rahn_1986#
L. A. Rahn and R. E. Palmer, “Studies of nitrogen self-broadening at high temperature with inverse Raman spectroscopy”, J. Opt. Soc. Am. B 3, 1164 (1986)
Source record · Catalogue · Review register
Source kind: measurement
Recorded technique: High-resolution quasi-cw inverse Raman spectroscopy (pp. 1164-1165): a single-mode Ar-ion probe near 514.5 nm locked to an etalon, and a pump from a single-mode cw dye laser (1 MHz) pulse-amplified to about 1 MW (22 ns, about 45 MHz = 0.0015 cm-1 FWHM), crossed at a 100 um waist in a furnace (alumina tube, 99.99 % N2, Pt-Pt 13 % Rh thermocouple within 2 mm of the focus). Raman shifts to 0.001 cm-1 (wavemeter and a 749-MHz etalon). N2 Q branch, v = 0 -> 1, J = 0-30, at 295-1500 K and 20-760 Torr; spectra at 1 atm (twice or more, once at 1000 K), and near the bandhead also at 0.23 and 0.5 atm (500 K) and 0.5 atm (730 K). Each line fitted as an isolated line (with the wings of its neighbours) by a Galatry profile (Doppler and Dicke narrowing, soft collisions), the optical diffusion coefficient D chosen per temperature to make the coefficient independent of pressure (Fig. 3); the collisional width divided by the pressure gives the coefficient.
Materials in structured entries: N2
Dataset quantities: raman_linewidth
Contents: 5 datasets; 2 formulas.
Curation notes#
Identity checked against the first page. Page numbers are journal pages (pdf pages 1-6 = pp. 1164-1169). Material: 14N2 (natural nitrogen, 99.99 %); no other isotopologue.
WIDTH CONVENTION. FULL widths. Table 1’s caption (p. 1167): ‘Collisional Self-Broadening Coefficients (FWHM) for the N2 Q Branch’, column head ‘2 gamma_j (cm-1 atm-1)’; Fig. 3 caption (p. 1166): ‘2 gamma_j refers to broadening coefficients (FWHM) and gamma_ij refers to S-matrix elements’; Eq. (3) (p. 1167): ‘the collisional-broadening portion of the linewidth Gamma_j (FWHM) for transition Q(j) is ... Gamma_j/2 = sum_{i != j} gamma_ij’. Per atm of pressure at the stated temperature (not per amagat): ‘dividing the fitted collisional width by the gas pressure’ (p. 1166). No Dicke term in the coefficient: the Doppler and Dicke effects are in the Galatry profile, and the coefficient is the high-pressure (collisional) limit (Fig. 3).
UNCERTAINTIES (pp. 1166-1167). ‘The 1-sigma error estimates (parentheses in Table 1) for the present results are derived from multiple measurements and from the quality of the fit (chi^2). Systematic errors, however, are not included in these estimates. Errors due to the uncertainty in D are expected to be of the same order or smaller’; the Doppler-related uncertainty is ‘of the order of the experimental reproducibility of +-3 %’; the isolated-line approximation may add error ‘for slightly overlapping transitions at low J’. D was 66-80 % of the kinetic-theory mass diffusion coefficient at 1000 K and above, ‘reproducible to only +-50 %’ (1.6 cm2 s-1 at 1300 K, p. 1166).
THE 295 K COLUMN is not this paper’s measurement: note a, ‘From Ref. 6’ = G. J. Rosasco, W. Lempert and W. S. Hurst, Chem. Phys. Lett. 97, 435 (1983) (rosasco_1983, which has a fourth author, A. Fein). Every value and error is exactly twice Rosasco et al.’s printed HWHM gamma_j (0.065(15) -> 0.130 (30), ..., 0.030(6) -> 0.060 (12); all 19 rows checked): Rahn and Palmer doubled Rosasco’s half widths to full widths. Recorded as reproduced (table1_295K). ‘Because the measurements at 295 K are in excellent agreement with the results of Rosasco et al., a detailed pressure-dependence study has not been performed at this temperature’ (p. 1165).
TABLE 1 GAPS. A dash marks a J not measured at that temperature (500 K: J = 19; 730 K: J = 0, 1; 1000 K: J = 0, 1, 17, 25; 1500 K: J = 0, 1, 15, 23); blank cells lie beyond the measured range. Not values; not recorded.
