hellwarth_1990
==============

R\. W\. Hellwarth, D\. M\. Pennington and M\. A\. Henesian, "Indices governing optical self\-focusing and self\-induced changes in the state of polarization in N2, O2, H2, and Ar gases", Phys\. Rev\. A 41, 2766 \(1990\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/hellwarth_1990.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.41\.2766 <https://doi.org/10.1103/PhysRevA.41.2766>`__

**Source kind:** compilation

**Recorded technique:** Analysis of published dc Kerr constants \(Carusotto et al\. 1985 at 515 nm, absolute and relative to He; older 633\-nm values of Buckingham and co\-workers\) and ESHG ratios to He \(Mizrahi and Shelton 1985\) on Bishop and Lam's He theory, through the Born\-Oppenheimer form of the third\-order response \(electronic sigma plus nuclear response functions a\(t\), b\(t\)\), with two dispersion formulas \(A\: linear\-index Sellmeier poles; B\: one fitted nonlinear pole omega\_0 per gas, tensor\-component\-specific\), to give the long\-wavelength \(LWL\) parameters and the degenerate four\-wave\-mixing c coefficients \(self\-focusing c1111, polarization change c1122\) from 261 to 1053 nm \(secs\. III\-VI\)\. No new measurement\.

**Materials in structured entries:** Ar, H2, He, N2, O2

**Dataset quantities:** hyperpolarizability\_ratio, kerr\_constant, nonlinear\_susceptibility

**Contents:** 54 datasets; 9 formulas.

Curation notes
--------------

Journal pages 2766\-2777 = PDF pages 1\-12 \(Table VII is on p\. 2774\)\. Identity checked against the first page\. N2, O2, Ar, H2, He; air \(0\.78 N2 \+ 0\.21 O2\) is not curated\: its rows are skipped\.

UNITS AND DEFINITIONS \(Gaussian esu throughout, p\. 2766\-2768\)\. Eqs\. \(1\)\-\(2\)\: real fields E\(r, t\) = Re sum\_i^\+ E\(r, omega\_i\) exp\(\-i omega\_i t\), P likewise \(full complex amplitudes, 'some authors express the fields in terms of Fourier amplitudes which are one\-half of the ordinary E and P amplitudes'\); n = \(1 \+ 4 pi chi\)^\(1/2\)\. Eq\. \(4\)\: P\_alpha^NL \(omega\) = D c\_\(alpha beta gamma delta\)\(omega\_i, omega\_j, omega\_k, omega\_l\) E\_beta\(omega\_j\) E\_gamma\(omega\_k\) E\_delta\(omega\_l\), omega\_i \+ omega\_j \+ omega\_k \+ omega\_l = 0, omega = \-omega\_i, 'The degeneracy factor D \.\.\. takes on the values 1, 3, or 6 when either all three, or any two, or none of the last three frequency arguments \.\.\. are equal' \(the Maker\-Terhune c tensor; 'sometimes denoted chi\(3\) \.\.\. and sometimes written 4 chi\(3\) when field conventions differ by a factor of 2'\)\. Isotropic form, Eq\. \(8\)\: c = d d c1122 \+ d d c1212 \+ d d c1221\. Eq\. \(11\)\: Delta n = n2 \<E^2\> = \(1/2\) n2 E\*\(omega\)\.E\(omega\); Eq\. \(12\)\: n2 = \(12 pi / n\) c1111\(\-omega, \-omega, omega, omega\) \(self\-focusing index, esu, per mean square field\)\. ESHG\: c1111\(\-2 omega, 0, omega, omega\) \(D = 3\); dc Kerr\: c1221\(\-omega, omega, 0, 0\) \(D = 3\); THG\: c1111\(\-3 omega, omega, omega, omega\) \(D = 1\)\. Born\-Oppenheimer form, Eq\. \(13\)\: P^NL\(t\) = \(1/2\) sigma E\(t\) E^2\(t\) \+ int ds \[a\(t \- s\) E\(t\) E^2\(s\) \+ b\(t \- s\) E\(s\) E\(t\)\.E\(s\)\], sigma the electronic \('nuclei frozen'\), a and b the isotropic \(vibrational Raman\) and anisotropic \(rotational\) nuclear responses, A\_nu, B\_nu their Fourier transforms \(Eq\. \(14\)\)\. LWL relations\: Eq\. \(15\) c1111\(\-omega, \-omega, omega, omega\) = sigma/8 \+ \(A0 \+ B0\)/6; Eq\. \(16\) A0 = \-B0/3 \(pure vibrational Q branch neglected\); Eq\. \(17\) c1122 = \(sigma \+ 2 B0\)/24, c1212 = \(sigma \+ 2 A0 \+ B0\)/24; Eq\. \(18\) ESHG and THG c1111 = sigma/8; Eq\. \(19\) \(n\_par \- n\_perp\) / \(2 pi E0^2\) = 24 c1221\(\-omega, omega, 0, 0\)/n \(dc Kerr; Carusotto et al\.'s K = \(n\_par \- n\_perp\) rho E0^2 as printed, p\. 2768\); Eq\. \(20\) 24 c1221\(\-omega, omega, 0, 0\)\_LWL = sigma \+ B0\. Eq\. \(21\), p\. 2769\: '5\.036 x 10^\-40 gamma\_zzzz\(omega\_4, omega\_1, omega\_2, omega\_3\) a\.u\. = 24 rho^\-1 c1111\(omega\_4, \.\.\.\) esu' \(Bishop and Lam's per\-atom gamma in atomic units\), and p\. 2770\: 'When converted to esu, the gamma parameter of Ref\. 16 \[Boyle et al\. 1966 = boyle\_1966\] equals 3 sigma/rho'\. So sigma = rho gamma\_T\(esu\)/3 with gamma\_T the Taylor\-series gamma, 1 au = 5\.036e\-40 esu\. Check \(2026\-09\-26\)\: He sigma = 1\.76e\-19 esu at 20 C, 760 Torr \(ideal rho = 2\.5035e19 cm^\-3\) gives gamma = 41\.9 au, Bishop and Lam's value; the Bishop\-Pipin update raises it 2\.9 % \(note 15, p\. 2776\) to ~43\.1; Ar sigma = 47\.4 gives 1128 au \(x 1\.029 = 1161\)\.

