lesiuk_2023b#
M. Lesiuk and B. Jeziorski, “Diamagnetic susceptibility of neon and argon including leading relativistic effects”, arXiv:2311.11357v1 [physics.atom-ph] (2023)
Source record · Catalogue · Review register
DOI: 10.48550/arxiv.2311.11357
Source kind: theory
Recorded technique: Ab initio composite calculation of the static diamagnetic susceptibility (magnetizability) chi_0 = -d^2E/dB^2 of the neon and argon atoms (Eq. (2)). Leading term chi_0^(0) = -(alpha^2/6) <sum_i r_i^2> (Eq. (3)): numerical Hartree-Fock <r^2> (Saito 2009, Eq. (23)), all-electron CCSD(T) in doubly augmented Gaussian basis sets up to 9Z extrapolated to the complete basis set with the Riemann-zeta formula (Eq. (24)), higher excitations CCSDT, CCSDTQ, CCSDTQP (argon’s from Lesiuk and Jeziorski 2023, Eq. (25)). The complete relativistic correction of order alpha^4: Dirac-equation terms (Eqs. (4)-(6)) and Breit terms (Eqs. (7)-(8)) as CCSD(T) expectation values in Slater-type bases (finite difference, Eq. (26)); the mass-velocity and one-electron Darwin corrections to the wavefunction by CC3 linear response (Eq. (27)); the orbit-orbit term at Hartree-Fock level (50 % uncertainty); the two-electron Darwin term neglected. QED estimated as -alpha log(alpha) times the largest relativistic term (100 % uncertainty, Eq. (29)); finite nuclear mass by reduced-mass scaling (Eq. (32), 20Ne and 40Ar, 50 % uncertainty); finite nuclear size about 1 ppm, neglected. CODATA 2018 constants, alpha = 1/137.035999 (p. 2).
Materials in structured entries: Ar, Ne
Dataset quantities: magnetic_susceptibility
Contents: 10 datasets; 0 formulas.
Curation notes#
The library copy is the arXiv preprint 2311.11357v1 (dated 21 November 2023, 12 pages; the file is named lesiuk-2024.pdf); no journal reference appears in it or in the library metadata. The published version (Phys. Rev. A 109, 012820 (2024), per Crossref as reported to the curators) is not in the library and was not checked: the citation is the preprint’s. Page numbers are the preprint’s pdf pages.
Atomic units: chi_0 in a0^3 (the Gaussian-atomic unit of the magnetizability, ‘where a0 is the Bohr radius’, abstract); 1 cm^3/mol = 11.205872 a.u. (p. 2, the authors’ conversion of a molar value N_A chi_0). The molar magnetic term of the Lorentz-Lorenz relation, A_mu = (4 pi/3) N_A chi_0 a0^3 (0.3738031 cm^3/mol per a.u., computed), is -3.16933e-5 cm^3/mol for Ne and -8.58046e-5 for Ar.
Results (abstract, p. 9, Table IX): chi_0 = -8.4786(7) x 10^-5 (Ne), -22.9545(32) x 10^-5 (Ar), ‘of the order of one part per ten thousand’ relative uncertainty (p. 9). The error is the quadrature sum of the components’ (‘not correlated in the statistical sense’, p. 8); no confidence level is stated. The dominant uncertainties are CCSD(T) basis-set extrapolation, the orbit-orbit term and QED (argon: all three comparable). Frequency dependence of chi is of order alpha^5 or quadratic in m_e/M_N and is not considered (p. 2): the values are static, and the package applies them at optical frequencies (TC-71). Isotopes: the finite-mass term is for 20Ne and 40Ar (p. 8).
Checks (2026-09-29): the Table IX contributions sum to the totals, -8.4786 and -22.9545, and their quadrature is 0.00065 and 0.00317 (printed (7), (32)); Eq. (3) with Eq. (23)’s <r^2>_HF (9.37184, 26.0344) and alpha = 1/137.035999 gives -8.31772 and -23.10612, Table IX’s chi_0^HF -8.3177 and -23.1061.
Table X (image checked) prints three misprints, two of them in the powers of ten: Barter et al.’s neon value as -7.80(16) x 10^-4 (erratum below: 10^-5); the second line of Barter et al.’s argon cell, the revised uncertainty of Rourke (2021), as -2.16(15) x 10^-5 (it is x 10^-4: rourke_2021’s argon A_mu, -8.09(57) x 10^-5 cm^3/mol, is -2.164(152) x 10^-4 a.u. by the conversion above, and the text, p. 9, says the uncertainty ‘has to be increased to about 7%’; not extracted, the dataset keeps Barter et al.’s own line); and its ‘this work’ argon value as -2.29548(32) x 10^-4 where the abstract, the text (p. 9) and Table IX’s total, which its rows reproduce, give -22.9545(32) x 10^-5 (the ‘this work’ row is not extracted) (TC-706). The label ‘FMS’ under ‘other corrections’ in Table IX is the finite nuclear size term (FNS in the text, p. 8), neglected.
