Line mixing effect in the ν2 band of CH3Br

Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

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Line mixing effect in the ν2 band of CH3Br F. Hmida a,c, S. Galalou a, F. Kwabia Tchana b, M. Rotger c, H. Aroui a,n a

Laboratoire de Dynamique Moléculaire et Matériaux Photoniques, UR11ES03, Université de Tunis, Ecole Nationale Supérieure d’Ingénieurs de Tunis, 5 Av Taha Hussein, 1008 Tunis, Tunisia LISA, Laboratoire Interuniversitaire des Systèmes Atmosphériques, UMR CNRS 7583, Université Paris-Est Créteil (UPEC) et Université Paris-Diderot (UPD), 61 Avenue du Général de Gaulle, 94010 Créteil Cedex, France c GSMA, Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 7331, Université de Reims Champagne Ardenne, Moulin de la Housse B.P. 1039, F-51687 Cedex Reims, France b

art ic l e i nf o

a b s t r a c t

Article history: Received 21 October 2016 Received in revised form 8 December 2016 Accepted 9 December 2016 Available online 15 December 2016

Line intensities, self broadening coefficients, as well as line mixing parameters and self-shift coefficients have been measured in the ν2 parallel band of CH3Br at room temperature for 38 rovibrational doublets with rotational quantum numbers 4 rJ r 47 and K¼ 0, 1. Measurements were made in the P and R branches located in the spectral range from 1260 to 1332 cm  1 using high-resolution Fourier transform spectra. These spectroscopic parameters have been retrieved from twelve spectra recorded at different pressures of pure CH3Br from 0.2 to 6.8 Torr. The spectra have been analyzed using a multi-pressure nonlinear least squares fitting of Rosenkranz profile taking into account line mixing effect. These spectra and results of pressure broadening coefficients and line intensities obtained with and without taking into account line mixing effect are compared, analyzed and discussed as function of the rotational quantum numbers and the branch. Analyzing of overlapped lines demonstrates an important mixing effect between the doublets components. On average the values of these spectroscopic parameters obtained when taking into account line mixing were found to be about 5% smaller than those obtained without taking into account this effect. On average, the accuracies of self-broadening coefficients and line intensities are estimated to be better than 3.8%. The mean accuracies of line-mixing and line-shift data are estimated to be about 20% and 17% respectively. The measured line mixing parameters are both positive and negative, while most of the lines have a negative shift coefficient. & 2016 Elsevier Ltd. All rights reserved.

Keywords: CH3Br Fourier transform infrared spectroscopy ν2 band Line mixing Line intensity Self-broadening Self-shift

1. Introduction Methyl halides are the subject of a very detailed attention in the spectroscopic study of the Earth's atmosphere. They are essential in the understanding of physico-chemical processes that exist in the atmosphere and where the absorbing molecules are influenced by collisions with other species. These halogen chemical compounds are used in agriculture as a plant fungicide, and automobile using leaded petrol [1]. It is also used in the fruitbearing production. These molecules have both natural and anthropogenic origins. Its sources include natural production from oceans [2] and biomass burning [3]. Therefore, methyl bromide is of great interest for atmospheric applications. This species is easily decomposed in the atmosphere by UV sun radiation with ozone depleting producing Br radicals that catalyze the destruction of ozone [4]. n

Corresponding author. E-mail address: [email protected] (H. Aroui).

http://dx.doi.org/10.1016/j.jqsrt.2016.12.015 0022-4073/& 2016 Elsevier Ltd. All rights reserved.

This radical is largely more destructive of ozone than the chlorine atoms coming from the chlorofluorocarbons compounds (CFC) [5]. Subsequently, since 2005 the use of CH3Br has been prevented under the Montreal protocol. Then, the accurate knowledge of the line spectroscopic parameters of methyl bromide in the atmospheric spectral windows is crucial for the retrievals of the atmospheric profiles and thereby for the monitoring of the composition of planetary atmosphere as well as the completion of the existing atmospheric database to guide future observations. Many studies have already been devoted to the analysis of the rovibrational spectra of CH3Br in order to determine line positions and line intensities [6–10]. Concerning the determination of broadening coefficients, several efforts have been made by different groups either on CH3Br self-broadened or perturbed by N2, O2 and air. Using a high-resolution Fourier transform spectrometer Jacquemart et al. [11] have measured line positions and intensities as well as self- and N2-broadening coefficients of about 1200 lines belonging to the ν6 band of both CH379Br and CH381Br isotopologues. The temperature dependence of broadening coefficients for 1400 lines in the same

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F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

band was also studied by Jacquemart and Tran [12]. In the same band, theoretical calculations of self- and N2-broadening coefficients were performed at room [13] and various temperatures [14]. Hoffman and Davies [15] have used a tunable diode laser absorption spectroscopy to measure at room temperature nitrogen, oxygen and self-broadening coefficients of 174 rotational transitions in the P, Q and R-branches of ν5 fundamental band of methyl bromide (CH379Br and CH381Br) around 6.9 mm region. Recently, we have reported room temperature self- and N2-broadening coefficients of 948 lines of CH3Br in the ν2 fundamental band using a Fourier transform spectrometer and a monospectrum non-linear least squares fitting of Voigt profile [16]. Otherwise, when the gas pressure increases, the lines overlap. Because of this line mixing effect [17,18], the usual Lorentz or Voigt line profile cannot correctly reproduce the experimental spectra. Then taking line-mixing into account is required for accurate treatments of atmospheric spectra. This may lead to significant improvements in the agreement between measured and calculated spectra with positive consequences for various types of retrievals such as species amounts, temperature and pressure profiles. Note that collisional line-mixing can notably affect the absorption spectra especially when transitions strongly overlap each other for instance, in the molecular band heads. Theoretically, pressure-induced line broadenings are generally described by a relaxation matrix (see for instance Ref. [19] and references therein). Its diagonal elements are the broadenings and shift coefficients of the lines, its off-diagonal elements are responsible for the interferences between the molecular transitions. In this framework, the first-order line-mixing effects have been studied in various molecules. Examples include CO2 [20,21], CH4 [22], and OCS [23]. However, for molecules of C3v symmetry the number of works is less. Line-mixing effects have been analyzed in the ν3 band of CH3F [24], and in the ν1 [25] and ν4 [26] bands of NH3. A simple approach is developed in Ref. [27] to model line interference in the 2ν6 band of CFC-22 perturbed by N2, and the ν5 band of CH3Cl perturbed by He [28]. Recently, spectra of the QQ branch of the ν1 parallel band of this molecule have been studied by Bray et al. [29]. Although many works were carried out about line mixing effect, very few data on this subject are available now in atmospheric databases such as HITRAN [30], GEISA [31] and JPL [32]. This is mainly due to the fact that they are small and their measurements are rather difficult. For the same reasons, line mixing effects in CH3Br spectra have received much less attention than pressure broadenings. Recently, line mixing effects in the ν6Q branch of self- and nitrogen-broadened methyl bromide have been studied by Tran et al.[33] using Fourier transform spectra recorded at room temperature. In order to model their spectra, the authors have used a theoretical approach based on the state-to-state rotational cross-sections calculated by means of a statistical exponential-gap fitting law. As a continuation of this work Gomez et al. [34] have studied line mixing at low temperature in the same band of CH3Br perturbed by nitrogen using spectra recorded at various temperatures and pressures. Comparisons between these spectra and calculations using both direct calculation from relaxation operator and Rosenkranz profile showed improvement compared to the usual Lorentz profile. The present work is devoted to the study of line mixing effect on measured line intensities and self-broadening coefficients of 38 doublets in the P and R branches of the ν2 band of CH3Br by analyzing twelve Fourier transform spectra recorded at room temperature. In addition, we have measured line mixing parameter and shift coefficient of the components of theses doublets. Each doublet consists of two component lines having the same J quantum number with K ¼ 0 or 1 and symmetry A þ or E. The

