Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)

G.L.Klimchitskaya

REVIEW 1 major objections 5 minor 1 cited by

Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)

T0 review · 1 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This comment argues that higher-order multipole corrections to the atom-wall Casimir-Polder interaction are negligibly small once the standard macroscopic validity condition is enforced, and that a recent recalculation overstates them by…

desk verdict A focused, largely persuasive critique of Jentschura's validity regimes, but the quantitative claim of 'negligible' corrections rests on an arbitrary factor-of-8 boundary. read the letter →

arxiv 2501.14803 v1 pith:LYIKUCYZ submitted 2025-01-14 physics.atom-ph

G.L.Klimchitskaya This is my paper · ORCID

classification physics.atom-ph

keywords atom-wallinteractionCasimir-PolderforceLifshitztheorymultipoleexpansionvanderWaalsadsorptiondielectricpermittivityphysisorptionpositronium

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

A recent paper recalculated the quadrupole, octupole, and hexadecupole corrections to the Casimir-Polder dipole attraction between an atom and a dielectric wall, and claimed that the quadrupole term is numerically significant for hydrogen and positronium near a quartz surface. This comment challenges that claim by pointing out that the distances used in the recalculation fall outside the validity domain of the macroscopic theory that generated the formulas. In that theory the wall is a continuous medium, so the separation from the wall must be large compared with the interatomic distance inside the wall. At the shortest legitimate separation, the quadrupole correction is about two tenths of a percent of the dipole term for positronium and five hundredths of a percent for hydrogen, and the higher terms are smaller still. If the comment is right, the practical lesson is that the dipole Lifshitz term already captures the atom-wall interaction in the semiclassical regime, and multipole corrections need not be added.

What carries the argument

The central object is the volume dielectric permittivity $\varepsilon(i\omega)$ of the wall material, which underlies the macroscopic Lifshitz description. The load-bearing restriction is that the wall can be treated as a continuous medium only for atom-wall separations $z$ much larger than the interatomic distance $d$, so the surface is spatially homogeneous at the scale of the atom. The comment then uses the asymptotic coefficients from the commented paper to show that the multipole terms are suppressed by powers of $d/z$ once $z$ is set to the physically allowed minimum.

What would settle it

Compute the atom-wall interaction energy for hydrogen or positronium above $\alpha$-quartz at separations between 1 nm and 10 nm with a microscopic calculation that treats the wall atoms explicitly, and separate the $z^{-3}$ from the $z^{-5}$ contribution. If a $z^{-5}$ component as large as 0.1 of the dipole term is confirmed at separations near 2-3 nm, the continuum lower bound would need revision and the multipole terms would not be negligible at physisorption distances.

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Extended reading notes

Core claim

The comment shows that the short-range condition used in the commented paper, $a_0 \ll z \ll a_0/\alpha$ with $a_0$ the Bohr radius, and the long-range condition $z \gg a_0/\alpha$, contradict the validity conditions of the macroscopic theory. The theory requires $d \ll z \ll \lambda_0$ for the short-range regime and $\lambda_0 \ll z \ll \hbar c/(k_B T)$ for the long-range regime, where $d$ is the interatomic distance in the wall and $\lambda_0$ a characteristic absorption wavelength. For $\alpha$-quartz with $d \approx 0.5$ nm, the shortest admissible separation is taken as $z_{\min}=4$ nm. Using the multipole coefficients tabulated in the commented paper, the ratio of quadrupole to dipole energy at this distance is $2.2\times10^{-3}$ for positronium and $5.2\times10^{-4}$ for hydrogen; the hydrogen octupole-to-dipole ratio is $7.6\times10^{-7}$. Hence all higher-order multipole corrections are negligible within the valid domain.

Load-bearing premise

The conclusion rests on the assumption that the macroscopic continuous-medium description of the wall is invalid at separations comparable to or smaller than the interatomic distance, so that 4 nm is the shortest distance at which the atom-wall formulas apply.

