tammer_1992
===========

R\. Tammer, K\. Löblein, K\. H\. Peting and W\. Hüttner, "Field calibrated measurements of the dc Kerr constants of helium and molecular hydrogen", Chem\. Phys\. 168, 151 \(1992\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/tammer_1992.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/0301\-0104\(92\)80117\-e <https://doi.org/10.1016/0301-0104%2892%2980117-e>`__

**Source kind:** measurement

**Recorded technique:** Absolute dc Kerr effect \(static\-field\-induced birefringence\) of H2 and He at 632\.8 nm \(He\-Ne laser\), with the Senarmont\-type ellipsometer and Kerr cell of Tammer & Hüttner \(tammer\_1990\), whose field integral is here calibrated absolutely by the rotational Stark effect of OCS\: the J = 7 \<\- 6 transition near 85139\.1 MHz was recorded in the Kerr capacitor at several fields \(12 Stark spectra\), simulated from the mechanically measured plate distance d\(y\) and the OCS dipole moment and anisotropy of Lahaye et al\. \(1986\), and the mean gap adjusted to fit\: integral of E^2 dy = \(2\.492 \+\- 0\.010\) x 10^12 V^2 m^\-1 at 12 kV, edge correction included \(pp\. 152\-154\)\. The new spacers \(FRIALIT\) replaced those of the 1990 work; the 1990 H2 data were re\-evaluated by comparison with new K\(T0, p\) at T0 = 303\.7 K \(correction factor 1\.0637 \+\- 0\.0031\)\. He\: 22 pressures between 76 and 97 bar at 303\.7 K \(lower pressures arced\), fitted by a straight line through the origin; H2\: 12 pressures, 5\.95\-49\.3 bar, at 303\.7 K \(p\. 154, 156\-157\)\.

**Materials in structured entries:** H2, He

**Dataset quantities:** hyperpolarizability, hyperpolarizability\_ratio, kerr\_constant, kerr\_virial\_coefficient, molar\_kerr\_constant

**Contents:** 12 datasets; 0 formulas.

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

Pages are the journal's \(151\-158; p\. = pdf page \+ 150\)\.

DEFINITIONS \(pp\. 151\-152\)\. n\_z \- n\_x = lambda K E^2 \(Eq\. 1\); K = \(27/\(2 lambda\)\) N A\_K for a dilute gas \(Eq\. 3; N moles per volume\) with A\_K = \(N\_A/\(81 eps0\)\) \[gamma \+ \(Delta alpha Delta alpha^0\)\_eff / 5 k\_B T\] \(Eq\. 4\), 'the first molar Kerr virial coefficient \.\.\. identical with the molar Kerr constant for an ensemble of non\-interacting molecules'; gamma = \(3/2\)\(gamma\_z \- gamma\_x\) \(Eq\. 5\), 'the anisotropy of the KE second hyperpolarizability'\: Buckingham's gamma\_K, the dc Kerr gamma\(\-w; w, 0, 0\) in the Taylor\-series convention \(the static expansion of Eq\. 9 carries \(1/6\) gamma E^3; shelton\_1994 Table VI reproduces the He value as 44\.3 au = 27\.6e\-64 / 6\.2354e\-65\)\. Molar Kerr constant mK = A\_K \+ B\_K N \+ C\_K N^2 \+ \.\.\. \(Eq\. 6\) with K = \(27/2\)\(f\(n, eps\)/\(lambda n\)\) N mK \(Eq\. 7\), f a local\-field function; the two used, f^\(2\) = \(\(n^2 \+ 2\)/3\)\(\(eps \+ 2\)/3\) and f^\(4\) = \(\(n^2 \+ 2\)/3\)^2\(\(eps \+ 2\)/3\)^2, are defined in tammer\_1990 \(Eqs\. 13\-14\) and give the superscripts \(2\) and \(4\)\. The unit C^4 m^4 J^\-3 of gamma is the SI unit of the optmat vocabulary; A\_K in C^2 m^5 J^\-2 mol^\-1, B\_K in C^2 m^8 J^\-2 mol^\-2 \(as printed\)\.

