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REVIEW 3 major objections 6 minor 55 references

Two- and three-body dispersion coefficients for interaction of Cu and Ag atoms with {Group} I, II, and XII elements

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper reports $C_6$ and $C_9$ van der Waals dispersion coefficients for copper and silver atoms with group I, II, and XII atoms and ions, many of them previously unavailable, and supports their reliability by comparing…

desk verdict Useful new tabulations of Cu/Ag dispersion coefficients, but the reliability claim outruns the evidence: no uncertainties and no benchmark for the partner dynamic polarizabilities that drive the new C9 values. read the letter →

arxiv 2504.15490 v1 pith:PSG4FLT6 submitted 2025-04-21 physics.atom-ph quant-ph

Harpreet Kaur , Jyoti , Neelam Shukla , Bindiya Arora This is my paper · ORCID
classification physics.atom-phquant-ph
keywords vanderWaalsdispersioncoefficientsC6coefficientC9three-bodydynamicdipolepolarizabilitysum-over-statesapproachrelativisticmany-bodymethodscopperatomssilver
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 produces the long-range van der Waals dispersion coefficients $C_6$ and $C_9$ for copper and silver atoms interacting with atoms and singly charged ions of groups I, II, and XII. Many of these numbers, including every three-body $C_9$ value and most coefficients involving group XII partners, have not been reported before. The authors build them from dynamic dipole polarizabilities at imaginary frequencies, computed with relativistic wave functions and a sum over intermediate states, and they check their inputs by comparing oscillator strengths, static polarizabilities, and available $C_6$ values with earlier calculations. Agreement mostly within about ten percent, with larger deviations for some Sr and Ba cases, is the basis for the claim that the new coefficients, including the unbenchmarked $C_9$ tables, are reliable enough for cold-atom, hybrid trap, and van der Waals complex studies.

What carries the argument

The load-bearing object is the imaginary-frequency dipole polarizability, written as a sum over intermediate states $$\alpha_v(i\omega)=\sum_{k\ne v}\frac{f_{vk}}{(E_v-E_k)^2+\$omega^{2}$},$$ where $f_{vk}$ is the oscillator strength of the dipole transition and the energies and matrix elements come from relativistic wave functions. Inserting these polarizabilities into the Casimir–Polder integrals turns every dispersion coefficient into a weighted product of the participating species' polarizabilities. This is what carries the argument: once the dynamic polarizabilities are accepted, the tabulated $C_6$ and $C_9$ values follow directly, with no additional fitted parameters.

What would settle it

An independent high-accuracy calculation of the three-body coefficient for Ag–Ag–Cs, predicted here to be 48,296 atomic units, that disagrees by more than the claimed few-percent accuracy of the inputs would show the imported partner polarizabilities are not reliable.

Watch

Extended reading notes

Core claim

The paper's central claim is that the leading dispersion interactions of ground-state Cu ($4S_{1/2}$) and Ag ($5S_{1/2}$) with partners from groups I, II, and XII are accurately given by the two-body and three-body dipole dispersion coefficients $$C_6 = \frac{3}{\pi}\int_0^\infty \alpha_A(i\omega)\alpha_B(i\omega)\,d\omega \quad\text{and}\quad C_9 = \frac{3}{\pi}\int_0^\infty \alpha_A(i\omega)\alpha_B(i\omega)\alpha_C(i\omega)\,d\omega,$$ evaluated with dynamic dipole polarizabilities from relativistic calculations. The polarizabilities themselves are sums over dipole transitions, with oscillator strengths computed by different many-body methods for different species: RMBPT for Cu and Ag, the multi-configuration Dirac-Fock method for group II and XII atoms, and the relativistic all-order method for monovalent partners. The reported $C_6$ values agree with earlier theoretical values mostly within about 1–10%, with the largest deviations (roughly 14–18%) for the Sr and Ba partners; the authors note that Ag–Cs has the largest $C_6$ and Cu–Be$^+$ the smallest in their set, and the $C_9$ values are all new.

Load-bearing premise

The whole table trusts the dynamic polarizabilities of the partner atoms and ions that are imported from the authors' earlier papers without being recomputed here, so a systematic error in those inputs would shift every $C_6$ and $C_9$ value.

Editorial extensions

If this is right

  • Cold-atom and hybrid atom–ion experiments involving Cu or Ag now have the leading two-body interaction strengths needed to estimate whether atom–atom or atom–ion pairs remain bound at ultracold temperatures.
  • The three-body coefficients allow estimates of non-additive contributions to the interaction potential, which matter for three-body recombination and for the stability of mixed-species traps.
  • The reported hierarchy—Ag–Cs largest $C_6$, Ag–Ag–Cs largest $C_9$, Cu–Be$^+$ and Cu–Zn$^+$ smallest—gives a quick guide to which combinations will interact most strongly.
  • Because most group XII values and all $C_9$ values were previously missing, the tables fill a specific gap in inputs for modeling van der Waals complexes and lattice or surface traps involving metallic atoms.