Editorial extensions

If this is right

At the shortest separation allowed by the macroscopic theory, all higher-order multipole corrections to the Casimir-Polder energy are below one percent of the dipole term, with quadrupole-to-dipole ratios $2.2\times10^{-3}$ for positronium and $5.2\times10^{-4}$ for hydrogen at $z=4$ nm.
The claimed modification of physisorption adsorption energies by the quadrupole term does not hold for separations within the theory's valid domain; the energy at such scales must instead come from a microscopic treatment.
For a perfectly conducting wall, the short-separation multipole expressions are not physically relevant because real conductors behave as perfect conductors only at separations above about $1\,\mu$m.
The standard practice of smoothly joining microscopic short-distance results with macroscopic results at larger distances is not a justification for moving the macroscopic lower bound down to a few ångströms.

Reading between the lines

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

If an explicit microscopic calculation between 1 and 4 nm finds a sizeable $z^{-5}$ contribution, the natural reading is not that the macroscopic multipole series works at short range but that the atom interacts with individual lattice sites; the two descriptions are not in tension because they apply in different domains.
One could test the comment's boundary by performing an atom-surface force measurement for positronium or hydrogen above a quartz surface at separations from 2 to 10 nm; a clean $z^{-5}$ signature at the level of 0.1 of the dipole term would indicate that the continuum lower bound needs revision.
The comment implicitly suggests a practical protocol for adsorption-energy calculations: use the dipole term above roughly 4 nm, switch to a local microscopic potential below it, and ignore multipole corrections entirely unless a microscopic calculation proves they are not already absorbed in the reference-plane shift.

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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

This comment makes a simple, useful point: Jentschura's multipole corrections to the Lifshitz atom-wall energy were computed at distances where the continuum description is questionable. The author goes back to Lifshitz's own statements and shows that the short-range condition is d << z << λ0, not a0 << z << a0/α. That is a legitimate and important correction, and the recomputation at z = 75.61 a.u. using Jentschura's own coefficients gives ratios that are indeed tiny. The arithmetic is straightforward and reproducible, which is good.

The main soft spot is the factor of 8 used to fix zmin = 4 nm. The condition z >> d is not quantified in the original Lifshitz references, and the author treats 8d as sufficient. The stress-test is right: at z = 2 nm (4d), the positronium quadrupole ratio is about 0.9%, which already exceeds the paper's own 0.5% error threshold. So the sweeping statement that 'all multipole corrections are negligibly small' depends on a convention that is asserted rather than derived. The paper would be stronger if it acknowledged this sensitivity and argued for the stricter bound more explicitly, or if it stated the corrections as a function of the chosen zmin.

There is also a notational issue in Eqs. (6), (7), and (10)–(12): the ratios are written as C50/C30 × z², which reads as multiplication by z². The numbers make clear that division is intended, so this is a typo, but it should be fixed in any revised version.

The comment's treatment of the perfect-conductor case is more debatable: the 1 µm threshold is taken from the author's own book and may not be universally accepted, but it is a side issue and does not affect the main argument.

Overall, the central claim holds up under scrutiny. Lifshitz theory is a continuum theory, and applying it at 0.5 nm from a quartz surface is hard to defend. Jentschura's large quadrupole corrections are likely artifacts of using the theory outside its intended regime. The comment deserves a serious referee; it is the kind of focused, literature-grounded criticism that should be published if the typo and the zmin justification are addressed. I would cite it if I worked in this subfield, and I would bring it to a reading group to spark discussion on validity regimes.

Referee Report

1 major / 5 minor

Summary. In this Comment, Klimchitskaya challenges the validity domain used in Jentschura's recent paper on multipole corrections to the atom-wall Casimir-Polder interaction. The Comment argues that, according to the original Lifshitz theory, the short-range regime is defined by d << z << λ0 (with d the interatomic separation in the wall and λ0 the characteristic absorption wavelength), not by a0 << z << a0/α as used by Jentschura, and that the long-range regime should be λ0 << z << ℏc/(kBT) (or z >> λ0 at T = 0), not z >> a0/α. Using zmin = 4 nm = 8d as the shortest admissible separation, the author recomputes the ratios of quadrupole and octupole corrections to the dipole term for hydrogen and positronium near α-quartz, using coefficients from Jentschura's tables, and obtains values below about 2.2 × 10^-3. This leads to the conclusion that all multipole corrections are negligibly small within the valid regime and that Jentschura's large corrections at z = 10 a.u. arise from applying the Lifshitz theory outside its domain of validity. The Comment also dismisses Jentschura's perfect-conductor short-range results as irrelevant, stating that a perfect-conductor description requires separations above about 1 μm.

