dawes_1968#
E. L. Dawes, Phys. Rev. 169, 47 (1968)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: One-term (average-energy) estimate of the third-harmonic coefficient alpha_zzzz(3nu) of the rare gases at 6943 A: Armstrong et al.’s sum over states with every excitation replaced by one average frequency nu_0 and the sums reduced with the Thomas-Reiche-Kuhn rule, the effective electron number N_0 and nu_0 taken from Cuthbertson’s fits to refractive-index data.
Materials in structured entries: Ar, He, Kr, Ne, Xe
Dataset quantities: hyperpolarizability, hyperpolarizability_ratio
Contents: 9 datasets; 5 formulas.
Curation notes#
Definition (p. 47): Eq. (3), alpha_zzzz(3nu) = (e^4/h^3) sum nu_ig Z_gi Z_ij Z_jk Z_kg A_ijk, ‘our Eq. (3) is their [Armstrong, Bloembergen, Ducuing and Pershan, Phys. Rev. 127, 1918 (1962)] Eq. (2.22), except for a factor of 1/4 which has been removed as per Ref. 1’ (New and Ward 1967): the same coefficient as New and Ward’s, i.e. Ward and New’s chi = gamma_T/6 (see ward_1969), in esu per atom. Lehmeier et al. 1985 divide these values by 4 (their Table 2 column (g)); Ward and New 1969 normalise them to He = 4.0.
Result (Eq. (9), p. 48): alpha_zzzz(3nu) ~ N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2)(nu_0^2 - 4 nu^2)(nu_0^2 - nu^2)], recorded as formulas below. Table I’s N_0 and nu_0 are reproduced from C. and M. Cuthbertson, Proc. Roy. Soc. (London) 135A, 40 (1932), whose fit is of the linear polarizability, Eq. (2), alpha^L = N_0 e^2 / (4 pi^2 m (nu_0^2 - nu^2)); not extracted as data. Columns (C) and (D) are New and Ward’s (1967) two sets of experimental ratios as ranges (not extracted). Table I’s caption prints the unit as ‘10^39 esu/atom’, a misprint for 10^-39 (abstract: 0.9 x 10^-39 esu/atom for He). No uncertainty is given; Ward and New 1969 find the helium value a factor 4 below Sitz and Yaris’s. Electronic, static atoms; nu (the fundamental) is the ruby 6943 A (printed).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
dawes_1968/alpha_3nu_He#
{
"id": "alpha_3nu_He",
"material": "He",
"file": "He/dawes_1968__alpha_3nu_He.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-39,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"process": "thg",
"convention": "ward_1969",
"part": "electronic"
}
}
Table I (p. 48), column (A): alpha_zzzz(3nu) calculated by Eq. (9) at 6943 A, 10^-39 esu/atom, New and Ward’s convention (= gamma_T/6). A crude one-term model: see the source notes.
dawes_1968/alpha_3nu_Ne#
{
"id": "alpha_3nu_Ne",
"material": "Ne",
"file": "Ne/dawes_1968__alpha_3nu_Ne.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-39,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"process": "thg",
"convention": "ward_1969",
"part": "electronic"
}
}
Table I (p. 48), column (A): alpha_zzzz(3nu) calculated by Eq. (9) at 6943 A, 10^-39 esu/atom, New and Ward’s convention (= gamma_T/6). A crude one-term model: see the source notes.
dawes_1968/alpha_3nu_Ar#
{
"id": "alpha_3nu_Ar",
"material": "Ar",
"file": "Ar/dawes_1968__alpha_3nu_Ar.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-39,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"process": "thg",
"convention": "ward_1969",
"part": "electronic"
}
}
Table I (p. 48), column (A): alpha_zzzz(3nu) calculated by Eq. (9) at 6943 A, 10^-39 esu/atom, New and Ward’s convention (= gamma_T/6). A crude one-term model: see the source notes.
dawes_1968/alpha_3nu_Kr#
{
"id": "alpha_3nu_Kr",
"material": "Kr",
"file": "Kr/dawes_1968__alpha_3nu_Kr.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-39,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"process": "thg",
"convention": "ward_1969",
"part": "electronic"
}
}
Table I (p. 48), column (A): alpha_zzzz(3nu) calculated by Eq. (9) at 6943 A, 10^-39 esu/atom, New and Ward’s convention (= gamma_T/6). A crude one-term model: see the source notes.
