shelton_1986_co2#

D. P. Shelton, J. Chem. Phys. 85, 4234 (1986)

Source record · Catalogue · Review register

Source kind: measurement

Recorded technique: ESHG with periodic phase matching as in shelton_1985_sf6 (electrode spacing 2.69 mm, 1.2-6.5 atm at 19-22 C), cw dye or argon-ion laser, 0.2-1.0 W; dye-laser wavelengths set to Na or Ne lines; sample CO2 (99.99 %) and reference N2 (99.999 %) in triplets; densities from the virial equation of state (p. 2).

Materials in structured entries: CO2, He, N2

Dataset quantities: hyperpolarizability, hyperpolarizability_ratio, phase_match_density_ratio

Contents: 11 datasets; 8 formulas.

Curation notes#

The by-product ratio Delta alpha_CO2 / Delta alpha_N2 (Delta alpha = alpha(2 omega) - alpha(omega)) is the phase-match density ratio rho_N2 / rho_CO2, filed under N2 with CO2 as reference_material as in shelton_1990. Table I gives the air wavelength and the vacuum wavenumber of the fundamental; the wavenumber is the abscissa.

Uncertainty (p. 2): the ratio accuracy ‘has been given as +-0.20%, a conservative estimate based on the absolute pressure gauge accuracy of +-0.15%. If the gauge is linear, the dispersion ratio accuracy will instead be set by the +-0.04% density ratio reproducibility’; Table I note c: ‘The tabulated error bars may be too pessimistic by as much as a factor of 5.’

The ratio has a minimum near 16 000 cm^-1: ‘in the red end of the visible the dispersion due to low frequency vibrational resonances becomes comparable to that due to high frequency electronic resonances’ (p. 6). The paper separates the vibrational part with the two infrared fundamentals (Eq. 14) and fits the electronic remainder (formulas below).

Table III lists CO2 infrared transition dipole moments (from Rothman’s intensities) and Raman transition polarizabilities used for the vibrational Kerr hyperpolarizability, and alpha = 293.3 x 10^-42 C^2 m^2 J^-1 at 632.8 nm ‘from the refractive index’ (Landolt-Bornstein; reproduced): not extracted (the infrared module uses HITRAN). The gamma values and Table II are hyperpolarizabilities and are not extracted.

THIRD-ORDER DATA (added 2026-09-26; supersedes the last sentence above). gamma is the ESHG <gamma>_ZZZZ of Shelton’s series (Taylor convention, SI C^4 m^4 J^-3), calibrated through Mizrahi & Shelton’s gamma_N2/gamma_He = 20.30 [1 + 6.55e-10 nu^2] (Eq. 2) and Sitz & Yaris’s gamma_He = 42.6 au [1 + 2.94e-10 nu^2] (Eq. 3, 1 au = 6.2360e-65 C^4 m^4 J^-3), nu the fundamental wavenumber in cm^-1: the old He calibration (shelton_1990 Table III(c) rescales these values; Shelton & Rice’s warning that the A, B of the 1985-86 papers are against nu^2 of ESHG, not nu_L^2, and on this He value, applies to the formulas below). The electronic dispersion of all processes is written gamma^e(-omega_s; omega_1, omega_2, omega_3) = gamma^e(0; 0, 0, 0) [1 + C omega_L^2] (Eq. 4), omega_L^2 = omega_s^2 + omega_1^2 + omega_2^2 + omega_3^2 (Eq. 5). The dc Kerr gamma is gamma_Kerr = (3/2)[<gamma>_ZZZZ - <gamma>_XZZX] (Eq. 9). Parts: the vibrational gamma^v_Kerr is calculated (Eqs. 6-11, Table III matrix elements) and found small (0 +- 2e-63); ‘the vibrational contributions to gamma_CO2 appear to be insignificant for ESHG and THG, but not for FWM and the dc Kerr effect’ (p. 4238). The literature dc Kerr value (558 +- 120e-63) is shown to be spurious (excluded; the reanalysis gives -61 +- 200e-63). Table III (transition dipoles and polarizabilities of 12C16O2, incl. the mean polarizability 293.3e-42 and anisotropy 235e-42 C^2 m^2 J^-1 at 632.8 nm, reproduced from refractive-index and depolarized-scattering literature) is not extracted (no quantity for transition matrix elements; the anisotropy is a reproduction of Bogaard et al. / Alms et al.).

