millot_1992 =========== G\. Millot, R\. Saint\-Loup, J\. Santos, R\. Chaux, H\. Berger and J\. Bonamy, "Collisional effects in the stimulated Raman Q branch of O2 and O2\-N2", J\. Chem\. Phys\. 96, 961 \(1992\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.462116 `__ **Source kind:** measurement **Recorded technique:** Stimulated Raman gain spectroscopy \(Dijon, p\. 2\)\: a frequency\-stabilised single\-mode Kr\-ion probe \(1 MHz jitter\) and a narrow\-band cw dye pump pulse\-amplified to 750 kW, polarizations parallel; absolute frequencies by a Michelson wavemeter; a second \(reference\) cell recorded simultaneously for the differential line\-shift measurement\. Fundamental Q branch \(v = 0 \-\> 1\) of 16O2 at 295\-1350 K and 150\-1550 Torr \(Table I\); O2\-N2 from dry air taken as 79 % N2, 21 % O2 \(p\. 5\)\. Each spectrum fitted with Eq\. \(8\)\: a sum of Galatry profiles with Rosenkranz first\-order line mixing \(Eq\. \(7\)\), the Dicke parameter fixed by Eq\. \(9\), the apparatus function \(a Gaussian of HWHM 1\.1e\-3 cm\-1\) neglected; the broadening coefficient of each Q\(N\) from a linear regression of the collisional widths over pressures \>= 300 Torr\. **Materials in structured entries:** O2 **Dataset quantities:** raman\_line\_shift, raman\_linewidth **Contents:** 44 datasets; 6 formulas. Curation notes -------------- Identity checked against the first page \(the pdf has a publisher cover page\: page numbers here are pdf pages, 2\-12 = journal pp\. 961\-971\)\. Material\: 16O2, X 3Sigma\_g\-, rotational levels labelled by N \(odd only\); each triplet \(J = N, N \+\- 1\) is treated as one line \(the 1Sigma approximation; the minimum pressure chosen so that the error is small, p\. 3\)\. No isotopologue is measured\. WIDTH CONVENTION\. Every width is a HALF width at half maximum per atm\: p\. 4, 'Gamma\_N the collisional half\-width at half\-maximum \(HWHM\)', p\. 5, 'gamma\_N = Gamma\_N/p represents the line broadening coefficient expressed in cm\-1 atm\-1'; Tables II, III, VI and VII\: 'HWHM in 10^\-3 cm\-1 atm\-1'\. Per atm at the stated temperature \(not per amagat\), except Table IV's mean shifts, 'in density units \(mk amagat\-1\)', 1 mk = 1e\-3 cm\-1\. The Dicke effect is in the line shape \(Galatry\), not in the coefficients\: the coefficients are the collisional \(Lorentzian\) part only\. The polarized Q branch widths are taken as purely isotropic widths \(depolarization ratios 1\.8\-4\.9 %, p\. 3\)\. UNCERTAINTIES\. Tables II and III\: 'The uncertainties correspond to twice the standard deviation' \(captions, p\. 7; also p\. 6\)\. Table IV\: 'one standard deviation'\. The theoretical Tables VI\-VIII have none\. The printed errors of the reproduced columns of Table II \(Ouazzany et al\.\) are as printed\. O2\-N2 \(Table III and the O2\-N2 columns of Table IV\) is derived from the air measurements by Eq\. \(10\), gamma\_N = C\_O2 gamma\_N\(O2\-O2\) \+ C\_N2 gamma\_N\(O2\-N2\), with the O2\-O2 values \(p\. 6\); the reference cell of the shift measurement held pure O2 at its partial pressure, so the O2\-N2 shift is measured directly \(p\. 7\)\. TABLE I \(p\. 6\), recording conditions \(as the image shows; the extraction shifts the temperature cells\)\: O2\-O2 295 K 150\-460 Torr N 1\-9 and 150\-1500 Torr N 11\-23; 446 K 240\-920 Torr N 1\-21; 769 K 300\-900 Torr N 3\-19; 990 K 760\-1520 Torr N 1\-21; 1317 K 900\-1530 Torr N 3\-29; 1350 K 760 Torr N 39\-55; O2\-N2 295 K 740 Torr, 446 K 740 Torr, 990 K 740\-1550 Torr, N 1\-21\. TABLE IV\. Its caption is extracted as a table note \('Experimental line shifting coefficients \(in 1e\-3 cm\-1 atm\-1\) for O2\-O2 and O2\-N2 measured at low pressure\. The uncertainties correspond to one standard deviation\.'\) and the running head as the caption; identified by the image and the text \(p\. 