ladenburg_1933#
R. Ladenburg and C. C. Van Voorhis, “The continuous absorption of oxygen between 1750 and 1300A and its bearing upon the dispersion”, Phys. Rev. 43, 315 (1933)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: Photographic-photometric absorption with a Cario-Schmidt-Ott fluorite vacuum spectrograph and a water-cooled capillary hydrogen discharge (many-line spectrum; CO lines for the longer wavelengths); intensity scale from five diaphragms of known open area (1.000-0.062, within 2 %); absorption tube 12.3 cm long (some exposures with the spectrograph filled, path 34.5 cm, agreeing within the errors); O2 from electrolysis at 0.079-1.86 mm Hg, the larger 425 cc volume always connected to limit the photochemical ‘clean up’ of O2; Eastman 3-0 plates, a photoelectric densitometer; the continuous background (scattered and fluorescence light) subtracted line by line (pp. 315-319). 1334-1670 A measured.
Materials in structured entries: O2
Dataset quantities: absorption_cross_section, oscillator_strength, refractivity
Contents: 3 datasets; 2 formulas.
Curation notes#
Journal pages 315-321 = PDF pages 1-7 (PDF page 8 repeats Fig. 3). Identity checked against the first page: Ladenburg and Van Voorhis, Phys. Rev. 43, 315, received 3 January 1933. O2 only.
Absorption: beta is defined by I = I0 exp(-beta p l), p in cm Hg at 20 C, l in cm (Eq. 1, p. 318); the results, ‘reduced to N.P.T.’, are the absorption coefficients alpha of Fig. 5 (figure only, 1750-1300 A, p. 319). N at N.P.T. is 2.706e19 cm^-3 (footnote 15, p. 320, with e = 4.770e-10, e/mc = 1.76e7, c = 2.998e10). ‘we estimate that the error of the beta values obtained may be as much as 5-10 percent’ (p. 319). The worked examples of p. 319 (one plate: beta = 5.28 at 1469 A and 4.36 at 1496 A, per cm Hg at 20 C) illustrate the background correction and are not results; not extracted. Text values: the maximum at nu = 69000 cm^-1, lambda = 1450 A (p. 319; the abstract prints 6.8e4 cm^-1 with 1450 A, p. 315), ‘about 490 cm^-1’ (abstract), and a layer of 0.0014 cm at N.P.T. halves the light there (p. 319; ln 2 / 0.0014 = 495 cm^-1, consistent). Between 1300 and 1100 A O2 at 0.25 mm is ‘practically transparent in a layer of 4 m length’ (p. 319). Oscillator strength (Eq. 2, p. 320): integral alpha dnu = pi N f e^2 / m c^2 = 2.38e7 f (cm^-2; reproduced with the footnote’s constants, 2.3805e7), giving f = 0.193. Temperature of the absorption measurements not stated beyond the 20 C of Eq. 1.
Dispersion (p. 315 and ‘Added in proof’, pp. 320-321): Ladenburg and Wolfsohn (Z. Phys. 79, 42 (1932), not in the library) described O2’s dispersion from the visible to 1920 A by three resonances (formula lw_1932). This paper adds the continuum’s contribution G(nu) = (1 / 2 pi^2) integral_a^b alpha(omega) d omega / (omega^2 - nu^2), a = 56000, b = 78000 cm^-1, computed by F. Seitz from Fig. 5 (Eq. 4), and fits the remainder H = (n - 1) - G by one term I (formula continuum_plus_one_term). Table I (x 10^7; image checked): G at 55000, 52084, 51020, 50000, 45000, 40000, 35000, 30000, 25000 cm^-1 = 1612, 1277, 1193, 1125, 907, 768, 680, 618, 573; H = 2312, 2315, 2316, 2288, 2268, 2241, 2220, 2202 and I = 2330, 2323, 2317, 2288, 2262, 2240, 2222, 2206 at the eight wave numbers 52084-25000. H = (n - 1) - G exactly in every row (checked 2026-09-25). G, H and I are not extracted: partial refractivities and a fit have no vocabulary quantity (format need reported; G is the check on a Kramers-Kronig integral of the Schumann-Runge continuum). ‘The possible error of the G-values is at least ten times that of the dispersion values which are accurate to within one unit’ (p. 320). The authors conclude (p. 321) that the usual formula with isolated resonances is a good approximation, the weak Schumann-Runge bands having no appreciable influence down to 1920 A.