Comparison (p. 9): the previous theory (including the authors’ own -8.484(19) x 10^-5 and -2.30(2) x 10^-4) agrees roughly; Barter et al. disagree for neon (and for argon only before Rourke’s revision of the uncertainty); Havens’ neon agrees. The authors ask for ‘new and independent measurements’.
Helium appears only as a test of the method (pp. 5-6): Paper I (Puchalski, Lesiuk and Jeziorski, Phys. Rev. A 108, 042812 (2023), not in the library) gives <r^2> = 2.38697, <sum l_i^2> = 0.018970526 and <sum r_i^2 nabla_i^2> = -0.139689120; the helium chi_0 itself is not printed here (not extracted).
Not extracted: Tables I-VIII (basis-set sequences of the components), the Table IX contribution rows (components of the totals), Table X’s theoretical rows without uncertainties (Yoshizawa and Hada -8.27e-5, -2.22e-4; Ruud et al. / Jaszunski et al. -8.48e-5, -2.31e-4; Reinsch and Meyer -8.57e-5, -2.32e-4; Levy and Perdew / Desclaux -8.31e-5, -2.30e-4) and its ‘this work’ row.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lesiuk_2023b/chi0_Ne#
{
"id": "chi0_Ne",
"material": "Ne",
"file": "Ne/lesiuk_2023b__chi0_Ne.csv",
"table": "tbl_070dd39bd6ec",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 1e-05,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table IX ‘total’: chi_0 = -8.4786(7) x 10^-5 a.u. (the table’s entries are x 10^5), static, 20Ne; also the abstract and p. 9. 0.064 % smaller in magnitude than lesiuk_2020’s -8.484(19) x 10^-5, which it supersedes (0.3 of that value’s sigma).
lesiuk_2023b/chi0_Ar#
{
"id": "chi0_Ar",
"material": "Ar",
"file": "Ar/lesiuk_2023b__chi0_Ar.csv",
"table": "tbl_070dd39bd6ec",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 1e-05,
"abscissa": "none",
"use": "primary",
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table IX ‘total’: chi_0 = -22.9545(32) x 10^-5 a.u., static, 40Ar; also the abstract and p. 9 (Table X’s -2.29548(32) x 10^-4 is a misprint, source notes). 0.22 % smaller in magnitude than lesiuk_2023’s nonrelativistic -2.3004(6) x 10^-4 (Eq. (35) there) and 0.20 % than its rounded -2.30(2) x 10^-4 (Eq. (39)), which it supersedes: the difference is mainly the mass-velocity correction to the wavefunction, +0.0529 x 10^-5.
lesiuk_2023b/havens_1933_Ne#
{
"id": "havens_1933_Ne",
"material": "Ne",
"file": "Ne/lesiuk_2023b__havens_1933_Ne.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 1e-05,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"G. G. Havens, Phys. Rev. 43, 992 (1933)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Havens [58]’: -8.574(9) x 10^-5 a.u., as converted by Lesiuk and Jeziorski; 1.1 % from their theory, ‘a good agreement’ (p. 9). The original is not in the library.
lesiuk_2023b/havens_1933_Ar#
{
"id": "havens_1933_Ar",
"material": "Ar",
"file": "Ar/lesiuk_2023b__havens_1933_Ar.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"G. G. Havens, Phys. Rev. 43, 992 (1933)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Havens [58]’: -2.15(2) x 10^-4 a.u. (6.3 % below the theory in magnitude). The original is not in the library.
lesiuk_2023b/mann_1936_Ne#
{
"id": "mann_1936_Ne",
"material": "Ne",
"file": "Ne/lesiuk_2023b__mann_1936_Ne.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 1e-05,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"K. E. Mann, Z. Phys. 98, 548 (1936)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Mann [59]’: -7.56(20) x 10^-5 a.u. The original is not in the library.
lesiuk_2023b/mann_1936_Ar#
{
"id": "mann_1936_Ar",
"material": "Ar",
"file": "Ar/lesiuk_2023b__mann_1936_Ar.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"K. E. Mann, Z. Phys. 98, 548 (1936)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Mann [59]’: -2.19(2) x 10^-4 a.u. The original is not in the library.
