Empirical values of the ground state energies for methane transitions between 5500 and 6150 cm^-1
8
Empirical values of the ground state energies for methane transitions between 5500 and 6150 cm-1 Jack S. Margolis The strengths of more than 1600 lines of CH 4 have been measured in the spectral interval between 5500 and 6150 cm-' at room temperature and reduced temperatures. The variation of the measured strengths allows the energy of the lower state of the transition to be determined empirically using the temperature dependence of the methane partition function and the Boltzmann factor for the energy level populations. An error analysis, based on assumed errors in the strength and temperature measurements, is included. The average measured uncertainty in J is 0.2. 1. Introduction The spectra of the atmospheres of the outer planets contain numerous absorptions of the methane mole- cule. The intepretation of these absorptions may be useful for the understanding of the structure of the atmospheres of these planets and their radiation bud- gets. Also, since the CH 4 bands overlap the bards of other molecules which may be found in the atmos- pheres of these planets, it is necessary to have a sub- stantially complete atlas of the methane lines in order to sort out which ones belong to which molecule. In general, the analysis of the spectrum of the CH 4 mole- cule is satisfactorily complete for the fundamentals and some of the low order overtone bands. However, the CH 4 spectrum gets rapidly exceedingly complex as the spectral order increases, and the bands at 6000 cm-' have proved to be resistant to straightforward analysis with present day theory and computational facilities. Nevertheless, it is important to gain at least an empirical understanding of the spectra for the pur- poses expressed above. To this end, the positions and strengths of the methane lines in the interval between 5500 and 6200 cm-' were measured at room tempera- ture. The results of these measurements appear in an earlier publication.' This compilation is useful for high spectral resolution studies of the atmospheric spectra, and may be used to determine whether a par- ticular line belongs to methane or some other molecule. The author is with Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91109. Received 31 July 1989. 0003-6935/90/152295-08$02.00/0. © 1990 Optical Society of America. But, because the planetary lines are formed at tem- peratures much different from room temperature lab- oratory conditions, the list must be enhanced appro- priately in order to determine the relative absorption strengths. The required values for the lower state energies of the observed transitions may be deter- mined by appropriate assignment of quantum num- bers to the transitions, if that is possible, or empirically by determining the temperature dependence of the absorption strengths under controlled conditions. The latter course is taken in the study reported here. The method and a discussion of the precision of the technique will be discussed in the following sections. The results reported here may be used in high reso- lution studies of atmospheric spectra, as described above, or they may also be used to derive coefficients of band models for low resolution studies of atmospheric spectra. In particular, it is hoped that they may be useful for atmospheric observations of the planet Jupi- ter by the NIMS (near infrared mapping spectrome- ter) instrument to be carried to an orbit around that planet by the Galileo spacecraft. II. Measurement As in the previously cited study' the measurements were carried out at the 1-m Fourier transform spec- trometer at the McMath Solar telescope of the Kitt Peak National Observatory (National Solar Observa- tory). The effective spectral resolution, after apodiza- tion, was -0.013 cm-'. This is somewhat less than the FWHM Doppler width of the CH 4 lines in this spectral interval; this resolution was selected as the optimum with respect to instrumental degradation of the spec- trum and signal-to-noise ratio. Individual interfero- grams, which require -4 min per scan, were added together for a total time of acquisition of -1 h. A single temperature controlled absorption cell, 80 cm 20 May 1990 / Vol. 29, No. 15 / APPLIED OPTICS 2295
Transcript of Empirical values of the ground state energies for methane transitions between 5500 and 6150 cm^-1
Empirical values of the ground state energies for methanetransitions between 5500 and 6150 cm-1
Jack S. Margolis
The strengths of more than 1600 lines of CH4 have been measured in the spectral interval between 5500 and6150 cm-' at room temperature and reduced temperatures. The variation of the measured strengths allowsthe energy of the lower state of the transition to be determined empirically using the temperature dependenceof the methane partition function and the Boltzmann factor for the energy level populations. An erroranalysis, based on assumed errors in the strength and temperature measurements, is included. The averagemeasured uncertainty in J is 0.2.
