Bandshapes and dipole correlation functions for the first overtone of CO compressed by N2

J Quant Spectrow Radlat Trans[erVol 27 No 2, pp 131-1401982

0022-4073/82/020131-1050300]0 © 1982PergamonPressLid

Printedm GreatBritain

BANDSHAPES

AND DIPOLE CORRELATION FUNCTIONS FOR THE FIRST OVERTONE OF CO COMPRESSED

B Y N2

J-P. BOUANICH Laboratoire d'lnfrarouge, Assocl~ au C N R S, Umverslt~ de Pans-Sud, Bfitiment 350, 91405 Orsay, France (Received 23 June 1981)

Abstraet--lnfrared spectra of the first overtone absorption band of CO compressed by N2 at pressures up to nearly 1000bar have been stud~ed at room temperature The integrated intensities, as well as the wavenumbers of the maximum absorption for the P- and R-branches and of the minimum absorphon between these branches, have been measured as functions of the N2 density The dipole moment autocorrelatmn function has been used to assess the Gordon J-diffusion model and the semvclassical M-model The normalized band contours are calculated by summing the absorption coefficients for the pressure-broadened rotatmnal lines with a modified Lorentz shape derived from an analysis of individual lines Thts model gives reasonable agreement with experiments for densltms below 200Am The discrepancy between calculated and experimental bandshapes, which increases with density, may be caused by strong overlappmg effects and a probable nonhnear variation of the llnewldths with density Consideration of interferences between adjacent rotational hnes in the frame of the impact approximation would not be sufficmnt to provide sahsfactory agreement with the experimentally observed band contours

1 INTRODUCTION

Infrared spectra of CO perturbed by N2 have been studied by several authors I-4 in the fundamental and the overtone at relatwely low pressures to obtam the widths of individual lines. Observations of the spectra have been reported at high pressures and low temperatures by Vu et al. 5 In a recent study, 6 the fundamental band intensities and contours for CO compressed by Ar in gas and hquid phases have been calculated from classical molecular dynamics with the use of quantum corrections. We have previously analyzed the bandshapes of the pure CO first overtone for pressures up to 104.5 bar 7 The bandprofiles of CO compressed by N2, which are almost identical to those of pure CO, have been inveshgated over a wider pressure range The analysis of correlation functions, which are obtained from Fourier transformations of the band contours, can provide informations about the rotational motions of the molecules. Among the theoretical models used for predictmg the correlation functions of compressed N208 and CO, 7 the best, which are considered here, are the classical J-rotational diffusion model of Gordon 9 and the semi-classical M-model lo A bandprofile cannot be considered to be the sum of Lorentz pressure-broadened individual lines for two reasons' the non-addihvtty effects due to overlapping hues Is and the influence of the finite duration of colhslons. I~ For spectra of self-perturbed CO, we have developed an empirical model 7 which involves summing of individual lines with modified Lorentz profiles and we have obtained a good representation for the band contours For CO-N2, we first analyze the shape of individual lines at low pressure and then assess the same model for representation of the bandprofile in a large density range. Finally, we determine hue-interference effects, which are taken into account tmplicttly m our model 2 EXPERIMENTAL PROCEDURE

The mixtures CO + N2 were introduced in a high pressure cell ~3with an effective absorbing pathlength of 226.5 cm. We used pressures of 0.091 and 0.114 bar for CO. For each pressure of CO, N2 was added in stages to about 20, 40, 60, 100, 150, 200, 400, 600, and 970 bar. The pressures were measured with Bourdon tube gauges having an accuracy of 0.5% of full scale The temperature was kept constant at 296_+ 1 K The spectra were recorded on a Czerny-type spectrometer with a resolution (full width at. half-height of the apparatus function) of about 0 8 cm -~. Except for the pressure of 20bar, for which the bandshapes were obtained from a deconvolution method, ~4 this spectral slitwidth is sufficiently small to avoid instrumental 131

132

J-P BOUANICH

corrections Emission lines of mercury in higher orders were used to calibrate the absorption spectra The densities of N2 were calculated by using the equation of state obtained by Jacobsen and StewartJ s These densities are expressed either in Amagat units d or in practical units 8 defined by 8 = = latm, T = 296 K), where n is the number of N2 moles per unit volume.

