Pressure Broadening, Shift, and Interference Effect for a Multiplet Line in the Rovibrational Anisotropic Stimulated Raman Spectrum of Molecular Oxygen

JOURNAL OF MOLECULAR SPECTROSCOPY ARTICLE NO.

176, 211–218 (1996)

0078

Pressure Broadening, Shift, and Interference Effect for a Multiplet Line in the Rovibrational Anisotropic Stimulated Raman Spectrum of Molecular Oxygen G. Millot, B. Lavorel, and G. Fanjoux Laboratoire de Physique de l’Universite´ de Bourgogne, CNRS, Faculte´ des Sciences Mirande, Universite´ de Bourgogne, B.P.138, Alle´e A. Savary, 21004 Dijon, France Received November 21, 1995

High-resolution stimulated inverse Raman spectroscopy has been applied to the study of collisional broadening, shifting, and line mixing for the OO(J, N Å 5) triplet line of the fundamental vibrational band of molecular oxygen. Accurate line broadening coefficients for the individual J components within the triplet have been measured for the first time and show a significant J dependence. The line broadening coefficients are larger than those previously obtained for unresolved pure rotational Raman lines. The additional broadening is expected to result from electronic spin relaxation. The pressure-induced line shift has been obtained for this line and compared to the value obtained for the fundamental Q branch. By applying the Rosenkranz perturbation treatment to the collisionally mixed components of the triplet line, we have been able to obtain an estimate of the coupling parameters. q 1996 Academic Press, Inc. INTRODUCTION

It has been demonstrated within these last years that coherent anti-Stokes Raman spectroscopy (CARS) is a versatile tool for temperature and concentration measurements in various gaseous media (1, 2). Among the probe molecules used, oxygen has been involved by CARS spectroscopy in many practical applications (3, 6). Collisional effects in the Raman Q branch of oxygen for self and water vapor collisions has been studied by stimulated Raman spectroscopy from a more fundamental point of view (7, 9). It results from these studies that oxygen may be confidently used as the probe molecule in CARS thermometry. However, in all works mentioned above, 16O2 has been treated with a 1Sg theory, as in the nitrogen molecule, in spite of the fact that the symmetry of its ground vibrational state of the electronic ground state is 3S0g . The electronic spin of 16O2 molecule is equal to one and consequently coupling of the electronic spin with the rotational angular momentum forms a triplet of states with total angular momentum J Å N, N { 1 where N is the rotational quantum number. N takes only odd values since the nuclear spin of the 16O oxygen atom is equal to zero. A rovibrational Raman spectrum results from transitions allowed by the selection rules DN Å 0, DJ Å 0 for isotropic scattering and DN Å 0, {2, DJ Å 0, {1, {2 for anisotropic scattering. The individual transitions are often identified with a= (N9), where X Å Q, S, O for DN Å 0, /2, 02 the notation Xa0 and a*, a9 Å 0, /, 0 for J Å N, N / 1, N 0 1, where 9 and * refer to the lower state and upper state, respectively. The individual transitions are also identified with the equivalent notation DNDJ(J, N), where J and N are quantum numbers for

the lower state. The strong isotropic Q branch of the fundamental vibrational band is a QQ branch. In the QQ branch the triplet structure is usually not resolved because of the extremely small differences between the transition frequencies. However, in a few particular cases, where a large pulse duration (10) or a molecular free-expansion jet (11) is used, the QQ(J, N) triplets can be partially resolved for N £ 3. But the very low pressure used in these experiments prevents any determination of collisional parameters. The differences between the transitions frequencies are much greater in the SS and OO branches and as a consequence the triplet structure can be resolved in these branches using standard high-resolution stimulated Raman spectroscopy (12). For the OO(J, 5) triplet the frequency spacing between lines is 0.074 cm01 and 0.031 cm01, whereas frequency separation with the other OO(J, N) triplets is greater than 10 cm01. So the lineshape study reduces to that of a single triplet and the influence of the neighboring triplets can be confidently neglected. The aim of this work is to analyze the collisional effects on the individual components of a OO(J, N) triplet. In this paper, we report the results of inverse Raman spectroscopy measurements on the OO(J, 5) triplet line in the fundamental vibrational band of 16O2. These experiments give self-broadened linewidths and line mixing coefficients of the three individual components, along with the lineshift of the whole triplet lines. A Rosenkranz perturbation treatment of line mixing is applied to the three closely spaced lines of the triplet. Following a description of the experimental procedure and the lineshape analysis, we present these results and compared them with previous Raman measurements and calculations on the Q branch.

