mizrahi_1985_arn2o2 =================== V\. Mizrahi and D\. P\. Shelton, Phys\. Rev\. Lett\. 55, 696 \(1985\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` No DOI is recorded. **Source kind:** measurement **Recorded technique:** Gas\-phase electric\-field\-induced second\-harmonic generation \(ESHG\) with periodic phase matching \(electrode spacing 2\.69 mm, optimal pressures of order 1 atm, about 100 atm for He\), cw rhodamine\-6G or DCM dye laser or argon\-ion laser, 700\.0\-457\.9 nm; Ar, N2 and O2 measured against He \(O2 and some Ar points via N2 as a transfer standard\) \(p\. 696\)\. **Materials in structured entries:** Ar, D2, H2, He, N2, O2 **Dataset quantities:** hyperpolarizability\_ratio **Contents:** 3 datasets; 6 formulas. Curation notes -------------- Title and authors from the observed text \(the library record is UNVERIFIED and carries no DOI\)\: 'Dispersion of Nonlinear Susceptibilities of Ar, N2, and O2 Measured and Compared', Victor Mizrahi and D\. P\. Shelton, received 29 April 1985; the citation Phys\. Rev\. Lett\. 55, 696 \(1985\) is the one given in Shelton \(1986, Ref\. 15, shelton\_1986\_krxe\), not read from this document\. No datasets\: the paper measures the nonlinear susceptibility ratios chi3\(omega\)/chi3\_He\(omega\) of Ar, N2, O2 \(Table I, lambda in air and nu in vacuum, 700\.0\-457\.9 nm\) and fits them \(Table II\); the phase\-match densities are not given\. Its only linear\-dispersion numbers are the effective resonance frequencies omega\_0 of Table III \(tbl\_e6ad0bfdfcc3; image checked\), 'chosen so that chi1\(omega\)/chi1\(0\) = \[1 \+ \(omega/omega\_0\)^2\] gives the best fit to linear\-dispersion data \(Ref\. 10\)', Ref\. 10 being Landolt\-Bornstein II/8 \(1962\)\: He 206, Ar 138, H2 113, D2 115, N2 126, O2 119, printed in units of '10^13 cm^\-1', evidently a misprint for 10^3 cm^\-1 \(206 x 10^3 cm^\-1 = 25\.5 eV for He, an effective resonance; 10^13 cm^\-1 would be about 10^9 eV\)\. They are the authors' one\-pole fits to other data, without alpha\(0\), so not a usable model; recorded here only\. Not extracted \(third\-order susceptibility, for later\)\: Table I ratios \(the Ar value printed 20\.99\(16\) at 600\.0 nm is presumably 30\.99\: its neighbours are 30\.88 and 31\.25; image checked\), Table II fits A\(1 \+ B omega^2\)\: Ar 25\.85\(19\), 7\.11\(26\)e\-10 cm^2; N2 20\.30\(11\), 6\.55\(20\)e\-10; O2 19\.73\(27\), 13\.64\(54\)e\-10 \(H2, D2 from Ref\. 5\), Table III's C\. THIRD\-ORDER DATA \(added 2026\-09\-26; supersedes "No datasets" and "Not extracted" above\)\. The library record is now VALIDATED\_WITH\_WARNINGS \(as the identity field says\)\. chi\(3\)\(omega\) is the ESHG susceptibility chi\_ijkl\(3\)\(\-2 omega; omega, omega, 0\), 'the case of the optical\-field polarization parallel to the static field' \(the stronger component\), 'related to the molecule\-fixed components by an isotropic average'; 'Details of the notational convention have been given elsewhere \[Ref\. 5 = mizrahi\_1985\_h2d2\], but in any case we shall be principally interested in ratios' \(p\. 696\)\: the ratios are per molecule, the same as Shelton's gamma ratios \(shelton\_1990 rescales these data as gamma, Table III\(a\)\)\. Expansion\: chi\(3\)\(omega\) = chi\(3\)\(0\)\(1 \+ a omega^2 \+ b omega^4 \+ \.\.\.\) \(Eq\. 1\), truncated to A\(1 \+ B omega^2\) for the fits \(Table II; omega the vacuum wavenumber of the fundamental in cm^\-1, not nu\_L^2\)\. Calibration \(Table II caption; Eq\. 2\)\: Sitz & Yaris's chi\_He\(3\)\(omega\) = 42\.6\(1 \+ B\_He omega^2\) au, B\_He = 2\.94e\-10 cm^2 = 1/\(58300 cm^\-1\)^2, 1 au = 6\.2353e\-65 C^4 m^4 J^\-3\. Uncertainty\: 'The error bars, which range from 0\.3% to 1\.5%, represent the total experimental uncertainty\. In particular, we believe that the systematic errors in the present experiment are negligible' \(p\. 696\); 'the results obtained in this work are uniformly 1\.5% larger than those previously reported' \(shelton\_1982; the CH4\-He step of that work is blamed\)\. Parts\: Ar electronic; N2, O2 total ESHG \(vibrational overtones 'give only a small contribution', p\. 