puchalski_2020 ============== M\. Puchalski, K\. Szalewicz, M\. Lesiuk and B\. Jeziorski, "QED calculation of the dipole polarizability of helium atom", Phys\. Rev\. A 101, 022505 \(2020\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.101\.022505 `__ **Source kind:** theory **Recorded technique:** Ab initio static dipole polarizability of the 4He atom\: the alpha^3 QED correction with the second electric\-field derivative of the Bethe logarithm computed two ways \(Schwartz's integral representation in the Pachucki\-Komasa form, explicitly correlated Slater\-geminal bases of K = 128\-512 functions, Sec\. II; and Goldman and Drake's sum over pseudostates, Sec\. III\), and the alpha^3/M QED recoil correction \(Sec\. IV, Eqs\. 64\-71\)\. Combined with the nonrelativistic, alpha^2, alpha^2/M, alpha^4 and finite\-size terms of Puchalski et al\. \(2016\) and Piszczatowski et al\. \(2015\) into the total of Table VIII \(p\. 11\)\. Static field only\: no frequency dependence\. **Materials in structured entries:** He **Dataset quantities:** molar\_refractivity, polarizability **Contents:** 3 datasets; 0 formulas. Curation notes -------------- Page numbers are the article pages 022505\-1 to \-13 \(= pdf pages\)\. Atomic units a0^3; the paper takes alpha = 1/137\.0359991, a0 = 0\.052917721 nm, m\_alpha = 7294\.2995361 m\_e and N\_A = 6\.02214076e23 \(2019 SI\) \(p\. 2\)\. Table VIII \(p\. 11\), 4He, a0^3 \(read on the image; the cells agree\)\: nonrelativistic 1\.3838099864 \(Ref\. 23 = puchalski\_2016\); alpha^2 relativistic \-0\.0000803599 \(Ref\. 23\); alpha^2/M relativistic recoil \-0\.0000000935\(1\) \(Ref\. 18 = piszczatowski\_2015\); alpha^3 QED without the field derivative of ln k0 0\.0000304738; the field\-derivative term 0\.0000001822; alpha^3/M QED recoil 0\.00000001112\(1\) \(new here\); alpha^4 QED 0\.00000056\(14\) \(the one\-loop part only, a 25 % allowance for the incomplete calculation; Ref\. 18\); finite nuclear size 0\.0000000217\(1\) \(Ref\. 18\); total 1\.38376078\(14\)\. Molar polarizability \(4 pi/3\) alpha\_d N\_A 0\.51725408\(5\) cm^3/mol; experiment \(Gaiser and Fellmuth 2018\) 0\.5172544\(10\)\. Note g\: 3He \(nonrelativistic 1\.38401218\(1\), recoil terms scaled by the mass ratio 1\.32711\) 0\.51732965\(5\) cm^3/mol \(no material for 3He; not extracted\)\. 'When no error bar is given, the last digit is certain' \(caption\); the uncertainties are convergence estimates and the alpha^4 allowance, level not stated\. The total's \(14\) is the alpha^4 allowance alone\. In the text\: the field derivative of the Bethe logarithm d^2 ln k0/dE^2 = 0\.0485572\(14\) a\.u\. \(integral representation, p\. 5\) and 0\.0487\(5\) \(sum over states, p\. 10\), against Lach et al\.'s \(2004\) 0\.0512\(4\), 'about six times the error estimate' of that paper \(p\. 10\); the alpha^3 QED correction for infinite mass 30\.6560\(1\)e\-6 a0^3, the recoil part 0\.01112\(1\)e\-6 \(alpha\_R1 0\.00484, alpha\_R2 0\.00087, alpha\_R3 0\.00541\), total 30\.6671\(1\)e\-6 \(abstract, p\. 10\); the alpha^2 correction with recoil \-80\.4534\(1\)e\-6 \(p\. 