Significance. If the argument holds, the Comment provides a useful clarification of the domain of validity of the Lifshitz theory for atom-wall interactions, with practical implications for physisorption calculations. It grounds the argument in original references from Lifshitz and collaborators and uses Jentschura's published coefficients, making the quantitative comparison transparently reproducible. The paper also offers a falsifiable prediction: multipole ratios scale as (d/z)^2 and fall below the 0.5% level for z ≳ 4 nm. The main contribution is conceptual, warning against applying macroscopic continuum electrodynamics at separations comparable to interatomic distances, where multipole expansions can be misleading. The argument is concise and well focused, although the quantitative negligibility claim depends on a conventional choice of the lower bound, as discussed below.

major comments (1)

[Eq. (8) and the paragraph following it, esp. Eq. (10)] The quantitative conclusion that all multipole corrections are negligibly small depends on an arbitrarily chosen lower bound. The manuscript quotes the Lifshitz condition z >> d, where d is the interatomic distance, but then sets zmin = 4 nm = 8d without derivation or sensitivity analysis. If the continuum description is valid already at z = 2 nm (4d), then using the intended division in Eq. (10), the positronium quadrupole/dipole ratio is about 0.88%, exceeding the paper's own 0.5% threshold based on the optical-data error; at z = 1 nm it is about 3.5%. The claim in the abstract that 'all multipole corrections ... turned out to be negligibly small' is therefore not robust to the factor-of-8 convention. The author should either justify the lower bound with a microscopic argument or a convergence test of the continuum approximation, or soften the conclusion to state that the corrections are small (≲1% for Ps, ≲0.1% for H) at the shortest separations where the continuum model is defensible. This does not undercut the primary point that Jentschura's short-range condition a0 << z << a0/α is inconsistent with the original Lifshitz condition, but it is load-bearing for the quantitative statement in the abstract.

minor comments (5)

[Eqs. (6), (7), (10), (11), (12)] The ratio formulas are typeset ambiguously: read literally, expressions such as C5/C3 × 10^2 mean multiplication by 10^2, but the reported numerical values (e.g., 0.124) show that division by 10^2 is intended. Please use an explicit fraction or parentheses, e.g., C5/(C3 z^2), to remove the ambiguity.
[Eq. (9)] The upper bound ℏc/(kBT) ≈ 7.6 μm in Eq. (9) is a finite-temperature condition; at T = 0 the retarded Casimir-Polder regime extends to arbitrarily large separations. The authors should clarify that Eq. (9) applies at room temperature and state the T = 0 case separately.
[Paragraph beginning 'It is necessary also to take into account'] The 0.5% error estimate from Ref. [3] is used as a negligibility threshold for the higher-order coefficients C5 and C7, but it is not stated whether that estimate covers the multipole polarizabilities and the extrapolation of the optical data to the imaginary-frequency axis. The authors should state this assumption explicitly.
[Paragraph beginning 'This conclusion remains unchanged'] The assertion that nonlocal dielectric permittivities can be introduced only in the continuous-medium model is plausible but is made without a supporting reference; adding a citation would strengthen the statement.
[Paragraph beginning 'In addition to the interaction of an atom'] The threshold of approximately 1 μm for modeling a wall as a perfect conductor is presented as a fact via Ref. [3] but is not derived. Since this threshold is larger than typical plasma-wavelength-based estimates (of order 100 nm), the authors should provide a more detailed justification or qualify the statement.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the comment's quantitative conclusion is an evaluation of Jentschura's own tabulated coefficients within an externally sourced Lifshitz validity window; the only self-citation is supporting, not load-bearing.

