brown_1992 ========== K\. W\. Brown, N\. H\. Rich and J\. W\. Nibler, "High resolution rotational CARS spectrum of oxygen", J\. Mol\. Spectrosc\. 151, 482 \(1992\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0022\-2852\(92\)90581\-8 `__ **Source kind:** measurement **Recorded technique:** High\-resolution pure rotational CARS \(pp\. 483\-485\)\: two yellow pump beams, the 568\.2 nm single\-mode Kr\+ line and a tunable single\-mode ring dye laser, each amplified by dye cells pumped by a seeded single\-frequency Nd\:YAG, with its 532 nm output as the probe; folded BOXCARS, crossed polarisations and an iodine cell to suppress the 532 nm background; the dye laser calibrated against the iodine atlas \(2 sigma = 0\.002 cm\-1\)\. O2 in a 10 cm cell at 70 Torr and room temperature \(300 K\), and in a free\-jet expansion \(rotational temperature about 25 K\) for the S\(1\) triplet\. Line positions and intensities from simulations of the CARS spectrum \(interference of chi' and chi'', Lorentzian collisional, Doppler and 0\.010 cm\-1 instrumental widths; pp\. 487\-490\)\. **Materials in structured entries:** O2 **Dataset quantities:** raman\_shift **Contents:** 2 datasets; 1 formula. Curation notes -------------- Identity checked against the first page\. PAGES\: pdf page n is journal p\. 481 \+ n \(Table I p\. 486\)\. MATERIAL\: 16O2 \(O2 as supplied\), X 3Sigma\_g\-, v = 0\: the pure rotational ^SS lines \(Delta N = Delta J = \+2\), labelled S\(J,N\) with J and N of the lower level \(S\(2,1\) is N = 1, J = 2 \-\> N = 3, J = 4\)\. The ^SR and ^SQ satellites were not measured\. WHAT THE COLUMNS ARE \(p\. 485 and p\. 490\)\. 'Observed'\: the wavenumbers of the CARS peak maxima; 'Corrected'\: 'the more correct transition values from spectral simulations', the peak positions after modelling the \|chi\|^2 interference of the triplet members \(the outer members of a triplet are pushed apart in CARS\), differing from the maxima by up to 0\.003 cm\-1 \(p\. 490\)\. The corrected values are the transition wavenumbers \(primary\); the observed maxima are kept as a check\. Wavenumbers in cm\-1 from the vacuum iodine\-atlas calibration \(vacuum not stated\)\. UNCERTAINTIES \(p\. 485\)\: 'A combination of the uncertainties in the I2 lines \(2 sigma = 0\.002 cm\-1\) and in the CARS peak determination leads us to an estimated uncertainty of \+\-0\.005 cm\-1 for the absolute rotational wavenumbers reported in Table I; relative wavenumbers within each triplet are believed to be accurate to 0\.001 cm\-1\.' CALCULATED LINES \(Eqs\. 1\-2, pp\. 485\-486; formula eq2\_levels\)\. The 'Corrected \- calculated' column compares with lines calculated from Eq\. \(2\) and 'the microwave constants suggested by Johns and Lepard \(14\)' \(J\. W\. C\. Johns and D\. W\. Lepard, J\. Mol\. Spectrosc\. 55, 374 \(1975\), not in the library\); the constants themselves are not printed\. 'Virtually all of the wavenumbers agree with the calculated values within the 0\.005 cm\-1 level of uncertainty' \(p\. 490\); the S\(20,19\) difference is 0\.006\. INTENSITIES \(notes; no quantity\)\. Table I's 'Simulated intensity' \(from the 300 K CARS simulations, converted to spontaneous Raman intensities, normalised to the highest\-J member of each triplet\) against Altmann et al\.'s calculated 298 K intensities \(Ref\. 2, Z\. Naturforsch\. 27, 56 \(1972\)\)\: the low\-J members are systematically higher than calculated \(e\.g\. S\(9,9\) 1\.00 against 0\.90\), which the authors suspect is a J dependence of the linewidth within a triplet \(p\. 491\)\. LINEWIDTHS \(model inputs, not measurements; notes\)\. The collisional \(Lorentzian\) FWHM at 70 Torr 'was estimated from earlier O2 pressure broadening studies \(4, 10, 16, 17\) to be 0\.006\-0\.009 cm\-1, depending on the N value'; 0\.001 cm\-1 in the jet \(p\. 489\)\. Doppler FWHM in the crossed\-beam geometry \(Eq\. 4, 1\.95 degree crossing\)\: 0\.00140\-0\.00142 cm\-1 at 300 K for N = 3\-19, x 0\.29 in the jet; instrumental FWHM 0\.010 cm\-1 \(the best fit; 0\.005 expected, p\. 