211 0022-2852/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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FIG. 1. Schematic diagram of the high resolution stimulated Raman spectrometer.

EXPERIMENTAL DETAILS

The simplified schematic of the stimulated Raman spectrometer is shown on Fig. 1. The probe beam is supplied by a single frequency Ar/ laser tuned to 514.675 nm. This commercial Ar/ laser (Coherent Innova 90) was frequency stabilized by actively locking its frequency to a stabilized external Fabry–Pe´rot cavity. The stabilization reduces the line width to about 1 MHz and the frequency drift to typically 10 MHz per hour. So, during the course of a scan which takes a few minutes its frequency is very stable and only measured at the beginning and at the end of each scan. The small frequency drift is assumed to vary linearly in time. The probe laser power was 650 mW. A single-mode cw ring dye laser (Coherent CR-699) pulse amplified to à350 kW by three dye amplifiers (PDA-1) serves as the pump laser source. The pulsed dye amplifiers are pumped by the frequency-doubled output of a single-mode Nd:YAG laser (Quanta-Ray GCR-3). The pulse duration is 7 ns at a 25 Hz repetition rate. The line width of the resultant tunable pump laser is nearly limited by the Fourier transform of its pulse width and is equal to 57 MHz HWHM. The probe and pump beams are then combined by a dichroic mirror before entering a multipass sample cell. They are collinearly focused by a 750-mm focal length lens. The multipass cell, built with two 500-mm focal length concave spherical mirrors with a reflection coefficient greater than 99.5% in the 410–690 nm range, leads to a gain of about 20 on the Raman signal for 25 passes with respect to a single-pass cell and so compensates for the weakness of the O branch with respect to the

Q branch. The intensity of the probe beam is modulated with a mechanical chopper. Since the pump laser operates at a longer wavelength (558.684 nm) than the probe laser, the transient signal induced on the probe by the pulsed pump results in an absorption of the probe beam, i.e., as a Raman loss. A system of prisms and filters is used to separate the probe laser from the pump laser. The Raman signal is then measured with a fast photodiode and then amplified and integrated by a boxcar system. To compensate for fluctuations in the pump laser power a second detector measures the pump intensity. On the other hand, we assume that the Nd:YAG laser intensity is very stable during the time necessary to obtain the recording. Accurate values for the Raman shifts were determined using the same method described previously (13–14). A cw wavemeter is used to simultaneously measure the frequencies of the Ar/ probe laser and the cw dye laser at the beginning and at the end of the dye scan. A confocal Fabry– Pe´rot e´talon (300-MHz FSR) monitors the frequency of the dye laser as it is swept across the Raman line. Absolute wavenumber calibration of the Raman shift is then obtained with an accuracy of about 10 MHz. LINESHAPE ANALYSIS AND RESULTS

Figure 2 shows the energy levels involved in the Raman transitions of the OO(J, 5) triplet. The spin–spin and spin– rotation interactions lead to a level structure with the J Å N highest, and the J Å N { 1 levels lower by about 2

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SRS OF A MULTIPLET LINE OF O2

FIG. 2. Schematic representation of the energy levels for the OO(J, 5) transitions.

wavenumbers, and separated from each other by about 0.2 wavenumber. In order to obtain accurate values of isolated line-broadening and shift parameters, the lineshape analysis must be as precise as possible, with each physical effect which contributes to line broadening, shifting, and mixing taken correctly into account. For our experimental conditions, the main contribution to the line profile is homogeneous collisional broadening. At the lower limit of the pressure range, however, the Doppler effect with Dicke narrowing and the apparatus function should both be included in the profile. On the other hand, at the upper limit of the pressure, for the case of blended lines, line mixing due to inelastic energy transfer also needs to be taken into account. Collisions change the magnitude and direction of the rotational angular momentum of the optically active molecule and thereby mix the lines by transferring intensity from one line to another. When the Doppler and collisional effects are simultaneously present a reduction of the Doppler width appears due to velocitychanging collisions. This phenomenon, called the Dicke effect, can be confidently represented by a soft collision model such as the well-known Galatry function. The complex Galatry (CG) function can be expressed by the equation 1 CG(xj, yj, z) Å q p

