buckingham_1968b#
A. D. Buckingham and B. J. Orr, “Electric birefringence in molecular hydrogen”, Proc. R. Soc. Lond. A 305, 259 (1968)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Absolute dc Kerr effect of H2 (British Oxygen high purity, > 99.9 %) at 6328 A (Spectra-Physics 125 He-Ne laser) with the phase-sensitive apparatus of Boyle et al. 1966 and Buckingham & Dunmur 1968, the Kerr cell jacketed and thermostatted (-30 to +60 C, +-0.2 C, electrodes 46 cm); 25-85 atm, fields 7-9 kV/cm; over 220 measurements in 17 sets, one temperature each. mK0 = (2/27) V_m (n_Z - n_X)/F_Z^2 fitted per set to mK0 = A_K + [B_K + A_K(2 A_eps + A_r/2)] V_m^-1 (Eq. 11), molar volumes from Michels & Goudeket’s virial coefficients, A_eps = 2.02 and A_r = 2.06 cm^3. D2 (Matheson, > 99.5 %) at 12 atm only, ten temperatures from -30 to +32 C (pp. 262-263).
Materials in structured entries: D2, H2
Dataset quantities: hyperpolarizability, kerr_virial_coefficient, molar_kerr_constant
Contents: 6 datasets; 0 formulas.
Curation notes#
Pages are the journal’s (259-269); pdf page 1 is the JSTOR cover, so p. = pdf page + 257. Not to be confused with buckingham_1968 (Buckingham & Dunmur, the inert gases). The library’s validation notes a table without caption (the B_0 table of p. 262) and an unmatched figure (Fig. 1); Tables 1 and 2 agree with their images.
THEORY (pp. 260-262): the quantum theory of the Kerr effect of a dilute gas of 1Sigma diatomic molecules. pi_ab = alpha_ab + beta_ab,c F_c + (1/2) gamma_ab,cd F_c F_d (Eq. 2; the Taylor-series convention); gamma = (1/10)(3 gamma_ab,ab - gamma_aa,bb) (Buckingham’s dc Kerr gamma_K); mK = (2/27) V_m lim (n_Z - n_X)/F_Z^2 (Eq. 7); for non-dipolar molecules mK = (4 pi N/405){5 gamma + (kT)^-1 (alpha_par^(0) - alpha_perp^(0))(alpha_par - alpha_perp)(1 - sigma_0 + (8/15) sigma_0^2 + ...)} (Eq. 9), sigma_0 = hcB_0/kT: the quantum correction factor is 0.76 for H2, 0.87 for D2, 0.99 for N2 at 300 K (p. 262, B_0 = 59.34, 29.91, 2.00 cm^-1). Appendix Eq. (A9) gives the form with nuclear-spin statistics. shelton_1987b later finds the optical-frequency orientation term 3/4 of this classical form (‘Buckingham’s ansatz ... is only valid in the static limit’).
RESULTS. Table 1 (p. 263): A_K and B_K per set; ‘It is estimated from table 1 that A_K can be determined with a reproducibility better than +-2 %. However, the uncertainty of the measurements, which is dependent on the calibration of voltmeters and the nulling Kerr cell, could be +-5 %’ (p. 264). gamma (p. 264): from each A_K with Eq. (9), (alpha_par^(0) - alpha_perp^(0)) = 0.300 A^3 (Kolos & Wolniewicz 1967), (alpha_par - alpha_perp) = 0.314 A^3 at 6328 A (Bridge & Buckingham 1966), hcB_0/k = 85.37 K: Table 2; ‘Their mean value is 0.277 e.s.u. and their standard deviation +-0.008 e.s.u. The absolute error, due to calibration uncertainties, is not greater than +-0.03 e.s.u.’ (abstract: (0.28 +- 0.03) x 10^-36 e.s.u.). In au (5.0367e-40 esu): 550 +- 60. The gamma term is only about 45 % of A_K and depends on the assumed anisotropies. D2 (pp. 264-265): A_K ‘calculated by assuming that B_K for deuterium equals that of hydrogen ... Their average value is (5.9 +- 0.6) x 10^14 e.s.u.’ (misprinted exponent, erratum below); gamma(D2) ‘0.24 +- 0.05 e.s.u.’ (10^-36), ‘less than 10^36 gamma for H2 by 14 %’, more than the 1 % expected. B_K(H2) = (1.34 +- 0.2) x 10^-12 e.s.u. over the range, no trend detected; calculated from the pair anisotropy 6 alpha^2/R^3 and a Lennard-Jones potential (29.2 K, 2.87 A): 0.50, 0.58, 0.66 at 332, 284, 245 K, ‘considerably smaller than the experimental result’ (p. 266). Slope dA_K/dT^-1: experiment (8.0 +- 2) x 10^-12 e.s.u. deg against the quantum 6.8 x 10^-12 at 284 K and the classical 12.75 x 10^-12 (p. 266). Fig. 1: the A_K points scatter +-1.3 % about the curve from the mean gamma (p. 266). Other values quoted, not stored: Bruce 1933’s upper limit 10^14 mK0 < 8.5 e.s.u. (82 atm, 4550 A) against this work’s 6.2 at 35 C and 82 atm; Guillien’s liquid H2 mK; J. F. Ward’s THG 10^36 gamma_thg = 0.45 +- 0.05 e.s.u. at 6943 A (personal communication); McLean & Yoshimine’s calculated static gamma_3333 = 0.20 x 10^-36; the H atom’s 0.6714 x 10^-36 (Sewell 1949).
SUPERSEDED: tammer_1990 (and tammer_1992, after its field calibration) measured the same quantity ten times more precisely; tammer_1990 Table 2 lists this paper as 3.43(37) x 10^-62 C^4 m^4 J^-3 (H2) and 3.0(6) (D2), i.e. 0.277 and 0.24 x 10^-36 esu, and finds its B_K^(4) twice its own. All datasets here are use = ‘check’.
Reproductions elsewhere: bishop_1991/expt_dc_kerr_H2 (row buckingham_orr_1968, 550 +- 60 au), tammer_1990/table2_literature_* (‘ref 3’), carusotto_1992 notes (3.81 and 3.31 x 10^-17 cm^2 statV^-2 amagat at 245 and 332 K: not values printed here, a conversion of Table 1), hellwarth_1990/kerr_buckingham_orr_H2. Not edited here, citing this paper: lundeen_1983, rosasco_1985, ward_1979, ward_1969.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
buckingham_1968b/table1_A_K_H2#
{
"id": "table1_A_K_H2",
"material": "H2",
"file": "H2/buckingham_1968b__table1_A_K_H2.csv",
"table": "tbl_4157737602db",
"quantity": "molar_kerr_constant",
"unit": "esu",
"scale": 1e-14,
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "check",
"uncertainty": {
"relative": 0.05,
"level": "not stated"
},
"parameters": {
"wavelength_nm": 632.8
}
}
Table 1 (p. 263): the first Kerr virial coefficient A_K (the zero-density molar Kerr constant, per mole, e.s.u.) of H2 for 17 sets at 245.4-332.4 K, 25-85 atm, 6328 A. Includes the orientation term. Reproducibility better than +-2 %; uncertainty (calibration) ‘could be +-5 %’ (p. 264), recorded as a relative 5 % (level not stated). Superseded by tammer_1990/tammer_1992.
buckingham_1968b/table1_B_K_H2#
{
"id": "table1_B_K_H2",
"material": "H2",
"file": "H2/buckingham_1968b__table1_B_K_H2.csv",
"table": "tbl_4157737602db",
"quantity": "kerr_virial_coefficient",
"unit": "esu",
"scale": 1e-12,
"abscissa": "temperature",
"abscissa_unit": "K",
"use": "check",
"uncertainty": {
"level": "not stated"
},
"parameters": {
"wavelength_nm": 632.8,
"order": 2
}
}
Table 1 (p. 263): the second Kerr virial coefficient B_K (e.s.u.) of H2 per set, 245.4-332.4 K. ‘B_K of hydrogen is found from table 1 to be (1.34 +- 0.2) x 10^-12 e.s.u. over the experimental temperature range. The experimental precision was insufficient to allow a trend with temperature to be detected’ (p. 266). No per-set uncertainty is printed.
