Experimental and theoretical study of absolute intensities of ozone spectral lines in the range 1850–2300 cm-1

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Experimental and theoretical study of absolute intensities of ozone spectral lines in the range 1850–2300 cm-1
  Pergamon J. Quant. Spectrosc. Radiat. Transfer Vol. 52 No. 314 pp. 341-355 1994 0022-4073( M)EOO43-6 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights eserved 0022-4073/94 7.00 0.00 EXPERIMENTAL AND THEORETICAL STUDY OF ABSOLUTE INTENSITIES OF OZONE SPECTRAL LINES IN THE RANGE 1850-23OOcm-’ A. BARBE,? J. J. PLATEAUX,? S. BOUAZZA,~ 0. SULAKSHINA,~ S. MIKHAILENKO, V. TYUTEREV,~ and S. TASHKCJN~ tGroupe de Spectromktrie Mol&ulaire et Atmosphtrique, Unit6 Associ&e au CNRS: URA D 1434, Facultt des Sciences BP 347, 51062 Reims CCdex, France, and ILaboratory of Theoretical Spectroscopy, Institute of Atmospheric Optics, 1 Akademicheskii Av., 634055 Tomsk. Russia Abstract-Ozone lines in the 1850-2300 cm-’ region have been recorded with the Reims FTS. Due to the high resolution (0.0018 cm-‘) and signal/noise ratio on the order of 800, 2420 precise frequencies have been measured, as well as absolute intensities of 638 well isolated lines. A new set of 15 effective dipole-moment parameters for the 2v,, v, + vj and 2v, bands is determined which reproduces within 2% about 2/3 of the measured line intensities. The total r.m.s. deviation of the fit for the 638 measured line intensities is 2.4%, which represents considerable improvement for ozone data in this region published so far. INTRODUCTION The present study involves high-resolution measurements of the line positions and line intensities in the 5 pm region which were obtained with the Fourier transform spectrometer built in Reims.’ Although this region has been recorded and analyzed several times as described by Rinsland et al,2 this work represents a real improvement in wavenumber accuracy and primarily in absolute intensities measurements, which is of importance for atmospheric retrieval of ozone in the atmosphere. In particular, great care has been taken to measure absolute ozone quantity in the cell and also to recover precise line strengths. The reduction of data and ozone generation have been described in three different papers.3-5 Finally, this work offers results pertaining mostly to intensities and leads to an improvement by a factor of 3 with respect to Ref. 2. EXPERIMENTAL DETAILS The different characteristics of the FTS are given in Refs. 3-5, i.e., the CaF, beamsplitter, InSb detector, and 3 m path difference. We then review the essential aspects of this work. It is known that the 5 pm spectral region is quite suitable for obtaining very good spectra, since the InSb detector is very sensitive to it. As the v, + V~ and is very strong, single path cells of 31 or 3.6 cm are used for recording most of the spectra. This permits one to obtain a S/N ratio of about 800 when recording the 1800-2400 cm-’ interval in 1 h. The S/N is of course degraded when using the white cell (1 m basic path, 8-36 m optical pathlength) for recording weak lines (mainly high values of zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA   and J for 2v, and 2v,). Our spectrometer works with a slightly wedged beam mixer and beam splitter. This allows one to avoid any problem of fringes affecting the 0 and 100% transmittance, and represents in this case a very important improvement for our study of line strengths. This small nonparallelism leads to a small asymmetry in line shapes, due to phase shift. This phase shift is now included in our fits, as explained in Refs. 6 and 7. In fact, this asymmetry must absolutely be taken into account for very precise wavenumber measurements (of the order of 10-scm-‘) and to derive line shifts, although intensity measurements are quasi insensitive to this instrumental problem. 341  342 A. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF ARBE et al To obtain line strengths with great accuracy, we have made fits on transmittance for line with absorption between 30 and 65%, and have used 10 different spectra with pathlengths ranging from 3.6 to 2016 cm and pressures from 0.42 to 66 torrs. In fact, high pressures of 0, have also been used to derive selfbroadening coefficients and then experimentally obtained coefficients were included in new fits with much lower pressure. This procedure finally leads to a set of line strengths from the different spectra. Then various sets give between 4 and 7 different values for each line, taking into account the maximum and minimum absorption explained above. The final result for the intensity of each line is the weighted average obtained from different spectra. This procedure permits one to obtain at least a reasonable idea of the dispersion of the results, but does not avoid any systematic problems such as non well-located zero transmittance, for instance. But we believe that the precision of relative line strengths is 3.5%. For absolute accuracy, we have to include the problem of absolute calibration of ozone in the cell, as well as a hypothetic systematic zero-level transmittance problem. Then the absolute accuracy of intensities is 6%. Figure 1 corresponds to one example of the recorded spectra where resolution and signal/noise ratio may be observed. In this figure, 4 line strengths are shown to point out the range of clearly obtained line strengths. In this figure, where 8 lines appear, we note that only 2 lines are given in Table 3, as they are sufficiently isolated to derive good line strengths. But of course all observed lines are calculated in the final compilation obtained in this work. Figure 2 gives one example of a fit between observed and calculated transmittance. The residual obs-calc shows agreement and then gives an idea of the accuracy of retrieval parameters. Note that most of the lines have been fitted in primarily Doppler shape to avoid the problem of wings of lines in case of Lorentzian shape. Line positions CALCULATIONS Most of measured ozone lines which fall in the 5 pm range belong to the 2v,, v, + v3 and 2v, bands. Because the vibrational frequencies o, and o3 are close, the upper rotation-vibrational 0.005 cm-l 0.26 126.16 0.26 0.36 0.46 0.56 Fig. 1. Typical example of recorded spectrum n the 2126.16-2126.56 cm-’ range. The four observed line strengths are given in IO-*’ x cm-‘/mol cm-‘.  Absolute intensities of ozone spectral lines 343 zyxwvutsrqpon 100 Transmittance Spectral range 0.030 cm-l 2096.15266 1011165<-0001266 Kn 1.550+21 +OS Obs -Calc -0.5 0 Transmittance Fig. 2. Example of a fit between observed and calculated transmittance. Note that the residual obs-calc is on the order of 0.1%. states which correspond to these transitions are coupled by strong resonance interactions: Coriolis-type interactions between the levels of (002) and (101) and of (101) and (200), as well as the Darling-Dennison interaction between the levels of the (200) and (002) states.2A*8 here are few localized perturbations of v, + v3 lines which require an explicit account of the resonance with the 3v, “shadow band” to achieve the experimental accuracy for positions of these perturbed lines.9*‘0 For intensity calculations, the model of the triad of interacting states {(002), (lOl), 200)) was found satisfactory for the majority of transitions. For the purpose of this study, effective wavefunctions needed in the theoretical analysis of line strengths were calculated in the frame of the triad model and correspond to the following fitting of line positions: Number of fitted line positions 2421 Number of Hamiltonian parameters 52 Weighted (dimensionless) standard deviation 1.19 R.M.S. residual 0.118 mK The values of these Hamiltonian parameters will be presented together with a complete analysis of energy levels and line positions” which is beyond the scope of the present paper. Line intensities The 638 observed intensities have been measured by a least-squares fit technique, with a relative precision of 3.5% and absolute determination of about 6%. In order to make the intensity data reduction, we use the formalism of the effective dipole-moment operator (see the review by Camy-Peyret and Flaud” for more details): Pi ff=CCeg{oj9@Zm}9 {A, B} = AB BA. (1) Here Oj is a notation of elementary independent vibrational-rotational operators. 0;‘s are coefficients appearing in the expansion of the effective dipole-moment operator. aZs are the direction cosines, mZ, = 4,. QSRT 52,3-4 --I  344 A. BARBE t l Table I. Two sets of transition-moment constants recovered from the measured intensities. Operators A J in Eq(3) UPPer state Transition moment constants ’ pJ Value Eh-Ol- Value Error Set I Set II 002 002 002 0.702028E-2 0.904598E-8 -.131888E-4 0.24E-4 0.82E-8 101 101 101 101 101 -.175830E-2 0.81E-5 O.l8888lE-4 -.282232E-5 0.3359883-8 0.4082201-l 0.7787803-7 0.721990E-8 -. 