- Email: [email protected]
Line strengths and self-broadened linewidths of N2O in the 2-μm region
JOURNAL
OF
MOLECULAR
SPECTROSCOPY
85,
205-214
(1981)
Line Strengths and Self-Broadened Linewidths N,O in the 2-pm Region 24°0-OOo0
and 01’2-OOOO
N. LACOME AND Laboratoire
of
Transitions
A. LEVY
d’lnfrarouge. AssociC au CNRS. UniversitP de Paris-Sud, Bdtiment 350, ORSAY CEDEX 91405, France
The strengths and self-broadened linewidths of the parallel 24°0-W0 and perpendicular 01’2-0000 bands of N,O have been measured with a precision better than 3%, using a deconvolution procedure. For both transitions, the coefficient of the vibration-rotation interaction polynomial, the values of the rotationless dipolar transition moment, and the band intensity have been calculated from the line strengths. For the total intensity the values found are S%$l = (1.325 -+ 0.021) x IO-* cm-“,atm-’ and Sgj,Li= (1.209 -C 0.018) x 10m2cm-*.atm-I. INTRODUCTION
Absorption parameters of N,O in the very near IR are not adequately known. Wavelengths measurements have been performed (1) with good precision but intensity data are more scarce (2-8). Therefore, using a classical spectrometer of moderate resolution, strengths and widths of the lines in the 40°0-OOOOand 32°0-OOo0 transitions have been systematically measured. All data have been obtained by a deconvolution method, which has been described previously (9). This is, in fact, a preliminary study carried on with the view of obtaining accurate values of the line parameters (strengths, widths and peak absorption values) that could be used later in theoretical calculations of band shapes under high pressure. In a recent paper (10) the influence of line overlapping on the shape of NzO bands was analyzed in detail by making use of the “low-pressure” constants. In the present work, we perform the analysis of some of the remaining bands of N,O in the 2-pm region; namely the 24°0-OOo0 and 01’2-OOOOtransitions. The 24°0-OOo0 transition is a parallel band belonging to the 40°0-OOOOpentad. It is sometimes denoted (40°0-OOoOo)111. The (40°0-OOoO)1and (40°0-OOoO)11components have been previously analyzed with the same method (9). The 01’2~OOOO transition is the neighbouring perpendicular band. Only lines of the P and R branches have been measured; the lines of the Q branch are too close to allow measurements in this pressure range with the apparatus used in this study. From experimental intensity data, the values of the rotationless vibration transition moment have been calculated as well as the expansion of the vibration-rotation interaction factor. Concerning the self-broadened linewidths, the obtained values are very close to those found for the other transitions of N,O and no significant deviation between different vibrational bands can be pointed out. 205
0022-2852/81/010205-10$02.00/O Copyright All rights
0 1981 by Academic of reproduction
Press,
in any form
Inc. reserved.
206
LACOME
AND LEVY
TABLE
I
Experimental Conditions
0112-OOOO band
24°0-OOo0 band
500 torr
600 torr
375 torr
P36-R36
P37-P3
P30-P8 Rl-R4
Pll-R34
P43-P3
P32-R12 R3-R21 P27-PlO Rl-R19
EXPERIMENTAL
DETAILS
Spectra of the two transitions have been recorded using a Czemy-Turner-type classical spectrometer (II). Its resolving power reached 100 000 and the full width at half intensity of the slit function was equal to 0.100 cm-l. The shape of this instrumental function can be considered as Gaussian to a very good approximation. All the experimental setup: source, slitwidths, grating, and detector, have been described previously (9). All spectra were recorded at room temperature under pressures ranging from 375 to 600 Torr. Temperature was checked with a thermocouple and pressure measured with a mercury manometer read by a cathetometer. The precision of pressure measurements was better than 0.3%. Each line of the two bands was scanned under several pressures and several path lengths. A White-type cell with 50 cm base length was used to achieve optical path lengths of 4 to 8 m. All experimental conditions are summarized in Table I. In order to get the true zero transmission level, some lines of the strong neighboring 32°0-OOo0 transition were scanned under high pressure. This precaution is necessary to eliminate the energy of shorter wavelengths in the recorded spectra. A linear wavenumber scale was provided by scanning the equidistant fringes with a Fabry-Perot interferometer all along the spectra. With this method the relative wavenumber scale can be calculated for every spectrum to better than 1%. In the 24°0-OOo0 transition, a few lines at the end of the R branch are blended by the edge of the P branch of the 0112-OOOO;therefore, most of the measured widths and strengths belong to the P branch. Similarly, for the 01’2-OOOO,the beginning of the P branch is masked by the Q branch and the edge of the R branch by the end of the P lines of the strong 32°0-OOo0. Therefore, only a few data were determined in these parts of the band; nevertheless, enough values are available to obtain a good precision in the evaluation of the rotation-vibration interaction polynomials.