PARTS\. For H2, A\_K includes the orientation term; gamma is A\_K minus the orientation term \(Delta alpha Delta alpha^0\)\_eff/5kT, calculated \(tammer\_1990, Eq\. 6\) from the J\-dependent ab initio anisotropies of Bishop & Cheung \(1980\) and Rychlewski \(1980\), 'The error of the so determined orientation term is less than 0\.2% and therefore negligible' \(p\. 158\)\: an electronic plus vibrational gamma\_K\. Checked here\: 81 eps0 A\_K/N\_A \- gamma gives the same orientation term in this Table 1 and in tammer\_1990's Table 1 at every temperature \(to 5e\-4 in 1e\-62 units\)\. He\: an atom, no orientation term, electronic\.

TABLE 1 \(p\. 155\)\: 'Corrected H2 dc KE data from table 1 of ref\. \[3\] \[tammer\_1990\], lambda = 632\.8 nm \.\.\. The H2 data at T0 = 303\.7 K in the last row have been obtained in the present work\. The errors given in parentheses in units of the least significant figure are standard deviations'; 'the errors are statistical contributions only' \(p\. 155\)\. Maximum pressure 115 bar\. Datasets\: A\_K \(the 13 re\-corrected rows, check; the new row, primary\), B\_K^\(4\) and B\_K^\(2\) \(kerr\_virial\_coefficient, order 2, check\), gamma \(check\)\. Not taken\: b' \(the p^2 coefficient of Eq\. 12, 10^\-24 C^2 m J^\-2 bar^\-2\), a and b \(K = a rho \+ b rho^2, tammer\_1990 Eq\. 12\), and 10^29 Delta = A\_K \- A\_K^calc \(the header's capital Delta is extracted as 'A'; the new row prints '\-'\)\. 'The total error of the new value A\_K listed in the last row of table 1 is the sum of a statistical \(one standard deviation, see table 1\) and a 1\.3% systematic contribution \.\.\. uncertainties for T\: 0\.11%, p\: 0\.25%, compensation current\: 0\.5% and field integral\: 0\.4%\. The previously assigned \[3\] field integral error was 0\.7%' \(p\. 155; the four add linearly to 1\.26 %\)\.

THE 1\.0637 CORRECTION\. 'Comparison with A\_K\(T0\) calculated with the ref\. \[3\] molecular parameters led to the correction factor 1\.0637 \+\- 0\.0031, in the sense that all values K, mK, and A\_K given in ref\. \[3\] should be multiplied by this number' \(p\. 154\)\. Checked here against tammer\_1990 Table 1\: the re\-corrected Table 1 is not the 1990 table times one factor\. A\_K\(1992\)/A\_K\(1990\) is 1\.0634 on average \(standard deviation 0\.0022, range 1\.0592 at 376\.5 K to 1\.0684 at 219\.5 K\), a\(1992\)/a\(1990\) 1\.0635 \(1\.0599\-1\.0660\), and b, B\_K^\(4\), B\_K^\(2\) differ by 0\.86\-1\.30 times\: the data were refitted, not rescaled\. The row printed 376\.5 K here is 376\.8 K in tammer\_1990 Table 1; its orientation term here \(3\.5731e\-62, from 81 eps0 A\_K/N\_A \- gamma\) corresponds to 376\.5 K rather than 376\.8 K \(3\.5712e\-62 x 376\.8/376\.5 = 3\.5740e\-62\), so the new table was evaluated at 376\.5 K\. Which temperature is right is not stated\.