THE SCALING LAW (Eqs. (1)-(3), p. 1167; recorded as the formula eq1_meg). The modified exponential-gap (MEG) law of Koszykowski et al. (Ref. 10; koszykowski_1987), with alpha = 0.023 +- 0.003 cm-1 atm-1, beta = 1.67 +- 0.15, delta = 1.26 +- 0.06 from their 295 K fits, and the temperature exponent fitted here to Table 1: ‘n = 1.346 +- 0.06 and T0 = 295 K’ (p. 1167; the page image was checked at 300 dpi: ‘+- 0.06’, one significant figure of error). koszykowski_1987 quotes this paper’s n as ‘1.346 +- 0.006’ (its p. 5): a tenfold smaller error than printed here. ‘The scaling law does slightly underestimate the experimental values for 1500 K’ (p. 1167). Note 32 (p. 1169) gives a replacement temperature function for T > 2000 K from tungsten-lamp CARS (formula note32_meg). Note 20 (pp. 1168-1169): ‘The value for alpha based on the exponential-gap scaling law cited in this reference [Koszykowski, Farrow and Palmer, Opt. Lett. 10, 478 (1985)] should be divided by 2.’
FIG. 6 (not extracted): N2 Q-branch broadening in the post-flame gases of a lean methane-air flame at 1730 K (Ref. 5, figure only), slightly above the self-broadening prediction. The water-vapour broadening is announced, not given.
What this bears on: the N2 Q-branch widths in use (docs/raman.md: Koszykowski et al.’s MEG law with Rahn and Palmer’s n = 1.346 ‘as they quote it’, TC-492). Table 1 gives the measured per-J FWHM at 500-1500 K directly; the MEG law with the printed parameters reproduces it to 2-4 % rms at 500-1000 K and 7 % low at 1500 K (see the formula’s check).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
rahn_1986/table1_295K#
{
"id": "table1_295K",
"material": "N2",
"file": "N2/rahn_1986__table1_295K.csv",
"table": "tbl_7d46e56fb640",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"abscissa": "label",
"use": "reproduced",
"reproduced_from": [
"rosasco_1983"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"transition": "Q(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 295
}
}
Table 1 (p. 1167), 295 K column, note a ‘From Ref. 6’ (Rosasco, Lempert and Hurst, Chem. Phys. Lett. 97, 435 (1983) = rosasco_1983): FWHM self-broadening coefficient 2 gamma_j of N2 Q(J), J = 0-18, cm-1 per atm. Every value and error is exactly twice rosasco_1983’s printed HWHM (its 298 K table); the paper calls this column 295 K, Rosasco et al. 298 K. The parenthesised error is Rosasco’s doubled (its level not stated there).
rahn_1986/table1_500K#
{
"id": "table1_500K",
"material": "N2",
"file": "N2/rahn_1986__table1_500K.csv",
"table": "tbl_7d46e56fb640",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 500
}
}
Table 1 (p. 1167), 500 K: FWHM collisional self-broadening coefficient 2 gamma_j of N2 Q(J), cm-1 per atm, J = 0-27 (J = 19 not measured, printed ‘-’). Galatry fits; the parenthesised error (last digits) is 1 sigma from repeated measurements and the fit, without systematic errors (p. 1167). Spectra at 1 atm, and at 0.23 and 0.5 atm near the bandhead (p. 1165).
rahn_1986/table1_730K#
{
"id": "table1_730K",
"material": "N2",
"file": "N2/rahn_1986__table1_730K.csv",
"table": "tbl_7d46e56fb640",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 730
}
}
Table 1 (p. 1167), 730 K: FWHM collisional self-broadening coefficient 2 gamma_j of N2 Q(J), cm-1 per atm, J = 2-26 (J = 0, 1 printed ‘-’). 1 sigma (last digits), without systematic errors (p. 1167). Spectra at 1 atm and, near the bandhead, 0.5 atm (p. 1165). Q(25) 0.0380 exceeds Q(24) 0.0359 and Q(26) 0.0333 (as printed; image checked).
rahn_1986/table1_1000K#
{
"id": "table1_1000K",
"material": "N2",
"file": "N2/rahn_1986__table1_1000K.csv",
"table": "tbl_7d46e56fb640",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 1000
}
}
Table 1 (p. 1167), 1000 K: FWHM collisional self-broadening coefficient 2 gamma_j of N2 Q(J), cm-1 per atm, J = 2-30 (J = 0, 1, 17, 25 printed ‘-’). 1 sigma (last digits), without systematic errors (p. 1167). The 1000 K spectrum was measured only once, at 1 atm (p. 1165).
rahn_1986/table1_1500K#
{
"id": "table1_1500K",
"material": "N2",
"file": "N2/rahn_1986__table1_1500K.csv",
"table": "tbl_7d46e56fb640",
"quantity": "raman_linewidth",
"unit": "cm-1/atm",
"abscissa": "label",
"use": "primary",
"uncertainty": {
"column": true,
"level": "1 sigma"
},
"parameters": {
"transition": "Q(J), v = 0 -> 1, per row",
"width": "fwhm",
"perturber": "self",
"temperature_k": 1500
}
}
Table 1 (p. 1167), 1500 K: FWHM collisional self-broadening coefficient 2 gamma_j of N2 Q(J), cm-1 per atm, J = 2-28 (J = 0, 1, 15, 23 printed ‘-’). 1 sigma (last digits), without systematic errors (p. 1167). At 1 atm the Lorentzian and Voigt collisional widths differ by up to 12 % (J = 16, 1500 K, p. 1166): the Galatry model’s D matters most here.
