mansfield_peck_1969 =================== C\. R\. Mansfield and E\. R\. Peck, "Dispersion of Helium", J\. Opt\. Soc\. Am\. 59, 199 \(1969\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` No DOI is recorded. **Source kind:** measurement **Recorded technique:** Compensated corner\-reflector Michelson interferometer, fringe shifts monitored simultaneously at two wavelengths while a 24 cm gas cell was evacuated to about 0\.01 torr and filled to nearly atmospheric pressure; mercury manometer with travelling microscope and meter bar \(corrected for mercury expansion and local gravity\), copper\-constantan thermocouple against an ice bath; helium of 99\.99 % minimum purity through a dry\-ice\-acetone trap\. The absolute refractivity was measured at the Hg green line \(5462\.258 A\); the other wavelengths were measured as refractivity ratios to it \(pp\. 199\-200\)\. **Materials in structured entries:** He **Dataset quantities:** oscillator\_strength, polarizability, refractivity **Contents:** 16 datasets; 7 formulas. Curation notes -------------- Identity unverified by the library\: the observed title and authors are "Dispersion of Helium", C\. R\. Mansfield and E\. R\. Peck \(University of Idaho, received 28 March 1968\); the original file is 'josa\-59\-2\-199\-2\.pdf', consistent with JOSA 59, 199 \(1969\)\. No DOI is recorded\. Reduction \(p\. 199\)\: values are converted to 760 torr, 0 degrees C with the Lorentz\-Lorenz form r0/r = rho0/rho \[1 \+ r0 \(1 \- P T0 / P0 T\) / 6\] and the density ratio rho0/rho = P0 T Z / \(P T0 Z0\), Z from the virial fit to White et al\. \(1960\)\: Z = 1 \+ \(0\.74062e\-8 T^2 \- 0\.061793e\-4 T \+ 16\.742e\-4\) P, P in atm, T in K\. A real\-gas reduction\. Wavelengths are vacuum wavelengths \(Table I heading and p\. 200\)\. Uncertainty \(p\. 200\)\: the absolute refractivity at 5462\.258 A, 760 torr, 0 degrees C, is \(n\-1\) x 10^5 = 3\.4950 \+\- 0\.0014, 'the standard deviation from the mean of 156 individual measurements'; 'a liberal estimate of the systematic errors resulting from impurities, pressure measurement, temperature measurement, and cell\-length measurement would raise the error of the absolute refractivity to \+\-0\.009' \(Table III prints \+\-0\.0088\)\. Every other value is the green\-line value divided by a measured ratio, so the absolute error is a scale error common to all points; the ratios are 'subject only to errors of the measurement of fringe shift and wavelength'\. The per\-point scatter is taken from the rms residual of the four\-parameter Eq\. \(4\) fit, 2\.9e\-5 in units of \(n\-1\) x 10^5, i\.e\. 0\.29 in the printed units of 1e\-9\. Table I's 'Deviation from Eq\. \(4\)' column is not extracted and does not reproduce\: the printed Eq\. \(4\) gives residuals \(fit minus value\) of 0\.02, \-0\.73, \-0\.06, \.\.\. and a free four\-parameter refit of the 13 fitted points reproduces neither sign of the printed column \(checked 2026\-09\-24\)\. The two excluded points, at which the refit lies 1\.6e\-9 and 4\.6e\-9 above the measurement, are printed with \-1\.72 and \-4\.23, so the column's sign is probably value minus fit, against its heading\. The theoretical refractivity \(p\. 202\) is computed from Eq\. \(5\) with Loschmidt's number and oscillator strengths and photoionisation cross sections from the literature \(Table II; Stewart and Webb 1963 for the continuum\), n \- 1 = \(3/2\) R \(1 \+ R/4\) with R the Lorentz\-Lorenz function\: an ideal\-gas density at 760 torr, 0 degrees C\. The 26 computed values are not tabulated, only fitted \(Eqs\. 6\-8\) and quoted at 5462\.258 A \(Table IV\)\. The paper's sum\-rule check \(p\. 202\)\: discrete F = 0\.447, continuum 1\.540, total 1\.998\. 