n(p, T)/n(p

3 INTENSITY AND WAVENUMBER MEASUREMENTS The integrated absorption coefficient S is defined as

kc00~]j 'd~, s= ) fb~.dk(00)[1-exp (-koT]

(1)

where l is the optical pathlength and k(~) is the measured absorption coefficient At room temperature, the factor exp is negligible for the overtone band Induced absorption is proportional to the product of the CO and N2 densities and should be comparable to the induced first overtone band of pure N2; 16 It ts estimated to be quite negligible. Thus, the intensity of the recorded bands should be equal to the pure CO band intensity and, therefore, independent of the N2 density. Indeed, we find (Table 1) that the intensity obtained per unit density of CO, So, increases with N2 density up to about 300Am. This result cannot be explained by experimental error in So, which is eshmated to be 5% and mainly caused by uncertainties in the determination of the baseline. The wavenumbers of the maximum absorption for the P- and R-branches, as well as for the minimum absorption or,, corresponding to the band center, are evaluated from synthetic bands obtained by summing the rotational lines with a modified Lorentz shape (see Section 5) The wavenumbers of these lines are calculated from the frequencies of the unperturbed CO lines 17 and from the very small L-dependent hneshifts estimated for J. < 2 0 in Ref. 4 We have assumed that these hneshlfts are equal to a constant value of - 0 0038 cm -~ atm -1 for J, >i 20 and are proportional to the density ~5. The results are compared with experimental wavenumbers (Table 1) The large uncertainty m o'm and the peak of the P-branch at d - 4 5 4 Am, 2 and 1.5 cm 1, respectively, are explained by a fiat P-branch and a very shallow band center Except for the two highest densities, reasonable agreement is obtained in the P-branch and the band center. As we shall see, large discrepancies arise between calculated and experimental bandshapes for d > 200 Am so that comparison between wavenumbers is less significant at high density: for example, at d - 454 Am, the calculated band does not present a maximum in the P-branch nor a minimum in the band center As m the case of compressed CO, 7 the peak of the R-branch is notably displaced from the calculated wavenumber at high density_

(-hctr[koT)

4 DIPOLE MOMENT CORRELATION FUNCTIONS The dipole moment correlation function ~b(t) is determined experimentally by the real part of the Fourier transform of the normalized spectral densay I(tr), VlZ, ~(t) = fb~,d I(cr) COS 2rrc(o" -- ~s)t do',

(2)

where the origin considered for each recorded band, ~rs, is slightly different from the band center 000,7 and I(tr) is given by

/(tr) = k(~)00 l/fhand k(o')00-J do-.

(3)

The correlation functions are calculated by using the classical J- and semi-classical Mrotational diffusion models. These models are characterized by the adjustable correlation time 7j for the rotational angular momentum Here, ~'j is expressed in reduced units of where Im is the moment of inertia of the CO molecule (at 296 K, I ps = 5 298 reduced units). Details concerning the mathematical expressions used to derive the calculated correlation functions are gwen in Ref. 8

(lm[ksT)~n,

center

,~2~cf

Equatlon

experlmental calculated

R - branch

experlmentai calculated

Band

experimental calculaaed

P - branch

S O (cm -2. Am -l )

d(Am)

(9) ]

2±0,5 6

00l

4287 8±0 5 4288 2

4259 8±0 5 4259,9

4231 423t

I 85

18,5

1±0 5 75

O 02

4287 8±05 4288 3

4260 4259

4231f0,5 4231 6

I 90

37

[

2±0 7 6

0 05

4288 3±0 5 4288 8

4 2 5 9 5Z0 7 4259,5

4231 4231

I 95

55

7±0 7 9

4±0 9 5

97

O 2

4288 2±0 5 4289 7

h258 4258

423I 4231

I

92

/

1

4287 6± 0 6 4290 4

4257±I 4257.3

422%5±0 4230

2 02

172

1

4286.5±0 4291.4

4254 2±1 4253.3

4228,3±1 4228 6

2.07

295

7

i

I

3

1

4284,7±0 4291

7

4 2 5 3 4±1 4 4248 5

4 2 2 8 4±1 4230,9

20l

371

Table 1 Band intensity, experimental and calculated wavenumbers (m C ~ -1) Of maximum absorptton for the Pand R-branches and the minimum absorpUon at the band center Each experimental value corresponds to an average of four experiments carried out around the specified densay

5

I

4282 5±0 8 4289 5

4249±2

4230,I±I

20l

454

o

8

O

¢m.

