Intensity and half width measurements of the (00°2-00°0) band of N2O

1. Quonr.

Specmm.

Rodianr.

Transfer.

Vol.

12, pp. 751-757.

Pergamon Press 1972. Printed in Great Britain

INTENSITY AND HALF WIDTH MEASUREMENTS OF THE (00”2-OO”0) BAND OF N20 JACK S. MARGOLIS Space Sciences Division,

Jet Propulsion Laboratory, California Pasadena, California 91103, U.S.A. (Received 2 September

Institute

of Technology,

1971)

Abstract-Measurements of the intensities and half widths of the lines of the (OO”240”O) band of N,O have been made with a spectral resolution 10.06 cm- ‘. The band intensity has been determined to be 1.29 crnm2 atm-’ at 296°K. The half widths have been measured for both N, and self broadening.

INTRODUCTION

THERE has been a recentqheightening of interest in the line intensities and pressure-broaden-

ing coefficients of atmospheric gases. These parameters are important for quantitative interpretation of observed absorption (or emission) in the atmosphere. The values of the line intensities also find use in the determination of the dipole-moment function and the half widths may be correlated with the electric moments of the molecules. Nitrous oxide (N,O) appears as a trace constituent of the earth’s atmosphere and a possible constituent of the atmospheres of terrestrial planets. This paper presents results of laboratory measurements of the line intensities and pressure-broadening coefficients for the 2v, band of N,O. This band appears in a spectral region which is quite clear of atmospheric absorptions. For this reason, it represents a potentially useful band for the spectroscopic monitoring of atmospheric N,O. The wavelengths and rotational constants used for this band have been reported by PLIVA.w The band intensity has been measured and reported on by VINCENT-GEISSE (2) but her measurements were obtained with lower resolution than was achieved in this study. The pressure-broadening coefficients (both N, and self-broadening) have been recently measured by TOTH(3) for the (O2”1LOO”O) and (10”140”0) bands. He found essentially no vibrational dependence, as is verified by the measurements made in this study. There have been other measurements of N,O half widths which have, however, varied considerably in their results. For the most part, these other investigations were carried out with lower resolution than in the work carried out by Toth or in this study. They are discussed by Toth and will not be gone into here. ToTH,‘~) TEJWANI and VARANASI(") and HIRONA”’ have applied Anderson’s theory to a calculation of the half widths. They all find the same general dependence of the half widths on rotational quantum number jm(,with maximum differences of 0.02 cm- ’ for some of the lines. The P-branch of the 2v, band of N,O is overlaid by the hot band (01’2-01’0), but the R branch is clear of any extraneous absorptions. This is well illustrated by the rapid scan 751

752

JACK S. MARG~LIS

spectrum in Fig. 1. The I-doubling splitting of the high J lines of the P branch band appear barely resolved in this tracing.

of the hot

rr c

4440

4330

4470

4410

44””

4300

33,:o

43/o

4360

4350

FREQUENCY, cm-'

FIG. I. Rapid

scan of the (00”2-OO”O1 band of N,O. The weak underlvine band (Oi ‘241 ‘0): 5 torr of N;O and 8 m path lengih. v

is the hot band

EXPERIMENTAL

The spectrometer and multitraversal absorption cell used for the measurements in this study have been described elsewhere.‘3’ All observations were made at room temperature (296°K). The spectral purity was determined by the maximum absorption with 200 torr of NH, and a path length of 16 m. (The combination band of v2 + v3 of NH, appears in this spectral region.) All detectable NH, absorptions disappeared after pumping on the cell for a day. Since many of the lines of the P branch are overlaid, or are close to the lines of the hot band, they could not be used for pressure-broadening coefficient determination. The intensities were measured at low pressures so that blending was not as serious. Nevertheless, there were about 15 lines in the P branch which were strongly enough blended that they were deleted from our measurements. All of the lines of the R-branch are clear of blends from extraneous lines from other bands, but the band head appears at relatively low J so that the intensity of lines up to only J = 49 and half widths up to J = 44 could be measured with satisfactory accuracy. The intensity measurements were all made with path lengths varying in steps of 8 m between 8 and 24 m. The pressures varied between 0.30 and 3.00 torr and were measured with a Baratron pressure gauge; they were determined to an accuracy of 1 per cent. At these pressures, the ratio of the Doppler width to the collision width is 8 or more so that the line has very nearly a Doppler shape. The spectral resolution attained for all of the measurements was 0.06 cm- 1 or less which is about 15 times the Doppler width. In order to obtain good accuracy in the measurements of the line strengths, we restricted our attention to lines which had a peak absorption of about 15 per cent or less. The pressure and path length were varied so that each line was measured several times under the appropriate conditions of absorption. The signal to noise ratio in these measurements varied between 100 and 200. The pressure range for the half-width measurements was 400-750 torr; the cells used for the half-width measurements were 8 m, 41.9 cm and 2.0 cm in length. The slit-function corrections to the half-width measurements were 20 per cent at the most. All of the optical components were at all times enclosed in a vacuum and no atmospheric or impurity

