rosasco_1983 ============ G\. J\. Rosasco, W\. Lempert, W\. S\. Hurst and A\. Fein, "Line interference effects in the vibrational Q\-branch spectra of N2 and CO", Chem\. Phys\. Lett\. 97, 435 \(1983\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0009\-2614\(83\)80524\-7 `__ **Source kind:** measurement **Recorded technique:** High\-resolution cw stimulated Raman \(Raman loss\) spectroscopy \(p\. 435\)\: a single\-mode Kr\-ion pump \(\< 20 MHz\) and a tunable ring\-dye probe \(about 1 MHz\), copropagating, parallel linear polarisations, pump modulated at 5\.4 MHz, multipass cell \(about 50\-fold\); frequency precision about 30 MHz \(0\.001 cm\-1\) over a Q branch\. Pure N2 and pure CO, v = 0 \-\> 1 Q branches, self\-broadened, about 20\-200 kPa \(0\.2\-2\.0 atm\), 298 K\. Line overlap described by a relaxation\-matrix model; the first\-order \(in density\) solution, Eq\. \(6\), fitted to spectra at 0\.2 and 0\.6 atm \(N2\) and 0\.2 and 0\.5 atm \(CO\) gives gamma\_j and Y\_j \(p\. 437\)\. **Materials in structured entries:** CO, N2 **Dataset quantities:** raman\_linewidth **Contents:** 2 datasets; 2 formulas. Curation notes -------------- Identity checked against the first page\. Page numbers are journal pages \(pdf pages 1\-6 = pp\. 435\-440\)\. Materials\: 14N2 and 12C16O \(natural gases\); no other isotopologue\. WIDTH CONVENTION\. HALF widths\. The paper never writes 'HWHM' against Table 1; the convention follows from Eq\. \(6\) \(p\. 436\)\: chi3''\(omega\) = \(n/24 hbar\) sum\_j alpha\_j^2 Delta rho\_0j p \[gamma\_j \- \(omega \- omega\_j\) Y\_j\] / \[\(omega \- omega\_j\)^2 \+ \(p gamma\_j\)^2\], 'with \.\.\. p the pressure, gamma\_j = W\_jj the line\-broadening coefficient'\. A Lorentzian gamma/\(x^2 \+ \(p gamma\)^2\) has its half width at half maximum at x = p gamma\: p gamma\_j is the HWHM, and gamma\_j the HWHM per atm\. Independent confirmation\: Rahn and Palmer \(rahn\_1986, Table 1, 'FWHM', note a 'From Ref\. 6' = this paper\) print exactly twice these values and errors for N2 \(all 19 rows\), and Farrow and Rahn \(farrow\_1985\) label their comparable Ar coefficients 'HWHM'\. Per atm of pressure at 298 K \('Line\-broadening and mixing\-coefficients at 298 K', Table 1 caption, p\. 438\), not per amagat\. The isolated\-line study behind the method \(Ref\. 6, Spectral Line Shapes Vol\. 2, not in the library\)\: Voigt at 0\.05 atm, Dicke narrowing with rising pressure, Lorentzian above 0\.2 atm; 'The collision component Gamma\(p\) is extracted using the known Doppler \(about 80 MHz\) and diffusion \(about 6 MHz at 1\.0 atm\) contributions', and Gamma\(p\) = p gamma holds to 2\.0 atm \(p\. 437\)\. UNCERTAINTIES\. gamma\_j\: the parenthesised digits \(last decimal\) are not described \(level not stated\)\. Y\_j\: the table's notes, poorly printed, read 'a\) \+\-20 %, J = 0\-3' and 'b\) \+\-50 %, J = 4\-18' \(the 'a' note's '\+\-20 %' is inferred from the partly legible scan, '\-20 \.,', and the legible 'b\) \+\-50 %'\), marked on J = 0 and J = 4 of each column\. THE LINE\-MIXING COEFFICIENTS Y\_j \(atm\-1\) have no quantity in the vocabulary\. They are recorded as the coefficients of Eq\. \(6\) in the formulas eq6\_N2 and eq6\_CO\. Definition, Eq\. \(7\) \(p\. 436\)\: Y\_j = 2 sum\_{j' \!