1. IntroductionThe spectra of the atmospheres of the outer planets
contain numerous absorptions of the methane mole-cule. The intepretation of these absorptions may beuseful for the understanding of the structure of theatmospheres of these planets and their radiation bud-gets. Also, since the CH4 bands overlap the bards ofother molecules which may be found in the atmos-pheres of these planets, it is necessary to have a sub-stantially complete atlas of the methane lines in orderto sort out which ones belong to which molecule. Ingeneral, the analysis of the spectrum of the CH 4 mole-cule is satisfactorily complete for the fundamentalsand some of the low order overtone bands. However,the CH4 spectrum gets rapidly exceedingly complex asthe spectral order increases, and the bands at 6000cm-' have proved to be resistant to straightforwardanalysis with present day theory and computationalfacilities. Nevertheless, it is important to gain at leastan empirical understanding of the spectra for the pur-poses expressed above. To this end, the positions andstrengths of the methane lines in the interval between5500 and 6200 cm-' were measured at room tempera-ture. The results of these measurements appear in anearlier publication.' This compilation is useful forhigh spectral resolution studies of the atmosphericspectra, and may be used to determine whether a par-ticular line belongs to methane or some other molecule.
The author is with Jet Propulsion Laboratory, 4800 Oak GroveDrive, Pasadena, California 91109.
Received 31 July 1989.0003-6935/90/152295-08$02.00/0.© 1990 Optical Society of America.
But, because the planetary lines are formed at tem-peratures much different from room temperature lab-oratory conditions, the list must be enhanced appro-priately in order to determine the relative absorptionstrengths. The required values for the lower stateenergies of the observed transitions may be deter-mined by appropriate assignment of quantum num-bers to the transitions, if that is possible, or empiricallyby determining the temperature dependence of theabsorption strengths under controlled conditions.The latter course is taken in the study reported here.The method and a discussion of the precision of thetechnique will be discussed in the following sections.
The results reported here may be used in high reso-lution studies of atmospheric spectra, as describedabove, or they may also be used to derive coefficients ofband models for low resolution studies of atmosphericspectra. In particular, it is hoped that they may beuseful for atmospheric observations of the planet Jupi-ter by the NIMS (near infrared mapping spectrome-ter) instrument to be carried to an orbit around thatplanet by the Galileo spacecraft.
II. MeasurementAs in the previously cited study' the measurements
were carried out at the 1-m Fourier transform spec-trometer at the McMath Solar telescope of the KittPeak National Observatory (National Solar Observa-tory). The effective spectral resolution, after apodiza-tion, was -0.013 cm-'. This is somewhat less than theFWHM Doppler width of the CH 4 lines in this spectralinterval; this resolution was selected as the optimumwith respect to instrumental degradation of the spec-trum and signal-to-noise ratio. Individual interfero-grams, which require -4 min per scan, were addedtogether for a total time of acquisition of -1 h. Asingle temperature controlled absorption cell, 80 cm
20 May 1990 / Vol. 29, No. 15 / APPLIED OPTICS 2295
Er
cr
0.
0. 100. 200. 300. 400. 200. 600. 700. 800.E" (CM-i)
Fig. 1. Percentage error in the determination of E" as a function ofE": The solid line is for an error of 2 K in the 180 K-temperaturemeasurement and the dashed line is for an error of 2 K in the 200 K-temperature measurement. Both curves correspond to an error of
1 K in the 296 K-temperature measurement.
long, was used to obtain all of the spectra used. Tem-peratures as low as 180 K are achievable by circulatingcold nitrogen gas, obtained from liquid nitrogen boil-off, through copper tubing soldered to the outside ofthe stainless steel cell. The reduced temperature runswere all obtained between 180 K and 220 K. Thepressures were measured using a temperature con-trolled Baratron capacitance gauge. The temperatureof the cold cell was monitored using a Ge resistancethermometer on the outside of the cell, and the read-ings so obtained were used for control purposes. TheRMS temperature fluctuations during the duration ofthe spectra were less than -2 K. The Ge resistancethermometer readings were not used in the analysis ofthe spectra; instead, a rotational temperature for theassigned lines of the 2v3 band was determined for eachof the spectra used in the analysis. This temperaturewas then used to derive empirical values for the lowerstates energy of the measured transitions.