545818E-5 O.l49334E-6 0.84E-8 0.28E-8 0.28E-7 0.83E-4 0.21E-7 0.293-8 0.94E-8 0.22E-7 0.704278E-2 O-243-4 O.S72178E-8 O.l7E-8 -.139830E-4 O.'fiOE-8 -.282857E-8 O-483-7 -.175520E-2 O.l2E-4 0.457312E-7 0.83E-8 -.112478E-5 O.l7E-8 O.l31473E-4 0.84E-8 -.258184E-5 0.28E-8 0.372373E-8 0.27E-7 0.4074'77E-1 0.50E-4 O.l10908E-8 0.20E-7 0.870834E-8 0.27E-8 -.898247E-5 O.lOE-5 O.l43979E-8 0.21E-7 FM5 residual 2.6% 2.4% Table 2. Statistics of the intensity fitting. 2”3 2”l “1 +v3 triad (total) Jaax, Kmax 43,12 54,lO 53,16 Number of data 53,16 96 263 279 638 Number of parameters 4 6 5 15 RMS 2.9 2.6 2.1 2.4  Absolute intensities of ozone spectral It is convenient’* to consider transition-moment operators lines “~2 defined by the equation 345 (2) The notation IO) stands for the ground vibration state, and ) V ) for upper vibration states of bands involved [in this paper (200), (101) and (002)]. A perturbation formulation leads to an expansion of a transition-moment operator (3) in terms of rotational operators Aj which are combinations of the direction cosines and of the angular-momentum components along the molecular axes. Parameters “pj are to be determined from experimental strengths. In the present paper we take into account terms up to the third order of a perturbation theory in Eqs. (l)-(3) according to the Amat-Nielsen ordering scheme both for A and B type bands (Table 1). The effective dipole-moment operator [Eq. (l)] is related to the srcinal dipole-moment by the same contact transformations as the effective triad Hamiltonian is related to the complete vibration-rotation one.“‘3 For this reason, in order to calculate line strengths one has to consider matrix elements of pea over effective wavefunctions. The latter are written as IV,, v2, I/,,J,K?,K)= 1 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJ o~cw,KYh (4) u= P) K where the {P } includes all vibrational states of the polyad under consideration. Here IV ) are harmonic oscillator wavefunctions, and I.Z, K, 7) are Wang functions. The coefficients C ;; were obtained simultaneously with vibration-rotation energies while fitting the line positions. The transition-moment constants “pL( were derived by a least-squares fit to measured line strengths using the expressions (l)-(4) and the GIP routineI for “inversed” spectroscopic problems. In Table 1, two sets of transition-moment constants for 2v,, vl + vl + v3 and 2v, bands, corresponding to 12 and 15 adjustable parameters, are presented. It is seen that observed line strengths are reproduced within the experimental accuracy. The statistics for each band separately is given in Table 2. Table 3 presents the list of 638 measured line intensities. In the last two columns, calculated intensities and relative discrepancies are displayed. Calculations for a few lines perturbed by resonance with 3v, band will be discussed separately. ‘O Because of limited space we were only able to include in this table those calculated lines which correspond to measured strengths. However in addition to this table, a more general line listing of the 2v,, vl + v3 and 2v, ozone bands (up to J < 80, K, c 22 for vl + v3 and up to J < 70 and K, < 20 for 2v, and 2v3) has been generated with an intensity cut-off of 1O-25 m-‘/molecule cm-‘. DISCUSSION We have been able to determine 15 effective dipole-moment parameters which result in a very satisfactory agreement between observed and calculated intensities: the overall r.m.s. residual is 2.4%. Table 4 gives the distribution of these residuals in comparison with that of the previous study.* Except for 1 weak line (which is the 30 8 22 t 31 7 25 transition of 2v,) all discrepancies do not exceed 7.2%. More than 85% of the line intensities are reproduced within 3.5% (which is the order of the experimental relative uncertainty) and more than 98% of the line intensities are reproduced within 6% (which is the order of the experimental absolute uncertainty). The histogram in Fig. 3 gives an idea of an overall coherency between measured and calculated line intensities for the previous’ and the present studies. On the other hand, Fig. 4, which shows 61/Z vs line frequencies, illustrates a coherency of previous transition-moment constants’ with the present experimental data.
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