2, = \-80\.3599 \- 0\.0935 of Table VIII\)\. CHECKED \(2026\-09\-29\)\: the components of Table VIII add to 1\.38376078182, the printed total 1\.38376078\(14\); 30\.4738 \+ 0\.1822 = 30\.6560 and \+ 0\.01112 = 30\.66712, the printed 30\.6560 and 30\.6671; the total times \(4 pi/3\) N\_A a0^3 \(the package's constants, 0\.37380311 cm^3/mol per a0^3\) is 0\.517254083 cm^3/mol, the printed 0\.51725408\(5\)\. AGAINST puchalski\_2016 \(the helium fit's backbone\)\: the static total rises by 0\.0104e\-6 a0^3 \(1\.38376077\(14\) to 1\.38376078\(14\), \+7\.5e\-9 relative, 0\.07 of the stated uncertainty\)\: the field\-derivative term is 0\.1822 in place of 2016's preliminary 0\.183\(1\) \(from this paper, then in preparation, Ref\. 18 of 2016\), and the QED recoil 0\.01112, which 2016 left out of its value \(p\. 10 of 2016\), is added\. The molar polarizability falls from 2016's 0\.51725413\(6\) to 0\.51725408\(5\) mostly through the new N\_A \(\-8\.8e\-8\)\. The paper does not revise the dispersion coefficients alpha\_2, alpha\_4, \.\.\.\: 'for helium the frequency dependent part of alpha\_d\(omega\) is small \.\.\. and does not have to be known with high relative accuracy' \(p\. 1\), and it notes that the index of refraction also depends on the magnetic susceptibility and, 'at the 10^\-7 level', on the magnetic and quadrupole terms of Pachucki and Puchalski \(pachucki\_2019\) \(p\. 1\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- puchalski\_2020/alpha\_static ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_static", "material": "He", "file": "He/puchalski_2020__alpha_static.csv", "table": "tbl_d93800f29266", "quantity": "polarizability", "unit": "au", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table VIII 'Total'\: the static electric dipole polarizability of 4He with all corrections, 1\.38376078\(14\) a0^3 \(p\. 11\)\. The newer value of the static total of puchalski\_2016 \(row \-2 of cauchy\_total, which the helium fit uses\), 7\.5e\-9 above it\: a check, not fitted beside it \(the two share every component but the alpha^3 field\-derivative and recoil terms\)\. Electric only\: the magnetic term chi\_0 is not included\. puchalski\_2020/molar\_polarizability ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "molar_polarizability", "material": "He", "file": "He/puchalski_2020__molar_polarizability.csv", "table": "tbl_d93800f29266", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "check", "uncertainty": { "column": true, "level": "not stated" } } Table VIII 'Molar polarizability \(4 pi/3\) alpha\_d N\_A'\: 0\.51725408\(5\) cm^3/mol, A\_eps of 4He \(static, electric\)\. The same number as alpha\_static converted with N\_A = 6\.02214076e23 \(reproduced to 1e\-9\)\: a check, not fitted beside it\. The value yang\_2025 \(puchalski\_He\) and rourke\_2021 \(A\_eps\_He\) quote\. puchalski\_2020/gaiser\_2018 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gaiser_2018", "material": "He", "file": "He/puchalski_2020__gaiser_2018.csv", "table": "tbl_d93800f29266", "quantity": "molar_refractivity", "unit": "cm3/mol", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "use": "reproduced", "reproduced_from": [ "gaiser_2018" ], "uncertainty": { "column": true, "level": "1 sigma" } } Table VIII 'Experiment, Ref\. \[58\]'\: Gaiser and Fellmuth's \(2018\) dielectric\-constant gas thermometry A\_eps = 0\.5172544\(10\) cm^3/mol, as in gaiser\_2018/molar\_polarizability\_He\. 'In agreement with but an order of magnitude' less accurate than theory \(abstract\); theory is 0\.3 of its sigma below\. Formulas -------- No formulas are recorded. Corrections ----------- No dataset errata are recorded in this source record. 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.