The gas pressure was limited <20 Torr for all mea-surements so that the pressure-broadened width of thelines remained small compared to the Doppler width.It was assumed that the self-broadened width of thelines was 0.085 cm-1 (HWHM)2,3 per atmosphere andthat the temperature dependence of the broadeningwas inverse square root. At 180 K and 5500 cm-1 theratio of Doppler width to pressure broadened width (ata self-pressure of 20 Torr) is 0.4. A Voigt profile wasused to analyze the spectra.
The details of how the absorption strengths are de-termined from the spectra were described in the previ-ous manuscript.' Briefly, a synthetic parametrizedspectrum is computed and compared to the observedspectrum. The parameters of the synthetic spectrumare then varied so as to reduce the sum of the squares ofthe residuals between the two.
2
C
LU
- I
0 1 2 3 4 5 6 7 8 9 1011I12
J-VALUEFig.2. Uncertainty of the effective Jvalue determination is shownfor an uncertainty of 5% in the strength measurement at both room
and reduced temperatures.
The empirical value of the lower state energy in atransition may be deduced by considering the tem-perature dependence of the absorption strength of asingle line
S(JT) = vS 0Q'1(T)H(J)exp[-E'(J)/kT], (1)
where v = frequency of the transitionJ = set of quantum numbers describing the
transitionQ(T) = partition function at temperature TH(J) = function describing the dependence of
the strength on the quantum numbersJ
E"(J) = lower state energy of the levels in-volved in the transition, and
So = band strength.The ratio of strengths observed at two different
temperatures may be easily derived from Eq. (1):
S(J,T1 )IS(J,T2) = (T2/T1)312 exp[-E"/k(Tll - T2-1)]. (2)
Q(T) is given sufficiently accurately for our purposesby the rotational partition function alone. This isgiven by Fox.4 Over the temperature range consid-ered it is satisfactory to take Q(T) to vary as the 3/2power of temperature. Equation (2) may be explicitlysolved for E". This allows a direct determination ofE" provided that the absorption strengths are mea-sured using at least two sufficiently different tempera-tures.
E = 1.5 ln(T 2/Tl) - ln[S(T 1)/S(T2)j0.69541[TlT 2/(T2 - T)].
(3)
N measurements of the strengths at different tempera-tures lead to N-1 determinations of E".