TABLE 2 \(p\. 155\), gamma\(H2\) at 632\.8 nm\: this work 4\.68\(14\) x 10^\-62 C^4 m^4 J^\-3, 'Remeasured after the field calibration\. The error contains a systematic contribution of 1\.3% in the original Kerr data'; 'Its error is obtained from that of A\_K in the last row of table 1 neglecting the uncertainty in the orientation term' \(p\. 155\)\. Checked\: \(0\.019 \+ 0\.013 x 7\.455\) x 10^\-29 x 81 eps0/N\_A = 0\.138 x 10^\-62\. In au \(6\.235377e\-65\)\: 751 \+\- 22\. Literature rows \(reproduced\)\: Shelton 1990 ESHG 4\.54\(3\) and Rosasco & Hurst 1986 ac Kerr 4\.52\(23\), both 'Extrapolated to dc KE using dispersion relations, see ref\. \[3\]\. Extrapolation errors and the uncertainty arising from normalizing to a theoretical gamma\_z\(He\) value \[19\] are not included'; theory 4\.53 \(Bishop, Pipin & Cybulski 1991\), 4\.45 \(Bishop, Pipin & Rérat 1990; the reference list prints 'J\. Phys\. Chem\. 92 \(1990\) 1902', tammer\_1990 'J\. Chem\. Phys\. 92 \(1990\) 1902'\), 4\.40 \(Bishop & Lam 1988\)\. The authors' weighted mean of these, 4\.55 x 10^\-62, 'is known to an uncertainty of less than \+\-3%' \(p\. 157\)\.

HELIUM \(pp\. 155\-156\)\. 'The error bars are standard deviations from the statistics of repeated field settings\. A straight line was fitted through the entries and the origin, resulting in the slope K/p = 1\.937\(10\) x 10^\-20 C^2 m J^\-2 bar^\-1' \(Eq\. 11; misprinted\: 10^\-21 is meant, erratum below\)\. 'higher order virial coefficients can be neglected \.\.\. estimating B\_K with aid of the theory of Buckingham et al\. \[17\]\: For p = 80 bar, a value amounting to only 0\.5% of A\_K'\: the pair term is not removed\. A\_K^\(2\) = 2\.321\(11\) and A\_K^\(4\) = 2\.312\(12\) x 10^\-30 C^2 m^5 J^\-2 mol^\-1 \(statistical errors only\); 'Adopting the first one we obtain, according to eq\. \(4\), the Kerr hyperpolarizability anisotropy of the helium atom as given in the first row of table 3' \(27\.6\(5\), 'The error contains a systematic contribution of 1\.3%'\)\. Checked\: 81 eps0 x 2\.321e\-30/N\_A = 27\.64e\-64; \(0\.011 \+ 0\.013 x 2\.321\) x 1\.1909e\-3 = 0\.49e\-64\. In au\: 44\.3 \+\- 0\.8 \(as shelton\_1994 Table VI\)\. Literature \(Table 3, reproduced\)\: Buckingham & Dunmur 1968 33\(2\) \(buckingham\_1968\), Boyle et al\. 1966 32\.0\(53\), theory 27\.57 \(Bishop & Pipin 1989 = bishop\_1989\) and 26\.78 \(Bishop & Lam 1988\)\. 'the present investigation is one order of magnitude more accurate' \(p\. 157\)\.

RATIO \(pp\. 156\-157\)\. 'gamma\(H2\) and gamma\(He\) have been determined with the same buildup and optical alignment of the Kerr apparatus\. Systematic errors therefore cancel when their ratio is considered\: we obtain gamma\(H2\)/gamma\(He\) = 16\.94\(17\) which compares with 16\.43 when the corresponding theoretical values \[6,8\] are combined\. The error estimate of the former value means one standard deviation sigma and presumes that the hydrogen orientation term in eq\. \(4\) as calculated in ref\. \[3\] is correct\.' Checked\: 4\.682e\-62/27\.64e\-64 = 16\.94\.

