Line intensities in the 1.5-μm spectral region of acetylene

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Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362 www.elsevier.com/locate/jqsrt

Line intensities in the 1.5-mm spectral region of acetylene H. Trana, J.-Y. Mandina,, V. Danaa, L. Re´galia-Jarlotb, X. Thomasb, P. Von der Heydenb a

Laboratoire de Physique Mole´culaire pour l’Atmosphe`re et l’Astrophysique, Universite´ Pierre et Marie Curie-Paris6; CNRS, UMR 1043, Case courrier 76, 4, Place Jussieu, 75252 Paris Cedex 05, France b Groupe de Spectrome´trie Mole´culaire et Atmosphe´rique, CNRS, UMR 6089, Universite´ de Reims-Champagne-Ardenne, Faculte´ des Sciences, BP 1039, 51687 Reims Cedex 2, France Received 5 March 2007; received in revised form 23 April 2007; accepted 24 April 2007

Abstract Line intensities are measured for 546 transitions belonging to 13 bands of the main isotopologue 12C2H2 of the acetylene molecule, in the 1.5-mm spectral domain. A multispectrum fitting procedure is used to retrieve line parameters from Fourier transform spectra. Prior to this work, line intensities were known for only 4 bands in this spectral region, from the work of El Hachtouki and Vander Auwera [Absolute line intensities in acetylene: the 1.5 mm region. J Mol Spectrosc 2002;216:355–62]. An excellent agreement is found with the results of these authors, showing that the accuracy of both results is likely better than 1% for the strong bands. However, the spectrum becomes very crowded when one wants to study weaker bands, so that the average accuracy of the intensities reported in the present work is 5%. From these data, vibrational transition dipole moments squared and Herman–Wallis coefficients have been determined for all the bands. r 2007 Elsevier Ltd. All rights reserved. Keywords: Acetylene; Infrared spectroscopy; Vibro-rotational transitions; Line intensities; Transition dipole moment

1. Introduction The acetylene molecule C2H2 is known for its atmospheric, planetologic, and astrophysical interest. C2H2 is also interesting from a theoretical point of view (see, e.g., [1–9]). As acetylene is a stable, quite easy to handle gas exhibiting well separated and regularly spaced lines, they are used for metrological purposes, especially in the 1.5-mm spectral domain of optical communications (see, e.g., [10–15] and references therein). The present paper is dedicated to this spectral region. The main studies dealing with the C2H2 spectrum between 6200 and 6900 cm1 are the following. Originally, Plyler et al. [16] determined spectrocopic constants for 5 bands. The first line intensity and collisional width measurements were performed by Varanasi and Bangaru [17] in the n1+n3 band. Later on, Baldacci et al. [18] published assignments of lines in 15 bands. Keppler et al. [19] improved the knowledge of this spectral range by bringing the number of analyzed bands up to 33. Among these bands, 18 were also studied by Kou et al. Corresponding author. Tel.: +33 1 44 27 44 75; fax: +33 1 44 27 70 33.

E-mail address: [email protected] (J.-Y. Mandin). 0022-4073/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jqsrt.2007.04.008

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[11] whose motivations were to perform a spectroscopic analysis that takes into account the characteristic clustering pattern of the vibrational levels of C2H2 [1–3], and to get a consistent set of reference line positions (accuracy: 0.0003 cm1). Kou et al. [11] also measured and predicted relative band intensities for 6 bands. These band intensities were later recalculated by Abbouti Temsamani et al. [20]. Absolute line intensities (accuracy: 2%) were measured by El Hachtouki and Vander Auwera [14] for the 4 strongest bands. Recently, Nadezhdinskii et al. [21] measured the self-broadening and self-shifting coefficients of a few lines of the n1+n3 band. Thus, before we started this work, C2H2 line assignments and positions were well known in the 1.5-mm spectral region. However, line intensities had been measured for the strongest bands only, and those of numerous other bands were still unknown. As this spectral domain is important for applications, measuring a maximum of line intensities, the more precisely as possible, is useful. Additionally, such a set of line intensity data will be useful to bring theoretical models into this energy range. In this aim, we measured 546 line intensities in 13 bands between 6295 and 6855 cm1, with a mean accuracy around 5%. The acetylene spectrum, experimental conditions and measurement methodology are presented in Section 2. When one is interested in weak bands, the spectrum becomes crowded and the measurement process is more and more difficult, so that we first focused our attention on not too weak bands, and on bands for which enough lines could be measured. For these bands, the rotational dependence of the squared transition dipole moment derived from line intensities could be modeled using Herman–Wallis factors. The measured line intensities, and the squared vibrational transition dipole moments and Herman–Wallis coefficients that we could obtain are given and discussed in Section 3. 2. Intensity measurements in the acetylene 1.5-lm spectrum 2.1. The acetylene spectrum near 1.5 mm: short theoretical description and experimental details Around 1.5 mm, the spectrum of C2H2 shows numerous parallel bands belonging to the DP ¼ 10 sequence of vibrational transitions, where P ¼ 5v1+3v2+5v3+v4+v5 is a pseudo-quantum number, and vi is the vibrational quantum number associated with the mode of vibration ni. In the following, the vibrational notations of Plı´ va [22,23] will be used, in order to facilitate comparisons with previous work that also used the same notations. Thus, vibrational levels are noted v1, v2, v3 (v4, v5)‘7 r, with ‘ ¼ j‘4+‘5j, ‘t being the vibrational angular momentum quantum number associated with the degenerated bending mode t, 7 being the symmetry type for S vibrational states (‘ ¼ 0), and r a roman numeral indicating the rank of the level, by decreasing energy value (r ¼ I for the highest energy level), inside the set of states having the same vibrational symmetry, and coupled by ‘-type resonances. The 4 bands studied in [14] and the 13 bands studied in this work are listed in Table 1, gathered according to the quantum numbers of the involved vibrational levels. Six cold combination bands are concerned. Their upper vibrational state belongs to the {10n5} polyad of interacting vibrational states, with the notation of Perevalov et al. [4]. Height (respectively 3) hot bands involve upper vibrational levels belonging to the {11n5} (respectively {12n5}) polyad. Finally, one should note that 9 bands are ‘-type doubled. The main characteristics of the spectral region studied are the following. When experimental conditions are chosen so that only the strongest bands are observed, the spectrum remains relatively clear, and the line intensity measurement process is quite easy. But when the absorption path length and pressure are increased to observe the weaker bands, the spectrum becomes very crowded. This is due to the increasing number of resonant vibrational states when the pseudo-quantum number P increases: the pattern of C2H2 vibrational levels shows more and more close-by levels, linked by numerous resonances [1–5]. This is directly observable on the spectrum which shows regularly spaced bunches of strongly overlapped lines, often unresolved, and containing numerous hidden weaker lines. These blendings concern often medium bands, whereas lines of weaker bands are well isolated inside microwindows between strong lines. These features of the spectrum increase with P, therefore, with the wavenumber of the involved spectral region. This generates difficulties we have not yet encountered at a so high level in previous works on C2H2, which concerned lower wavenumber regions (see, e.g., [7–9,24] and references therein). As our aim was to get information about line intensities, even for very weak bands, we had to cope with this problem. The multispectrum fitting procedure [25] is a

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Table 1 List of the bands studied in the DP ¼ 10 series of transitions of Banda

n1+n3 n2+n3+2n04 n2+n3+2n05 n1+n2+(n4+n5)0+ 2n2+(3n4+n5)0+ 2n2+(n4+3n5)0+ 2n1+n14n15 2n3+n15n14 2n3+n14n15 2n1+n15n14 n1+n3+n14n14 n1+n3+n15n15 n1+n2+(2n4+n5)1 IIn14 n1+n2+(n4+2n5)1 IIn15 n1+n3+2n042n04 n1+n3+2n242n24 n1+n3+(n4+n5)0+(n4+n5)0+

Center (cm1)b

6556.47 6449.10 6690.57 6623.14 6413.90 6654.25 6567.21 6606.50 6362.12 6804.69 6529.80 6534.74 6594.25 6600.18 6502.38 6503.52 6506.91

12

C2H2 around 6600 cm1

Upper levelc v1v2v3(v4v5)‘7 r

Polyadd

101(00)0+ 011(20)0+ 011(02)0+ 110(11)0+ 020(31)0+ 020(13)0+ 200(10)1 002(01)1 002(10)1 200(01)1 101(10)1 101(01)1 110(21)1 II 110(12)1 II 101(20)0+ 101(20)2 101(11)0+

{10n5} {10n5} {10n5} {10n5} {10n5} {10n5} {11n5} {11n5} {11n5} {11n5} {11n5} {11n5} {11n5} {11n5} {12n5} {12n5} {12n5}

Lower levelc

Symmetry

GS GS GS GS GS GS (01)1 (10)1 (01)1 (10)1 (10)1 (01)1 (10)1 (01)1 (20)0+ (20)2 (11)0+

S +u’S S +u’S S +u’S S +u’S S +u’S S +u’S Pg’Pu Pu’Pg Pg’Pu Pu’Pg Pu’Pg Pg’Pu Pu’Pg Pg’Pu S +u’S Du’Dg S +g’S

+ g + g + g + g + g + g

+ g + u

a Bands are gathered according to the quantum numbers of the involved vibrational levels. All the quoted bands have been assigned by Keppler et al. [19]. b Compiled from [14,19]. c A full notation is given for the vibrational levels (only v4 and v5 are quoted for the lower level, since v1, v2, and v3 are equal to zero for this level in our case, and GS is used for the ground state). d For convenience, the polyad to which the upper vibrational level belongs is also recalled.

powerful tool to treat overlapping lines. However, blendings were often so important that it was impossible to retrieve any significant data for many lines. To study the C2H2 1.5-mm region, 10 spectra were obtained with the GSMA step-by-step interferometer [26,27]. Experimental conditions are gathered in Table 2. The apparatus was used with a tungsten radiation source, SiO2 splitting and mixing plates, InSb detectors, and CaF2 cell windows. Pressures were measured with an accuracy of 0.5% using MKS Baratron 10- and 100-Torr manometers. One should note the very good quality of the spectra: the SNR is around 1000, the zero transmission level is correct as observed with strongly saturated lines, no channeling is observed, and no impurities could be detected. This allowed precise intensity measurements on the whole, even if the accuracy was degraded for numerous lines for the reasons explained above. 2.2. Measurement procedure and results The measurement procedure has already been detailed in previous works, so that only what is essential is recalled here. A careful preparation of the spectra is necessary before applying the multispectrum procedure. It requires first an accurate knowledge of the apparatus function. Thus, one has to determine an effective value of the iris radius for each spectrum, in order to take accurately into account the throughput (the values found are usually slightly different from the nominal one, see Table 2). The phase error has also to be estimated for each spectrum to allow accurate wavenumber calibration and line position measurements. For our spectra, the phase errors are very small (about 0.01 rad). However, they can lead to systematic errors on the measured line positions that can be as large as 5  105 cm1. Taking the phase error into account in the treatment reduces these errors to a negligible level. Once the apparatus function is determined, the absolute wavenumber scale of each spectrum has to be calibrated, since raw wavenumbers are shifted towards low wavenumbers because of the throughput. To perform the calibration, we used well-isolated lines whose accurate absolute positions have been measured by Kou et al. [11]. The dispersion (SD of the residuals) of the obtained shifts gives an estimation of the precision

