z., & Asplund, M. 2012, MNRAS, 427, 27

2012
[15]

R., Serenelli, A., et al

Bergemann, M., Ruchti, G. R., Serenelli, A., et al. 2014, A&A , 565, A89

2014
[16]

A., Lyubimkov, L

Boyarchuk, A. A., Lyubimkov, L. S., & Sakhibullin, N. A. 1985 , Astrophysics, 22, 203

1985
[17]

Bridges, J. M. 1973, in Phenomena in Ionized Gases, EleventhInternational Con- ference, ed. I. Štoll, 418– +, (B)

1973
[18]

& Giddings, J

Butler, K. & Giddings, J. 1985, Newsletter on the analysis of astronomical spec- tra, No. 9, University of London

1985
[19]

2019, arXiv e -prints

Creevey, O., Grundahl, F., Thévenin, F., et al. 2019, arXiv e -prints

2019
[20]

L., Thévenin, F., Boyajian, T

Creevey, O. L., Thévenin, F., Boyajian, T. S., et al. 2012, A& A, 545, A17 Den Hartog, E. A., Ru ﬀoni, M. P ., Lawler, J. E., et al. 2014, ApJS, 215, 23

2012
[21]

1968, Zeitschrift fur Physik, 211, 404

Drawin, H.-W. 1968, Zeitschrift fur Physik, 211, 404

1968
[22]

Drawin, H. W. 1969, Zeitschrift fur Physik, 225, 483 4 http://adsabs.harvard.edu/abstract_service.html 5 http://simbad.u-strasbg.fr/simbad/ Article number, page 10 of 11 Mashonkina et al.: NLTE line formation for Fe i and Fe ii in atmospheres of late-type stars

1969
[23]

R., Martin, G

Fuhr, J. R., Martin, G. A., & Wiese, W. L. 1988, Journal of Phys ical and Chem- ical Reference Data, 17 Gaia Collaboration, Brown, A. G. A., V allenari, A., et al. 20 18, A&A, 616, A1

1988
[24]

G., Carretta, E., Eriksson, K., & Gustafsson, B

Gratton, R. G., Carretta, E., Eriksson, K., & Gustafsson, B. 1999, A&A, 350, 955

1999
[25]

& Sauval, A

Grevesse, N. & Sauval, A. J. 1999, A&A, 347, 348

1999
[26]

L., & Tan, K

Grupp, F., Kurucz, R. L., & Tan, K. 2009, A&A, 503, 177

2009
[27]

2008, A &A, 486, 951

Gustafsson, B., Edvardsson, B., Eriksson, K., et al. 2008, A &A, 486, 951

2008
[28]

R., Nordlander, T., et al

Karovicova, I., White, T. R., Nordlander, T., et al. 2018, MN RAS, 475, L81

2018
[29]

1991, Journal of Physics B Atomic Molecular Phy sics, 24, L127

Kaulakys, B. 1991, Journal of Physics B Atomic Molecular Phy sics, 24, L127

1991
[30]

J., Shi, J., & Gehren, T

Korn, A. J., Shi, J., & Gehren, T. 2003, A&A, 407, 691

2003
[31]

& Kock, M

Kroll, S. & Kock, M. 1987, Astron. and Astrophys. Suppl. Ser. , 67, 225, (KK)

1987
[32]

Kurucz, R. L. 1992, Rev. Mexicana Astron. Astroﬁs., 23

1992
[33]

Kurucz, R. L. 2009, Robert L. Kurucz on-line database of observed and predicted atomic transitions

2009
[34]

M., Asplund, M., et al

Lind, K., Amarsi, A. M., Asplund, M., et al. 2017, MNRAS, 468, 4311

2017
[35]

2012, MNRAS, 427, 50

Lind, K., Bergemann, M., & Asplund, M. 2012, MNRAS, 427, 50

2012
[36]

J., & Grupp, F

Mashonkina, L., Gehren, T., Shi, J.-R., Korn, A. J., & Grupp, F. 2011, A&A, 528, A87

2011
[37]

2017b, A&A, 608, A89 Meléndez, J

Mashonkina, L., Jablonka, P ., Sitnova, T., Pakhomov, Y ., & N orth, P . 2017b, A&A, 608, A89 Meléndez, J. & Barbuy, B. 2009, A&A, 497, 611

