may_2008#

E. F. May, M. R. Moldover and J. W. Schmidt, “Electric and magnetic susceptibilities of gaseous oxygen: Present data and modern theory compared”, Phys. Rev. A 78, 032522 (2008)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevA.78.032522

Source kind: measurement

Recorded technique: A 64-rod (10 pF) cross capacitor (relative permittivity epsilon_r from capacitance ratios at 2 kHz, Eq. 14) and a quasispherical microwave cavity resonator (complex n^2 = epsilon_r mu_r from TM/TE mode frequencies at 2.4-7.3 GHz, Eq. 15), in two pressure vessels in one stirred-liquid bath, filled from one gas supply: O2 (99.998 %, the cylinder of Schmidt and Moldover 2003) along isotherms 273.20, 293.21 and 323.18 K up to 6.5 MPa; both instruments calibrated with helium against its ab initio properties (A_eps(He) = 0.5117254 cm^3/mol). Temperature 5 mK (ITS-90), densities from the NIST O2 equation of state (pp. 5-7).

Materials in structured entries: O2

Dataset quantities: molar_refractivity, polarizability

Contents: 7 datasets; 0 formulas.

Curation notes#

Identity VALIDATED; first page checked (pdf page 1: Phys. Rev. A 78, 032522 (2008), received 13 May 2008, published 25 September 2008). Page numbers are the article’s pages 1-14 (= pdf pages). ‘All uncertainties reported in this work are one standard uncertainty’ (p. 1).

STATIC ELECTRIC POLARIZABILITY (pp. 9-11). O2 has no dipole moment, so the zero-density molar polarizability A_eps of the Clausius-Mossotti expansion (Eqs. 1-3) is the static molecular polarizability; a dielectric (2 kHz) measurement, so it contains no magnetic term, and O2 has no infrared-active vibration, so it is the electronic polarizability averaged over the thermally populated states (the small temperature dependence A_tau is ‘centrifugal stretching’, p. 9). From Eq. (18) (the difference of the O2 and He polynomial coefficients, independent of apparatus parameters and of the equation of state): A_eps = 3.9578 +- 0.0002 (273 K), 3.9582 +- 0.0002 (293 K), 3.95824 +- 0.00007 cm^3/mol (323 K) (p. 11). A fit of the present and Schmidt and Moldover’s (2003) epsilon_r(p, T) data to Eq. (19) gives A_eps,273K = 3.95760 cm^3/mol, b_eps = 0.16 cm^3/mol, c_eps = -50 cm^6/mol^2, A_tau = 0.0037 cm^3/mol (standard error 9e-7; b_eps, c_eps and A_tau ‘have little physical significance’, p. 9: not extracted). A_tau = 0.0026 +- 0.0011 cm^3/mol from the 323 and 273 K values. Recommended: the average of the two methods, A_eps,273K = 3.9576 +- 0.0008 cm^3/mol, alpha_e = (1.7456 +- 0.0003) x 10^-40 F m^2 (pp. 2, 11; 3 eps0 A_eps/N_A recomputes 1.74563e-40, checked 2026-09-25). 0.7 % above Minaev’s and 0.1 % below Wheatley’s ab initio values (both at 0 K, p. 3).

Other values quoted (p. 3), reproduced here: Schmidt and Moldover (2003, Ref. 17; the same capacitor method and gas cylinder) alpha_e = 1.7461e-40 F m^2 at 273 K; Younglove (1972, Ref. 20; compressed liquid O2 at 100-140 K) 1.7447e-40; ab initio Minaev (2004) 1.7329e-40 and Wheatley (2007) 1.7477e-40.

REPRODUCTIONS OF THIS PAPER: zhao_2026’s may_2008_O2 (3.9582(2) at 293 K and 3.95824(7) at 323 K) are this paper’s Eq. (18) values (identical, checked), and its may_2008_297K_O2 an interpolation of them; rourke_2021 has no O2 values (its gases are He, Ne, Ar, N2), so there is nothing to compare there.

MAGNETIC SUSCEPTIBILITY (no quantity in the vocabulary; not extracted as data). The molar magnetic susceptibility at zero frequency and density, 293.15 K: chi_M00 = (42.92 +- 0.06) x 10^-9 m^3/mol with the electronic g factor constrained to 2.0039 (Table IV, recommended column; unconstrained 43.07 +- 0.31), second magnetic virial coefficient b_mu = -1.8 +- 0.5 cm^3/mol (p. 14); chi_M00^meas/chi_M00^calc = 0.9998 +- 0.0014 against Minaev’s ab initio 42.93e-9. Table I lists the earlier values (Van Vleck 42.6, Davis 42.88, Minaev 42.93 theory; Sone 41.86, Weiss and Piccard 42.52, ICT 42.71, Burris and Hause 42.74 +- 0.42, Kaye and Laby 42.75, Mingelgrin 42.94, Bauer and Piccard 43.34 (the CRC Handbook value), Wills and Hector 43.73; x 10^-9 m^3/mol). In the zero-density limit chi_M = 3 x (molar magnetizability) (p. 4), so the A_mu of the refractometry working equation (n^2 - 1)/(n^2 + 2) = (A_eps + A_mu) rho is chi_M/3 = 0.01431 cm^3/mol for O2 at 293.15 K (computed). Note: zhao_2026’s O2 A_mu, 3449e-6 cm^3/mol, equals the CRC value 43.34e-9 m^3/mol divided by 4 pi (3.4489e-3, a cgs molar susceptibility), not chi_M/3 (14.45e-3 for the CRC value): a factor 4 pi/3 apart (TC-203). The static paramagnetic susceptibility does not follow optical frequencies (its dispersion is set by transitions near 60 GHz, pp. 4-5), so whether any of it belongs in an optical A_R is a separate question.