S*

H

`

dtexp ixjt 0 yjt

0

JD

1 / 2 [1 0 zt 0 exp(0zt)] 2z

[1] ,

transition frequency of the Oa= D the Doppler a0(N9) line, with g* half-width at half-maximum (HWHM), Dj is the collisional frequency shift of the Oa= a0(N9) line (Dj Å Pdj), Gj is the collisional width (HWHM) of the Oa= a0(N9) line (Gj Å Pgj), and b Å (kT)/(2pcmD) is the effective frequency of velocitychanging collisions (elastic collisions), where m is the mass of the active molecule, and D is the optical diffusion coefficient. Since the velocity-changing collision rate is a kinetic effect, b is assumed to be independent of j, so that all lines are expected to have the same b. As the Dicke effect is very small for our spectra, the narrowing parameter b cannot be confidently adjusted. So b has been fixed to a previous estimate (7). On the other hand, the possible influence of line mixing which can appear at the higher pressures has been also considered. In the case of a small overlap, the Rosenkranz first-order perturbation is adequate and the lineshape profile can be written with reduced parameters in the form R(xj, yj, hj) Å

v 0 v j 0 Dj g*D

, yj Å

Gj g*D

,zÅ

b g*D

.

F(xj, yj, hj, z) Å

1 (Re CG(xj, yj, z) 0 hjIm CG(xj, yj, z)). p

S(xj, yj, hj, z) Å F(xj, yj, hj, z)∗G,

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[4]

where the sign ∗ characterizes the convolution product. The lineshape for the triplet is then simply the sum of the contributions given by spectral components, I(v) Å A ∑ IjS(xj, yj, hj, z) / B, j

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[3]

In the low pressure limit, when line mixing disappears, the dispersive contribution does not act (hj Å 0) and Eq. [3] corresponds to the usual Galatry profile. The apparatus function has been included in the lineshape profile as well by making a convolution between F and a Gaussian function G(1.9 1 1003 cm01 HWHM). The final individual line profile is thus

In these equations j denotes all the quantum numbers which characterize the transition (j å £9N9J9, £*N*J*). vj is the

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[2]

where mj Å 1/(xj 0 iyj) with xj Å (v 0 vj)/g*D, yj Å pgj/g*D, and hj Å pYj, where p is the pressure and Yj is the line mixing coefficient of the transition j. The decomposition of the Rosenkranz profile into individual Lorentzian and dispersive components has the advantage of simultaneously accounting for Dicke narrowing and line mixing effects through the following expression:

with the reduced parameters depending on the temperature T and pressure p, xj Å

1 (Im mj 0 hj Re mj), p

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MILLOT, LAVOREL, AND FANJOUX

TABLE 1 Wavenumbers and Relative Intensities of the OO(J, 5) Lines of the O2 Fundamental Band

Note. Numbers in parentheses are three standard deviations in units of the last digit quoted.