=

134

J.-P. BOUANICH

The Tj values are obtained by fitting the correlation functions to experimental ~b(t), especially around the minimum of the curves. For d > 50 Am, the Tj values, which are found to be smaller for the J-model than for the corresponding M-model, obey roughly the relations ~ j - i = 1.25 x 10-3d (Am) for the J-model and ~'7 ~= 0.8 × 10-3d (Am) for the M-model. The semi-classical M-model is generally better than the classical J-model, which is not surprising since, in the former, the intensity and frequency distributions are treated quantum-mechanically. For densities of 18.5 Am (Fig. la) and 37 Am, these models provide satisfactory descriptions of the correlation functions, except between 0.6 and 0.75 ps, For the densities 55-172 Am, the agreement is good up to 0.8 ps (Fig. lb); t h e d i s c r e p a n c y which appears at longer times, is probably caused 7 by large spacing between rotational levels of CO. For higher densities, the theoretical ~b(t) curves are located above the experimental curves in the short time range t < 0.3 ps (Fig. 2a); for d - 450 Am, the experimental curve falls between the theoretical curves at t > 0.5 ps (Fig. 2b).

(t)

10

c~(t)

08

O6 (o)

(b)

o~

o2

t

o~ 02 o41

06]

081 '11t(ps)

\ 021

04

06

08

] t(ns)

-o 2

Fig 1. Correlattonfunctions for CO compressed by N2 at 18.5Am (a) and 92 Am (b), - - , experimental curve, +, classical J-diffusion model with r: = 35 (a) and TI= 9 (b); o, semt-classlcalM-diffusionmodel with ~-j= 40 (a) and cj = 14 (b)

10 08

~(t)

o.81° k (~(t) O6

06

Co) o/, o21

O~

°t.

01.

-o

(b)

06

0.8_~_

t (ps)_

,.~o~ o,6 o~.~l.,~/ °e°-

-0 2

Fig 2 Correlationfunctions for CO compressed by N2 at 371 Am (a) and 454 Am (b), , experimental curve, +, classical J-diffusion model with rj = 2 (a) and rl = 16 (b), o, semi-classicalM-diffusionmodel with ~-j = 3 5 (a) and ~-j = 2 8 Co).

Bandshapes and dipole correlation functions

135

5 CALCULATION OF THE BANDSHAPES

Experimental lineshape We have first studied the shape of the pressure-broadened individual hnes In 1971, ~s we performed experiments in the 0 - 2 band of CO (pressure = 60 torr) compressed by N2 at about 3 and 3.3 bar in a 1 m cell with a Czerny-type spectrometer (resolution 0.07 cm -j) Several hnes were chosen in the P-branch, where overlapping is negligible; these have been analyzed in the spectral range o-,/+ Ao. with A o . - 5T,/. Here, o.0 is the wavenumber of the hne i--)/including the frequency shift and y,/is the halfwidth at half-intensity for this line. The line contours were deduced from a deconvolution method j4 and were found to be asymmetrical, as for pure CO The absorption coefficient k,t(~r + ) corresponding to o-,/+ Act is slightly greater than k,t(~- ). Comparison between the symmetrized absorption coefficient of a deconvoluted line and a Lorentz contour with the same height and w~dth shows the following features in the region Io ' - o.,:l < 3',t, the deconvoluted profile is slightly narrower than the Lorentz profile; in the region Y,/<~lo.-o.,/l<~2Y,/, the agreement 1s satisfactory; in the wings Io--o.,/l>2T,/, the deconvoluted profile generally decreases faster than the Lorentz shape. The absorption coefficient of a pressure-broadened hne t ~ . f may be expressed as the product

k,r(o.) = k(o.,t) × ~,/(o-),

(4)

where the general form function 5~(o-) used is 7 ~t(o-) = exp [-a(Io- - o-,tl/K,t) , ]K,t/[K,I 2 2 + (o- - o-,t)2]

(5)

Here, a and n are adjustable parameters and K,/is given, in good approximation for a < 0.5, by 1 Ol

K,/ = Y,I (1 - ~ /

.

