Line shape in the low-frequency wing of self-broadened CO<sub>2</sub>
lines

V. Menoux; R. Le Doucen; C. Boulet

doi:10.1364/AO.26.000554

Applied Optics
Vol. 26,
Issue 3,
pp. 554-562
(1987)
•https://doi.org/10.1364/AO.26.000554

Line shape in the low-frequency wing of self-broadened CO₂ lines

V. Menoux, R. Le Doucen, and C. Boulet

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V. Menoux, R. Le Doucen, and C. Boulet, "Line shape in the low-frequency wing of self-broadened CO₂ lines," Appl. Opt. 26, 554-562 (1987)

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Abstract

The shape of the far wings of self-broadened CO₂ lines has been investigated in the spectral region (2140–2250 cm⁻¹), i.e., on the low wavenumber side of the lines of the most intense band (ν₃ of ¹²C¹⁶O₂). The experimental results have been compared to calculated values based on the AFGL 1982 compilation. From this comparison it appears that the wings of the lines on the low wavenumber side of the centers decay much more rapidly than do Lorentz lines, by about the same amount as has been previously shown for the high wavenumber side. However, an asymmetrical correcting line shape factor is needed to obtain good agreement between experimental and synthetic spectra.

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σ (cm⁻¹)	P_a(Torr)	α_obs(σ) (cm⁻¹)	α_calc(σ) χ sym	δ %	α_calc(σ) χ asym	δ %
2143.64	1646	4.44 10⁻⁵			4.03 10⁻⁵	− 9.2
2146.76	1646	4.48 10⁻⁵			4.38 10⁻⁵	− 2.2
2148.64	1646	4.58 10⁻⁵			4.92 10⁻⁵	+ 7.4
2151.88	1646	5.04 10⁻⁵			4.95 10⁻⁵	− 1.8
2155.58	1646	5.91 10⁻⁵			5.63 10⁻⁵	− 4.7
2157.22	1646	5.94 10⁻⁵	8.8 10⁻⁵	48.	5.63 10⁻⁵	− 5.2
2160.18	787	2.08 10⁻⁵	2.66 10⁻⁵	28.	1.91 10⁻⁵	− 8.2
	907	2.61 10⁻⁵	3.42 10⁻⁵	31.	2.4 10⁻⁵	− 8
	1200	4.09 10⁻⁵	5.4 10⁻⁵	32.	3.7 10⁻⁵	− 9.5
	1500	5.8 10⁻⁵	8 10⁻⁵	38.	5.35 10⁻⁵	− 7.7
	1646	6.3 10⁻⁵	9.4 10⁻⁵	49.	6.25 10⁻⁵	− 0.8
	1800	8.25 10⁻⁵	1.11 10⁻⁴	35.	7.3 10⁻⁵	− 11.5
	1951	9.52 10⁻⁵	1.3 10⁻⁴	37.	8.5 10⁻⁵	8.5 10⁻⁵
2.163.18	1646	7.25 10⁻⁵			7.06 10⁻⁵	− 2.6
2171.2	1646	6.5 10⁻⁵			5.65 10⁻⁵	− 13.
2174.05	487	1.4 10⁻⁵
	691	2.34 10⁻⁵	unserviceable with AFGL 1982’s compilation (see text)
	901	3.42 10⁻⁵	unserviceable with AFGL 1982’s compilation (see text)