spacing frequency Δs between these components is small enough (o0.0236 cm  1) to induce overlapping of spectral line at low pressure transferring populations between these close components. Indeed, the CH3Br broadening is important so that even at 2 Torr we already observe the mixture of the lines especially in wings. In such conditions, the off-diagonal elements of the relaxation matrix should be used to account for spectral analysis. We have analyzed various Fourier Transform spectra as well as results of line parameters obtained with and without the consideration of line mixing effect. Then, we compared these results with previous data obtained using Voigt profile. The remainder of this paper is organized as follows. The next section is devoted to a description of the experimental details. Fitting procedures will be outlined in Section 3. The results of line intensities, self- broadening, as well as self-mixing and self-shift are discussed in Section 4. Measurement accuracies are analyzed in Section 5. Conclusion and remarks are addressed in Section 6.

2. Experimental details The spectra of CH3Br self-perturbed at room temperature (T ¼295 71 K) in the ν2 band in the spectral region from 1260 to 1332 cm  1 have been recorded by means of a high-resolution Fourier transform spectrometer, Bruker IFS 125 HR located at the LISA facility in Creteil. This experimental setup was equipped with a KBr/Ge beam splitter. A silicon carbide Globar source and a liquid nitrogen cooled HgCdTe (MCT) detector were used in conjunction with an optical filter, with a band pass of 1150–1550 cm  1. The spectrometer is placed under vacuum to limit the absorption of atmospheric molecules essentially H2O and CO2. The gas was contained in an absorption cell made of Pyrex glass with an optical path length of 0.849 (2) m. It is a White-type multi-pass cell with a base length of 0.20 m. The spectra were recorded with a resolution of 0.002 cm  1. These spectra were recorded at a series of twelve pressures ranging from 0.203 to 6.811 Torr. An overview of the detailed experimental conditions is given in Table 1. The sample pressure in the cell was measured using calibrated MKS Baratron capacitance manometers (2 or 10 Torr full scale) with a reading accuracy of 0.12%, according to the manufacturer. The samples of methyl bromide in natural abundances (50.54% of 79Br and 49.46% of 81Br) were provided with stated purities of 99% without further purification. The interferograms were transformed into spectra using a Fourier transform procedure included in the Bruker software OPUS package [35]. Fig. 1 shows an overview of transmittance spectrum in the ν2 band of CH3Br in the region between 1250 and 1337 cm  1 at the pressure of 2.046 (10) Torr. Table 1 Sample pressure and the number of scan for each spectrum. CH3Br pressure (Torr)

Number of scans

0.2034 (10) 0.6160 (31) 1.003 (5) 1.499 (7) 2.046 (10) 2.490 (12) 3.087 (15) 3.626 (18) 4.511 (23) 5.625 (28) 6.205 (31) 6.811 (34)

452 460 444 444 448 444 392 392 396 420 444 456

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

1,0

Transmittance

0,8

0,6

0,4

0,2

0,0

R Branch

P Branch 1260

1280

1300

1320

Wavenumber (cm ) Fig. 1. Transmittance spectrum of CH3Br recorded at room temperature (T¼ 295 7 1 K) at a pressure of 2.046 (10) Torr in the spectral range between 1250 and 1337 cm  1. The cell length is 0.849 (2) m.

coupling with all other lines of the same branch. This parameter is related to the relaxation matrix whose off-diagonal elements are responsible for intensity exchanges and interferences between the optical transitions. As expressed by the numerator of this equation, this profile is the sum of a Lorentz profile and of a mixing term. This profile describes the effects of non-additivity of line widths when the gas density increases, or when a spectrum has clusters of close lines. As the broadening increases and the lines overlap the collision-induced transfers of population became increasingly important and the spectral shape cannot be modeled without taking the line mixing process into account. This process leads to a decrease of absorption in the wings of lines, and an increase of the troughs between coupled lines. The experimental spectra were analyzed using the following expression for the transmission and the collisional absorption coefficient given by Eq. (1): τ C (σ ) =

To illustrate line mixing effect, we plotted in Fig. 2 the transmittance spectra of CH3Br around 1281 cm  1 exhibiting some lines of the P branch at the pressures of 1.499 (7) and 3.087(15) Torr. At low pressure the lines are separated, but when the pressure increases the lines widen and begin to overlap.

3. Fitting Procedure A multi-pressure fitting procedure has been used to retrieve line spectroscopic parameters by fitting twelve spectra recorded at different pressures. This procedure consists of a non linear least squares method in which line parameters (position, intensity, broadening, line mixing parameter and baseline) were determined by fitting small interval frequency with a width depending upon the complexity of the considered region. A single run of a FORTRAN code is enough to fit successively all sample pressures and to obtain these parameters for each of the twelve spectra. These spectra were analyzed by taking into account line mixing effects. Within impact theory and for moderately overlapping lines at low pressure, as considered in this work, the collisional absorption coefficient α(s) is assumed to have a Rosenkranz profile [36] that has been used in numerous works [37,38]:

α (σ ) =

PY ( σ − σ k ) + Pγk P ∑ Sk k π lines k ( σ − σ k )2 + ( Pγk )2

(1)

In this equation k represents the line νiJiKi- νfJfKf, Sk its integrated intensity in cm  2, sk its wavenumber in cm  1, γk its half width in cm  1, and Yk its line-mixing parameter representing the 1,0

Transmittance

0,8

0,6

0,4

0,2

1.499 Torr

0,0

3.087 Torr

1281,10

1281,15

1281,20

1281,25

1281,30

Wavenumber (cm ) Fig. 2. Transmittance spectra of CH3Br around 1281 cm  1 showing some lines of the P branch of the ν2 band at pressures of 1.499 (7) and 3.087 (15) Torr.