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

Datasets#

shelton_1986_co2/density_N2_over_CO2#

{
  "id": "density_N2_over_CO2",
  "material": "N2",
  "file": "N2/shelton_1986_co2__density_N2_over_CO2.csv",
  "table": "tbl_ba9d1caa914e",
  "quantity": "phase_match_density_ratio",
  "abscissa_unit": "cm-1",
  "wavelength_medium": "vacuum",
  "density": "real",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "reference_material": "CO2",
    "harmonic": 2,
    "process": "ESHG (electric-field-induced second-harmonic generation), periodic phase matching",
    "definition": "rho_gas / rho_reference_gas at equal wave-vector mismatch |Delta k| = (4 pi / lambda) |n(2w) - n(w)|; to first order in density = [alpha_ref(2w) - alpha_ref(w)] / [alpha_gas(2w) - alpha_gas(w)]; lambda = fundamental",
    "sample_gas": "CO2",
    "shelton_reference_gas": "N2",
    "printed_as": "Delta alpha_CO2 / Delta alpha_N2"
  }
}

Table I, Delta alpha_CO2 / Delta alpha_N2 = rho_N2 / rho_CO2 as printed, 5 fundamentals 488.0-692.9 nm (air), abscissa the printed vacuum wavenumber.

shelton_1986_co2/gamma_CO2_over_N2#

{
  "id": "gamma_CO2_over_N2",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__gamma_CO2_over_N2.csv",
  "table": "tbl_ba9d1caa914e",
  "quantity": "hyperpolarizability_ratio",
  "unit": "1",
  "abscissa_unit": "cm-1",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "reference_material": "N2",
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

Table I (p. 4235): gamma_CO2/gamma_N2 by ESHG, as printed (Eq. 1, gamma_B/gamma_A = (S_B/S_A)^(1/2) (rho_B n’_B / rho_A n’_A)^-1, n’ = (n_0^4 n_omega^3 n_2omega)^(1/6); ZZZZ component, fields parallel). ‘The accuracy of the ratio is about +-0.3%’ (p. 4234). The raw measurement behind gamma_CO2.

shelton_1986_co2/gamma_CO2#

{
  "id": "gamma_CO2",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__gamma_CO2.csv",
  "table": "tbl_ba9d1caa914e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "cm-1",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

Table I (p. 4235): gamma_CO2 in 1e-63 C^4 m^4 J^-3 at five wavelengths (row: air wavelength; abscissa: vacuum wavenumber), ‘Obtained using Refs. 14 and 20 for calibration’ (note d): gamma_N2/gamma_He from Mizrahi & Shelton (mizrahi_1985_arn2o2; formula calibration_N2_over_He) and Sitz & Yaris’s gamma_He (formula calibration_He, 42.6 au static). ‘An uncertainty of +-0.4% due to the gamma_N2/gamma_He calibration has been assumed in assigning the error bars’; ‘No allowance has been made for the uncertainty of gamma_He’ (~1 %) (p. 4235). Total ESHG gamma. shelton_1990 Table III(c) reproduces these on the new He calibration (e.g. 85.27 at 692.9 nm against 84.1 here).

shelton_1986_co2/table2_dc_kerr#

{
  "id": "table2_dc_kerr",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__table2_dc_kerr.csv",
  "table": "tbl_c8ef15b5d66e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "excluded",
  "reproduced_from": [
    "buckingham_1970"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "total"
  }
}

Table II (p. 4235): ‘Hyperpolarizability of CO2 measured by several nonlinear optical processes’, in 1e-63 C^4 m^4 J^-3, ‘Conversion factor 1 esu = 7.4279 x 10^-25 C^4 m^4 J^-3 has been used’ (note b: this includes the factor 6 between Ward’s per-molecule esu chi and Shelton’s gamma, since 1 au = 6.235377e-65 SI = 5.0367e-40 esu). nu_L^2 as printed: 4.99, 8.64, 14.47, 12.44, 22.65, 24.88 x 10^8 cm^-2. Reproduced (converted by the author). Note c: gamma(-omega; 0, 0, omega), from Ref. 21 (Buckingham et al. 1970), the zero-temperature intercept of the first Kerr virial coefficient against 1/T. EXCLUDED: the author shows it is ‘spurious, the result of a single bad data point’: dropping the lowest-temperature point changes the intercept to -61 x 10^-63 (dataset text_dc_kerr_reanalysed) (pp. 4237-4238). The original is now in the library (buckingham_1970, Table 2: gamma = 5.6 +- 1.2 x 10^-61 C^4 m^4 J^-3; 558 here is 81 eps0/N x the intercept 4.7 x 10^-28 at more digits, or a conversion through esu: not digit-identical). Recomputed from its Table 1: without the 252 K point the intercept is -0.53 x 10^-28, i.e. gamma = -63 x 10^-63, as the author found.