	1105	4.85 10⁻⁵			4.22 10⁻⁵	− 13.
	1315	6.19 10⁻⁵	8.52	37.6	5.86 10⁻⁵	− 5.3
	1410	7.37 10⁻⁵	9.8	33.	6.62 10⁻⁵	− 9.2
	1575	9.30 10⁻⁵	1.22 10⁻⁴	30.5	8.27 10⁻⁵	− 11.
	1973	1.35 10⁻⁴	1.91 10⁻⁴	41.5	1.28 10⁻⁴	− 5.2
	2138	1.59 10⁻⁴	2.24 10⁻⁴	41.	1.50 10⁻⁴	− 5.7
2178.	1410	8.63 10⁻⁵	1.09 10⁻⁴	26.	7.71 10⁻⁵	− 10.7
2181.6	1410	1.024 10⁻⁵			9.31 10⁻⁵	− 9
2184.36	1410	1.16 10⁻⁴			1.052 10⁻⁴	− 9.3
2187.88	1410	1.42 10⁻⁴			1.29 10⁻⁴	− 9.
2191.88	1410	1.76 10⁻⁴			1.57 10⁻⁴	− 10.8
2194.28	344	1.22 10⁻⁵	1.53 10⁻⁵	25.	1.24 10⁻⁵	1.6
	445	1.93 10⁻⁵	2.4 10⁻⁵	24.4	2.07 10⁻⁵	7.
	646	4.3 10⁻⁵	4.8 10⁻⁵	11.6	4.1 10⁻⁵	− 4.6
	756	5.93 10⁻⁵	6.58 10⁻⁵	11.	5.58 10⁻⁵	− 5.9
	843	7.39 10⁻⁵	8. 10⁻⁵	8.3	6.73 10⁻⁵	− 8.9
	932	8.98 10⁻⁵	9.65 10⁻⁵	7.5	8.2 10⁻⁵	− 8.7
	1027	1.084 10⁻⁴	1.162 10⁻⁴	7.2	9.85 10⁻⁵	− 9
	1410	1.97 10⁻⁴	2.13 10⁻⁴	8.1	1.8 10⁻⁴	− 8.6
2196 07	1410	2.23 10⁻⁴			2.06 10⁻⁴	− 7.6
2201.25	491	4.32 10⁻⁵	4.32 10⁻⁵	0.	3.85 10⁻⁵	− 10.8
	608	6.90 10⁻⁵	6.56 10⁻⁵	− 5	5.9 10⁻⁵	− 14.
	760	1.01 10⁻⁴	9.92 10⁻⁵	− 1.8	9. 10⁻⁵	− 10.
	912	1.45 10⁻⁴	1.4 10⁻⁴	− 3.4	1.26 10⁻⁴	− 13.
	1003	1.7 10⁻⁴	1.68 10⁻⁴	− 1.2	1.54 10⁻⁴	− 9.4
	1216	2.36 10⁻⁴	2.46 10⁻⁴	4.2	2.2 10⁻⁴	− 6.8
2203.52	1003	1.92 10⁻⁴			1.79 10⁻⁴	− 6.8
2206.94	1003	2.57 10⁻⁴			2.42 10⁻⁴	− 5.8
2210.3	195	1.55 10⁻⁵	1.65 10⁻⁵	6.5	1.6 10⁻⁵	3.2
	301	3.7 10⁻⁵	3.94 10⁻⁵	6.5	3.81 10⁻⁵	3
	407	6.56 10⁻⁵	7.1 10⁻⁵	8.2	6.8 10⁻⁵	3.6
	496	1. 10⁻⁴	1.04 10⁻⁴	4.	9.9 10⁻⁵	− 1.
	602	1.45 ⁻⁴	1.48 10⁻⁴	2.	1.42 10⁻⁵	− 2.
	694	1.9 10⁻⁴	1.92 10	1.	1.88 10⁻⁵	− 1.
2220.64	390	2.25 10⁻⁴			2.15 10⁻⁴	− 4.4
2222.68	390	3.26 10⁻⁴			3.02 10⁻⁴	− 7.4
2224.84	390	3.51 10⁻⁴			3.65 10⁻⁴	+ 4.
2225.84	56	1.02 10⁻⁵			1.02 10⁻⁵	0.
	89	2.4 10⁻⁵			2.57 10⁻⁵	7.1
	151	6.63 10⁻⁵			7.46 10⁻⁵	+ 12.
	180	1.08 10⁻⁴			1.06 10⁻⁴	− 2.
	213	1.29 10⁻⁴			1.42 10⁻⁴	10.
	241	1.82 10⁻⁴			1.82 10⁻⁴	0.
	274	2.2 10⁻⁴			2.35 10⁻⁴	6.8
2226.88	391	6.2 10⁻⁴			6.77 10⁻⁴	9.
2229.46	391	9.28 10⁻⁴			1.02 10⁻³	10.
2231.42	391	1.12 10⁻³			1.17 10⁻³	4.5
2234.46	391	1.20 10⁻³	1.18 10⁻³	− 1.7	1.20 10⁻³	0.
2238.28	391	1.95 10⁻³			2. 10⁻³	2.5
2244.5	193	1.07 10⁻³			1.11 10⁻³	3.6
2246.38	193	1.3 10⁻³			1.4 10⁻³	7.7
2249.	193	1.86 10⁻³			2.09 10⁻³	12.4
2250.84	193	2.13 10⁻³			2.29 10⁻³	7.5