7, 'The results are reported in Table IV'\)\. The shift is negative \(to lower Raman frequency\); 'of the order of \-3\.5e\-3 cm\-1 atm\-1 for O2 at 295 K' \(p\. 3\)\. TABLE V \(p\. 9, not in the extracted tables\: a 'code' block; page image checked\)\: the inputs of the semiclassical calculation, reproduced from Refs\. 33\-38 \(not extracted\)\: atom\-atom e\_OO = 0\.26e\-10 erg A^6/molecule, d\_OO = 0\.25e\-7 erg A^12/molecule, e\_NN = 0\.25e\-10, d\_NN = 0\.29e\-7; Lennard\-Jones eps\(O2\) = 120 K, sigma\(O2\) = 3\.55 A, eps\(N2\) = 97 K, sigma\(N2\) = 3\.73 A; quadrupole moments Q\(O2\) = \-0\.39 D A, Q\(N2\) = \-1\.4 D A; vibrational parameters of O2 \(1/alpha\) d alpha/d xi = 1\.32, \(1/Q\) dQ/d xi = \-2, \<1\|xi\|1\> \- \<0\|xi\|0\> = 0\.826e\-2, a\_01 = 1\.09e\-2, b\_01 = \-3\.3e\-2\. The semiclassical shifts use an adjustable y = 2 \(p\. 10\)\. OTHER TEXT VALUES\. The collisional reorientation contribution gamma\_elas^ori is about 4e\-3 cm\-1 atm\-1 at room temperature \(average over N, p\. 7\)\. The Q\(N\) depolarization ratios \(1\.8 % for N = 1 to 4\.9 % for N = 11\) and R = 0\.717 are Hill et al\.'s \(p\. 3\)\. For O2, D\_m0 = 0\.189 cm2 s\-1 at 1 atm and 273\.15 K \(Jost\), D = \(2/3\) D\_m and alpha = 1\.5 are assumed \(p\. 5\)\. FORMULAS \(Table IX, p\. 10\)\. The fits were checked by recomputing Table II and Table III from Eq\. \(12\), gamma\(N\) = \-sum\_{N' \!= N} W\_{N'N}, with the O2 levels E\_N = B N\(N\+1\), B = 1\.438 cm\-1 \(shelton\_1987 Table 2; D neglected\), odd N to 119, downward rates by detailed balance \(scratch, 2026\-09\-26\)\: see each formula's check\. Eq\. \(16\) as printed, with exp\[\(E\_N' \- E\_N\>\)/kT\], violates detailed balance \(rho\_N W\_N'N is not symmetric\) and gives widths two to three times Table II's at 295 K \(N = 7\: 138 against 45\.3 mk/atm, ECS\-P\); with exp\[\(E\_N \- E\_N\>\)/kT\] \(E\_N the initial level\) it is symmetric and reproduces the tables \(see the ECS formulas\)\: the printed E\_N' is probably a misprint for E\_N\. The adiabatic factor Omega is not defined in the paper \('the adiabatic factor proportional to l\_c'\); the checks assume De Pristo's form Omega\_N = \[1 \+ \(omega\_{N,N\-1} l\_c/v\)^2/6\]^\-1 with omega\_{N,N\-1} = 2 pi c \(E\_N \- E\_{N\-1}\) and v the mean relative speed \(8kT/pi mu\)^\(1/2\); with omega from the N \-\> N\-2 spacing, or without the 2 pi, the reproduction is 2\-8 times worse\. solprop\: its O2 vibrational width, 2933389355\.65 Hz/amagat FWHM, is Table II's Q\(7\) at 295 K, 45\.3 \+\- 0\.8 \(2 sigma\) x 1e\-3 cm\-1/atm HWHM, doubled and converted with 1 atm = 0\.92593 amagat at 295 K \(ideal gas\)\: 2 x 45\.3e\-3 x 29\.9792458e9 / 0\.92593 = 2\.9334e9\. The HWHM\-to\-FWHM doubling is right\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- millot\_1992/table2\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_295K", "material": "O2", "file": "O2/millot_1992__table2_295K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 295 } } Table II \(p\. 7\), 295 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. solprop's O2 vibrational width is the N = 7 value\. millot\_1992/table2\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_446K", "material": "O2", "file": "O2/millot_1992__table2_446K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 446 } } Table II \(p\. 7\), 446 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. millot\_1992/table2\_769K ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_769K", "material": "O2", "file": "O2/millot_1992__table2_769K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 769 } } Table II \(p\. 7\), 769 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. millot\_1992/table2\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_990K", "material": "O2", "file": "O2/millot_1992__table2_990K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 990 } } Table II \(p\. 