490\)\. Not taken as data \(assumed, from Refs\. 4, 10, 16, 17\: jammu\_1966 is Ref\. 4\)\. FIGURES \(not digitised\)\: Fig\. 1 level scheme; Fig\. 3 S\(9\) in the jet and the cell; Figs\. 4\-5 interference shifts of CARS against Raman line pairs\. RELATION TO OTHER RECORDS\. yu\_2012 uses these 30 lines \(\+\-0\.005 cm\-1, N'' = 3\-21 as it states\) in its global fit\. rouille\_1992's v = 0 constants reproduce this Table I's 'Corrected \- calculated' column to \+\-0\.0005 cm\-1 \(see eq2\_levels\)\: the Johns\-Lepard and Rouille constants agree at that level\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- brown\_1992/table1\_corrected ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_corrected", "material": "O2", "file": "O2/brown_1992__table1_corrected.csv", "table": "tbl_ad5d63e4a91f", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "primary", "uncertainty": { "absolute": 0.005, "level": "not stated" }, "parameters": { "transition": "S(J,N): v = 0, Delta N = Delta J = +2, per row" } } Table I \(p\. 486\), 'Corrected'\: the ^SS\(N\) triplet lines of the pure rotational Raman spectrum of 16O2 \(v = 0\), N = 1\-19, J = N \+ 1, N, N \- 1 \(rows S\(J,N\) as printed, lower level\), from simulations of the CARS spectra at 70 Torr and 300 K \(the S\(1\) triplet from the 25 K jet\)\. Estimated absolute uncertainty \+\-0\.005 cm\-1 \(relative within a triplet 0\.001; p\. 485\)\. brown\_1992/table1\_observed ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_observed", "material": "O2", "file": "O2/brown_1992__table1_observed.csv", "table": "tbl_ad5d63e4a91f", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "uncertainty": { "absolute": 0.005, "level": "not stated" }, "parameters": { "transition": "S(J,N): v = 0, Delta N = Delta J = +2, per row" } } Table I \(p\. 486\), 'Observed'\: the CARS peak maxima, shifted from the true line positions by the triplet interference \(up to 0\.003 cm\-1, p\. 490\)\: check, beside table1\_corrected\. Formulas -------- brown\_1992/eq2\_levels ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq2_levels", "material": "O2", "equation": "Eqs. (1)-(2), pp. 485-486", "printed": "H_rot = B (J - S)^2 + 2 lambda (S_z^2 - S^2) + gamma (J - S).S; F1(N) = F2(N) + B_0 (2N + 3) - lambda - gamma/2 - [lambda^2 - 2 lambda (B_0 - gamma/2) + (2N + 3)^2 (B_0 - gamma/2)^2]^(1/2); F2(N) = B_0 N(N + 1) - D_0 N^2 (N + 1)^2; F3(N) = F2(N) - B_0 (2N - 1) - lambda - gamma/2 + [lambda^2 - 2 lambda (B_0 - gamma/2) + (2N - 1)^2 (B_0 - gamma/2)^2]^(1/2)", "variable": "N the rotational quantum number (odd for 16O2); F1, F2, F3 the term values of J = N + 1, N, N - 1 in cm-1; B_0, D_0, lambda (spin-spin) and gamma (spin-rotation) of v = 0; the S(J,N) line = F_i(N + 2) - F_i(N) with the same i", "state": "16O2 X 3Sigma_g-, v = 0", "density": "unknown", "range": "v = 0, N = 1-21 (the lines of Table I)", "coefficients": { "constants": "not printed: 'the microwave constants suggested by Johns and Lepard (14)'" }, "check": "Scratch (2026-09-27), with rouille_1992's v = 0 constants (B_0 1.437676476, D_0 4.84256e-6, lambda 1.984751322, gamma = mu_0 -8.42539e-3 cm-1) in place of the unprinted Johns-Lepard ones: the Corrected - calculated column is reproduced to +-0.0005 cm-1 for S(1,1)-S(20,19) (e.g. S(4,3) +0.0026 against +0.003, S(20,19) +0.0061 against +0.006, S(9,9) -0.0003 against 0.000). EXCEPTION: F3(1) (N = 1, J = 0) as printed is wrong by 1.085 cm-1 (S(0,1) comes out 15.167 against 16.252): for N = 1, (2N - 1)(B_0 - gamma/2) < lambda, and the square root must be taken as -(lambda - B_0 + gamma/2); rouille_1992's special-case Eq. (10) gives 16.2529, the printed difference -0.001. Brown et al.'s own calculation evidently treated it correctly." } The Hamiltonian's spin\-spin term 2 lambda \(S\_z^2 \- S^2\) differs from the \(2/3\) lambda \(3 S\_z^2 \- S^2\) of rouille\_1992 only by a constant, so lambda has the same meaning in both; gamma is rouille\_1992's mu\. 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.