shelton_1986_co2/table2_cars#

{
  "id": "table2_cars",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__table2_cars.csv",
  "table": "tbl_c8ef15b5d66e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "W. G. Rado, Appl. Phys. Lett. 11, 123 (1967)",
    "lundeen_1983"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "cars",
    "convention": "T",
    "part": "total",
    "stokes_nm": "975 (row 1), 683 (row 2)"
  }
}

Table II (p. 4235): ‘Hyperpolarizability of CO2 measured by several nonlinear optical processes’, in 1e-63 C^4 m^4 J^-3, ‘Conversion factor 1 esu = 7.4279 x 10^-25 C^4 m^4 J^-3 has been used’ (note b: this includes the factor 6 between Ward’s per-molecule esu chi and Shelton’s gamma, since 1 au = 6.235377e-65 SI = 5.0367e-40 esu). nu_L^2 as printed: 4.99, 8.64, 14.47, 12.44, 22.65, 24.88 x 10^8 cm^-2. Reproduced (converted by the author). Four-wave mixing gamma(-2 omega_1 + omega_2; omega_1, omega_1, -omega_2) (CARS-type), rows: note d, ‘from Ref. 23 [Rado 1967], as corrected and given in Ref. 24 [Lundeen et al. 1983]’, at 694 and 975 nm (the abscissa is the pump, 694 nm; Stokes 975 nm); note e, ‘From Ref. 24’, at 532 and 683 nm (pump 532 nm, Stokes 683 nm). The wavelengths are printed to three figures.

shelton_1986_co2/table2_eshg#

{
  "id": "table2_eshg",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__table2_eshg.csv",
  "table": "tbl_c8ef15b5d66e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1979",
    "shelton_1982"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1986_co2/table2_thg#

{
  "id": "table2_thg",
  "material": "CO2",
  "file": "CO2/shelton_1986_co2__table2_thg.csv",
  "table": "tbl_c8ef15b5d66e",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1969"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "total"
  }
}

shelton_1986_co2/text_dc_kerr_reanalysed#

{
  "id": "text_dc_kerr_reanalysed",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "check",
  "reproduced_from": [
    "buckingham_1970"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "total"
  }
}

1 inline points in the source record.

pp. 4237-4238: excluding the lowest-temperature point of Buckingham et al.’s nine measurements (252-337 K) ‘changes the intercept from gamma_Kerr = 558 x 10^-63 to -61 x 10^-63 C^4 m^4 J^-3 ... giving the revised estimate gamma_Kerr = -61 +- 200 x 10^-63’ (error: statistical uncertainty of the fit plus the systematic uncertainty of the total birefringence). The author’s reanalysis of another group’s data.

shelton_1986_co2/text_dc_kerr_gentle#

{
  "id": "text_dc_kerr_gentle",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "gentle_1989"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "total"
  }
}

1 inline points in the source record.

Note added in proof (p. 4238): ‘As yet unpublished measurements by I. R. Gentle, D. R. Laver, and G. L. D. Ritchie ... give gamma_Kerr = +110 +- 39 x 10^-63 C^4 m^4 J^-3’. A pre-publication value of gentle_1989 (J. Phys. Chem. 93, 3035 (1989)), which publishes gamma^K = (0.125 +- 0.032) x 10^-60 C m^4 V^-3, i.e. 125 +- 32 x 10^-63 (gentle_1989/table2_gamma_K_CO2): not the same number; the published one supersedes this. The wavelength is not stated here; gentle_1989 measured at 632.8 nm (its Fig. 1 and Table I captions), which confirms the 632.8 nm recorded here (TC-233). Shelton & Rice 1994 quote the published value as 2005 +- 513 au.

shelton_1986_co2/text_dc_kerr_electronic#

{
  "id": "text_dc_kerr_electronic",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "check",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic"
  }
}

1 inline points in the source record.

p. 4237: ‘Equation (4) and our measurements of gamma_ESHG may be combined to estimate gamma^e_Kerr = +72.6 x 10^-63 C^4 m^4 J^-3 at lambda = 632.8 nm for CO2’ (the electronic dc Kerr gamma predicted from the ESHG dispersion with a common C omega_L^2 law); with gamma^v_Kerr the prediction is gamma_Kerr = +73 +- 2 x 10^-63.

shelton_1986_co2/text_dc_kerr_vibrational#

{
  "id": "text_dc_kerr_vibrational",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "SI",
  "scale": 1e-63,
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational"
  }
}

