nie_2025
========

Z\.\-L\. Nie, J\. Wang, C\.\-L\. Hu, Y\. R\. Sun, C\.\-F\. Cheng, Y\. Tan and S\.\-M\. Hu, "Polarizability of molecular hydrogen and gas metrology", Phys\. Rev\. A 111, 012801 \(2025\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/nie_2025.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.111\.012801 <https://doi.org/10.1103/PhysRevA.111.012801>`__

**Source kind:** measurement

**Recorded technique:** Fabry\-Perot gas refractometers \(USTC; the instrument of zhao\_2026\)\: 10 cm ULE cavities \(R ~ 99\.9 %, FSR 1\.5 GHz, mode width ~0\.4 MHz\) in a vacuum cell in an aluminium cylinder at about 297\.53 K \(calibrated platinum resistance thermometer, \< 5 mK\), a 1566 nm fibre laser \(\< 10 kHz\) PDH\-locked to a cavity mode, the mode frequency beaten against a reference laser \(drift ~0\.1 Hz/s\)\. n \- 1 from the mode shift, Eq\. \(2\), with the bulk modulus K = 3\.3372e10 Pa and mirror\-deformation d\_1 = 1\.6119e\-13 Pa^\-1 \(Opt\-1; d\_2 = 0 for Opt\-2\) calibrated at 70 kPa with ARGON against a Fluke PG7601 piston gauge \(11 ppm\) taking A\_eps\(Ar\) = 4\.140686\(10\) cm^3/mol \(Gaiser and Fellmuth 2018, gaiser\_2018\)\. Pressure from an Inficon CDGSci manometer calibrated against the optical gauge, u = sqrt\(\(20e\-6 p\)^2 \+ \(1\.5 Pa\)^2\)\. Gases 99\.9999 %; H2 through a liquid\-nitrogen trap\. Pressure points 2\-100 kPa, several series; the static A\_eps from each point through Eqs\. \(1\) and \(3\), weighted mean \(pp\. 1\-4\)\.

**Materials in structured entries:** H2, N2, Ne

**Dataset quantities:** cauchy\_moment, molar\_refractivity

**Contents:** 15 datasets; 0 formulas.

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

Identity VALIDATED; first page checked \(pdf page 1\: Phys\. Rev\. A 111, 012801 \(2025\), published 7 January 2025\)\. Page numbers are the article pages 1\-5 \(= pdf pages\)\.

WHAT IS MEASURED AND WHAT IS PRINTED \(the same scheme as zhao\_2026, whose record explains it at length\)\. The refractometer measures n \- 1 at 1566 nm \(vacuum\)\. Eq\. \(1\) reduces it to the refractive molar polarization A\_eps'\(omega\) \+ A\_mu; the authors subtract A\_mu \(Table I; Refs\. 32, 33\) and convert to the static A\_eps with Eq\. \(3\), the electronic dipole sums S\(\-4\), S\(\-6\), S\(\-8\) of Table I \('S parameters are from Ref\. \[21\]', Olney et al\. 1997, for all four gases\)\. They are not Olney et al\.'s own sums but comparison rows of Olney's Table 3 \(olney\_1997, curated 2026\-09\-26\)\: N2 and H2 are Zeiss et al\.'s DOSD \(zeiss\_1977\), Ne and Ar Kumar and Meath's \(kumar\_1985\); the parenthesised uncertainties are not in Olney et al\. and are Nie et al\.'s own\. Only the static A\_eps is printed \(Table II, the text, the abstract\)\. The datasets A\_R\_1566\_\* are RECONSTRUCTED by tools/extract/nie\_2025\.py, inverting Eq\. \(3\) exactly \(see its docstring\: the reduced\-mass factor applied to H2 with the proton mass, \+5 ppm; omitted for N2 and Ne, \< 0\.1 ppm\)\. Their A\_mu convention is that of Rourke \(A\_mu = chi\_M/3, SI\)\: Ar \-80\.9\(6\)e\-6 cm^3/mol equals rourke\_2021's \-8\.09\(57\)e\-5, and Ne \-29\.2\(6\)e\-6 is near lesiuk\_2020's chi\_0 converted, \-31\.7e\-6\.

WHAT THE STATIC VALUES INCLUDE\. As in zhao\_2026\: the electronic polarizability plus the \(negative\) infrared response at 1566 nm, which the conversion does not remove; no static vibrational polarizability\. N2, Ne and H2 have no infrared\-active vibration, so here the static values are the electronic \(vibrationally and rotationally averaged, 297\.53 K\) static polarizabilities\. For H2 the value is for normal hydrogen at 297\.53 K; the natural D/H ratio 'should be corrected by \-2 x 10^\-6' \(p\. 4\)\.