7\), 990 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. millot\_1992/table2\_1317K ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_1317K", "material": "O2", "file": "O2/millot_1992__table2_1317K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1317 } } Table II \(p\. 7\), 1317 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. millot\_1992/table2\_1350K ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_1350K", "material": "O2", "file": "O2/millot_1992__table2_1350K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1350 } } Table II \(p\. 7\), 1350 K\: O2 self\-broadening coefficient of the Q\(N\) lines of the fundamental \(v = 0 \-\> 1\), HWHM in 1e\-3 cm\-1 per atm, 2 sigma\. \(the fundamental Q branch at 1350 K is measured only for N = 39\-55; Table I\) millot\_1992/table2\_ouazzany\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_ouazzany_295K", "material": "O2", "file": "O2/millot_1992__table2_ouazzany_295K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "reproduced", "reproduced_from": [ "Y. Ouazzany, J. P. Boquillon and B. Lavorel, Can. J. Phys. 65, 1588 (1987)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 295 } } Table II \(p\. 7\), column '295 K^a', note a 'Data from Ref\. 5'\: high\-resolution CARS Q\(N\) HWHM \(N = 1\-17\) of Ouazzany, Boquillon and Lavorel, as Millot et al\. print them; 'the agreement \.\.\. is quite correct \.\.\. our data are more accurate' \(p\. 6\)\. millot\_1992/table2\_anisotropic\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_anisotropic_295K", "material": "O2", "file": "O2/millot_1992__table2_anisotropic_295K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N) anisotropic (depolarized) component, v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 295 } } Table II \(p\. 7\), column '295 K^b', note b 'Pure anisotropic linewidths'\: this paper's Q\(N\) widths with crossed pump and probe polarizations \(the anisotropic Q\-branch component\), HWHM in 1e\-3 cm\-1/atm; 'the precision of our measurements is not very high' \(p\. 3\); none for N = 1, 3\. millot\_1992/table2\_berard\_293K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_berard_293K", "material": "O2", "file": "O2/millot_1992__table2_berard_293K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "reproduced", "reproduced_from": [ "M. Berard, P. Lallemand, J. P. Cebe and M. Giraud, J. Chem. Phys. 78, 672 (1983)" ], "parameters": { "transition": "S(N) pure rotational, per row", "width": "hwhm", "perturber": "self", "temperature_k": 293 } } Table II \(p\. 7\), column '293 K^c', note c 'Experimental data from Ref\. 29'\: the pure rotational Raman S\(N\) HWHM of Berard et al\. \(rows by the N of the lower level\), as printed, no errors; compared with this paper's anisotropic Q widths \(p\. 7\)\. millot\_1992/table2\_hot1\_1350K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_hot1_1350K", "material": "O2", "file": "O2/millot_1992__table2_hot1_1350K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 1 -> 2, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1350 } } Table II \(p\. 7\), column '1350 K^d', note d 'First hot band'\: the Q\(N\) self\-broadening HWHM of the v = 1 \-\> 2 band at 1350 K, 2 sigma; 'no significant systematic differences' from the fundamental at 1317 K \(p\. 7\)\. millot\_1992/table2\_hot2\_1350K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_hot2_1350K", "material": "O2", "file": "O2/millot_1992__table2_hot2_1350K.csv", "table": "tbl_23bcbc0cdebf", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 2 -> 3, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1350 } } Table II \(p\. 