Reproduced here, not in the library: Ladenburg and Wolfsohn’s dispersion (dataset lw_refractivity, formula lw_1932); Koch’s (1912) resonance at 1421 A from the dispersion of air (footnote 16, p. 320; air is not curated). Fig. 5 is a figure only; Ditchburn and Heddle (1953, ditchburn_1953, Fig. 4) replot Ladenburg and Van Voorhis’s points. Comparisons: watanabe_1953 (380 cm^-1 at about 1420 A) and metzger_1964 (402 +- 20) are lower; ditchburn_1953 agrees (490 cm^-1 at 1450 A).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
ladenburg_1933/lw_refractivity#
{
"id": "lw_refractivity",
"material": "O2",
"file": "O2/ladenburg_1933__lw_refractivity.csv",
"table": "tbl_0010b8557526",
"quantity": "refractivity",
"scale": 1e-07,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"state": "1atm_0C",
"use": "reproduced",
"reproduced_from": [
"R. Ladenburg and G. Wolfsohn, Zeits. f. Physik 79, 42 (1932)"
],
"uncertainty": {
"absolute": 1,
"level": "bound"
}
}
Table I column (n(nu) - 1) x 10^7: ‘the values of the dispersion of oxygen (n(nu) - 1) measured by Ladenburg-Wolfsohn (L-W)’, at eight round wave numbers 52084-25000 cm^-1 (1920-4000 A): at round wave numbers, so probably smoothed or interpolated, not the measured lines. ‘accurate to within one unit’ (1e-7, p. 320; recorded as a bound). State: N.P.T. (the paper’s formulas refer n - 1 to N at N.P.T., footnote 15; L-W’s own reduction is not described here; 1 atm, 0 C assumed); density unknown. The wave numbers are 1/lambda (vacuum or air not stated; the difference, 7 cm^-1 at 25000 cm^-1, moves n - 1 by under 0.1e-7). The original is not in the library: this reproduction is the best copy available (missing-O). The three-term formula lw_1932 reproduces the column to 3e-7 with C 0.30 % larger than the footnote’s constants give.
ladenburg_1933/sr_maximum#
{
"id": "sr_maximum",
"material": "O2",
"table": "text",
"quantity": "absorption_cross_section",
"unit": "Mb",
"scale": 0.036954915004,
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "primary",
"uncertainty": {
"relative": 0.1,
"level": "bound"
}
}
1 inline points in the source record.
Abstract (p. 315) and p. 319: the maximum absorption coefficient of the Schumann-Runge continuum ‘reduced to N.P.T. is about 490 cm^-1’, at nu = 69000 cm^-1, lambda = 1450 A (the abstract’s ‘6.8 x 10^4 cm^-1’ is the rounded position; 1450 A is 68970 cm^-1), read from the smooth curve of Fig. 5. scale = 1e18 / 2.706e19 (the paper’s N at N.P.T.) to Mb: 18.1 Mb. 10 % from the stated error of the beta values (‘as much as 5-10 percent’, p. 319), recorded as a bound. The only printed value of the measured curve (Fig. 5 is a figure).
ladenburg_1933/continuum_f#
{
"id": "continuum_f",
"material": "O2",
"table": "text",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check"
}
1 inline points in the source record.
Abstract and p. 320: f = 0.193 from integral alpha(nu) dnu = 2.38e7 f (Eq. 2, N = 2.706e19) over the absorption curve of Fig. 5 (range not stated; G uses 56000-78000 cm^-1), ‘compared with 0.202 calculated from the dispersion measurements’. Index abscissa: an integrated strength. Compare ditchburn_1953 (0.215 +- 0.020), watanabe_1953 (0.161), metzger_1964 (0.142). A check.
