birch_1991
==========

K\. P\. Birch, "Precise determination of refractometric parameters for atmospheric gases", J\. Opt\. Soc\. Am\. A 8, 647 \(1991\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/birch_1991.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/JOSAA\.8\.000647 <https://doi.org/10.1364/JOSAA.8.000647>`__

**Source kind:** measurement

**Recorded technique:** NPL automatic fringe\-counting air refractometer at 633 nm \(He\-Ne laser; 632\.99 nm in the Table 2 caption\) with a dual\-compartment Pyrex cell in a stirred water bath \(four calibrated platinum resistance thermometers\), quadrature signals analysed by Heydemann's method; each gas flowed through the cell and was measured repeatedly near atmospheric pressure \(99\.8\-103\.7 kPa\) at about 14\.66 and 19\.5 degrees C; pressure from a Ruska DDR6000 barometer; the refractometer checked against Edlen's equation with dry air before each gas \(pp\. 647\-648\)\.

**Materials in structured entries:** Ar, CO2, He, Kr, N2, N2O, Ne, O2

**Dataset quantities:** polarizability, refractivity

**Contents:** 41 datasets; 0 formulas.

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

Reduction \(p\. 648\)\: the density d = p m/\(Z R T\) \(Eq\. 2\.1\) with the compressibility factor Z from Dymond and Smith's compilation of virial coefficients \(real gas; the virial contribution to the uncertainty 'of the order of 4 parts per 1e5'\), molar masses from the BIPM; the molar refraction \[R\] = R' M from the Lorentz\-Lorenz formula \(Eqs\. 2\.2\-2\.3\), printed in 1e\-30 m^3, i\.e\. per molecule \(M the molecular mass\)\: \[R\] = N\_A alpha/\(3 eps0\) / N\_A; alpha\-bar = 3 \[R\]/\(4 pi\) \(Eq\. 2\.4\) is a polarizability volume in 1e\-30 m^3 = A^3\. 'The uncertainty at the 99 % level in the values given for density, molar refraction, and molecular polarizability was calculated to be \<= \+\-2\.0 parts per 1e4 for all the gases except for nitrous oxide, for which it was found to be \+\-2\.5 parts per 1e4' \(p\. 648\)\. Table 2's n \- 1 at 101 325 Pa and 15 degrees C follow from Eq\. \(2\.5\) with the same densities, 'shown with the estimated uncertainty at the 99 % level' \(p\. 649\)\. Wavelength\: 632\.99 nm, a vacuum wavelength \(the He\-Ne line\); refractivities are not reduced with Edlen's air formula\.

Checks \(2026\-09\-24\)\: every run's \[R\] follows from its printed n \- 1 and density to 1e\-4 or better except helium, whose printed densities 0\.17071 and 0\.17070 kg/m^3 give \[R\] 0\.8671 and 0\.8675 instead of the printed 0\.8666 and 0\.8670; the printed \[R\] follow from densities 0\.17081 and 0\.17080, which is also what the ideal gas with B = 11\.9 cm^3/mol gives at the run's p and T\. So the helium density column is probably misprinted \(1e\-4 kg/m^3\) and \[R\] right; the density is not extracted \(printed cells only\)\. The means and alpha\-bar follow from the runs; Table 2's own values follow from the means with virial densities to within the rough second virial coefficients used for the check \(1\-3e\-4\)\. The first CO2 run's pressure is printed '10 1188\.6' \(image\), i\.e\. 101 188\.6 Pa\.

Helium\: Birch's \[R\] = 0\.8668e\-30 m^3 \(A\_R = 0\.52200 cm^3/mol\) is 3\.4e\-3 above the ab initio value \(puchalski\_2016\: 0\.52026369 cm^3/mol at 632\.99 nm\), '1\.1e\-7 in n at 1 atm' \(stone\_2004, which calls it 'seriously inconsistent'\); puchalski\_2016 reproduces it as 0\.5220\(3\) with an uncertainty it assumes\. Neon\: 'the range of the derived values for the molar refraction of neon was larger than that expected \.\.\. may have been attributable to a low\-level contamination' \(p\. 649\)\. The paper gives no refractivity virial coefficients \(none are measured\)\. N2O\: \[R\] 12\.4506 vs the additive estimate 10\.7 \(p\. 649, discussion only\)\. The CO2 correction to air refractivity, 1\.45 \(measured\) and 1\.48 \(Edlen\) x 1e\-10 per ppm of excess CO2 \(p\. 649\)\. Air \(Table 3\: specific refraction 1\.5040e\-4 m^3/kg, molar refraction 7\.2338e\-30 m^3; the composition table\) is not a curated species; the Lorentz\-Lorenz formula and additivity are found valid for air at 20\-115 kPa, 10\-30 degrees C\.

