buckingham_1968b
================

A\. D\. Buckingham and B\. J\. Orr, "Electric birefringence in molecular hydrogen", Proc\. R\. Soc\. Lond\. A 305, 259 \(1968\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/buckingham_1968b.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1098/rspa\.1968\.0117 <https://doi.org/10.1098/rspa.1968.0117>`__

**Source kind:** measurement

**Recorded technique:** Absolute dc Kerr effect of H2 \(British Oxygen high purity, \> 99\.9 %\) at 6328 A \(Spectra\-Physics 125 He\-Ne laser\) with the phase\-sensitive apparatus of Boyle et al\. 1966 and Buckingham & Dunmur 1968, the Kerr cell jacketed and thermostatted \(\-30 to \+60 C, \+\-0\.2 C, electrodes 46 cm\); 25\-85 atm, fields 7\-9 kV/cm; over 220 measurements in 17 sets, one temperature each\. mK0 = \(2/27\) V\_m \(n\_Z \- n\_X\)/F\_Z^2 fitted per set to mK0 = A\_K \+ \[B\_K \+ A\_K\(2 A\_eps \+ A\_r/2\)\] V\_m^\-1 \(Eq\. 11\), molar volumes from Michels & Goudeket's virial coefficients, A\_eps = 2\.02 and A\_r = 2\.06 cm^3\. D2 \(Matheson, \> 99\.5 %\) at 12 atm only, ten temperatures from \-30 to \+32 C \(pp\. 262\-263\)\.

**Materials in structured entries:** D2, H2

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

**Contents:** 6 datasets; 0 formulas.

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

Pages are the journal's \(259\-269\); pdf page 1 is the JSTOR cover, so p\. = pdf page \+ 257\. Not to be confused with buckingham\_1968 \(Buckingham & Dunmur, the inert gases\)\. The library's validation notes a table without caption \(the B\_0 table of p\. 262\) and an unmatched figure \(Fig\. 1\); Tables 1 and 2 agree with their images\.

THEORY \(pp\. 260\-262\)\: the quantum theory of the Kerr effect of a dilute gas of 1Sigma diatomic molecules\. pi\_ab = alpha\_ab \+ beta\_ab,c F\_c \+ \(1/2\) gamma\_ab,cd F\_c F\_d \(Eq\. 2; the Taylor\-series convention\); gamma = \(1/10\)\(3 gamma\_ab,ab \- gamma\_aa,bb\) \(Buckingham's dc Kerr gamma\_K\); mK = \(2/27\) V\_m lim \(n\_Z \- n\_X\)/F\_Z^2 \(Eq\. 7\); for non\-dipolar molecules mK = \(4 pi N/405\){5 gamma \+ \(kT\)^\-1 \(alpha\_par^\(0\) \- alpha\_perp^\(0\)\)\(alpha\_par \- alpha\_perp\)\(1 \- sigma\_0 \+ \(8/15\) sigma\_0^2 \+ \.\.\.\)} \(Eq\. 9\), sigma\_0 = hcB\_0/kT\: the quantum correction factor is 0\.76 for H2, 0\.87 for D2, 0\.99 for N2 at 300 K \(p\. 262, B\_0 = 59\.34, 29\.91, 2\.00 cm^\-1\)\. Appendix Eq\. \(A9\) gives the form with nuclear\-spin statistics\. shelton\_1987b later finds the optical\-frequency orientation term 3/4 of this classical form \('Buckingham's ansatz \.\.\. is only valid in the static limit'\)\.