full rationale

The derivation chain is not circular. The central claim—that multipole corrections are negligible in the Lifshitz-theory regime—is obtained by taking Jentschura's published C3, C5, C7 values and evaluating C5/(C3 z^2) or C7/(C3 z^4) at a chosen zmin = 75.61 a.u. This is arithmetic using the opponent's own numbers, not a fitted parameter renamed as a prediction. The validity window d << z << λ0 is imported from citations to Lifshitz, Dzyaloshinskii, Pitaevskii, and the Lifshitz-Pitaevskii textbook, i.e., from external sources, not from this comment's own conclusions. The specific choice zmin = 4 nm = 8d is an interpretive convention rather than a derived bound; it affects the numerical smallness but does not make the result equivalent to its input by construction. The only self-reference is Ref. [3], co-authored by the present author, cited for the 0.5% coefficient error and the ~1 micrometer perfect-conductor validity threshold; both are supporting details. Even without Ref. [3], the quadrupole ratios at the chosen zmin are 2.2e-3 for positronium and 5.2e-4 for hydrogen, so the negligibility conclusion does not rest on the self-citation. The multiplication signs displayed in Eqs. (10)-(12) are typographical; the numerical values show that division was intended, and this is a notational flaw rather than a circular step. No step reduces the claimed result to its inputs by definition or by self-citation chain.

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

The central claim rests on two domain assumptions about the validity of the Lifshitz theory: distances must exceed interatomic spacings, and the short/long-range boundaries are set by the material absorption wavelength. These are cited from the literature rather than derived. The illustrative numbers also depend on the chosen d and zmin values. No new entities are introduced.

free parameters (2)

d (interatomic distance in alpha-quartz) = 0.5 nm
Chosen from lattice constants of alpha-quartz, stated as approximately 5 Å; used to set the lower bound d << z for Lifshitz theory.
zmin (shortest admissible separation) = 4 nm = 75.61 a.u.
Chosen as 8 times d to satisfy the macroscopic condition d << z; the numerical estimates of correction ratios depend on this choice.

assumptions (4)

domain assumption The Lifshitz theory is applicable only when the atom-wall separation is large compared to interatomic distances in the wall material.
Stated as a quote from Refs. [2,6,9] and used to reject Jentschura's 0.5 nm results. This is the load-bearing premise.
domain assumption The short-range regime of the Lifshitz formula extends up to distances much smaller than the characteristic absorption wavelength lambda_0, not up to a0/alpha.
Cites Refs. [2,3,6-9]; used to define the upper bound of the short-range regime.
domain assumption The long-range regime extends from lambda_0 to about 7.6 micrometers at room temperature, rather than z >> a0/alpha.
Cites Refs. [2,3,6-9]; used to argue Jentschura's long-range condition is also wrong.
domain assumption A perfectly conducting wall model is valid only for separations above about 1 micrometer.
Assigned to Ref. [3], one of whose authors is the present author; used to dismiss Jentschura's perfect-conductor short-range results.

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Cite this review

Pith. "Pith review of Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)." pith.science (2026). https://pith.science/paper/LYIKUCYZ

@misc{pith2026250114803,
  author       = {Pith},
  title        = {Pith review of: Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $\alpha$-quartz, and physisorption" (arXiv:2308.04656v3)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LYIKUCYZ}},
  note         = {Machine review of arXiv:2501.14803}
}

abstract

Recently U. D. Jentschura [Phys. Rev. A $\bf 109$, 012802 (2024)] rederived the multipole corrections to the dipole part of the atom-wall interaction described by the Lifshitz theory using the concept of volume dielectric permittivity. These corrections were computed for the hydrogen and positronium atoms in close proximity to the $\alpha$-quartz wall and claimed to be numerically significant within the short-range regime. Here, it is shown that the application areas of the obtained expressions both in the short-and long-range asymptotic regimes are indicated incorrectly, in contradiction with those dictated by the Lifshitz theory. As a result, within the valid application areas, all multipole corrections to the Casimir-Polder dipole part of the atom-wall interaction turned out to be negligibly small.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Reply to Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, alpha-quartz, and physisorption" (arXiv:2501.14803)
physics.atom-ph 2025-02 unverdicted novelty 2.0 of 10

The Reply maintains that the short-range expansion limits in Ref [3] are correct for zero-temperature Lifshitz theory and that physisorption applications are valid via a reference-plane correction.