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

Datasets
--------

birch\_1991/alpha\_N2
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_N2",
     "material": "N2",
     "file": "N2/birch_1991__alpha_N2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.998 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_N2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_N2",
     "material": "N2",
     "file": "N2/birch_1991__runs_N2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_N2 \(primary\); a check\.

birch\_1991/kerl\_1982\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerl_1982_N2",
     "material": "N2",
     "file": "N2/birch_1991__kerl_1982_N2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "K. Kerl, Z. Phys. Chem. Neue Folge 129, 129 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[21\] Kerl \(1982\), scanning\-wavelength interferometry; 'always systematically higher' \(p\. 649\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/peck\_1966\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "peck_1966_N2",
     "material": "N2",
     "file": "N2/birch_1991__peck_1966_N2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "peck_1966"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[16\] Peck and Khanna \(1966\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/refractivity\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_N2",
     "material": "N2",
     "file": "N2/birch_1991__refractivity_N2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_N2\: a check\.

birch\_1991/alpha\_O2
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_O2",
     "material": "O2",
     "file": "O2/birch_1991__alpha_O2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.97 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_O2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_O2",
     "material": "O2",
     "file": "O2/birch_1991__runs_O2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_O2 \(primary\); a check\.

birch\_1991/kerl\_1982\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerl_1982_O2",
     "material": "O2",
     "file": "O2/birch_1991__kerl_1982_O2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "K. Kerl, Z. Phys. Chem. Neue Folge 129, 129 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[21\] Kerl \(1982\), scanning\-wavelength interferometry; 'always systematically higher' \(p\. 649\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/refractivity\_O2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_O2",
     "material": "O2",
     "file": "O2/birch_1991__refractivity_O2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_O2\: a check\.

birch\_1991/alpha\_Ar
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__alpha_Ar.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.998 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_Ar
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__runs_Ar.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_Ar \(primary\); a check\.

birch\_1991/cuthbertson\_1910\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1910_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__cuthbertson_1910_Ar.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1910"
     ]
   }

Table 2, reference \[14\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 84, 13 \(printed 1911\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/kerl\_1982\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerl_1982_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__kerl_1982_Ar.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "K. Kerl, Z. Phys. Chem. Neue Folge 129, 129 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[21\] Kerl \(1982\), scanning\-wavelength interferometry; 'always systematically higher' \(p\. 649\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/peck\_1964\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "peck_1964_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__peck_1964_Ar.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "peck_1964"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[17\] Peck and Fisher \(1964\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/refractivity\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_Ar",
     "material": "Ar",
     "file": "Ar/birch_1991__refractivity_Ar.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_Ar\: a check\.

birch\_1991/alpha\_CO2
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_CO2",
     "material": "CO2",
     "file": "CO2/birch_1991__alpha_CO2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.995 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_CO2
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_CO2",
     "material": "CO2",
     "file": "CO2/birch_1991__runs_CO2.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_CO2 \(primary\); a check\.

birch\_1991/edlen\_1966\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "edlen_1966_CO2",
     "material": "CO2",
     "file": "CO2/birch_1991__edlen_1966_CO2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "edlen_1966"
     ]
   }

Table 2, reference \[9\] Edlen \(1966\)\: the CO2 refractivity 'predicted by Edlen' \(p\. 649\), derived by Birch from Edlen's air formula, not a value Edlen prints, as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/refractivity\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_CO2",
     "material": "CO2",
     "file": "CO2/birch_1991__refractivity_CO2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_CO2\: a check\.

birch\_1991/simmons\_1978\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "simmons_1978_CO2",
     "material": "CO2",
     "file": "CO2/birch_1991__simmons_1978_CO2.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "A. C. Simmons, Opt. Commun. 25, 211 (1978)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[20\] Simmons \(1978\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/alpha\_Ne
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__alpha_Ne.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.995 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_Ne
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__runs_Ne.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_Ne \(primary\); a check\.

birch\_1991/cuthbertson\_1910\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1910_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__cuthbertson_1910_Ne.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1910"
     ]
   }

Table 2, reference \[14\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 84, 13 \(printed 1911\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/cuthbertson\_1932\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1932_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__cuthbertson_1932_Ne.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1932"
     ]
   }

Table 2, reference \[15\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 135, 40 \(1932\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/kerl\_1982\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerl_1982_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__kerl_1982_Ne.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "K. Kerl, Z. Phys. Chem. Neue Folge 129, 129 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[21\] Kerl \(1982\), scanning\-wavelength interferometry; 'always systematically higher' \(p\. 649\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/refractivity\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_Ne",
     "material": "Ne",
     "file": "Ne/birch_1991__refractivity_Ne.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_Ne\: a check\.

birch\_1991/alpha\_He
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_He",
     "material": "He",
     "file": "He/birch_1991__alpha_He.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.995 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_He
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_He",
     "material": "He",
     "file": "He/birch_1991__runs_He.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_He \(primary\); a check\.