RESULTS\. Table 1 \(p\. 263\)\: A\_K and B\_K per set; 'It is estimated from table 1 that A\_K can be determined with a reproducibility better than \+\-2 %\. However, the uncertainty of the measurements, which is dependent on the calibration of voltmeters and the nulling Kerr cell, could be \+\-5 %' \(p\. 264\)\. gamma \(p\. 264\)\: from each A\_K with Eq\. \(9\), \(alpha\_par^\(0\) \- alpha\_perp^\(0\)\) = 0\.300 A^3 \(Kolos & Wolniewicz 1967\), \(alpha\_par \- alpha\_perp\) = 0\.314 A^3 at 6328 A \(Bridge & Buckingham 1966\), hcB\_0/k = 85\.37 K\: Table 2; 'Their mean value is 0\.277 e\.s\.u\. and their standard deviation \+\-0\.008 e\.s\.u\. The absolute error, due to calibration uncertainties, is not greater than \+\-0\.03 e\.s\.u\.' \(abstract\: \(0\.28 \+\- 0\.03\) x 10^\-36 e\.s\.u\.\)\. In au \(5\.0367e\-40 esu\)\: 550 \+\- 60\. The gamma term is only about 45 % of A\_K and depends on the assumed anisotropies\. D2 \(pp\. 264\-265\)\: A\_K 'calculated by assuming that B\_K for deuterium equals that of hydrogen \.\.\. Their average value is \(5\.9 \+\- 0\.6\) x 10^14 e\.s\.u\.' \(misprinted exponent, erratum below\); gamma\(D2\) '0\.24 \+\- 0\.05 e\.s\.u\.' \(10^\-36\), 'less than 10^36 gamma for H2 by 14 %', more than the 1 % expected\. B\_K\(H2\) = \(1\.34 \+\- 0\.2\) x 10^\-12 e\.s\.u\. over the range, no trend detected; calculated from the pair anisotropy 6 alpha^2/R^3 and a Lennard\-Jones potential \(29\.2 K, 2\.87 A\)\: 0\.50, 0\.58, 0\.66 at 332, 284, 245 K, 'considerably smaller than the experimental result' \(p\. 266\)\. Slope dA\_K/dT^\-1\: experiment \(8\.0 \+\- 2\) x 10^\-12 e\.s\.u\. deg against the quantum 6\.8 x 10^\-12 at 284 K and the classical 12\.75 x 10^\-12 \(p\. 266\)\. Fig\. 1\: the A\_K points scatter \+\-1\.3 % about the curve from the mean gamma \(p\. 266\)\. Other values quoted, not stored\: Bruce 1933's upper limit 10^14 mK0 \< 8\.5 e\.s\.u\. \(82 atm, 4550 A\) against this work's 6\.2 at 35 C and 82 atm; Guillien's liquid H2 mK; J\. F\. Ward's THG 10^36 gamma\_thg = 0\.45 \+\- 0\.05 e\.s\.u\. at 6943 A \(personal communication\); McLean & Yoshimine's calculated static gamma\_3333 = 0\.20 x 10^\-36; the H atom's 0\.6714 x 10^\-36 \(Sewell 1949\)\.

SUPERSEDED\: tammer\_1990 \(and tammer\_1992, after its field calibration\) measured the same quantity ten times more precisely; tammer\_1990 Table 2 lists this paper as 3\.43\(37\) x 10^\-62 C^4 m^4 J^\-3 \(H2\) and 3\.0\(6\) \(D2\), i\.e\. 0\.277 and 0\.24 x 10^\-36 esu, and finds its B\_K^\(4\) twice its own\. All datasets here are use = 'check'\.

Reproductions elsewhere\: bishop\_1991/expt\_dc\_kerr\_H2 \(row buckingham\_orr\_1968, 550 \+\- 60 au\), tammer\_1990/table2\_literature\_\* \('ref 3'\), carusotto\_1992 notes \(3\.81 and 3\.31 x 10^\-17 cm^2 statV^\-2 amagat at 245 and 332 K\: not values printed here, a conversion of Table 1\), hellwarth\_1990/kerr\_buckingham\_orr\_H2\. Not edited here, citing this paper\: lundeen\_1983, rosasco\_1985, ward\_1979, ward\_1969\.

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

Datasets
--------

buckingham\_1968b/table1\_A\_K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_A_K_H2",
     "material": "H2",
     "file": "H2/buckingham_1968b__table1_A_K_H2.csv",
     "table": "tbl_4157737602db",
     "quantity": "molar_kerr_constant",
     "unit": "esu",
     "scale": 1e-14,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "check",
     "uncertainty": {
       "relative": 0.05,
       "level": "not stated"
     },
     "parameters": {
       "wavelength_nm": 632.8
     }
   }

Table 1 \(p\. 263\)\: the first Kerr virial coefficient A\_K \(the zero\-density molar Kerr constant, per mole, e\.s\.u\.\) of H2 for 17 sets at 245\.4\-332\.4 K, 25\-85 atm, 6328 A\. Includes the orientation term\. Reproducibility better than \+\-2 %; uncertainty \(calibration\) 'could be \+\-5 %' \(p\. 264\), recorded as a relative 5 % \(level not stated\)\. Superseded by tammer\_1990/tammer\_1992\.

buckingham\_1968b/table1\_B\_K\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_B_K_H2",
     "material": "H2",
     "file": "H2/buckingham_1968b__table1_B_K_H2.csv",
     "table": "tbl_4157737602db",
     "quantity": "kerr_virial_coefficient",
     "unit": "esu",
     "scale": 1e-12,
     "abscissa": "temperature",
     "abscissa_unit": "K",
     "use": "check",
     "uncertainty": {
       "level": "not stated"
     },
     "parameters": {
       "wavelength_nm": 632.8,
       "order": 2
     }
   }

Table 1 \(p\. 263\)\: the second Kerr virial coefficient B\_K \(e\.s\.u\.\) of H2 per set, 245\.4\-332\.4 K\. 'B\_K of hydrogen is found from table 1 to be \(1\.34 \+\- 0\.2\) x 10^\-12 e\.s\.u\. over the experimental temperature range\. The experimental precision was insufficient to allow a trend with temperature to be detected' \(p\. 266\)\. No per\-set uncertainty is printed\.