'We have not estimated the absolute accuracy of the computation\.' Not extracted\: Table V \(effective F values and absorption wavelengths of one\-term formulas\), Table VII \(Becquerel\-equation constants\) and Table VIII \(Verdet constants derived from the dispersion formulas through the Becquerel equation, printed in 'min/Oe cm' with no power of ten, and a ratio r to the unquoted measurement of Ingersoll and Liebenberg\)\: they are derived from dispersion formulas, not measured\. The dielectric\-constant column of Table VI \(\(k \- 1\) at 760 torr, 20 degrees C, twice the extrapolated n' \- 1\) has no quantity of its own; its polarizability column is extracted\. Table VI's alpha follows from \(k\-1\) by Clausius\-Mossotti with the ideal\-gas density at 760 torr, 20 degrees C \(6\.462e\-5 gives 0\.2054e\-24 cm^3; checked 2026\-09\-24\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mansfield\_peck\_1969/experiment ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "experiment", "material": "He", "file": "He/mansfield_peck_1969__experiment.csv", "table": "tbl_aae92dff687e", "quantity": "refractivity", "scale": 1e-09, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "real", "use": "primary", "uncertainty": { "absolute": 0.29, "level": "rms", "systematic_relative": 0.0026 } } The 13 points the paper fitted \(Table I\)\. The 5462\.258 A value is the measured absolute refractivity; the others are it divided by measured ratios, so the relative values are far better than the absolute scale\. mansfield\_peck\_1969/experiment\_excluded ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "experiment_excluded", "material": "He", "file": "He/mansfield_peck_1969__experiment_excluded.csv", "table": "tbl_aae92dff687e", "quantity": "refractivity", "scale": 1e-09, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "real", "use": "excluded" } 9660\.434 and 15300\.153 A, printed in parentheses with footnote a, 'Values not included while fitting dispersion formulas'\: they 'deviated far enough from the trial formulas that it was thought that they unduly affected the formulas' \(p\. 200\)\. They lie 1\.6e\-9 and 4\.6e\-9 \(5e\-5 and 1\.3e\-4 relative\) below a four\-parameter fit of the other 13\. mansfield\_peck\_1969/oscillator\_strengths ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "oscillator_strengths", "material": "He", "file": "He/mansfield_peck_1969__oscillator_strengths.csv", "table": "tbl_330bf663e80e", "quantity": "oscillator_strength", "abscissa_unit": "um-1", "wavelength_medium": "vacuum", "use": "reproduced", "reproduced_from": [ "B. Schiff and C. L. Pekeris, Phys. Rev. 134, A640 (1964)", "W. L. Wiese, M. W. Smith and B. M. Glennon, Atomic Transition Probabilities, NBS Natl. Std. Ref. Data System 4, Vol. 1 (U. S. Government Printing Office, Washington, D. C., 1953), p. 11", "musulin_1964", "A. Dalgarno and A. L. Stewart, Proc. Phys. Soc. (London) 76, 49 (1960)" ] } Table II\: F\_n and wavenumbers of 1s^2 1S \-\> 1s np 1P \(rows 1s2p\.\.1s10p\), of the doubly excited \(2s, np\) \(2s2p\.\.2s6p\) and \(3s, np\) \(3s2p\.\.3s4p\) series\. Footnotes \(image\)\: a Schiff and Pekeris \(n = 2, 3\), b Wiese et al\. \(Ref\. 29; n = 4\-6\), c Musulin and Epstein \(Ref\. 25; n = 7\-10 and the sum from 11\)\. The \(2s, np\) values for n = 2\-6 are Dalgarno and Stewart's \(p\. 202\); the three sum rows \(1snp\_11\+, 2snp\_7\+, 3snp\_5\+\) are the paper's estimates lumped at one wavenumber \(the 1snp\_11\+ sum 'assumed to act at 505\.5 A', the mean of the 10P and series\-limit wavelengths\)\. The text \(p\. 202\) says the \(2s, np\) sum from n = 7 'was estimated by the ratio test to be 0\.00122', but the table prints 0\.00137 \(not corrected\: which is meant is not known\)\. Wavenumbers of the \(2s, np\) levels come from Dalgarno and Stewart's E = 4\.81 \- 1\.58/n^2 Ry; those of the \(3s, np\) levels are rough estimates \(p\. 202\)\. The library's CSV merges each series label into the preceding sum row; the row ids follow the image\. mansfield\_peck\_1969/koch\_1913 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "koch_1913", "material": "He", "file": "He/mansfield_peck_1969__koch_1913.csv", "table": "tbl_cd9d9ebee3ff", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "J. Koch, Ark. Mat. Astr. Fys. 9, 1 (1913)" ] } Table III, at 5462\.258 A as quoted by Mansfield and Peck; the original is not in the library, and its wavelength medium and reduction are not stated here\. mansfield\_peck\_1969/cuthbertson ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "cuthbertson", "material": "He", "file": "He/mansfield_peck_1969__cuthbertson.csv", "table": "tbl_cd9d9ebee3ff", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "cuthbertson_1932" ], "uncertainty": { "absolute": 0.05, "level": "not stated" } } Table III prints '3\.4890 \+\- 0\.05 \(?