TABLE I \(p\. 2770; image checked; tools/extract/hellwarth\_1990\.py\)\: dc Kerr \(n\_par \- n\_perp\)/\(2 pi E0^2\) in 1e\-19 esu at 20 C, 760 Torr; 'Values in parentheses are limits of error of last figures given by source\. All other values have estimated error limits of \+\-10 %'\. Footnotes\: a, Carusotto et al\.'s value divided by their He value; b, that ratio times the He theory \(1\.83 at 515 nm, 1\.80 at 633 nm, g\); c, Carusotto et al\.'s absolute value \(Nuovo Cimento 5D, 328 \(1985\); not in the library; 2\-3 % errors, He \+\-7 %, their He 9 % above Bishop and Lam, p\. 2770\); d, Buckingham et al\., Trans\. Faraday Soc\. 66, 1548 \(1970\) \(no He calibration\); e, Buckingham and Dunmur \(1968\) = buckingham\_1968, 'as quoted \.\.\. divided by the helium value also given there'; f, Buckingham and Orr, Proc\. R\. Soc\. A 305, 259 \(1968\) \(no He calibration\); g, Bishop and Lam's per\-atom value \(ideal gas, ~\+\-3 %\)\. Average\: c weighted three times b\. ERRATUM\: H2 'Normalized to He' printed 3\.2; b = a x 1\.83 holds for N2 \(129 \-\> 236\), O2 \(281 \-\> 514\), Ar \(25\.5 \-\> 46\.7\) and gives 59/1\.83 = 32\.2 for H2\. Checks\: N2 average \(236 \+ 3 x 257\)/4 = 251\.75 \(252 printed\), Ar 49\.7, H2 62\.8 \(63\); O2 \(515 \+ 3 x 559\)/4 = 548\.0 against 549 printed \(1 unit; not corrected\)\.

TABLE II \(p\. 2771, CSV; image checked\)\: sigma \(1e\-19 esu, 20 C, 760 Torr\) = Mizrahi and Shelton's ESHG ratio to He, extrapolated to the LWL with Eq\. \(22\) and multiplied by He's 1\.76 \(Bishop and Lam\); errors in parentheses \(absolute\: 36\.5\(1\.4\) = \+\- 1\.4\)\. Eq\. \(22\)\: c1111\(\-2 omega, omega, omega, 0\) = \(sigma/8\)\(1 \- 6 omega^2/omega\_0^2\)^\-1, the MS data \(700\-450 nm\) spanning 0\.12\-0\.35 omega\_0\.

TABLES V AND VII \(pp\. 2772, 2774\)\: sigma \+ B0 \(= 24 c1221 LWL\) from each Kerr value divided by F^A\(\-omega, omega, 0, 0\) = \(1 \- omega^2/omega\_s^2\)^\-2 \(V\) or F\_1221^B = \(1 \- 13 omega^2 / 6 omega\_0^2\)^\-1 \(VII\); parentheses = relative weights of the average \(footnotes b of V, a of VII\), not errors\. Ar\: the average \(44\.4, 42\.9\) is replaced in the calculations by 47\.4, 'directly from sigma of Table II' \(\+\-5 %\) \(row 'used'\)\. Estimated uncertainty of these values '~\+\-10 %' \(VII caption, V footnote c\)\. Structural fixes in the script \(averages misplaced in the cells of Table V; Table VII's H2 49\.7\(3\) printed without its wavelength\: 633 nm, it is 52\.5/F\_1221^B\(633\)\)\.

TABLES VI AND VIII \(pp\. 2773, 2775\)\: DFWM c coefficients \(\-omega, \-omega, omega, omega\), 'omega\(cm^\-1\) = lambda^\-1', 1e\-19 esu, 20 C, 760 Torr, from formula A \(VI\: F^A = \(1 \- omega^2/omega\_s^2\)^\-4; c1122 = \[2\(sigma \+ B0\) \- sigma\] F^A/24, c1111 = \[\(sigma \+ B0\)/9 \+ sigma/72\] F^A\) and formula B \(VIII\: c1122 = \[2\(sigma \+ B0\) \- sigma\] F\_1122^B/24, c1212 = \[\(sigma \+ B0\)/72 \+ sigma/36\] F\_1212^B, c1111 = c1122 \+ 2 c1212; notes a and b of Table VIII say 'Table VIII' for the sigma \+ B0 source, meaning Table VII\)\. Uncertainty '\+\-10 %' \(Kerr\), Ar \+\-5 % \(VIII caption\); formula A 'at least \+\-10 %'\. CHECK \(2026\-09\-26, scratch script\)\: with sigma \(Table II\), sigma \+ B0 \(Table V averages, Ar 47\.4\) and omega\_s \(Table III\), formula A reproduces all 20 curated entries of Table VI to \<= 0\.6 %; with Table VII's averages and omega\_0 \(Table IV\), formula B reproduces Table VIII's c1122 and c1212 to \<= 0\.3 %, except Ar at 261 nm\: c1212 printed 2\.45 against 3\.14 computed \(and so c1111 9\.74 against 11\.11; the printed row is self\-consistent, 4\.84 \+ 2 x 2\.45 = 9\.74\)\. Not corrected \(no printed alternative\); flagged in the dataset notes\. O2 1053 nm c1111 printed 58\.2 against c1122 \+ 2 c1212 = 58\.54 \(and 58\.52 computed\)\: a 0\.6 % inconsistency, not corrected\. Air c1111 at 333 and 522 nm \(104, 61\.8\) disagree with 0\.78 N2 \+ 0\.21 O2 \(57\.3, 39\.3\)\: air skipped anyway\.

