Radiative lifetimes of some states of NeII

J. Qwnt. Spctmsc. Radiat Printed in Great Britain.

Tmnsfer Vol. 35, No. 6, pp. 481-493,

0022.4073/86 S3.00+ .oO Per@mon Journals Ltd.

1986

PRESSURE BROADENING OF AMMONIA LINES IN THE 6475 8, BAND AT ROOM AND LOW TEMPERATURES+ CHARLESE. KEFFER,~CHARLESP. CONNERLUI~ W. H. Department

of Chemistry, Washington

University,

(Received 12 August

SMITH St. Louis, MO 63130, U.S.A.

1985)

Abstract-Measurements of pressure broadened half-widths have been performed for four ammonia vibration-rotation lines in the 6475 A band. Self-, hydrogen- and helium-broadening have been measured over a temperature range of 175-295 K. Pressure broadening coefficients and temperature dependence indices have been obtained for each line and broadening gas. A rotational quantum number dependence for the line width has been observed for all broadening gases studied.

INTRODUCTION

Ammonia absorption features in the 6475 A band (traditionally referred to as the 6450 A band or as 5v, after Badger’) are prominent in the spectra of Jupiter and Saturn.2 These features are expected to be a sensitive probe of the pressure and temperature conditions under which line formation occurs in Jupiter and Saturn. Also, information about the atmospheric cloud structure and the ammonia abundance is implicit in the planetary spectra of these vibration-rotation lines. The importance of laboratory data in modeling planetary atmospheres and the fact that the absorption features in the 6475 A ammonia band are unsaturated, even for the large abundances encountered in the atmospheres of Jupiter and Saturn, has led to several laboratory studies of this absorption band. In particular, line positions, line strengths, pressure broadening coefficients and several attempts at a rotational analysis for the band have been obtained by several authors. Rank, Fink and Wiggins’ measured hydrogenbroadening coefficients for 18 lines in the 6475 A ammonia band. Mason4 measured selfbroadened half-widths for six lines and line strengths for ten lines in the 6475 A band. Giver, Miller and Boese5 presented an atlas for the entire band and also measured intensities and self-broadening coefficients for 31 selected lines which are prominent in the Jupiter spectrum or are reasonably unblended in the laboratory spectrum. Also, Keffer, Conner and Smith6 have determined hydrogen-broadening coefficients for four isoloated lines in the 6475 8, band. A rotational analysis by McBride and Nicholls’ was based on the assumption that nearly all of the lines in the 6475 8, band are part of the 5v, overtone. A later analysis by Johns and Abe,8 taken at higher spectral resolution and lower pressures than McBride and Nicholls used, concluded that the 6475 8, ammonia band is due to an overlap of overtone and combination bands with 5v, being the most prominent one in the region. The most recent analysis of this band has been carried out by Lehmann and COY.~ They have assigned 190 lines in the spectrum and concluded that the 6475 8, band is an overlap of parallel and perpendicular bands and that the upper levels are best described in the local mode terminology as the A and E components of a state with five quanta of N-H stretch in one bond. All of these previous studies of the 6475 %, ammonia band have been performed at room temperature. Low temperature measurements are essential to the proper analysis of the observations of the atmospheres of Jupiter and Saturn. Therefore, we have extended the previous work to temperatures appropriate to the atmospheres of these planets.

+This research has been supported by NSF under grant AST 83-03108. tPresent address: Battelle Pacific Northwest Laboratories, RTL Building, Richland, WA 99352, U.S.A.