2009
[38]

Nave, G., Johansson, S., Learner, R. C. M., Thorne, A. P ., & Br ault, J. W. 1994, ApJS, 94, 221 O’Brian, T. R., Wickli ﬀe, M. E., Lawler, J. E., Whaling, W., & Brault, J. W. 1991, Journal of the Optical Society of America B Optical Phy sics, 8, 1185

1994
[39]

Pauls, U., Grevesse, N., & Huber, M. C. E. 1990, Astron. and As trophys., 231, 536

1990
[40]

Raassen, A. J. J. & Uylings, P . H. M. 1998, A&A, 340, 300

1998
[41]

U., Sneden, C., Lawler, J

Roederer, I. U., Sneden, C., Lawler, J. E., et al. 2018, ApJ, 8 60, 125

2018
[42]

R., Bergemann, M., Serenelli, A., Casagrande, L

Ruchti, G. R., Bergemann, M., Serenelli, A., Casagrande, L. , & Lind, K. 2013, MNRAS, 429, 126 Ruﬀoni, M. P ., Den Hartog, E. A., Lawler, J. E., et al. 2014, MNRAS , 441, 3127

2013
[43]

L., et al

Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Ph ys. Scr, 90, 054005

2015
[44]

Seaton, M. J. 1962, in Atomic and Molecular Processes, ed. D. R. Bates, 375

1962
[45]

& Trujillo Bueno, J

Shchukina, N. & Trujillo Bueno, J. 2001, ApJ, 550, 970

2001
[46]

2015, ApJ, 808, 148

Sitnova, T., Zhao, G., Mashonkina, L., et al. 2015, ApJ, 808, 148

2015
[47]

M., Mashonkina, L

Sitnova, T. M., Mashonkina, L. I., Ezzeddine, R., & Frebel, A . 2019, MNRAS, 485, 3527

2019
[48]

J., Kobayashi, C., et al

Sneden, C., Cowan, J. J., Kobayashi, C., et al. 2016, ApJ, 817 , 53

2016
[49]

& Holweger, H

Steenbock, W. & Holweger, H. 1984, A&A, 130, 319

1984
[50]

1971, PASJ, 23, 217

Tanaka, K. 1971, PASJ, 23, 217

1971
[51]

2019, in Astrono mical Society of the Paciﬁc Conference Series, V ol

Tsymbal, V ., Ryabchikova, T., & Sitnova, T. 2019, in Astrono mical Society of the Paciﬁc Conference Series, V ol. 518, Astronomical Socie ty of the Paciﬁc Conference Series, ed. D. O. Kudryavtsev, I. I. Romanyuk, & I . A. Y akunin, 247–252 Y akovleva, S. A., Barklem, P . S., ...

2019
[52]

Zhang, H. L. & Pradhan, A. K. 1995, A&A, 293, 953

1995
[53]

L., et al

Zhao, G., Mashonkina, L., Y an, H. L., et al. 2016, ApJ, 833, 22 5 Article number, page 11 of 11

2016

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

M., Lind, K., Asplund, M., Barklem, P

Amarsi, A. M., Lind, K., Asplund, M., Barklem, P . S., & Collet , R. 2016, MN- RAS, 463, 1518

work page 2016

[2] [2]

2003, The Messenge r, 114, 10

Bagnulo, S., Jehin, E., Ledoux, C., et al. 2003, The Messenge r, 114, 10

work page 2003

[3] [3]

Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantele t, G., & Andrae, R. 2018, AJ, 156, 58

2018

[4] [4]

Barklem, P . S. 2016, Phys. Rev. A, 93, 042705

work page 2016

[5] [5]

Barklem, P . S. 2017, KAULAKYS: Inelastic collisions between hydrogen atoms and Rydberg atoms

work page 2017

[6] [6]

Barklem, P . S. 2018, A&A, 612, A90

work page 2018

[7] [7]

Bautista, M. A. 1997, A&AS, 122, 167

work page 1997

[8] [8]

A., Lind, K., & Bergemann, M

Bautista, M. A., Lind, K., & Bergemann, M. 2017, A&A, 606, A12 7

work page 2017