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Table 2 Experimental conditions and characteristics of the spectra recorded in the 1.5-mm region using the stepping-mode interferometer in Reims Commercial sample (air liquide alphagaz) Natural C2H2 Stated purity Maximum path difference

97.760% of 12C2H2 99.55% 51.92 cm (spectrum 1) 75.25 cm (spectra 2–5) 82.25 cm (spectra 6–10) E9.6  103 cm1 (spectrum 1) E6.6  103 cm1 (spectra 2–5) E6.1  103 cm1 (spectra 6–10) 1.25  103 cm1 E1000 1040 mm 2.00 mm 5266–7899 cm1 6250–6900 cm1

Unapodized FWHM resolution

Spectral step after post-zero filling SNR Collimator focal length Nominal iris radius Free spectral range Involved spectral domain Spectrum number

Effective iris radius (mm)a

Total pressure 70.5%b (hPa)

Absorbing path 71 cmb

Temperature 70.5 Kb

1 2 3 4 5 6 7 8 9 10

1.89(4) 1.89(4) 1.84(6) 1.90(4) 1.94(5) 1.82(6) 1.87(5) 1.89(4) 1.89(4) 1.93(6)

79.98 39.95 13.59 6.414 1.949 13.55 5.350 3.336 1.998 1.333

3216.6 3216.6 3216.6 3216.6 3216.6 2416.6 2416.6 2416.6 2416.6 2416.6

295.15 295.15 296.65 296.45 295.85 295.35 295.55 295.35 295.25 295.35

a

1 SD between parentheses in unit of the last digit. Absolute uncertainty (excess digits are given only as a guide).

b

of our calibration, i.e., 0.0003 cm1 (1 SD). Combining the accuracy announced in [11] (0.0003 cm1) and the precision of our calibration, we estimate that the average accuracy of our measured positions is around 0.0005 cm1 for well-isolated lines. Note that the average of the 95% confidence intervals (i.e., 2 SD) returned by the fits for the adjusted line positions is one order of magnitude smaller than the precision, namely 0.00003 cm1, but these confidence intervals do not estimate the actual statistical uncertainties, they only show the good quality of the spectra and of the adjustments. The multispectrum procedure was run in the following conditions. A Voigt profile was used to calculate the absorption coefficient of the lines, and the self-broadening coefficients were fixed to the values calculated according to [28]. The self-shift coefficients were fixed to zero. Measured lines cover a very wide range of intensity values: roughly from 1022 to 1025 cm mol1 at 296 K. Usually, we adjusted simultaneously at least 6 and 8 spectra in most cases. Our aim being to perform quantitative spectroscopy, we validated our measured line intensities with the experimental results of other authors, to estimate the true accuracy of all measurements. A sample of 50 strong and well-isolated lines measured by El Hachtouki and Vander Auwera [14] was chosen, having various intensities (from 1.7  1022 to 1.6  1023 cm mol1), and well spread over the spectrum (from 6630 and 6680 cm1). Those lines were treated using the spectra numbers 5 and 8–10. For each line, we have calculated the ratio r ¼ 100  ðour adjusted intensity  measured intensity ½14Þ=measured intensity ½14,

(1)

both line intensities being given for pure 12C2H2, i.e., for a sample containing 100% of 12C2H2. Values found for the ratio r do not exhibit any systematic trend with respect to wavenumber nor strength, except for a larger

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dispersion of r for the weakest lines. The average value of r is r ¼ +0.20 (64) %, with 1.0%oro+1.5%, 1 SD being given between parenthesis in the unit of the last quoted digit. This comparison is excellent, allowing to say that, for those lines, the accuracy of both works is likely better than 1%, to be compared with the accuracy estimated in [14], i.e., 2%). This shows again that Fourier transform spectroscopy is an efficient tool to retrieve accurate parameters for lines of whole bands when the spectroscopy of the studied molecule is well known, as also recently observed for carbon dioxide [29,30]. It is worth noticing that the two involved interferometers are of different kinds: one of them is a hand-made step-by-step one (this of GSMA in Reims [26,27]), whereas the other is a commercial fast-scanning one (the Bruker IFS120HR of ULB in Brussels [14]). However, because of the reasons explained above, the accuracy is not so good for other bands reported in this paper. On the whole, the accuracy of our measured intensities is estimated to be about 5%, but it could be worse for very weak or overlapped lines. Due to the good agreement between [14] and this work, the 4 bands studied in [14] were not measured again. We obtained 546 line intensities in the 13 other bands. They are listed in Table 3, with 4 significant digits since the 2 SD confidence intervals returned by the fits are on average 0.4%.

Table 3 Line positions and intensities for bands of the

12

C2H2 molecule in the 1.5-mm regiona Scalc

%

|R|2obs

(1.0%) (0.2%) (0.2%) (0.1%) (0.1%) (0.1%) (0.1%) (0.1%) (0.3%) (0.3%) (0.1%) (0.1%) (0.1%) (0.1%) (0.2%) (0.3%) (0.2%) (0.1%) (0.2%) (0.2%) (0.4%)

3.867E-25 1.585E-24 7.082E-25 2.792E-24 1.200E-24 4.558E-24 1.886E-24 6.899E-24 2.751E-24 9.685E-24 3.716E-24 1.258E-23 4.637E-24 1.643E-23 5.507E-24 1.612E-23 5.065E-24 1.373E-23 3.914E-24 9.288E-24 2.147E-24

2.63 12.29 15.40 8.79 6.98 4.96 4.26 3.56 6.34 12.63 6.17 5.27 3.95 0.48 0.79 7.83 3.45 1.93 0.23 2.70 5.71

7.534E-08 9.551E-08 7.820E-08 1.059E-07 1.106E-07 1.147E-07 1.201E-07 1.166E-07 1.188E-07 1.169E-07 1.288E-07 1.344E-07 1.405E-07 1.583E-07 1.620E-07 1.774E-07 1.718E-07 1.712E-07 1.691E-07 1.662E-07 1.622E-07

(0.1%) (0.2%) (0.2%) (0.2%) (0.1%) (0.3%) (0.2%) (0.1%) (0.2%) (0.4%) (0.3%) (0.8%)

6.562E-24 1.220E-23 4.795E-24 1.744E-23 1.550E-23 4.715E-24 3.690E-24 2.667E-24 6.610E-24 1.786E-24 4.261E-24 6.350E-25

3.13 0.65 1.90 2.73 1.64 7.97 3.59 0.34 2.62 3.24 3.88 0.81

1.760E-07 1.687E-07 1.687E-07 1.537E-07 1.384E-07 1.258E-07 1.210E-07 1.135E-07 1.108E-07 9.853E-08 9.931E-08 7.677E-08

5.342E-25 (0.7%) 3.851E-25 (0.6%)

5.438E-25 3.860E-25

1.80 0.23

4.385E-08 4.730E-08

Sobs

Line

Position

n2+n3+2n04 Pee24 Pee23 Pee22 Pee21 Pee20 Pee19 Pee18 Pee17 Pee16 Pee15 Pee14 Pee13 Pee12 Pee9 Pee8 Pee7 Pee6 Pee5 Pee4 Pee3 Pee2

6390.71026 6393.12546 6395.56085 6398.03514 6400.48409 6402.93362 6405.38306 6407.83101 6410.27899 6412.73151 6415.17427 6417.62157 6420.06916 6427.41491 6429.86215 6432.30501 6434.74384 6437.17324 6439.59101 6441.99491 6444.38356

(9) (2) (2) (1) (1) (1) (1) (1) (3) (2) (1) (1) (1) (1) (2) (2) (1) (1) (2) (2) (3)

3.768E-25 1.807E-24 6.137E-25 3.061E-24 1.290E-24 4.796E-24 1.970E-24 6.662E-24 2.587E-24 8.599E-24 3.500E-24 1.195E-23 4.461E-24 1.651E-23 5.551E-24 1.749E-23 5.246E-24 1.400E-23 3.905E-24 9.044E-24 2.031E-24

Ree1 Ree3 Ree4 Ree9 Ree11 Ree12 Ree14 Ree16 Ree17 Ree18 Ree19 Ree22

6453.76187 6458.35147 6460.62812 6471.92089 6476.42864 6478.68110 6483.18229 6487.67810 6489.92274 6492.16550 6494.40775 6501.13656

(1) (1) (2) (1) (1) (3) (2) (1) (1) (3) (2) (5)

6.774E-24 1.228E-23 4.888E-24 1.793E-23 1.525E-23 4.367E-24 3.562E-24 2.658E-24 6.788E-24 1.730E-24 4.433E-24 6.402E-25

n2+n3+2n05 Pee25 Pee22

6627.44719 (6) 6635.45478 (5)

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Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Pee21 Pee17 Pee16 Pee15 Pee14 Pee13 Pee12 Pee10 Pee8 Pee6 Pee5 Pee4 Pee3 Pee2

6638.09625 6648.57214 6651.15928 6653.73253 6656.29186 6658.83575 6661.36476 6666.38287 6671.33692 6676.23467 6678.66100 6681.07288 6683.46996 6685.85297

(2) (1) (3) (1) (2) (1) (1) (3) (3) (2) (1) (2) (1) (6)

1.513E-24 3.060E-24 1.205E-24 4.063E-24 1.538E-24 4.898E-24 1.789E-24 1.953E-24 1.940E-24 1.715E-24 4.578E-24 1.307E-24 3.085E-24 6.810E-25

(0.2%) (0.1%) (0.3%) (0.1%) (0.3%) (0.1%) (0.1%) (0.2%) (0.3%) (0.2%) (0.1%) (0.2%) (0.1%) (0.6%)

1.448E-24 3.039E-24 1.173E-24 4.007E-24 1.496E-24 4.940E-24 1.779E-24 1.958E-24 1.969E-24 1.766E-24 4.740E-24 1.340E-24 3.159E-24 7.264E-25

4.30 0.69 2.66 1.38 2.73 0.86 0.56 0.26 1.49 2.97 3.54 2.52 2.40 6.67

5.044E-08 5.161E-08 5.331E-08 5.323E-08 5.454E-08 5.310E-08 5.430E-08 5.464E-08 5.456E-08 5.412E-08 5.395E-08 5.453E-08 5.462E-08 5.241E-08

Ree3 Ree4 Ree6 Ree8 Ree10 Ree13 Ree14 Ree15 Ree16 Ree17 Ree18 Ree19 Ree20 Ree21 Ree22 Ree23 Ree24 Ree25

6699.83960 6702.11876 6706.63190 6711.08419 6715.47055 6721.93830 6724.06283 6726.17214 6728.26652 6730.34705 6732.41428 6734.46873 6736.51625 6738.52055 6740.55268 6742.56633 6744.57106 6746.56798

(1) (2) (1) (1) (1) (1) (3) (1) (2) (1) (2) (1) (5) (2) (4) (2) (8) (3)

4.043E-24 1.610E-24 2.018E-24 2.128E-24 2.060E-24 5.137E-24 1.550E-24 4.113E-24 1.155E-24 3.023E-24 8.392E-25 2.078E-24 5.141E-25 1.257E-24 3.405E-25 7.828E-25 1.988E-25 4.298E-25

(0.1%) (0.2%) (0.1%) (0.1%) (0.1%) (0.1%) (0.2%) (0.1%) (0.2%) (0.1%) (0.2%) (0.1%) (0.6%) (0.2%) (0.5%) (0.2%) (0.9%) (0.4%)

4.125E-24 1.631E-24 1.981E-24 2.103E-24 2.019E-24 4.889E-24 1.463E-24 3.874E-24 1.121E-24 2.874E-24 8.056E-25 2.002E-24 5.441E-25 1.312E-24 3.461E-25 8.099E-25 2.076E-25 4.717E-25