UNLABELLED TABLE \(p\. 157, 'table 4' in the text; tbl\_2b285a6d3881, checked against the image; not stored, as no quantity holds a Kerr constant against pressure\)\: K of H2 at 303\.7 K and 632\.8 nm at 12 pressures from 5\.953 to 49\.274 bar \(10^18 K from 0\.3733\(42\) to 3\.0492\(35\) C^2 m J^\-2\), with the mass density, 10^4\(n \- 1\), 10^4\(eps \- 1\) and the molar Kerr constants mK^\(4\), mK^\(2\) \(7\.43\-7\.53 x 10^\-29\); 'Extrapolation to zero density leads to A\_K = 7\.46\(2\) x 10^\-29 \.\.\. in the last line of table 1' \(caption\), offered as a calibration standard for dc Kerr measurements \(p\. 157\)\. Eqs\. \(13\)\-\(14\)\: K = \(27/\(2 lambda\)\)\(\(p/k\_B T\) A\_K \+ b' p^2\) with b'\-bar = \-\(8\.1 \+\- 5\.4\) x 10^\-24 C^2 m J^\-2 bar^\-2, 'the error meaning three standard deviations', the weighted mean of Table 1's b' \(p\. 157\)\: a formula for H2 K\(T, p\) in the paper \(the A\_K term is per unit of k\_B T, whose units the text does not reconcile; not recorded as a formula\)\.

Reproductions elsewhere\: shelton\_1994/table6\_He\_dc\_kerr\_expt \(row 'ref 11', 44\.3 \+\- 0\.8 au\)\. The library copy has no validation warnings; the Table 2 and 3 cells were read from the JSON and agree with the images\.

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

Datasets
--------

tammer\_1992/table1\_A\_K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_K_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table1_A_K_H2.csv",
     "table": "tbl_4d048dca076d",
     "quantity": "molar_kerr_constant",
     "unit": "C2 m5 J-2 mol-1",
     "scale": 1e-29,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "wavelength_nm": 632.8
     }
   }

Table 1 \(p\. 155\), rows 1\-13\: A\_K of H2 against temperature, 196\.1\-411\.7 K, from tammer\_1990's Table 1 re\-evaluated with the calibrated field integral \(the 1990 values times about 1\.0637, refitted; see the record's notes\)\. Statistical standard deviations only; the systematic part is not restated for these rows \(tammer\_1990 gave 1\.1 % for p, T and E; the field\-integral part is now 0\.4 %\)\. The row printed 376\.5 K is 376\.8 K in tammer\_1990\. Includes the orientation term \(Eq\. 4\)\.

tammer\_1992/table1\_A\_K\_H2\_this\_work
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_K_H2_this_work",
     "material": "H2",
     "file": "H2/tammer_1992__table1_A_K_H2_this_work.csv",
     "table": "tbl_4d048dca076d",
     "quantity": "molar_kerr_constant",
     "unit": "C2 m5 J-2 mol-1",
     "scale": 1e-29,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma",
       "systematic_relative": 0.013
     },
     "parameters": {
       "wavelength_nm": 632.8
     }
   }

Table 1 \(p\. 155\), last row\: A\_K of H2 at 303\.7 K measured in this work after the field calibration, 7\.455\(19\) x 10^\-29 C^2 m^5 J^\-2 mol^\-1 \(the caption of the unlabelled table\: 7\.46\(2\)\)\. sigma\: the statistical standard deviation; 'The total error of the new value A\_K \.\.\. is the sum of a statistical \(one standard deviation\) and a 1\.3% systematic contribution' \(p\. 155\), recorded as systematic\_relative \(its level is not stated\: the linear sum of the stated T, p, compensation\-current and field\-integral uncertainties\)\. Includes the orientation term \(Eq\. 4\); table2\_gamma\_H2 is the same measurement with it subtracted\: fit one or the other\.

tammer\_1992/table1\_B\_K4\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_K4_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table1_B_K4_H2.csv",
     "table": "tbl_4d048dca076d",
     "quantity": "kerr_virial_coefficient",
     "unit": "C2 m8 J-2 mol-2",
     "scale": 1e-34,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "wavelength_nm": 632.8,
       "order": 2
     }
   }

Table 1 \(p\. 155\)\: the second molar Kerr virial coefficient B\_K^\(4\) of H2 \(Eq\. 6, with the local\-field function f^\(4\) of tammer\_1990 Eq\. 14\), 13 re\-corrected rows and the new 303\.7 K row \(row '303\.7 \(this work\)'\)\. Standard deviations \(statistical\)\.