CONVERSION CHECK \(for the reader; not data\)\: Ar c1111\(1053 nm, VIII\) = 6\.09e\-19 esu \-\> n2 = 12 pi c1111 = 2\.30e\-17 esu per \<E^2\>; with I = \(c n / 8 pi\)\|E\|^2 and Delta n = \(1/2\) n2 \|E\|^2 this is 4 pi n2 / c = 9\.6e\-20 cm2/W \(x 1e7 from erg/s to W\) at 20 C, 1 atm\.

TEXT \(notes only\)\: air at 1053 nm and 20 C\: c1122\(\-omega, \-omega, omega, omega\) = \(24 \+\- 3\) x 10^\-19 esu \(Eq\. \(33\), formula A 23\.86, B 23\.8\) and n2 = \(1\.2 \+\- 0\.2\) x 10^\-16 esu \(Eq\. \(34\), B value 32\.55 of c1111\); Ar n2 5\.4 times less than air's, its ICSP coefficient 11 times less; 1\-ns pulses may see a c1221 of air ~20 % lower \(Raman linewidths ~3 GHz\) \(p\. 2776\)\. Shimoji et al\.'s 308\-nm air n2 ~2\.9e\-16 esu per atm at 300 K against 1\.6e\-16 \(A\) and 3\.9e\-16 \(B\) at 333 nm\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

hellwarth\_1990/kerr\_ratio\_carusotto\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_ratio_carusotto_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_ratio_carusotto_N2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "hyperpolarizability_ratio",
     "unit": "1",
     "scale": 1.0,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "reference_material": "He",
       "process": "dc_kerr",
       "part": "total"
     }
   }

Table I, 'Normalized to He' \(footnote a\)\: Carusotto et al\.'s 515\-nm Kerr constant divided by their He value, at the same density\. A ratio of dc Kerr responses \(electronic plus orientational\), not of electronic gammas\.

hellwarth\_1990/kerr\_ratio\_carusotto\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_ratio_carusotto_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_ratio_carusotto_O2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "hyperpolarizability_ratio",
     "unit": "1",
     "scale": 1.0,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "reference_material": "He",
       "process": "dc_kerr",
       "part": "total"
     }
   }

Table I, 'Normalized to He' \(footnote a\)\: Carusotto et al\.'s 515\-nm Kerr constant divided by their He value, at the same density\. A ratio of dc Kerr responses \(electronic plus orientational\), not of electronic gammas\.

hellwarth\_1990/kerr\_ratio\_carusotto\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_ratio_carusotto_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_ratio_carusotto_Ar.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "hyperpolarizability_ratio",
     "unit": "1",
     "scale": 1.0,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "reference_material": "He",
       "process": "dc_kerr",
       "part": "total"
     }
   }

Table I, 'Normalized to He' \(footnote a\)\: Carusotto et al\.'s 515\-nm Kerr constant divided by their He value, at the same density\. A ratio of dc Kerr responses \(electronic plus orientational\), not of electronic gammas\.

hellwarth\_1990/kerr\_ratio\_carusotto\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_ratio_carusotto_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_ratio_carusotto_H2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "hyperpolarizability_ratio",
     "unit": "1",
     "scale": 1.0,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "reference_material": "He",
       "process": "dc_kerr",
       "part": "total"
     }
   }

Table I, 'Normalized to He' \(footnote a\)\: Carusotto et al\.'s 515\-nm Kerr constant divided by their He value, at the same density\. A ratio of dc Kerr responses \(electronic plus orientational\), not of electronic gammas\. ERRATUM\: printed 3\.2, corrected to 32\.2 \(source notes\)\.

hellwarth\_1990/kerr\_ratio\_buckingham\_dunmur\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_ratio_buckingham_dunmur_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_ratio_buckingham_dunmur_Ar.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "hyperpolarizability_ratio",
     "unit": "1",
     "scale": 1.0,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "buckingham_1968"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "reference_material": "He",
       "process": "dc_kerr",
       "part": "total"
     }
   }

Table I, 'Normalized to He' at 633 nm \(footnote e\)\: Buckingham and Dunmur's Ar value divided by their He value, 22\(3\) = 22 \+\- 3 \(limits of error\)\.