(6)

The average profile of several symmet~'ic hnes in the first overtone band of CO perturbed by N2 may be fitted with n = 2 5 and a = 0.006. The agreement is nearly as good as with the Lorentz shape in the central range of the lines but better in the wings.

The models 0 and II The spectral density I,i(tr) for an mdwidual hne is related to the vibrational dipole moment matrix element Ro~~ by

87r 3 . Jm] F ( m ) l R ~ 2 1 E;q(o.) LtCo.) = ~ No/, 2J, + 1 °' -C K, t '

(7)

where m = - J , for a P-line and m = J, + 1 for a R-line, F ( m ) IS the vibration-rotation coupling function, C is a normahzation factor such that C = f ~¢(o.)x K~ J do-; Nov, is the imtial level population for CO (the final level can be neglected at room temperature) and is given by No/, = Nop, = No(2J, + 1) exp [-E(J,)/ksT]/Q,,

(8)

where p, is the matrix density for CO, No the number denstty of CO molecules, Qr the rotational partition function, and E(J,) = [ B o - DoJ,(J, + l)]J,(J, + 1) is the rotational energy. To determine the band contours, we have considered the sum of pressure-broadened lines with spectral densities given by Eq. (7) and a Lorentz shape (model 0), as well as a modified Lorentz shape [see Eq. (5)] with n = 2 (model II). The general form used for the normahzed

J-P

136

BOUAN1CFI

spectral density of the band is

I(o0 = 1 j~ P,R exp [-E(J,)/knT]F(m)lm[ exp [ - a . \(~-E-~"]K,/ ]]

K,!

x

/

2 (~- ~,A2/ r,/+

2,.,,

P ~

exp[-E(J,)/kBT]F(m)[ml,

(9)

where the summation over 3", 1s extended from 1 to 43 m the P-branch (J/= J, - 1) and from 0 to 42 in the R-branch ( J / = J, + 1). For model 0, C = ¢r, a, = 0 and K , / = 3',t For model II, n = 2, C = [1 - ~(a2u2)]~ • exp a2 with ¢(x) = ~

exp ( - t 2) dt

1 + 2a 2

K,/ = 3",f l + a2.

and

It should be noted that the lineshapes correspondmg to as = 1 are close to a gaussian line, which we consider as a limit profile. Therefore, we shall not use ~2 values greater than 1. For a2 = 1 we obtain by using Eq (6), [K,/[3",/] = 1.5, instead of 1.634 the true value of this ratio. The vibration-rotation coupling function used for the first overtone band is ~9 F(m)=l+54x10

3 m + 4 x 1 0 - S m 2.

(10)

We have assumed that this functton remains valid whatever the N2 denstty may be, i.e. the molecular interactions CO-N2 have no influence on the intensities of individual lines. The halfwidths of the lines 3",/ are assumed to be proportional to the density such that y¢ = 3"o& where 3'o refers to halfwidths measured at 1 atm and 296 K. From experiments at 299 K, 4 we have deduced experimental data for yo(m) correspondmg to 296 K (Fig. 3). Since 43 rotatmnal .L levels of CO are taken into account, we have extrapolated the smooth curve fitting the halfwidths up to Iml = 43 For the extrapolation, we have assumed that, at high Iml, the true halfwtdths are slightly larger than the calculated values. This calculation has been carried out on the basts of the Anderson-Tsao-Curnutte theory by considering the dispersion potential -4Ej:(tr~dr)63"jP2(cos O) with 2° tq2 = 3.756 ,~, ~12 = 97 62 K, 3'1 = 0.167 (the subscript 1 refers to CO and 2 to N2) and the electrostatic contributions with #~ = 0 l12D, Q~ = 2 . 0 5 D . ~ , fh = 3 5D ,~2, 02 = 1.75D. ,~. For the interruption function S2(b), we have used the following cutoff procedures' S2(b ~< b0) = 1 for impact parameters bo [defined by S2(bo) = 1] greater than the distance of closest approach d,,, and S2(b < de) = 1.