The gas temperature inside the cell was determinedspectroscopically from the rotational temperature ofthe 2 3-band. For this purpose Eq. (1) may be used;room temperature measurements of the manifold
2296 APPLIED OPTICS / Vol. 29, No. 15 / 20 May 1990
I I I I I I I I I I I
o +o +
0 1 6 6 6 d b 6 1
o 6666 9 9 9 9o +
0 +
+ +
I I I I I I I I I I I
I
-2
Table 1. Empirical Values Calculated for Ground State Energies of Transitions In Methane
8.0 (0.0)8.0 (0.1)7.1 (0.0)7.0 (0.0)7.0 (0.0)6.5 (0.0)6.5 (0.7)7.2 (0.5)6.1 (0.6)6.2 (0.1)6.1 (0.2)6.1 (0.1)4.5 (0.3)7.2 (0.3)5.2 (0.0)5.1 (0.0)5.0 (0.4)5.5 (0.6)5.1 (0.1)4.7 (0.4)5.2 (0.0)5.1 (0.0)2.5 (0.3)3.8 (0.0)4.0 (0.0)4.1 (0.0)3.2 (0.0)3.0 (0.1)3.2 (0.0)6.1 (0.1)2.7 (0.0)2.5 (0.1)9.5 (0.2)9.0 (0.1)8.1 (0.0)8.1 (0.1)8.7 (0.0)9.0 (0.0)9.1 (0. 0)6.9 (0.1)5.6 (0.2)6.9 (0.1)7.0 (0.1)8.0 (0.0)8.1 (0.0)7.0 (0.0)6.9 (0.1)6.0 (0.0)6.9 (0.3)6.4 (0.1)6.6 (0.0)6.1 (0.0)5.3 (0.2)
Freq/ (
5583.163155583.490655583.504975583.601205583.721845583.888105584.344745584.385255584.570785584.673415584.727515584.865305584.946235585.074125585.667825585.747305586.119585586.604565586.691035586.840005587.198245591.292015594.014525597.140975602.434765602.488385604.056755604.101505606.536025607.658255615.586615615.663365622.603555622.909765624.390955624.597035624.694795625.648535628.110225630.387545630.884285632.178785632.234715632.511535633.015065633.119885633.639955634.141055634.445755634.637455637.767505639.611375639.690815642.29428
S
1.9321.2090.7682.0580.7841.9492.2183.9441.8792.3051.0071.8071.2062. 8133. 6462.8245.4001.8662.7750.8231.8281. 2540.8383. 1451.0001.9640.7910.9133.0270.9703.7992.4770.8845. 2502.8551.1373. 2232.3912.4001.0740.9332.9321.1062 .3370.7502.2802.7693. 2740.7730.7941.6910.8740.9331.628
E"
299145237153115104154108161112295110232102103
64663534
1128
63371-3
246247176
7519
1183842716771616471
114177
4112121113188114121113168
72223
67163174
(20)(29)(65)( 0)( 1)( 9)( 2)( 3)( 3)( 0)( 0)( 1)( 8)( 5)( 9)( 1)( 0)( 0)( 1)( 1)( 1)( 1)( 8)( 1)(13)( 9)( 1)( 1)( 2)( 2)( 2)( 3)( 2)( 1)( 1)( 3)( 2)( 2)( 3)( 3)( 2)( 2)( 5)( 1)( 1)( 3)( 0)( 2)( 3)( 3)( 1)( 1)( 2)( 6)
J"
7.14.86.34.94.24.05.04.15.14.27.04.16.24.04.03 :03.12.12.14.20.93.07.90.46.46.45.33.31.54.32.22.43.23.13.23.03.13.24.25.30.54.24.34.25.54.24.34.25.23.36.13.15.15.3
(0.3)(0.5)(0. 9)(0. 0)(0. 0)(0.2)(0. 0)(0. 1)(0. 1)(0. 0)(0. 0)(0. 0)(0. 1)(0. 1)(0.2)(0. 0)(0. 0)(0. 0)(0. 0)(0. 0)(0. 1)(0.0)(0. 1)(0.4)(0.2)(0. 1)(0. 0)(0. 0)(0. 1)(0. 0)(0. 1)(0. 1)(0. 1)(0. 0)(0. 0)(0. 1)(0. 1)(0. 1)(0. 1)(0. 1)(0.2)(0. 0)(0. 1)(0. 0)(0. 0)(0. 1)(0. 0)(0.1)(0.1)(0. 1)(0. 0)(0. 0)(0. 0)(0. 1)