353

+∞

∫−∞

⎡ FApp (σ − σ ′) × exp ⎢ −ℓ ⎣

+∞

∫−∞

⎤ αDop (σ ′ − σ ″) α (σ ″) dσ ″⎥ dσ ′ ⎦

(2)

FApp is the Fourier transform apparatus function, αDop is the Doppler profile and, l is the cell length. The collisional parameters for a given temperature were obtained through a non-linear least squares multi-pressure fitting procedure in which all spectra at various pressures are successively adjusted using Eq. (2). The parameters deduced from the fits for a line k are the quantities γk, sk, Yk, and Sk. Note that some line widths and line intensities among 76 transitions studied in this work were already published in [10,16]. In these works a Voigt profile were used to model the Fourier Transform spectra. An example of multi-pressure fitting procedure with and without including line mixing for the pressures 1.499 and 6.811 Torr is shown in Fig. 3a and b in the case of the doublet components R79(30,A þ ,0) and R79(30,E,1) centered at 1323.58168 and 1323.59906 cm  1 respectively and pertaining to the ν2 band of CH379Br. For the plot (a), a Voigt profile without taking into account line mixing effect (Y ¼0) is used to adjust the observed spectrum. In the plot (b) the line mixing effect is taken into account in the fit (Y≠0). Measured minus calculated deviations are given in the lower part of each plot. Looking the residual of Fig. 3a, one can observe that at P¼1.499 Torr taking into account line-mixing effect don’t improve significantly the fitted spectra since the pressure is not high enough to allow the overlap of lines. However, at pressure P¼6.811 Torr, we can see obviously at Fig. 3a that fitting spectra without line-mixing leads to an important residuals which are reduced significantly when line-mixing effects are taken into account (Fig. 3b). Then from these figures the need to take into account the line mixing effect is clearly highlighted. One can attempt to improve the precision of the dataset and to reduce the fit residuals by taking Dicke narrowing and speed-dependent broadening into account. These two effects are neglected in this work. As mentioned by Pine et al. [39] for the ν1 band of NH3, they are probably masked by the large self-broadenings of CH3Br with a large dipole moment m¼ 1.8203 D [8]. We note that some doublets aren’t enough isolated, then the frequency interval used to fit the observed spectra contain lines other those pertaining to the doublet of interest. Therefore, the line-mixing processes can occur not only between the two components of the doublets but also between more than two transitions. In addition all branches of the ν2 parallel band centered at about 1305.90 cm  1 are influenced by the Coriolis interactions with the ν5 perpendicular band centered at 1442.88 cm  1. These interactions may perturb the line positions, intensities, line widths and line mixing.

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

Transmittance

354

1,1 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 1323,57 0,06

1.499 Torr

6.811 Torr

(a)

1323,58

Cal Without1 Exp Without1 Cal Without6 Exp Without6

1323,59

1323,60

1323,61

0,00 -0,06 1323,57

1323,58

1323,59

1323,60

1323,61

-1

σ (cm ) 1.499 Torr

1,0

Transmittance

0,9 0,8

6.811 Torr

0,7 0,6 0,5 0,4

(b )

0,3

Cal With1 Exp With1 Cal With6 Exp With6

0,2 0,1 0,0 1323,57

1323,58

1323,59

1323,60

1323,61

0,06 0,00 -0,06 1323,57

1323,58

1323,59

1323,60

1323,61

-1

σ (cm ) Fig. 3. Multi-pressure fit of the doublet components R79(30,A þ ,0) and R79(30,E,1) of the ν2 band centered at 1323.58168 and 1323.59906 cm  1 respectively for the two pressures 1.499 and 6.811 Torr: (a) without taking into account line mixing effect (Y ¼0); (b) with taking into account line mixing effect (Y≠0).

0,00025

In the following results of line spectroscopic parameters are discussed as function of rotational quantum numbers and branches. These parameters have been measured at room temperature T ¼295 K for 38 doublets (76 lines) of the P and R branches of the ν2 fundamental parallel band of two isotopic species CH379Br and CH381Br. The discussion focuses on the effect of line mixing on line intensities and collisional broadening coefficients. Note that for some lines which are too weak, no reliable fit could be obtained. Then their collisional parameters have not been determined, so these lines have been disregarded. 4.1. Line intensities Fig. 4 represents typical plots of integrated intensities Sk in cm-2 as a function of the pressure P in atm for the P81(37,A þ ,0) line in the ν2 band derived from the fit using Eqs. (1) and (2) with (Yk≠0) and without (Yk ¼ 0) taking into account line mixing effects. One can observe that the straight lines go well through the measured points. In this figure the error bars are estimated as one time standard deviation derived from the linear fit to which we added 2% of Sk representing the unknown systematic errors. The line intensities S0 in cm  2 atm  1 are determined as the slopes of the best-fit lines. The values of S0 for the R and P branches are presented in Table 2 which illustrates the dependence of this parameter on the J and K quantum numbers (4 rJ r47 and

S (cm )

4. Results, comparisons and discussion

0,00020

Without

0,00015

With

0,00010

0,00005

0,00000 0,000

0,002

0,004

0,006

0,008

0,010

P(atm) Fig. 4. Pressure dependence of intensity parameter Skwith (Yk≠0) and without (Yk ¼ 0) taking into account line mixing effect for the P81(37,A þ ,0) line in the ν2 band of CH3Br.

K ¼0, 1) for both isotopic species. We have listed for each line, the rotational assignment, the position frequency, and the measured line intensity obtained without and with line mixing as well as the estimated uncertainties. At first sight, as revealed by this table the intensities of most A þ components are greater than those of the E components. This is true for 66 lines out of 76. A plot (no shown here) of the line intensities of the E components versus those of the A þ ones leads roughly to a linear behavior with a slope of about 0.83 70.04 for

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

S0Without(cm-2.atm-1)

S0With(cm-2.atm-1)