Line interference effects The formahsm which ts briefly presented here has been developed by Bonamy et a111 in the fast modulation hypothesis (some of the notation of Ref. 11 has been changed). Another approximation, the initial chaos hypothests, implies that, at the initial t~me of the mteraction L ( crn-1 ~tm-~) 0438 0.07 005 005 004 003 I

I

I

I

I

I

I

I

5

10

35

20

25

30

35

40

Irni

Fig 3 CO hne halfwtdths broadened by N2, x, calculated values, -~ experimental values, --, smoothed

and extrapolated data

B a n d s h a p e s and dipole correlation f u n c t i o n s

137

matter-radiation, the density operator p~2(t = 0) can be expressed as the product p~(0)p2(0), neglecting thus the coupling V~2 between the matrix densities of the actwe and perturber molecules. The expression for the band contour, which includes the nonadditivity effects resulting from interference of overlapping lines, Is

l(tr) ~ Re ~, /z,1P,f(o~),

(11)

where lz,f is the reduced dipole matrix element for the active molecule and is related to the vibrational transition moment R ~ by

I/z'tl2 = IR~'I2F(m) 2~?~+ 1'

(12)

and P,f(o) Is obtained by an inversion of the matrix relation

r['

P,'r(°') G,'r.,I( tr ) = P,/~i,;

(I 3)

G,,r,,l(o) is derived from the elements of the non-diagonal relaxation matrix (A)8, i e G,,r.,r(a) = i(# - o-,r)8,,,+r - (( i'['I(A)BliD).

(14)

Here, tr,l is the ¢wavenumber of the unperturbed hne i~[ The matrix elements of (A)B .are . obtained by separating the vibration-rotation degrees of freedom from the classical degrees (translation), performing a classical average over the translation, and limiting the treatment to the second order in the molecular interaction potentml. They can be expressed in terms of d,~ the lineshift, Y,I, and the cross correlation term Y,I.,'r', i.e.

(( i' f'I(A)Bl iD) = -(Y,f -id,r)8,,'8r - 7,'r, ,i( 1 - 8,,,~)

(15)

The cross correlation terms have been evaluated under the same conditions as in Ref. 7 by using approximations in the description of collisions (straight line trajectory, relative constant velocity), which requires a cutoff procedure. We have considered the anisotropic intermolecular potential used for the halfwidth calculation of isolated lines, which involves electrostatic interactions produced by the quadrupolar moment of N2 and the dipolar, quadrupolar and octopolar moments of CO. This potential gives rise to couplings between lines such as AJ =J'-J, = - 1 , ---2, -+3 corresponding to the interactions /Zl- Q2, Q I - Q2 and dispersion, O1 - f12, respectwely. The normalized profiles have been generated by considering experimental lineshifts, widths extrapolated up to Iml = 43, as well as calculated cross correlation terms and assuming that 3',t, ~',,',~', and d,I are proportional to the density 8. 6 RESULTS AND DISCUSSION Comparisons between experimental and calculated normalized spectral densities I(~r) for the models 0 and II are illustrated in Figs. 4-6. It should be noted that the observed bands spread out over 220-280cm-' (the extension of the bands increases roughly with the N2 density), whereas the calculated bands with the same intensity extend over the entire frequency range. As may be seen in Figs. 4 and 5, a discrepancy appears between experimental and calculated bandshapes for Lorentzian lines (model 0) and Increases with density The calculated spectral densities are lowered in the central range of the P- and R-branches and enhanced in the wings and in the centers of the bands The results are greatly improved with model II by adjusting the a2 parameter. In the density range 18-172 Am, the fitted a2 values vary from 0.01 to 1 (Table 1). On the whole, this model yields a reasonable description of the experimental results, especially in the wings of the band (Figs. 4 and 5). However, the depth between the two branches is shghtly more pronounced than the experimental depth and the calculated spectra remain generally lowered around the peaks of QSRT VoL 27, No 2 ~