2.03 1.30 1.83 1.17 1.99 4.83 5.61 5.81 2.94 4.93 4.00 3.66 5.84 4.38 1.64 3.46 4.43 9.75

5.356E-08 5.355E-08 5.434E-08 5.289E-08 5.203E-08 5.123E-08 5.079E-08 4.996E-08 4.754E-08 4.757E-08 4.609E-08 4.488E-08 3.987E-08 3.941E-08 3.938E-08 3.760E-08 3.615E-08 3.332E-08

2n2+(3n4+n5)0+ Pee21 Pee20 Pee19 Pee18 Pee17 Pee16 Pee15 Pee14 Pee12 Pee11 Pee10 Pee8 Pee7 Pee5 Pee4 Pee3

6363.03240 6365.45576 6367.88389 6370.31422 6372.74850 6375.18632 6377.62643 6380.07057 6384.96384 6387.41099 6389.85588 6394.73618 6397.16767 6402.00480 6404.40835 6406.79846

(2) (7) (2) (5) (1) (3) (2) (3) (2) (1) (2) (2) (2) (2) (3) (5)

5.875E-25 2.356E-25 8.481E-25 3.363E-25 1.188E-24 4.812E-25 1.633E-24 5.720E-25 7.015E-25 2.182E-24 8.115E-25 8.077E-25 2.139E-24 1.821E-24 5.219E-25 1.174E-24

(0.3%) (0.8%) (0.2%) (0.6%) (0.2%) (0.4%) (0.2%) (0.4%) (0.3%) (0.1%) (0.3%) (0.3%) (0.3%) (0.2%) (0.3%) (0.6%)

5.855E-25 2.387E-25 8.626E-25 3.416E-25 1.199E-24 4.602E-25 1.566E-24 5.823E-25 6.880E-25 2.184E-24 7.539E-25 7.560E-25 2.183E-24 1.820E-24 5.153E-25 1.215E-24

0.34 1.32 1.71 1.58 0.93 4.36 4.10 1.80 1.92 0.09 7.10 6.40 2.06 0.05 1.26 3.49

2.044E-08 2.030E-08 2.040E-08 2.060E-08 2.090E-08 2.222E-08 2.231E-08 2.116E-08 2.222E-08 2.189E-08 2.369E-08 2.370E-08 2.181E-08 2.239E-08 2.271E-08 2.169E-08

Ree1 Ree2 Ree3 Ree4 Ree5 Ree6 Ree9

6418.56532 6420.88014 6423.18359 6425.47529 6427.75691 6430.03077 6436.81490

(5) (4) (1) (2) (2) (2) (1)

8.473E-25 3.983E-25 1.667E-24 6.461E-25 2.127E-24 8.080E-25 2.525E-24

(0.7%) (0.6%) (0.2%) (0.4%) (0.2%) (0.3%) (0.2%)

8.607E-25 4.203E-25 1.623E-24 6.449E-25 2.188E-24 7.922E-25 2.554E-24

1.58 5.52 2.64 0.19 2.87 1.96 1.15

2.213E-08 2.128E-08 2.303E-08 2.242E-08 2.170E-08 2.270E-08 2.176E-08

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Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Ree11 Ree13 Ree15 Ree17

6441.32339 6445.83241 6450.34777 6454.87317

(2) (1) (4) (3)

2.254E-24 2.013E-24 1.682E-24 1.275E-24

(0.2%) (0.1%) (0.6%) (0.4%)

2.389E-24 2.071E-24 1.677E-24 1.276E-24

5.99 2.88 0.30 0.08

2.056E-08 2.094E-08 2.131E-08 2.091E-08

2n2+(n4+3n5)0+ Pee17 Pee15 Pee12 Pee10 Pee7 Pee6 Pee5 Pee3

6612.51364 6617.68507 6625.27211 6630.23583 6637.56419 6639.98140 6642.38591 6647.16184

(3) (2) (6) (3) (2) (3) (5) (2)

1.068E-24 1.499E-24 7.157E-25 8.082E-25 2.301E-24 7.593E-25 2.111E-24 1.381E-24

(0.3%) (0.2%) (0.6%) (0.7%) (0.2%) (0.4%) (0.6%) (0.2%)

1.134E-24 1.538E-24 7.058E-25 7.905E-25 2.344E-24 7.321E-25 1.975E-24 1.326E-24

6.18 2.60 1.38 2.19 1.87 3.58 6.44 3.98

1.812E-08 1.974E-08 2.184E-08 2.274E-08 2.262E-08 2.410E-08 2.501E-08 2.458E-08

Ree1 Ree2 Ree4 Ree5 Ree6 Ree7 Ree8 Ree9 Ree10 Ree11 Ree13 Ree14 Ree15 Ree17 Ree18 Ree19 Ree20 Ree21

6658.92937 6661.25163 6665.86457 6668.15380 6670.42884 6672.69068 6674.93696 6677.16688 6679.37828 6681.57028 6685.89016 6688.01517 6690.11346 6694.22730 6696.23977 6698.22017 6700.16939 6702.08367

(1) (5) (6) (2) (2) (1) (3) (3) (2) (1) (2) (4) (1) (1) (6) (3) (8) (6)

9.359E-25 4.397E-25 6.731E-25 2.268E-24 8.187E-25 2.563E-24 8.527E-25 2.424E-24 8.120E-25 2.466E-24 1.948E-24 5.817E-25 1.494E-24 1.076E-24 2.870E-25 7.300E-25 2.190E-25 4.777E-25

(1.5%) (0.5%) (0.7%) (0.2%) (0.2%) (0.1%) (0.3%) (0.3%) (0.2%) (0.1%) (0.2%) (0.5%) (0.1%) (0.2%) (0.7%) (0.3%) (0.9%) (0.5%)

9.326E-25 4.533E-25 6.862E-25 2.310E-24 8.284E-25 2.586E-24 8.711E-25 2.574E-24 8.260E-25 2.335E-24 1.950E-24 5.778E-25 1.513E-24 1.093E-24 3.020E-25 7.381E-25 1.972E-25 4.664E-25

0.35 3.09 1.95 1.85 1.18 0.90 2.16 6.19 1.72 5.31 0.10 0.67 1.27 1.58 5.23 1.11 9.95 2.37

2.356E-08 2.264E-08 2.252E-08 2.230E-08 2.217E-08 2.192E-08 2.131E-08 2.014E-08 2.062E-08 2.169E-08 1.954E-08 1.916E-08 1.825E-08 1.703E-08 1.585E-08 1.586E-08 1.708E-08 1.506E-08

2n1+n14n15 Pee30 Pee26 Pee22 Pee20 Pee16 Pee14 Pee12 Pee11 Pee10 Pee8 Pee7 Pee6 Pee4

6484.29407 (5) 6496.80881 (7) 6508.87991 (1) 6514.75011 (1) 6526.15174 (1) 6531.68334 (4) 6537.10289 (1) 6539.77039 (3) 6542.40898 (0) 6547.60020 (3) 6550.15503 (1) 6552.68036(10) 6557.64488 (3)

1.137E-24 2.773E-24 6.815E-24 1.261E-23 2.219E-23 2.499E-23 2.647E-23 9.334E-24 2.864E-23 3.302E-23 9.296E-24 2.451E-23 1.783E-23

(0.5%) (0.9%) (0.1%) (0.2%) (0.2%) (0.5%) (0.1%) (0.5%) (0.1%) (0.4%) (0.2%) (1.4%) (0.4%)

1.024E-24 3.119E-24 7.757E-24 1.131E-23 2.034E-23 2.494E-23 2.866E-23 9.961E-24 3.057E-23 2.986E-23 9.443E-24 2.598E-23 1.876E-23

9.94 12.48 13.82 10.31 8.34 0.20 8.27 6.72 6.74 9.57 1.58 6.00 5.22

2.721E-05 2.081E-05 1.972E-05 2.454E-05 2.317E-05 2.094E-05 1.902E-05 1.916E-05 1.903E-05 2.218E-05 1.963E-05 1.871E-05 1.866E-05

Ree2 Ree6 Ree9 Ree10 Ree11 Ree12 Ree14 Ree15 Ree16 Ree18 Ree20

6574.11370 6582.89018 6589.16542 6591.19899 6593.20386 6595.17903 6599.04169 6600.92878 6602.78690 6606.41529 6609.92411

1.409E-23 3.000E-23 1.074E-23 3.200E-23 1.133E-23 2.868E-23 2.448E-23 7.093E-24 1.937E-23 1.548E-23 1.051E-23

(0.1%) (0.5%) (0.1%) (0.2%) (0.8%) (0.1%) (0.1%) (0.2%) (0.1%) (0.4%) (0.1%)

1.414E-23 2.943E-23 1.076E-23 3.174E-23 1.020E-23 2.896E-23 2.465E-23 7.406E-24 1.972E-23 1.486E-23 1.061E-23

0.35 1.90 0.19 0.81 9.97 0.98 0.69 4.41 1.81 4.01 0.95

1.909E-05 1.939E-05 1.896E-05 1.915E-05 2.112E-05 1.884E-05 1.894E-05 1.830E-05 1.881E-05 2.005E-05 1.920E-05

(1) (4) (1) (1) (6) (0) (0) (2) (1) (2) (1)

ARTICLE IN PRESS H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

349

Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Ree22 Ree26 Ree29 Ree30 Ree32

6613.31568 6619.74318 6624.25325 6625.69628 6628.49358

(2) (6) (9) (6) (6)

7.734E-24 2.769E-24 3.928E-25 8.019E-25 5.058E-25

(0.5%) (0.3%) (1.6%) (0.8%) (0.8%)

7.171E-24 2.810E-24 4.067E-25 9.017E-25 4.750E-25

7.28 1.48 3.54 12.45 6.09

2.107E-05 1.964E-05 1.960E-05 1.817E-05 2.207E-05

Pff31 Pff29 Pff28 Pff27 Pff23 Pff15 Pff14 Pff12 Pff11 Pff10 Pff9 Pff7

6481.28034(27) 6487.60562 (8) 6490.72934(15) 6493.82480 (4) 6505.94545 (8) 6528.89691 (0) 6531.64416 (3) 6537.05734 (3) 6539.72344 (3) 6542.36048 (1) 6544.97151 (1) 6550.11043 (1)

5.938E-25 1.190E-24 6.076E-25 1.944E-24 5.006E-24 2.071E-23 7.430E-24 8.992E-24 2.927E-23 9.407E-24 2.997E-23 2.679E-23

(2.4%) (1.1%) (1.7%) (0.5%) (1.0%) (0.0%) (0.3%) (0.4%) (0.3%) (0.2%) (0.2%) (0.1%)

6.000E-25 1.126E-24 5.047E-25 2.010E-24 5.487E-24 2.118E-23 7.811E-24 9.091E-24 2.863E-23 9.814E-24 2.963E-23 2.772E-23

1.04 5.38 16.94 3.40 9.61 2.27 5.13 1.10 2.19 4.33 1.13 3.47

2.003E-05 2.132E-05 2.426E-05 1.946E-05 1.825E-05 1.932E-05 1.877E-05 1.946E-05 2.008E-05 1.880E-05 1.981E-05 1.887E-05

Rff1 Rff2 Rff5 Rff6 Rff7 Rff9 Rff10 Rff11 Rff12 Rff14 Rff15 Rff15 Rff16 Rff17 Rff19 Rff21 Rff22 Rff23 Rff24 Rff25 Rff26 Rff27 Rff29