R79(4,A þ ,0) R79(4,E,1) R79(5,A þ ,0) R79(5,E,1) R79(6,A þ ,0) R79(6,E,1) R79(23,A þ ,0) R79(23,E,1) P79(25,A þ ,0) P79(25,E,1) R79(29,A þ ,0) R79(29,E,1) P79(29,A þ ,0) P79(29,E,1) R79(30,A þ ,0) R79(30,E,1) P79(30,A þ ,0) P79(30,E,1) R79(31,A þ ,0) R79(31,E,1) R79(32,A þ ,0) R79(32,E,1) P79(32,A þ ,0) P79(32,E,1) P79(34,A þ ,0) P79(34,E,1) R79(35,A þ ,0) R79(35,E,1) P79(35,A þ ,0) P79(35,E,1) P79(41,A þ ,0) P79(41,E,1) R79(47,A þ ,0) R79(47,E,1) R81(4,A þ ,0) R81(4,E,1) R81(5,A þ ,0) R81(5,E,1) R81(6,A þ ,0) R81(6,E,1) R81(7,A þ ,0) R81(7,E,1) R81(12,A þ ,0) R81(12,E,1) R81(13,A þ ,0) R81(13,E,1) R81(16,A þ ,0) R81(16,E,1) R81(17,A þ ,0) R81(17,E,1) R81(19,A þ ,0) R81(19,E,1) R81(20,A þ ,0) R81(20,E,1) P81(25,A þ ,0) P81(25,E,1) R81(33,A þ ,0) R81(33,E,1) R81(36,A þ ,0) R81(36,E,1) P81(36,A þ ,0) P81(36,E,1) P81(37,A þ ,0) P81(37,E,1) P81(38,A þ ,0) P81(38,E,1) R81(40,A þ ,0) R81(40,E,1) P81(40,A þ ,0) P81(40,E,1) R81(43,A þ ,0) R81(43,E,1) R81(45,A þ ,0) R81(45,E,1)

1309.05647 1309.08010 1309.66924 1309.69288 1310.27736 1310.30099 1319.95817 1319.97838 1288.72023 1288.74013 1323.07702 1323.09472 1285.73216 1285.75068 1323.58168 1323.59906 1284.97497 1284.99344 1324.0821 1324.09869 1324.48317 1324.49965 1283.45023 1283.46777 1281.90991 1281.92685 1326.04021 1326.0555 1281.13411 1281.15068 1276.40189 1276.41602 1331.50638 1331.51479 1309.01526 1309.03889 1309.62582 1309.64923 1310.23189 1310.25525 1310.83363 1310.85709 1313.77900 1313.80141 1314.35426 1314.37687 1316.05728 1316.07869 1316.61593 1316.63723 1317.72083 1317.74156 1318.26689 1318.28744 1288.75835 1288.77876 1324.97367 1324.98875 1326.41817 1326.43296 1280.42793 1280.44408 1279.64799 1279.6637 1278.86421 1278.87971 1328.28534 1328.29826 1277.28609 1277.30021 1329.64106 1329.65321 1330.52426 1330.53467

0.02407 0.0007 0.02117 0.0006 0.0284 7 0.0013 0.0303 7 0.0011 0.0295 7 0.0009 0.0301 70.0010 0.05677 0.0056 0.0417 70.0019 0.0455 70.0015 0.0459 70.0018 0.03187 0.0010 0.03527 0.0011 0.04337 0.0014 0.03737 0.0014 0.03077 0.0010 0.02797 0.0016 0.0362 7 0.0015 0.03547 0.0014 0.0296 7 0.0012 0.0264 70.0008 0.0298 7 0.0012 0.0289 7 0.0008 0.0299 7 0.0010 0.0270 70.0009 0.0290 7 0.0011 0.0248 7 0.0006 0.02977 0.0013 0.02077 0.0007 0.0269 7 0.0011 0.0260 7 0.0008 0.01947 0.0004 0.01527 0.0004 0.0088 7 0.0004 0.01187 0.0003 0.02357 0.0009 0.02277 0.0007 0.0265 7 0.0011 0.0258 7 0.0009 0.03337 0.0020 0.0364 70.0010 0.03387 0.0011 0.0288 7 0.0016 0.0565 7 0.0022 0.04167 0.0011 0.05127 0.0020 0.0429 70.0019 0.05247 0.0024 0.04727 0.0025 0.0506 70.0020 0.0463 70.0015 0.05217 0.0022 0.0519 70.0026 0.04857 0.0018 0.04357 0.0013 0.04447 0.0019 0.04167 0.0016 0.02677 0.0007 0.0284 7 0.0023 0.01907 0.0007 0.01977 0.0007 0.01957 0.0007 0.02007 0.0007 0.0232 7 0.0006 0.01837 0.0011 0.01597 0.0007 0.01737 0.0010 0.0239 7 0.0008 0.0153 7 0.0005 0.01597 0.0005 0.0157 70.0007 0.01097 0.0006 0.0090 7 0.0011 0.01087 0.0003 0.0090 7 0.0004

0.0230 7 0.0007 0.020770.0006 0.02747 0.0010 0.0305 7 0.0010 0.0280 7 0.0010 0.0286 7 0.0008 0.052470.0042 0.0404 7 0.0016 0.0415 70.0016 0.0425 7 0.0015 0.03047 0.0008 0.03497 0.0009 0.0436 7 0.0018 0.03477 0.0013 0.0290 7 0.0012 0.02747 0.0009 0.03497 0.0012 0.03047 0.0012 0.0290 7 0.0008 0.02737 0.0008 0.0313 70.0012 0.0263 7 0.0014 0.02977 0.0010 0.0300 70.0011 0.0286 7 0.0011 0.02447 0.0006 0.02777 0.0010 0.0203 7 0.0008 0.0256 7 0.0008 0.0254 7 0.0008 0.0186 70.0008 0.0166 7 0.0007 0.00707 0.0002 0.00977 0.0004 0.023570.0008 0.0225 7 0.0006 0.0253 7 0.0009 0.023570.0007 0.0329 7 0.0012 0.0329 7 0.0009 0.03577 0.0010 0.03127 0.0013 0.0512 70.0016 0.0382 7 0.0013 0.0481 7 0.0019 0.0423 7 0.0019 0.05217 0.0020 0.0443 70.0017 0.050770.0021 0.0500 70.0021 0.04977 0.0014 0.04517 0.0014 0.0445 70.0016 0.0414 70.0013 0.0426 7 0.0019 0.0388 7 0.0016 0.02687 0.0008 0.02757 0.0014 0.01947 0.0007 0.0203 7 0.0007 0.01967 0.0007 0.01967 0.0006 0.0215 70.0007 0.0184 70.0009 0.0182 70.0012 0.01657 0.0005 0.0251 70.0009 0.01607 0.0005 0.01627 0.0006 0.01477 0.0006 0.01027 0.0008 0.0089 70.0004 0.0100 70.0003 0.0080 70.0003

r0(cm-1)

S0Without(cm-2.atm-1)

S0With(cm-2.atm-1)

R81(47,A þ ,0) R81(47,E ,1)

