tang_1974 ========= K\. T\. Tang and K\. K\. Poon, J\. Opt\. Soc\. Am\. 64, 1582 \(1974\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/josa\.64\.001582 `__ **Source kind:** theory **Recorded technique:** Continued\-factorization series for the dynamic polarizability giving upper and lower bounds on n \- 1 from Cauchy moments and excitation energies, compared with the Pade approximants of Langhoff and Karplus \(1969\); bounded estimates of oscillator strengths from the moments\. **Materials in structured entries:** Ar, Kr, Ne, Xe **Dataset quantities:** cauchy\_moment, oscillator\_strength, refractivity **Contents:** 29 datasets; 0 formulas. Curation notes -------------- All refractivities at NTP \(0 degrees C, 1 atm\) with n \- 1 = 2 pi N\_0 alpha\(omega\), 2 pi N\_0 = 0\.2502e\-4 \(Tables II\-VI, note a\)\: ideal\-gas density\. Wavelengths are nominal vacuum wavelengths\. The bounds are rigorous for the moments used, which are themselves fits \(Langhoff and Karplus's for Tables II\-V\); the paper shows that for Xe those moments are incompatible with Kingston's calculation and the measurements and recommends another set \(Table I, row 2\), used in Table VI\. All computed columns are checks; the columns reproduced from other papers name them\. Tables VII and VIII \(atomic hydrogen\) are not extracted \(hydrogen atoms are not a species of the package\); Tables X and XI \(argon oscillator\-strength bounds\) are summarised by their converged values, taken from the text\. The figures \(argon refractivity between the resonance lines, Figs\. 3\-6\) are not digitised\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- tang\_1974/cauchy\_Ne ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_Ne", "material": "Ne", "file": "Ne/tang_1974__cauchy_Ne.csv", "table": "tbl_d9080d4b7bd8", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } Table I, S\(\-2\)\.\.S\(\-8\) 'taken directly from' Langhoff and Karplus 1969 \(footnote a\), identical to langhoff\_1969/cauchy\_Ne \(printed there with one more digit\)\. tang\_1974/cauchy\_Ar ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_Ar", "material": "Ar", "file": "Ar/tang_1974__cauchy_Ar.csv", "table": "tbl_d9080d4b7bd8", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } Table I, S\(\-2\)\.\.S\(\-8\) 'taken directly from' Langhoff and Karplus 1969 \(footnote a\), identical to langhoff\_1969/cauchy\_Ar\. tang\_1974/cauchy\_Kr ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_Kr", "material": "Kr", "file": "Kr/tang_1974__cauchy_Kr.csv", "table": "tbl_d9080d4b7bd8", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } Table I, S\(\-2\)\.\.S\(\-8\) 'taken directly from' Langhoff and Karplus 1969 \(footnote a\), identical to langhoff\_1969/cauchy\_Kr \(printed there with one more digit\)\. tang\_1974/cauchy\_Xe ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_Xe", "material": "Xe", "file": "Xe/tang_1974__cauchy_Xe.csv", "table": "tbl_d9080d4b7bd8", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } Table I, S\(\-2\)\.\.S\(\-8\) 'taken directly from' Langhoff and Karplus 1969 \(footnote a\), identical to langhoff\_1969/cauchy\_Xe \(printed there with one more digit\)\. tang\_1974/cauchy\_recommended\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_recommended_Xe", "material": "Xe", "file": "Xe/tang_1974__cauchy_recommended_Xe.csv", "table": "tbl_d9080d4b7bd8", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table I, row \(2\), 'values we recommend for Xe' \(footnote c\)\: obtained 'by recasting the three\-term empirical Sellmeier equation of Abjean et al\. into the Cauchy equation', then 'modified so that they are within the bounds established by Starkschall and Gordon' \(p\. 