20 May 1990 / Vol. 29, No. 15 / APPLIED OPTICS 2297
S E"Freq. (cm-)
5500.816535501.715355511.819095511. 841005512. 616205514.296285523.252925523.310545523.336295524.303515524.411485524.432755524.716455524.726865530.333845530.525225534.340305534.354835534.491505534.508375535.140895535.396415544.976575545 785235545.977985546.194905556.329745556.436805556.574895566.681745567.191265567.294885574.231005574.989175575.405235575.475135575.919205576.015505576.312125577.941905577.990175578.242705578.502085578.549625578.676605579.353135579.875115579.911365580.135975580.377055580.687315582.978975583.14952
1.1010.9981.9622.1591.6022.3181.5960.8314.187'0.9100.8280.8172.1752.1451.1241.3431.2550.8021.3481.2041.4051.9912.5732.8811.7994.8784.5262.7772.7760.8461.8881.2021.0101.4991.5040.8971.3430.8330.7801.3941.5211.2831.2611.2390.9522. 6461.6751.7241.2710.9231.3903.8722.422
374378298291296255257310229231224223127303168160155187161138167162
4696
104109
696271
2275245
524474382386439469479285189287292375384296288218285251260223176
( 1)( 8)( 1)( 1)( 1)( 1)(57)(40)(40)( 5)(13)( 3)(18)(34)( 1)( 0)(23)(40)( 7)(19)( 0)( 1)(11)( 2)( 0)( 0)( 1)( 5)( 0)( 6)( 1)( 4)(18)( 7)( 2)( 4)( 4)( 3)( 0)(11)( 7)( 4)( 5)( 1)( 1)( 2)( 4)( 2)(19)( 7)( 3)( 1)(11)
Table I, continued
Freq. (crm 1) S E" a" Freq. (mil) S E""
5642.80472 0.836 169 ( 4) 5.2 (0.1) 5735.40883 1.548 387 ( 4) 8.1 (0.0)5642.90051 1.016 191 (29) 5.6 (0.5) 5738.04720 1.351 390 ( 3) 8.2 (0.0)5643.15231 1.925 -0 ( 1) 0.0 (0.3) 5739.69031 2.365 306 ( 1) 7.2 (0.0)5643.25612 1.049 138 (27) 4.7 (0.5) 5739.84744 0.987 396 ( 2) 8.2 (0.0)5643.26547 1.830 275 (37) 6.8 (0.5) 5740.45780 2.259 293 ( 0) 7.0 (0.0)5643.86526 0.763 231 ( 8) 6.2 (0.1) 5740.90458 1.516 368 ( 1) 7.9 (0.0)5646.04374 1.646 218 ( 0) 6.0 (0.0) 5744.04826 0.750 244 ( 4) 6.3 (0.1)5647.32017 1.100 223 ( 7) 6.1 (0.1) 5745.55333 1.193 235 ( 1) 6.2 (0.0)5647.78189 1.413 80 ( 3) 3.5 (0.1) 5746.91491 3.485 305 ( 2) 7.2 (0.0)5647.84709 3.175 230 ( 1) 6.2 (0.0) 5747.65560 0.824 207 ( 8) 5.8 (0.1)5648.53172 1.621 229 ( 0) 6.1 (0.0) 5748.15312 0.894 488 ( 5) 9.2 (0.0)5648.60023 2.048 223 ( 0), 6.0 (0.0) 5748.87297 2.063 299 ( 4) 7.1 (0.1)5653.83024 1.528 227 ( 0) 6.1 (0.0) 5752.09801 1.982 232 ( 3) 6.2 (0.1)5654.38185 1.200 309 ( 2) 7.2 (0.0) 5752.13488 