Intensity and half width measurements of the (Oo”240°0) band of N,O

753

absorptions were observed. The N,O gas samples were purchased from the Baker Chemical Company and were guaranteed to have a purity of 99 per cent or more. INTENSITY MEASUREMENTS Since all of the intensity measurements were made with pressures less than 3.0 torr, the lines were characterized by Voigt profiles with a small value of the parameter (b,lb,)(ln 2)“‘, where b, = half width due to collisions and b, = Doppler width. The tables of JANNSSONand KORB(@were used to convert the measured equivalent widths of individual lines to their line strengths. In using the tables, it was assumed that all of the lines had the same pressure-broadening coefficients. Subsequent measurements of the half widths indicate that 0.090 I b,(cm-‘) I 0.14. At the highest pressure used and for the strongest line measured the effect of the assumption of a uniform pressure-broadening coefficient was about 0.5 per cent. This is comparable to the accuracy obtained by linearly interpolating in the tables and so no effort was made to correct for the variation of the half widths. The line strength of each line was determined by averaging measurements at several different pressures and paths. They are listed in Table 1. The line strengths of the P and R branch lines of the X-X (OO”2LOo”O) band are given by S(m) =

~co(rn)~rn~ 5 IR(m)l’ exp[ - aE(m)],

(1)

where E(m) = o0 + Bm(m - 1) - Dm2(m - 1)2,Q = &(2J + 1) exp[ - oE,], (r = hc/kT ; q, = 4417.379cm-‘, B = 0.4190111 cm-‘, and D = 1.784x lo-‘cm-’ (from PLIVA(‘)); Q is the partition function for N,O and has been tabulated over the temperature range 20& 350°K by GRAY YOUNG,.(‘) N, is the number density of N,O molecules and 1R(m)12 is the square of the dipole transition moment between the states in question. This latter factor may be expressed as a product of a factor independent of rotation and a power series in m : IR(m)l’ = IR(0)12[1+am+bm2+...].

(2)

The measured line strengths were used to determine the parameters of the dipole-transition moment in equation (2). This was done by making a weighted least-squares adjustment of \R(0)12,a, and b to the equation lR(0)12[1+am+bm] =

S(m) exp[rrE(m)] 3hcQ

bl&4

8nZN,’

(3)

The weights were taken to be S(m)/dS(m), where 6S(m) is the standard deviation of the measurement of S(m). The values of IR(O)l, a and b determined in this way are IR(O)(= (5.58+0.03)x 10e3 Debyes, a = (-0.625f0.014)~ 10-j, and b = (1.53*0.05)x 10e5. The errors quoted here are statistical errors which were derived by standard techniques from a least-squares analysis. @)The band strength for the band was calculated by evaluating the sum S, = C S(m), m where the S(m) are calculated from equation (1) using the values of IR(O)l’,a, and b reported above. The results for T = 296°K is S, = 1.29 cmW2 atm-‘. This should be compared

154

JACK S. MARCXILIS

TABLE I. MEASURED

AND COMPUTED VALUES FOR THE LINE STRENGTHS (cm-’ atm-‘) OF THE (00”240”0) BAND

R Branch J 0

1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 21 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 41 48 49

Obs. 0.262 x IO-’ 0.563 0.777 1.03 1.21 1.49 1.63 1.90 2.08 2.09 2.24 2.41 2.41 2.40 2.61 2.50 2.58 2.50 2.51 2.50 2.28 2.28 2.06 2.02 1.94 1.I4 1.64 1.56 1.53 1.34 1.21 1.14 1.02 0.908 0.810 0.740 0.657 0.589 0.567 0.444 0.412 0.371 0.318 0.246 0.206 0.187 0.169 0.125 0.105 0.107

P Branch Calc.

0.260 x lo-’ 0.518 0.770 1.015 1.248 1.467 1.670 1.860 2.020 2.170 2.290 2.390 2.46 2.52 2.55 2.56 2.55 2.52 2.48 2.42 2.34 2.25 2.16 2.05 1.94 1.83 1.71 1.59

Obs.

Calc.