NOT INDEPENDENT OF ARGON\: the pressure scale \(K, d\) is calibrated with argon's A\_eps from gaiser\_2018 at one point \(70 kPa\); every result here is relative to it\. zhao\_2026 in turn calibrates with this paper's N2 value\.

UNCERTAINTY \(Table II, ppm; the level is not stated in the table, taken as one standard uncertainty like the paper's k = 1 gauge uncertainties\)\: T 16, p 25, K 11, purity 1, outgas 0\.2/0\.9/0\.5, frequency and L\_cav \< 0\.1, statistics 9/26/5, A\_mu 0\.1/0\.6/0\.2, B\_eps 3/\<0\.1/2, B\_T 12/20/4, S\(i\) 7/1/12 \(N2/Ne/H2\); totals 36, 46, 35 \(each the root sum of squares, checked\)\. The reconstructed A\_R keeps all but S\(i\) and A\_mu\: 35\.2 \(N2\), 45\.6 \(Ne\), 32\.4 \(H2\) ppm\.

COMPARISONS \(computed 2026\-09\-25\)\: H2 static 2\.031027\(71\) is 26 ppm above raj\_2018's normal\-H2 static average at 296\.15 K \(5\.4332744 au = 2\.030975 cm^3/mol\) and 0\.00023 above Sun et al\.'s 2\.03080\(12\), which omits relativistic and QED terms \(the authors estimate 60 ppm, p\. 4\)\. Ne static 0\.994742\(46\) is 31 ppm above gaiser\_2018's 0\.9947114\(24\)\. N2 4\.38705\(16\) is 59 ppm above the Egan et al\. value 4\.38679\(7\)\. The reconstructed Ne A\_R\(1566\) 0\.995627\(45\) is 44 ppm above rourke\_2021's A\_R at 1550 nm \(0\.9956018\(34\)\) moved to 1566 nm with Olney's sums \(0\.995583\)\. Lesiuk et al\.'s Ne value as quoted, 0\.99470\(13\) cm^3/mol, is 2\.66103 au, not lesiuk\_2020's alpha\_0 2\.66080 au \(0\.994615 cm^3/mol; 86 ppm lower\)\: the quoted value may include something else \(the magnetic term would lower it\); not resolved\.

Text values not extracted as datasets\: Egan et al\.'s Ne 0\.994598\(16\) cm^3/mol \(p\. 4; Nie et al\.'s conversion of egan\_2019, like the N2 value of Table II\); Klopper et al\.'s 0\.99503\(75\) \(already gaiser\_2018/klopper\_2004\_Ne\); the calibration value A\_eps\(Ar\) = 4\.140686\(10\) \(gaiser\_2018's\)\. Not extracted\: Table I's B\_T and B\_eps \(Ar \-16\.1\(5\), 1\.72\(11\); Ne 11\.0\(5\), \-0\.0930\(5\); N2 \-5\.5\(3\), 1\.12\(30\); H2 14\.1\(1\), 0\.06\(10\); cm^3/mol and cm^6/mol^2 at about 297\.5 K, sources Refs\. 34\-37 not assigned per gas\), the argon column \(a calibration input, not a result\), the per\-pressure points \(figures only\)\.

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

Datasets
--------

nie\_2025/A\_R\_1566\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "A_R_1566_N2",
     "material": "N2",
     "file": "N2/nie_2025__A_R_1566_N2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

RECONSTRUCTED \(not printed\)\: A\_eps'\(omega\) \+ A\_mu at 1566 nm \(vacuum\) and 297\.53 K, = Table II's static 4\.38705 \+ \(4 pi/3\) N\_A a0^3 \[S\(\-4\) w^2 \+ S\(\-6\) w^4 \+ S\(\-8\) w^6\] \(Table I, Olney's sums\) \+ A\_mu \(\-52\.1e\-6\), by tools/extract/nie\_2025\.py\. Uncertainty\: Table II without S\(i\) and A\_mu, 35\.2 ppm, one sigma\. Tied to gaiser\_2018's argon A\_eps through the pressure calibration\.

nie\_2025/A\_R\_1566\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "A_R_1566_Ne",
     "material": "Ne",
     "file": "Ne/nie_2025__A_R_1566_Ne.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

RECONSTRUCTED \(not printed\), as A\_R\_1566\_N2\: 0\.994742 \+ Olney's dispersion \+ A\_mu \(\-29\.2e\-6\) at 1566 nm, 297\.53 K; 45\.6 ppm\. 44 ppm above rourke\_2021's 1550 nm A\_R moved to 1566 nm \(source notes\)\.