6\)\. Derived from a published fit, so a check\. tang\_1974/upper41\_Ne ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "upper41_Ne", "material": "Ne", "file": "Ne/tang_1974__upper41_Ne.csv", "table": "tbl_59039d75fc92", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Upper bound \[alpha\(omega\)\]\_4,1 from the continued\-factor series \(Eq\. \(17\)\) with Table I's moments \(Langhoff and Karplus's\)\. tang\_1974/pade\_Ne ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pade_Ne", "material": "Ne", "file": "Ne/tang_1974__pade_Ne.csv", "table": "tbl_59039d75fc92", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } 'Padé value' column\: Langhoff and Karplus's Table III values, with the error bounds Tang and Poon computed by their method \(sigma column; half the spread of the bounds, not declared as an uncertainty\)\. tang\_1974/mean\_Ne ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mean_Ne", "material": "Ne", "file": "Ne/tang_1974__mean_Ne.csv", "table": "tbl_59039d75fc92", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Mean of the \[alpha\(omega\)\]\_4,1 upper bound and the \[2,1\]\_alpha Pade lower bound with the hybrid error bound \(sigma column, not declared\), 'the best value' from the information given \(p\. 5\)\. tang\_1974/upper41\_Ar ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "upper41_Ar", "material": "Ar", "file": "Ar/tang_1974__upper41_Ar.csv", "table": "tbl_6787ce6f0228", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Upper bound \[alpha\(omega\)\]\_4,1 from the continued\-factor series \(Eq\. \(17\)\) with Table I's moments \(Langhoff and Karplus's\)\. tang\_1974/pade\_Ar ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pade_Ar", "material": "Ar", "file": "Ar/tang_1974__pade_Ar.csv", "table": "tbl_6787ce6f0228", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } 'Padé value' column\: Langhoff and Karplus's Table III values, with the error bounds Tang and Poon computed by their method \(sigma column; half the spread of the bounds, not declared as an uncertainty\)\. tang\_1974/mean\_Ar ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mean_Ar", "material": "Ar", "file": "Ar/tang_1974__mean_Ar.csv", "table": "tbl_6787ce6f0228", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Mean of the \[alpha\(omega\)\]\_4,1 upper bound and the \[2,1\]\_alpha Pade lower bound with the hybrid error bound \(sigma column, not declared\), 'the best value' from the information given \(p\. 5\)\. tang\_1974/upper41\_Kr ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "upper41_Kr", "material": "Kr", "file": "Kr/tang_1974__upper41_Kr.csv", "table": "tbl_fa3fc33a90fd", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Upper bound \[alpha\(omega\)\]\_4,1 from the continued\-factor series \(Eq\. \(17\)\) with Table I's moments \(Langhoff and Karplus's\)\. tang\_1974/pade\_Kr ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pade_Kr", "material": "Kr", "file": "Kr/tang_1974__pade_Kr.csv", "table": "tbl_fa3fc33a90fd", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } 'Padé value' column\: Langhoff and Karplus's Table III values, with the error bounds Tang and Poon computed by their method \(sigma column; half the spread of the bounds, not declared as an uncertainty\)\. tang\_1974/mean\_Kr ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mean_Kr", "material": "Kr", "file": "Kr/tang_1974__mean_Kr.csv", "table": "tbl_fa3fc33a90fd", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Mean of the \[alpha\(omega\)\]\_4,1 upper bound and the \[2,1\]\_alpha Pade lower bound with the hybrid error bound \(sigma column, not declared\), 'the best value' from the information given \(p\. 5\)\. tang\_1974/upper41\_Xe ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "upper41_Xe", "material": "Xe", "file": "Xe/tang_1974__upper41_Xe.csv", "table": "tbl_cc7175832502", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Upper bound \[alpha\(omega\)\]\_4,1 from the continued\-factor series \(Eq\. \(17\)\) with Table I's moments \(Langhoff and Karplus's\)\. tang\_1974/pade\_Xe ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "pade_Xe", "material": "Xe", "file": "Xe/tang_1974__pade_Xe.csv", "table": "tbl_cc7175832502", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "langhoff_1969" ] } 'Lower bound Padé \[2,1\]\_alpha'\: Langhoff and Karplus's xenon values, which Tang and Poon found to be lower bounds throughout \(p\. 