N,O LINE STRENGTHS DECONVOLUTION
207
AND WIDTHS PROCEDURE
The deconvolution procedure used here has been described previously. Only some minor details have been modified. So, we will just summarize the main steps of the calculation. First, the experimental profile is represented in the form
h(x) =
P(x).exp
Log 2.x* AY
1
with
IV
P(x) = c u&P’, II=1
(1)
where Ay is adjusted and the parameters a, calculated by a least-squares fitting of the absorbance in the sampling range (--s, +s). Then, from these parameters, and from the value of Au, half-width (HWHM) of the apparatus function, the true profile of the line is analytically calculated. In this study, the sampling range was taken equal to (-2.5 x robs, +2.5 x I,,,_), robs being the half-width (HWHM) of the observed profile; the Ay parameter was adjusted, for each line, in order to obtain the minimum of P(x) for x equal to robs. This a priori determination of Ay value gives good precision for the values of the a, parameters and avoids repeated fittings to test the precision. For each line two calculations were made with the polynomials P(x) of degree 6 and 8, respectively. Only the one giving the most precise deconvolution was retained. For a few lines, both calculations yielded meaningless results; this can be attributed to various causes, such as an instability of the output signal or an inaccurate determination of the base line of the spectrum or a blending by a foreign transition line. In all these cases both runs were discarded. RESULTS
FOR LINEWIDTHS
The experimental data for the linewidths I(m) are summarized in Table II for both transitions. As can be seen from Figs. 1 and 2, the dispersion of the values is very small. Taking into account all factors of uncertainties, the limit of error on each linewidth determination reaches 5 x 1O-3cm-‘. Therefore, the precision for the values given in Table II, which are the average values of several measurements, is much better. This can easily be seen by calculating the average deviation F = (114 En [robs - I,,,,,, 1: for both transitions 6 is less than or equal to 3 x 10e3 cm-l. In consideration of the above-mentioned precision the difference between the linewidths of the two transitions are not discernable and furthermore they are very close to those of the 32°0-OOo0 and 10°O-OO”l bands, previously studied (9, 12). So, this is an additional proof of the absence of a vibrational effect on N20 linewidths. RESULTS
FOR LINE STRENGTHS
For every studied line, two values of the strength were determined. The first one S(m) was obtained by a direct integration of the deconvoluted profile, the second one by application of the Lorentz relation (in this pressure range, it is well known that the Lorentz shape is a very good approximation of the profile)
208
LACOME
AND LEVY
TABLE P(m)
T lml
1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 30 39 40 41 42
in 10m3cm-l atm-’ at 300K
T
24"O - 00'0 band
weigh$
observed
3
: 4 3 2 1
141.3 131.1 122.2 121.6 118.4 117.9 112.9 111.0 115.8 109.3 110.0 113.8 109.7 106.0 107.4 105.4 104.6 105.7 105.0 103.3 102.5 101.7 102.6 106.4 107.6 104.5 102.8 102.7 94.4 91.1 86.9 87.4 93.1 80.9 82.6 83.1 83.6
3 2
75.9 85.2
1 9 9
6 6
1 9 9 7
5 6 6 8 7 1 9 10 8 : : 8 4 : : 4 0
II
smoothed
142.6 136.2 130.7 126.0 122.1 118.8 116.2 114.0 112.3 110.9 109.9 109.1 108.6 108.1
107.8 107.5 107.3 101.0 106.7 106.3 105.8 105.2 104.5 103.6 102.6 101.4 100.2 98.7 97.2 95.5 93.7 91.9 90.0 88.2 86.3 04.5 82.8 81.3 79.9
0112 - 00'0 band
weigh+?
observed
1 2 5
165.7 140.9 138.2
5
123.5
3 2 1 6 9 9 10 11 7 6 7 8 5 7 3 6 9 7 6
120.0 119.4 102.1 112.2 112.0 110.4 106.9 106.7 103.9 106.1 101.4 103.1 101.9 103.0 104.0 102.9 100.3 103.1 08.7
1 1
97.0 99.1
smoothed
162.2 152.6 144.4 137.4 131.5 126.6 122.5 119.1 116.3 114.1 112.3 110.8 109.7 108.7 107.8 107.1 106.4 105.6 104.9 104.1 103.3 102.3 101.3 100.2 99.0 97.8 96.6 95.4 94.3 93.3
70.8 78.1 77.1
* The weight values represent the number in the smoothing for each point.
of experimental
data
included
S,,,,.(IH) = z-X-(a,,).r(~z), where /\(ao) is the absorption coefficient at the center of the line. When the two resulting values were not in good agreement, both data were eliminated. Then, the remaining values were averaged. On the whole, the data points that were rejected for all the above-mentioned causes represented less than 10% of the total number of experimental determinations. The precision of the final value of each line strength can at least be taken equal to 5% of the scatter
N,O LINE STRENGTHS
I rim)
209
AND WIDTHS
c~-r h-’
0.150
o.loo~~
I
1
1
1
I
0
10
20
30
40
Iml
FIG. 1. Self-broadened linewidths at 300K in the 24°0-OOo0 band (in cm-’ atm-I). (0) Experimental values, (-) smoothed curve.
of the data. The data are respectively plotted on Figs. 3 and 4 for transitions 24°0-OOo0 and 01’2-OOOOand listed in Tables III and IV. From these experiments strengths, the square of the transition dipole moment can be extracted by the relation S(m) [R(m)]2 = 3hc 8n3 cr(m).X(m)g,,
Qint
(2)
No
with
L
exp -
hc
kt
II
c+(m)
x Exp
- s
[B,yrm(m - 1) - D,m2(m
I A(m)
= (m (
lY1 i
for a parallel Z-I; band,
I
1
10
1
1
1
20
30
10
Irnl
FIG. 2. Self-broadened linewidths at 300K in the 0112-OO@0band (in cm-’ atm-I). (0) Experimental values. (-) smoothed curve.