lesiuk_2023b/barter_1960_Ne#
{
"id": "barter_1960_Ne",
"material": "Ne",
"file": "Ne/lesiuk_2023b__barter_1960_Ne.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"C. Barter, R. G. Meisenheimer, and D. P. Stevenson, J. Phys. Chem. 64, 1312 (1960)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Barter el al. [60]’ (sic): printed -7.80(16) x 10^-4 a.u., read as x 10^-5 (erratum below): 8 % below the theory in magnitude, the ‘large discrepancy’ of p. 9. nie_2025 uses the same value, -29.2(6) x 10^-6 cm^3/mol (A_mu, its Table I). The original is not in the library.
lesiuk_2023b/barter_1960_Ar#
{
"id": "barter_1960_Ar",
"material": "Ar",
"file": "Ar/lesiuk_2023b__barter_1960_Ar.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"C. Barter, R. G. Meisenheimer, and D. P. Stevenson, J. Phys. Chem. 64, 1312 (1960)"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, experimental, ‘Barter el al. [60]’, first line: -2.16(2) x 10^-4 a.u., note a, ‘original error estimate’. Not an independent measurement: ‘an average of three previous measurements (used to calibrate the apparatus)’ (p. 9). Rourke (2021) raised the uncertainty to about 7 % (the table’s second line, note b, -2.16(15), misprinted x 10^-5; source notes); with it the theory, 6.3 % larger in magnitude, agrees. This is the value behind rourke_2021’s recommended argon A_mu and nie_2025’s A_mu (-80.9(6) x 10^-6 cm^3/mol). The original is not in the library.
lesiuk_2023b/lesiuk_jeziorski_Ne#
{
"id": "lesiuk_jeziorski_Ne",
"material": "Ne",
"file": "Ne/lesiuk_2023b__lesiuk_jeziorski_Ne.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 1e-05,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"lesiuk_2020"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, theoretical, ‘Lesiuk and Jeziorski [25, 27]’: -8.484(19) x 10^-5 a.u., lesiuk_2020’s chi_0 (abstract and p. 10 there; nonrelativistic with an allowance for the relativistic terms), which fit/Ne uses (TC-71). Superseded by chi0_Ne.
lesiuk_2023b/lesiuk_jeziorski_Ar#
{
"id": "lesiuk_jeziorski_Ar",
"material": "Ar",
"file": "Ar/lesiuk_2023b__lesiuk_jeziorski_Ar.csv",
"table": "tbl_e0613af46035",
"quantity": "magnetic_susceptibility",
"unit": "au",
"scale": 0.0001,
"abscissa": "none",
"use": "reproduced",
"reproduced_from": [
"lesiuk_2023"
],
"uncertainty": {
"column": true,
"level": "not stated"
}
}
Table X, theoretical, ‘Lesiuk and Jeziorski [25, 27]’: -2.30(2) x 10^-4 a.u., lesiuk_2023’s Eq. (39) (-2.3004(6) x 10^-4 from <r^2>, nonrelativistic, 1 % allowed), which fit/Ar uses (TC-71). Superseded by chi0_Ar.
Formulas#
No formulas are recorded.
Corrections#
[
{
"dataset": "barter_1960_Ne",
"row": "",
"column": "scale",
"printed": "0.0001",
"corrected": "1e-05",
"reason": "Table X prints Barter et al.'s neon chi_0 as -7.80(16) x 10^-4 a.u., ten times every other neon entry of the table (experimental -7.56e-5 and -8.574e-5, theoretical -8.27e-5 to -8.57e-5, this work -8.4786e-5); read as x 10^-5 it is 8 % below the theory with a 2 % stated uncertainty, the persistent disagreement the text describes.",
"evidence": "Circumstantial: p. 9, 'the present results are in disagreement with the experimental data of Barter et al.' and, after Rourke's revision for argon, 'for neon a large discrepancy remains', a disagreement at the level of the other experiments, not an order of magnitude. The same table misprints the power of ten of Barter et al.'s revised argon line (10^-5 for 10^-4; source notes). Corroborated by nie_2025, whose Table I takes A_mu from Barter et al. (its Ref. 32): neon -29.2(6) x 10^-6 cm^3/mol, which is -7.81(16) x 10^-5 a.u. by the conversion in the source notes (argon -80.9(6) x 10^-6, i.e. -2.164(16) x 10^-4 a.u., Barter et al.'s argon line here). Not stated by the authors; the original (J. Phys. Chem. 64, 1312 (1960)) is not in the library. Checked 2026-09-29 against the table image and the text."
}
]
Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.