Formulas#
ladenburg_1933/lw_1932#
{
"id": "lw_1932",
"material": "O2",
"equation": "p. 315 (quoted from Ladenburg and Wolfsohn 1932); Eq. (3) without the integral, p. 320",
"printed": "n(nu) - 1 = C Sigma_s f_s / (nu_s^2 - nu^2), C = N e^2 / 2 pi m c^2; lambda_1 = 1899A, lambda_2 = 1468A, lambda_3 = 544A, f_1 = 4.0 x 10^-5, f_2 = 0.202, f_3 = 5.93",
"variable": "nu: wave number in cm^-1 (nu_s = 1 / lambda_s); N = 2.706e19 cm^-3 at N.P.T.",
"state": "1atm_0C",
"density": "unknown",
"range": "visible to 1920 A (the L-W data, 1920-4000 A in Table I)",
"coefficients": {
"lambda_1": "1899",
"lambda_2": "1468",
"lambda_3": "544.4",
"f_1": "4.04e-5",
"f_2": "0.202",
"f_3": "5.928"
},
"check": "With C from footnote 15's constants (N e^2 / 2 pi m c^2 = 1.2060e6 cm^-2) the formula gives 0.28-0.38 % less than Table I's (n - 1) column (3576.0 against 3589 at 52084 cm^-1, 2765.7 against 2775 at 25000); with C = 1.2096e6 cm^-2 (0.30 % larger, the value that reproduces Table I's I column, see continuum_plus_one_term) it reproduces the column to within 3e-7 (3505.0 against 3508 at 51020 cm^-1, the others within 2.4e-7). The source of the 0.30 % is not identified. Checked 2026-09-25."
}
Reproduced from R. Ladenburg and G. Wolfsohn, Z. Phys. 79, 42 (1932), not in the library. Coefficients as printed on pp. 320-321 (lambda_3 = 544.4 A, f_3 = 5.928, f_1 = 4.04e-5); p. 315 prints them rounded (544 A, 5.93, 4.0e-5). lambda_1 is ascribed to the Schumann-Runge band (5, 0), lambda_2 to the Schumann-Runge continuum. The authors call the lambda_1 term physically unmeaningful once the continuum is allowed for (p. 321).
ladenburg_1933/continuum_plus_one_term#
{
"id": "continuum_plus_one_term",
"material": "O2",
"equation": "Eq. (4) and Table I, p. 320",
"printed": "n(nu) - 1 = C Sigma_s f_s / (nu_s^2 - nu^2) + (1 / 2 pi^2) integral alpha(omega) d omega / (omega^2 - nu^2); one term: f_s = 7.143, lambda_s = 1 / nu_s = 501.3A",
"variable": "nu: wave number in cm^-1; alpha(omega): the measured absorption coefficient at N.P.T. (Fig. 5), integrated over 56000-78000 cm^-1",
"state": "1atm_0C",
"density": "unknown",
"range": "1920-4000 A (the L-W data of Table I)",
"coefficients": {
"f_s": "7.143",
"lambda_s": "501.3"
},
"check": "The one term C f_s / (nu_s^2 - nu^2) with footnote 15's constants (C = 1.2060e6 cm^-2) gives 0.29-0.32 % less than Table I's I column at all eight wave numbers (2323.2 against 2330 at 52084 cm^-1); with C = 1.2096e6 cm^-2 it reproduces I to 0.5e-7 in every row. H = (n - 1) - G exactly. The integral term G is tabulated only (Table I) and rests on Fig. 5. Checked 2026-09-25."
}
The paper’s generalised dispersion formula with the Schumann-Runge continuum as a distributed absorption (Kramers-Kronig with the measured alpha) and one line for everything above it, fitted to H = (n - 1) - G: ‘the values f_s = 7.143 and lambda_s = 501.3A instead of f_3 = 5.928 and lambda_3 = 544.4A’ (p. 320). Not a closed form: needs G (Table I, in the record’s notes) or the absorption curve.
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 review register for the checks and decisions.