Reference graph

Works this paper leans on

12 extracted references · 11 canonical work pages · cited by 1 Pith paper

[1]

We can however approach this problem in purely macro- scopic fashion (since the distance between the bodies is assumed to be large compared to interatomic distances)

5 nm. In fact, by citing Ref. [5], Ref. [1] advocates that the short-range expressions are actually valid down to distance regions of a few angstroms away from the surface. The long-range regime, as stated in Ref. [1], holds at atom-wall distances z ≫ a0 α . (3) The analytic expressions for El(z) obtained in Ref. [1] in the short-range regime are given by...

work page
[2]

a good treatment of the spatial variation of the interaction potential along the surface

5 nm ≈ 10 a.u. the overlap between the wave functions of the ground-state hydrogen atom and the wall atoms is already negligibly small. In addition, Ref. [1] mentions the result [5] that at atom-wall separations down to 4 – 7 a.u. the interaction energy can be presented in the form V (z) ≈ − C3 (z − z0)3 , (13) where C3 = C(3)0 is deﬁned in Eq. (5) with l...

work page 2023
[3]

U. D. Jentschura, Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, α -quartz, and physisorption, Phys. Rev. A 109, 012802 (2024)

work page 2024
[4]

E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics , Pt. 2 (Pergamon Press, Oxford, 1981)

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[5]

Bordag, G

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Eﬀect (Oxford University Press, Oxford, 2015)

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[6]

Tao and A

J. Tao and A. M. Rappe, Physical Adsorption: Theory of van der Waals Interactions between Particles and Clean Surfaces, Phys. Rev. Lett. 112, 106101 (2014)

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Zaremba and W

E. Zaremba and W. Kohn, Van der Waals interaction between an atom and a solid surface, Phys. Rev. B 13, 2270 (1976)

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I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevski i, The general theory of van der Waals forces, Usp. Fiz. Nauk 73, 381 (1961) [Adv. Phys. 10, 165 (1961)]

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M. Antezza, L. P. Pitaevskii, and S. Stringari, Eﬀect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate, Phys. Rev. A 70, 053619 (2004)

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

We can however approach this problem in purely macro- scopic fashion (since the distance between the bodies is assumed to be large compared to interatomic distances)

5 nm. In fact, by citing Ref. [5], Ref. [1] advocates that the short-range expressions are actually valid down to distance regions of a few angstroms away from the surface. The long-range regime, as stated in Ref. [1], holds at atom-wall distances z ≫ a0 α . (3) The analytic expressions for El(z) obtained in Ref. [1] in the short-range regime are given by...

work page

[2] [2]

a good treatment of the spatial variation of the interaction potential along the surface

5 nm ≈ 10 a.u. the overlap between the wave functions of the ground-state hydrogen atom and the wall atoms is already negligibly small. In addition, Ref. [1] mentions the result [5] that at atom-wall separations down to 4 – 7 a.u. the interaction energy can be presented in the form V (z) ≈ − C3 (z − z0)3 , (13) where C3 = C(3)0 is deﬁned in Eq. (5) with l...

work page 2023

[3] [3]

U. D. Jentschura, Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, α -quartz, and physisorption, Phys. Rev. A 109, 012802 (2024)

work page 2024

[4] [4]

E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics , Pt. 2 (Pergamon Press, Oxford, 1981)

work page 1981

[5] [5]

Bordag, G

M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Eﬀect (Oxford University Press, Oxford, 2015)

work page 2015

[6] [6]

Tao and A

J. Tao and A. M. Rappe, Physical Adsorption: Theory of van der Waals Interactions between Particles and Clean Surfaces, Phys. Rev. Lett. 112, 106101 (2014)

2014

[7] [7]

Zaremba and W

E. Zaremba and W. Kohn, Van der Waals interaction between an atom and a solid surface, Phys. Rev. B 13, 2270 (1976)

work page 1976

[8] [8]

I. E. Dzyaloshinskii, E. M. Lifshitz, and L. P. Pitaevski i, The general theory of van der Waals forces, Usp. Fiz. Nauk 73, 381 (1961) [Adv. Phys. 10, 165 (1961)]

work page 1961