1 inline points in the source record.

p. 4237: the vibrational dc Kerr hyperpolarizability of CO2 from the doubly enhanced terms (Eq. 11, Table III matrix elements, all positive): -1.1 x 10^-63; alpha^2/hbar Omega terms +0.4 x 10^-63; mu^4/(hbar omega)^3 terms ~1e-65; mu beta/hbar Omega terms 2 x 10^-63 if CO2’s hyper-Raman beta is as large as CH4’s. ‘Our best estimate of gamma^v_Kerr from the incomplete data at our disposal is 0 +- 2 x 10^-63 C^4 m^4/J^-3’ (sic). Wavelength: the dc Kerr comparison is at 632.8 nm; the doubly enhanced terms are frequency independent.

Formulas#

shelton_1986_co2/vibrational_eq14#

{
  "id": "vibrational_eq14",
  "material": "CO2",
  "equation": "Eq. (14), p. 6",
  "printed": "Delta alpha_CO2^v (C^2 m^2 J^-1) = +0.70 x 10^-34 nu^-2",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "range": "optical frequencies (Omega_mg << omega)",
  "coefficients": {
    "a": "0.70e-34"
  },
  "check": "With Eq. (15) and the fit below it reproduces the five measured ratios to 0.0006 (see electronic_fit). Checked 2026-09-25."
}

The vibrational part of alpha(2 omega) - alpha(omega), from the two infrared-active fundamentals (Eq. 13).

shelton_1986_co2/n2_eq15#

{
  "id": "n2_eq15",
  "material": "N2",
  "equation": "Eq. (15), p. 6",
  "printed": "Delta alpha_N2 (C^2 m^2 J^-1) = 3.117 x 10^-50 nu^2 [1 + 3.076 x 10^-10 nu^2 + 17.58 x 10^-20 nu^4]",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "range": "the visible (shelton_1986's measurements, 458-700 nm)",
  "coefficients": {
    "a": "3.117e-50",
    "b": "3.076e-10",
    "c": "17.58e-20"
  },
  "reproduced_from": [
    "shelton_1986"
  ],
  "check": "Used with Eq. (14) and electronic_fit to reproduce Table I (see there). Not checked against shelton_1986's own fit here."
}

alpha(2 omega) - alpha(omega) of N2 in SI, from Shelton and Mizrahi, Phys. Rev. A 33, 72 (1986).

shelton_1986_co2/electronic_fit#

{
  "id": "electronic_fit",
  "material": "CO2",
  "equation": "Fig. 3 caption, p. 6",
  "printed": "Delta alpha_CO2^e / Delta alpha_N2 = A [1 + B nu^2 + C nu^4]; A = 1.7087, B = 0.0266 x 10^-10 cm^2, C = 14.5 x 10^-20 cm^4",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "range": "14427-20487 cm^-1 (488.0-692.9 nm)",
  "coefficients": {
    "A": "1.7087",
    "B": "0.0266e-10",
    "C": "14.5e-20"
  },
  "check": "Adding back Eq. (14) / Eq. (15) it gives 1.7688, 1.7608, 1.7567, 1.7595, 1.7652 against the measured 1.7689, 1.7603, 1.7573, 1.7593, 1.7654 (within 0.0006). Checked 2026-09-25."
}

Fitted to the measured ratios minus the vibrational part.

shelton_1986_co2/electronic_eq16a#

{
  "id": "electronic_eq16a",
  "material": "CO2",
  "equation": "Eq. (16a), p. 6",
  "printed": "Delta alpha_CO2^e (C^2 m^2 J^-1) = 5.33 x 10^-50 nu^2 [1 + 3.1 x 10^-10 nu^2 + 32 x 10^-20 nu^4]",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "range": "488-693 nm",
  "coefficients": {
    "a": "5.33e-50",
    "b": "3.1e-10",
    "c": "32e-20"
  },
  "check": "Divided by Eq. (15) it gives 1.7207 at 14427.1 cm^-1 and 1.7489 at 20486.7 against electronic_fit's 1.7204 and 1.7543 (0.3 % at the blue end). Checked 2026-09-25."
}

The electronic dispersion alpha^e(2 omega) - alpha^e(omega) of CO2 from this experiment.