birch\_1991/cuthbertson\_1910\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1910_He",
     "material": "He",
     "file": "He/birch_1991__cuthbertson_1910_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1910"
     ]
   }

Table 2, reference \[14\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 84, 13 \(printed 1911\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/cuthbertson\_1932\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1932_He",
     "material": "He",
     "file": "He/birch_1991__cuthbertson_1932_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1932"
     ]
   }

Table 2, reference \[15\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 135, 40 \(1932\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/hey\_1988\_He
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hey_1988_He",
     "material": "He",
     "file": "He/birch_1991__hey_1988_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "J. D. Hey, H. S. T. Driver and D. B. Fish, Am. J. Phys. 56, 646 (1988)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[19\] Hey, Driver and Fish \(1988\), laser interferometry, as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/kerl\_1982\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kerl_1982_He",
     "material": "He",
     "file": "He/birch_1991__kerl_1982_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "K. Kerl, Z. Phys. Chem. Neue Folge 129, 129 (1982)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[21\] Kerl \(1982\), scanning\-wavelength interferometry; 'always systematically higher' \(p\. 649\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/mansfield\_peck\_1969\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "mansfield_peck_1969_He",
     "material": "He",
     "file": "He/birch_1991__mansfield_peck_1969_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "mansfield_peck_1969"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table 2, reference \[18\] Mansfield and Peck \(1969\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\); \+\- level not stated\.

birch\_1991/refractivity\_He
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_He",
     "material": "He",
     "file": "He/birch_1991__refractivity_He.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_He\: a check\.

birch\_1991/alpha\_N2O
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_N2O",
     "material": "N2O",
     "file": "N2O/birch_1991__alpha_N2O.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.00025,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.997 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(nitrous oxide \+\-2\.5\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_N2O
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_N2O",
     "material": "N2O",
     "file": "N2O/birch_1991__runs_N2O.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_N2O \(primary\); a check\.

birch\_1991/refractivity\_N2O
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_N2O",
     "material": "N2O",
     "file": "N2O/birch_1991__refractivity_N2O.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_N2O\: a check\.

birch\_1991/alpha\_Kr
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_Kr",
     "material": "Kr",
     "file": "Kr/birch_1991__alpha_Kr.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 0.0002,
       "level": "99 % confidence"
     }
   }

Table 1, alpha\-bar = 3 \[R\]/\(4 pi\) \(1e\-30 m^3, a polarizability volume\) from the mean molar refraction \(printed in the same row\) of the runs; 99\.99 % purity\. Uncertainty '\<= \+\-2\.0 parts per 1e4' at the 99 % level \(p\. 648\) \(level\: 99 % confidence\)\.

birch\_1991/runs\_Kr
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "runs_Kr",
     "material": "Kr",
     "file": "Kr/birch_1991__runs_Kr.csv",
     "table": "tbl_6072c809ac8e",
     "quantity": "polarizability",
     "unit": "angstrom3",
     "scale": 0.238732414637843,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 1, the molar refraction \[R\] of each run \(1e\-30 m^3 per molecule; scale 3/\(4 pi\) gives the polarizability volume\), rows numbered in print order; each run's temperature \(degrees C\), pressure \(Pa\), measured \(n \- 1\) x 1e8 and real\-gas density \(kg/m^3\) are in the printed cells\. Their mean is alpha\_Kr \(primary\); a check\.

birch\_1991/cuthbertson\_1910\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cuthbertson_1910_Kr",
     "material": "Kr",
     "file": "Kr/birch_1991__cuthbertson_1910_Kr.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "unknown",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1910"
     ]
   }

Table 2, reference \[14\] Cuthbertson and Cuthbertson, Proc\. R\. Soc\. London A 84, 13 \(printed 1911\), as given by Birch at 632\.99 nm, 101 325 Pa, 15 degrees C \(how it was brought to these conditions is not stated\)\.

birch\_1991/refractivity\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "refractivity_Kr",
     "material": "Kr",
     "file": "Kr/birch_1991__refractivity_Kr.csv",
     "table": "tbl_10576f9abc2b",
     "quantity": "refractivity",
     "scale": 1e-06,
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "state": "1atm_15C",
     "density": "real",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "99 % confidence"
     }
   }

Table 2, first row\: Birch's 10^6 \(n \- 1\) at 632\.99 nm, 101 325 Pa, 15 degrees C, computed from the mean molar refraction and the real\-gas density \(Eq\. 2\.5; reproduced to rounding with virial densities, checked 2026\-09\-24\), uncertainty at the 99 % level \(level\: 99 % confidence\)\. The same information as alpha\_Kr\: a check\.

Formulas
--------

No formulas are recorded.

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

No dataset errata are recorded in this source record.

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