buckingham_1968b/table2_gamma_H2#
{
"id": "table2_gamma_H2",
"material": "H2",
"file": "H2/buckingham_1968b__table2_gamma_H2.csv",
"table": "tbl_a2e5fa68c008",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-36,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"columns": {
"temperature": "K"
},
"use": "check",
"uncertainty": {
"absolute": 0.03,
"level": "bound"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K"
}
}
Table 2 (p. 264): 10^36 gamma (e.s.u.) of H2 per set (temperature as the extra column), from each A_K minus the quantum-corrected orientation term of Eq. (9) with the anisotropies of Kolos & Wolniewicz (static 0.300 A^3) and Bridge & Buckingham (optical 0.314 A^3): Buckingham’s gamma_K at 6328 A, electronic plus vibrational. Mean 0.277, standard deviation +-0.008; ‘The absolute error, due to calibration uncertainties, is not greater than +-0.03 e.s.u.’ (a bound, applied to every value). Superseded (tammer_1992: 4.68(14) x 10^-62 C^4 m^4 J^-3 = 0.378 x 10^-36 esu).
buckingham_1968b/text_gamma_H2#
{
"id": "text_gamma_H2",
"material": "H2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-36,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"use": "check",
"uncertainty": {
"column": true,
"level": "bound"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K"
}
}
1 inline points in the source record.
p. 264: ‘Their mean value is 0.277 e.s.u. and their standard deviation +-0.008 e.s.u. The absolute error, due to calibration uncertainties, is not greater than +-0.03 e.s.u.’; abstract: gamma = (0.28 +- 0.03) x 10^-36 e.s.u. (550 +- 60 au). The dc Kerr gamma_K of H2 at 6328 A over 245-332 K; electronic plus vibrational (orientation term subtracted with Eq. 9). The error is a bound. Superseded by tammer_1992.
buckingham_1968b/text_A_K_D2#
{
"id": "text_A_K_D2",
"material": "D2",
"table": "text",
"quantity": "molar_kerr_constant",
"unit": "esu",
"scale": 100000000000000.0,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
}
}
1 inline points in the source record.
p. 264: ‘The measurements on deuterium were much less accurate than those for hydrogen, owing to the small quantity available. Values of A_K, calculated by assuming that B_K for deuterium equals that of hydrogen, were insufficiently precise to yield a meaningful temperature dependence. Their average value is (5.9 +- 0.6) x 10^14 e.s.u.’ D2 at 12 atm, ten temperatures from -30 to +32 C. The exponent is misprinted (erratum below: 10^-14, as Table 1’s 10^14 A_K for H2). Level of the error not stated.
buckingham_1968b/text_gamma_D2#
{
"id": "text_gamma_D2",
"material": "D2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-36,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K"
}
}
1 inline points in the source record.
p. 265: ‘An approximate estimate of the hyperpolarizability 10^36 gamma of deuterium can be obtained in a similar manner. The result is 0.24 +- 0.05 e.s.u., which is less than 10^36 gamma for H2 by 14 %. This difference is greater than expected from approximate theoretical considerations which indicate that gamma(D2) should be less than gamma(H2) by little more than 1 %.’ dc Kerr gamma_K of D2 at 6328 A, electronic plus vibrational. Superseded (tammer_1990: 4.17(16) x 10^-62 SI).
Formulas#
No formulas are recorded.
Corrections#
[
{
"dataset": "text_A_K_D2",
"row": "",
"column": "scale",
"printed": "100000000000000.0",
"corrected": "1e-14",
"reason": "p. 264 prints the D2 average A_K as '(5.9 +- 0.6) x 10^14 e.s.u.'; a molar Kerr constant of 10^14 e.s.u. is impossible, and Table 1 gives H2's as '10^14 A_K (e.s.u.)' = 5.5-6.3, i.e. A_K = 5.5-6.3 x 10^-14 e.s.u.; D2's must be of the same order (the orientation term is somewhat larger and gamma similar).",
"evidence": "Page image of p. 264 checked: '(5·9 ± 0·6) × 10^14 e.s.u.' is printed, not an extraction error. Table 1 (p. 263, image checked) heads the H2 column '10^14 A_K (e.s.u.)'. Checked 2026-09-26."
}
]
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.