dawes_1968/alpha_3nu_Xe#
{
"id": "alpha_3nu_Xe",
"material": "Xe",
"file": "Xe/dawes_1968__alpha_3nu_Xe.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability",
"unit": "esu",
"scale": 1e-39,
"abscissa_unit": "nm",
"use": "primary",
"parameters": {
"process": "thg",
"convention": "ward_1969",
"part": "electronic"
}
}
Table I (p. 48), column (A): alpha_zzzz(3nu) calculated by Eq. (9) at 6943 A, 10^-39 esu/atom, New and Ward’s convention (= gamma_T/6). A crude one-term model: see the source notes.
dawes_1968/ratio_Ne#
{
"id": "ratio_Ne",
"material": "Ne",
"file": "Ne/dawes_1968__ratio_Ne.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"reference_material": "He",
"process": "thg",
"part": "electronic"
}
}
Table I (p. 48), column (B): column (A) relative to He (1.7/0.9 = 1.89, 28/0.9 = 31.1, 71/0.9 = 78.9, 222/0.9 = 246.7: reproduce). Not independent of alpha_3nu_Ne.
dawes_1968/ratio_Ar#
{
"id": "ratio_Ar",
"material": "Ar",
"file": "Ar/dawes_1968__ratio_Ar.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"reference_material": "He",
"process": "thg",
"part": "electronic"
}
}
Table I (p. 48), column (B): column (A) relative to He (1.7/0.9 = 1.89, 28/0.9 = 31.1, 71/0.9 = 78.9, 222/0.9 = 246.7: reproduce). Not independent of alpha_3nu_Ar.
dawes_1968/ratio_Kr#
{
"id": "ratio_Kr",
"material": "Kr",
"file": "Kr/dawes_1968__ratio_Kr.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"reference_material": "He",
"process": "thg",
"part": "electronic"
}
}
Table I (p. 48), column (B): column (A) relative to He (1.7/0.9 = 1.89, 28/0.9 = 31.1, 71/0.9 = 78.9, 222/0.9 = 246.7: reproduce). Not independent of alpha_3nu_Kr.
dawes_1968/ratio_Xe#
{
"id": "ratio_Xe",
"material": "Xe",
"file": "Xe/dawes_1968__ratio_Xe.csv",
"table": "tbl_f296ada000f8",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "nm",
"use": "check",
"parameters": {
"reference_material": "He",
"process": "thg",
"part": "electronic"
}
}
Table I (p. 48), column (B): column (A) relative to He (1.7/0.9 = 1.89, 28/0.9 = 31.1, 71/0.9 = 78.9, 222/0.9 = 246.7: reproduce). Not independent of alpha_3nu_Xe.
Formulas#
dawes_1968/eq9_He#
{
"id": "eq9_He",
"material": "He",
"equation": "Eq. (9), p. 48, with Table I's N_0 and nu_0",
"printed": "alpha_zzzz(3nu) = N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2) (nu_0^2 - 4 nu^2) (nu_0^2 - nu^2)]",
"variable": "nu: the fundamental frequency in Hz (cycles per second); Gaussian units (e, m, h in cgs); result in esu per atom, New and Ward's convention (gamma_T/6)",
"range": "Below the first resonance nu_0/3; evaluated by the paper at 6943 A only",
"coefficients": {
"N_0": "1.224",
"nu_0_1e15_cps": "6.19"
},
"check": "With nu = c/6943 A and CODATA e, m, h (Gaussian), Eq. (9) gives 0.923 x 10^-39 esu against Table I's 0.9 (computed 2026-09-26; He-Kr within 2.5 %, Xe 1.7 % low: the printed values are rounded, and no single correction is implied)."
}
Process: THG, gamma(-3w; w, w, w), electronic. N_0 and nu_0 are Cuthbertson’s (1932) refractive-index fit parameters (reproduced in Table I), not fitted to nonlinear data. Dawes notes the same procedure could give the dc and Kerr coefficients (p. 48).
dawes_1968/eq9_Ne#
{
"id": "eq9_Ne",
"material": "Ne",
"equation": "Eq. (9), p. 48, with Table I's N_0 and nu_0",
"printed": "alpha_zzzz(3nu) = N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2) (nu_0^2 - 4 nu^2) (nu_0^2 - nu^2)]",
"variable": "nu: the fundamental frequency in Hz (cycles per second); Gaussian units (e, m, h in cgs); result in esu per atom, New and Ward's convention (gamma_T/6)",
"range": "Below the first resonance nu_0/3; evaluated by the paper at 6943 A only",
"coefficients": {
"N_0": "2.411",
"nu_0_1e15_cps": "6.26"
},
"check": "With nu = c/6943 A and CODATA e, m, h (Gaussian), Eq. (9) gives 1.715 x 10^-39 esu against Table I's 1.7 (computed 2026-09-26; He-Kr within 2.5 %, Xe 1.7 % low: the printed values are rounded, and no single correction is implied)."