487

488

CHARLES

E. KEFFER et al.

EXPERIMENTAL

Pressure broadened spectra for ammonia have been acquired using a dye laser spectrometer and nonresonant photoacoustic detectors constructed in this laboratory. The photoacoustic detector used for low temperature measurements is described in detail elsewhere. lo It consists of a vacuum insulated photoacoustic cell which is cooled by flowing liquid nitrogen (or cold nitrogen gas) and simultaneously heated by a variable transformer controlled heating tape. Temperatures in the range 77-300 K are obtained to & 1 K. The dye laser spectrometer and the room temperature photoacoustic detector have been described previously. I* Briefly, the dye laser spectrometer consists of a passively stabilized single frequency ring dye laser pumped by the multiline output from an argon ion laser which is amplitude modulated at 30 Hz. The dye laser has been interfaced to a minicomputer which performs the scan control and data acquisition tasks. The photoacoustic detector used for room temperature measurements is a IO” long block of aluminum with a l/4” diameter hole which forms the acoustic cavity. The ends are cut at Brewster’s angle to allow intracavity operation and fused silica windows attached using Apiezon wax. A single miniature electret microphone is centered lengthwise in the acoustic cavity. Acoustic signals are detected with a lock-in amplifier and stored by the computer concurrently with interference fringes from an 8 GHz confocal etalon. The etalon fringes are used for a relative frequency calibration. Absolute wavelength measurements are made to better that 1 part in IO6 using a Michelson interferometer wavemeter. We have used a 1.5 second integration time per point and a 0.3 second lock-m time constant. Anhydrous ammonia (J, T. Baker) was used without further purification. Pressure measurements in the cell were made with an accuracy of I!Z1.5% using a capacitance manometer and temperature measurements were made using a silicon diode temperature sensor with an accuracy of f 1 K. The dense spectra of ammonia in the 6475 A band leads to blending of neighboring lines and therefore presents a serious problem in accurately measuring the line profiles for absorptions in this ammonia band. Special attention was given to selecting lines for pressure broadening measurements which are affected least by this problem. Selection was made on the basis of two criteria. First, preference was given to lines which dominate the region of the spectrum in which they are located; i.e. neighboring lines should have only a fraction of the intensity of the line being studied. Also important is to select lines which have the greatest frequency interval separating them from neighboring lines. We have selected four lines in the 6475 8, ammonia band which meet these two criteria and which have a high enough intensity to be measured at high SIN. These lines are located at 6454.06, 6455.84, 6457.12 and 6460.50 A. Figures l-4 illustrate these four lines and how they satisfy the selection criteria. Having selected these four lines as the best candidates for pressure broadening measurements, experiments were designed so as to determine the pressure broadening coefficients

WAVELENGTH

t.fi,

Fig. 1. Ammonia feature at 6454.06 A. Spectrum was taken at a pressure of 6 Torr and a temperature of 17.5 K.

Pressure

Fig. 2. Ammonia

broadening

of ammonia

feature at 6455.84 A. Spectrum was taken at a pressure of 6 Torr and a temperature of 176 K.

WAVELENGTH

Fig. 3. Ammonia

Fig. 4. Ammonia

lines

(A)

feature at 6457.12 A. Spectrum was taken at a pressure of 6 Torr and a temperature of2OOK.

feature at 6460.50 A. Spectrum was taken at a pressure of 8 Torr and a temperature of 180 K.

490

CHARLES E. KEFFER et al

in the most accurate way possible. For each choice of line, collision partner and temperature, an attempt was made to maximize S/N, minimize blending, and maximize the amount that the line was broadened. Since these conditions are in opposition, it was necessary to select pressures for each experiment that would achieve the best compromise. Each line is unique and required careful selection of the conditions under which it was studied, ANALYSIS

The experimental line profiles were fit to the Voigt line shape function using a nonlinear least squares curve fitting routine. ** The value of chi-square was minimized with respect to the following four free parameters: (line center), (Lorentzian half-width), (baseline-a zero offset), (intensity-a multiplicative factor).

WO aL

B

I

Values for the Voigt function used in fitting the ammonia spectra were calculated to an accuracy of 1 part in lo6 using the algorithm developed by Armstrong.r3 The goodness of fit of the Voigt function to the data was measured by the value of the reduced chi-square for each fit. In addition, the residuals of the fit, i.e. the calculated values minus the observed values, were examined for any systematic deviation from the model profile. The Lorentzian half-widths determined for each line were plotted against the broadening gas pressure to determine the pressure broadening coefficient by linear regression analysis. The pressure broadening coefficients were assumed to follow a usual (cf. Varanasi, Giver and Valero I4 and Margolis and Sarangils) power law dependence on temperature of

Y(T)= y&J CT,/ T)n, where y is the pressure broadening coefficient, To is room temperature and n is the temperature dependence index. The temperature dependence index has been determined by linear regression analysis of plots of -In y vs. In T. An example of such a plot is shown in Fig. 5. E 55-

0.45-

52

53

54

55 In

56

57

T

Fig. 5. Temperature dependence index determination. Data shown are for ammonia self-broadening in the 6455.84 A line.

Pressure broadening of ammonia lines

491

We have observed the output profile of the scanning laser and determined that its effective full-width at half-maximum is 300-400 MHz. This corresponds to a resolving power of about 1.5 x lo6 at the wavelengths used. The effect of the laser bandwidth on the experimentally observed spectral line profiles must either be demonstrated to be negligible or else accounted for in the analysis of the line profiles. We have determined this effect by the following analysis. First, the most isolated lines observed were selected in order to eliminate any possibility of blended lines affecting the determination. These lines are at 6455.84 and 6457.12 A. Least squares fits to the self-broadening data for these lines were examined to see if there was any residual width remaining after extrapolating to 0 pressure. The average y-intercept for these data sets was found to be 0.0012 cm-‘. This is less than 0.5% of the self-broadening coefficients for these lines and therefore smaller than the error expected from other sources. This indicates that the Voigt function, as used, has accurately accounted for the actual spectral line widths. However, it does not exclude the possibility that instrumental broadening has been included in the Lorentzian contribution, which is a free parameter. To investigate this possibility, spectra of the 6457.12 8, line at the lowest pressure used were fit with a purely Gaussian function. This line was selected for this analysis since it has a smaller self-broadening coefficient than the 6455.84 8, line and so should be more nearly Doppler width at minimum pressure. At room temperature, the results of these Gaussian least squares fits give no indication of any measurable deviation from the expected Doppler width. Even at 175 K, where the Doppler width is less and the pressure broadening is greater, the line width obtained from the Gaussian function was less than 2% above the Doppler width, even when the expected pressure broadening was completely ignored. We have concluded that the laser bandwidth has not caused any significant broadening of the spectral line profiles. Therefore, no correction has been made for instrumental broadening. RESULTS