6571.86856 (6) 6574.14806 (2) 6580.81647 (2) 6582.98326 (1) 6585.12204 (0) 6589.31481 (0) 6591.36886 (1) 6593.39501 (1) 6595.39278 (2) 6599.30296 (0) 6601.21636 (4) 6601.21648 (2) 6603.10034 (1) 6604.95648 (1) 6608.58293 (2) 6612.09532 (1) 6613.80901 (5) 6615.49375 (1) 6617.14925(11) 6618.77716 (3) 6620.37559 (4) 6621.94591 (2) 6625.00000(11)

7.603E-24 4.642E-24 2.634E-23 9.729E-24 3.524E-23 3.130E-23 1.053E-23 2.971E-23 9.630E-24 8.009E-24 1.986E-23 2.218E-23 6.585E-24 1.666E-23 1.155E-23 8.376E-24 2.369E-24 5.402E-24 1.672E-24 3.412E-24 8.678E-25 1.930E-24 1.058E-24

(0.9%) (0.2%) (0.2%) (0.1%) (0.1%) (0.1%) (0.1%) (0.1%) (0.3%) (0.2%) (0.6%) (0.6%) (0.2%) (0.1%) (0.3%) (0.1%) (0.6%) (0.1%) (1.4%) (0.4%) (0.5%) (0.3%) (1.4%)

8.182E-24 4.731E-24 2.697E-23 9.850E-24 3.127E-23 3.226E-23 1.055E-23 3.045E-23 9.580E-24 8.100E-24 2.179E-23 2.180E-23 6.422E-24 1.677E-23 1.216E-23 8.344E-24 2.256E-24 5.420E-24 1.427E-24 3.341E-24 8.574E-25 1.955E-24 1.088E-24

7.62 1.92 2.39 1.24 11.27 3.07 0.19 2.49 0.52 1.14 9.72 1.71 2.48 0.66 5.28 0.38 4.77 0.33 14.65 2.08 1.20 1.30 2.84

1.790E-05 1.887E-05 1.870E-05 1.888E-05 2.151E-05 1.846E-05 1.896E-05 1.851E-05 1.904E-05 1.867E-05 1.718E-05 1.918E-05 1.930E-05 1.867E-05 1.779E-05 1.875E-05 1.958E-05 1.856E-05 2.178E-05 1.896E-05 1.876E-05 1.827E-05 1.794E-05

2n3+n15n14 Pee25 Pee21 Pee18 Pee17 Pee16 Pee15 Pee13 Pee11 Pee10 Pee5 Pee3

6542.22696 6553.33007 6561.43865 6564.10475 6566.74744 6569.37024 6574.55919 6579.67363 6582.20209 6594.57592 6599.40121

(3) (1) (4) (2) (2) (1) (2) (1) (2) (1) (2)

1.332E-24 3.468E-24 1.630E-24 5.944E-24 2.292E-24 7.894E-24 9.874E-24 1.035E-23 3.514E-24 7.861E-24 4.768E-24

(0.6%) (0.2%) (0.5%) (0.3%) (0.3%) (0.2%) (0.3%) (0.1%) (0.3%) (0.2%) (0.2%)

1.342E-24 3.183E-24 1.764E-24 6.096E-24 2.307E-24 7.743E-24 9.235E-24 1.028E-23 3.514E-24 7.966E-24 4.893E-24

0.75 8.22 8.22 2.56 0.65 1.91 6.47 0.68 0.00 1.34 2.62

4.319E-06 4.578E-06 3.795E-06 3.978E-06 4.027E-06 4.108E-06 4.261E-06 3.973E-06 3.931E-06 3.822E-06 3.762E-06

Ree5 Ree7 Ree8 Ree9

6620.23554 6624.66615 6626.85343 6629.02182

(1) (1) (1) (1)

9.902E-24 1.120E-23 4.173E-24 1.166E-23

(0.2%) (0.2%) (0.2%) (0.1%)

9.741E-24 1.141E-23 3.932E-24 1.190E-23

1.63 1.87 5.78 2.06

3.946E-06 3.832E-06 4.157E-06 3.851E-06

ARTICLE IN PRESS 350

H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

Table 3 (continued ) Scalc

|R|2obs

Line

Position

Sobs

Ree10 Ree11 Ree12 Ree13 Ree14 Ree15 Ree16 Ree19 Ree20 Ree21 Ree22 Ree23 Ree24 Ree25 Ree27 Ree29

6631.17078 (1) 6633.30010 (0) 6635.40944 (1) 6637.49897 (1) 6639.56792 (1) 6641.61704 (1) 6643.64114 (1) 6649.59376 (0) 6651.53291 (2) 6653.45021 (1) 6655.34407 (2) 6657.21515 (1) 6659.06294(10) 6660.88676 (3) 6664.46251 (5) 6667.94099 (6)

4.104E-24 1.117E-23 3.627E-24 9.836E-24 3.046E-24 8.355E-24 2.455E-24 4.891E-24 1.389E-24 3.403E-24 9.553E-25 2.293E-24 6.191E-25 1.435E-24 8.616E-25 4.705E-25

(0.1%) (0.1%) (0.2%) (0.1%) (0.1%) (0.1%) (0.1%) (0.1%) (0.2%) (0.2%) (0.3%) (0.2%) (0.6%) (0.2%) (0.3%) (0.9%)

3.917E-24 1.138E-23 3.605E-24 1.010E-23 3.095E-24 8.404E-24 2.497E-24 4.872E-24 1.369E-24 3.414E-24 9.340E-25 2.270E-24 6.052E-25 1.434E-24 8.616E-25 4.928E-25

4.56 1.88 0.61 2.68 1.61 0.59 1.71 0.39 1.44 0.32 2.23 1.00 2.25 0.07 0.00 4.74

4.136E-06 3.894E-06 4.010E-06 3.901E-06 3.965E-06 4.030E-06 4.011E-06 4.185E-06 4.264E-06 4.223E-06 4.370E-06 4.354E-06 4.451E-06 4.395E-06 4.482E-06 4.372E-06

Pff18 Pff16 Pff14 Pff13 Pff12 Pff9 Pff8 Pff6 Pff4

6560.43843 6565.93081 6571.33055 6573.99471 6576.63576 6584.41806 6586.96531 6591.99008 6596.92157

(7) (2) (1) (4) (3) (1) (1) (1) (1)

5.560E-24 6.237E-24 7.954E-24 3.190E-24 9.635E-24 3.548E-24 1.007E-23 8.740E-24 6.501E-24

(0.8%) (0.4%) (0.2%) (0.7%) (0.4%) (0.2%) (0.1%) (0.1%) (0.1%)

4.922E-24 6.535E-24 8.157E-24 2.963E-24 9.519E-24 3.460E-24 1.021E-23 8.982E-24 6.557E-24

11.47 4.78 2.55 7.12 1.20 2.48 1.39 2.77 0.86

4.354E-06 3.678E-06 3.758E-06 4.149E-06 3.901E-06 3.952E-06 3.803E-06 3.750E-06 3.821E-06

Rff5 Rff8 Rff9 Rff10 Rff11 Rff12 Rff14 Rff15 Rff16 Rff17 Rff19

6620.18023 6626.69670 6628.82105 6630.92075 6632.99685 6635.04715 6639.07509 6641.05132 6643.00343 6644.92793 6648.70446

(1) (1) (2) (1) (1) (0) (3) (1) (0) (1) (2)

3.392E-24 1.128E-23 3.865E-24 1.088E-23 3.955E-24 1.016E-23 8.136E-24 2.580E-24 6.721E-24 1.913E-24 1.485E-24

(0.1%) (0.1%) (0.3%) (0.1%) (0.1%) (0.1%) (0.7%) (0.2%) (0.1%) (0.2%) (0.3%)

3.221E-24 1.158E-23 3.879E-24 1.144E-23 3.673E-24 1.041E-23 8.835E-24 2.647E-24 7.029E-24 2.043E-24 1.487E-24

5.04 2.66 0.36 5.15 7.13 2.46 8.59 2.60 4.58 6.80 0.13

4.058E-06 3.753E-06 3.840E-06 3.664E-06 4.150E-06 3.761E-06 3.549E-06 3.757E-06 3.685E-06 3.609E-06 3.850E-06

2n3+n14n15 Pee24 Pee21 Pee20 Pee19 Pee18 Pee17 Pee16 Pee15 Pee14 Pee13 Pee12 Pee11 Pee10 Pee9 Pee8 Pee7 Pee6 Pee2

6298.71362 6307.46367 6310.31750 6313.15146 6315.95662 6318.73662 6321.49125 6324.21983 6326.92246 6329.59989 6332.25221 6334.87750 6337.48048 6340.05634 6342.60778 6345.13450 6347.63621 6357.39249

(5) (8) (4) (6) (2) (4) (3) (3) (2) (3) (1) (4) (2) (3) (2) (4) (3) (6)

1.882E-25 1.190E-25 4.726E-25 1.704E-25 5.958E-25 2.295E-25 7.912E-25 3.243E-25 9.856E-25 3.678E-25 1.168E-24 4.530E-25 1.238E-24 4.434E-25 1.342E-24 4.192E-25 1.096E-24 3.708E-25

(0.5%) (0.9%) (0.4%) (0.6%) (0.2%) (0.5%) (0.3%) (0.3%) (0.3%) (0.3%) (0.1%) (0.4%) (0.2%) (0.4%) (0.2%) (0.5%) (0.3%) (0.7%)

1.909E-25 1.225E-25 4.451E-25 1.771E-25 6.256E-25 2.420E-25 8.297E-25 3.112E-25 1.034E-24 3.756E-25 1.206E-24 4.222E-25 1.304E-24 4.378E-25 1.290E-24 4.105E-25 1.135E-24 3.592E-25

1.43 2.94 5.82 3.93 5.00 5.45 4.87 4.04 4.91 2.12 3.25 6.80 5.33 1.26 3.87 2.08 3.56 3.13

8.819E-07 8.690E-07 9.498E-07 8.605E-07 8.519E-07 8.485E-07 8.531E-07 9.322E-07 8.526E-07 8.761E-07 8.666E-07 9.599E-07 8.491E-07 9.061E-07 9.309E-07 9.135E-07 8.636E-07 9.234E-07

Ree2

6369.03440 (4)

6.008E-25 (0.6%)

6.397E-25

6.47

8.401E-07

%

ARTICLE IN PRESS H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

351

Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Ree3 Ree5 Ree6 Ree8 Ree9 Ree10 Ree12 Ree13 Ree14 Ree16 Ree17 Ree19 Ree20

6371.28879 6375.71887 6377.89600 6382.17387 6384.27411 6386.34861 6390.41833 6392.41210 6394.38163 6398.23715 6400.12207 6403.81820 6405.64575

(8) (4) (1) (1) (4) (2) (1) (4) (1) (2) (5) (7) (7)

3.094E-25 4.203E-25 1.322E-24 1.441E-24 4.812E-25 1.389E-24 1.284E-24 4.455E-25 1.086E-24 8.595E-25 2.852E-25 1.891E-25 4.422E-25

(0.9%) (0.4%) (0.2%) (0.1%) (0.5%) (0.2%) (0.2%) (0.4%) (0.2%) (0.2%) (0.9%) (0.8%) (0.8%)