7\), column '1350 K^e', note e 'Second hot band'\: Q\(N\) HWHM of the v = 2 \-\> 3 band at 1350 K, 2 sigma\. millot\_1992/table3\_N2\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_N2_295K", "material": "O2", "file": "O2/millot_1992__table3_N2_295K.csv", "table": "tbl_7b0c5f5de7ea", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 295 } } Table III \(p\. 7\), 295 K\: broadening coefficient of the O2 Q\(N\) lines by N2, HWHM in 1e\-3 cm\-1/atm \(of N2\), 2 sigma; derived from the air measurement by Eq\. \(10\) with the O2\-O2 values\. millot\_1992/table3\_N2\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_N2_446K", "material": "O2", "file": "O2/millot_1992__table3_N2_446K.csv", "table": "tbl_7b0c5f5de7ea", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 446 } } Table III \(p\. 7\), 446 K\: broadening coefficient of the O2 Q\(N\) lines by N2, HWHM in 1e\-3 cm\-1/atm \(of N2\), 2 sigma; derived from the air measurement by Eq\. \(10\) with the O2\-O2 values\. millot\_1992/table3\_N2\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_N2_990K", "material": "O2", "file": "O2/millot_1992__table3_N2_990K.csv", "table": "tbl_7b0c5f5de7ea", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "2 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 990 } } Table III \(p\. 7\), 990 K\: broadening coefficient of the O2 Q\(N\) lines by N2, HWHM in 1e\-3 cm\-1/atm \(of N2\), 2 sigma; derived from the air measurement by Eq\. \(10\) with the O2\-O2 values\. millot\_1992/table4\_self\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_self_295K", "material": "O2", "file": "O2/millot_1992__table4_self_295K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 295 } } Table IV \(p\. 8\), 295 K, O2\-O2\: collisional shift coefficient of the O2 Q\(N\) lines, 1e\-3 cm\-1 per atm, 1 sigma; differential two\-cell measurement\. millot\_1992/table4\_self\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_self_446K", "material": "O2", "file": "O2/millot_1992__table4_self_446K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 446 } } Table IV \(p\. 8\), 446 K, O2\-O2\: collisional shift coefficient of the O2 Q\(N\) lines, 1e\-3 cm\-1 per atm, 1 sigma; differential two\-cell measurement\. millot\_1992/table4\_self\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_self_990K", "material": "O2", "file": "O2/millot_1992__table4_self_990K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 990 } } Table IV \(p\. 8\), 990 K, O2\-O2\: collisional shift coefficient of the O2 Q\(N\) lines, 1e\-3 cm\-1 per atm, 1 sigma; differential two\-cell measurement\. millot\_1992/table4\_self\_1317K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_self_1317K", "material": "O2", "file": "O2/millot_1992__table4_self_1317K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 1317 } } Table IV \(p\. 8\), 1317 K, O2\-O2\: collisional shift coefficient of the O2 Q\(N\) lines, 1e\-3 cm\-1 per atm, 1 sigma; differential two\-cell measurement\. millot\_1992/table4\_N2\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_N2_295K", "material": "O2", "file": "O2/millot_1992__table4_N2_295K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 295 } } Table IV \(p\. 8\), 295 K, O2\-N2\: shift coefficient of the O2 Q\(N\) lines by N2, 1e\-3 cm\-1 per atm \(of N2\), 1 sigma; the reference cell held pure O2 at its partial pressure in air, so the difference is the N2 shift \(p\. 7\)\. millot\_1992/table4\_N2\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_N2_446K", "material": "O2", "file": "O2/millot_1992__table4_N2_446K.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 446 } } Table IV \(p\. 8\), 446 K, O2\-N2\: shift coefficient of the O2 Q\(N\) lines by N2, 1e\-3 cm\-1 per atm \(of N2\), 1 sigma; the reference cell held pure O2 at its partial pressure in air, so the difference is the N2 shift \(p\. 