9
210
LACOME AND LEVY Slml
m lO*
cm-2atK’
3
m
FIG. 3. Line strengths at 300K in the 24”0-OO”0 transition (in IO+ cm-’ atm-‘). (0) Experimental values, (-) calculated curve obtained from values of R(0)and F(m) given in Table VI.
A(m)=$+ll
for a perpendicular
E-II band.
In this expression, g,., uVfl,B,,,, and D,. have the usual significance and v” denotes the lower level; the wavenumbers o(m) are expressed as a power series in m: u(m) = Ii aimi. For both transitions, the ai coefficients and the ground-state constants introduced in the calculation are those of Ref. (1). Then, from the squares (R(m)12 of the transition dipole moment we extracted the value of the rotationless transition moment R(0) and the coefficients of the vibration-rotation interaction factor F(m) using the relation (R(m)(’ = IWO)12F(m) with F(m) = 1 + C,m + C2m2
for a parallel band,
F(m) = (1 + lrn)”
for a perpendicular
band (13).
FIG. 4. Line strengths at 300K in the 01’2-OO”0 transition (in IO-’ cm-’ atm-I). (e) Experimental values, (-_) calculated curve obtained from values of R(0)and .$ given in Table VII.
N,O LINE STRENGTHS
211
AND WIDTHS
TABLE III Line Intensities at 300K in the 24°0-OO”0 Transition in 10m4cm-* atm-’
r /ml 1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 la 19 20 :: 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
r
P - Branch
3bserved
W eight
3 9 7 9 10 9 10 10 11 10 8 6 5 7 9 9 7 3 4 6 5 0 9 10 9 10 12 11 a 5 6 3 9 5 4 3 5 1 4 4 2 1
0.521 0.725 0.918 1.154 1.327 1.495 1.660 1.772 1.921 1.957 2.005 2.224 2.293 2.171 2.269 2.228 2.166 2.222 2.103 2.016 1.955 1.991 1.835 1.772 1.724 1.579 1.446 1.304 1.285 1.206 1.054 1.049 0.956 0.711 0.758 0,649 0.540 0.531 0.372 0.362 0.362 0.321
!alculated 0.244 0.483 0.715 0.938 1.149 1.347 1.528 1.693 1.839 1.966 2.013 2.160 2.221 2.273 2.300 2.309 2.300 2.215 2.235 2.181 2.115 2.039 1.955 1.863 1.766 1.665 1.562 1.458 1.354 1.251 1.150 1.052 0.958 0.868 0.783 0.703 0.629 0.560 0.496 0.437 0.384 0.335 0.292 0.253 0.218
R - Branch
jbserved
?ight
0.801 0.951 1.237 1.579 1.699 1.931 2.012 2.140 2.200 2.450 2.515 2.551 2.632 2.640 2.601 2.637 2.534 2.484 2.376 2.285 2.223 2.212 1.981 1.890 1.894 1.667 1.683 1.523 1.465 1.316 1.253 0.965
2 7 7 4 6 6 a 7 a 5 a a 5 3 4 8 10 a 3 5 1 3 3 2 4 6 4 4 4 4 1 2
klculated 0.245 0.490 0.731 0.966 1.191 1.406 1.607 1.793 1.962 2.112 2.243 2.353 2.443 2.511 2.559 2.566 2.594 2.563 2.555 2.510 2.451 2.378 2.295 2.202 2.101 1.993 1.882 1.767 1.651 1.420 1.307 1.198 1.092 0.991 0.095 0.005 0.720 0.642 0.569 0.503 0.442 0.307 0.337 0.292 0.252
-
Thus, for the 24°0-OOo0 band, the values of /R(m) I* were first calculated from the S(m) data; then by a least-squares fitting the coefficients R(O), C,, and Cs were determined using the relation /Z?(m)/* = IR(O)(**(l + C,m + C2m2).