= j} \(alpha\_j'/alpha\_j\) W\_j'j / \(omega\_j' \- omega\_j\), W the relaxation matrix \(Eq\. \(5\)\); 'first order in density'; all alpha\_j equal in the paper's normalisation\. Eq\. \(6\) with Table 1 'yields good agreement with the data up to 2\.0 atm' \(p\. 437\)\. TEXT VALUES \(notes only\)\. N2 line shifts 'less than 0\.001 cm\-1 atm\-1' \(Ref\. 6\); CO Q\(14\) shift about 0\.0045\(9\) cm\-1 atm\-1 \(sign not printed\); CO B1 \- B0 from \-0\.017511\(6\) cm\-1 \(0\.2 atm\) to \-0\.017495\(8\) cm\-1 \(1\.0 atm\) \(p\. 438\)\. Fitting the pure Lorentzian model with free T gives temperatures 'about 40 K too low' at 1 atm \(p\. 437\)\. Eq\. \(8\) \(p\. 438\), the state\-to\-state rate law used to model gamma\_j and Y\_j \(power law about 0\.5 with N\_x = N\_c at low j, exponential gap with N\_0 at high j; results in Fig\. 3 for CO only\)\: no fitted constants are printed\. What this bears on\: the N2 Q\-branch self\-broadening at room temperature \(the N2 Q widths in use, TC\-492\) and line mixing, which is not yet modelled \(docs/raman\.md, 'Line mixing'\)\. This is the source of Rahn and Palmer's 295 K column and of Farrow and Rahn's self\-broadening correction \(farrow\_1985\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- rosasco\_1983/table1\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_N2", "material": "N2", "file": "N2/rosasco_1983__table1_N2.csv", "table": "tbl_ee3e296d7c2c", "quantity": "raman_linewidth", "unit": "cm-1/atm", "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(J), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 298 } } Table 1 \(p\. 438\), N2 column gamma\_j\: HWHM self\-broadening coefficient of the Q\(J\) lines \(v = 0 \-\> 1\), cm\-1 per atm, 298 K, J = 0\-18 \(HWHM from Eq\. \(6\)\: see the source notes\)\. Fitted with Eq\. \(6\) \(line mixing included\) to 0\.2 and 0\.6 atm spectra\. Error in the last digits, level not stated\. rahn\_1986 prints these doubled as its 295 K FWHM column\. rosasco\_1983/table1\_CO ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_CO", "material": "CO", "file": "CO/rosasco_1983__table1_CO.csv", "table": "tbl_ee3e296d7c2c", "quantity": "raman_linewidth", "unit": "cm-1/atm", "abscissa": "label", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q(J), v = 0 -> 1, per row", "width": "hwhm", "perturber": "self", "temperature_k": 298 } } Table 1 \(p\. 438\), CO column gamma\_j\: HWHM self\-broadening coefficient of the Q\(J\) lines \(v = 0 \-\> 1\), cm\-1 per atm, 298 K, J = 0\-18 \(HWHM from Eq\. \(6\)\: see the source notes\)\. Fitted with Eq\. \(6\) to 0\.2 and 0\.5 atm spectra\. Error in the last digits, level not stated\. 'in excellent agreement with the recently reported \[32\] widths of P\- and R\-branch lines in the infrared vibrational overtone spectrum' \(p\. 438\)\. Formulas -------- rosasco\_1983/eq6\_N2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq6_N2", "material": "N2", "equation": "Eqs. (6)-(7), p. 436; Table 1 (tbl_ee3e296d7c2c), p. 438", "printed": "chi3''(omega) = (n/24 hbar) sum_j alpha_j^2 Delta rho_0j p [gamma_j - (omega - omega_j) Y_j] / [(omega - omega_j)^2 + (p gamma_j)^2]; Y_j = 2 sum_{j' != j} (alpha_j'/alpha_j) W_j'j / (omega_j' - omega_j)", "variable": "omega = omega_a - omega_b the Raman frequency, omega_j the Q(j) line position (in cm-1, as gamma_j); p: pressure in atm; gamma_j = W_jj the HWHM broadening coefficient