AND DISCUSSION

Room temperature pressure broadening coefficients (7) are presented in Table 1 for the four lines and three broadening gases used. For self-broadening, we have used 5-75 Torr of NH,. For foreign gas broadening, we have used 5-7 Torr of NH 3 with 100-250 Torr H2 and 100-400 Torr He. Comparison is made with the previous studies of this absorption band where those data sets overlap the present study. Rank et al. 3 have studied measurements in the hydrogen-broadening while Giver et al. 5 have made self-broadening 6475 A ammonia band. Helium-broadening has been studied for the first time in this absorption band in the present study. Our self-broadening coefficients are in reasonable agreement with those of Giver et al.

Table 1. Room temperature pressure broadening coefficients in the 6475 A ammonia band Lehmannet aL GaseS

NHs:H2

NHs:He

NH,:NH,

Wavelength

assignment

(‘4)

(J,K)

~(295) (cm-‘/a&

6454.06 6455.84 6457.12 6460.50

21 22 10 11

6454.06 6455.84 6457.12 6460.50

21 22 10 11

0.03899~.0014 0.0391Of.0021 0.03629f.0013 0.04113+.0022

6454.06 6455.84 6457.12 6460.50

21 22 10 11

0.4316f.012 0.5932k.014 0.3449*.0070 0.5922k.012

Giver et al. &n-l /atm)

Rank

et aL

(cm -I /atm)

0.081 0.072 Margolis et al. Y, + v2rv*+ v3 (cm -I latm)

0.565f.06 0.67f.065 0.36f.015 0.59*.055

0.411*.024: 0.584f.011 0.368f.003

Vhe uncertainties listed represent one standard deviation. *These self-broadened half-widths are for lines of the same lower state quantum numbers as the lines observed in the present study of the 6475 8, band.

CHARLES E. KEFFER~?~~.

492

Comparison of our hydrogen-broadening results with those of Rank et al. shows little similarity. We believe that the higher resolving power and lower pressure range of the present study can account for the differences in self- and hydrogen-broadening coefficients where they exist. Low temperature pressure broadening coefficients for the four lines which we studied are given in Table 2. No values of low temperature pressure broadening coefficients for lines in the 6475 8, ammonia band have been published previously. The lowest temperature used for these measurements was 175 K, since the ammonia condensed below an acceptable pressure level for lower temperature studies. Self-broadening measurements were limited to 200 K for the same reason. The data of Tables 1 and 2 shows a variation of the broadening coefficient among the different lines observed. This is especially apparent in the self-broadening case where resonant interactions are more likely to occur during collisions. We have listed the lower state assignments of Lehmann and Coy16 for these four lines in Table 1. Also listed in Table 1 are self-broadening coefficients, for the same values of .I and K, as measured by Margolis and Sarangi I5 in the (v, + v& and (v2 + u&bands of ammonia. Using the proposed assignments of Lehmann and Coy, we note a close agreement between the self-broadening coefficients of Margolis and Sarangi for the infrared combination bands which they observed and our own room temperature results for the 6475 8, band. Margolis has also observed hydrogen-broadening in the (v, + vz)- and (v2 + v,)-bands of ammonia. I7 Again, we notice similarity between his results and our own for the same values of J and K. Margolis has observed that the quantum number trend in half-width is to decrease as J increases, for fixed K, and increase as K increases, for a fixed J. Varanasi’* has also observed this same behavior for self-broadening in the v,-band of ammonia. The present results concur with these observations in nearly every case. Finally, we note that the Anderson I9 theory of pressure broadening predicts a half-width dependence on quantum number very similar to that which we have observed experimentally. Specifically, for self-broadening the line width should be proportional to (K *IJ(J+ 1))2/X, where x refers to the dominant type of intermolecular interaction.20 For dipole-dipole interactions, x = 4. Therefore, the theory predicts, using the Lehmann and Coy assignments, that the lines at 6454.06, 6460.50 and 6455.84 8, will have self-broadened widths in the ratio of 1:1.7:2. Experimentally, we determine the widths are in the ratio of 1:1.7:1.7. The temperature dependence index n has been determined by least squares analysis for each ammonia line and broadening gas studied. The resulting values are given in Table 3. Since no other low temperature results are known for the 6475 8, absorption band, comparison can only be made with the infrared study of Margolis and Sarangi.‘5 They obtained an average value for n of 0.57 for hydrogen-broadening. This compares very well with the average value from our results of 0.60 for hydrogen-broadening. For self-broadening, Margolis and Sarangi obtained values for n ranging from 0.70 to 2.04 for the lines which they investigated. Their conclusion was that, for self-broadening, the value of n seemed to Table 2. Low temperature pressure broadening coefficients in the 6475 .k ammonia band Gases