	Results of the fit		Theoretical values*

	A₀	A₁	B₁
σ(cm⁻¹)	(10⁻⁶ cm⁻¹)	(10⁻⁵ cm⁻¹ atm⁻²)	(10⁻⁵ cm⁻¹ atm⁻²)
2225.84	(−0.028 ± 2.7)	189 ± 5	180.
2210.3	(1.24 ± 1)	22.9 ± 0.2	22.5
2201.25	(0.52 ± 1.46)	9.7 ± 0.2	9.1
2194.28	0.6 ± 0.2	5.91 ± 0.02	5.3
2178.	2.7 ± 0.7	2.35 ± 0.02	2.25
2174.05	7.33 ± 0.7	1.87 ± 0.02	1.85
2160.18	7.1 ± 0.5	1.32 ± 0.01	1.16

line frequencies cm⁻¹	line intensities (molecules⁻¹ cm)	upper vibrational level	lower level	line	isotope
2159.6949	4.85 10⁻²⁵	20012	20001	P 24	626
2159.9929	1.71 10⁻²⁴	10012	10001	R 2	636
2160.0624	9.58 10⁻²⁴	21101	02201	P 7	626
2160.2895	8.78 10⁻²⁴	11112	11101	P 13	626
2160.7074	1.97 10⁻²⁴	21101	10001	R 60	626
2160.8050	8.28 10⁻²⁴	21101	02201	P 6	626

n°	Band identification		Banda)	$s_{v}^{o}$ vibrational a)
	upper level	lover level	center cm⁻¹	intnsity (10⁻²² cm/mol)	isotope
1	00011	00001	2349.143	959800	626
2	01111	01101	2336.633	76600	626
3	00011	00001	2283.488	9602	636
4	02211	02201	2324.141	3080	626
5	00011	00001	2332.113	3330	628
6	10012	10002	2327.433	1934.	626
7	10011	10001	2326.598	1183.	626
8	01111	01101	2271.760	818.	636
9	00011	00001	2265.973	38.8	638
10	02211	02201	2260.048	34.6	636
11	10012	10002	2261.909	20.3	636
12	10011	10001	2262.847	12.3	636

σ cm⁻¹	2250.84	2238.28	2225.84	2210.3	2194.28	2174.05	2160.18	2143.64
P_a (Torr)	193	391	180	496	756	1410	1500	1646
κ(σ)	0.71	0.46	0.237	4.57 10⁻²	1.54 10⁻²	7.3 10⁻³	5.9 10⁻³	4.5 10⁻³

0 ⩽ \|σ\| ⩽ 3 cm⁻¹	χ = 1

3 ⩽ \|σ\| ⩽ 10 cm⁻¹	$χ = 1.47 exp [- \frac{∣ σ ∣}{7.782}]$

10 ⩽ \|σ\| ⩽ 120 cm⁻¹	$χ = 0.535 exp [- \frac{∣ σ ∣}{36.535}]$

\|σ\| ⩾ 120 cm⁻¹
σ < 0	σ > 0
$χ = .889 exp [- \frac{∣ σ ∣}{31.627}]$	$χ = .220 exp [- \frac{∣ σ ∣}{50.063}]$

Abstract

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Tables (7)

Equations (3)

Applied Optics