in cm-1 atm-1 (dataset table1_N2); Y_j the first-order line-mixing coefficient in atm-1; n the number density; alpha_j = (all equal); Delta rho_0j the thermal population difference of the 0 and 1 levels at J", "state": "pure N2, 298 K", "density": "unknown", "range": "fitted to 0.2 and 0.6 atm; 'good agreement with the data up to 2.0 atm' (p. 437); first order in density", "coefficients": { "Y_Q0": "0.46", "Y_Q1": "0.6", "Y_Q2": "0.21", "Y_Q3": "0.05", "Y_Q4": "0.04", "Y_Q5": "0.04", "Y_Q6": "0.03", "Y_Q7": "0.03", "Y_Q8": "-0.03", "Y_Q9": "0.03", "Y_Q10": "-0.03", "Y_Q11": "0.03", "Y_Q12": "0.03", "Y_Q13": "-0.03", "Y_Q14": "0.03", "Y_Q15": "0.03", "Y_Q16": "0.03", "Y_Q17": "0.03", "Y_Q18": "0.03", "Y_error_J0_3": "20 %", "Y_error_J4_18": "50 %" }, "check": "No printed spectrum value to reproduce (Figs. 1-2 are figures). Sum rule (scratch, 2026-09-27): detailed balance, rho_j W_j'j = rho_j' W_jj', makes Eq. (7) satisfy sum_j rho_j Y_j = 0 (all alpha_j equal), separately for even and odd J in N2, whose collisions conserve the nuclear-spin symmetry. With 298 K Boltzmann populations (B = 1.99 cm-1, even:odd weights 2:1) the printed Y_j give sum_j rho_j Y_j = +0.046 atm-1 against sum_j rho_j |Y_j| = 0.060 (even J +0.025, odd J +0.021): the printed N2 values do NOT satisfy the sum rule. The CO values do, nearly: -0.010 against 0.084 (B = 1.92). The N2 column is badly printed (the signs of J = 8, 10, 13 are faint dashes; image checked at 400 dpi); lost minus signs at high J are a possible cause, not established." } The line\-mixing coefficients Y\_j of Table 1's N2 column, as printed \(the marks a\) and b\) on J = 0 and J = 4 dropped\: they are the error notes, \+\-20 % for J = 0\-3 and \+\-50 % for J = 4\-18\)\. 'No values of Q branch line\-mixing coefficients have been reported in the literature' \(p\. 438\)\. Line mixing is not modelled yet \(TC\-492\)\. rosasco\_1983/eq6\_CO ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "eq6_CO", "material": "CO", "equation": "Eqs. (6)-(7), p. 436; Table 1 (tbl_ee3e296d7c2c), p. 438", "printed": "chi3''(omega) = (n/24 hbar) sum_j alpha_j^2 Delta rho_0j p [gamma_j - (omega - omega_j) Y_j] / [(omega - omega_j)^2 + (p gamma_j)^2]; Y_j = 2 sum_{j' != j} (alpha_j'/alpha_j) W_j'j / (omega_j' - omega_j)", "variable": "as eq6_N2, with gamma_j the dataset table1_CO", "state": "pure CO, 298 K", "density": "unknown", "range": "fitted to 0.2 and 0.5 atm; good to 2.0 atm (p. 437); first order in density", "coefficients": { "Y_Q0": "1.24", "Y_Q1": "0.63", "Y_Q2": "0.16", "Y_Q3": "0.006", "Y_Q4": "-0.04", "Y_Q5": "-0.06", "Y_Q6": "-0.06", "Y_Q7": "-0.06", "Y_Q8": "-0.06", "Y_Q9": "-0.06", "Y_Q10": "-0.06", "Y_Q11": "-0.06", "Y_Q12": "-0.06", "Y_Q13": "-0.05", "Y_Q14": "-0.05", "Y_Q15": "-0.04", "Y_Q16": "-0.04", "Y_Q17": "-0.03", "Y_Q18": "-0.03", "Y_error_J0_3": "20 %", "Y_error_J4_18": "50 %" }, "check": "Sum rule as for eq6_N2 (scratch, 2026-09-27; all J mix, one sum): sum_j rho_j Y_j = -0.0097 atm-1 against sum_j rho_j |Y_j| = 0.084 at 298 K with B = 1.92 cm-1: zero to 12 % of the scale, within the stated +-20-50 %. Fig. 3b compares the Y_j with the rate-law predictions (figure only)." } The line\-mixing coefficients Y\_j of Table 1's CO column, as printed \(marks a\) and b\) dropped\)\. 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.