Not extracted: Table III (epsilon_r - 1 and mu_r - 1 at 2.6-7.2 GHz; no quantity for a permittivity at a pressure), Table II (apparatus parameters), Table IV’s relaxation parameters, the helium results.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

may_2008/eq18_O2#

{
  "id": "eq18_O2",
  "material": "O2",
  "table": "text",
  "quantity": "molar_refractivity",
  "unit": "cm3/mol",
  "abscissa_unit": "nm",
  "use": "primary",
  "excluded_rows": {
    "273": "averaged into recommended_O2 (the paper's recommended 273 K value)"
  },
  "uncertainty": {
    "column": true,
    "level": "1 sigma"
  },
  "parameters": {
    "temperature_k": 293.21
  }
}

3 inline points in the source record.

p. 11: A_eps from Eq. (18) at each isotherm (273.20, 293.21, 323.18 K; rows are the temperatures as printed, ‘273 K’, ‘293 K’, ‘323 K’), one standard uncertainty. The 293 and 323 K values carry the temperature dependence (A_tau = 0.0026 +- 0.0011 cm^3/mol per unit T/273.16 K - 1). zhao_2026’s may_2008_O2 reproduces the 293 and 323 K values. The dataset’s temperature_k is the first isotherm; the rows differ.

may_2008/alpha_e_O2#

{
  "id": "alpha_e_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability",
  "unit": "SI",
  "scale": 1e-40,
  "abscissa_unit": "nm",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "1 sigma"
  }
}

1 inline points in the source record.

pp. 2, 11: alpha_e = (1.7456 +- 0.0003) x 10^-40 F m^2 from recommended_O2 through Eq. (3) (no dipole moment): the same value, not independent. F m^2 = C m^2/V.

may_2008/schmidt_moldover_2003_O2#

{
  "id": "schmidt_moldover_2003_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability",
  "unit": "SI",
  "scale": 1e-40,
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "schmidt_2003"
  ]
}

1 inline points in the source record.

p. 3: ‘The measurements of Schmidt and Moldover at 273 K determined oxygen’s alpha_e = 1.7461 x 10^-40 F m^2’ (A_eps = 3.9587 cm^3/mol). The original is schmidt_2003: 3 eps0 A_eps/N_A of its preferred O2 fit, A_eps,273 = 3.95875 (09) cm^3/mol with A_tau (Table V; dataset A_eps_tau_O2), is 1.74613e-40 F m^2, this value (checked 2026-09-26). May et al. REFIT Schmidt and Moldover’s epsilon_r(p, T) data together with their own (Eq. 19): recommended_O2 is not independent of schmidt_2003’s O2 values (double-counting risk: fit one or the other). Uncertainty not quoted here (the original’s is (09) in the last digits, level not stated).

may_2008/younglove_1972_O2#

{
  "id": "younglove_1972_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability",
  "unit": "SI",
  "scale": 1e-40,
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "B. A. Younglove, J. Res. Natl. Bur. Stand., Sect. A 76, 37 (1972)"
  ]
}

1 inline points in the source record.

p. 3: from Younglove’s measurements ‘at temperatures between 100 and 140 K with compressed liquid O2 at densities between 25000 and 35000 mol m^-3’, alpha_e = 1.7447e-40 F m^2 (row 120: the middle of the temperature range, a label only). A liquid-density extrapolation; uncertainty not quoted. The original is not in the library.

may_2008/minaev_2004_O2#

{
  "id": "minaev_2004_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability",
  "unit": "SI",
  "scale": 1e-40,
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "B. F. Minaev, Spectrochim. Acta, Part A 60, 1027 (2004)"
  ]
}

1 inline points in the source record.

p. 3: Minaev’s ab initio static value, 1.7329e-40 F m^2, for the ground state ‘at 0 K’ (row 0). 0.7 % below this paper’s measurement.

may_2008/wheatley_2007_O2#

{
  "id": "wheatley_2007_O2",
  "material": "O2",
  "table": "text",
  "quantity": "polarizability",
  "unit": "SI",
  "scale": 1e-40,
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "R. J. Wheatley, J. Comput. Chem. 29, 445 (2007) (as printed)"
  ]
}

1 inline points in the source record.

p. 3: Wheatley’s calculated static value, 1.7477e-40 F m^2, ground state at 0 K (row 0); this paper’s measurement is 0.1 % smaller.

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 review register for the checks and decisions.