(3)
For the perpendicular transition 01’2-OOOO,a similar method was used but the least-squares adjustment was done using the form (R(m)/ = JR(O)1 .(1 + Sm,
(4)
212
LACOME AND LEVY
for the determination of JR(O)] and 5. The linear dependence of IZ?(m) 1 upon m allowed a determination of the { coefficients although the number of data points was not very important in the R branch. Nevertheless, the precision of the t-value is not very satisfactory and it should be interesting to perform some more experiments at very low pressure in order to determine some additional line strengths by a more appropriate method. For both transitions, \R(O) 1,Cl,C2,and 5 values are presented in Tables VI and VII. From these coefficients, all the line strengths were recalculated. The corresponding values are plotted in Figs. 3 and 4 and compared with experimental data in Tables III and IV. For the perpendicular transition 01’2-OOOO,the line strengths of the Q branch which were not measurable with our spectrometer were predicted using the parameters determined from data of the P and R branches. The obtained values
TABLE IV Line Intensities at 300K in the 24°0-O000 Transition in 10m4crnm2atm-’
T lml
Observed
weight
1 2 3 4 5 6 7
a 9 10 11 12 13 14 15 16 17
la 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
r
P-BRANCH
0.804 0.894
3 5
1.000 1.030 1.051 1.020 1.049 1.011 1.000 0.999 0.994 0.951 0.909 0.798 0.858 0.702 0.718 0.598 0.633 0.585 0.565
17 11 12 19 21 a 13 10 10 9 15 5 13 16 15 6 1 2 7
0.468
2
R-BRANCH
mDothed
0.120 0.237 0.349 0.455 0.555 0.647 0.130 0.804 0.868 0.921 0.965 0.998 1.021 1.034 1.038 1.033 1.019 0.999 0.972 0.939 0.902 0.860 0.816 0.169 0.121 0.672 0.623 0.574 0.521 0.480 0.436 0.394 0.354 0.316
weight 0.265
2
0.514 0.609
4 12
0.891
7
1.000
2
1.243
4
0.243 0.364 0.482 0.596 0.704 0.806 0.900 0.986 1.062 1.128 1.183 1.221 1.261 1.283 1.295 1.297 1.289 1.272 1.241 1.214 1.175 1.130 1.080 1.027 0.971 0.913 0.853 0.794 0.735 0.676 0.619 0.565 0.512 0.462 0.415
N,O LINE STRENGTHS
213
AND WIDTHS
TABLE V Linestrengths
in the 01’2-0000 Q branch (in 10m4cmm2 atm-‘) S(J)
J
0.363 0.601 0.831 1.051 1.259 1.452 1.629 1.788 1.927 2.046 2.144 2.221 2.276 2.311 2.326 2.322 2.300 2.261 2.208 2.142 2.065 1.978 1.883 1.783 1.678 1.571 1.462 1.354 1.247 1.143
1
2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
are summarized
in Table V. The total Q-branch intensity so predicted
s Qbranch=
1 S,(J) J
= 6.01
x
10e3 cm-2.atm-1
at 300K and 1 atm (with a precision of 1%). TABLE VI 24°0-OO”0 Transition R(O)
(5.259 *
5
(1.422 i 0.2313)x10-~
C2
(1.675 f o.l2l)xlo-4
'band
(1.325 k
0.017)~10-~
0.021~)~10-~
Debye
cm-2 Atm-'
is
LACOME
214
AND LEVY
TABLE
VII
01’2-0000 Transition R (0)
(5.203
5
(4.42
sband (P+R)
(6.091
f
0.125)~10-~
CIII-~ Atm-’
(I.203
+- O.Ol8)~10-~
cm_2 Atm-I
‘band
RESULTS
f 0.026)~10-~
Debye
+ 2.66)x10-’
FOR BAND STRENGTHS
The band intensity (intensity of the P and R branches only, for the 0112-OOOO band) can be computed by the relation S$(P +
NoIR(0)12~
R) = g
(5)
with a=
+r 1 IA(m)*F(m)*cr(m).exp m=--mQint I
i
- E
[B,m(m
- 1) - D,.m*(m - l)*]
II
or directly by summation of the individual intensities of the lines. The computed values at 300K are presented in Tables VI and VII. For both transitions under study, the direct summation method gives the same value as that obtained by Eq. (5). RECEIVED:
February
22, 1980 REFERENCES
1. 2. 3. 4. 5.
C. AMIOT AND G. GLJELACHVILI, J. Mol. Spectrosc. 51, 475-491 (1974). R. A. ToTH,J. Mol. Spectrosc. 40, 588-604 (1971). J. S. MARCOUS, J. Quant. Spectrosc. Radiat. Transfer 12, 751-757 (1972). J. E. LOWDER, J. Quanr. Spectrosc. Radiat. Transfer 12, 873-880 (1972). L. D. TUBBS AND D. WILLIAMS, J. Opt. Sot. Amer. 63, 859-863 (1973).
6. R. A. TOTH AND C. B. FARMER, J. Mol. Spectrosc. 55, 182-191 (1975). 7. J. P. BOISSY, A. VALENTIN. PH. CARDINET, M. L. CLAUDE. AND A. HENRY, J. Spectrosc. 57, 391-396 (1975). 8. P. VARANASI AND F. K. Ko, J. Quant. Spectrosc. Radiat. Transfer 18, 465-470 (1977). 9. N. LACOME AND A. LEVY, J. Mol. Spectrosc. 71, 175-192 (1978). 10. N. LACOME AND A. LEVY, Mol. Phys. 39, 1221-1232 (1980). II. C. HAEUSLER, Y. CORNET, AND P. BARCHEWITZ, J. Phys. Radium 21, 809-818 (1960). I2. N. LACOME, C. BOULET, AND E. ARIE, Canad. J. Phys. 51, 302-310 (1973). 13. H. D. DOWNING, B. J. KROHN, AND R. H. HUNT, J. Mol. Spectrosc. 55,66-80 (1975).