1.839 300 ( 5) 7.1 (0.1)5655.24796 0.877 231 ( 4) 6.2 (0.1) 5752.64322 2.921 226 ( 2) 6.1 (0.0)5655.30338 0.866 244 (20) 6.4 (0.3) 5752.87645 1.488 478 ( 2) 9.1 (0.0)5655.40066 0.784 103 (11) 4.0 (0.2) 5754.00553 4.418 229 ( 0) 6.1 (0.0)5655.88016 1.372 301 (25) 7.1 (0.3) 5757.63877 0.916 566 ( 8) 9.9 (0.1)5656.29523 1.095 326 (19) 7.4 (0.2) 5759.26320 1.045 247 ( 2) 6.4 (0.0)5656.98518 2.766 320 (29) 7.3 (0.4) 5760.15245 0.995 157 ( 2) 5.0 (0.0)5661.24650 0.974 353 ( 5) 7.7 (0.1) 5760.19822 2.165 225 ( 0) 6.1 (0.0)5662.05887 0.896 21 ( 3) 1.6 (0.2) 5760.88831 1.163 455 (20) 8.8 (0.2)5662.22820 1.237 402 ( 4) 8.3 (0.1) 5761.33697 1.420 232 ( 4) 6.2 (0.1)5662.38584 2.437 377 (17) 8.0 (0.2) 5763.29105 0.884 423 ( 7) 8.5 (0.1)5663.10722 0.775 371 ( 2) 7.9 (0.0) 5763.30735 1.143 219 ( 4) 6.0 (0.1)5664.57174 1.217 381 ( 8) 8.1 (0.1) 5763.59570 4.792 237 ( 0) 6.3 (0.0)5667.23975 1.156 446 ( 9) 8.7 (0.1) 5764.47821 3.556 165 ( 1) 5.1 (0.0)5668.09607 0.765 486 ( 0) 9.2 (0.0) 5766.03730 2.945 164 ( 1) 5.1 (0.0)5668.63532 0.900 432 ( 1) 8.6 (0.0) 5767.52602 0.810 470 (10) 9.0 (0.1)5669.11474 1.265 458 ( 0) 8.9 (0.0) 5767.70504 0.876 490 ( 3) 9.2 (0.0)5673.69288 1.043 533 (11) 9.6 (0.1) 5768.81406 0.927 304 ( 0) 7.1 (0.0)5681.03510 1.183 21 (15) 1.6 (0.7) 5770.08658 0.877 393 ( 3) 8.2 (0.0)5686.15382 0.816 82 ( 5) 3.5 (0.1) 5770.86797 0.770 402 ( 3) 8.3 (0.0)5696.20589 1.518 63 ( 2) 3.0 (0.1) 5772.14566 1.412 171 ( 0) 5.2 (0.0)5698.60030 0.836 670 (13) 10.8 (0.1) 5772.86753 1.034 494 ( 4) 9.2 (0.0)5699.12752 0.815 75 ( 1) 3.3 (0.0) 5773.04396 0.996 479 ( 2) 9.1 (0.0)5700.86039 0.785 79 ( 8) 3.4 (0.2) 5773.62335 1.520 83 ( 5) 3.5 (0.1)5701.71914 1.227 582 ( 0) 10.1 (0.0) 5773.77537 1.052 287 ( 1) 6.9 (0.0)5712.34881 0.771 549 ( 3) 9.8 (0.0) 5773.83805 2.946 170 ( 0) 5.2 (0.0)5714.29576 1.215 482 ( 4) 9.1 (0.0) 5774.16502 0.761 100 ( 3) 3.9 (0.1)5714.33465 1.153 579 ( 0) 10.0 (0.0) 5774.67771 1.622 112 ( 1) 4.2 (0.0)5714.64714 1.213 475 ( 9) 9.0 (0.1) 5776.47245 1.016 333 ( 2) 7.5 (0.0)5716.32843 0.769 222 (10) 6.0 (0.2) 5777.15842 2.620 390 ( 2) 8.2 (0.0)5717.79791 0.947 108 ( 0) 4.1 (0.0) 5777.21728 0.787 436 (28) 8.6 (0.3)5722.07936 0.982 121 ( 1) 4.4 (0.0) 5777.38138 5.499 114 ( 0) 4.2 (0.0)5723.97504 1.159 489 ( 6) 9.2 (0.1) 5777.79874 0.778 213 ( 0) 5.9 (0.0)5726.68411 1.894 484 ( 2) 9.1 (0.0) 5778.15861 3.373 113 ( 1) 4.2 (0.0)5726.83625 2.930 