7\)\. millot\_1992/table4\_mean\_self ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_mean_self", "material": "O2", "file": "O2/millot_1992__table4_mean_self.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/amagat", "scale": 0.001, "abscissa": "temperature", "abscissa_unit": "K", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q branch, v = 0 -> 1, mean over N", "perturber": "self" } } Table IV \(p\. 8\), last row\: 'Mean value in density units \(mk amagat^\-1\)' over N, O2\-O2, against temperature, 1 sigma\. 'the mean values over N expressed in density units weakly depend on the temperature' \(p\. 7\)\. millot\_1992/table4\_mean\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table4_mean_N2", "material": "O2", "file": "O2/millot_1992__table4_mean_N2.csv", "table": "tbl_84280b026de1", "quantity": "raman_line_shift", "unit": "cm-1/amagat", "scale": 0.001, "abscissa": "temperature", "abscissa_unit": "K", "use": "primary", "uncertainty": { "column": true, "level": "1 sigma" }, "parameters": { "transition": "Q branch, v = 0 -> 1, mean over N", "perturber": "N2" } } Table IV \(p\. 8\), last row\: mean shift over N per amagat, O2\-N2, at 295 and 446 K, 1 sigma\. millot\_1992/table6\_Q\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_295K", "material": "O2", "file": "O2/millot_1992__table6_Q_295K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 295 } } Table VI \(p\. 9\), 295 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_Q\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_446K", "material": "O2", "file": "O2/millot_1992__table6_Q_446K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 446 } } Table VI \(p\. 9\), 446 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_Q\_769K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_769K", "material": "O2", "file": "O2/millot_1992__table6_Q_769K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 769 } } Table VI \(p\. 9\), 769 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_Q\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_990K", "material": "O2", "file": "O2/millot_1992__table6_Q_990K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 990 } } Table VI \(p\. 9\), 990 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_Q\_1317K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_1317K", "material": "O2", "file": "O2/millot_1992__table6_Q_1317K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1317 } } Table VI \(p\. 9\), 1317 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_Q\_1350K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_Q_1350K", "material": "O2", "file": "O2/millot_1992__table6_Q_1350K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 1350 } } Table VI \(p\. 9\), 1350 K\: O2 self\-broadening HWHM of Q\(N\) calculated with the semiclassical theory of Robert and Bonamy \(Ref\. 12; Eq\. \(14\), parameters of Table V\)\: theory, compared, not fitted\. millot\_1992/table6\_S\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table6_S_295K", "material": "O2", "file": "O2/millot_1992__table6_S_295K.csv", "table": "tbl_6eda03db14cb", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "S(N) pure rotational, per row", "width": "hwhm", "perturber": "self", "temperature_k": 295 } } Table VI \(p\. 9\), column '295 K^b', note b 'S\(N\) linewidths'\: the semiclassical O2 self\-broadening HWHM of the pure rotational S\(N\) lines at 295 K \(rows by the lower N\)\. Theory\. millot\_1992/table7\_N2\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table7_N2_295K", "material": "O2", "file": "O2/millot_1992__table7_N2_295K.csv", "table": "tbl_6dcaeaf58dd1", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 295 } } Table VII \(p\. 9\), 295 K\: O2\-N2 broadening HWHM of Q\(N\) calculated with the semiclassical theory \(Ref\. 