\)', the query mark the paper's\. The value is Cuthbertson and Cuthbertson's 1932 mean at the green line, 0\.00003489 \(cuthbertson\_1932, p\. 45, three measurements 3489, 3485, 3492 e\-8\), so the paper is the 1932 one \(Ref\. 7\); the \+\-0\.05 is Mansfield and Peck's guess\. The same value is Table III of cuthbertson\_1932 at 5462 A\. mansfield\_peck\_1969/theory ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "theory", "material": "He", "file": "He/mansfield_peck_1969__theory.csv", "table": "tbl_acc0ad617db8", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "ideal", "use": "check" } The paper's own oscillator\-strength sum \(Table IV, 'Present calc\.'\); its absolute accuracy was not estimated\. The corrected Eqs\. \(7\) and \(8\), fitted to the same computation, give 3\.49784 here, 7e\-5 above the printed 3\.4976; the printed 'percentage difference' 0\.02 does not follow from 3\.4976 and 3\.4950 \(0\.074 %\)\. mansfield\_peck\_1969/korwin\_1934 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "korwin_1934", "material": "He", "file": "He/mansfield_peck_1969__korwin_1934.csv", "table": "tbl_acc0ad617db8", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "J. Korwin, Z. Physik 91, 1 (1934)" ] } Theoretical value \(Table IV\)\. mansfield\_peck\_1969/musulin\_epstein\_1964 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "musulin_epstein_1964", "material": "He", "file": "He/mansfield_peck_1969__musulin_epstein_1964.csv", "table": "tbl_acc0ad617db8", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "musulin_1964" ] } Theoretical value \(Table IV\), 15\.7 % below this experiment as printed \(the numbers give 14\.6 %\)\. musulin\_1964's formula gives 3\.130e\-5 at 5462 A, not 2\.983e\-5\: the origin of this number is unclear\. mansfield\_peck\_1969/karplus\_kolker\_1963 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "karplus_kolker_1963", "material": "He", "file": "He/mansfield_peck_1969__karplus_kolker_1963.csv", "table": "tbl_acc0ad617db8", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "M. Karplus and J. J. Kolker, J. Chem. Phys. 39, 2997 (1963)" ] } Theoretical value \(Table IV\); citation as printed \(Ref\. 24\)\. mansfield\_peck\_1969/migneron\_levinger\_1965 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "migneron_levinger_1965", "material": "He", "file": "He/mansfield_peck_1969__migneron_levinger_1965.csv", "table": "tbl_acc0ad617db8", "quantity": "refractivity", "scale": 1e-05, "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "migneron_1965" ] } Theoretical value at 5500 A \(Table IV\), 'not of sufficient accuracy to permit dispersion formulas to be fitted' \(p\. 202\)\. mansfield\_peck\_1969/alpha\_cuthbertson ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_cuthbertson", "material": "He", "file": "He/mansfield_peck_1969__alpha_cuthbertson.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "reproduced", "reproduced_from": [ "cuthbertson_1932" ] } Table VI\: Mansfield and Peck's static extrapolation of a dispersion formula fitted to Cuthbertson and Cuthbertson's 1932 data \(the 1932 one\-term formula gives 1\.32614e27/38313\.7e27 = 3\.4613e\-5 at 0 degrees C, i\.e\. \(k \- 1\) = 6\.450e\-5 at 20 degrees C against the printed 6\.453\: probably their own refit\)\. mansfield\_peck\_1969/alpha\_experiment ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_experiment", "material": "He", "file": "He/mansfield_peck_1969__alpha_experiment.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "check", "uncertainty": { "relative": 0.0037, "level": "not stated" } } Table VI\: the static extrapolation of the experimental dispersion formulas \(Eq\. \(3\) gives the printed \(k\-1\) = 6\.462e\-5 at 20 degrees C exactly\), not an independent measurement; \(k \- 1\) x 10^5 = 6\.462 \+\- 0\.024\. mansfield\_peck\_1969/alpha\_theory ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_theory", "material": "He", "file": "He/mansfield_peck_1969__alpha_theory.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "check" } Table VI\: the paper's oscillator\-strength sum in the static limit \('direct computation'\)\. mansfield\_peck\_1969/alpha\_chung\_hurst\_1966 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_chung_hurst_1966", "material": "He", "file": "He/mansfield_peck_1969__alpha_chung_hurst_1966.