nie\_2025/A\_R\_1566\_H2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "A_R_1566_H2",
     "material": "H2",
     "file": "H2/nie_2025__A_R_1566_H2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

RECONSTRUCTED \(not printed\), as A\_R\_1566\_N2\: 2\.031027 \+ \(1 \+ m\_e/m\_p\)^3 x Olney's dispersion \+ A\_mu \(\-17\.0e\-6\) at 1566 nm, 297\.53 K, normal hydrogen \(natural D/H; \-2 ppm for pure H2 isotopologue, p\. 4\); 32\.4 ppm\.

nie\_2025/static\_N2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "static_N2",
     "material": "N2",
     "file": "N2/nie_2025__static_N2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

Table II 'This work'\: A\_eps = 4\.38705\(16\) cm^3/mol \(36 ppm, k = 1\), the static electronic value derived from the 1566 nm measurement with Olney's sums\. Not independent of A\_R\_1566\_N2\: a check\. zhao\_2026 calibrates its cavity with this value\. At 297\.53 K\.

nie\_2025/static\_Ne
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "static_Ne",
     "material": "Ne",
     "file": "Ne/nie_2025__static_Ne.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

Table II 'This work'\: A\_eps = 0\.994742\(46\) cm^3/mol \(46 ppm\), static, from A\_R\_1566\_Ne\: a check\. 31 ppm above gaiser\_2018 \(0\.7 sigma\)\.

nie\_2025/static\_H2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "static_H2",
     "material": "H2",
     "file": "H2/nie_2025__static_H2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

Table II 'This work' and Eq\. \(4\)\: A\_eps = 2\.031027\(71\) cm^3/mol at 297\.53 K \(35 ppm\), normal hydrogen, static electronic, from A\_R\_1566\_H2\: a check\. 26 ppm above raj\_2018's normal\-H2 static average at 296\.15 K\.

nie\_2025/egan\_2019\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "egan_2019_N2",
     "material": "N2",
     "file": "N2/nie_2025__egan_2019_N2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "check",
     "reproduced_from": [
       "egan_2019"
     ],
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     }
   }

Table II 'Expt\.' \(note a, Ref\. 40, Egan et al\. 2019\)\: 'The static polarizability according to the value obtained by Egan et al\.' \(p\. 4\), 4\.38679\(7\) cm^3/mol\: Nie et al\.'s static conversion of egan\_2019's optical A\_R, not a printed Egan value\. Derived\: a check\.

nie\_2025/gaiser\_2018\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "gaiser_2018_Ne",
     "material": "Ne",
     "file": "Ne/nie_2025__gaiser_2018_Ne.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "gaiser_2018"
     ],
     "uncertainty": {
       "column": true,
       "level": "1 sigma"
     }
   }

Table II 'Expt\.' \(note a, Ref\. 39\)\: 0\.9947114\(24\) cm^3/mol, identical to gaiser\_2018's molar\_polarizability\_Ne \(DCGT\)\.

nie\_2025/hohm\_kerl\_1990\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "hohm_kerl_1990_H2",
     "material": "H2",
     "file": "H2/nie_2025__hohm_kerl_1990_H2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "hohm_1990"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II 'Expt\.' \(note a, Ref\. 25, Hohm and Kerl, Mol\. Phys\. 69, 803 \(1990\) = hohm\_1990\)\: 2\.033\(4\) cm^3/mol\. The number itself is not printed in hohm\_1990 \(its H2 values are temperature fits at 632\.99 nm and a 0 K extrapolation\); how Nie et al\. derived a static molar value from it is not said\. Level not stated\.

nie\_2025/olney\_1997\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "olney_1997_N2",
     "material": "N2",
     "file": "N2/nie_2025__olney_1997_N2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "olney_1997"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II 'Theor\.' \(note b, Ref\. 21\)\: 4\.3887\(18\) cm^3/mol, 'with an uncertainty of 410 ppm' \(p\. 4\); a dipole\-sum \(DOSD\) static value\. Olney et al\. \(curated since 2026\-09\-26 as olney\_1997\) print no such number\: 4\.3887 cm^3/mol is 11\.7407 au, and their N2 values are 11\.75 \(Table 3, refined, the Hohm and Kerl 1990 polarizability it was renormalised to\: 4\.3922 cm^3/mol\), 11\.74 \(Zeiss et al\.'s DOSD row\: 4\.3885\), 11\.743 \(Langhoff and Karplus\: 4\.3896\) and 11\.54 \(Table 1, unrefined\); nor do they print an uncertainty\. How Nie et al\. obtained 4\.3887\(18\) is not established \(checked 2026\-09\-26\)\.