Reading between the lines

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

  • Not stated in the paper, but the product structure of the Casimir–Polder integrals implies that if a partner's dynamic polarizability is later improved, every coefficient involving that partner can be rescaled without recalculating the Cu or Ag side of the integrand.
  • Ratios such as $C_9$(Cu–Cu–X)/$C_6$(Cu–X) may be more stable against systematic errors than the absolute values because some errors would partially cancel; this is a testable cross-check the paper does not perform.
  • A natural next check is to measure trap-loss or photoassociation spectra for one of the predicted pairs, for example Ag–Cs or Cu–Hg, and invert the data for $C_6$; that would provide the first experimental benchmark for these tables.
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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 static dipole polarizabilities of Cu and Ag obtained from relativistic sum-over-states calculations and uses them, together with dynamic polarizabilities of partner atoms and ions taken from the authors' earlier work [38,52,53], to evaluate C6 two-body and C9 three-body van der Waals dispersion coefficients for Cu and Ag interacting with group I, II, and XII atoms and singly charged ions. Many of the reported C6 coefficients and all of the reported C9 coefficients are new. Validation consists of comparisons of Cu and Ag static polarizabilities and oscillator strengths with literature values, and comparisons of a subset of C6 coefficients with two earlier calculations. The authors conclude that the overall agreement establishes the reliability of the reported values.

Significance. If the tabulated coefficients are accurate, the paper would provide a useful data set for modeling ultracold collisions, hybrid atom-ion traps, and long-range interaction potentials involving Cu and Ag, especially for combinations that were previously unavailable. The methods are standard (Casimir-Polder integrals over imaginary-frequency polarizabilities) and the static polarizability comparisons are favorable for several test cases. However, the significance is limited by the absence of uncertainty estimates for every reported coefficient, by the fact that all C9 values are unbenchmarked products of imported dynamic polarizabilities, and by unexplained 14-18% deviations in two C6 comparisons.

major comments (3)
  1. [§IV.A, Tables I-II] The reliability claim in §IV.A ('can be considered reliable') is based on comparisons of static dipole polarizabilities and oscillator strengths. Static alpha(0) is a single point of the integrands in Eqs. (2) and (4); agreement at zero frequency does not validate the dynamic polarizabilities at all imaginary frequencies that contribute to the integrals. The partner-species dynamic polarizabilities are imported from Refs. [38,52,53] without being recomputed or assigned uncertainties. Since the paper presents no uncertainty for any C6 or C9 value and no propagation of input errors, the reliability claim for the tabulated coefficients is not quantitatively supported. Please provide uncertainty estimates propagated from the input polarizabilities or a sensitivity analysis showing how C6 and C9 change under plausible variations of the partner polarizabilities.
  2. [§IV.B, Table III] The statement of 'good agreement' with earlier C6 results is weakened by the deviations in Table III for Cu-Sr (14.25%) and Ag-Sr (18.00%) with respect to Ref. [49]. These are considerably larger than the sub-percent to few-percent deviations quoted for lighter group I and II partners, and no specific explanation is offered for these two cases. In addition, all group XII C6 entries have no external comparison. The authors should either quantify and physically explain these outliers or temper the reliability claim so that it does not extend indiscriminately to every tabulated C6 value.
  3. [§IV.B, Table IV] All C9 coefficients in Table IV are reported without any comparison to previously published three-body dispersion coefficients and without uncertainties. Equation (4) is a product of three dynamic polarizabilities, so relative errors in any partner species propagate directly into C9, on top of errors in the Cu or Ag polarizabilities. The existing checks on static polarizabilities and on selected C6 values do not certify these new C9 values. At minimum, the authors should provide an independent check for at least one C9 (for example against a known Axilrod-Teller-Muto coefficient for a well-studied triad), or clearly state in the abstract and conclusion that the C9 values are exploratory and should be used with caution until benchmarked.
minor comments (6)
  1. [§IV.B] The name 'Simalkowski' in the text should be 'Smialkowski', matching Ref. [49].
  2. [§IV.A] There is a typo on 'plarizabilities' that should read 'polarizabilities' in the discussion of the main contribution to the static polarizability.
  3. [Table I] Several entries are listed as '~ 0' rather than explicit numerical values; providing three significant digits (or a stated truncation threshold) would make the table more informative and reproducible.
  4. [§IV.B] The text refers to Cu and Ag as belonging to 'group XI', while the title and abstract use 'Group I, II, and XII'; please clarify the Roman-numeral group nomenclature so that Cu/Ag (group 11, formerly IB) are not confused with group XII (Zn, Cd, Hg).
  5. [§II] No numerical details are given for the quadrature used to evaluate the integrals in Eqs. (2) and (4); specifying the frequency grid and convergence criteria would improve reproducibility.
  6. [Data Availability] Since this is a data-oriented paper, the statement that data are not publicly available reduces its utility; consider depositing the dynamic polarizability tables and the final C6/C9 tables in a repository.