12\)\. Theory\. millot\_1992/table7\_N2\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table7_N2_446K", "material": "O2", "file": "O2/millot_1992__table7_N2_446K.csv", "table": "tbl_6dcaeaf58dd1", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 446 } } Table VII \(p\. 9\), 446 K\: O2\-N2 broadening HWHM of Q\(N\) calculated with the semiclassical theory \(Ref\. 12\)\. Theory\. millot\_1992/table7\_N2\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table7_N2_990K", "material": "O2", "file": "O2/millot_1992__table7_N2_990K.csv", "table": "tbl_6dcaeaf58dd1", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 990 } } Table VII \(p\. 9\), 990 K\: O2\-N2 broadening HWHM of Q\(N\) calculated with the semiclassical theory \(Ref\. 12\)\. Theory\. millot\_1992/table7\_N2\_1315K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table7_N2_1315K", "material": "O2", "file": "O2/millot_1992__table7_N2_1315K.csv", "table": "tbl_6dcaeaf58dd1", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 1315 } } Table VII \(p\. 9\), 1315 K\: O2\-N2 broadening HWHM of Q\(N\) calculated with the semiclassical theory \(Ref\. 12\)\. Theory\. millot\_1992/table7\_N2\_2000K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table7_N2_2000K", "material": "O2", "file": "O2/millot_1992__table7_N2_2000K.csv", "table": "tbl_6dcaeaf58dd1", "quantity": "raman_linewidth", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "width": "hwhm", "perturber": "N2", "temperature_k": 2000 } } Table VII \(p\. 9\), 2000 K\: O2\-N2 broadening HWHM of Q\(N\) calculated with the semiclassical theory \(Ref\. 12\)\. Theory\. millot\_1992/table8\_self\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_self_295K", "material": "O2", "file": "O2/millot_1992__table8_self_295K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 295 } } Table VIII \(p\. 10\), 295 K, \(A\) pure O2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_N2\_295K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_N2_295K", "material": "O2", "file": "O2/millot_1992__table8_N2_295K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 295 } } Table VIII \(p\. 10\), 295 K, \(B\) O2\-N2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_self\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_self_446K", "material": "O2", "file": "O2/millot_1992__table8_self_446K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 446 } } Table VIII \(p\. 10\), 446 K, \(A\) pure O2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_N2\_446K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_N2_446K", "material": "O2", "file": "O2/millot_1992__table8_N2_446K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 446 } } Table VIII \(p\. 10\), 446 K, \(B\) O2\-N2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_self\_769K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_self_769K", "material": "O2", "file": "O2/millot_1992__table8_self_769K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 769 } } Table VIII \(p\. 10\), 769 K, \(A\) pure O2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_N2\_769K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_N2_769K", "material": "O2", "file": "O2/millot_1992__table8_N2_769K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 769 } } Table VIII \(p\. 10\), 769 K, \(B\) O2\-N2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_self\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_self_990K", "material": "O2", "file": "O2/millot_1992__table8_self_990K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 990 } } Table VIII \(p\. 10\), 990 K, \(A\) pure O2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_N2\_990K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_N2_990K", "material": "O2", "file": "O2/millot_1992__table8_N2_990K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 990 } } Table VIII \(p\. 