where Ij is the intensity of the j line, A the scale factor, and B a constant baseline. A nonlinear least-squares fitting routine with numerical derivatives is used to fit all parameters, i.e., the linewidths Gj, the perturbed frequencies vj / Dj, the intensities Ij, the line mixing coefficients Yj, the scale factor A, and the constant baseline B. In the first step of the interactive procedure, the line intensities and frequencies and the broadening coefficients have been fitted using spectra recorded in the pressure range 18.7–45.1 Torr. Quick fits are first carried out for a few spectra, leading to accurate estimations for the broadening coefficients. These estimations are then used as initial values for all spectra. During this first step, the line mixing coefficients Yj have been fixed to zero values. Thirtysix spectra have been used to determine the relative intensities and the absolute frequencies of the individual components. The averaged values for the intensity ratios and for the absolute frequencies are reported in Table 1 and compared with previous determinations. To simplify the notation 0 / the lines O0 (5), O00(5), O/ (5) are labelled 0, 0, / respectively. The absolute frequency represents the average unperturbed frequencies deduced from the observed frequencies by subtracting the collisional shift determined at higher pressure. The absolute frequencies obtained in this work are in very good agreement with those determined by Rouille´ et al. (12). The accuracy of our data is better due to the large number of data which have been averaged and due to the accurate lineshape analysis. / (5) lines with The relative intensities of the O00(5) and O/ 0 respect to the intensity of the O0(5) line are compared with Loe¨te’s calculations (15) assuming either Hund’s coupling case (b) or the intermediate case between Hund’s cases (a) and (b). Our observed relative intensities are in very good agreement with the calculations, in particular with those of

the intermediate case. However, deviation of the coupling scheme from the pure Hund’s case (b) has only a small effect. For the pressure range 216.9–1498 Torr line overlapping arises, so a convolution of the Rosenkranz profile with the Galatry function is necessary (Eq. [3] with hj x 0). Because it is very difficult to accurately adjust four parameters per line (vj / Dj, gj, Ij, Yj) due to strong correlations between them, the relative intensities Ij/I0 and the unperturbed frequencies vj of the triplet have been held fixed to the values previously determined at low pressure. In the same way, it is not possible to simultaneously adjust a pressure shift Dj and a line mixing coefficient Yj per line. As a consequence, only an overall collisional shift D has been adjusted for the three components. On the other hand, at the first order of approximation, the line mixing coefficients are related to the square of the matrix element of the polarizability tensor through the relation (16)

∑ rj(aj(2))2Yj Å 0,

where rj is the population density at thermodynamic equilibrium and aj the matrix element of the anisotropic polarizability a(2) for the j transition. Equation [6] can also be written as

∑ IjYj Å 0.

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[7]

j

By introducing the relative intensities we obtained Y0 Å

0I0 0I/ Y0 0 Y/ I0 I0

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[6]

j

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SRS OF A MULTIPLET LINE OF O2

FIG. 3. The OO(J, 5) triplet recorded at 295 K and 132.5 Torr. The calculated spectrum is obtained using a Galatry profile. The residual is given beneath the spectrum.

Thus Eq. [5] has been used to fit the experimental lineshape of the triplet with the following adjusted parameters: A, B, D, Y0, Y/. 0 The line mixing coefficient Y0 for the O0 (5) line has been obtained thanks to the relation (8). For the pressure range (45.1–216.9 Torr) over which must of the spectra have been recorded, line mixing is still negligible and Eq. [3] with hj Å 0 is also used to fit the experimental spectra. At each iteration in the nonlinear least-squares fitting procedure, the three parameters (position, intensity, width) of each line are determined. It was found that the relative intensities and the absolute frequencies initially determined in the first step of the procedure reproduce the observed spectra quite well, and, for each line, the final adjusted intensity and frequency were quite close to their initial estimated value. So most of our attention has been paid to the broadening coefficient. A typical observed spectrum at a pressure of 132.5 Torr is shown in Fig. 3, where calculated best-fit line profile is also plotted. Self-broadening coefficients have been measured for the three components of the triplet. The values are reported in Table 2; the error limits shown are {3s (99% confidence limit) from the least-squares fits of gj. From this part of the study, two important remarks must be made. First, the line broadening coefficients exhibit small but significant variations with J. So the assumption of constant line width within each triplet is incorrect. This result fortuitously confirms the assumption made by Brown and coworkers (17) in their tentative interpretation of a systematic deviation between experimental and theoretical intensities of the SS(N, J) lines in the pure rotational CARS spectrum of oxygen. But we think that this deviation is too large to be totally explained by a J-dependent linewidth variation