Formulas#
rahn_1986/eq1_meg#
{
"id": "eq1_meg",
"material": "N2",
"equation": "Eqs. (1)-(3), p. 1167",
"printed": "gamma_ji = alpha p (T0/T)^n [(1 + 1.5 E_i/kT delta)/(1 + 1.5 E_i/kT)]^2 exp(-beta Delta E_ij/kT) (i < j); gamma_ij = [(2J_i + 1)/(2J_j + 1)] gamma_ji exp(Delta E_ij/kT); Gamma_j/2 = sum_{i != j} gamma_ij",
"variable": "p: pressure in atm; T in K, T0 = 295 K; E_i the rotational term energy of the lower level J_i, Delta E_ij = E_j - E_i, kT all in cm-1; alpha in cm-1 atm-1; Gamma_j the collisional FWHM of Q(j) in cm-1 (Gamma_j / p is Table 1's 2 gamma_j). 1.5 E_i/kT delta is read as 1.5 E_i/(kT delta), as koszykowski_1987 prints it",
"state": "pure N2, self-broadening",
"density": "unknown",
"range": "295-1500 K (Table 1), J = 0-30; the rate law is for rotationally inelastic collisions, 'if vibrational dephasing is unimportant' (p. 1167)",
"coefficients": {
"alpha": "0.023",
"alpha_error": "0.003",
"beta": "1.67",
"beta_error": "0.15",
"delta": "1.26",
"delta_error": "0.06",
"a": "1.5",
"n": "1.346",
"n_error": "0.06",
"T0": "295"
},
"check": "Against Table 1 (scratch, 2026-09-27), summing the rates out of J over the levels of the same parity (J +- 2, +- 4, ...; nuclear-spin symmetry is conserved) to J = 80, with Bendtsen's B0 = 1.989574 and D = 5.76e-6 cm-1 (bendtsen_1974) and k = 0.6950348 cm-1/K: model/table - 1 is mean -2.9 %, rms 3.3 % at 295 K (Rosasco's column; -5.5 to +0.5 %); +1.7 %, rms 4.1 % at 500 K (worst Q(27) +13.6 %); -1.0 %, rms 2.3 % at 730 K; -0.3 %, rms 3.1 % at 1000 K; -7.0 %, rms 7.4 % at 1500 K (-2.7 to -10.7 %), as the paper says ('slightly underestimate ... for 1500 K'). The model at 295 K for Q(0), Q(2), Q(4) is 0.1264, 0.0991, 0.0916 cm-1/atm, which agrees with another extraction's evaluation of koszykowski_1987's law (126.3, 99.0, 91.6 x 1e-3)."
}
alpha, beta and delta are Koszykowski et al.’s (Ref. 10, fitted at 295 K); only n is fitted here (to Table 1, Fig. 5). The paper’s n error is printed ‘+- 0.06’ (koszykowski_1987 quotes ‘+- 0.006’). The 1.5 ‘includes N-N internuclear separation distances, characteristic collision interaction lengths, and reduced masses’ (p. 1167). No nuclear-spin degeneracy factor appears in the rates; the parity restriction of the check is a physical constraint the paper does not state.
rahn_1986/note32_meg#
{
"id": "note32_meg",
"material": "N2",
"equation": "Ref. note 32, p. 1169",
"printed": "replace (T0/T)^n in Eq. (1) by f(T) = [(1 - e^-m)/(1 - e^(-m T/T0))] (T0/T)^0.5, m = 0.1487, with alpha = 0.023, beta = 1.67, delta = 1.21",
"variable": "T in K, T0 = 295 K (from Eq. (1)); otherwise as eq1_meg",
"state": "pure N2, self-broadening",
"density": "unknown",
"range": "'linewidths above 2000 K are better predicted' (tungsten-lamp CARS, Farrow, Trebino and Palmer, 'to be submitted to Appl. Opt., 1986'); also 'better overall agreement' with Fig. 5, 'especially those for 1500 K'",
"coefficients": {
"alpha": "0.023",
"beta": "1.67",
"delta": "1.21",
"m": "0.1487",
"T0": "295"
},
"check": "Against Table 1 as for eq1_meg (scratch, 2026-09-27): mean -0.0 %, rms 3.1 % at 295 K; +1.8 %, rms 5.5 % at 500 K; -1.6 %, rms 3.3 % at 730 K; +0.5 %, rms 4.3 % at 1000 K; -2.0 %, rms 3.7 % at 1500 K. The 1500 K bias of eq1_meg (-7 %) is removed, as the note says; T0 = 295 K is assumed (the note does not restate it)."
}
Announced in a note from later work (Farrow, Trebino and Palmer); not fitted in this paper. f(T0) = 1.
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.