hellwarth\_1990/kerr\_he\_scaled\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_he_scaled_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_he_scaled_N2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote b\: the He\-normalized ratio times the He theory value \(1\.83 at 515 nm, 1\.80 at 633 nm\)\: this paper's rescaling of Carusotto \(515 nm\) or Buckingham and Dunmur \(Ar, 633 nm\)\. Derived\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_carusotto\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_carusotto_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_carusotto_N2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote c\: Carusotto et al\.'s absolute Kerr constant at 515 nm as given there \(their errors 2\-3 %, He \+\-7 %\)\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_average\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_average_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_average_N2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985",
       "buckingham_1970"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound",
       "relative_rows": {
         "515": 0.1
       }
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Average'\: this paper's evaluation \(absolute value weighted 3 to 1 against the He\-scaled one\); the 633\-nm entry repeats the single value there\. Derived from reproduced values\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_he\_scaled\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_he_scaled_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_he_scaled_O2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote b\: the He\-normalized ratio times the He theory value \(1\.83 at 515 nm, 1\.80 at 633 nm\)\: this paper's rescaling of Carusotto \(515 nm\) or Buckingham and Dunmur \(Ar, 633 nm\)\. Derived\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_carusotto\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_carusotto_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_carusotto_O2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote c\: Carusotto et al\.'s absolute Kerr constant at 515 nm as given there \(their errors 2\-3 %, He \+\-7 %\)\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_average\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_average_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_average_O2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Average'\: this paper's evaluation \(absolute value weighted 3 to 1 against the He\-scaled one\); the 633\-nm entry repeats the single value there\. Derived from reproduced values\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_he\_scaled\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_he_scaled_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_he_scaled_Ar.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985",
       "buckingham_1968"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound",
       "relative_rows": {
         "515": 0.1
       }
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote b\: the He\-normalized ratio times the He theory value \(1\.83 at 515 nm, 1\.80 at 633 nm\)\: this paper's rescaling of Carusotto \(515 nm\) or Buckingham and Dunmur \(Ar, 633 nm\)\. Derived\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_carusotto\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_carusotto_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_carusotto_Ar.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote c\: Carusotto et al\.'s absolute Kerr constant at 515 nm as given there \(their errors 2\-3 %, He \+\-7 %\)\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_average\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_average_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_average_Ar.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985",
       "buckingham_1968"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound",
       "relative_rows": {
         "515": 0.1
       }
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Average'\: this paper's evaluation \(absolute value weighted 3 to 1 against the He\-scaled one\); the 633\-nm entry repeats the single value there\. Derived from reproduced values\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_he\_scaled\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_he_scaled_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_he_scaled_H2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote b\: the He\-normalized ratio times the He theory value \(1\.83 at 515 nm, 1\.80 at 633 nm\)\: this paper's rescaling of Carusotto \(515 nm\) or Buckingham and Dunmur \(Ar, 633 nm\)\. Derived\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_carusotto\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_carusotto_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_carusotto_H2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote c\: Carusotto et al\.'s absolute Kerr constant at 515 nm as given there \(their errors 2\-3 %, He \+\-7 %\)\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_average\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_average_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_average_H2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "carusotto_1985",
       "buckingham_1968b"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Average'\: this paper's evaluation \(absolute value weighted 3 to 1 against the He\-scaled one\); the 633\-nm entry repeats the single value there\. Derived from reproduced values\: 'check'\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_carusotto\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_carusotto_He",
     "material": "He",
     "file": "He/hellwarth_1990__kerr_carusotto_He.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "carusotto_1985"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 'Absolute' with footnote c\: Carusotto et al\.'s absolute Kerr constant at 515 nm as given there \(their errors 2\-3 %, He \+\-7 %\)\. Unit\: \(n\_par \- n\_perp\)/\(2 pi E0^2\) in esu \(= 24 c1221\(\-omega, omega, 0, 0\)/n, Eq\. \(19\)\)\.

hellwarth\_1990/kerr\_buckingham\_1970\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_buckingham_1970_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_buckingham_1970_N2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "buckingham_1970"
     ],
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 633 nm, footnote d\: 251\(36\) = 251 \+\- 36 \(limits of error\), from Buckingham et al\. \(1970\), 'which has no value for He by which to calibrate the static electric field'\.

hellwarth\_1990/kerr\_buckingham\_orr\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_buckingham_orr_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_buckingham_orr_H2.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "buckingham_1968b"
     ],
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, 633 nm, footnote f\: from Buckingham and Orr \(1968\), 'which has no value for He by which to calibrate the static electric field'\.

hellwarth\_1990/kerr\_bishop\_lam\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_bishop_lam_He",
     "material": "He",
     "file": "He/hellwarth_1990__kerr_bishop_lam_He.csv",
     "table": "tbl_223eea4ff99e",
     "quantity": "kerr_constant",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "ideal",
     "use": "reproduced",
     "reproduced_from": [
       "D. M. Bishop and B. Lam, Phys. Rev. A 37, 464 (1988)"
     ],
     "uncertainty": {
       "relative": 0.03,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 293.15
     }
   }

Table I, He 'Absolute' footnote g\: 'From the value per atom calculated from Eqs\. \(14\) and \(16\) of Ref\. 15 \[Bishop and Lam\], assuming ideal gas law; error estimated as ~\+\-3 %'\. Rows 515, 633 nm and inf \(static\)\. Theory, the calibration of every 'b' value\.

hellwarth\_1990/sigma\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__sigma_N2.csv",
     "table": "tbl_0c2959460533",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "mizrahi_1985_arn2o2"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "static",
       "convention": "hellwarth_sigma",
       "part": "electronic"
     }
   }

Table II\: sigma, the electronic parameter of Eq\. \(13\), in the long\-wavelength limit \(row LWL, wavelength inf\)\: Mizrahi and Shelton's ESHG ratio to He extrapolated with Eq\. \(22\) and multiplied by He's 1\.76\. Derived from mizrahi's ratios\: 'check'\. Error in parentheses \(absolute\)\.

hellwarth\_1990/sigma\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__sigma_O2.csv",
     "table": "tbl_0c2959460533",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "mizrahi_1985_arn2o2"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "static",
       "convention": "hellwarth_sigma",
       "part": "electronic"
     }
   }

Table II\: sigma, the electronic parameter of Eq\. \(13\), in the long\-wavelength limit \(row LWL, wavelength inf\)\: Mizrahi and Shelton's ESHG ratio to He extrapolated with Eq\. \(22\) and multiplied by He's 1\.76\. Derived from mizrahi's ratios\: 'check'\. Error in parentheses \(absolute\)\.

hellwarth\_1990/sigma\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__sigma_Ar.csv",
     "table": "tbl_0c2959460533",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "mizrahi_1985_arn2o2"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "static",
       "convention": "hellwarth_sigma",
       "part": "electronic"
     }
   }

Table II\: sigma, the electronic parameter of Eq\. \(13\), in the long\-wavelength limit \(row LWL, wavelength inf\)\: Mizrahi and Shelton's ESHG ratio to He extrapolated with Eq\. \(22\) and multiplied by He's 1\.76\. Derived from mizrahi's ratios\: 'check'\. Error in parentheses \(absolute\)\.

hellwarth\_1990/sigma\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__sigma_H2.csv",
     "table": "tbl_0c2959460533",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "reproduced_from": [
       "mizrahi_1985_h2d2"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "static",
       "convention": "hellwarth_sigma",
       "part": "electronic"
     }
   }