within each triplet. On the other hand, we find that the highJ width is narrower than that at low J, the opposite of the trend seen by Brown et al. We note that the highest J has the smaller line width, which is similar to the line width decrease usually observed with increasing N. The second remark concerns the magnitude of the broadening coefficients. The values reported in Table 2 are higher than the expected values from observed and calculated pure rotational Raman line width (7, 18, 19). The self-broadening coefficient of the S0(3) rotational Raman transition measured by Be´rard et al. at 293 K is 0.0499 cm01 atm01. This value has been extracted from experimental spectra recorded at high pressure (typically 20 atm) and with medium instrumental resolution (0.2 cm01 FWHM). So, in the conventional Raman experiment of Be´rard et al., the S0 triplets have not been resolved, since the individual components of the pure rotational lines are closely spaced, similarly to the vibrational SS(J, N) components. The S0(N) line broadening coefficients have been also calculated with the R–B semiclassical model (20) by different authors. The semiclassical calculated values are g Å 0.0458 cm01 atm01 for the S0(5) line at 295 K (7) and g Å 0.0459 cm01 atm01 for the S0(3) line at 295 K (19). In principle our rovibrational linewidths contains an elastic vibrational contribution, but the calculations of Looney and Rosasco suggest that this vibrational dephasing contribution to the linewidth at 295 K is less than 0.25 1 1003 cm01 atm01. So this vibrational contribution can reasonably be neglected, and consequently is not responsible for the large discrepancies between our broadening coefficients and those previously determined. Our data clearly show that the J linewidths are not only the sum of two terms, an inelastic term due to collisions which transfer rotational energy out of the rotational states involved in the optical transition and an elastic term due to collisions which reorient the molecule, but contain an additional contribution due to the relaxation of the electronic spin. In the semiclassical calculations, it is assumed that the intermolecular potential

TABLE 2 Line Broadening and Line Mixing Coefficients of the OO(J, 5) Lines of the O2 Fundamental Band

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FIG. 4. The OO(J, 5) triplet recorded at 295 K and 754.2 Torr. The dotted line is the best fit of the theoretical profile to the experimental data given by a sum of Lorentzian lines (a) and by a Rosenkranz profile (b). The residual spectrum has been magnified three times.

is independent of the electronic spin of the molecule. Therefore with this assumption collisions do not affect the magnitude or orientation of the spin angular momentum. This result will be confirmed with the line mixing analysis that we will describe now. The simulated spectra with Yj x 0 match the experimental data reasonably well, as can be seen in Fig. 4 (b) at a pressure of 754.2 Torr. At this pressure the Galatry function reduces to the Lorentzian. Figure 4 (a) shows the deviation from a sum of Lorentzian line shapes (Yj Å 0). The line mixing coefficients extracted from several experimental spectra recorded in the pressure range mentioned above (216.9–1498 Torr) are reported in Table 2. The accuracy of the Yj parameters not being very good, the results must be considered

essentially as estimates. The difficulties in obtaining accurate line mixing coefficients come from the fact that broadening due to a sudden change in the nuclear rotational angular momentum N has a dominant effect on the triplet line shape with respect to broadening and line mixing due to variation of the electronic spin during a collision. An interpretation of our results can be attempted starting from outlines developed by Gordon (21) and Corey et al. (22). The pressure broadening mechanisms strongly depend on whether the spin and rotation are coupled together strongly (Hund’s case (a)) or weakly (Hund’s case (b)). When the spin is coupled strongly to the molecular axes (case (a)), then during a collision the spin follows changes in the molecular rotation. In other words, the spin follows the molecular axes adiabatically. The condition for a strong coupling is that the electronic angular momentum (spin) precession frequency about the nuclear axes be large compared to the frequency of molecular rotation. When the spin is weakly coupled to the molecular axes (case (b)), then during a collision the spin is not affected by changes in the molecular rotational motion. The spin always sees the collision as a sudden change in the rotational angular momentum. The condition for a weak coupling is that the spin precession frequency be small compared to the molecular rotation frequency. Oxygen in its ground state, 3S0, can often be considered as an example of a pure case (b). In that case, collisions do not affect the magnitude and (or) orientation of the spin angular momentum, but cause a sudden change in the nuclear rotational angular momentum N. The total angular momentum J is only affected through the recoupling of N to S after the collisions. In a pure Hund’s case (b), we can introduce a collisional selection rule D(J 0 N) Å 0. For a given (J, N) level the number of relaxation channels for inelastic collisions is similar to that of a S/ molecule and there is no additional broadening and no J line mixing. Actually, oxygen in its electronic ground state is not discribable as a pure Hund’s case (b) molecule as it is observed from the point of view of line intensities. O2 is better represented by an intermediate case between (a) and (b) the deviation from a pure Hund’s case (b) description being nevertheless relatively small. We expect that this deviation is partially responsible for the additional broadening and for the line mixing that we observe for the J components of the OO(J, 5) triplet. Self-collisions with direct effects on the spin due to direct spin coupling may also contribute to broadening and mixing. Figure 5 shows that the pressure dependence of the overall frequency of the triplet exhibits good linearity, which proves that line mixing effect has been correctly taken into account in the lineshape profile. The overall pressure shift deduced from this pressure dependence is 0(4.1 { 0.4)1003 cm01 atm01, where the uncertainty represents three times