J-P ]]OUANICH

138 I (o),,103

_16 10-

I

I I

I

I

I

i

I

/,200

I

i

4300

4250

o( cm -1 )

Fig 4_ Spectral densities for CO compressed by N2, (a) d = 36 5 Am (,5 = 39_5),(b) d = 53 7 Am (8 = 58_2), --, experimental data, ×, model 0 (sum of Iorentzlans), o, model II with a2 = 0 02 (a) and a2 = 0 05 (b)

I (0)~103

~

.

10

5

j.

,o

"7:: .I-"

/

i,.__-+

I

I

I

Ii

/,1200

I

I

I

I

I I /,250

°

I

I

I

I 4300

a(cm -1 )

Fig 5 Spectral densities for CO compressed by N2, (a) d = 90 4 Am (8 = 98), (b) d = 171 9 Am (,5 = 186 3), --. experimental data, ×, model 0, o, model II with a2=02 (a) and a2 = 1 (b), models including overlapping effects w,th AJ = _+1,-+2, -+3 A and AJ = -+1, -+2 •

the P- and R-branches. Compared to the calculated values, the observed R-branch exhibits a noticeable red shift which increases with density. This frequency shift c a n n o t be explained by possible non-vahdlty of the vibration-rotation coupling function F ( m ) for the 0-2 band of CO perturbed by N2. Use of F ( m ) = 1 for d = 172 Am leads only to a slight reduction of the frequency shift for o" > 4290 cm-L At higher densities, large discrepancies arise between the experimental band contours and those calculated with model II for a 2 = 1 (Fig. 6). In our models, we have assumed binary collisions and a linear density dependence of line broadening. These assumptions are probably no longer valid. Indeed, a non-linear behaviour for pure rotational lines of H C I broadened by Ar at densities ranging from 100 to 480 Am has been observed by Frenkel et al. 2~ and interpreted on the basis of statistical correlations between the perturber atoms. ~2 The slight non-hnearity of the linewidths with density arising from the use of Eq. 6 for a s = 1 is not sufficient. A calculation carried out by using model II with'8 = 350 instead of 490.6 for the determination of linewldths gives a better description of the observed band contour corresponding to d =

139

Bandshapes and dipole correlatton functions I/o)-~o 3

Ib) 5-

•

•

i

o

t

J

Q

,

o I

I

1

~200

A

I

I

I

I

/.250

L

l

J

I

I

t*300

I

a(cm-1)

A ~

• -

Fig 6. Spectral densities for CO compressed by N2, (a) d = 297 1Am (~ = 322), (b) d = 452 6 Am (6 = 490 6), --, experimental data, ×, model 0; o, model I1 with a2 = 1,., model 1I with az = I and 8 = 350, A, model including overlappingeffects w~thAJ = +1, _+2,_+3