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "reproduced", "reproduced_from": [ "D. T. Chung and R. P. Hurst, Phys. Rev. 152, 35 (1966)" ] } Table VI, theoretical \(the dielectric constant was 'computed from alpha'\)\. mansfield\_peck\_1969/alpha\_maryott\_buckley\_1953 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_maryott_buckley_1953", "material": "He", "file": "He/mansfield_peck_1969__alpha_maryott_buckley_1953.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "reproduced", "reproduced_from": [ "A. A. Maryott and F. Buckley, Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State, NBS Circ. 537 (1953), p. 3" ], "uncertainty": { "relative": 0.0062, "level": "not stated" } } Table VI\: the review's recommended dielectric constant, \(k \- 1\) x 10^5 = 6\.50 \+\- 0\.04 at 760 torr, 20 degrees C, converted to alpha by Mansfield and Peck\. mansfield\_peck\_1969/alpha\_chung\_1968 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_chung_1968", "material": "He", "file": "He/mansfield_peck_1969__alpha_chung_1968.csv", "table": "tbl_a09b6733c084", "quantity": "polarizability", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "angstrom", "use": "reproduced", "reproduced_from": [ "K. C. Chung, Phys. Rev. 166, 1 (1968)" ] } Table VI, theoretical\. Formulas -------- mansfield\_peck\_1969/eq1 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq1", "material": "He", "equation": "Eq. (1), p. 200", "printed": "(n - 1) x 10^5 = 1470.091/(423.98 - sigma^2); rms residual = 5.7 x 10^-5", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "real", "range": "480.1-2058.7 nm (the 13 fitted points of Table I)", "coefficients": { "b": "1470.091", "c": "423.98" }, "check": "Residuals against the 13 fitted points of Table I, rms 0.63e-9 (quoted 0.57e-9); extrapolated to sigma = 0 and to 20 degrees C (x 273.15/293.15, times 2) it gives (k - 1) = 6.4617e-5 (Table VI: 6.462 from the recommended formula). Checked 2026-09-24." } Two\-parameter fit to the experimental data\. mansfield\_peck\_1969/eq2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq2", "material": "He", "equation": "Eq. (2), p. 200", "printed": "(n - 1) x 10^5 = 2.212693 + 196.0586/(156.25 - sigma^2); rms residual = 4.2 x 10^-5", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "real", "range": "480.1-2058.7 nm (the 13 fitted points of Table I)", "coefficients": { "a": "2.212693", "b": "196.0586", "c": "156.25" }, "check": "Residuals against the 13 fitted points of Table I, rms 0.41e-9 (quoted 0.42e-9). Checked 2026-09-24." } Three\-parameter fit to the experimental data \(a constant plus one pole\)\. mansfield\_peck\_1969/eq3 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq3", "form": "dn_sigma2", "terms": { "scale": "1e-5", "B": [ "1452.449", "-0.0009278" ], "C": [ "418.95", "-1.3331" ] }, "range_nm": [ 480.1, 2058.7 ], "material": "He", "equation": "Eq. (3), p. 200", "printed": "(n - 1) x 10^5 = 1452.449/(418.95 - sigma^2) + 0.0009278/(1.3331 + sigma^2); rms residual = 3.6 x 10^-5", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "real", "range": "480.1-2058.7 nm (the 13 fitted points of Table I)", "coefficients": { "b1": "1452.449", "c1": "418.95", "b2": "0.0009278", "c2": "-1.3331" }, "check": "Against the 13 fitted points: residuals (fit - value) have a mean of +0.38e-9 and an rms about that mean of 0.36e-9 (quoted rms 0.36e-9); the offset (1.1e-5 relative) is what the rounding of 418.95 to two decimals allows (+-0.005 moves the fit by 0.42e-9). Static limit at 20 degrees C (x 273.15/293.15, times 2): (k - 1) = 6.4620e-5, Table VI's 'present expt.' 6.462 exactly. Checked 2026-09-24." } The paper's recommended formula for interpolation \(p\. 201\)\. The second term is printed with '\+' in both places; 'both Sellmeier constants are negative' \(p\. 