nie\_2025/lesiuk\_2020\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "lesiuk_2020_Ne",
     "material": "Ne",
     "file": "Ne/nie_2025__lesiuk_2020_Ne.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "lesiuk_2020"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table II 'Theor\.' \(note b, Ref\. 23\)\: 0\.99470\(13\) cm^3/mol\. Does not equal lesiuk\_2020's alpha\_0 = 2\.66080 au, which is 0\.994615 cm^3/mol \(86 ppm lower\); 0\.99470 is 2\.66103 au\. Not resolved; use lesiuk\_2020 itself\.

nie\_2025/sun\_2021\_H2
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sun_2021_H2",
     "material": "H2",
     "file": "H2/nie_2025__sun_2021_H2.csv",
     "table": "tbl_2c3bf20e3331",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "D. Sun, Y. P. Zhang, X. J. Wei, L. M. Wang and Z.-C. Yan, Phys. Rev. A 103, 062813 (2021)"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 297.53
     }
   }

Table II 'Theor\.' \(note b, Ref\. 26\)\: 2\.03080\(12\) cm^3/mol at 297\.53 K, non\-Born\-Oppenheimer static polarizabilities of the rotational levels in Hylleraas coordinates, thermally averaged; 'the contributions from the relativistic and QED effects have not been included', estimated at 60 ppm \(p\. 4\)\. The original is not in the library\.

nie\_2025/olney\_moments\_N2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "olney_moments_N2",
     "material": "N2",
     "file": "N2/nie_2025__olney_moments_N2.csv",
     "table": "tbl_c8f73c6e439f",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "zeiss_1977"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table I\: S\(\-4\) 30\.11\(9\), S\(\-6\) 101\.8\(9\), S\(\-8\) 385\(6\) au \('S parameters are from Ref\. \[21\]', Olney et al\. 1997\)\. CORRECTED ATTRIBUTION \(2026\-09\-26\)\: these are not Olney et al\.'s sums \(their own N2 row is 30\.02, 100\.8, 378\.7\: olney\_1997/moments\_N2\) but the Zeiss et al\. \(1977\) DOSD row \[49\] of Olney's Table 3 \(30\.11, 101\.8, 384\.6; olney\_1997/zeiss\_1977\_N2\), identical to zeiss\_1977/moments\_N2 \(385 is 384\.6 rounded\)\: reproduced\_from set to zeiss\_1977\. The parenthesised uncertainties \(0\.3, 0\.9, 1\.6 %\) are printed by neither Olney nor Zeiss\: Nie et al\.'s own\.

nie\_2025/olney\_moments\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "olney_moments_Ne",
     "material": "Ne",
     "file": "Ne/nie_2025__olney_moments_Ne.csv",
     "table": "tbl_c8f73c6e439f",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "kumar_1985"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table I\: S\(\-4\) 2\.886\(2\), S\(\-6\) 5\.063\(18\), S\(\-8\) 10\.86\(4\) au\. Neon has curated ab initio moments \(lesiuk\_2020, pawlowski\_2005\)\: this copy is a check on them\. CORRECTED ATTRIBUTION \(2026\-09\-26\)\: Nie et al\. cite Olney et al\. \(Ref\. \[21\]\), but these are the Kumar and Meath \(1985\) DOSD row \[54\] of Olney's Table 3 \(olney\_1997/kumar\_1985\_Ne\), identical to kumar\_1985/moments\_Ne; Olney et al\.'s own neon sums are 2\.938, 5\.137, 10\.95 \(olney\_1997/moments\_Ne\)\. reproduced\_from set to kumar\_1985\. The parenthesised uncertainties are Nie et al\.'s own\.

nie\_2025/olney\_moments\_H2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "olney_moments_H2",
     "material": "H2",
     "file": "H2/nie_2025__olney_moments_H2.csv",
     "table": "tbl_c8f73c6e439f",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "zeiss_1977"
     ],
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

Table I\: S\(\-4\) 19\.96\(8\), S\(\-6\) 82\.94\(51\), S\(\-8\) 367\(4\) au\. Hydrogen has curated ab initio dispersion \(raj\_2018, rychlewski\_1983\)\: this copy is a check on them\. CORRECTED ATTRIBUTION \(2026\-09\-26\)\: Nie et al\. cite Olney et al\. \(Ref\. \[21\]\), but these are the Zeiss et al\. \(1977\) DOSD row \[49\] of Olney's Table 3 \(19\.96, 82\.94, 367\.0; olney\_1997/zeiss\_1977\_H2\), identical to zeiss\_1977/moments\_H2; Olney et al\.'s own H2 sums are 20\.04, 83\.18, 367\.0 \(olney\_1997/moments\_H2\)\. reproduced\_from set to zeiss\_1977\. The parenthesised uncertainties are Nie et al\.'s own\.

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.