kumar_1985
==========

A\. Kumar and W\. J\. Meath, Can\. J\. Chem\. 63, 1616 \(1985\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/kumar_1985.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1139/v85\-272 <https://doi.org/10.1139/v85-272>`__

**Source kind:** compilation

**Recorded technique:** Constrained dipole oscillator strength distributions \(DOSDs\)\: measured photoabsorption and fast\-electron energy\-loss oscillator\-strength data \(discrete lines from Moore's levels and several f\-value sources; continuum from the references in Tables 8\-11; Henke et al\. and Veigele's photoelectric cross sections at high energy; the Stobbe formula above 100 keV\), each spectral region scaled by \(1 \+ a\_j\) \(Eq\. \[5\]\) so that the whole distribution satisfies the Thomas\-Reiche\-Kuhn sum rule S\_0 = Z and two molar refractivities R\_lambda = \(4 pi/3\) N\_A alpha\_d\(lambda\) \(Eq\. \[6\]\); the adopted DOSD is the one of least overall adjustment \(STD, about 0\.5\)\. Starting distributions followed Berkowitz's \(1979\) analysis of the rare\-gas spectra \(pp\. 1616\-1618, 1623\)\.

**Materials in structured entries:** Ar, Kr, Ne, Xe

**Dataset quantities:** cauchy\_moment, interval\_oscillator\_strength, molar\_refractivity

**Contents:** 16 datasets; 0 formulas.

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

Only the rare gases are curated\: HF, HCl and HBr \(Tables 1\-7, and their columns in Table 2\) are not species of the package and are skipped\.

Dipole sums S\_k = sum\_i \(E\_i/2R\)^k f\_i \+ integral \(E/2R\)^k \(df/dE\) dE \(Eqs\. \[1\], \[4\]\), atomic units \(energies in hartree\); S\_\-2 = alpha\_d/a0^3 is the static polarizability, S\_0 = Z by construction, and S\_\-2, S\_\-4, S\_\-6, \.\.\. are the Cauchy coefficients of alpha\(omega\)\.

Refractivity constraints \(captions of Tables 8\-11 and p\. 1623\)\: Ne R\(5462\.25 A\) = 1\.00537 and R\(2894\.44 A\) = 1\.02573 cm^3/mol from Cuthbertson and Cuthbertson \(1932\) 'correcting for non\-ideal behaviour by using the second virial coefficient of Michels et al\.'; Ar R\(6329\.9 A\) = 4\.1973 and R\(4766\.2 A\) = 4\.2407 from Coulon, Montixi and Occelli \(1981\); Kr R\(2632\.1 A\) = 7\.0106 and R\(1770\.9 A\) = 8\.3522 from Smith, Huber and Parkinson \(1976\); Xe R\(2537\.0 A\) = 12\.1423 and R\(1702\.0 A\) = 17\.7290 from Bideau\-Mehu et al\. \(1981\)\. These are extracted as reproduced molar refractivities \(constraint\_\*\); the S\_k \(k \< 0\) are therefore not independent of those refractivity data\. Wavelengths are vacuum wavelengths \(they are those sources' vacuum values\: 5462\.23/2894\.44 A, 263\.21/177\.09 nm, 253\.7/170\.2 nm\)\.

Uncertainties \(p\. 1628\)\: 'For the rare gases the estimated errors in the S\_k, for \-6 \<~ k \<~ 0, are \<~1%\. L\_0 and S\_1 are uncertain by ~2%'; S\_k for k \>= 1, 'particularly for k = 2, can have uncertainties of ~3%'; all 'under the assumption that the values of the molar refractivity constraints \.\.\. are reliable \(errors \<~0\.5%\)'\. No level stated\.

Table 12 misprint\: Leonard and Barker's krypton S\_\-4 is printed '5\.665' without its power of ten \(image checked\); 56\.65 fits between S\_\-3 = 29\.44 and S\_\-5 = 116\.4 and the adopted 56\.32 \(erratum\)\.