shelton_1986_co2/landolt_eq16b#

{
  "id": "landolt_eq16b",
  "material": "CO2",
  "equation": "Eq. (16b), p. 6",
  "printed": "Delta alpha_CO2^LB (C^2 m^2 J^-1) = 5.37 x 10^-50 nu^2 [1 + 3.6 x 10^-10 nu^2 + 16 x 10^-20 nu^4]",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "range": "derived from refractive indices at 237.9-546.2 nm",
  "coefficients": {
    "a": "5.37e-50",
    "b": "3.6e-10",
    "c": "16e-20"
  },
  "reproduced_from": [
    "Landolt-Bornstein, Zahlenwerte und Funktionen (Springer, Berlin, 1962), Band II, Teil 8"
  ],
  "check": "Not checked (the tabulated refractive indices are not in the library)."
}

Derived by the author from Landolt-Bornstein’s CO2 refractive indices, for comparison with Eq. (16a) (‘in good agreement’).

shelton_1986_co2/gamma_fit#

{
  "id": "gamma_fit",
  "material": "CO2",
  "equation": "Fig. 1 caption, p. 4235",
  "printed": "gamma = A[1 + B nu^2]; A = 65.0 x 10^-63 C^4 m^4 J^-3 and B = 14.07 x 10^-10 cm^2, where nu is given in cm^-1",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2; for ESHG nu_L^2 = 6 nu^2, so B/6 = 2.345e-10 cm^2 is the nu_L^2 coefficient)",
  "process": "eshg",
  "convention": "T",
  "part": "total",
  "range": "14427-20487 cm^-1 (488.0-692.9 nm, Table I)",
  "coefficients": {
    "A": "65.0e-63",
    "B": "14.07e-10"
  },
  "coefficient_units": {
    "A": "C^4 m^4 J^-3",
    "B": "cm^2"
  },
  "calibration": "N2 (Eq. 2) and He (Sitz & Yaris, Eq. 3): the old calibration",
  "check": "Gives 84.04 at 14427.1 cm^-1 and 99.53 at 19429.8 cm^-1 against Table I's 84.1 +- 0.5 and 99.4 +- 0.5. Checked 2026-09-26."
}

Least-squares straight line of gamma against nu^2. Superseded by shelton_1990 Table IV (gamma_0 = 71.50e-63, A = 1.252e-10, B = 2.405e-20 against nu_L^2, with 1064 and 1319 nm and the new He calibration).

shelton_1986_co2/calibration_N2_over_He#

{
  "id": "calibration_N2_over_He",
  "material": "N2",
  "equation": "Eq. (2), p. 4234",
  "printed": "gamma_N2/gamma_He = 20.30 [1 + (6.55 x 10^-10 cm^2) nu^2]",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1",
  "process": "eshg",
  "convention": "T",
  "part": "total",
  "range": "'Over the range of frequencies employed in the present measurements' (488-693 nm)",
  "coefficients": {
    "ratio0": "20.30",
    "B": "6.55e-10"
  },
  "coefficient_units": {
    "ratio0": "1",
    "B": "cm^2"
  },
  "reproduced_from": [
    "mizrahi_1985_arn2o2"
  ],
  "check": "Not checked against mizrahi_1985_arn2o2 here."
}

The N2/He ESHG ratio ‘adequately represented by’ this line, from Ref. 14 (Mizrahi & Shelton, Phys. Rev. Lett. 55, 696 (1985)); the calibration of gamma_CO2.

shelton_1986_co2/calibration_He#

{
  "id": "calibration_He",
  "material": "He",
  "equation": "Eq. (3), p. 4235",
  "printed": "gamma_He = 42.6 a.u. [1 + (2.94 x 10^-10 cm^2) nu^2], where nu is given in cm^-1 and 1 a.u. = 6.2360 x 10^-65 C^4 m^4 J^-3",
  "variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (ESHG)",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "the visible (the measurements)",
  "coefficients": {
    "gamma0": "42.6",
    "B": "2.94e-10"
  },
  "coefficient_units": {
    "gamma0": "au (1 au = 6.2360e-65 C^4 m^4 J^-3)",
    "B": "cm^2"
  },
  "reproduced_from": [
    "P. Sitz and R. Yaris, J. Chem. Phys. 49, 3546 (1968)"
  ],
  "check": "At 514.5 nm (19430 cm^-1) it gives 47.33 au = 2.951e-63 C^4 m^4 J^-3, shelton_1982's calibrant 2.950e-63. Checked 2026-09-26."
}

Sitz & Yaris’s ab initio He (Ref. 20), the old calibration of the 1982-86 papers; ‘thought to be accurate to 1%’ (p. 4235). Bishop & Pipin’s later value (bishop_1989; shelton_1990 Table II) is 43.104 au static, about 1.3 % higher at 514.5 nm.

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.