Table II\: sigma, the electronic parameter of Eq\. \(13\), in the long\-wavelength limit \(row LWL, wavelength inf\)\: Mizrahi and Shelton's ESHG ratio to He extrapolated with Eq\. \(22\) and multiplied by He's 1\.76\. Derived from mizrahi's ratios\: 'check'\. Error in parentheses \(absolute\)\. Note a\: 'See also Ref\. 21' \(Mizrahi and Shelton, Phys\. Rev\. A 32, 3454 \(1985\) = mizrahi\_1985\_h2d2\)\.

hellwarth\_1990/sigma\_He
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_He",
     "material": "He",
     "file": "He/hellwarth_1990__sigma_He.csv",
     "table": "tbl_0c2959460533",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "D. M. Bishop and B. Lam, Phys. Rev. A 37, 464 (1988)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "static",
       "convention": "hellwarth_sigma",
       "part": "electronic"
     }
   }

Table II, He\: 1\.76\(0\.05\), Bishop and Lam's theory \(Ref\. 15\), the calibration of the other sigma values\. Note 15 \(p\. 2776\)\: Bishop and Pipin's corrections raise it by 2\.9 %\.

hellwarth\_1990/kerr\_lwl\_A\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_A_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_lwl_A_N2.csv",
     "table": "tbl_2ee7689e92b6",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table V\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula A from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_B\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_B_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__kerr_lwl_B_N2.csv",
     "table": "tbl_3b8085ea2a30",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table VII\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula B from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_A\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_A_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_lwl_A_O2.csv",
     "table": "tbl_2ee7689e92b6",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table V\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula A from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_B\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_B_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__kerr_lwl_B_O2.csv",
     "table": "tbl_3b8085ea2a30",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table VII\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula B from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_A\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_A_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_lwl_A_Ar.csv",
     "table": "tbl_2ee7689e92b6",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table V\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula A from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Row 'used' = 47\.4, the Ar value taken from sigma \(Table II\) for the calculations \(footnote f\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_B\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_B_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__kerr_lwl_B_Ar.csv",
     "table": "tbl_3b8085ea2a30",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table VII\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula B from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Row 'used' = 47\.4, the Ar value taken from sigma \(Table II\) for the calculations \(footnote b\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_A\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_A_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_lwl_A_H2.csv",
     "table": "tbl_2ee7689e92b6",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table V\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula A from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/kerr\_lwl\_B\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerr_lwl_B_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__kerr_lwl_B_H2.csv",
     "table": "tbl_3b8085ea2a30",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "hellwarth_sigma",
       "part": "total"
     }
   }

Table VII\: sigma \+ B0 = 24 c1221\(\-omega, omega, 0, 0\)\_LWL \(Eq\. \(20\)\) extrapolated with formula B from the Kerr value at the wavelength named in the row id \(515, 633 nm\); row 'average' the paper's weighted average\. All rows are long\-wavelength limits \(wavelength inf\)\. Weights in parentheses are dropped \(kept in 'printed'\)\. Derived\: 'check'\. Estimated uncertainty ~\+\-10 %\.

hellwarth\_1990/dfwm\_A\_c1122\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1122_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__dfwm_A_c1122_N2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VI\: c1122\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_A\_c1111\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1111_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__dfwm_A_c1111_N2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VI\: c1111\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1122\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1122_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__dfwm_B_c1122_N2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VIII\: c1122\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1212\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1212_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__dfwm_B_c1212_N2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1212"
     }
   }

Table VIII\: c1212\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1111\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1111_N2",
     "material": "N2",
     "file": "N2/hellwarth_1990__dfwm_B_c1111_N2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VIII\: c1111\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_A\_c1122\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1122_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__dfwm_A_c1122_O2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VI\: c1122\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_A\_c1111\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1111_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__dfwm_A_c1111_O2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VI\: c1111\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1122\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1122_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__dfwm_B_c1122_O2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VIII\: c1122\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1212\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1212_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__dfwm_B_c1212_O2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1212"
     }
   }

Table VIII\: c1212\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1111\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1111_O2",
     "material": "O2",
     "file": "O2/hellwarth_1990__dfwm_B_c1111_O2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VIII\: c1111\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\. The 1053\-nm value 58\.2 is 0\.6 % below c1122 \+ 2 c1212 = 58\.54 \(source notes\)\.

hellwarth\_1990/dfwm\_A\_c1122\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1122_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__dfwm_A_c1122_Ar.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VI\: c1122\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_A\_c1111\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1111_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__dfwm_A_c1111_Ar.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VI\: c1111\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1122\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1122_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__dfwm_B_c1122_Ar.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.05,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VIII\: c1122\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1212\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1212_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__dfwm_B_c1212_Ar.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.05,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1212"
     }
   }

Table VIII\: c1212\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\. The 261\-nm row does not follow formula B \(c1212 3\.14 and c1111 11\.11 computed against 2\.45 and 9\.74 printed; every other entry agrees to \<= 0\.6 %\)\: doubtful \(source notes, TC\-283\)\.

hellwarth\_1990/dfwm\_B\_c1111\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1111_Ar",
     "material": "Ar",
     "file": "Ar/hellwarth_1990__dfwm_B_c1111_Ar.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.05,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VIII\: c1111\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\. The 261\-nm row does not follow formula B \(c1212 3\.14 and c1111 11\.11 computed against 2\.45 and 9\.74 printed; every other entry agrees to \<= 0\.6 %\)\: doubtful \(source notes, TC\-283\)\.

hellwarth\_1990/dfwm\_A\_c1122\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1122_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__dfwm_A_c1122_H2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VI\: c1122\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_A\_c1111\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_A_c1111_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__dfwm_A_c1111_H2.csv",
     "table": "tbl_03c27c55bc84",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VI\: c1111\(\-omega, \-omega, omega, omega\) from formula A, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1122\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1122_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__dfwm_B_c1122_H2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1122"
     }
   }

Table VIII\: c1122\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1212\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1212_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__dfwm_B_c1212_H2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1212"
     }
   }