Integrated oscillator strengths \(Tables 8\-11\)\: the format has no quantity for an oscillator strength integrated over a photon\-energy interval \(it needs two energies\)\. They are stored as oscillator\_strength with an index abscissa \(the row's position\) and the interval in eV as the row id, e\.g\. '21\.47\-21\.57' or 'discrete\:16\.67\-21\.48' \(the whole discrete spectrum\); the reference number of each cell's data is in the printed cell\. Only the 'Adopted DOSD' column is extracted; the other columns are the integrated initial input data of individual references \(one reference per cell, several references per column\), not extracted\. Table 9 \(image checked\)\: Ar initial\-data column 2 prints '7\.374 \(81\)' at 30\.0\-35\.0 eV, apparently for 7\.374\(\-1\); not extracted\.

No pseudo\-spectrum is given\: 'The pseudo\-DOSDs for the hydrogen halides and the rare gases will be presented elsewhere' \(p\. 1628; Kumar and Meath, Mol\. Phys\. 54, 823 \(1985\), not in the library\)\. Not extracted\: the logarithmic sums L\_k \(no quantity\), Table 12's footnotes \(Hartree\-Fock S\_2, S\_1, S\_\-1 of Cummings 1975 and CI of Saxon 1973, Naon et al\. 1975; the Ne CI S\_2 '2\.599' and HF S\_1 '1\.514\(3\)' are misprinted for 2\.599\(4\) and 1\.514\(2\), compare kumar\_2010\)\.

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

Datasets
--------

kumar\_1985/dosd\_Ne
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_Ne",
     "material": "Ne",
     "file": "Ne/kumar_1985__dosd_Ne.csv",
     "table": "tbl_9594b1549318",
     "quantity": "interval_oscillator_strength",
     "abscissa_unit": "eV",
     "columns": {
       "x_upper": "eV"
     },
     "use": "check"
   }

Table 8 'Adopted DOSD'\: the integrated dipole oscillator strength over each photon\-energy interval \(eV, the row id; first row the whole discrete spectrum, 16\.67\-21\.48 eV\); the index abscissa is the row's position \(the format has no integrated\-oscillator\-strength quantity, source notes\)\. Absorption edges 48\.5 eV \(L1\) and 866\.9 eV \(K\)\. Data sources of the adopted cells \(reference numbers in the printed cells\)\: Radler and Berkowitz 1979, Samson 1966, Ederer and Tomboulian 1964, Henke et al\. \(33\), Veigele \(34\) and the Stobbe formula; discrete part from Moore's levels and refs\. 60\-65\. The column sums to 10\.0003 \(S\_0 = 10 by construction\)\.

kumar\_1985/dosd\_Ar
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_Ar",
     "material": "Ar",
     "file": "Ar/kumar_1985__dosd_Ar.csv",
     "table": "tbl_be26a24107d8",
     "quantity": "interval_oscillator_strength",
     "abscissa_unit": "eV",
     "columns": {
       "x_upper": "eV"
     },
     "use": "check"
   }

Table 9 'Adopted DOSD'\: the integrated dipole oscillator strength over each photon\-energy interval \(eV, the row id; first row the whole discrete spectrum, 11\.62\-15\.60 eV\); the index abscissa is the row's position \(the format has no integrated\-oscillator\-strength quantity, source notes\)\. Absorption edges 245\.2 \(L3\), 247\.3 \(L2\), 320\.0 \(L1\) and 3202\.9 eV \(K\)\. Data sources of the adopted cells \(reference numbers in the printed cells\)\: Huffman et al\. 1963, Carlson et al\. 1973, West and Marr 1976, Hubbell 1977 and the Stobbe formula; discrete part from refs\. 11, 60 and 62\. The column sums to 17\.9994 \(S\_0 = 18 by construction\)\.