Circularity Check

0 steps flagged · score 1.0 of 10

No construction-level circularity: C6 and C9 are Casimir-Polder integrals over independently computed Cu/Ag polarizabilities and previously published partner polarizabilities; no fitted input is renamed as a prediction.

full rationale

The derivation chain is explicit and non-circular at the level of construction: C6=(3/pi) integral alpha_A(iw) alpha_B(iw) dw (Eq. 2) and C9=(3/pi) integral alpha_A(iw) alpha_B(iw) alpha_C(iw) dw (Eq. 4). The Cu and Ag dynamic polarizabilities are computed in this paper via sum-over-states using oscillator strengths from RMBPT/MCDF wave functions, and the static values are checked against four independent theoretical calculations (Refs. [46-49]) and experiment, with deviations mostly below 10%. The partner-species dynamic polarizabilities are imported from the authors' earlier works [38,52,53], which is a self-citation that is load-bearing for every Table III and Table IV entry; however, those inputs were not fitted to the C6 or C9 values reported here, and the reported coefficients are products of the stated inputs rather than definitions of them. The paper's broader reliability claim goes beyond what its checks establish, because agreement at zero frequency does not certify the full imaginary-frequency integrands, and the C9 values in Table IV have no external benchmarks; that is an evidentiary and correctness limitation, not a reduction of a prediction to its own inputs. Under the required standard of exhibiting a specific reduction by construction, no circular step is present. Score 1 reflects the minor but real self-citation concern, without treating it as forced agreement.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The calculation depends on standard quantum mechanical formulas and on polarizability inputs from the authors' prior work. The only tuning choice is the summation cutoff, which is not quantified. No new physical entities are introduced.

free parameters (1)
  • Main/tail summation cutoff
    The valence polarizability is split into a main part summed over low-lying transitions and a tail part treated with Dirac-Fock; the paper neither specifies nor tests the cutoff, so the truncation is an unquantified computational choice.
assumptions (4)
  • domain assumption Dynamic dipole polarizability is accurately computed by the sum-over-states expression with a finite set of low-lying transitions plus Dirac-Fock core and tail contributions.
    Section II.B and III.A: the main contribution is summed over selected transitions; the tail and core use DF wave functions. Accuracy depends on convergence, which is not demonstrated.
  • domain assumption The dynamic polarizabilities of group I, II, and XII atoms and ions from Refs [38,52,53] are accurate enough for C6 and C9.
    Section IV.A states these values are taken from the authors' previous works and are not recomputed or independently benchmarked in this paper.
  • domain assumption Experimental energies from NIST used for the sum-over-states are accurate and complete for the included transitions.
    Section I: 'We used experimental energies wherever possible to increase the accuracy of our calculation.'
  • standard math The Casimir-Polder integrals (Eqs. 2 and 4) give the leading long-range van der Waals interaction coefficients.
    Standard second-order perturbation theory in the dipole approximation; the paper relies on it without derivation.

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Pith. "Pith review of Two- and three-body dispersion coefficients for interaction of Cu and Ag atoms with {Group} I, II, and XII elements." pith.science (2026). https://pith.science/paper/PSG4FLT6

@misc{pith2026250415490,
  author       = {Pith},
  title        = {Pith review of: Two- and three-body dispersion coefficients for interaction of Cu and Ag atoms with Group I, II, and XII elements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PSG4FLT6}},
  note         = {Machine review of arXiv:2504.15490}
}
abstract

The mounting interest in conducting thorough analyses and studies of long-range interactions stems from their wide-ranging applications in cold atomic physics, making it a compelling area for research. In this work, we have evaluated long range van der Waals dispersion (vdW) interactions of Cu and Ag atoms with atoms of group I (Li, Na, K, Rb, Cs, and Fr), II (Be, Mg, Ca, Sr, and {Ba}), XII (Zn, Cd, and Hg) {as well as} singly charged ions of group II (Be$^+$, Mg$^+$, Ca$^+$, Sr$^+$, and {Ba$^+$}) and XII (Zn$^+$, Cd$^+$, and Hg$^+$) by calculating $C_6$(two-body) and $C_9$ (three-body) vdW dispersion coefficients. In order to obtain these $C_6$ and $C_9$ coefficients, we have evaluated the dynamic dipole polarizability of the considered atoms using appropriate relativistic methods and the sum-over-states approach. To ascertain the accuracy of our results, we have compared the evaluated static dipole polarizabilities of Cu and Ag atoms and their oscillator strengths for dominant transitions {with} available literature. The calculated values of $C_6$ dispersion coefficients have also been compared with the previously reported results.

Figures

Figures reproduced from arXiv: 2504.15490 by the authors.

Figure 1
Figure 1. FIG. 1: Dynamic dipole polarizability [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

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