Mol.
OF
MOLECULAR
SPECTROSCOPY
85,
205-214
(1981)
Line Strengths and Self-Broadened Linewidths N,O in the 2-pm Region 24°0-OOo0
and 01’2-OOOO
N. LACOME AND Laboratoire
of
Transitions
A. LEVY
d’lnfrarouge. AssociC au CNRS. UniversitP de Paris-Sud, Bdtiment 350, ORSAY CEDEX 91405, France
The strengths and self-broadened linewidths of the parallel 24°0-W0 and perpendicular 01’2-0000 bands of N,O have been measured with a precision better than 3%, using a deconvolution procedure. For both transitions, the coefficient of the vibration-rotation interaction polynomial, the values of the rotationless dipolar transition moment, and the band intensity have been calculated from the line strengths. For the total intensity the values found are S%$l = (1.325 -+ 0.021) x IO-* cm-“,atm-’ and Sgj,Li= (1.209 -C 0.018) x 10m2cm-*.atm-I. INTRODUCTION
Absorption parameters of N,O in the very near IR are not adequately known. Wavelengths measurements have been performed (1) with good precision but intensity data are more scarce (2-8). Therefore, using a classical spectrometer of moderate resolution, strengths and widths of the lines in the 40°0-OOOOand 32°0-OOo0 transitions have been systematically measured. All data have been obtained by a deconvolution method, which has been described previously (9). This is, in fact, a preliminary study carried on with the view of obtaining accurate values of the line parameters (strengths, widths and peak absorption values) that could be used later in theoretical calculations of band shapes under high pressure. In a recent paper (10) the influence of line overlapping on the shape of NzO bands was analyzed in detail by making use of the “low-pressure” constants. In the present work, we perform the analysis of some of the remaining bands of N,O in the 2-pm region; namely the 24°0-OOo0 and 01’2-OOOOtransitions. The 24°0-OOo0 transition is a parallel band belonging to the 40°0-OOOOpentad. It is sometimes denoted (40°0-OOoOo)111. The (40°0-OOoO)1and (40°0-OOoO)11components have been previously analyzed with the same method (9). The 01’2~OOOO transition is the neighbouring perpendicular band. Only lines of the P and R branches have been measured; the lines of the Q branch are too close to allow measurements in this pressure range with the apparatus used in this study. From experimental intensity data, the values of the rotationless vibration transition moment have been calculated as well as the expansion of the vibration-rotation interaction factor. Concerning the self-broadened linewidths, the obtained values are very close to those found for the other transitions of N,O and no significant deviation between different vibrational bands can be pointed out. 205
0022-2852/81/010205-10$02.00/O Copyright All rights
0 1981 by Academic of reproduction
Press,
in any form
Inc. reserved.
206
LACOME
AND LEVY
TABLE
I
Experimental Conditions
0112-OOOO band
24°0-OOo0 band
500 torr
600 torr
375 torr
P36-R36
P37-P3
P30-P8 Rl-R4
Pll-R34
P43-P3
P32-R12 R3-R21 P27-PlO Rl-R19
EXPERIMENTAL
DETAILS
Spectra of the two transitions have been recorded using a Czemy-Turner-type classical spectrometer (II). Its resolving power reached 100 000 and the full width at half intensity of the slit function was equal to 0.100 cm-l. The shape of this instrumental function can be considered as Gaussian to a very good approximation. All the experimental setup: source, slitwidths, grating, and detector, have been described previously (9). All spectra were recorded at room temperature under pressures ranging from 375 to 600 Torr. Temperature was checked with a thermocouple and pressure measured with a mercury manometer read by a cathetometer. The precision of pressure measurements was better than 0.3%. Each line of the two bands was scanned under several pressures and several path lengths. A White-type cell with 50 cm base length was used to achieve optical path lengths of 4 to 8 m. All experimental conditions are summarized in Table I. In order to get the true zero transmission level, some lines of the strong neighboring 32°0-OOo0 transition were scanned under high pressure. This precaution is necessary to eliminate the energy of shorter wavelengths in the recorded spectra. A linear wavenumber scale was provided by scanning the equidistant fringes with a Fabry-Perot interferometer all along the spectra. With this method the relative wavenumber scale can be calculated for every spectrum to better than 1%. In the 24°0-OOo0 transition, a few lines at the end of the R branch are blended by the edge of the P branch of the 0112-OOOO;therefore, most of the measured widths and strengths belong to the P branch. Similarly, for the 01’2-OOOO,the beginning of the P branch is masked by the Q branch and the edge of the R branch by the end of the P lines of the strong 32°0-OOo0. Therefore, only a few data were determined in these parts of the band; nevertheless, enough values are available to obtain a good precision in the evaluation of the rotation-vibration interaction polynomials.