388 ( 2) 8.1 (0.0) 5778.38067 0.802 111 ( 3) 4.1 (0.1)5727.33442 1.748 386 ( 3) 8.1 (0.0) 5778.55362 0.856 480 (14) 9.1 (0.1)5727.61635 1.145 384 ( 3) 8.1 (0.0) 5778.88408 3.022 306 ( 1) 7.2 (0.0)5728.33819 1.415 456 ( 3) 8.9 (0.0) 5779.44042 1.327 414 ( 7) 8.4 (0.1)5729.26053 0.990 498 ( 0) 9.3 (0.0) 5781.60962 1.042 120 ( 2) 4.3 (0.1)5730.26115 1.763 473 ( 1) 9.0 (0.0) 5781.70741 1.137 372 ( 7) 8.0 (0.1)5731.97708 0.860 163 ( 1) 5.1 (0.0) 5782.81506 1.514 397 ( 7) 8.2 (0.1)
2298 APPLIED OPTICS / Vol. 29, No. 15 / 20 May 1990
Table , continued
Freq. (an-1)
5806.122535806.408455806.475525806.923675807.795375808.874845809.154385810.933265811.469305811.704305811. 823245812.215595812. 643755813.802765815.180515817.755685819.721765822.171935822. 795945824.089995825.691795829.868375834. 242245834. 731545835. 107475835.308415835. 975365836.299545836.905865838.357085839.240285840.273605840.588675843.981745845.695785845.704755846.207675846 .309445846.377595847.497485847.921575848.082645849.405565849.781825849.790465850.478515850.500655 851. 676595851. 724505851. 814175852. 512475852.749875852.834015853.25747
S
5. 9430.9311.4402. 5980. 9893. 5260.9440.8421.4131.3941. 2592. 9731. 3912. 3301. 1292.4070. 9880. 8671. 2273. 1140. 9356. 8492. 6951. 1590. 8041. 9460. 9241. 0871. 3220. 8362. 0702. 3892. 5362. 3122. 1090. 9720. 9291. 8575. 5351.4440. 9690.9405.0441.4151. 7561. 5751.4101. 5781.9982,. 3514. 8162.1240. 8580. 878
73 (0)231. 7)
36 (4)70 C1)
167 (2)73 (0)65 (0)
117 (0)116 (0)
73 (2)105 (10)
38 (0)20 (0)39 (1)69 (2)20 (1)39 (2)
115 (4)23 (1)67 (1)41 (0)
8 (1)5 (0)
284 (5)164 (0)231 (0)109 (2)161 (2)
68 (3)52 (1)31 (5 )34 (4)3 9 (0)69 (1)28 (4)
149 (5)79 (2)39 (2 )6 3 (0)10 (11)
140 (8)82 (4)
116 (0)118 (22)121 (15)
69 (6)7 5 (3)
114 (3)71 (1)
119 (2)74 (0)68 (1)58 (3 )
157 (3)
3. 3 (0.0)6.2 (0. 1)2. 2 (0. 2)3. 2 (0. 0)5. 2 (0.0)-3. 3 (0. 0)3. 1 (0. 0)4. 3 (0. 0)4.2 (0. 0)3. 3 (0. 1)4.0 (0. 2)2. 2 (0. 0)1. 5 (0. 0)2. 3 (0. 1)3.2 (0. 1)1. 5 (0. 1)2. 3 (0. 1)4. 2 (0. 1)1. 7 (0. 1)3. 1 (0. 0)2. 3 (0. 0)0.9 (0. 1)0. 6 (0. 0)6. 9 (0. 1)5. 1 (0. 0)6. 2 (0. 0)4. 1 (0.06)5. 1 (0. 0)3. 1 (0. 1)2. 7 (0. 0)2.0 (0. 2)2. 1 (0. 2)2. 3 (0. 0)3. 2 (0. 0)1. 9 (0. 2)4. 9 (0. 1)3.4 (0. 1)2 .3 (0. 1)3.0 (0. 0)1. 0 (0. 6)4. 7 (0. 2)3 .5 (0. 1)4. 2 (0. 0)4. 3 (0. 5)4. 3 (0. 3)3 .2 (0. 2)3. 3 (0. 1)4. 2 (0. 1)3. 2 (0. 0)4. 3 (0. 0)3 .3 (0. 0)3. 1 (0. 0)2. 9 (0. 1)5.0 (0. 1)