kumar\_1985/dosd\_Kr
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_Kr",
     "material": "Kr",
     "file": "Kr/kumar_1985__dosd_Kr.csv",
     "table": "tbl_d6de19f0cf8e",
     "quantity": "interval_oscillator_strength",
     "abscissa_unit": "eV",
     "columns": {
       "x_upper": "eV"
     },
     "use": "check"
   }

Table 10 'Adopted DOSD'\: the integrated dipole oscillator strength over each photon\-energy interval \(eV, the row id; first row the whole discrete spectrum, 10\.03\-13\.85 eV\); the index abscissa is the row's position \(the format has no integrated\-oscillator\-strength quantity, source notes\)\. Absorption edges 1675 \(L3\), 1727 \(L2\), 1921 \(L1\) and 14330 eV \(K\)\. Data sources of the adopted cells \(reference numbers in the printed cells\)\: Carter and Hudson 1973, Rustgi et al\. 1964, West and Marr 1976, Veigele \(34\) and the Stobbe formula; discrete part from refs\. 60, 89 and 90\. The column sums to 35\.9987 \(S\_0 = 36 by construction\)\.

kumar\_1985/dosd\_Xe
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dosd_Xe",
     "material": "Xe",
     "file": "Xe/kumar_1985__dosd_Xe.csv",
     "table": "tbl_b6cd2000760f",
     "quantity": "interval_oscillator_strength",
     "abscissa_unit": "eV",
     "columns": {
       "x_upper": "eV"
     },
     "use": "check"
   }

Table 11 'Adopted DOSD'\: the integrated dipole oscillator strength over each photon\-energy interval \(eV, the row id; first row the whole discrete spectrum, 8\.44\-11\.99 eV\); the index abscissa is the row's position \(the format has no integrated\-oscillator\-strength quantity, source notes\)\. Absorption edges 4782 \(L3\), 5104 \(L2\), 5453 \(L1\) and 34560 eV \(K\)\. Data sources of the adopted cells \(reference numbers in the printed cells\)\: Matsunaga et al\. 1965, Rustgi et al\. 1964, Cairns et al\. 1969, Lang and Watson 1975, Lukirskii et al\. 1964/1966, Veigele \(34\) and the Stobbe formula; discrete part from refs\. 60 and 89\. The column sums to 53\.9976 \(S\_0 = 54 by construction\)\.

kumar\_1985/moments\_Ne
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_Ne",
     "material": "Ne",
     "file": "Ne/kumar_1985__moments_Ne.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check",
     "uncertainty": {
       "relative": 0.01,
       "level": "not stated",
       "relative_rows": {
         "2": 0.03,
         "1": 0.02,
         "0": 0.0
       }
     }
   }

Table 12 'Adopted'\: S\_k for k = 2, 1, 0, \-1/2, \-1, \.\.\., \-10 \(rows by k, \-0\.5 for \-1/2\) from the adopted constrained DOSD, atomic units \(E in units of 2R, Eq\. \[1\]\)\. Superseded by kumar\_2010 \(the same method with improved high\-energy behaviour\)\: a check\. Estimated errors '\<~1%' for \-6 \<~ k \<~ 0, S\_1 '~2%', S\_2 '~3%' \(p\. 1628\); none stated below k = \-6 \(dominated by the lowest excitation energies, 'largely unaffected by the constraints'\)\.

kumar\_1985/moments\_Ar
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_Ar",
     "material": "Ar",
     "file": "Ar/kumar_1985__moments_Ar.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check",
     "uncertainty": {
       "relative": 0.01,
       "level": "not stated",
       "relative_rows": {
         "2": 0.03,
         "1": 0.02,
         "0": 0.0
       }
     }
   }