N,O LINE STRENGTHS DECONVOLUTION
207
AND WIDTHS PROCEDURE
The deconvolution procedure used here has been described previously. Only some minor details have been modified. So, we will just summarize the main steps of the calculation. First, the experimental profile is represented in the form
h(x) =
P(x).exp
Log 2.x* AY
1
with
IV
P(x) = c u&P’, II=1
(1)
where Ay is adjusted and the parameters a, calculated by a least-squares fitting of the absorbance in the sampling range (--s, +s). Then, from these parameters, and from the value of Au, half-width (HWHM) of the apparatus function, the true profile of the line is analytically calculated. In this study, the sampling range was taken equal to (-2.5 x robs, +2.5 x I,,,_), robs being the half-width (HWHM) of the observed profile; the Ay parameter was adjusted, for each line, in order to obtain the minimum of P(x) for x equal to robs. This a priori determination of Ay value gives good precision for the values of the a, parameters and avoids repeated fittings to test the precision. For each line two calculations were made with the polynomials P(x) of degree 6 and 8, respectively. Only the one giving the most precise deconvolution was retained. For a few lines, both calculations yielded meaningless results; this can be attributed to various causes, such as an instability of the output signal or an inaccurate determination of the base line of the spectrum or a blending by a foreign transition line. In all these cases both runs were discarded. RESULTS
FOR LINEWIDTHS
The experimental data for the linewidths I(m) are summarized in Table II for both transitions. As can be seen from Figs. 1 and 2, the dispersion of the values is very small. Taking into account all factors of uncertainties, the limit of error on each linewidth determination reaches 5 x 1O-3cm-‘. Therefore, the precision for the values given in Table II, which are the average values of several measurements, is much better. This can easily be seen by calculating the average deviation F = (114 En [robs - I,,,,,, 1: for both transitions 6 is less than or equal to 3 x 10e3 cm-l. In consideration of the above-mentioned precision the difference between the linewidths of the two transitions are not discernable and furthermore they are very close to those of the 32°0-OOo0 and 10°O-OO”l bands, previously studied (9, 12). So, this is an additional proof of the absence of a vibrational effect on N20 linewidths. RESULTS
FOR LINE STRENGTHS
For every studied line, two values of the strength were determined. The first one S(m) was obtained by a direct integration of the deconvoluted profile, the second one by application of the Lorentz relation (in this pressure range, it is well known that the Lorentz shape is a very good approximation of the profile)
208
LACOME
AND LEVY
TABLE P(m)
T lml
1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 30 39 40 41 42
in 10m3cm-l atm-’ at 300K
T
24"O - 00'0 band
weigh$
observed
3
: 4 3 2 1
141.3 131.1 122.2 121.6 118.4 117.9 112.9 111.0 115.8 109.3 110.0 113.8 109.7 106.0 107.4 105.4 104.6 105.7 105.0 103.3 102.5 101.7 102.6 106.4 107.6 104.5 102.8 102.7 94.4 91.1 86.9 87.4 93.1 80.9 82.6 83.1 83.6
3 2
75.9 85.2
1 9 9
6 6
1 9 9 7
5 6 6 8 7 1 9 10 8 : : 8 4 : : 4 0
II
smoothed
142.6 136.2 130.7 126.0 122.1 118.8 116.2 114.0 112.3 110.9 109.9 109.1 108.6 108.1
107.8 107.5 107.3 101.0 106.7 106.3 105.8 105.2 104.5 103.6 102.6 101.4 100.2 98.7 97.2 95.5 93.7 91.9 90.0 88.2 86.3 04.5 82.8 81.3 79.9
0112 - 00'0 band
weigh+?
observed
1 2 5
165.7 140.9 138.2
5
123.5
3 2 1 6 9 9 10 11 7 6 7 8 5 7 3 6 9 7 6
120.0 119.4 102.1 112.2 112.0 110.4 106.9 106.7 103.9 106.1 101.4 103.1 101.9 103.0 104.0 102.9 100.3 103.1 08.7
1 1
97.0 99.1
smoothed
162.2 152.6 144.4 137.4 131.5 126.6 122.5 119.1 116.3 114.1 112.3 110.8 109.7 108.7 107.8 107.1 106.4 105.6 104.9 104.1 103.3 102.3 101.3 100.2 99.0 97.8 96.6 95.4 94.3 93.3
70.8 78.1 77.1
* The weight values represent the number in the smoothing for each point.
of experimental
data
included
S,,,,.(IH) = z-X-(a,,).r(~z), where /\(ao) is the absorption coefficient at the center of the line. When the two resulting values were not in good agreement, both data were eliminated. Then, the remaining values were averaged. On the whole, the data points that were rejected for all the above-mentioned causes represented less than 10% of the total number of experimental determinations. The precision of the final value of each line strength can at least be taken equal to 5% of the scatter
N,O LINE STRENGTHS
I rim)
209
AND WIDTHS
c~-r h-’
0.150
o.loo~~
I
1
1
1
I
0
10
20
30
40
Iml
FIG. 1. Self-broadened linewidths at 300K in the 24°0-OOo0 band (in cm-’ atm-I). (0) Experimental values, (-) smoothed curve.
of the data. The data are respectively plotted on Figs. 3 and 4 for transitions 24°0-OOo0 and 01’2-OOOOand listed in Tables III and IV. From these experiments strengths, the square of the transition dipole moment can be extracted by the relation S(m) [R(m)]2 = 3hc 8n3 cr(m).X(m)g,,
Qint
(2)
No
with
L
exp -
hc
kt
II
c+(m)
x Exp
- s
[B,yrm(m - 1) - D,m2(m
I A(m)
= (m (
lY1 i
for a parallel Z-I; band,
I
1
10
1
1
1
20
30
10
Irnl
FIG. 2. Self-broadened linewidths at 300K in the 0112-OO@0band (in cm-’ atm-I). (0) Experimental values. (-) smoothed curve.