tammer\_1992/table1\_B\_K2\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_K2_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table1_B_K2_H2.csv",
     "table": "tbl_4d048dca076d",
     "quantity": "kerr_virial_coefficient",
     "unit": "C2 m8 J-2 mol-2",
     "scale": 1e-34,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "wavelength_nm": 632.8,
       "order": 2
     }
   }

Table 1 \(p\. 155\)\: the second molar Kerr virial coefficient B\_K^\(2\) of H2 \(Eq\. 6, with the local\-field function f^\(2\) of tammer\_1990 Eq\. 13\), 13 re\-corrected rows and the new 303\.7 K row \(row '303\.7 \(this work\)'\)\. Standard deviations \(statistical\)\. A\_K does not depend on the choice of f; B\_K does \(tammer\_1990 p\. 159\)\.

tammer\_1992/table1\_gamma\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_gamma_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table1_gamma_H2.csv",
     "table": "tbl_4d048dca076d",
     "quantity": "hyperpolarizability",
     "unit": "SI",
     "scale": 1e-62,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K"
     }
   }

Table 1 \(p\. 155\), last column\: gamma = \(3/2\)\(gamma\_z \- gamma\_x\) of H2 at 632\.8 nm, from A\_K at each temperature \(the extra column\) minus the calculated orientation term \(tammer\_1990 Eqs\. 5\-6\), 13 re\-corrected rows \(4\.567\-4\.803\) and the new row '303\.7 \(this work\)' \(4\.682\(22\), the value of table2\_gamma\_H2 with its statistical error only\)\. Statistical standard deviations\. The 13 rows scatter more \(standard deviation 0\.076, mean 4\.699\) than their errors \(0\.02\-0\.04\) and than the same rows in tammer\_1990 \(0\.046\), and fall from 4\.80 at 196\.1 K to 4\.57 at 411\.7 K; tammer\_1990 found no temperature dependence\.

tammer\_1992/table2\_gamma\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_gamma_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table2_gamma_H2.csv",
     "table": "tbl_05229ef25c1e",
     "quantity": "hyperpolarizability",
     "unit": "SI",
     "scale": 1e-62,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K",
       "temperature_k": 303.7
     }
   }

Table 2 \(p\. 155\) and abstract\: gamma\(H2\) = 4\.68\(14\) x 10^\-62 C^4 m^4 J^\-3 \(751 \+\- 22 au\), the dc Kerr hyperpolarizability anisotropy \(3/2\)\(gamma\_z \- gamma\_x\) at 632\.8 nm and 303\.7 K, 'Remeasured after the field calibration'\. Electronic plus vibrational\: the orientation term, calculated from ab initio anisotropies, is subtracted from A\_K \(Eq\. 4\)\. The error is the statistical standard deviation of A\_K plus a 1\.3 % systematic part of A\_K, added linearly and propagated to gamma without the \(negligible, \< 0\.2 %\) uncertainty of the orientation term \(p\. 155\)\: its level is not stated\. Same measurement as table1\_A\_K\_H2\_this\_work\.

tammer\_1992/table2\_literature\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_literature_H2",
     "material": "H2",
     "file": "H2/tammer_1992__table2_literature_H2.csv",
     "table": "tbl_05229ef25c1e",
     "quantity": "hyperpolarizability",
     "unit": "SI",
     "scale": 1e-62,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "reproduced",
     "reproduced_from": [
       "shelton_1990",
       "rosasco_1986",
       "bishop_1991",
       "bishop_1990b",
       "D. M. Bishop and B. Lam, J. Chem. Phys. 89, 1571 (1988)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K"
     }
   }