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nitude of the rotational angular momentum N and of elastic collisions which change the direction of N. Collisions which change the spin directly or indirectly through the coupling with N may be responsible for this additional broadening and for the line mixing within the triplet. The overall pressure shift coefficient is in good agreement with previous values obtained for Raman lines of the fundamental isotropic Q-branch. By application of the Rosenkranz perturbation theory for line mixing, we have been able to estimate the line mixing parameters. A high pressure spectrum (4.4 atm) clearly shows the influence of line mixing and demonstrates that a FIG. 5. Collision-induced line shift vs pressure. Let us recall that 1 mk Å 1003 cm01.

the standard deviation. This value is relatively close to the values measured for the isotropic Q-branch lines by stimulated Raman spectroscopy (7) (about 03.1 1 1003 cm01 atm01) and to the values measured by Fanjoux et al. (23) for the isotropic Q(15) line by high resolution CARS ((03.1 { 0.9)1003 cm01 atm01). Figure 6 displays the OO(J, 5) triplet recorded at 4.4 atm. Part (a) of this figure shows the large deviation from a sum of Lorentzian lineshapes, whereas part (b) gives results of the fit by assuming that the triplet is equivalent to a single line. We see that the triplet is very well reproduced by a single Lorentzian whose width is 0.0482 1003 cm01 atm01. This value is in good agreement with those obtained in a similar way by Be´rard et al. by fitting a single Lorentzian to observed spectra recorded at pressure around 20 atm (0.0499 1003 cm01 atm01). It is also much closer to the semiclassical calculations which neglect the influence of the electronic spin. We explain this effect by the presence of line mixing due to electronic spin relaxation which leads to a pure Lorentzian whose width decreases with the density and completely cancels in the high density limit. So the additional broadening observed at low pressure vanishes at high pressure due to line mixing effects and the lineshape profile comes only from changes of the rotational angular momentum N. CONCLUSION

The Raman self-broadening coefficients of a multiplet line of the fundamental vibrational band molecular oxygen have been measured for the first time. The data show a J dependence and clearly evidence the presence of an additional source of broadening that we attribute to the spin relaxation. It seems clear from this work that the J resolved line broadening coefficients cannot be simply accounted for by the contributions of inelastic collisions which changes the mag-

FIG. 6. The OO(J, 5) triplet recorded at 295 K and 4.4 atm. The solid curve gives the best fit to the experimental data for a sum of Lorentzian lines (a) and of a single Lorentzian line (b). In case (a), the individual line parameters (positions, widths, intensities) have been fixed to the values determined at low pressure (p õ 216.9 Torr). In case (b), the parameters of the single line are adjusted.

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single Lorentzian matches the experimental spectra very well with a width much smaller than those obtained at low pressure for the individual components. This explains the discrepancy between our J resolved Raman line broadening coefficients and high pressure rotational coefficients measured with low resolution. ACKNOWLEDGMENTS The authors thank G. Rouille´ for providing his high pressure multipass cell. The authors express also their thanks and appreciation to Y. Avignon for her technical assistance. The Centre National de la Recherche Scientifique, Paris, the Ministe`re de l’Education Nationale, and the Conseil Re´gional de Bourgogne are gratefully acknowledged for their financial support of this work.

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