5\); at 1600 A this column prints 15\.460 where Langhoff and Karplus misprint 15\.640 \(erratum in langhoff\_1969\)\. tang\_1974/lower42\_Xe ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "lower42_Xe", "material": "Xe", "file": "Xe/tang_1974__lower42_Xe.csv", "table": "tbl_cc7175832502", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Lower bound \[alpha\(omega\)\]\_4,2 \(Eq\. \(32\)\) with Table I's set \(1\) and epsilon\_2 = 0\.3516 au\: above the Pade lower bound \(p\. 6\)\. tang\_1974/mean\_Xe ~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mean_Xe", "material": "Xe", "file": "Xe/tang_1974__mean_Xe.csv", "table": "tbl_cc7175832502", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Mean of \[alpha\(omega\)\]\_4,1 and \[alpha\(omega\)\]\_4,2 with the error bound \(sigma column, not declared\), from Langhoff and Karplus's moments, which Tang and Poon show to be unsatisfactory for Xe \(p\. 6\)\. tang\_1974/saxon\_1973\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "saxon_1973_Ne", "material": "Ne", "file": "Ne/tang_1974__saxon_1973_Ne.csv", "table": "tbl_59039d75fc92", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "R. P. Saxon, J. Chem. Phys. 59, 1539 (1973)" ] } Table II, 'Previous calculation'\: 'interpolated estimates based on' Saxon's calculated dynamic polarizabilities \(footnote e, p\. 6\), not Saxon's own numbers\. The original is not in the library\. tang\_1974/kingston\_1964\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kingston_1964_Ar", "material": "Ar", "file": "Ar/tang_1974__kingston_1964_Ar.csv", "table": "tbl_6787ce6f0228", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "kingston_1964" ] } 'Previous calculation'\: 'quoted directly from Kingston' \(p\. 6\), identical to kingston\_1964\. tang\_1974/kingston\_1964\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kingston_1964_Kr", "material": "Kr", "file": "Kr/tang_1974__kingston_1964_Kr.csv", "table": "tbl_fa3fc33a90fd", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "kingston_1964" ] } 'Previous calculation'\: 'quoted directly from Kingston' \(p\. 6\), identical to kingston\_1964\. tang\_1974/kingston\_1964\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kingston_1964_Xe", "material": "Xe", "file": "Xe/tang_1974__kingston_1964_Xe.csv", "table": "tbl_cc7175832502", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "kingston_1964" ] } 'Previous calculation'\: 'quoted directly from Kingston' \(p\. 6\), identical to kingston\_1964\. tang\_1974/mean\_recommended\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "mean_recommended_Xe", "material": "Xe", "file": "Xe/tang_1974__mean_recommended_Xe.csv", "table": "tbl_f64c046e444d", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } Table VI, mean of the \[alpha\(omega\)\]\_4,1 and \[2,1\]\_alpha bounds from the recommended moments \(Table I, set \(2\)\), with the error bound \(sigma column, not declared\)\. At 1500 A the bound spans \+\-11\.6\. tang\_1974/kingston\_1964\_table6\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "kingston_1964_table6_Xe", "material": "Xe", "file": "Xe/tang_1974__kingston_1964_table6_Xe.csv", "table": "tbl_f64c046e444d", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "kingston_1964" ] } Table VI, Kingston's values again; the 1900 A value is misreproduced \(erratum\)\. tang\_1974/starkschall\_gordon\_1971\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "starkschall_gordon_1971_Xe", "material": "Xe", "file": "Xe/tang_1974__starkschall_gordon_1971_Xe.csv", "table": "tbl_f64c046e444d", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "G. Starkschall and