696; the Table III note says subtracting the vibrational part would reduce C by 1 for H2, D2, less for the others\)\. Table III \(C of chi\(3\)\(omega\)/chi\(3\)\(0\) = 1 \+ C \(omega/omega\_0\)^2 with omega\_0 from linear dispersion\: He 13, Ar 19, H2 15, D2 15, N2 15, O2 23; \+\-0\.6\) is a re\-expression of the fits, kept in these notes; the models of Owyoung \(C = 6\) and Ward \(C = 10\) 'underestimate the dispersion' \(p\. 698\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mizrahi\_1985\_arn2o2/ratio\_Ar\_over\_He ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ratio_Ar_over_He", "material": "Ar", "file": "Ar/mizrahi_1985_arn2o2__ratio_Ar_over_He.csv", "table": "tbl_1008a085d5aa", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "electronic" } } Table I \(p\. 697\)\: chi\(3\)\(omega\)/chi\(3\)\_He\(omega\) for Ar by ESHG, 19 lines 700\.0\-457\.9 nm \(row\: air wavelength; abscissa\: vacuum wavenumber\); parenthesised last\-digit uncertainties as sigma\. Rows 694\.3, 690\.0, 670\.0, 660\.0 are marked a\: 'obtained by first measuring against N2 used as a transfer standard, and then using the smoothed values for chi\_N2/chi\_He'\. Row 600\.0 corrected by an erratum \(printed 20\.99\)\. The ratio is the measurement \(He the reference, Sitz & Yaris's chi\_He for absolute values\); shelton\_1990 Table III\(a\) re\-expresses these on Bishop & Pipin's He \(reproduced there\)\. mizrahi\_1985\_arn2o2/ratio\_N2\_over\_He ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ratio_N2_over_He", "material": "N2", "file": "N2/mizrahi_1985_arn2o2__ratio_N2_over_He.csv", "table": "tbl_1008a085d5aa", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "total" } } Table I \(p\. 697\)\: chi\(3\)\(omega\)/chi\(3\)\_He\(omega\) for N2 by ESHG, 19 lines; parenthesised last\-digit uncertainties as sigma\. Total ESHG \(vibration and rotation included; small\)\. mizrahi\_1985\_arn2o2/ratio\_O2\_over\_He ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ratio_O2_over_He", "material": "O2", "file": "O2/mizrahi_1985_arn2o2__ratio_O2_over_He.csv", "table": "tbl_1008a085d5aa", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "total" } } Table I \(p\. 697\)\: chi\(3\)\(omega\)/chi\(3\)\_He\(omega\) for O2 by ESHG, 18 lines \(none at 457\.9 nm\); the whole column is marked a\: measured against N2 as transfer standard and converted with the smoothed N2/He curve \(formula table2\_N2\), so O2's ratios carry N2's calibration\. Total ESHG\. Formulas -------- mizrahi\_1985\_arn2o2/table2\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_Ar", "material": "Ar", "equation": "Table II, p. 697", "printed": "f(omega) = A(1 + B omega^2); Ar: A = 25.85 +- 0.19, B = (7.11 +- 0.26) x 10^-10 cm^2", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2)", "process": "eshg", "convention": "T", "part": "electronic", "range": "14282-21831 cm^-1 (700.0-457.9 nm)", "coefficients": { "A": "25.85", "B": "7.11e-10" }, "coefficient_units": { "A": "1 (chi_Ar/chi_He)", "B": "cm^2" }, "check": "Gives 29.60 at 14282 cm^-1, 30.95 at 16662 cm^-1 (the corrected 30.99) and 34.61 at 21831 cm^-1 against 29.67, 30.99, 34.41. Checked 2026-09-26." } Weighted least\-squares fit of the ratio to He; 'The excellent quality of the fits \(chi^2 test\) indicates that terms in omega^4 and higher are unimportant at this level of accuracy' \(p\. 696\)\. Used as the Ar calibration curve by shelton\_1986\_krxe \(its Eq\. 7\)\. mizrahi\_1985\_arn2o2/table2\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_N2", "material": "N2", "equation": "Table II, p. 697", "printed": "f(omega) = A(1 + B omega^2); N2: A = 20.30 +- 0.11, B = (6.55 +- 0.20) x 10^-10 cm^2", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1", "process": "eshg", "convention": "T", "part": "total", "range": "14282-21831 cm^-1", "coefficients": { "A": "20.30", "B": "6.55e-10" }, "coefficient_units": { "A": "1 (chi_N2/chi_He)", "B": "cm^2" }, "check": "Gives 23.62 at 15798 cm^-1 against 23.72(10). Checked 2026-09-26." } The N2 calibration curve of shelton\_1985\_sf6, shelton\_1986\_co2 and shelton\_1986\_ch4 \(their Eq\. 