2.898E-25 4.071E-25 1.341E-24 1.465E-24 4.909E-25 1.448E-24 1.320E-24 4.087E-25 1.121E-24 8.925E-25 2.596E-25 1.892E-25 4.745E-25

6.33 3.14 1.44 1.67 2.02 4.25 2.80 8.26 3.22 3.84 8.98 0.05 7.30

9.549E-07 9.235E-07 8.817E-07 8.797E-07 8.769E-07 8.581E-07 8.703E-07 9.751E-07 8.669E-07 8.615E-07 9.829E-07 8.941E-07 8.336E-07

Pff23 Pff21 Pff20 Pff19 Pff18 Pff17 Pff16 Pff15 Pff14 Pff13 Pff12 Pff11 Pff10 Pff9 Pff7 Pff3

6302.60113 6308.24160 6311.02392 6313.78394 6316.52023 6319.23421 6321.92536 6324.59442 6327.23998 6329.86652 6332.47027 6335.05282 6337.61449 6340.15560 6345.17651 6354.98236

(3) (2) (7) (2) (5) (2) (5) (2) (7) (1) (6) (1) (3) (1) (1) (5)

2.509E-25 3.738E-25 1.561E-25 5.286E-25 2.103E-25 7.377E-25 2.627E-25 9.838E-25 3.145E-25 1.123E-24 3.725E-25 1.236E-24 4.242E-25 1.295E-24 1.317E-24 6.536E-25

(0.4%) (0.3%) (0.8%) (0.2%) (0.6%) (0.2%) (0.5%) (0.2%) (0.7%) (0.1%) (0.6%) (0.2%) (0.3%) (0.2%) (0.2%) (0.5%)

2.377E-25 3.637E-25 1.470E-25 5.269E-25 2.069E-25 7.209E-25 2.749E-25 9.286E-25 3.431E-25 1.122E-24 4.005E-25 1.262E-24 4.336E-25 1.310E-24 1.230E-24 6.166E-25

5.26 2.70 5.83 0.32 1.62 2.28 4.64 5.61 9.09 0.09 7.52 2.10 2.22 1.16 6.61 5.66

9.441E-07 9.193E-07 9.502E-07 8.974E-07 9.092E-07 9.154E-07 8.550E-07 9.477E-07 8.200E-07 8.953E-07 8.320E-07 8.758E-07 8.751E-07 8.840E-07 9.579E-07 9.482E-07

Rff1 Rff3 Rff4 Rff5 Rff6 Rff7 Rff10 Rff11 Rff12 Rff14 Rff15 Rff16 Rff17 Rff19 Rff21

6366.79054 6371.37712 6373.64072 6375.88289 6378.10528 6380.30616 6386.78183 6388.89696 6390.98956 6395.10604 6397.13047 6399.12763 6401.10324 6404.97973 6408.75102

(4) (2) (3) (1) (4) (1) (3) (3) (4) (4) (4) (6) (4) (2) (3)

3.839E-25 8.154E-25 3.517E-25 1.193E-24 4.371E-25 1.420E-24 4.812E-25 1.333E-24 4.405E-25 3.595E-25 1.047E-24 3.136E-25 7.653E-25 5.823E-25 4.022E-25

(0.4%) (0.2%) (0.3%) (0.2%) (0.4%) (0.2%) (0.3%) (0.3%) (0.4%) (0.5%) (0.5%) (0.6%) (0.4%) (0.3%) (0.4%)

3.681E-25 8.694E-25 3.544E-25 1.220E-24 4.465E-25 1.420E-24 4.814E-25 1.392E-24 4.383E-25 3.719E-25 1.002E-24 2.957E-25 7.735E-25 5.628E-25 3.872E-25

4.12 6.62 0.77 2.26 2.15 0.00 0.04 4.43 0.50 3.45 4.30 5.71 1.07 3.35 3.73

9.330E-07 8.390E-07 8.877E-07 8.747E-07 8.756E-07 8.944E-07 8.941E-07 8.569E-07 8.991E-07 8.648E-07 9.344E-07 9.488E-07 8.851E-07 9.256E-07 9.292E-07

2n1+n15n14 Pee23 Pee21 Pee19 Pee18 Pee17 Pee16 Pee15 Pee14 Pee13 Pee12 Pee11

6744.44481 6750.19305 6755.84514 6758.63601 6761.40106 6764.14395 6766.86214 6769.55629 6772.22567 6774.87116 6777.49204

(6) (5) (3) (6) (3) (5) (2) (5) (2) (4) (2)

1.727E-25 2.541E-25 3.664E-25 1.389E-25 5.112E-25 1.980E-25 6.270E-25 2.382E-25 7.648E-25 2.688E-25 8.509E-25

(0.6%) (0.5%) (0.3%) (1.1%) (0.4%) (0.5%) (0.2%) (0.5%) (0.2%) (0.4%) (0.2%)

1.682E-25 2.561E-25 3.691E-25 1.446E-25 5.028E-25 1.914E-25 6.450E-25 2.378E-25 7.761E-25 2.765E-25 8.704E-25

2.61 0.79 0.74 4.10 1.64 3.33 2.87 0.17 1.48 2.86 2.29

3.378E-07 3.256E-07 3.250E-07 3.141E-07 3.321E-07 3.376E-07 3.168E-07 3.260E-07 3.204E-07 3.157E-07 3.171E-07

ARTICLE IN PRESS 352

H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Pee10 Pee9 Pee8 Pee7 Pee5 Pee4

6780.08863 6782.66117 6785.20928 6787.73243 6792.70533 6795.15503

(4) (2) (4) (2) (2) (8)

2.922E-25 9.014E-25 3.078E-25 8.449E-25 6.764E-25 1.890E-25

(0.4%) (0.2%) (0.4%) (0.2%) (0.2%) (0.9%)

2.983E-25 9.000E-25 2.943E-25 8.416E-25 6.825E-25 1.880E-25

2.09 0.16 4.39 0.39 0.90 0.53

3.174E-07 3.241E-07 3.380E-07 3.241E-07 3.192E-07 3.234E-07

Ree3 Ree4 Ree5 Ree6 Ree7 Ree9 Ree11 Ree13 Ree15 Ree17 Ree19 Ree21 Ree23

6813.86006 6816.08621 6818.28699 6820.46342 6822.61398 6826.84040 6830.96604 6834.99041 6838.91398 6842.73590 6846.45642 6850.07483 6853.59112

(2) (5) (2) (4) (2) (3) (2) (5) (2) (3) (3) (4) (5)

5.805E-25 2.458E-25 8.258E-25 3.113E-25 9.564E-25 1.003E-24 9.165E-25 8.277E-25 6.572E-25 5.088E-25 3.656E-25 2.578E-25 1.695E-25

(0.3%) (0.6%) (0.2%) (0.4%) (0.2%) (0.3%) (0.2%) (0.5%) (0.3%) (0.3%) (0.3%) (0.5%) (0.6%)

5.866E-25 2.389E-25 8.218E-25 3.004E-25 9.545E-25 9.866E-25 9.327E-25 8.177E-25 6.708E-25 5.173E-25 3.762E-25 2.588E-25 1.687E-25

1.05 2.81 0.48 3.50 0.20 1.64 1.77 1.21 2.07 1.67 2.90 0.39 0.47

3.154E-07 3.275E-07 3.195E-07 3.291E-07 3.178E-07 3.217E-07 3.102E-07 3.188E-07 3.078E-07 3.083E-07 3.039E-07 3.107E-07 3.127E-07

Pff20 Pff18 Pff17 Pff14 Pff13 Pff12 Pff11 Pff10 Pff9 Pff8 Pff7 Pff5 Pff4

6752.68661 6758.33911 6761.12767 6769.34535 6772.03447 6774.69901 6777.33828 6779.95259 6782.54175 6785.10561 6787.64387 6792.64610 6795.10901

(4) (3) (6) (2) (4) (2) (4) (2) (3) (2) (9) (5) (3)

2.971E-25 4.110E-25 1.636E-25 6.878E-25 2.484E-25 8.021E-25 2.835E-25 8.766E-25 3.042E-25 8.743E-25 2.890E-25 2.326E-25 5.403E-25

(0.4%) (0.4%) (0.6%) (0.2%) (0.4%) (0.2%) (0.5%) (0.2%) (0.4%) (0.2%) (1.0%) (0.5%) (0.3%)

2.921E-25 4.131E-25 1.602E-25 6.899E-25 2.511E-25 8.078E-25 2.833E-25 8.765E-25 2.947E-25 8.696E-25 2.770E-25 2.257E-25 5.606E-25

1.68 0.51 2.08 0.31 1.09 0.71 0.07 0.01 3.12 0.54 4.15 2.97 3.76

3.179E-07 3.124E-07 3.214E-07 3.155E-07 3.136E-07 3.152E-07 3.181E-07 3.183E-07 3.289E-07 3.207E-07 3.331E-07 3.295E-07 3.083E-07

Rff2 Rff3 Rff4 Rff5 Rff6 Rff7 Rff8 Rff10 Rff12 Rff14 Rff16 Rff18 Rff19 Rff20 Rff22

6811.63593 6813.89478 6816.12783 6818.33474 6820.51665 6822.67226 6824.80223 6828.98397 6833.06231 6837.03624 6840.90544 6844.67003 6846.51291 6848.32963 6851.88407

(3) (7) (2) (5) (2) (4) (4) (2) (4) (4) (3) (4) (9) (4) (4)

4.252E-25 1.957E-25 7.120E-25 2.761E-25 9.008E-25 3.215E-25 9.906E-25 9.626E-25 8.923E-25 7.598E-25 5.801E-25 4.387E-25 1.211E-25 3.071E-25 2.079E-25

(0.3%) (0.8%) (0.2%) (0.6%) (0.2%) (0.5%) (0.5%) (0.2%) (0.5%) (0.5%) (0.3%) (0.4%) (1.0%) (0.4%) (0.5%)

4.332E-25 1.962E-25 7.192E-25 2.751E-25 9.049E-25 3.196E-25 9.864E-25 9.717E-25 8.822E-25 7.459E-25 5.909E-25 4.408E-25 1.241E-25 3.104E-25 2.067E-25

1.88 0.26 1.01 0.36 0.46 0.59 0.42 0.95 1.13 1.83 1.86 0.48 2.48 1.07 0.58

3.141E-07 3.191E-07 3.165E-07 3.207E-07 3.178E-07 3.209E-07 3.200E-07 3.149E-07 3.206E-07 3.218E-07 3.089E-07 3.118E-07 3.049E-07 3.085E-07 3.119E-07

n1+n2+(2n4+n5)1IIn14 Pee27 Pee19 Pee17 Pee15 Pee14 Pee13 Pee12 Pee11

6523.06140 6545.92570 6551.39348 6556.76750 6559.42133 6562.04910 6564.65626 6567.23824

(9) (2) (1) (3) (2) (1) (5) (2)

1.482E-24 8.175E-24 1.132E-23 1.429E-23 6.447E-24 1.914E-23 6.848E-24 1.933E-23

(1.3%) (0.3%) (0.1%) (0.4%) (0.3%) (0.3%) (0.6%) (0.3%)

1.505E-24 8.869E-24 1.204E-23 1.540E-23 5.670E-24 1.847E-23 6.573E-24 2.066E-23

1.55 8.49 6.36 7.77 12.05 3.50 4.02 6.88

8.168E-06 7.483E-06 7.592E-06 7.451E-06 9.106E-06 8.276E-06 8.299E-06 7.433E-06

ARTICLE IN PRESS H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

353

Table 3 (continued ) |R|2obs

Line

Position

Sobs

Scalc

Pee8 Pee5

6574.86583 (4) 6582.29593 (3)