452 6 Am (Fig. 6b). the experimental relative intensity for the peaks of the P- and R-branches and for the band center are well represented. However the experimental R-branch is notably narrower and shifted. The narrowing effect associated with an enhancement m the central range of the band, which appears from comparison with bandshapes obtained from model 0, is stronger than that predtcted by model II, it is probably caused by strong correlations between adjacent rotational hnes The normalized profiles deduced from evaluation of the cross-term contributions (see Section 5) corresponding to n J = +_1, _+2, _+3 give, for d < 300 Am, satisfactory agreement in the wings and the summits of the P- and R-branches (Figs 5 and 6a). The agreement is less good than that obtained with model II for am and the maximum absorption wavenumber of the P-branch, but the frequency shift between experimental and calculated R-branches is notably reduced However, the spectral density at the band center is lowered too much Thus, the cross-term contributions derived from an arbitrary cutoff procedure may have been overestimated for small J values Therefore, we have considered the nonaddlttvity effects arising only from the hne couplings AJ=_+I, _+2 caused by the mterachons # j - Q 2 , Q ~ - Q 2 and the dispersion energy As may be seen in F~g. 5, these effects have been reduced but the agreement around the band center is still unsatisfactory. Thus, whatever the cross-term contributions may be, it seems that consideration of interference effects within the ~mpact approximahon cannot yield satisfactory band profiles. Assuming that, for the densities considered, absorption of pressure-induced Q-branch is negligible, the discrepancy between calculated and experimental normalized spectral densities may be caused by non-vahdity of the initial chaos hypothesis for the rotational level J = 0 ~2 and/or by the influence of the finite duration of colhsions It should be noted that the calculated spectra exhibit the same behaviour at lower dens~hes, where quadratic contributions m density are probably qutte negligible We estimate that a full treatment must, at least, take into account simultaneously the finite duration of collisions and the nonaddltivity effects 7 CONCLUSION We have found that the intensity for the first overtone band of CO compressed by N2 increases with the N2 density. Except for the R-branch, experimental and calculated wavenumbers are in good agreement for d < 300Am The correlation functions have been approximately described with the M- and J-models by fitting the correlation times z~ for the rotational angular momentum In first approximation, the reciprocal zj values appear to vary hnearly with density. Model II has been successfully used to describe the bandshapes at N2 densities up to nearly 200 Am At higher densities, the band contours cannot be considered to

140

J-P BOUANICH

be the simple s u m of p r e s s u r e - b r o a d e n e d individual lines, w h a t e v e r the profile a d o p t e d for these lines m a y be, b e c a u s e of s t r o n g o v e r l a p p i n g effects and a n o n l i n e a r d e n s i t y d e p e n d e n c e of hnewidths.

Acknowledgement--The author Is mdepted to Mrs A Jean-Louis for her contributions in the spectral analysis REFERENCES 1 T C James and E K Plyler, J Chem Phys 40, 221 (1%4) 2_ D A Draegert and D Wdhams, J Opt Soc Am 58, 1399 (1%8) 3 J P Bouamch and C Haeusler, JQSRT 12, 695 (1972) 4 J P Bouamch and C Brodbeck, JQSRT 13, 1 (1973) 5 H Vu, M R Atwood and B Vodar, J Chem Phys 38, 2671 (1%3) 6 P H Berens and K R Wilson, J Chem Phys 74, 4872 (1981) 7 J P Bouamch, Nguyen-Van-Thanh, and H Strapehas, JQSRT 26, 53 (1981) 8 Nguyen-Van-Thanh, J P Bouamch, and I RossL Molec Phys 40, 869 (1980) 9 R G Gordon, J Chem Phys 44, 1830 (1%6) 10 T E EaglEs and R E D McClung, J Chem Phys 61, 4070 (1974) 11 J Bonamy, L Bonamy, and D Robert, J Chem Phys 67, 4441 (1977) 12 C Boulet, Th~se de Doctorat ~s-Sclences Physiques, Umverslt~ de Parls-Sud (1979) 13 C Brodbeck, J P Bouanlch, P Flgul~re, and H Szwarc, J Chem Phys 74, 77 (1981) 14, R N Jones, R Venkataraghavan, and J W Hopkins, Spectrochlm. Acta 23A, 925,941 (1%7) 15 R. T Jacobsen and R B Stewart, J Phys Chem Re[ Data 2, 757 (1973) 16 M M Shapiro and H P Gush, Can J Phys 44, 949 (1%6) 17 A W Mantz and J P Madlard, J_ Molec Spectrosc 73, 466 (1974) 18 J P Bouamch, Th~se de Doctorat ~s-Sclences Physiques, Unlverslt6 Paris VI (1973) 19 C L Korb, R H Hunt and E K Plyler, J Chem Phys 48, 4252 (1%8) 20 J O H~rschfelder, C F Curtlss, and R B Bird, Molecular Theory o[ Gases and Liquids Wiley, New York (1%7) 21 D Frenkel, D J Gravesteyn, and J van der Elsken, Chem Phys Lett_ 40, 9 (1976) 22 D Frenkel and J van der Elsken, J Chem Phys 67. 4243 (1977)