Table VIII\: c1212\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

hellwarth\_1990/dfwm\_B\_c1111\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dfwm_B_c1111_H2",
     "material": "H2",
     "file": "H2/hellwarth_1990__dfwm_B_c1111_H2.csv",
     "table": "tbl_757adefa584f",
     "quantity": "nonlinear_susceptibility",
     "unit": "esu",
     "scale": 1e-19,
     "abscissa_unit": "nm",
     "state": {
       "pressure_pa": 101325.0,
       "temperature_c": 20.0
     },
     "density": "unknown",
     "use": "check",
     "uncertainty": {
       "relative": 0.1,
       "level": "bound"
     },
     "parameters": {
       "process": "kerr",
       "convention": "maker_terhune_c",
       "part": "total",
       "component": "1111"
     }
   }

Table VIII\: c1111\(\-omega, \-omega, omega, omega\) from formula B, rows by wavelength \(nm\) and LWL \(inf\)\. n2 = 12 pi c1111 / n \(Eq\. \(12\)\)\. Calculated from Kerr and ESHG data \(the long\-pulse response\: electronic plus adiabatic rotational and vibrational\)\: 'check'\. Uncertainty '\+\-10 %' \(Ar in Table VIII \+\-5 %\); formula A's larger at short wavelengths\.

Formulas
--------

hellwarth\_1990/formula\_A\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_A_N2",
     "material": "N2",
     "equation": "Eqs. (23)-(25), p. 2772-2773, with Table III (p. 2771) and the LWL values of Tables II and V",
     "printed": "c(ijkl) = c(ijkl)_LWL F^A(ijkl), F^A(omega_4, omega_1, omega_2, omega_3) = prod_(i=1..4) (1 - omega_i^2 / omega_s^2)^-1; c1122(-w,-w,w,w)_LWL = [2(sigma + B0) - sigma]/24, c1111_LWL = (sigma + B0)/9 + sigma/72, c1221(-w,w,0,0)_LWL = (sigma + B0)/24",
     "variable": "omega: wavenumber in cm^-1 (omega = 1/lambda, Table VI caption); omega_s in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < ~omega_s/2; Table VI down to 261-333 nm ('the shortest wavelengths tabulated are those below which formula B is known to have larger than 10 % error')",
     "coefficients": {
       "omega_s": "131e3",
       "sigma": "36.5",
       "sigma_plus_B0": "242"
     },
     "check": "Reproduces every Table VI entry of N2 (c1122, c1111) to <= 0.6 % (checked 2026-09-26)."
   }

omega\_s\: Table III, 'taken from Ref\. 20' \(Landolt\-Boernstein, Table 2863\)\: the single\-pole Sellmeier frequency of the linear index, reproduced\. sigma \+ B0\: Table V average\.

hellwarth\_1990/formula\_B\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_B_N2",
     "material": "N2",
     "equation": "Eqs. (26)-(31), p. 2773-2774, with Table IV (p. 2771) and the LWL values of Tables II and VII",
     "printed": "c1122(ijkl) = c1122(ijkl)_LWL F^B_1122(ijkl), F^B_1122 = (1 - omega_1122^2 / omega_0^2)^-1, omega_1122^2 = [13 omega_L^2 + 6(omega_i omega_j + omega_k omega_l)]/12 (likewise 1212 with omega_i omega_k + omega_j omega_l, 1221 with omega_i omega_l + omega_j omega_k), omega_L^2 = omega_i^2 + omega_j^2 + omega_k^2 + omega_l^2",
     "variable": "omega: wavenumber in cm^-1; omega_0 in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < 2 omega_0 / 3 (He: < 10 % at 2 omega_0/3, < 3 % at omega_0/2); Table VIII down to 3/omega_0",
     "coefficients": {
       "omega_0": "115e3",
       "omega_0_uncertainty": "10e3",
       "sigma": "36.5",
       "sigma_plus_B0": "240"
     },
     "check": "Reproduces Table VIII's N2 c1122, c1212 and c1111 to <= 0.6 % (checked 2026-09-26)."
   }

omega\_0\: Table IV, fitted to Mizrahi and Shelton's ESHG dispersion with Eq\. \(22\); 'the uncertainties quoted span the values which give a satisfactory fit'\. sigma \+ B0\: Table VII average\. Special cases\: ESHG c1111\(2w,w,w,0\) = \(sigma/24\)\[1/\(1 \- 7 w^2/w0^2\) \+ 2/\(1 \- 11 w^2/2 w0^2\)\] \(Eq\. \(32\)\), approximated by Eq\. \(22\) \(sigma/8\)\(1 \- 6 w^2/w0^2\)^\-1 within 0\.2 % over the MS range; dc Kerr F^B\_1221\(\-w,w,0,0\) = \(1 \- 13 w^2/6 w0^2\)^\-1 \(Table VII caption\)\.

hellwarth\_1990/formula\_A\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_A_O2",
     "material": "O2",
     "equation": "Eqs. (23)-(25), p. 2772-2773, with Table III (p. 2771) and the LWL values of Tables II and V",
     "printed": "c(ijkl) = c(ijkl)_LWL F^A(ijkl), F^A(omega_4, omega_1, omega_2, omega_3) = prod_(i=1..4) (1 - omega_i^2 / omega_s^2)^-1; c1122(-w,-w,w,w)_LWL = [2(sigma + B0) - sigma]/24, c1111_LWL = (sigma + B0)/9 + sigma/72, c1221(-w,w,0,0)_LWL = (sigma + B0)/24",
     "variable": "omega: wavenumber in cm^-1 (omega = 1/lambda, Table VI caption); omega_s in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < ~omega_s/2; Table VI down to 261-333 nm ('the shortest wavelengths tabulated are those below which formula B is known to have larger than 10 % error')",
     "coefficients": {
       "omega_s": "113e3",
       "sigma": "37.8",
       "sigma_plus_B0": "517"
     },
     "check": "Reproduces every Table VI entry of O2 (c1122, c1111) to <= 0.6 % (checked 2026-09-26)."
   }

omega\_s\: Table III, 'taken from Ref\. 20' \(Landolt\-Boernstein, Table 2863\)\: the single\-pole Sellmeier frequency of the linear index, reproduced\. sigma \+ B0\: Table V average\.