0.260 x lo- * 0.558 0.788 0.948 1.19 1.36 1.66

0.259 x lo-’ 0.515 0.763 1.00 1.23 1.44 1.63

2.07 1.95

1.96 2.10

2.25

2.38

2.16

2.19

1.83 1.94 1.84 1.59 1.48

2.01 1.90 1.79 1.68 1.57 1.46

1.41

1.45

1.36

1.24

1.32 1.15

1.13

1.oo

1.23 1.13

0.893 0.762

0.925 0.833

0.631 0.574

0.664 0.589

0.434 0.426

0.457 0.399

0.325 0.262 0.239 0.200 0.161 0.142 0.111 0.104

0.301 0.260 0.223 0.190 0.162 0.137 0.116 0.097 1

1.34

1.03 0.927 0.833 0.744 0.662 0.586 0.517 0.453 0.396 0.344 0.298 0.256 0.220 0.187 0.159 0.135 0.113 0.0951

The column labeled Calc. was computed according “least squares” values of IR(O)l*, a and b. The average measured strengths is about 5 per cent.

to equation (1) using the standard deviation of the

Intensity

and half width measurements

155

of the (OO”24@O) band of N,O

to the value reported by VINCENT~EISSE!‘) S, = 1.55 cm-’ atm- ‘. This larger value may be due to the lower resolution of the spectra available to her so that she included some of the intensity due to the hot band, which would add about 6 per cent to the intensity of the band in question. HALF

WIDTHS

The half widths of N,O were measured for both N, and self-broadening. In the former case, the partial pressure of the N,O was kept to less than one per cent of the total pressure. In the latter case, it was necessary to use a short (2 cm) cell in order to keep the absorption down to reasonable values for the strongest lines. The results of the half-width measurements are presented in Table 2 and Fig. 2, as a function of the rotational quantum number

FIG. 2. Measured

and computed

values of the half widths of the (OO”24W’O) band. The computed are from Ref. (3).

values

m, thereby combining the results for the P- and R-branches. The column labeled Calc. is taken from ToTH'~) and contains the results of his calculations based on a modified Anderson-Tsao-Curnutte theory. The agreement here for most lines is within experimental error. The agreement of the measurements made here with Toth’s measurements on the (02”1-00”0) and (10°14WO) bands is also within experimental error and we may conclude that the dependence of the half widths on vibration must be small.

756

JACK

TABLI:

2.

MEASURED

AND

S.

COMPUTED

I.INES OF THE

b‘ I 2 3 4 5

6 I 8 9

I0 II 12 13 14 IS I6 17 18 19 20 21 22 23 24 75 26 27 28 29 30 31 3’ 3; 34 35 36 37 38 39 40 41 42 43 44 45 46 41

MARGOISS

VALUES

N, Broadened h, (Calc.)

0.0965 cm 0.1009 0.0993 0.0964 0.0960 0.0938 0.0922 0.09 1 I 0.0906 0.089 I 0.089 1 0.0873 0.0858 0.0845 0.0851 0.0830 0.0825 0.0824 0.083 1 0.0839 0.0804 0.0799 0.0789 0.0806 0.0792 0.0790 0.0769 0.0785 0.0773 0.0778 0.0755 0.0780 0.0769 0.0733 0.0765 0.0794 0.0803

’

0.0926 cm 0.0883 0.0883 0.0889 0.0900 0.0909 0.09 I4 0.09 I 5 0.09 I 3 0.0902

0.0867

0.0822

0.0788

0.0763

0.0753

0.0747

0.0747

0.0749

0.0744

OF THE SELF AND

(00”2200”0)

h,

’

N,

BROADENHI)

“AND

Self Broadened h, (Calc.)

O.l39cm-’ 0.135 0. I30 0.129 0.128 0.127 0.124 0. I26 0. I24 0.125 0.123 0. I22 0.123 0.1 I9 0.122 0.122 0.1 I9 0.1 I8 0.1 I7 0.117 0.112 0.1 14 0. IO9 0.109 0.108 0.106 0. I04 0.103 0.101 0.103 0.100 0.101 0.096 0.101 0.097 0.097 0.096 0.0931 0.095 0.093 0.093 0.092 0.090 0.086 0.089

The computed values are from Ref. (3). The average measured half widths is about 7 per cent.

standard

0.138cm

’

0.127

0.117

0.102

0.079

deviation

of the

Intensity and half width measurements

of the (00”2-00”0) band of N,O

157

Acknowledgemenfs-I am indebted to Dr. R. TOTH for many useful discussions and for the opportunity to see the results of his measurements prior to publication. This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract Number NAS 7-100, sponsored by the National Aeronautics and Space Administration.

REFERENCES

I. J. PLIVA, J. Molec. Spectrosc. 25, 62 (1968). 2. 3. 4. 5. 6. 7. 8.

J. VINCENT-GEESE, Ann. Phys. lo,46 (1955). R. A. TOTH, to be published. G. D. T. TUWANI and P. VARANASI, JQSRT, 11, 1711 (1971). M. HIRONO,J. Phys. Sot. Japan 26, 1479 (1969). P. A. JANSSONand C. L. KORR. JOSRTI. 1399 (1968). ’ L. D. GRAY YOUNG, JQSRT 12,307 (1972). Y. BEER, Introduction to the Theory ofError. Addison-Wesley,

Reading,

Mass. (1958).