Table 12 'Adopted'\: S\_k for k = 2, 1, 0, \-1/2, \-1, \.\.\., \-10 \(rows by k, \-0\.5 for \-1/2\) from the adopted constrained DOSD, atomic units \(E in units of 2R, Eq\. \[1\]\)\. Superseded by kumar\_2010 \(the same method with improved high\-energy behaviour\)\: a check\. Estimated errors '\<~1%' for \-6 \<~ k \<~ 0, S\_1 '~2%', S\_2 '~3%' \(p\. 1628\); none stated below k = \-6 \(dominated by the lowest excitation energies, 'largely unaffected by the constraints'\)\.

kumar\_1985/moments\_Kr
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_Kr",
     "material": "Kr",
     "file": "Kr/kumar_1985__moments_Kr.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check",
     "uncertainty": {
       "relative": 0.01,
       "level": "not stated",
       "relative_rows": {
         "2": 0.03,
         "1": 0.02,
         "0": 0.0
       }
     }
   }

Table 12 'Adopted'\: S\_k for k = 2, 1, 0, \-1/2, \-1, \.\.\., \-10 \(rows by k, \-0\.5 for \-1/2\) from the adopted constrained DOSD, atomic units \(E in units of 2R, Eq\. \[1\]\)\. Superseded by kumar\_2010 \(the same method with improved high\-energy behaviour\)\: a check\. Estimated errors '\<~1%' for \-6 \<~ k \<~ 0, S\_1 '~2%', S\_2 '~3%' \(p\. 1628\); none stated below k = \-6 \(dominated by the lowest excitation energies, 'largely unaffected by the constraints'\)\.

kumar\_1985/moments\_Xe
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_Xe",
     "material": "Xe",
     "file": "Xe/kumar_1985__moments_Xe.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check",
     "uncertainty": {
       "relative": 0.01,
       "level": "not stated",
       "relative_rows": {
         "2": 0.03,
         "1": 0.02,
         "0": 0.0
       }
     }
   }

Table 12 'Adopted'\: S\_k for k = 2, 1, 0, \-1/2, \-1, \.\.\., \-10 \(rows by k, \-0\.5 for \-1/2\) from the adopted constrained DOSD, atomic units \(E in units of 2R, Eq\. \[1\]\)\. Superseded by kumar\_2010 \(the same method with improved high\-energy behaviour\)\: a check\. Estimated errors '\<~1%' for \-6 \<~ k \<~ 0, S\_1 '~2%', S\_2 '~3%' \(p\. 1628\); none stated below k = \-6 \(dominated by the lowest excitation energies, 'largely unaffected by the constraints'\)\.

kumar\_1985/leonard\_barker\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "leonard_barker_Ne",
     "material": "Ne",
     "file": "Ne/kumar_1985__leonard_barker_Ne.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "P. J. Leonard and J. A. Barker, in Theoretical Chemistry, Advances and Perspectives, Vol. 1 (1975), p. 117",
       "P. J. Leonard, M.Sc. Thesis, Melbourne, Australia (1968)"
     ]
   }

Table 12 'Leonard and Barker'\: S\_k \(k = 2 \.\.\. \-8, integer k only\) of Leonard and Barker's DOSD \(Stobbe formula above the K edge, hence S\_2, S\_1 8\-11 % and 2\-4 % low, p\. 1627\)\.

kumar\_1985/leonard\_barker\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "leonard_barker_Ar",
     "material": "Ar",
     "file": "Ar/kumar_1985__leonard_barker_Ar.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "P. J. Leonard and J. A. Barker, in Theoretical Chemistry, Advances and Perspectives, Vol. 1 (1975), p. 117",
       "P. J. Leonard, M.Sc. Thesis, Melbourne, Australia (1968)"
     ]
   }

Table 12 'Leonard and Barker'\: S\_k \(k = 2 \.\.\. \-8, integer k only\) of Leonard and Barker's DOSD \(Stobbe formula above the K edge, hence S\_2, S\_1 8\-11 % and 2\-4 % low, p\. 1627\)\.

