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 `__ · :doc:`Catalogue ` · :doc:`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^\(0\) = \-\(alpha^2/6\) \ \(Eq\. \(3\)\)\: numerical Hartree\-Fock \ \(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 \\_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 \ = 2\.38697, \ = 0\.018970526 and \ = \-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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 \, nonrelativistic, 1 % allowed\), which fit/Ar uses \(TC\-71\)\. Superseded by chi0\_Ar\. Formulas -------- No formulas are recorded. Corrections ----------- .. code-block:: text [ { "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 :doc:`review register ` for the checks and decisions.