9
210
LACOME AND LEVY Slml
m lO*
cm-2atK’
3
m
FIG. 3. Line strengths at 300K in the 24”0-OO”0 transition (in IO+ cm-’ atm-‘). (0) Experimental values, (-) calculated curve obtained from values of R(0)and F(m) given in Table VI.
A(m)=$+ll
for a perpendicular
E-II band.
In this expression, g,., uVfl,B,,,, and D,. have the usual significance and v” denotes the lower level; the wavenumbers o(m) are expressed as a power series in m: u(m) = Ii aimi. For both transitions, the ai coefficients and the ground-state constants introduced in the calculation are those of Ref. (1). Then, from the squares (R(m)12 of the transition dipole moment we extracted the value of the rotationless transition moment R(0) and the coefficients of the vibration-rotation interaction factor F(m) using the relation (R(m)(’ = IWO)12F(m) with F(m) = 1 + C,m + C2m2
for a parallel band,
F(m) = (1 + lrn)”
for a perpendicular
band (13).
FIG. 4. Line strengths at 300K in the 01’2-OO”0 transition (in IO-’ cm-’ atm-I). (e) Experimental values, (-_) calculated curve obtained from values of R(0)and .$ given in Table VII.
N,O LINE STRENGTHS
211
AND WIDTHS
TABLE III Line Intensities at 300K in the 24°0-OO”0 Transition in 10m4cm-* atm-’
r /ml 1 2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 la 19 20 :: 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
r
P - Branch
3bserved
W eight
3 9 7 9 10 9 10 10 11 10 8 6 5 7 9 9 7 3 4 6 5 0 9 10 9 10 12 11 a 5 6 3 9 5 4 3 5 1 4 4 2 1
0.521 0.725 0.918 1.154 1.327 1.495 1.660 1.772 1.921 1.957 2.005 2.224 2.293 2.171 2.269 2.228 2.166 2.222 2.103 2.016 1.955 1.991 1.835 1.772 1.724 1.579 1.446 1.304 1.285 1.206 1.054 1.049 0.956 0.711 0.758 0,649 0.540 0.531 0.372 0.362 0.362 0.321
!alculated 0.244 0.483 0.715 0.938 1.149 1.347 1.528 1.693 1.839 1.966 2.013 2.160 2.221 2.273 2.300 2.309 2.300 2.215 2.235 2.181 2.115 2.039 1.955 1.863 1.766 1.665 1.562 1.458 1.354 1.251 1.150 1.052 0.958 0.868 0.783 0.703 0.629 0.560 0.496 0.437 0.384 0.335 0.292 0.253 0.218
R - Branch
jbserved
?ight
0.801 0.951 1.237 1.579 1.699 1.931 2.012 2.140 2.200 2.450 2.515 2.551 2.632 2.640 2.601 2.637 2.534 2.484 2.376 2.285 2.223 2.212 1.981 1.890 1.894 1.667 1.683 1.523 1.465 1.316 1.253 0.965
2 7 7 4 6 6 a 7 a 5 a a 5 3 4 8 10 a 3 5 1 3 3 2 4 6 4 4 4 4 1 2
klculated 0.245 0.490 0.731 0.966 1.191 1.406 1.607 1.793 1.962 2.112 2.243 2.353 2.443 2.511 2.559 2.566 2.594 2.563 2.555 2.510 2.451 2.378 2.295 2.202 2.101 1.993 1.882 1.767 1.651 1.420 1.307 1.198 1.092 0.991 0.095 0.005 0.720 0.642 0.569 0.503 0.442 0.307 0.337 0.292 0.252
-
Thus, for the 24°0-OOo0 band, the values of /R(m) I* were first calculated from the S(m) data; then by a least-squares fitting the coefficients R(O), C,, and Cs were determined using the relation /Z?(m)/* = IR(O)(**(l + C,m + C2m2).