hellwarth\_1990/formula\_B\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_B_O2",
     "material": "O2",
     "equation": "Eqs. (26)-(31), p. 2773-2774, with Table IV (p. 2771) and the LWL values of Tables II and VII",
     "printed": "c1122(ijkl) = c1122(ijkl)_LWL F^B_1122(ijkl), F^B_1122 = (1 - omega_1122^2 / omega_0^2)^-1, omega_1122^2 = [13 omega_L^2 + 6(omega_i omega_j + omega_k omega_l)]/12 (likewise 1212 with omega_i omega_k + omega_j omega_l, 1221 with omega_i omega_l + omega_j omega_k), omega_L^2 = omega_i^2 + omega_j^2 + omega_k^2 + omega_l^2",
     "variable": "omega: wavenumber in cm^-1; omega_0 in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < 2 omega_0 / 3 (He: < 10 % at 2 omega_0/3, < 3 % at omega_0/2); Table VIII down to 3/omega_0",
     "coefficients": {
       "omega_0": "90e3",
       "omega_0_uncertainty": "5e3",
       "sigma": "37.8",
       "sigma_plus_B0": "494"
     },
     "check": "Reproduces Table VIII's O2 c1122, c1212 and c1111 to <= 0.6 % (checked 2026-09-26)."
   }

omega\_0\: Table IV, fitted to Mizrahi and Shelton's ESHG dispersion with Eq\. \(22\); 'the uncertainties quoted span the values which give a satisfactory fit'\. sigma \+ B0\: Table VII average\. Special cases\: ESHG c1111\(2w,w,w,0\) = \(sigma/24\)\[1/\(1 \- 7 w^2/w0^2\) \+ 2/\(1 \- 11 w^2/2 w0^2\)\] \(Eq\. \(32\)\), approximated by Eq\. \(22\) \(sigma/8\)\(1 \- 6 w^2/w0^2\)^\-1 within 0\.2 % over the MS range; dc Kerr F^B\_1221\(\-w,w,0,0\) = \(1 \- 13 w^2/6 w0^2\)^\-1 \(Table VII caption\)\.

hellwarth\_1990/formula\_A\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_A_Ar",
     "material": "Ar",
     "equation": "Eqs. (23)-(25), p. 2772-2773, with Table III (p. 2771) and the LWL values of Tables II and V",
     "printed": "c(ijkl) = c(ijkl)_LWL F^A(ijkl), F^A(omega_4, omega_1, omega_2, omega_3) = prod_(i=1..4) (1 - omega_i^2 / omega_s^2)^-1; c1122(-w,-w,w,w)_LWL = [2(sigma + B0) - sigma]/24, c1111_LWL = (sigma + B0)/9 + sigma/72, c1221(-w,w,0,0)_LWL = (sigma + B0)/24",
     "variable": "omega: wavenumber in cm^-1 (omega = 1/lambda, Table VI caption); omega_s in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < ~omega_s/2; Table VI down to 261-333 nm ('the shortest wavelengths tabulated are those below which formula B is known to have larger than 10 % error')",
     "coefficients": {
       "omega_s": "130e3",
       "sigma": "47.4",
       "sigma_plus_B0": "47.4"
     },
     "check": "Reproduces every Table VI entry of Ar (c1122, c1111) to <= 0.6 % (checked 2026-09-26)."
   }

omega\_s\: Table III, 'taken from Ref\. 20' \(Landolt\-Boernstein, Table 2863\)\: the single\-pole Sellmeier frequency of the linear index, reproduced\. sigma \+ B0\: Table V average \(Ar\: 47\.4 from sigma, footnote f\)\.

hellwarth\_1990/formula\_B\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_B_Ar",
     "material": "Ar",
     "equation": "Eqs. (26)-(31), p. 2773-2774, with Table IV (p. 2771) and the LWL values of Tables II and VII",
     "printed": "c1122(ijkl) = c1122(ijkl)_LWL F^B_1122(ijkl), F^B_1122 = (1 - omega_1122^2 / omega_0^2)^-1, omega_1122^2 = [13 omega_L^2 + 6(omega_i omega_j + omega_k omega_l)]/12 (likewise 1212 with omega_i omega_k + omega_j omega_l, 1221 with omega_i omega_l + omega_j omega_k), omega_L^2 = omega_i^2 + omega_j^2 + omega_k^2 + omega_l^2",
     "variable": "omega: wavenumber in cm^-1; omega_0 in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < 2 omega_0 / 3 (He: < 10 % at 2 omega_0/3, < 3 % at omega_0/2); Table VIII down to 3/omega_0",
     "coefficients": {
       "omega_0": "115e3",
       "omega_0_uncertainty": "10e3",
       "sigma": "47.4",
       "sigma_plus_B0": "47.4"
     },
     "check": "Reproduces Table VIII's Ar c1122, c1212 and c1111 to <= 0.6 %, except the 261-nm c1212 (3.14 computed, 2.45 printed) and hence c1111 (checked 2026-09-26)."
   }

omega\_0\: Table IV, fitted to Mizrahi and Shelton's ESHG dispersion with Eq\. \(22\); 'the uncertainties quoted span the values which give a satisfactory fit'\. sigma \+ B0\: Table VII average \(Ar\: 47\.4 from sigma, footnote b\)\. Special cases\: ESHG c1111\(2w,w,w,0\) = \(sigma/24\)\[1/\(1 \- 7 w^2/w0^2\) \+ 2/\(1 \- 11 w^2/2 w0^2\)\] \(Eq\. \(32\)\), approximated by Eq\. \(22\) \(sigma/8\)\(1 \- 6 w^2/w0^2\)^\-1 within 0\.2 % over the MS range; dc Kerr F^B\_1221\(\-w,w,0,0\) = \(1 \- 13 w^2/6 w0^2\)^\-1 \(Table VII caption\)\.

