boyle_1966#
L. L. Boyle, A. D. Buckingham, R. L. Disch and D. A. Dunmur, “Higher Polarizability of the Helium Atom”, J. Chem. Phys. 45, 1318 (1966)
Source record · Catalogue · Review register
DOI: 10.1063/1.1727755
Source kind: measurement
Recorded technique: dc Kerr effect of helium gas: a 130 cm pair of parallel stainless-steel electrodes (separation 0.454 +- 0.001 cm) inside a 150 cm high-pressure cylinder; 3-6 kV rms at about 500 cps; the doubled-frequency ellipticity nulled by a calibrated nitrobenzene Kerr cell (‘linear’ detection, phase-sensitive detector at 1000 cps); cw He-Ne laser at 6328 A through a Glan-Thompson prism. Densities from Michels and Wouters’s second and third virial coefficients; gamma from the least-squares slope of (n_par - n_perp)/F^2 against density (Fig. 2). Also an analytic perturbation calculation of alpha, gamma and the field-gradient polarizabilities B, C of the helium atom (screening approximation with a field-dependent screening constant, to second order in the interelectronic perturbation) (pp. 1318-1323).
Materials in structured entries: He
Dataset quantities: hyperpolarizability, polarizability
Contents: 4 datasets; 0 formulas.
Curation notes#
Identity checked against the first page (J. Chem. Phys. 45, 1318 (1966), received 7 April 1966). Page numbers are the journal’s: pdf page 1 is the publisher’s cover, so p. = pdf page + 1316. No tables were extracted by the library: the values are text values, entered inline with their pages.
CONVENTION (p. 1318). m = alpha F + (1/6) gamma F^3 + ... (Eq. 1): Buckingham’s Taylor-series convention, ‘T’ (Shelton and Rice’s gamma; the library’s text of the abstract renders the factor as 1/2, but the page image prints 1/6, as Eq. 1 does). The energy form E = E_0 - (1/2) alpha F^2 - (1/24) gamma F^4 (Eq. 6) agrees. For a dilute gas of spherical molecules n_par - n_perp = (2/3) pi N gamma F^2 (Eq. 2, Gaussian units, N the number density; Fig. 2 plots it against the MEAN SQUARE field, so F^2 is the mean square of the applied field). For an atom gamma_par = 3 gamma_perp, so gamma here equals the dc Kerr gamma^K = (3/2)(gamma_par - gamma_perp) = gamma_zzzz(-w; w, 0, 0). Units: esu (cm^5 statC^-2 per molecule in Buckingham’s usage); 1 au = 5.0367e-40 esu (shelton_1994), so 2.6e-38 esu = 51.6 au (shelton_1994 prints 51.6 +- 8, bishop_1989 52 +- 8). Converted nothing on entry.
THE MEASUREMENT (p. 1319). ‘A least-squares fit of the results recorded in Fig. 2 leads to gamma_He = (2.6 +- 0.4) x 10^-38 esu’ at 6328 A (dataset expt_dc_kerr_He; the level of +-0.4 is not stated; the scatter is attributed to transient noise with 5-15 min integration). No density dependence of the slope was discernible. Temperature and pressures are not stated (Fig. 2 spans about 0.5-4.5 x 10^-3 mol cm^-3). Hydrogen at most 0.25 mole % (its molar Kerr constant about 50 times helium’s): ‘At worst ... the error due to this impurity is within the experimental error’. The wavelength: ‘a cw helium-neon laser operating at a wavelength of 6328 A’ (the He-Ne line’s air wavelength; the text calls lambda in Eq. 3 the vacuum wavelength; stored as standard air, a 0.03 % difference). ‘The experimentally measured hyperpolarizability is not the static one (nor is it the one responsible for second optical harmonic generation), but in the case of the helium atom it should not differ significantly from the static value’ (p. 1319). The same apparatus and group remeasured helium in 1968 (buckingham_1968: ‘The new value ... differs only slightly from the earlier one’: 0.027 +- 0.002 x 10^-36 esu = 53.6 au); the two lie 17 % and 21 % above the later calibrated value (tammer_1992: 44.3 au) and the ab initio 44.211 au at 632.8 nm (shelton_1994, Table VI): use = check.