2\)\. mizrahi\_1985\_arn2o2/table2\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_O2", "material": "O2", "equation": "Table II, p. 697", "printed": "f(omega) = A(1 + B omega^2); O2: A = 19.73 +- 0.27, B = (13.64 +- 0.54) x 10^-10 cm^2", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1", "process": "eshg", "convention": "T", "part": "total", "range": "14282-20981 cm^-1", "coefficients": { "A": "19.73", "B": "13.64e-10" }, "coefficient_units": { "A": "1 (chi_O2/chi_He)", "B": "cm^2" }, "check": "Gives 29.89 at 19430 cm^-1 against 29.93(26). Checked 2026-09-26." } O2 was measured against N2 \(transfer standard\)\. mizrahi\_1985\_arn2o2/table2\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_H2", "material": "H2", "equation": "Table II, p. 697", "printed": "f(omega) = A(1 + B omega^2); H2 (note a: 'Data for H2 and D2 come from Ref. 5'): A = 14.72 +- 0.09, B = (9.01 +- 0.22) x 10^-10 cm^2", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1", "process": "eshg", "convention": "T", "part": "total", "range": "the data of Ref. 5 (457.9-700 nm)", "coefficients": { "A": "14.72", "B": "9.01e-10" }, "coefficient_units": { "A": "1 (chi_H2/chi_He)", "B": "cm^2" }, "reproduced_from": [ "mizrahi_1985_h2d2" ], "check": "B equals mizrahi_1985_h2d2's uncorrected H2/He column B = 9.01(22)e-10 cm^2 (its Table I caption); A not compared here." } Reproduced from Ref\. 5 \(then to be published\: Mizrahi & Shelton, Phys\. Rev\. A 32, 3454 \(1985\)\)\. mizrahi\_1985\_arn2o2/table2\_D2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_D2", "material": "D2", "equation": "Table II, p. 697", "printed": "f(omega) = A(1 + B omega^2); D2 (note a): A = 14.54 +- 0.11, B = (8.54 +- 0.26) x 10^-10 cm^2", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1", "process": "eshg", "convention": "T", "part": "total", "range": "the data of Ref. 5", "coefficients": { "A": "14.54", "B": "8.54e-10" }, "coefficient_units": { "A": "1 (chi_D2/chi_He)", "B": "cm^2" }, "reproduced_from": [ "mizrahi_1985_h2d2" ], "check": "Not checked against mizrahi_1985_h2d2 (which gives the H2/D2 ratio, not D2/He)." } Reproduced from Ref\. 5\. mizrahi\_1985\_arn2o2/he\_calibration ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "he_calibration", "material": "He", "equation": "Eq. (2), p. 697; Table II caption", "printed": "chi_He(3)(omega)/chi_He(3)(0) = 1 + [omega/(58 300 cm^-1)]^2; chi_He(3)(omega) = 42.6(1 + B_He omega^2), in atomic units (1 a.u. = 6.2353 x 10^-65 C^4 m^4 J^-3); B_He = 2.94 x 10^-10 cm^2 with omega in inverse centimeters", "variable": "omega: vacuum wavenumber of the fundamental in cm^-1", "process": "eshg", "convention": "T", "part": "electronic", "range": "the visible (the measurements)", "coefficients": { "gamma0": "42.6", "B": "2.94e-10", "omega_0": "58300" }, "coefficient_units": { "gamma0": "au", "B": "cm^2", "omega_0": "cm^-1" }, "reproduced_from": [ "P. Sitz and R. Yaris, J. Chem. Phys. 49, 3546 (1968)" ], "check": "1/58300^2 = 2.942e-10 cm^2 = B_He. Checked 2026-09-26." } 'which adequately represents the ab initio results of Sitz and Yaris' \(p\. 697; the reference list prints the journal as 'Chem\. Phys\. 49, 3546', meaning J\. Chem\. Phys\.\)\. The old He calibration, 1\.3 % below Bishop & Pipin's at 514\.5 nm \(see shelton\_1982\)\. Corrections ----------- .. code-block:: text [ { "dataset": "ratio_Ar_over_He", "row": "600.0", "column": "value", "printed": "20.99", "corrected": "30.99", "reason": "A dropped first digit: the Ar ratios rise smoothly from 29.6 to 34.4 over the table, and 20.99 sits between 30.88 (610.0 nm) and 31.25 (590.0 nm).", "evidence": "Table image checked: it prints 20.99(16). The paper's own fit (Table II: 25.85 [1 + 7.11e-10 x 16662^2]) gives 30.95 at this line; shelton_1990 Table III(a) lists Ar at 600.0 nm as 90.05e-63 C^4 m^4 J^-3, which is 30.99 times Sitz & Yaris's gamma_He there (42.6 au x 1.0816 x 6.2353e-65 = 2.873e-63 C^4 m^4 J^-3; 30.99 x 2.873e-63 = 89.0e-63) scaled by the same 1.011 rescaling that shelton_1990 applies at the other lines (632.8 nm: 30.21 -> 87.09e-63), whereas 20.99 would give 60.3e-63. Checked 2026-09-26." } ] Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register ` for the checks and decisions.