7.049E-24 (0.5%) 1.551E-23 (0.5%)

6.950E-24 1.604E-23

1.40 3.42

7.990E-06 7.555E-06

Ree1 Ree2 Ree4 Ree5 Ree7 Ree10 Ree12 Ree13 Ree14 Ree15 Ree16 Ree17 Ree18 Ree21 Ree22 Ree23 Ree25 Ree26

6598.89726 (4) 6601.18476 (4) 6605.69562 (2) 6607.91852 (1) 6612.30014 (2) 6618.70103 (1) 6622.85492 (1) 6624.89628 (0) 6626.91372(14) 6628.90603 (1) 6630.87371 (2) 6632.81614 (1) 6634.73322 (2) 6640.32533 (1) 6642.1352 (10) 6643.91771 (1) 6647.39756 (2) 6649.09461 (7)

5.728E-24 3.100E-24 5.374E-24 1.870E-23 2.381E-23 7.484E-24 6.475E-24 1.852E-23 5.973E-24 1.522E-23 4.375E-24 1.165E-23 3.350E-24 5.684E-24 1.564E-24 3.821E-24 2.253E-24 5.755E-25

(0.4%) (0.5%) (0.2%) (0.1%) (0.2%) (0.1%) (0.1%) (0.0%) (1.7%) (0.1%) (0.2%) (0.1%) (0.3%) (0.1%) (0.4%) (0.1%) (0.2%) (0.9%)

5.784E-24 3.343E-24 5.526E-24 1.897E-23 2.198E-23 7.400E-24 6.707E-24 1.865E-23 5.665E-24 1.524E-23 4.489E-24 1.172E-23 3.349E-24 5.824E-24 1.576E-24 3.784E-24 2.332E-24 5.987E-25

0.98 7.84 2.83 1.44 7.69 1.12 3.58 0.70 5.16 0.13 2.61 0.60 0.03 2.46 0.77 0.97 3.51 4.03

7.589E-06 7.087E-06 7.391E-06 7.468E-06 8.164E-06 7.557E-06 7.173E-06 7.356E-06 7.790E-06 7.355E-06 7.160E-06 7.284E-06 7.307E-06 7.068E-06 7.168E-06 7.271E-06 6.916E-06 6.862E-06

Pff26 Pff24 Pff20 Pff16 Pff14 Pff13 Pff9 Pff7 Pff6

6528.61378(23) 6534.06277(24) 6544.70764(14) 6555.06373 (6) 6560.14104 (2) 6562.65878 (4) 6572.60009(11) 6577.49414 (1) 6579.92344 (1)

2.093E-24 3.595E-24 7.635E-24 1.502E-23 1.682E-23 5.758E-24 6.281E-24 6.432E-24 1.774E-23

(1.5%) (3.0%) (1.8%) (1.0%) (0.3%) (0.5%) (0.8%) (0.2%) (0.1%)

1.968E-24 3.239E-24 7.476E-24 1.378E-23 1.709E-23 6.187E-24 7.126E-24 6.640E-24 1.831E-23

5.97 9.90 2.08 8.26 1.61 7.45 13.45 3.23 3.21

8.957E-06 9.287E-06 8.430E-06 8.874E-06 7.961E-06 7.502E-06 7.008E-06 7.649E-06 7.624E-06

Rff3 Rff4 Rff6 Rff7 Rff8 Rff9 Rff11 Rff12 Rff13 Rff14 Rff15 Rff16 Rff17 Rff18 Rff19 Rff20 Rff21 Rff22 Rff24 Rff26

6603.58947 6605.89332 6610.46403 6612.73032 6614.98369 6617.22423 6621.66015 6623.85778 6626.03920 6628.20498 6630.35262 6632.48440 6634.59716 6636.69153 6638.76606 6640.81916 6642.85017 6644.86008 6648.80632 6652.64949

(3) (1) (1) (2) (3) (1) (1) (1) (1) (7) (5) (2) (3) (1) (2) (1) (6) (3) (1) (2)

4.554E-24 1.611E-23 2.072E-23 7.410E-24 2.240E-23 7.468E-24 7.076E-24 2.012E-23 6.194E-24 1.675E-23 4.913E-24 1.333E-23 3.838E-24 9.860E-24 2.882E-24 7.148E-24 1.843E-24 4.926E-24 3.003E-24 1.753E-24

(0.3%) (0.1%) (0.1%) (0.3%) (0.4%) (0.1%) (0.1%) (0.1%) (0.1%) (0.1%) (0.7%) (0.2%) (0.4%) (0.1%) (0.2%) (0.1%) (0.8%) (0.5%) (0.1%) (0.3%)

4.516E-24 1.651E-23 2.065E-23 7.274E-24 2.240E-23 7.476E-24 7.026E-24 1.985E-23 6.125E-24 1.672E-23 4.993E-24 1.321E-23 3.825E-24 9.824E-24 2.764E-24 6.902E-24 1.888E-24 4.588E-24 2.892E-24 1.731E-24

0.83 2.48 0.34 1.84 0.00 0.11 0.71 1.34 1.11 0.18 1.63 0.90 0.34 0.37 4.09 3.44 2.44 6.86 3.70 1.25

7.662E-06 7.389E-06 7.542E-06 7.632E-06 7.466E-06 7.431E-06 7.438E-06 7.459E-06 7.416E-06 7.320E-06 7.165E-06 7.320E-06 7.252E-06 7.229E-06 7.482E-06 7.405E-06 6.954E-06 7.621E-06 7.317E-06 7.086E-06

n1+n2+(n4+2n5)1IIn15 Pee17 Pee16 Pee12 Pee10

6557.09349 6559.81766 6570.46556 6575.64828

(7) (3) (9) (1)

1.106E-24 3.624E-24 5.863E-24 5.944E-24

(1.1%) (0.3%) (0.9%) (0.2%)

1.068E-24 3.687E-24 5.478E-24 5.976E-24

3.44 1.74 6.57 0.54

3.939E-06 3.765E-06 4.192E-06 3.930E-06

Ree2

6607.11333 (4)

3.101E-24 (0.4%)

2.984E-24

3.77

4.180E-06

%

ARTICLE IN PRESS 354

H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

Table 3 (continued ) Scalc

Sobs

%

|R|2obs

Line

Position

Ree3 Ree4 Ree5 Ree7 Ree8 Ree10 Ree11 Ree12 Ree13 Ree18 Ree19 Ree20 Ree22 Ree24

6609.37575 6611.61524 6613.83183 6618.19466 6620.34148 6624.56376 6626.63620 6628.68535 6630.70932 6640.44357 6642.30975 6644.14990 6647.74472 6651.22861

(3) (3) (5) (8) (1) (6) (2) (1) (2) (2) (4) (1) (7) (2)

1.379E-24 4.927E-24 1.812E-24 2.300E-24 6.835E-24 6.201E-24 2.312E-24 5.747E-24 1.763E-24 2.867E-24 8.625E-25 2.074E-24 1.166E-24 8.724E-25

(0.3%) (0.3%) (0.5%) (0.8%) (0.2%) (0.8%) (0.3%) (0.1%) (0.2%) (0.2%) (0.5%) (0.2%) (0.8%) (0.3%)

1.351E-24 4.946E-24 1.890E-24 2.188E-24 6.739E-24 6.607E-24 2.112E-24 5.964E-24 1.837E-24 2.911E-24 8.163E-25 2.030E-24 1.337E-24 8.338E-25

2.03 0.39 4.30 4.87 1.40 6.55 8.65 3.78 4.20 1.53 5.36 2.12 14.67 4.42

4.101E-06 3.995E-06 3.837E-06 4.184E-06 4.023E-06 3.693E-06 4.288E-06 3.756E-06 3.720E-06 3.693E-06 3.931E-06 3.769E-06 3.160E-06 3.716E-06

Pff21 Pff17 Pff15 Pff 8 Pff 7 Pff 6

6548.08459 6558.46125 6563.55620 6580.97999 6583.42147 6585.84826

(2) (5) (2) (3) (2) (5)

1.672E-24 3.078E-24 4.336E-24 1.903E-24 5.832E-24 1.992E-24

(0.3%) (0.8%) (0.3%) (0.4%) (0.3%) (0.8%)

1.538E-24 3.158E-24 4.127E-24 1.979E-24 5.687E-24 1.753E-24

8.01 2.60 4.82 3.99 2.49 12.00

3.962E-06 3.680E-06 4.025E-06 3.821E-06 4.088E-06 4.544E-06

Rff1 Rff3 Rff5 Rff6 Rff7 Rff9 Rff10 Rff11 Rff12 Rff13 Rff14 Rff15 Rff17 Rff18 Rff19 Rff21 Rff22 Rff23 Rff24 Rff25 Rff27

6604.88145 (5) 6609.52722 (7) 6614.12644 (1) 6616.40710 (9) 6618.67807 (1) 6623.17948 (1) 6625.41102 (2) 6627.62830 (1) 6629.83286 (2) 6632.02119 (1) 6634.19563 (3) 6636.35542 (2) 6640.62294 (2) 6642.73142 (3) 6644.82214 (1) 6648.94654 (1) 6650.97889 (6) 6652.98914 (4) 6654.97439(11) 6656.94141 (3) 6660.79488(11)

1.594E-24 3.717E-24 5.453E-24 2.063E-24 6.446E-24 6.535E-24 2.091E-24 6.125E-24 2.106E-24 5.223E-24 1.619E-24 4.849E-24 3.239E-24 9.686E-25 2.343E-24 1.590E-24 4.136E-25 1.003E-24 2.539E-25 6.291E-25 3.782E-25

(0.7%) (0.7%) (0.2%) (1.3%) (0.1%) (0.1%) (0.2%) (0.1%) (0.3%) (0.1%) (0.3%) (0.2%) (0.3%) (0.3%) (0.2%) (0.1%) (0.7%) (0.5%) (1.3%) (0.4%) (1.3%)

1.719E-24 4.048E-24 5.658E-24 2.064E-24 6.543E-24 6.717E-24 2.190E-24 6.295E-24 1.972E-24 5.462E-24 1.651E-24 4.423E-24 3.360E-24 9.538E-25 2.402E-24 1.620E-24 4.345E-25 1.034E-24 2.696E-25 6.240E-25 3.570E-25

7.84 8.91 3.76 0.05 1.50 2.79 4.73 2.78 6.36 4.58 1.98 8.79 3.74 1.53 2.52 1.89 5.05 3.09 6.18 0.81 5.61

3.734E-06 3.687E-06 3.853E-06 3.984E-06 3.914E-06 3.834E-06 3.746E-06 3.797E-06 4.144E-06 3.688E-06 3.756E-06 4.171E-06 3.611E-06 3.771E-06 3.590E-06 3.541E-06 3.399E-06 3.425E-06 3.287E-06 3.476E-06 3.559E-06

n1+n3+2n042n04 Pee26 Pee25 Pee23 Pee20 Pee19 Pee18 Pee17 Pee16 Pee15 Pee13 Pee12 Pee9 Pee8 Pee5

6433.69757 6436.64199 6442.45813 6451.00315 6453.80368 6456.57968 6459.32944 6462.05455 6464.75303 6470.07730 6472.69619 6480.40619 6482.92938 6490.37794