201\), i\.e\. B2 = \-0\.0009278 over \(sigma2^2 \- sigma^2\) with sigma2^2 = \-1\.3331, which is the printed form\. The printed sign is confirmed by the static\-limit check\. mansfield\_peck\_1969/eq4 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq4", "material": "He", "equation": "Eq. (4), p. 200", "printed": "(n - 1) x 10^5 = 1467.196/(423.15 - sigma^2) + 0.00002125/(0.71530 - sigma^2); rms residual = 2.9 x 10^-5", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "real", "range": "480.1-2058.7 nm (the 13 fitted points of Table I)", "coefficients": { "b1": "1467.196", "c1": "423.15", "b2": "0.00002125", "c2": "0.71530" }, "check": "Against the 13 fitted points: rms 0.38e-9 (quoted 0.29e-9); a free refit of the same form gives 1467.60/(423.264 - s^2) + 2.100e-5/(0.71292 - s^2) with rms 0.30e-9, so the printed coefficients are a rounded or slightly different solution. The printed deviation column of Table I does not reproduce (see notes). Checked 2026-09-24." } The second term puts a pole at 1\.18 um inside the data, which 'does not exist in helium' \(possibly water vapour\); the paper recommends Eq\. \(3\) for interpolation\. mansfield\_peck\_1969/eq6 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq6", "material": "He", "equation": "Eq. (6), p. 202", "printed": "(n - 1) x 10^5 = 1499.65775/(432.0852 - sigma^2); rms residual = 4.8 x 10^-5", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "ideal", "range": "the 26 computed wavelengths (those of Table I and of Cuthbertson and Cuthbertson)", "coefficients": { "b": "1499.65775", "c": "432.0852" }, "check": "At 5462.258 A: 3.49788 (Table IV prints 3.4976 for the computation). Static limit at 20 degrees C: (k - 1) = 6.468e-5, Table VI's 'present theor. work'. Checked 2026-09-24." } One\-pole fit to the paper's theoretical values\. mansfield\_peck\_1969/eq7 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq7", "material": "He", "equation": "Eq. (7), p. 202", "printed": "(n - 1) x 10^5 = 0.563419516 - 1058.08288/(363.9286 - sigma^2); rms residual = 7.3 x 10^-7", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "ideal", "range": "the 26 computed wavelengths", "coefficients": { "a": "0.563419516", "b": "1058.08288", "c": "363.9286" }, "check": "As printed it gives -2.3710 at 5462.258 A (negative); with '+' before the pole term it gives 3.49784, agreeing with Eq. (8) (3.49784) to 1e-10 and, in the static limit, 3.470811 against Eq. (8)'s 3.470810 (Table VI: 6.468 at 20 degrees C). Checked 2026-09-24." } Misprinted sign\: the corrected form is \(n \- 1\) x 10^5 = 0\.563419516 \+ 1058\.08288/\(363\.9286 \- sigma^2\)\. mansfield\_peck\_1969/eq8 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq8", "form": "dn_sigma2", "terms": { "scale": "1e-5", "B": [ "645.686373", "1290.41989" ], "C": [ "318.1312", "895.3867" ] }, "range_nm": [ 275.3, 2058.7 ], "material": "He", "equation": "Eq. (8), p. 202", "printed": "(n - 1) x 10^5 = 645.686373/(318.1312 - sigma^2) 1290.41989/(895.3867 - sigma^2); rms residual = 4.5 x 10^-10", "variable": "sigma: vacuum wavenumber in um^-1", "state": "1atm_0C", "density": "ideal", "range": "the 26 computed wavelengths", "coefficients": { "b1": "645.686373", "c1": "318.1312", "b2": "1290.41989", "c2": "895.3867" }, "check": "With '+' between the terms: 3.49784 at 5462.258 A (Table IV prints 3.4976 for the computation itself, 7e-5 lower, which the fit's quoted residual does not explain); static limit 3.470810, i.e. (k - 1) = 6.4680e-5 at 20 degrees C, Table VI's 'direct computation' 6.468. Checked 2026-09-24." } The operator between the two terms is missing in print; the corrected form is \(n \- 1\) x 10^5 = 645\.686373/\(318\.1312 \- sigma^2\) \+ 1290\.41989/\(895\.3867 \- sigma^2\) \('the Sellmeier constants in Eq\. \(8\) are all positive', p\. 202\)\. The paper recommends it for the region covered\. Corrections ----------- .. code-block:: text [ { "dataset": "oscillator_strengths", "row": "1s4p", "column": "x", "printed": "19.4195", "corrected": "19.1495", "reason": "The 1s4p wavenumber is printed above the 1s5p value (19.395), which breaks the Rydberg series; 19.1495 is the printed digits with '41' and '14' transposed.", "evidence": "A Rydberg fit sigma_n = I - R/(n - delta)^2 (R = 10.9722 um^-1) to the paper's own n = 5-10 wavenumbers (residuals below 0.0035) gives I = 19.8303, delta = -0.0166 and sigma_4 = 19.150 (and 18.625, 17.132 for n = 3, 2 against the printed 18.6211, 17.1130); checked 2026-09-24. The table image tbl_330bf663e80e.jpg shows 19.4195 as extracted." } ] 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.