buckingham\_1968b/table2\_gamma\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table2_gamma_H2",
     "material": "H2",
     "file": "H2/buckingham_1968b__table2_gamma_H2.csv",
     "table": "tbl_a2e5fa68c008",
     "quantity": "hyperpolarizability",
     "unit": "esu",
     "scale": 1e-36,
     "abscissa_unit": "angstrom",
     "wavelength_medium": "standard_air",
     "columns": {
       "temperature": "K"
     },
     "use": "check",
     "uncertainty": {
       "absolute": 0.03,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K"
     }
   }

Table 2 \(p\. 264\)\: 10^36 gamma \(e\.s\.u\.\) of H2 per set \(temperature as the extra column\), from each A\_K minus the quantum\-corrected orientation term of Eq\. \(9\) with the anisotropies of Kolos & Wolniewicz \(static 0\.300 A^3\) and Bridge & Buckingham \(optical 0\.314 A^3\)\: Buckingham's gamma\_K at 6328 A, electronic plus vibrational\. Mean 0\.277, standard deviation \+\-0\.008; 'The absolute error, due to calibration uncertainties, is not greater than \+\-0\.03 e\.s\.u\.' \(a bound, applied to every value\)\. Superseded \(tammer\_1992\: 4\.68\(14\) x 10^\-62 C^4 m^4 J^\-3 = 0\.378 x 10^\-36 esu\)\.

buckingham\_1968b/text\_gamma\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_gamma_H2",
     "material": "H2",
     "table": "text",
     "quantity": "hyperpolarizability",
     "unit": "esu",
     "scale": 1e-36,
     "abscissa_unit": "angstrom",
     "wavelength_medium": "standard_air",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "bound"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K"
     }
   }

1 inline points in the source record.

p\. 264\: 'Their mean value is 0\.277 e\.s\.u\. and their standard deviation \+\-0\.008 e\.s\.u\. The absolute error, due to calibration uncertainties, is not greater than \+\-0\.03 e\.s\.u\.'; abstract\: gamma = \(0\.28 \+\- 0\.03\) x 10^\-36 e\.s\.u\. \(550 \+\- 60 au\)\. The dc Kerr gamma\_K of H2 at 6328 A over 245\-332 K; electronic plus vibrational \(orientation term subtracted with Eq\. 9\)\. The error is a bound\. Superseded by tammer\_1992\.

buckingham\_1968b/text\_A\_K\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_A_K_D2",
     "material": "D2",
     "table": "text",
     "quantity": "molar_kerr_constant",
     "unit": "esu",
     "scale": 100000000000000.0,
     "abscissa_unit": "angstrom",
     "wavelength_medium": "standard_air",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 264\: 'The measurements on deuterium were much less accurate than those for hydrogen, owing to the small quantity available\. Values of A\_K, calculated by assuming that B\_K for deuterium equals that of hydrogen, were insufficiently precise to yield a meaningful temperature dependence\. Their average value is \(5\.9 \+\- 0\.6\) x 10^14 e\.s\.u\.' D2 at 12 atm, ten temperatures from \-30 to \+32 C\. The exponent is misprinted \(erratum below\: 10^\-14, as Table 1's 10^14 A\_K for H2\)\. Level of the error not stated\.

buckingham\_1968b/text\_gamma\_D2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_gamma_D2",
     "material": "D2",
     "table": "text",
     "quantity": "hyperpolarizability",
     "unit": "esu",
     "scale": 1e-36,
     "abscissa_unit": "angstrom",
     "wavelength_medium": "standard_air",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "process": "dc_kerr",
       "convention": "T",
       "part": "electronic_vibrational",
       "component": "K"
     }
   }

1 inline points in the source record.

p\. 265\: 'An approximate estimate of the hyperpolarizability 10^36 gamma of deuterium can be obtained in a similar manner\. The result is 0\.24 \+\- 0\.05 e\.s\.u\., which is less than 10^36 gamma for H2 by 14 %\. This difference is greater than expected from approximate theoretical considerations which indicate that gamma\(D2\) should be less than gamma\(H2\) by little more than 1 %\.' dc Kerr gamma\_K of D2 at 6328 A, electronic plus vibrational\. Superseded \(tammer\_1990\: 4\.17\(16\) x 10^\-62 SI\)\.

Formulas
--------

No formulas are recorded.

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

.. code-block:: text

   [
     {
       "dataset": "text_A_K_D2",
       "row": "",
       "column": "scale",
       "printed": "100000000000000.0",
       "corrected": "1e-14",
       "reason": "p. 264 prints the D2 average A_K as '(5.9 +- 0.6) x 10^14 e.s.u.'; a molar Kerr constant of 10^14 e.s.u. is impossible, and Table 1 gives H2's as '10^14 A_K (e.s.u.)' = 5.5-6.3, i.e. A_K = 5.5-6.3 x 10^-14 e.s.u.; D2's must be of the same order (the orientation term is somewhat larger and gamma similar).",
       "evidence": "Page image of p. 264 checked: '(5·9 ± 0·6) × 10^14 e.s.u.' is printed, not an extraction error. Table 1 (p. 263, image checked) heads the H2 column '10^14 A_K (e.s.u.)'. 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.