10\), 990 K, \(B\) O2\-N2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_self\_1317K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_self_1317K", "material": "O2", "file": "O2/millot_1992__table8_self_1317K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "self", "temperature_k": 1317 } } Table VIII \(p\. 10\), 1317 K, \(A\) pure O2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. millot\_1992/table8\_N2\_1317K ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table8_N2_1317K", "material": "O2", "file": "O2/millot_1992__table8_N2_1317K.csv", "table": "tbl_9dc671631d22", "quantity": "raman_line_shift", "unit": "cm-1/atm", "scale": 0.001, "abscissa": "label", "use": "check", "parameters": { "transition": "Q(N), v = 0 -> 1, per row", "perturber": "N2", "temperature_k": 1317 } } Table VIII \(p\. 10\), 1317 K, \(B\) O2\-N2\: Q\(N\) line\-shift coefficient calculated with the semiclassical theory \(y = 2\), 1e\-3 cm\-1/atm\. Theory\. Formulas -------- millot\_1992/meg\_O2\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "meg_O2_O2", "material": "O2", "equation": "Eq. (15), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "-Re W_N'N = alpha (T/T0)^-N [(1 + a E_N/kT delta)/(1 + a E_N/kT)]^2 exp(-beta E_N'N/kT), N' > N; gamma(N) = -sum_{N' != N} W_N'N (Eq. (12))", "variable": "T in K, T0 = 295 K; E_N the rotational energy of the (lower) level N, E_N'N = |E_N' - E_N|; a = 1.5 (the paper's choice, p. 10); alpha in mk/atm (1 mk = 1e-3 cm-1): the rates and the HWHM gamma(N) in 1e-3 cm-1 per atm; downward rates by detailed balance", "state": "pure O2", "density": "unknown", "range": "295-1350 K, N 1-55 (the data fitted)", "coefficients": { "alpha": "16.70", "alpha_error": "0.20", "N": "1.32", "N_error": "0.01", "delta": "1.32", "delta_error": "0.03", "beta": "1.45", "beta_error": "0.03", "a": "1.5", "sigma": "0.99", "T0": "295" }, "check": "Recomputed Table II (56 values, 295-1350 K) from Eqs. (12) and (15) with the O2 levels of B = 1.438 cm-1 (scratch, 2026-09-26): rms 0.78 mk/atm, worst 2.7 (N = 21 at 295 K and N = 55 at 1350 K), against the printed sigma = 0.99. Reproduces the fit." } MEG law of Koszykowski et al\. \(Ref\. 14\)\. The \+\- are the fit errors; sigma is 'the standard deviation obtained for the whole set of data \(all temperatures\)', in mk/atm\. 'The MEG law seems to be the best model' \(p\. 11\)\. millot\_1992/meg\_O2\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "meg_O2_N2", "material": "O2", "equation": "Eq. (15), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "-Re W_N'N = alpha (T/T0)^-N [(1 + a E_N/kT delta)/(1 + a E_N/kT)]^2 exp(-beta E_N'N/kT), N' > N; gamma(N) = -sum_{N' != N} W_N'N (Eq. (12))", "variable": "T in K, T0 = 295 K; E_N the rotational energy of the (lower) level N, E_N'N = |E_N' - E_N|; a = 1.5 (the paper's choice, p. 10); alpha in mk/atm (1 mk = 1e-3 cm-1): the rates and the HWHM gamma(N) in 1e-3 cm-1 per atm; downward rates by detailed balance", "state": "O2 perturbed by N2", "density": "unknown", "range": "295-990 K, N 1-21", "coefficients": { "alpha": "17.00", "alpha_error": "0.40", "N": "1.31", "N_error": "0.01", "delta": "1.30", "delta_error": "0.05", "beta": "1.41", "beta_error": "0.05", "a": "1.5", "sigma": "0.74", "T0": "295" }, "check": "Recomputed Table III (27 values) as for meg_O2_O2 (scratch, 2026-09-26): rms 1.03 mk/atm, worst 2.2, against the printed sigma = 0.74." } Fitted to the O2\-N2 coefficients of Table III \(derived from air by Eq\. \(10\)\)\. millot\_1992/ecs\_p\_O2\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ecs_p_O2_O2", "material": "O2", "equation": "Eqs. (16)-(17), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma (ECS-P)", "variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm", "state": "pure