hellwarth\_1990/formula\_A\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_A_H2",
     "material": "H2",
     "equation": "Eqs. (23)-(25), p. 2772-2773, with Table III (p. 2771) and the LWL values of Tables II and V",
     "printed": "c(ijkl) = c(ijkl)_LWL F^A(ijkl), F^A(omega_4, omega_1, omega_2, omega_3) = prod_(i=1..4) (1 - omega_i^2 / omega_s^2)^-1; c1122(-w,-w,w,w)_LWL = [2(sigma + B0) - sigma]/24, c1111_LWL = (sigma + B0)/9 + sigma/72, c1221(-w,w,0,0)_LWL = (sigma + B0)/24",
     "variable": "omega: wavenumber in cm^-1 (omega = 1/lambda, Table VI caption); omega_s in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < ~omega_s/2; Table VI down to 261-333 nm ('the shortest wavelengths tabulated are those below which formula B is known to have larger than 10 % error')",
     "coefficients": {
       "omega_s": "111e3",
       "sigma": "27.9",
       "sigma_plus_B0": "55.8"
     },
     "check": "Reproduces every Table VI entry of H2 (c1122, c1111) to <= 0.6 % (checked 2026-09-26)."
   }

omega\_s\: Table III, 'taken from Ref\. 20' \(Landolt\-Boernstein, Table 2863\)\: the single\-pole Sellmeier frequency of the linear index, reproduced\. sigma \+ B0\: Table V average\.

hellwarth\_1990/formula\_B\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_B_H2",
     "material": "H2",
     "equation": "Eqs. (26)-(31), p. 2773-2774, with Table IV (p. 2771) and the LWL values of Tables II and VII",
     "printed": "c1122(ijkl) = c1122(ijkl)_LWL F^B_1122(ijkl), F^B_1122 = (1 - omega_1122^2 / omega_0^2)^-1, omega_1122^2 = [13 omega_L^2 + 6(omega_i omega_j + omega_k omega_l)]/12 (likewise 1212 with omega_i omega_k + omega_j omega_l, 1221 with omega_i omega_l + omega_j omega_k), omega_L^2 = omega_i^2 + omega_j^2 + omega_k^2 + omega_l^2",
     "variable": "omega: wavenumber in cm^-1; omega_0 in 10^3 cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "unknown",
     "range": "omega_L < 2 omega_0 / 3 (He: < 10 % at 2 omega_0/3, < 3 % at omega_0/2); Table VIII down to 3/omega_0",
     "coefficients": {
       "omega_0": "100e3",
       "omega_0_uncertainty": "10e3",
       "sigma": "27.9",
       "sigma_plus_B0": "54.8"
     },
     "check": "Reproduces Table VIII's H2 c1122, c1212 and c1111 to <= 0.6 % (checked 2026-09-26)."
   }

omega\_0\: Table IV, fitted to Mizrahi and Shelton's ESHG dispersion with Eq\. \(22\); 'the uncertainties quoted span the values which give a satisfactory fit'\. sigma \+ B0\: Table VII average\. Special cases\: ESHG c1111\(2w,w,w,0\) = \(sigma/24\)\[1/\(1 \- 7 w^2/w0^2\) \+ 2/\(1 \- 11 w^2/2 w0^2\)\] \(Eq\. \(32\)\), approximated by Eq\. \(22\) \(sigma/8\)\(1 \- 6 w^2/w0^2\)^\-1 within 0\.2 % over the MS range; dc Kerr F^B\_1221\(\-w,w,0,0\) = \(1 \- 13 w^2/6 w0^2\)^\-1 \(Table VII caption\)\.

hellwarth\_1990/formula\_B\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "formula_B_He",
     "material": "He",
     "equation": "Eqs. (26)-(31) and Table IV (p. 2771, note a: 'Fit to the calculations of Ref. 15')",
     "printed": "as formula_B_N2, omega_0 = 158 +- 5 (10^3 cm^-1); text p. 2774: 'the choice omega_0 = 161146 cm^-1 reproduced all the BL results to better than 10 % at omega_L = 2 omega_0/3, and to better than 3 % at omega_L = omega_0/2 ... In the limit of low frequencies, the asymptotic data were fit even better ... by omega_0 = 153009 cm^-1'",
     "variable": "omega: wavenumber in cm^-1",
     "state": "20 C, 760 Torr (c in 1e-19 esu)",
     "density": "ideal",
     "range": "omega_L < 2 omega_0 / 3",
     "coefficients": {
       "omega_0": "158e3",
       "omega_0_uncertainty": "5e3",
       "sigma": "1.76"
     },
     "check": "Not checked against Bishop and Lam (not in the library). Table VII's He values 1.83 (515 nm) and 1.80 (633 nm) = 1.76 x F^B_1221 'agree with the values calculated in BL ... to within 0.5 %' (footnote c)."
   }

The He dispersion that justifies formula B; He's LWL c1122 = c1212 = c1221 = sigma/24 \(A0 = B0 = 0\)\.

Corrections
-----------

.. code-block:: text

   [
     {
       "dataset": "kerr_ratio_carusotto_H2",
       "row": "515",
       "column": "value",
       "printed": "3.2",
       "corrected": "32.2",
       "reason": "A lost digit: the He-normalized H2 Kerr constant is printed 3.2.",
       "evidence": "Table I's footnote b values are the normalized value times 1.83 (the He theory at 515 nm): N2 129 -> 236, O2 281 -> 514 (515 printed), Ar 25.5 -> 46.7; for H2 the printed b value 59 requires 59 / 1.83 = 32.2, and Carusotto's absolute H2 64.1 over their He 1.99 is 32.2. Table image checked: '3.2^a'."
     }
   ]

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.