Wavelength (A)

y(225)

(cm -I latm)

74200)

(cm -’ /atm)

y(175) (cm --L/atm)

NHx:HI

6454.06 6455.84 6457.12 6460.50

0.1286f.O069+ 0.1221f.0026 0.1151*.0047 0.1317f.0029

0.1374&0028 0.1344f.0033 0.1413f.0022 0.1431f.0035

NH,:He

6454.06 6455.84 6457.12 6460.50

0.0548f.0017 0.0409*.0054 0.0479Ifr.0023 0.0497*.0013

0.0527~.0014 0.0431*.0044 0.0407*.0011 0.0538f.OcM

NH,:NH,

6454.06 6455.84 6457.12 6460.50

0.5396&.0075 0.7502&.016 0.3816f.012 0.7227f.026

+Tbe uncertainties listed represent one standard deviation.

0.6008f.057 0.8174~.0086 0.5159f.010 0.8484f.0093

Pressure broadening of ammonia lines Table 3. Ammonia

493

temperature dependence index. Wavelenth CR)

Index (n)

NH,:HI

6454.06 6455.84 6457.12 6460.50

0.48 0.53 0.71 0.69

NH,:He

6454.06 6455.84 6457.12 6460.50

0.58 0.20 0.23 0.55

NH,:NHp

6454.06 6455.84 6457.12 6460.50

0.85 0.85 0.95 0.89

Gases

have a strong dependence on the quantum numbers J and K and an average might not be of any physical significance. Our own results for self-broadening show no apparent quantum number dependence for the temperature dependence index, with each value of n quite close to the average of 0.89. The value of n for helium-broadening shows considerable variation among the four lines studied here with an average value of 0.39. Birnbaum*O has applied Anderson’s theory of pressure broadening to determine that the temperature dependence index should be given by n = (X+ 4) /2x, where x again takes on values which depend on the dominant type of intermolecular interaction involved. The dominant interactions present in our experiments are dipole-dipole for self-broadening, dipole-quadrupole for hydrogen-broadening and dispersion or dipole-induced-dipole for helium-broadening. Therefore, the values for the temperature dependence index expected from these interactions are 1.0 for self-broadening, 0.83 for hydrogen-broadening and 0.70 for helium-broadening. Only the self-broadening data are in reasonable agreement with the Anderson theory. In fact, the helium- and hydrogen-broadening temperature dependences are closer to the value of 0.5 expected from kinetic theory than to the values predicted by Anderson’s theory of pressure broadening. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

R. M. Badger, Phys. Rev. 35, 1038 (1930). W. H. Smith, W. Macy and W. Cochran, Icarus 42, 93 (1980). D. H. Rank, U. Fink and T. A. Wiggins, Astrophys .I 143, 980 (1966). H. P. Mason, Astrophys. Space Sci. 7, 424 (1970). L. P. Giver, R. W. Boese and J. H. Miller, J. Atmos. Sci 26, 941 (1969). C. E. Keffer, C. P. Conner and W. H. Smith, JQsRT33, 193 (1985). J. 0. P. McBride and R. W. Nicholls, Can. J. Phys. 50, 93 (1972). J. W. C. Johns and K. Abe, unpublished manuscript (1973). K. K. Lehmann and S. L. COY, J. Chem. Phys. 81, 3744 (1984). C. E. Keffer, C. P. Conner a&l W. H. Smith, Rev. Sci. Inns& 56, 2161 (1985). C. E. Keffer, C. P. Conner and W. H. Smith, Chem Phys Left. 104, 475 (1984). P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences. McGraw-Hill, New York (1969). B. H. Armstrong, JQSRT 7, 61 (1967). P. Varanasi, L. P. Giver and F. P. J. Valero, JQSRTJO, 481 (1983). J. S. Margolis and S. Sarangi, JQSRT 16, 405 (1976). K. K. Lehmann, private communication (1984). J. S. Margolis, JQSRT 15, 637 (1975). P. Varanasi, JQSRT 12, 1283 (1972). P. W. Anderson, Phys Rev. 76, 647 (1949). G. Bimbaum, Advances in Chemical Physics, Intermoleculur Forces (Edited by J. 0. Hirschfelder), Vol. 12. Interscience, New York (1967).