O2", "density": "unknown", "range": "295-1350 K, N 1-55", "coefficients": { "A0": "24.50", "A0_error": "0.80", "N": "1.01", "N_error": "0.01", "l_c": "1.23", "l_c_error": "0.09", "gamma": "0.90", "gamma_error": "0.01", "sigma": "1.34", "T0": "295" }, "check": "Recomputed Table II (56 values) from Eqs. (12), (16), (17) (scratch, 2026-09-26) only after two assumptions: exp[(E_N - E_N>)/kT] for the printed exp[(E_N' - E_N>)/kT] (the printed form breaks detailed balance and gives two to three times the widths at 295 K), and De Pristo's Omega_N = [1 + (omega_{N,N-1} l_c/v)^2/6]^-1, omega_{N,N-1} = 2 pi c (E_N - E_{N-1}), v = (8kT/pi mu)^(1/2), l_c in A: rms 1.27 mk/atm, worst 4.8, against the printed sigma = 1.34." } ECS\-P of Bonamy et al\. \(Ref\. 16\)\. The l\_c unit A is printed\. millot\_1992/ecs\_p\_O2\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ecs_p_O2_N2", "material": "O2", "equation": "Eqs. (16)-(17), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma (ECS-P)", "variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm", "state": "O2 perturbed by N2", "density": "unknown", "range": "295-990 K, N 1-21", "coefficients": { "A0": "23.00", "A0_error": "0.70", "N": "1.03", "N_error": "0.02", "l_c": "1.60", "l_c_error": "0.20", "gamma": "0.87", "gamma_error": "0.01", "sigma": "0.99", "T0": "295" }, "check": "Recomputed Table III (27 values) with the assumptions of ecs_p_O2_O2 and mu = 14.93 amu (scratch, 2026-09-26): rms 1.72 mk/atm, worst 4.3, against the printed sigma = 0.99." } Fitted to Table III\. millot\_1992/ecs\_ep\_O2\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ecs_ep_O2_O2", "material": "O2", "equation": "Eqs. (16), (18), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma exp(-beta E_L/kT) (ECS-EP)", "variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm", "state": "pure O2", "density": "unknown", "range": "295-1350 K, N 1-55", "coefficients": { "A0": "19.08", "A0_error": "0.52", "N": "1.02", "N_error": "0.01", "l_c": "4.26", "l_c_error": "0.49", "gamma": "0.81", "gamma_error": "0.01", "beta": "0.056", "beta_error": "0.003", "sigma": "1.11", "T0": "295" }, "check": "Recomputed Table II (56 values) with the assumptions of ecs_p_O2_O2 (scratch, 2026-09-26): rms 1.01 mk/atm, worst 3.8, against the printed sigma = 1.11." } ECS\-EP \(Refs\. 13, 17, 39\)\: E\_L the rotational energy of level L\. The l\_c unit A is printed\. millot\_1992/ecs\_ep\_O2\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ecs_ep_O2_N2", "material": "O2", "equation": "Eqs. (16), (18), p. 10; Table IX (tbl_e1df02577bc9), p. 10", "printed": "Re W_N'N = (2N'+1) exp[(E_N' - E_N>)/kT] Omega_N>^2 sum_L (N N' L; 0 0 0)^2 (2L+1) Omega_L^-2 Re W_0L (Eq. (16)), with -Re W_0L = A0 (T/T0)^-N / [L(L+1)]^gamma exp(-beta E_L/kT) (ECS-EP)", "variable": "T in K, T0 = 295 K; N> the greater of N and N'; Omega the adiabatic factor 'proportional to the characteristic interaction length l_c' (not defined further); A0 in mk/atm; gamma(N) = -sum W_N'N (Eq. (12)) the HWHM in 1e-3 cm-1/atm", "state": "O2 perturbed by N2", "density": "unknown", "range": "295-990 K, N 1-21", "coefficients": { "A0": "20.13", "A0_error": "0.62", "N": "1.04", "N_error": "0.02", "l_c": "3.86", "l_c_error": "0.73", "gamma": "0.81", "gamma_error": "0.01", "beta": "0.050", "beta_error": "0.002", "sigma": "0.79", "T0": "295" }, "check": "Recomputed Table III (27 values) with the assumptions of ecs_p_O2_O2 and mu = 14.93 amu (scratch, 2026-09-26): rms 1.14 mk/atm, worst 2.9, against the printed sigma = 0.79." } The O2\-N2 l\_c is printed '3\.86 \+\- 0\.73' without the unit A the other l\_c carry \(image checked\); taken as A\. 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 :doc:`review register ` for the checks and decisions.