1331.39027 1331.39959

0.0059 70.0003 0.0054 70.0002

0.0055 7 0.0002 0.0049 70.0002

the two sets of values obtained with and without considering line mixing effect. For the P81(37,A þ ,0) line plotted in Fig. 4, the intensity values are 0.021570.0007 cm  2 atm  1 and 0.023270.0006 cm  2 atm  1 obtained with (Yk≠0) and without (Yk ¼0) line mixing effect respectively. In Table 2, we notice that most line intensities (56 lines among a total of 76 lines) derived without taking into account line mixing effect are greater than those for which this effect is taken into account. This effect is also demonstrated by Fig. 5 which is a plot of the S0 parameter of the two branches of the two isotopic species obtained with line mixing as function of those obtained without including this effect. The slope of the best-fit line is 0.93 70.01 showing clearly the need of taking into account line mixing to model line intensities of the doublet profiles of the ν2 band of CH3Br. This effect could be evaluated when one calculates the average of the absolute relative difference between the results obtained with and without including line mixing effect. D = SWiithout − SWith /SWiithout For the line verifying S0With oS0without, the achieved value is about 5.3% larger than the estimated measured uncertainty (∼4.0%). Fig. 6 illustrates the J rotational dependencies of the present values of S0 obtained with and without including the mixing effect in the P and R branches of the two isotopic species, together with those of Ref. [10] obtained using a Voigt profile without taking into account line mixing process. For the twelve transitions studied in common (with the same branch and the same J and K quantum numbers), the line intensities measured by these authors are systematically greater than ours, with a difference value of about 19% larger than the measured uncertainty. Fig. 6 shows that the measured line intensities of the two branches increase with J until reaching a maximum around Jmax ¼18, then they decrease monotonically. This value coincides roughly with that of the most populated level of CH3Br at room temperature (Jp ¼17). Again this figure shows the line mixing effect with smaller values of S0when this effect is taken into account; most of these values are located lower than the others.

0,07 0,06

-1

r0(cm-1)

Transition

0,05 0,04

-2

Transition

Table 2 (continued )

S0 with (cm .atm )

Table 2 Line intensities in the ν2 band of the two isotopic species CH379Br and CH381Br at 295 K obtained with and without considering line mixing effect.

355

0,03

Slope = 0.93 (0.01)

0,02 0,01 0,00 0,00

0,01

0,02

0,03

0,04

0,05

-2

-1

0,06

0,07

0,08

S0 without (cm .atm ) Fig. 5. Comparison of the line intensities of CH3Br obtained with and without including the line mixing effect in the P and R branches of the ν2 band of the two isotopic species.

356

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

Without With Ref. [10]

0,06

S (cm .atm )

0,05

0,04

0,03

0,02

0,01

0,00

0

10

20

30

40

50

J Fig. 6. Line intensity as function of J quantum numbers for the P and R branches of the ν2 band of the two isotopic species of CH3Br. The results are obtained with and without including line mixing effect. The points with green color are that of Ref. [10]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4.2. Self-Broadening coefficients This paragraph is dedicated to discuss the line mixing effect on line broadening. So we have measured self-broadening coefficients of the considered lines of the P and R branches of the ν2 band of the two isotopic species of CH3Br self-perturbed. Fig. 7 illustrates the collisional width as function of pressure for the R81(13,A þ ,0) line with and without including the line mixing effect. As shown by this figure, the line width γk varies linearly with the pressure. The pressure broadening coefficients γ0 in cm  1 atm  1 are determined as the slopes of the best-fit lines. The results are presented in Table 3 which illustrates the dependence of γ0 on the J and K quantum numbers (4 rJ r47 and K ¼0, 1) and the symmetries (A þ or E) for the P and R branches of both isotopic species. For the R81(13,A þ ,0) line plotted in this figure, the measured values of γ0 are 0.4256 70.0147 cm  1 atm  1 and 0.3980 7 0.0112 cm  1 atm  1 obtained without (Yk ¼ 0) and with (Yk≠ 0) line mixing process respectively. These values demonstrate again the need of taking into account this effect for the ν2 doublets of CH3Br studied in this work. Looking at Table 3, most of the broadening coefficients derived when this effect is taken into account, are smaller than those for which this process is neglected. This is true for 57 lines among a total of 76 lines. This effect is also demonstrated by Fig. 8, which represents a plot of the γ0 parameters of the two branches of the two isotopic 0,0040

Without

0,0035 0,0030

With

γ (cm )

0,0025 0,0020 0,0015 0,0010 0,0005 0,0000 0,000

0,002

0,004

0,006

0,008

0,010

P(atm) Fig. 7. Pressure dependence of collisional line width γk with (Yk≠0) and without (Yk ¼ 0) taking into account line mixing effect for the R81(13,A þ ,0) line in the ν2 band.

species obtained with line mixing as function of those obtained without including this effect. The slope of the best-fit lines is 0.957 0.02 showing again the importance of line mixing effect. Our results obtained with line mixing effect are also compared with those reported recently in Ref. [16] in the same band and the same branches using a Voigt profile neglecting line mixing process. As shown in Fig. 9 our values are generally smaller for the 39 lines studied in common with a mean value of 0.330 cm  1 atm  1 smaller than that obtained in Ref. [16] with a mean value of 0.347 cm  1 atm  1. Otherwise, as observed previously [40–42], distinctive dependencies of the spectroscopic parameters upon the rotational quantum numbers can be observed. Table 3 illustrates the J rotational dependencies of present values of self broadening coefficients achieved with and without neglecting line mixing effect in the P and R branches of the two isotopic species. In agreement with Ref. [16], these coefficients tend to increase until reaching a maximum at about Jmax ¼20, then decrease monotonically at higher J. On the other hand, for some C3V molecules, broadening coefficients of P, Q and R-branch lines of the same K and m (m ¼  J, J, Jþ 1 for the P, Q, and R-branch respectively) can be compared. For the present data set, the measured self-broadening coefficients vary with the type of branch but without systematic trends. While a very few lines have nearly equal values within the experimental errors, the differences are generally much larger. These differences range from 0.1% to 24% for the 12 lines out of 76 having the same values of K and m . This lack of dependence is also seen for self-broadening coefficients obtained for other molecules including the NH3 one studied by Brown et al. [41] using far-infrared measurements. 4.3. Line mixing coefficients For each component of 38 doublets, we have plotted the quantity Yk derived from the fit of spectra using Eqs. (1) and (2) as a function of pressure P. Fig. 9 displays two examples of plots for the R81(12,A þ ,0) and R81(16,E,1) lines. One can notices that the straight lines go through the measured points. The line mixing coefficients Y0 in atm  1 are determined as the slopes of the bestfit lines and are presented in Table 3 which illustrates for the A þ and E components symmetries the variation of Y0 on J for K ¼ 0 and K ¼1. The average of absolute values of Y0 is 8.81 atm  1 with an average value of uncertainty of about 20%. The largest line mixing effect occurred in the P79(41,A þ ,0) line with Y0 ¼ 29.08 7 3.41 atm  1. The smallest one is obtained for the P81(37,E,1) line with Y0 ¼1.10 70.51 atm  1 and a relatively large error. In contrast to the line intensities and self-broadening coefficients, Table 3 does not reveal any systematic dependencies of Y0 parameter with J. However Fig. 10 which represents Y0 values in atm  1 as function of J for the two branches of the two isotopic species illustrates a small increase of this parameter with J. The slope of this increase is about 0.23 70.08 atm  1. This behavior could be explained in part by the decreasing of the frequency space Δs between the doublet components (A þ ,0) and (E,1). This decrease is shown by Fig. 11 which presents the splitting Δs as function of J for the two branches. This splitting could be smaller or of the same magnitude as the line widths. This may be easily explained by the following equation which reveals that line mixing parameter Y0is inverse proportional to Δs [38,43,44]:

Y = 2∑ l≠ k

dl l W k , dk Δσ

(3)

The summation is over all lines that contribute to the line interference effect provided that the collisionnal transition selection

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

357

Table 3 Self-broadening coefficients, line mixing coefficients and self-shift coefficients in the ν2 band of the two isotopic species CH379Br and CH381Br at 295 K. The self-broadening coefficients are obtained with and without considering line mixing effect. Transition

γ0Without(cm-1.atm-1)

γ0With(cm-1.atm-1)

Y0(atm-1)

δ0(cm-1.atm-1)

R79(4,A þ ,0) R79(4,E,1) R79(5,A þ ,0) R79(5,E,1) R79(6,A þ ,0) R79(6,E,1) R79(23,A þ ,0) R79(23,E,1) P79(25,A þ ,0) P79(25,E,1) R79(29,A þ ,0) R79(29,E,1) P79(29,A þ ,0) P79(29,E,1) R79(30,A þ ,0) R79(30,E,1) P79(30,A þ ,0) P79(30,E,1) R79(31,A þ ,0) R79(31,E,1) R79(32,A þ ,0) R79(32,E,1) P79(32,A þ ,0) P79(32,E,1) P79(34,A þ ,0) P79(34,E,1) R79(35,A þ ,0) R79(35,E,1) P79(35,A þ ,0) P79(35,E,1) P79(41,A þ ,0) P79(41,E,1) R79(47,A þ ,0) R79(47,E,1) R81(4,A þ ,0) R81(4,E,1) R81(5,A þ ,0) R81(5,E,1) R81(6,A þ ,0) R81(6,E,1) R81(7,A þ ,0) R81(7,E,1) R81(12,A þ ,0) R81(12,E,1) R81(13,A þ ,0) R81(13,E,1) R81(16,A þ ,0) R81(16,E,1) R81(17,A þ ,0) R81(17,E,1) R81(19,A þ ,0) R81(19,E,1) R81(20,A þ ,0) R81(20,E,1) P81(25,A þ ,0) P81(25,E,1) R81(33,A þ ,0) R81(33,E,1) R81(36,A þ ,0) R81(36,E,1) P81(36,A þ ,0) P81(36,E,1) P81(37,A þ ,0) P81(37,E,1) P81(38,A þ ,0) P81(38,E,1) R81(40,A þ ,0) R81(40,E,1) P81(40,A þ ,0) P81(40,E,1) R81(43,A þ ,0) R81(43,E,1) R81(45,A þ ,0) R81(45,E,1)

0.3828 7 0.0121 0.33537 0.0111 0.37257 0.0127 0.3282 7 0.0148 0.36607 0.0122 0.35757 0.0111 0.54317 0.0221 0.46767 0.0169 0.40197 0.0163 0.45007 0.0187 0.42747 0.0130 0.4270 70.0168 0.4269 7 0.0130 0.41347 0.0185 0.3693 7 0.0151 0.31057 0.0097 0.35757 0.0097 0.3794 70.0140 0.3405 7 0.0115 0.34197 0.0105 0.31847 0.0101 0.3629 7 0.0135 0.35707 0.0116 0.34167 0.0096 0.34977 0.0114 0.34337 0.0112 0.33697 0.0092 0.29067 0.0096 0.30337 0.0106 0.34927 0.0093 0.27857 0.0210 0.26147 0.0103 0.17277 0.0097 0.1752 7 0.0088 0.35177 0.0103 0.36437 0.0114 0.30607 0.0102 0.34877 0.0138 0.4090 7 0.0132 0.4182 70.0362 0.35137 0.0117 0.33697 0.0127 0.45077 0.0166 0.44467 0.0187 0.4256 7 0.0147 0.43747 0.0198 0.4855 7 0.0329 0.4448 7 0.0192 0.42007 0.0169 0.5007 70.0133 0.45117 0.0218 0.5237 70.0274 0.4229 7 0.0136 0.46197 0.0135 0.4828 7 0.0153 0.44017 0.0154 0.31937 0.0121 0.38767 0.0142 0.27917 0.0119 0.2938 7 0.0110 0.2846 7 0.0103 0.2982 7 0.0115 0.3698 7 0.0157 0.27297 0.0124 0.2932 7 0.0090 0.2596 7 0.0102 0.2965 7 0.0158 0.25047 0.0075 0.24447 0.0089 0.2596 7 0.0102 0.21927 0.0081 0.1994 7 0.0101 0.1945 7 0.0071 0.2007 70.0104

0.3576 70.0131 0.3257 70.0115 0.3639 7 0.0128 0.3348 7 0.0151 0.3443 7 0.0110 0.3566 7 0.0113 0.51377 0.0165 0.4525 7 0.0154 0.3969 7 0.0144 0.4379 70.0151 0.39167 0.0132 0.4072 70.0121 0.41997 0.0174 0.41637 0.0149 0.3262 7 0.0105 0.30247 0.0109 0.3527 70.0133 0.3758 70.0128 0.35097 0.0127 0.35467 0.0109 0.33057 0.0143 0.35477 0.0145 0.3527 70.0103 0.3684 70.0118 0.3483 70.0112 0.33987 0.0110 0.3062 70.0097 0.3028 7 0.0104 0.31277 0.0117 0.33827 0.0102 0.26687 0.0104 0.28107 0.0106 0.1721 70.0087 0.1592 7 0.0075 0.3489 70.0104 0.36767 0.0107 0.3017 70.0103 0.31747 0.0084 0.39117 0.0129 0.4045 70.0140 0.3166 7 0.0098 0.3402 7 0.0305 0.42417 0.0138 0.41287 0.0142 0.3980 7 0.0112 0.43507 0.0147 0.47027 0.0251 0.4392 7 0.0161 0.41547 0.0186 0.48197 0.0159 0.4581 7 0.0147 0.4932 70.0192 0.4106 7 0.0168 0.45777 0.0195 0.4762 70.0168 0.43747 0.0184 0.31507 0.0134 0.3787 70.0200 0.29157 0.0129 0.29157 0.0129 0.26677 0.0094 0.27827 0.0130 0.3485 70.0161 0.27007 0.0117 0.28337 0.0089 0.27927 0.0092 0.3030 7 0.0160 0.2539 7 0.0120 0.2594 7 0.0104 0.24567 0.0115 0.1982 7 0.0103 0.1947 70.0077 0.1921 70.0070 0.1759 7 0.0089