Table 2 \(p\. 155\), the comparison rows, all given as the dc Kerr gamma\_K of H2 at 632\.8 nm\: 'ref 19' Shelton 1990 ESHG \(shelton\_1990\), 4\.54\(3\), and 'ref 20' Rosasco & Hurst 1986 ac Kerr \(rosasco\_1986\), 4\.52\(23\), both 'Extrapolated to dc KE using dispersion relations, see ref\. \[3\]\. Extrapolation errors and the uncertainty arising from normalizing to a theoretical gamma\_z\(He\) value \[19\] are not included' \(note b; converted values, not the originals' numbers\); theory 'ref 6' Bishop, Pipin & Cybulski 1991 \(bishop\_1991, 4\.53\: its Table XVI total gamma^K at 632\.8 nm\), 'ref 5' Bishop, Pipin & Rérat 1990 \(4\.45; = bishop\_1990b, re\-pointed 2026\-09\-27\: its Table X gamma^K\(H2, 6328 A\) = 714 au x 6\.23538e\-65 = 4\.452e\-62, checked\) and 'ref 4' Bishop & Lam 1988 \(4\.40\)\. Level of the errors not stated\.

tammer\_1992/table3\_gamma\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table3_gamma_He",
     "material": "He",
     "file": "He/tammer_1992__table3_gamma_He.csv",
     "table": "tbl_2ce09dc63f8c",
     "quantity": "hyperpolarizability",
     "unit": "SI",
     "scale": 1e-64,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic",
       "component": "K",
       "temperature_k": 303.7
     }
   }

Table 3 \(p\. 156\) and abstract\: gamma\(He\) = 27\.6\(5\) x 10^\-64 C^4 m^4 J^\-3 \(44\.3 \+\- 0\.8 au\), the dc Kerr hyperpolarizability anisotropy \(3/2\)\(gamma\_z \- gamma\_x\) at 632\.8 nm and 303\.7 K, from A\_K^\(2\) = 2\.321\(11\) x 10^\-30 \(text\_A\_K\_He\) by Eq\. \(4\); electronic\. Measured at 76\-97 bar, fitted through the origin; the pair term \(B\_K, about 0\.5 % of A\_K at 80 bar by Buckingham et al\.'s theory\) is not removed\. 'The error contains a systematic contribution of 1\.3%' \(note a\)\: the statistical standard deviation of A\_K plus 1\.3 % of A\_K, added linearly; level not stated\. Checked\: 27\.64 and 0\.49 from A\_K^\(2\)\.

tammer\_1992/table3\_literature\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table3_literature_He",
     "material": "He",
     "file": "He/tammer_1992__table3_literature_He.csv",
     "table": "tbl_2ce09dc63f8c",
     "quantity": "hyperpolarizability",
     "unit": "SI",
     "scale": 1e-64,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "reproduced",
     "reproduced_from": [
       "buckingham_1968",
       "boyle_1966",
       "bishop_1989",
       "D. M. Bishop and B. Lam, Phys. Rev. A 37, 464 (1988)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic",
       "component": "K"
     }
   }

Table 3 \(p\. 156\), the comparison rows for He at 632\.8 nm, in 10^\-64 C^4 m^4 J^\-3\: 'ref 15' Buckingham & Dunmur 1968 dc Kerr \(buckingham\_1968\), 33\(2\); 'ref 16' Boyle et al\. 1966 dc Kerr, 32\.0\(53\) \(boyle\_1966, re\-pointed 2026\-09\-27\: its \(2\.6 \+\- 0\.4\) x 10^\-38 esu is 51\.62 au = 32\.19\(50\) x 10^\-64; this reprint's conversion is 0\.6 % lower and its uncertainty 6 % larger, not explained\); theory 'ref 8' Bishop & Pipin 1989 \(bishop\_1989\), 27\.57; 'ref 7' Bishop & Lam 1988, 26\.78\. Level of the errors not stated; the authors think Buckingham & Dunmur's error 'probably underestimated' \(p\. 157\)\.

tammer\_1992/text\_A\_K\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_A_K_He",
     "material": "He",
     "table": "text",
     "quantity": "molar_kerr_constant",
     "unit": "C2 m5 J-2 mol-1",
     "scale": 1e-30,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 303.7
     }
   }

2 inline points in the source record.