(3)
For the perpendicular transition 01’2-OOOO,a similar method was used but the least-squares adjustment was done using the form (R(m)/ = JR(O)1 .(1 + Sm,
(4)
212
LACOME AND LEVY
for the determination of JR(O)] and 5. The linear dependence of IZ?(m) 1 upon m allowed a determination of the { coefficients although the number of data points was not very important in the R branch. Nevertheless, the precision of the t-value is not very satisfactory and it should be interesting to perform some more experiments at very low pressure in order to determine some additional line strengths by a more appropriate method. For both transitions, \R(O) 1,Cl,C2,and 5 values are presented in Tables VI and VII. From these coefficients, all the line strengths were recalculated. The corresponding values are plotted in Figs. 3 and 4 and compared with experimental data in Tables III and IV. For the perpendicular transition 01’2-OOOO,the line strengths of the Q branch which were not measurable with our spectrometer were predicted using the parameters determined from data of the P and R branches. The obtained values
TABLE IV Line Intensities at 300K in the 24°0-O000 Transition in 10m4crnm2atm-’
T lml
Observed
weight
1 2 3 4 5 6 7
a 9 10 11 12 13 14 15 16 17
la 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
r
P-BRANCH
0.804 0.894
3 5
1.000 1.030 1.051 1.020 1.049 1.011 1.000 0.999 0.994 0.951 0.909 0.798 0.858 0.702 0.718 0.598 0.633 0.585 0.565
17 11 12 19 21 a 13 10 10 9 15 5 13 16 15 6 1 2 7
0.468
2
R-BRANCH
mDothed
0.120 0.237 0.349 0.455 0.555 0.647 0.130 0.804 0.868 0.921 0.965 0.998 1.021 1.034 1.038 1.033 1.019 0.999 0.972 0.939 0.902 0.860 0.816 0.169 0.121 0.672 0.623 0.574 0.521 0.480 0.436 0.394 0.354 0.316
weight 0.265
2
0.514 0.609
4 12
0.891
7
1.000
2
1.243
4
0.243 0.364 0.482 0.596 0.704 0.806 0.900 0.986 1.062 1.128 1.183 1.221 1.261 1.283 1.295 1.297 1.289 1.272 1.241 1.214 1.175 1.130 1.080 1.027 0.971 0.913 0.853 0.794 0.735 0.676 0.619 0.565 0.512 0.462 0.415
N,O LINE STRENGTHS
213
AND WIDTHS
TABLE V Linestrengths
in the 01’2-0000 Q branch (in 10m4cmm2 atm-‘) S(J)
J
0.363 0.601 0.831 1.051 1.259 1.452 1.629 1.788 1.927 2.046 2.144 2.221 2.276 2.311 2.326 2.322 2.300 2.261 2.208 2.142 2.065 1.978 1.883 1.783 1.678 1.571 1.462 1.354 1.247 1.143
1
2 3 4 5 6 7 a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
are summarized
in Table V. The total Q-branch intensity so predicted
s Qbranch=
1 S,(J) J
= 6.01
x
10e3 cm-2.atm-1
at 300K and 1 atm (with a precision of 1%). TABLE VI 24°0-OO”0 Transition R(O)
(5.259 *
5
(1.422 i 0.2313)x10-~
C2
(1.675 f o.l2l)xlo-4
'band
(1.325 k
0.017)~10-~
0.021~)~10-~
Debye
cm-2 Atm-'
is
LACOME
214
AND LEVY
TABLE
VII
01’2-0000 Transition R (0)
(5.203
5
(4.42
sband (P+R)
(6.091
f
0.125)~10-~
CIII-~ Atm-’
(I.203
+- O.Ol8)~10-~
cm_2 Atm-I
‘band
RESULTS
f 0.026)~10-~
Debye
+ 2.66)x10-’
FOR BAND STRENGTHS
The band intensity (intensity of the P and R branches only, for the 0112-OOOO band) can be computed by the relation S$(P +
NoIR(0)12~
R) = g
(5)
with a=
+r 1 IA(m)*F(m)*cr(m).exp m=--mQint I
i
- E
[B,m(m
- 1) - D,.m*(m - l)*]
II
or directly by summation of the individual intensities of the lines. The computed values at 300K are presented in Tables VI and VII. For both transitions under study, the direct summation method gives the same value as that obtained by Eq. (5). RECEIVED:
February
22, 1980 REFERENCES
1. 2. 3. 4. 5.
C. AMIOT AND G. GLJELACHVILI, J. Mol. Spectrosc. 51, 475-491 (1974). R. A. ToTH,J. Mol. Spectrosc. 40, 588-604 (1971). J. S. MARCOUS, J. Quant. Spectrosc. Radiat. Transfer 12, 751-757 (1972). J. E. LOWDER, J. Quanr. Spectrosc. Radiat. Transfer 12, 873-880 (1972). L. D. TUBBS AND D. WILLIAMS, J. Opt. Sot. Amer. 63, 859-863 (1973).
6. R. A. TOTH AND C. B. FARMER, J. Mol. Spectrosc. 55, 182-191 (1975). 7. J. P. BOISSY, A. VALENTIN. PH. CARDINET, M. L. CLAUDE. AND A. HENRY, J. Spectrosc. 57, 391-396 (1975). 8. P. VARANASI AND F. K. Ko, J. Quant. Spectrosc. Radiat. Transfer 18, 465-470 (1977). 9. N. LACOME AND A. LEVY, J. Mol. Spectrosc. 71, 175-192 (1978). 10. N. LACOME AND A. LEVY, Mol. Phys. 39, 1221-1232 (1980). II. C. HAEUSLER, Y. CORNET, AND P. BARCHEWITZ, J. Phys. Radium 21, 809-818 (1960). I2. N. LACOME, C. BOULET, AND E. ARIE, Canad. J. Phys. 51, 302-310 (1973). 13. H. D. DOWNING, B. J. KROHN, AND R. H. HUNT, J. Mol. Spectrosc. 55,66-80 (1975).
Mol.