-4.61 7 1.18 8.197 1.36 -3.427 0.62 -22.327 0.94 -8.507 0.86 -2.06 70.44 3.51 70.65 -2.787 1.02 -3.267 0.86 20.95 7 1.93 10.86 71.20 3.30 7 0.73 -7.777 1.19 19.78 71.52 -16.117 0.54 -10 .23 7 0.70 9.81 7 0.84 13.09 71.63 -1.20 71.00 5.7071.29 5.32 7 1.06 16.447 1.89 -5.057 0.981 3.62 7 0.86 -2.457 1.10 2.22 7 0.64 6.92 7 0.94 14.26 71.22 3.79 7 0.69 4.3570.60 29.08 7 3.41 19.15 7 2.07 11.337 3.24 7.45 7 2.54 9.28 7 0.97 10.88 70.95 -11.707 1.02 6.02 7 1.02 2.23 7 1.00 5.277 1.24 -6.837 1.16 9.03 7 1.00 -13.667 0.59 8.40 7 0.93 -13.63 7 1.32 7.25 7 0.59 -28.537 2.52 18.84 7 0.82 -6.041 70.16 15.727 1.92 4.447 1.11 16.277 2.02 -6.15 70.87 8.43 7 0.55 -16.53 7 1.44 3.00 70.40 -3.507 0.96 2.977 0.73 -1.677 0.84 -3.64 71.45 9.93 7 1.26 4.667 1.01 -8.01 7 1.61 1.107 0.51 -1.75 70.44 9.107 0.78 10.81 71.22 19.46 72.10 8.30 7 1.10 9.85 7 1.45 -3.06 72.08 4.39 7 1.98 8.217 1.65 8.05 7 2.78

0.01617 0.0062 -0.02317 0.0023 -0.0363 7 0.0019 0.0692 7 0.0058 0.02007 0.0048 -0.01567 0.0039 -0.0638 7 0.0047 0.05617 0.0063 -0.0166 7 0.0047 -0.08717 0.0070 -0.08647 0.0070 -0.07937 0.0065 -0.0285 7 0.0049 -0.0545 7 0.0048 0.0046 7 0.0024 -0.0128 70.0034 -0.0469 7 0.0031 -0.07927 0.0072 -0.01947 0.0029 -0.0282 7 0.0033 -0.03777 0.0038 -0.1260 70.0066 -0.0076 70.0039 -0.0227 70.0023 0.0028 7 0.0009 -0.0164 7 0.0036 -0.01787 0.0042 -0.05247 0.0020 -0.02147 0.0033 -0.02727 0.0015 -0.10317 0.0095 -0.0446 7 0.0048 -0.01747 0.0063 -0.0309 7 0.0085 -0.0399 7 0.0066 -0.03317 0.0021 -0.0581 7 0.0032 -0.01147 0.0028 -0.01557 0.0025 -0.01957 0.0054 0.0080 7 0.0021 -0.02767 0.0021 0.03317 0.0043 -0.0436 7 0.0036 0.0320 70.0060 -0.04337 0.0018 0.09977 0.0128 -0.0939 7 0.0039 -0.02477 0.0039 -0.0860 7 0.0059 -0.03597 0.0057 -0.0694 7 0.0079 -0.0123 70.0043 -0.0597 70.0023 0.0260 70.0034 -0.03367 0.0033 -0.01177 0.0027 -0.0283 7 0.0039 -0.01427 0.0033 -0.02247 0.0043 -0.0256 7 0.0036 -0.0288 7 0.0028 -0.0205 7 0.0055 -0.00417 0.0002 -0.01077 0.0031 -0.01947 0.0044 -0.07137 0.0041 -0.03107 0.0064 -0.03117 0.0029 -0.0333 70.0042 -0.03317 0.0067 -0.02247 0.0090 -0.02157 0.0026 -0.02777 0.0056

358

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

Table 3 (continued ) Transition

γ0Without(cm-1.atm-1)

γ0With(cm-1.atm-1)

Y0(atm-1)

δ0(cm-1.atm-1)

R81(47,A þ ,0) R81(47,E,1)

0.1879 7 0.0162 0.1986 7 0.0164

0.17107 0.0151 0.1758 70.0133

8.20 7 2.50 14.21 71.59

-0.01577 0.0048 -0.0265 7 0.0074

0,6

35 30 25 20 15

Y0(atm )

-1

γ0 with (cm .atm )

0,5

-1

-1

0,4

0,3

10 5 0 -5 -10

Slope = 0.95 (0.02)

-15 -20

0,2

-25 -30

0,1

-35

0,1

0,2

0,3

0,4

0,5

-1

10

0,6

20

γ0 without (cm .atm ) Fig. 8. Comparison of the self broadening coefficients of CH3Br obtained with and without including the line mixing effect in the P and R branches of the two isotopic species. 0,16

R (16,E,1)

0,12

30

40

J

-1

Fig. 10. Line mixing parameter in atm  1 at 295 K versus J for all lines of the two branches of the two isotopic species CH379Br and CH381Br studied in this work. The horizontal line in green indicates a line mixing parameter of zero. The straight line in blue color is a linear fit of the all experimental values with a slope of 0.23 70.08 atm  1. The line mixing coefficients are both positive () and negative (♦). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0,024

0,08

0,022

0,04

Y

0,020

0,00 -1

Δσ(cm )

0,018

R (12,A ,0)

-0,04 -0,08

0,000

0,016 0,014 0,012

0,002

0,004

0,006

0,008

0,010

0,010

P(atm)

0,008

Fig. 9. Pressure dependence of the line mixing parameter Yk for the R81(12,A þ ,0) and R81(16,E,1) lines of the ν2 band of CH3Br.

rules are valid. Δσ = σ l − σ k with sk and sl the unperturbed posiand l = νi Ji′ , νf J′f

0

10

20

30

40

50

J Fig. 11. Plot of frequency separation Δs in cm  1 between the doublet components studied in this work as function of J rotational quantum number showing a monotonically decrease of this splitting.

tions of the doublet state vectors k = νi Ji , νf Jf

4.4. Shift coefficients Fig. 12 represents for a line k, a plot of the pressure-induced shift sk–s0 versus P for the line R79(32,E,1) of the ν2 band of CH379Br selfperturbed. The center position of this line shifts toward the lower

0,0000

-0,0002

R79(32,E,1)

-0,0004

-1

σk-σ0(cm )

corresponding to the lines k and l, respectively; dk and dlare their reduced matrix elements of the dipole moment, and W is the offdiagonal element (line-coupling coefficient) of the relaxation matrix [19]. On the other hand, as seen in Fig. 10 and Table 3, one can observe that line mixing parameters are both positive and negative; they are positive for 45 lines among a total of 76. 20 doublets out of 38 are bipolar (the two components have opposite sign of Y). On the other hand, our results could be compared with those of Ref. [33], unfortunately no values of line mixing parameters have been reported by the authors of this work.