7.524E-25 2.717E-24 4.254E-24 2.512E-24 9.272E-24 3.649E-24 1.271E-23 5.384E-24 1.587E-23 1.882E-23 6.600E-24 2.339E-23 7.897E-24 1.788E-23

(0.5%) (0.2%) (0.1%) (0.6%) (0.1%) (0.4%) (0.1%) (0.1%) (0.1%) (0.1%) (0.2%) (0.2%) (0.2%) (0.1%)

6.919E-25 2.684E-24 4.316E-24 2.652E-24 9.488E-24 3.718E-24 1.292E-23 4.917E-24 1.658E-23 1.994E-23 7.110E-24 2.319E-23 7.599E-24 1.799E-23

8.04 1.21 1.45 5.57 2.33 1.89 1.69 8.67 4.47 5.97 7.72 0.84 3.77 0.61

1.000E-04 9.281E-05 8.985E-05 8.558E-05 8.803E-05 8.814E-05 8.805E-05 9.775E-05 8.520E-05 8.349E-05 8.189E-05 8.816E-05 9.057E-05 8.584E-05

(4) (2) (1) (4) (1) (9) (0) (1) (1) (1) (1) (1) (2) (0)

ARTICLE IN PRESS H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

355

Table 3 (continued ) |R|2obs

Line

Position

Sobs

Scalc

Pee4 Pee3

6492.82562 (3) 6495.25464 (1)

4.875E-24 (0.3%) 1.219E-23 (0.1%)

5.068E-24 1.190E-23

3.95 2.35

8.283E-05 8.791E-05

Ree1 Ree2 Ree3 Ree4 Ree5 Ree9 Ree10

6507.04964 6509.34144 6511.61727 6513.87912 6516.12395 6524.93507 6527.07806

(1) (4) (0) (4) (5) (2) (6)

8.994E-24 4.322E-24 1.587E-23 5.916E-24 2.047E-23 2.421E-23 7.819E-24

(0.2%) (0.2%) (0.1%) (0.4%) (0.6%) (0.3%) (0.7%)

8.292E-24 4.042E-24 1.558E-23 6.183E-24 2.096E-23 2.448E-23 7.979E-24

7.80 6.49 1.82 4.51 2.41 1.12 2.05

9.169E-05 9.013E-05 8.558E-05 8.015E-05 8.154E-05 8.156E-05 8.057E-05

n1+n3+2n242n24 Pee22 Pee21 Pee19 Pee18 Pee17 Pee16 Pee15 Pee14 Pee13 Pee12 Pee8 Pee 7

6445.70910 6448.59454 6454.28591 6457.09341 6459.87806 6462.63892 6465.37772 6468.09483 6470.78981 6473.46301 6483.93404 6486.48814

(9) (3) (0) (1) (1) (1) (1) (3) (1) (2) (2) (1)

1.732E-24 6.197E-24 9.430E-24 3.837E-24 1.316E-23 4.921E-24 1.659E-23 6.411E-24 1.949E-23 7.468E-24 7.301E-24 2.198E-23

(1.1%) (0.4%) (0.0%) (0.1%) (0.2%) (0.1%) (0.1%) (0.3%) (0.1%) (0.2%) (0.4%) (0.3%)

1.828E-24 6.724E-24 9.702E-24 3.802E-24 1.321E-23 5.026E-24 1.693E-23 6.237E-24 2.033E-23 7.226E-24 7.519E-24 2.120E-23

5.54 8.50 2.88 0.91 0.38 2.13 2.05 2.71 4.31 3.24 2.99 3.55

1.728E-04 1.681E-04 1.773E-04 1.841E-04 1.817E-04 1.786E-04 1.787E-04 1.875E-04 1.749E-04 1.885E-04 1.771E-04 1.891E-04

Ree3 Ree4 Ree6 Ree8 Ree10 Ree16 Ree18 Ree19

6512.71588 6514.92908 6519.24845 6523.44390 6527.52848 6539.23993 6542.95739 6544.77517

(5) (2) (4) (1) (3) (5) (7) (1)

1.311E-23 5.472E-24 6.926E-24 8.059E-24 7.874E-24 5.190E-24 4.400E-24 1.012E-23

(1.1%) (0.3%) (0.2%) (0.1%) (0.3%) (2.8%) (0.8%) (0.3%)

1.279E-23 5.700E-24 7.693E-24 8.632E-24 8.642E-24 5.413E-24 4.072E-24 1.037E-23

2.44 4.17 11.07 7.11 9.75 4.30 7.45 2.47

1.870E-04 1.751E-04 1.642E-04 1.703E-04 1.662E-04 1.749E-04 1.971E-04 1.780E-04

Pff28 Pff27 Pff26 Pff24 Pff23 Pff21 Pff20 Pff18 Pff17 Pff14 Pff13 Pff12 Pff10 Pff9 Pff7

6428.38676 6431.39531 6434.37761 6440.27264 6443.18400 6448.93647 6451.77722 6457.38686 6460.15600 6468.32131 6470.99458 6473.64399 6478.87089 6481.44828 6486.53054

(7) (6) (3) (6) (3) (1) (1) (2) (3) (2) (1) (0) (0) (1) (6)

1.150E-24 5.675E-25 2.190E-24 3.819E-24 1.447E-24 2.263E-24 8.401E-24 1.222E-23 4.635E-24 1.836E-23 6.776E-24 2.225E-23 2.366E-23 8.088E-24 6.804E-24

(0.9%) (0.8%) (0.5%) (0.7%) (0.4%) (0.1%) (0.2%) (0.3%) (0.3%) (0.3%) (0.1%) (0.0%) (0.1%) (0.2%) (0.8%)

1.202E-24 5.322E-25 2.094E-24 3.466E-24 1.457E-24 2.225E-24 8.078E-24 1.135E-23 4.385E-24 1.867E-23 6.765E-24 2.166E-23 2.320E-23 7.736E-24 .067E-24

4.52 6.22 4.38 9.24 0.69 1.68 3.84 7.12 5.39 1.69 0.16 2.65 1.94 4.35 3.87

1.745E-04 1.945E-04 1.908E-04 2.010E-04 1.812E-04 1.855E-04 1.897E-04 1.964E-04 1.928E-04 1.794E-04 1.827E-04 1.874E-04 1.860E-04 1.907E-04 1.756E-04

Rff4 Rff5 Rff6 Rff7 Rff8 Rff9 Rff12 Rff15 Rff22 Rff26

6514.97268 6517.18335 6519.36909 6521.52951 6523.66527 6525.77662 6531.95948 6537.91640 6550.93378 6557.80755

(1) (4) (1) (3) (4) (2) (1) (3) (4) (7)

1.723E-23 6.463E-24 2.375E-23 8.097E-24 2.394E-23 9.220E-24 2.456E-23 6.197E-24 6.361E-24 2.058E-24

(0.2%) (0.4%) (0.2%) (0.3%) (0.7%) (0.2%) (0.1%) (0.4%) (1.0%) (0.8%)

1.710E-23 6.838E-24 2.309E-23 8.288E-24 2.588E-23 8.736E-24 2.376E-23 6.084E-24 5.781E-24 2.217E-24

0.75 5.80 2.78 2.36 8.10 5.25 3.26 1.82 9.12 7.73

1.838E-04 1.724E-04 1.876E-04 1.782E-04 1.687E-04 1.925E-04 1.885E-04 1.858E-04 2.007E-04 1.693E-04

%

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356 Table 3 (continued ) Line

Scalc

Sobs

Position

%

|R|2obs

n1+n3+(n4+n5)0+(n4+n5)0+ Pee26 6437.52467 Pee24 6443.45756 Pee22 6449.28864 Pee20 6455.02117 Pee16 6466.18718 Pee14 6471.62154 Pee13 6474.30172 Pee11 6479.58848 Pee10 6482.19507 Pee8 6487.33466 Pee7 6489.86807 Pee5 6494.85971

(5) (3) (4) (1) (1) (1) (1) (2) (0) (1) (3) (2)

1.201E-24 2.074E-24 3.152E-24 5.026E-24 9.458E-24 1.168E-23 4.120E-24 4.633E-24 1.496E-23 1.446E-23 4.785E-24 3.920E-24

(0.5%) (0.3%) (0.5%) (0.1%) (0.1%) (0.1%) (0.1%) (0.3%) (0.0%) (0.1%) (0.3%) (0.2%)

1.270E-24 2.102E-24 3.300E-24 4.913E-24 9.188E-24 1.147E-23 4.173E-24 4.707E-24 1.457E-23 1.450E-23 4.639E-24 3.849E-24

5.75 1.35 4.70 2.25 2.85 1.80 1.29 1.60 2.61 0.28 3.05 1.81

8.426E-05 8.790E-05 8.507E-05 9.112E-05 9.169E-05 9.067E-05 8.794E-05 8.767E-05 9.148E-05 8.881E-05 9.188E-05 9.071E-05

Ree0 Ree1 Ree2 Ree7 Ree12 Ree20 Ree21

(8) (8) (4) (6) (4) (8) (7)

2.859E-24 1.738E-24 7.764E-24 5.199E-24 1.482E-23 5.445E-24 1.434E-24

(0.8%) (0.9%) (0.5%) (0.8%) (0.5%) (1.0%) (0.6%)

2.749E-24 1.813E-24 7.975E-24 5.331E-24 1.467E-23 5.234E-24 1.438E-24

3.85 4.32 2.72 2.54 1.01 3.88 0.28

9.263E-05 8.540E-05 8.671E-05 8.687E-05 8.997E-05 9.266E-05 8.885E-05

6509.24737 6511.55930 6513.84523 6524.89602 6535.29947 6550.54227 6552.32252

a Bands are listed in the same order as in Table 1. The quoted line position is the measured one in cm1, with its 2 SD confidence interval (in 105 cm1) between parenthesis. Sobs and Scalc are measured and calculated intensities, respectively, for pure 12C2H2 (i.e., for a sample containing 100% of 12C2H2), in cm mol1 at 296 K. The 2 SD confidence interval (in %) is given between parenthesis against Sobs. % is the ratio 100  (ScalcSobs)/Sobs. |R|2obs is the experimental transition dipole moment squared value, in D2 (1 D ¼ 3.33546  1030 C m), deduced from Sobs.

But, again, one should take into account the fact that these very good statistical uncertainties do not always represent the true precision. For example, in the cases where the adjustments are very good despite strong overlappings, one has to suspect inaccurate results. 3. Empirical data reduction From each line intensity S(T0) adjusted using the multispectrum fitting procedure, expressed in cm mol1 at the standard temperature T0 ¼ 296 K for pure 12C2H2, i.e., for a sample containing 100% of 12C2H2, we used the following formula to deduce the transition dipole moment squared |R|2, in D2 (1 debye ¼ 3.33546  1030 C m)


  (2) SðT 0 Þ ¼ ð1=4p0 Þ 8p3 =3hc g00 n0 =gV QðT 0 Þ jRj2 LðJ; ‘Þ exp hcE 00 =kT 0 1  exp hcn0 =kT 0 , where 1/4pe0 ¼ 1036 erg cm3 D2; h is Planck’s constant equal to 6.6260755  1027 erg s (1 erg ¼ 107 J); c is vacuum speed of light equal to 2.99792458  1010 cm s1; g00 is the statistical weight due to nuclear spin of the lower level (1 for s-type levels and 3 for a-type levels); n0 is the transition wavenumber in cm1; gV depends on the degeneracy of the levels involved, being 2 if both upper and lower vibrational states are degenerated and 1 otherwise; Q(T0) is the total internal partition function at temperature T0; L(J,‘) is the Ho¨nl-London factor, J being the rotational quantum number of the lower level of the transition, and ‘ its secondary vibrational quantum number ð‘ ¼ j‘4 þ ‘5 jÞ; E00 , in cm1, is the energy of the lower level; k is Boltzmann’s constant equal to 1.380658  1016 erg K1. For parallel bands (D‘ ¼ 0), the Ho¨nl-London factors are given by LðJ; ‘Þ ¼ ðJ þ 1 þ ‘ÞðJ þ 1  ‘Þ=ðJ þ 1ÞðRbranchÞ,

(3)

LðJ; ‘Þ ¼ ðJ þ ‘ÞðJ  ‘Þ=JðPbranchÞ.