kumar\_1985/leonard\_barker\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "leonard_barker_Kr",
     "material": "Kr",
     "file": "Kr/kumar_1985__leonard_barker_Kr.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "P. J. Leonard and J. A. Barker, in Theoretical Chemistry, Advances and Perspectives, Vol. 1 (1975), p. 117",
       "P. J. Leonard, M.Sc. Thesis, Melbourne, Australia (1968)"
     ]
   }

Table 12 'Leonard and Barker'\: S\_k \(k = 2 \.\.\. \-8, integer k only\) of Leonard and Barker's DOSD \(Stobbe formula above the K edge, hence S\_2, S\_1 8\-11 % and 2\-4 % low, p\. 1627\)\.

kumar\_1985/leonard\_barker\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "leonard_barker_Xe",
     "material": "Xe",
     "file": "Xe/kumar_1985__leonard_barker_Xe.csv",
     "table": "tbl_1b74f66df9be",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "P. J. Leonard and J. A. Barker, in Theoretical Chemistry, Advances and Perspectives, Vol. 1 (1975), p. 117",
       "P. J. Leonard, M.Sc. Thesis, Melbourne, Australia (1968)"
     ]
   }

Table 12 'Leonard and Barker'\: S\_k \(k = 2 \.\.\. \-8, integer k only\) of Leonard and Barker's DOSD \(Stobbe formula above the K edge, hence S\_2, S\_1 8\-11 % and 2\-4 % low, p\. 1627\)\.

kumar\_1985/constraint\_Ne
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "constraint_Ne",
     "material": "Ne",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "cuthbertson_1932"
     ]
   }

2 inline points in the source record.

Table 8 caption and p\. 1623\: the molar\-refractivity constraints, from Cuthbertson and Cuthbertson \(1932\) corrected for non\-ideality with Michels et al\.'s \(1960\) second virial coefficient \(by Kumar and Meath\)\.

kumar\_1985/constraint\_Ar
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "constraint_Ar",
     "material": "Ar",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "R. Coulon, G. Montixi and R. Occelli, Can. J. Phys. 59, 1555 (1981)"
     ]
   }

2 inline points in the source record.

Table 9 caption and p\. 1623\: the molar\-refractivity constraints from Coulon et al\. \(1981\), not in the library \(so this reproduction may be fitted\)\. The vacuum medium is inferred from the values \(the He\-Ne 6328\.2 A and Ar\+ 4764\.9 A air lines\)\.

kumar\_1985/constraint\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "constraint_Kr",
     "material": "Kr",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "smith_1976"
     ]
   }

2 inline points in the source record.

Table 10 caption and p\. 1623\: the molar\-refractivity constraints from Smith, Huber and Parkinson \(1976\) at their 263\.21 and 177\.09 nm \(vacuum\)\.

kumar\_1985/constraint\_Xe
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "constraint_Xe",
     "material": "Xe",
     "table": "text",
     "quantity": "molar_refractivity",
     "unit": "cm3/mol",
     "abscissa_unit": "angstrom",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "bideau_mehu_1981"
     ]
   }

2 inline points in the source record.

Table 11 caption and p\. 1623\: the molar\-refractivity constraints from Bideau\-Mehu et al\. \(1981\), whose table lists 253\.7 and 170\.2 nm; the paper prints 2537\.0 and 1702\.0 A\.

Formulas
--------

No formulas are recorded.

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

.. code-block:: text

   [
     {
       "dataset": "leonard_barker_Kr",
       "row": "-4",
       "column": "value",
       "printed": "5.665",
       "corrected": "5.665e1",
       "reason": "The power of ten '(1)' is missing: S_-4 of krypton is about 56 (the adopted value is 5.632(1) = 56.32), and the column rises monotonically from S_-3 = 29.44 to S_-5 = 116.4.",
       "evidence": "Table image tbl_1b74f66df9be.jpg prints '5.665' with no exponent in the Leonard and Barker krypton column, beside '5.632(1)' adopted; every other entry of the S_-3 ... S_-8 rows carries (1) or (2) for krypton. Checked 2026-09-24."
     }
   ]

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.