-0,0006

-0,0008

-0,0010

-0,0012 0,000

0,002

0,004

0,006

0,008

0,010

P(atm) Fig. 12. Plot of the pressure-induced shift sk–s0 versus P for the line R79(32,E,1) of the ν2 band of CH379Br self-perturbed.

F. Hmida et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 189 (2017) 351–360

0,12 0,08

δ (cm atm )

0,04 0,00 -0,04 -0,08 -0,12 -0,16 -0,20

10

20

30

40

J Fig. 13. Pressure shift coefficient in cm  1 atm  1 at 295 K versus J for all lines of the two branches of the isotopic species CH379Br and CH381Br. The horizontal line indicates a pressure shift coefficient of zero. The pressure shift coefficients are both positive (♦) and negative ().

frequency. The self-shift coefficient δ0 in cm  1 atm  1 is determined as the slope of the best-fit line. The results for all lines of the two branches of the ν2 band of the two isotopic species are presented in Table 3 along with the estimated uncertainties. Fig. 13 is a plot of the self-shift coefficients in cm  1 atm  1 versus J for all lines. The horizontal line indicates a pressure-induced shift coefficient of zero. As may be seen by this figure and Table 3, most of the lines have negative shift. For CH379Br isotope species in the P and R branches, 28 lines out of 34 have negative shifts with an average value of 0.0326 cm  1 atm  1. On the other hand, for CH381Br 37 lines out of 42 have also negative shifts with an average value of -0.0430 cm  1 atm  1. The mean value over all absolute values of shift coefficient is 0.0365 7 0.0061 cm  1 atm  1. 11 doublets out of 38 have opposite sign of shift coefficients; one of the two doublet components illustrates a shift of its center toward higher frequencies, while the other component shifts toward lower frequencies, so they are shifting towards each other. This mutual line-attraction should be smaller for the doublets with large splitting. This is not the case for blended lines or for the doublets with great splitting containing more than the doublet components. Table 3 and Fig. 13 do not reveal any systematic dependencies of line shift coefficients versus J quantum number, except for some E components for which the absolute values of the shift coefficient appear to decrease with J. For example, the shift coefficients of the R81(16,E,1), R81(17,E,1), R81(19,E,1) and R81(20,E,1) lines are  0.0939 70.0029,  0.086070.0059, 0.069470.0079 and –0.05977 0.0023 cm  1 atm  1 respectively. For most of the lines studied here, the shifts are large ranging from about  0.1260 to þ0.0997 cm–1 atm  1. Similar large values of shifts are reported for other molecules such as NH3 and CH3CN studied by Arouiet al. [37] and by Rinsland et al. [45] respectively. The smallest one is δ0 ¼0.0028 70.0009 cm  1 atm  1 obtained for the P79(34,A þ ,0). The largest one is obtained for the R79(32,E,1) line with δ0 ¼  0.1260 70.0066 cm  1 atm–1.

5. Measurement accuracies Considering the unknown systematic uncertainties the experimental uncertainties reported in Tables 2 and 3, are estimated as one time standard deviation derived from the linear fit to which we added 2% of the spectroscopic parameters (S0, γ0, Y0 or γ0) determined in this work. Note that for few lines, the mixing and

359

shift coefficient accuracies can attain more than 40% or are of the same order of magnitude as the parameter themselves, this makes them difficult to measure reliably. The experimental uncertainties vary widely depending on the quality of spectral lines which is related essentially to the overlapping of neighboring lines. For line intensities, the mean value of the estimated accuracies is about 3.6% for the values obtained with considering line mixing effect and 4.0% for those obtained with neglecting this effect. It varies from 2.0% to 12.0%. Most of these accuracies are less than 4.0%. For self broadening, the mean value of the accuracies is about 3.9% for the values obtained with line mixing effect, and 4.0% for those without line mixing. It varies from 2.7% to 9.0%. The accuracies of line mixing parameters have a mean value of about 20% and vary from 4 to 83% for the R(31,A þ ,0) with a small line mixing coefficient of Y0 ¼1.2 71.0 atm  1. Table 3 also reveals that the shift coefficients are more accurate than the line-mixing parameters. The mean value of accuracies is about 17% for line shift coefficients. The minimum value of the line shift accuracy is 2.4% whereas the maximum value is 52.2% obtained for the R79(30,A þ ,0) with a value of shift coefficient of 0.004670.0024 cm  1 atm  1. If one considers only the accuracyo 15% (this is true for 39 line-mixing parameters and 41 line-shift coefficients out of a total of 76 lines), the mean value of accuracies became about 10% for the mixing data and 9% for shift ones.

6. Conclusion We have measured line intensities, self-broadening coefficients, as well as pressure line mixing and pressure induced shift coefficients of 38 doublets components (76 lines) in the ν2 band of CH3Br self-perturbed at T¼ 295 K using a high resolution Fourier transform spectrometer and a multi-pressure fitting technique. Comparisons between Fourier transform spectra and calculated ones using the Rosenkranz absorption profile taking into account line-mixing effect showed significant improvement compared to the usual Lorentz profile. Then this effect needs to be addressed and accounted for the closest line of the ν2 band of CH3Br even at low pressure. Our measurement have demonstrated that the values of line intensities and pressure broadening coefficient achieved with taking into account line mixing effect are about 5% smaller than those obtained with neglecting this effect. The mean value of uncertainties is about 4% for broadening coefficients and the line intensities. That of line mixing is estimated to be 20%, and that of line shift is around 17%. The measured line mixing parameters appear to decrease with the doublet splitting Δs, and are rather large and bipolar for numerous doublets. The self-shift coefficients are large and mostly negative. Contrary to the line intensities and broadening coefficients which present a maximum when varying the rotational quantum number J, no significant branch- and rotational-dependencies are observed for line mixing and shift parameters.

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