R. Gordon, J. Chem. Phys. 54, 663 (1971)" ] } Table VI, 'Previous calculation'\: Starkschall and Gordon's linear\-programming bounds, as midpoint and half\-range \(sigma column, not declared\)\. The original is not in the library\. tang\_1974/abjean\_1971\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "abjean_1971_Xe", "material": "Xe", "file": "Xe/tang_1974__abjean_1971_Xe.csv", "table": "tbl_f64c046e444d", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "abjean_1971" ] } Table VI, 'Measured', Abjean et al\. \(interferometry\), 2200\-1800 A at round wavelengths\: the formula column of abjean\_1971's Table 3 \(values of their three\-term fit, not measurements\)\. The measurements themselves \(abjean\_1971/experiment\_Xe\) are fitted\. tang\_1974/chashchina\_shreider\_1969\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "chashchina_shreider_1969_Xe", "material": "Xe", "file": "Xe/tang_1974__chashchina_shreider_1969_Xe.csv", "table": "tbl_f64c046e444d", "quantity": "refractivity", "scale": 0.0001, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "reproduced", "reproduced_from": [ "G. I. Chashchina and E. Ya. Shreider, Opt. Spectrosc. 27, 79 (1969)" ] } Table VI, 'Measured', Chashchina and Shreider \(line shifts\), 2200\-1600 A at round wavelengths\: values of their smoothing Sellmeier formula\. The 1500 A value \(27\.789\) is not extracted\: their xenon measurements stop at 1550 A, so it is an extrapolation\. The original is not in the library\. tang\_1974/cauchy\_chashchina\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cauchy_chashchina_Ar", "material": "Ar", "file": "Ar/tang_1974__cauchy_chashchina_Ar.csv", "table": "tbl_e64e93bfd6da", "quantity": "cauchy_moment", "unit": "au", "abscissa": "order", "abscissa_unit": "1", "use": "check" } Table IX, the 18 Cauchy moments S\(\-2n\), n = 1\.\.18 \(rows by moment order \-2n\), 'obtained by recasting the three\-term Sellmeier formula of Chashchina, Gladushchak, and Shreider' \(footnote a\); printed as mantissa x 10^k and stored as mantissa e k\. Derived from a published fit\: a check\. S\(\-2\) = 11\.044 and S\(\-4\) = 29\.236 against 11\.052 and 29\.26 from Leonard's \(1974\) adjusted version of that formula \(\+0\.07 %, \+0\.08 %\: Leonard's adjustment\)\. tang\_1974/oscillator\_strengths\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "oscillator_strengths_Ar", "material": "Ar", "table": "text", "quantity": "oscillator_strength", "abscissa_unit": "hartree", "use": "check" } 2 inline points in the source record. p\. 6\: the continued\-factor bounds on the oscillator strengths of argon's two resonance lines from Table IX's moments and Moore's energies \(epsilon\_1 = omega\_1 = 0\.4272 au from Table I, epsilon\_2 = 0\.4347 au from the text\)\: '\[f1\]\_n,2 and \[f1\]\_n,3 have converged to 0\.1385 from opposite directions\. The value to which f2 converges is 0\.1418'; their sum 0\.2803 matches Chashchina et al\.'s 0\.28 \+\- 0\.02 from Wolfsohn's method\. Tables X and XI \(the bounds for n = 1\-18 moments\) are not extracted\. Derived from Chashchina et al\.'s Sellmeier fit\: a check\. Formulas -------- No formulas are recorded. Corrections ----------- .. code-block:: text [ { "dataset": "kingston_1964_table6_Xe", "row": "1900", "column": "value", "printed": "9.984", "corrected": "9.884", "reason": "Kingston's calculated xenon value at 1900 A is 9.884; Tang and Poon's Table VI misreproduces it as 9.984.", "evidence": "Kingston 1964, Table I (image tbl_368145603687.jpg) prints 9.884; Tang and Poon's own Table V (previous calculation, same source) prints 9.884; Langhoff and Karplus 1969, Table III, print 9.884. With 9.884 the column's increments grow steadily (0.289, 0.372, 0.499, 0.711, 1.118 from 2200 A down); 9.984 would make them 0.599 then 0.611. Table image tbl_f64c046e444d.jpg shows 9.984." } ] Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register ` for the checks and decisions.