p\. 156\: 'Using the two local\-field functions f^\(2\)\(n, eps\) and f^\(4\)\(n, eps\) discussed in ref\. \[3\] leads to the corresponding first virial Kerr coefficients A\_K^\(2\) = 2\.321\(11\) and A\_K^\(4\) = 2\.312\(12\), respectively, both in units of 10^\-30 C^2 m^5 J^\-2 mol^\-1 \(statistical errors only\)'\. He at 303\.7 K, 76\-97 bar, fit through the origin \(the pair term, about 0\.5 %, not removed\)\. The paper adopts A\_K^\(2\) for gamma \(table3\_gamma\_He, the same measurement\: fit one or the other\); the systematic 1\.3 % is not included here\.

tammer\_1992/text\_K\_per\_p\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_K_per_p_He",
     "material": "He",
     "table": "text",
     "quantity": "kerr_constant",
     "unit": "C2 m J-2 bar-1",
     "scale": 1e-20,
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "state": {
       "pressure_pa": 100000.0,
       "temperature_k": 303.7
     },
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 303.7
     }
   }

1 inline points in the source record.

Eq\. \(11\), p\. 156\: the phenomenological Kerr constant of He \(n\_z \- n\_x = lambda K E^2, Eq\. 1\) per unit pressure, K/p = 1\.937\(10\) x 10^\-20 C^2 m J^\-2 bar^\-1 as printed, the slope of a straight line through the origin and 22 points at 76\-97 bar, 303\.7 K \(Fig\. 2\)\: the Kerr constant at 1 bar and 303\.7 K of that linear fit \(the state records this; the pair term, about 0\.5 % at 80 bar, is inside the slope\)\. The exponent is misprinted\: 10^\-21 is meant \(erratum below\)\. Error\: the statistical standard deviation of the slope\.

tammer\_1992/text\_ratio\_H2\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_ratio_H2_He",
     "material": "H2",
     "table": "text",
     "quantity": "hyperpolarizability_ratio",
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "process": "dc_kerr",
       "part": "electronic_vibrational",
       "reference_material": "He",
       "component": "K",
       "temperature_k": 303.7
     }
   }

1 inline points in the source record.

pp\. 156\-157\: 'Systematic errors therefore cancel when their ratio is considered\: we obtain gamma\(H2\)/gamma\(He\) = 16\.94\(17\) which compares with 16\.43 when the corresponding theoretical values \[6,8\] are combined\. The error estimate of the former value means one standard deviation sigma and presumes that the hydrogen orientation term in eq\. \(4\) as calculated in ref\. \[3\] is correct\.' The dc Kerr gamma\_K of H2 \(electronic plus vibrational, orientation term subtracted\) over that of He \(electronic\), both at 632\.8 nm and 303\.7 K; from the same measurements as table2\_gamma\_H2 and table3\_gamma\_He \(4\.682e\-62/27\.64e\-64 = 16\.94\)\.

Formulas
--------

No formulas are recorded.

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

.. code-block:: text

   [
     {
       "dataset": "text_K_per_p_He",
       "row": "",
       "column": "scale",
       "printed": "1e-20",
       "corrected": "1e-21",
       "reason": "Eq. (11) prints K/p = 1.937(10) x 10^-20 C^2 m J^-2 bar^-1 for helium. With K = (27/(2 lambda)) N A_K (Eq. 3), N = p/RT, lambda = 632.8 nm and T = 303.7 K, the paper's own A_K^(2) = 2.321 x 10^-30 C^2 m^5 J^-2 mol^-1 gives K/p = 1.96 x 10^-21 per bar (1.2 % above 1.937, the local-field factor f^(2) at 80-97 bar); 10^-20 would imply A_K ten times larger, and gamma(He) = 276 x 10^-64. The same relation holds for the H2 table: 7.46 x 10^-29 gives K/p = 6.30 x 10^-20 per bar, against the measured 0.3733 x 10^-18 / 5.953 bar = 6.27 x 10^-20.",
       "evidence": "Page image of p. 156 checked (Eq. 11 prints 10^-20; not an extraction error). Fig. 2 (p. 156) plots K / 10^-19 C^2 m J^-2 against p: about 1.5-1.9 on its scale at 76-97 bar, i.e. K/p of about 2 x 10^-21 per bar. 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 </register>` for the checks and decisions.