THE CALCULATION (pp. 1319-1322). Hydrogenic product functions with the screening constant Z = 27/16 made field-dependent by the variation principle (Eq. 14), the interelectronic perturbation H_v to second order with the n = 2 excited states only: alpha = alpha(0) + alpha(1) + alpha(2) = 1.1099 + (1.2332 - 1.1099) + 0.1356 = 1.3688 au = 0.2027 A^3, gamma = 14.238 (zeroth order) + 9.745 (first; 23.983 cumulative) + 7.1820 (second) = 31.1648 au = 1.570 x 10^-38 esu (the static gamma, 60 % of the experiment); the observed alpha is 0.2051 A^3 ([11], Dalgarno’s review). Datasets calc_static_gamma_He, calc_alpha_He, observed_alpha_He. Hydrogen atom (not a material): alpha_H = 9/2 au = 0.6668e-24 cm^3, gamma_H = 10665/8 au = 0.6714e-36 esu (exact). Field-gradient polarizabilities of helium (no quantity): B(0) = -3.239 au, B(0) + B(1) = -4.968 au = -2.271e-40 esu; C(0) = 0.6496 au, C(0) + C(1) = 0.9685 au = 4.018e-42 cm^5 (previous results 3.74-4.96e-42); hydrogen B = -213/2 au, C = 15/2 au.
REPRODUCTIONS ELSEWHERE (re-pointed 2026-09-27): bishop_1989’s expt_dc_kerr row boyle_1966 (52 +- 8 au), shelton_1994’s table6_He_dc_kerr_expt row ‘ref 31’ (51.6 +- 8 au: 2.6e-38/5.0367e-40 = 51.62 and 0.4e-38 -> 7.9, checked), tammer_1992’s table3_literature_He row ‘ref 16’ (32.0(53) x 10^-64 C^4 m^4 J^-3, where this paper’s 2.6(4) x 10^-38 esu is 51.62 au x 6.23538e-65 = 32.19(50) x 10^-64: Tammer et al.’s conversion is 0.6 % lower and its uncertainty 6 % larger, not explained); hellwarth_1990 converts ‘the gamma parameter of Ref. 16’ to its sigma.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
boyle_1966/expt_dc_kerr_He#
{
"id": "expt_dc_kerr_He",
"material": "He",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-38,
"abscissa_unit": "angstrom",
"wavelength_medium": "standard_air",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic"
}
}
1 inline points in the source record.
p. 1319: ‘gamma_He = (2.6 +- 0.4) x 10^-38 esu’ from the dc Kerr effect of helium at 6328 A (He-Ne), the least-squares slope of (n_par - n_perp)/F^2 against density through Eq. (2); T convention (Eq. 1). For an atom gamma is also gamma^K. Superseded by the same group’s buckingham_1968 (0.027 +- 0.002 x 10^-36 esu = 53.6 au) and 17 % above the modern calibrated value (tammer_1992, 44.3 au). The level of +-0.4 is not stated; temperature not stated.
boyle_1966/calc_static_gamma_He#
{
"id": "calc_static_gamma_He",
"material": "He",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"process": "static",
"convention": "T",
"part": "electronic"
}
}
1 inline points in the source record.
p. 1322: the calculated static gamma = gamma(0) + gamma(1) + gamma(2) = 31.1648 a.u. = 1.570 x 10^-38 esu, to second order in the interelectronic perturbation with only the n = 2 excited states; 60 % of the measured value (72 % of bishop_1989’s static 43.104 a.u.). A crude model calculation; T convention (Eq. 6: E = E_0 - alpha F^2/2 - gamma F^4/24).
boyle_1966/calc_alpha_He#
{
"id": "calc_alpha_He",
"material": "He",
"table": "text",
"quantity": "polarizability",
"unit": "au",
"abscissa_unit": "nm",
"use": "check"
}
1 inline points in the source record.
p. 1322: the calculated static polarizability alpha(0) + alpha(1) + alpha(2) = 1.3688 a.u. = 0.2027 x 10^-24 cm^3, 1.2 % below the observed 0.2051 (observed_alpha_He); ‘This may be fortuitous’ (p. 1322). A crude model calculation.
boyle_1966/observed_alpha_He#
{
"id": "observed_alpha_He",
"material": "He",
"table": "text",
"quantity": "polarizability",
"unit": "cm3",
"scale": 1e-24,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"A. Dalgarno, Adv. Phys. 11, 281 (1962)"
]
}
1 inline points in the source record.
pp. 1318, 1321: ‘The observed value of alpha is 0.2051 A^3’ (abstract), ‘the experimental value, 0.2051 x 10^-24 cm^3’ with Ref. 11 (Dalgarno’s review; not in the library). Static; no uncertainty given.
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.