(4)

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357

In Eq. (2), the E00 energy values have been taken from the HITRAN database [31] or from line positions measured by Kabbadj et al. [32]. To calculate the partition function Q(T0), we used the values tabulated by Fischer et al. [33]. At 296 K, Q(T0) is equal to 414.03. Let us recall that in our previous works, we had used the value calculated by Gamache et al. [34], i.e., 412.53 at 296 K. The small difference between these two values (0.37%) will have consequence only on the transition moments squared. The effect on the retrieved line

Table 4 Summary of 12C2H2 experimental vibrational transition dipole moments squared |R0|2 and Herman–Wallis coefficients for 13 bands in the 1.5-mm spectral regiona Band

|R0|2

n2+n3+2n04 n2+n3+2n05 2n2+(3n4+n5)0+ 2n2+(n4+3n5)0+ 2n1+n14n15

1.718(40)  10 70.086 5.568(101)  10870.280 2.250(43)  10870.110 2.364(49)  10870.120 1.932(39)  10570.097

2n3+n15n14 2n3+n14n15 2n1+n15n14 n1+n2+(2n4+n5)1 IIn14

3.854(59)  10670.190 8.946(100)  10770.450 3.202(20)  10770.160 7.706(104)  10670.390

n1+n2+(n4+2n5)1IIn15

4.030(98)  10670.200

n1+n3+2n042n04 n1+n3+2n242n24 n1+n3+(n4+n5)0+(n4+n5)0+

8.506(224)  10570.430 1.824(28)  10470.091 8.907(120)  10570.450

A1 7

A2 4

N

RMS (%)

6.01(45)  10 2.25(29)  104 1.10(47)  104 3.94(57)  104 e+8.4(33)  105

33 34 27 26 64

6 4 3 4 6

e+1.00(24)  104

51 63 58 57

4 4 2 5

46

5

23 45 19

5 5 3

4

7.1(60)  10 1.44(40)  103 9.4(72)  104 e1.69(71)  103 f7.6(63)  104

e5.9(26)  104 e1.39(58)  103 f1.75(56)  103

f3.0(20)  105

e9.8(56)  105 f1.11(40)  104 1.53(94)  103

a

Transition dipole moment squared in debye2

Bands are given in the same order as in Table 1. Confidence intervals (2 SD, in unit of the last quoted digit) are given between parentheses. For the |R0|2 values, in D2 (1 D ¼ 3.33546  1030 C m), the accuracy (75%) is added after the 7 signs. Non-reported Herman–Wallis coefficients had to be fixed to zero. N is the number of line intensities measured in each band (including both e and f subbranches in case of ‘-type doubling). The RMS of the adjustment is also given for each band (e and f sub-branches being adjusted simultaneously in case of ‘-type doubling).

1.5x10-7

1.0x10-7

5.0x10-8

-20

-10

0 m

10

20

Fig. 1. Variation of the transition dipole moment squared |R|2, in D2 (1 D ¼ 3.33546  1030 C m) vs. m, for the band n2+n3+2n04. The solid line has been calculated using the constants found in this work (see Table 4).

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Transition dipole moment squared in debye2

358

5x10-8

4x10-8

3x10-8

-20

-10

0 m

10

20

Transition dipole moment squared in debye2

Fig. 2. Variation of the transition dipole moment squared |R|2 vs. m, for the band n2+n3+2n05. See caption of Fig. 1.

2.0x10-8

1.5x10-8

-20

-10

0 m

10

20

Fig. 3. Variation of the transition dipole moment squared |R|2 vs. m, for the band 2n2+(3n4+n5)0+. See caption of Fig. 1.

intensities will be negligible, since they depend only on the ratios of the partition function values at the reference temperature 296 K and at the temperature of each spectrum, all very close to 296 K. Data reduction was achieved by fitting the measured transition dipole moments squared to the following expression:
2 jRj2 ¼ jR0 j2 1 þ A1 m þ A2 m2 .

(5)

m is equal to J in the P-branch and J+1 in the R-branch. |R0|2 is the vibrational transition dipole moment squared, and A1 and A2 are Herman–Wallis coefficients. Note that the term between parentheses in Eq. (5) is squared, contrary to what we sometimes did in previous works concerning C2H2 (see, e.g. [8,9]). In case of ‘type doubling, the two e and f sub-branches were adjusted simultaneously, leading to the same value of |R0|2

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359

2.5x10-8

2.0x10-8

1.5x10-8

1.0x10-8 -20

-10

0 m

10

20

Transition dipole moment squared in debye2

Fig. 4. Variation of the transition dipole moment squared |R|2 vs. m, for the band 2n2+(n4+3n5)0+. See caption of Fig. 1.

2.5x10-5

2.0x10-5

1.5x10-5

1.0x10-5

-30

-20

-10

0 m

10

20

30

Fig. 5. Variation of the transition dipole moment squared |R|2, in D2 (1 D ¼ 3.33546  1030 C m) vs. m, for the band 2n1+n14n15. The curves have been calculated using the constants found in this work (see Table 4). The solid line and solid triangles are for the e sub-branch, and the dotted line and open triangles are for the f sub-branch.

but to different Herman–Wallis coefficients for each sub-branch. Transition dipole moment squared values, |R|2, deduced from the experimental line intensities are reported in Table 3, and vibrational transition dipole moment squared values, |R0|2, and Herman–Wallis coefficients obtained from an unweighted fit of the |R|2 are listed in Table 4. The best examples of fits have been plotted in Figs. 1–8. The average RMS of these fits is 4.5%, which is larger than what we observed for C2H2 at lower wavenumbers (see, e.g., [7–9,24]). Such an increase of the residuals can result from the difficulties encountered for the measurements, as explained in Section 2.1, and from the strong resonances affecting levels of the same polyad. For example, one can see that experimental values of Figs. 1, 2, 4 are not randomly distributed around the calculated curve, but follow regular variations or oscillations vs. J, which cannot all be due to the same systematic errors in the measurement process.

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Transition dipole moment squared in debye2

360

1x10-6

9x10-7

8x10-7

7x10-7

6x10-7

5x10-7

-20

-10

0 m

10

20

Transition dipole moment squared in debye2

Fig. 6. Variation of the transition dipole moment squared |R|2, in D2 (1 D ¼ 3.33546  1030 C m) vs. m, for the band 2n3+n14n15. The straight line has been calculated using the constant found in this work (see Table 4). Solid and open triangles are for the e and f subbranches, respectively.

3.4x10-7 3.3x10-7 3.2x10-7 3.1x10-7 3.0x10-7 2.9x10-7 2.8x10-7 2.7x10-7 -20

-10

0 m

10

20

Fig. 7. Variation of the transition dipole moment squared |R|2 vs. m, for the band 2n1+n15n14. See caption of Fig. 5.

4. Conclusion In this paper, C2H2 absolute line intensities have been measured in the 1.5-mm spectral domain of interest for metrological applications. About 550 experimental intensities have been obtained in 13 bands for which no individual absolute line intensity data existed before this work. Comparisons with previous results obtained in the 4 strongest bands [14] showed an excellent agreement (better than 1%). However, numerous and strong overlaps made the measurement process very difficult for the other bands, and decreased the mean accuracy to 5%, despite the very good quality of the spectra. The rotational dependence of the transition dipole moment squared could be modeled using Herman–Wallis factors, so that vibrational transition dipole moments squared and Herman–Wallis coefficients have been obtained for each band. The dispersion of experimental

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H. Tran et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 108 (2007) 342–362

361

9x10-5

8x10-5

7x10-5

6x10-5 -20

-10

m

0

10

20

Fig. 8. Variation of the transition dipole moment squared |R|2 vs. m, for the band n1+n3+(n4+n5)0+(n4+n5)0+. See caption of Fig. 1.

values around calculated ones appeared to be larger than what was usually observed in lower wavenumber spectral regions of acetylene. This can be due to the increased difficulty of the measurements. However, as experimental values are not always randomly spread over calculated ones, one could also suspect that strong vibro-rotational resonances occur when the rank P ¼ 5v1+3v2+5v3+v4+v5 of the polyad of interacting states increases, namely when the wavenumber increases. A few bands in the 1.5-mm region have not yet been studied because a large number of the corresponding lines are hidden or strongly blended. We plan to measure line intensities in these bands, in order to get additional information on the transition dipole moments squared in the DP ¼ 10 series of transition. Acknowledgment The authors acknowledge Mr. D. De´catoire for his contribution to this work. References [1] Herman M, Lie´vin J, Vander Auwera J, Campargue C. Global and accurate vibration hamiltonians from high-resolution molecular spectroscopy. Adv Chem Phys 1999;108:1–431 (New York: Wiley). [2] Herman M, Campargue C, El Idrissi MI, Vander Auwera J. Vibrational spectroscopic database on acetylene, X1S+g (12C2H2, 12C2D2, and 13C2H2). J Phys Chem Ref Data 2003;32:921–1361. [3] Abbouti Temsamani M, Herman M. The vibrational energy levels in acetylene 12C2H2: towards a regular pattern at higher energies. J Chem Phys 1995;102:6371–84. [4] Perevalov VI, Lobodenko EI, Teffo JL. Reduced effective Hamiltonian for global fitting of C2H2 rovibrational lines. In: Proceedings of the XIIth symposium and school on high-resolution molecular spectroscopy, St. Petersburg, Russia (SPIE 1997;3090:143–9.) [5] Lyulin OM, Perevalov VI. Line intensities of vibration-rotational transitions of acetylene molecule in the 1.5-mm region. Atmos Ocean Opt 2004;17:485–8. [6] Perevalov VI, Lyulin OM, Jacquemart D, Claveau C, Teffo JL, Dana V, et al. Global fitting of line intensities of acetylene molecule in the infrared using the effective operator approach. J Mol Spectrosc 2003;218:180–9. [7] Lyulin OM, Perevalov VI, Mandin JY, Dana V, Jacquemart D, Re´galia-Jarlot L, et al. Line intensities of acetylene in the 3-mm region: new measurements of weak hot bands and global fitting. JQSRT 2006;97:81–98. [8] Lyulin OM, Perevalov VI, Mandin JY, Dana V, Gueye F, Thomas X, et al. Line intensities of acetylene: measurements in the 2.5-mm spectral region and global modeling in the DP ¼ 4 and 6 series. JQSRT 2007;103:496–523. [9] Lyulin OM, Perevalov VI, Gueye F, Mandin JY, Dana V, Thomas X, et al. Line positions and intensities of acetylene in the 2.2-mm region. JQSRT 2007;104:133–54. [10] Sakai Y, Sudo S, Ikegami T. Frequency stabilization of laser diodes using 1.51–1.55 mm absorption lines of 12C2H2 and 13C2H2. IEEE J Quant Electron 1992;28:75–81.

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