}
Process: THG, gamma(-3w; w, w, w), electronic. N_0 and nu_0 are Cuthbertson’s (1932) refractive-index fit parameters (reproduced in Table I), not fitted to nonlinear data. Dawes notes the same procedure could give the dc and Kerr coefficients (p. 48).
dawes_1968/eq9_Ar#
{
"id": "eq9_Ar",
"material": "Ar",
"equation": "Eq. (9), p. 48, with Table I's N_0 and nu_0",
"printed": "alpha_zzzz(3nu) = N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2) (nu_0^2 - 4 nu^2) (nu_0^2 - nu^2)]",
"variable": "nu: the fundamental frequency in Hz (cycles per second); Gaussian units (e, m, h in cgs); result in esu per atom, New and Ward's convention (gamma_T/6)",
"range": "Below the first resonance nu_0/3; evaluated by the paper at 6943 A only",
"coefficients": {
"N_0": "4.352",
"nu_0_1e15_cps": "4.12"
},
"check": "With nu = c/6943 A and CODATA e, m, h (Gaussian), Eq. (9) gives 28.48 x 10^-39 esu against Table I's 28 (computed 2026-09-26; He-Kr within 2.5 %, Xe 1.7 % low: the printed values are rounded, and no single correction is implied)."
}
Process: THG, gamma(-3w; w, w, w), electronic. N_0 and nu_0 are Cuthbertson’s (1932) refractive-index fit parameters (reproduced in Table I), not fitted to nonlinear data. Dawes notes the same procedure could give the dc and Kerr coefficients (p. 48).
dawes_1968/eq9_Kr#
{
"id": "eq9_Kr",
"material": "Kr",
"equation": "Eq. (9), p. 48, with Table I's N_0 and nu_0",
"printed": "alpha_zzzz(3nu) = N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2) (nu_0^2 - 4 nu^2) (nu_0^2 - nu^2)]",
"variable": "nu: the fundamental frequency in Hz (cycles per second); Gaussian units (e, m, h in cgs); result in esu per atom, New and Ward's convention (gamma_T/6)",
"range": "Below the first resonance nu_0/3; evaluated by the paper at 6943 A only",
"coefficients": {
"N_0": "4.932",
"nu_0_1e15_cps": "3.57"
},
"check": "With nu = c/6943 A and CODATA e, m, h (Gaussian), Eq. (9) gives 71.33 x 10^-39 esu against Table I's 71 (computed 2026-09-26; He-Kr within 2.5 %, Xe 1.7 % low: the printed values are rounded, and no single correction is implied)."
}
Process: THG, gamma(-3w; w, w, w), electronic. N_0 and nu_0 are Cuthbertson’s (1932) refractive-index fit parameters (reproduced in Table I), not fitted to nonlinear data. Dawes notes the same procedure could give the dc and Kerr coefficients (p. 48).
dawes_1968/eq9_Xe#
{
"id": "eq9_Xe",
"material": "Xe",
"equation": "Eq. (9), p. 48, with Table I's N_0 and nu_0",
"printed": "alpha_zzzz(3nu) = N_0 e^4 / (16 pi^4 m^2 h) (nu_0^2 + 6 nu^2) / [nu_0 (nu_0^2 - 9 nu^2) (nu_0^2 - 4 nu^2) (nu_0^2 - nu^2)]",
"variable": "nu: the fundamental frequency in Hz (cycles per second); Gaussian units (e, m, h in cgs); result in esu per atom, New and Ward's convention (gamma_T/6)",
"range": "Below the first resonance nu_0/3; evaluated by the paper at 6943 A only",
"coefficients": {
"N_0": "5.548",
"nu_0_1e15_cps": "3.00"
},
"check": "With nu = c/6943 A and CODATA e, m, h (Gaussian), Eq. (9) gives 218.2 x 10^-39 esu against Table I's 222 (computed 2026-09-26; He-Kr within 2.5 %, Xe 1.7 % low: the printed values are rounded, and no single correction is implied)."
}
Process: THG, gamma(-3w; w, w, w), electronic. N_0 and nu_0 are Cuthbertson’s (1932) refractive-index fit parameters (reproduced in Table I), not fitted to nonlinear data. Dawes notes the same procedure could give the dc and Kerr coefficients (p. 48).
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.