20 May 1990 I Vol. 29, No. 15 I APPLIED OPTICS 2299
SFreq. cm 1)
5783.018855783.034485784.188745784.257065784.300965785.240875785.270955785.359965785.473815785.824955785.842475785.887795786.435265786.968945788.103715788.287435789.064295789.204985790.272525790. 285135790. 387695790.448155791.477635792.417415792.902075793.129085793.156675793.390095793.644215793.946075794.259695794.694655794. 877125795.553675795. 565695795.950605797.171405797.906675798.626635798.680345799.151785799.923685800.835095801. 211785801.689945801. 838155802.082795802.501825802.616805802.750915803.354325804.308895804.384855804.96837
1. 6090. 8532 . 3030.8031. 2892. 8251. 6280. 7981. 8612. 6961. 6601. 2001. 7131. 8501. 1502. 1091. 6414.4842. 6554. 8412. 3952.0341.4561. 1162.0411. 2701. 671I. 1094.4831. 1301. 8270. 9680. 9162. 9271 .7090. 9973. 1892. 3471.0341. 2501. 3992. 5023. 0552. 5180. 7772. 5810. 9081. 3952. 2251.4240. 8412. 6761.4316. 757
212 4)358 (16)267 5)361 (10)226 C4)116 C2)313 C1)331 C0)314 C3)281 3 3)350 (11)305 (1)225 C2)
74 (1)299 2 2)
71 (0)308 2 2)
70 (0)184 (23)269 (22)223 (1)231 3 3)236 (0)230 3 3)
72 C1)237 C.1)179 (3)168 (0)232 C0)390 C4)132 C0)244 ( 8)225 (1)146 (40)227 (87)313 (3)
70 (0)165 (2)
36 (0)165 (3)164 (1)166 (1)105 (0)
54 (3)76 (0)
116 3 3)121 (1)115 2 2)120 (2)168 (4)41 3 3)
114 (1)233 (4)115 (0)
5. 9 (0. 1)7. 8 (0. 2)6. 7 (0. 1)7. 8 (0. 1)6. 1 (0. 1)4.2 (0. 1)7.3 (0. 0)7. 5 (0. 0)7. 3 (0. 0)6. 9 (0. 0)7. 7 (0. 1)7. 2 (0. 0)6. 1 (0. 0).3. 3 (0. 0)7. 1 (0. 0)3. 2 (0. 0)7. 2 (0. 0)3. 2 (0. 0)5. 5 (0.4)6. 7 (0. 3)6. 1 (0. 0)6. 2 (0.0)'6. 2 (0. 0)6. 2 (0. 0)3. 3 (0. 0)6. 3 (0. 0)5.4 (0. 1)5. 2 (0. 0)6.2 (0. 0)8. 2 (0. 0)4.6 (0. 0)6.4 (0. 1)6. 1 (0. 0)4. 8 (0. 7)6. 1 (1.3)7 .3 (0. 0)3.2 (0. 0)5.1 (0. 0)2. 2 (0. 0)5. 2 (0. 1)5.1 (0. 0)5. 2 (0. 0)4.0 (0. 0)2. 8 (0. 1)3.4 (0. 0)4. 2 (0. 1)4.3 (0. 0)4.2 (0. 0)4. 3 (0. 0)5 .2 (0. 1)2.4 (0. 1)4. 2 (0. 0)6. 2 (0. 1)4.2 (0. 0)
E ., .2,11
Table 1, continued
12942
11751
10835
130169220209225218277385306165171142187
48159166227292133201153363410234224239136199230227217234223238241
72182285200140202311235160322793201425
FV.
( 1)( 0)( 2)( 4)( 2)( 2)( 2)(17)(13)( 6)(14)( 3)(13)( 5)( 3)( 2)( 0)(18)( 5)( 4)( 3)( 4)( 1)( 8)(14)( 6)( 2)(11)
(220)( 3)( 1)( 2)( 3)(28)(13)( 4)( 5)( 0)( 2)( 0)( 3)( 1)( 6)( 3)( 4)(10)( 2)( 1)( 2)( 3)( 4)( 6)(14)( 7)
4.5 (0.0)2.4 (0.0)4.3 (0.0)2.7 (0.2)4.1 (0.1)2.1 (0.1)4.5 (0.1)5.2 (0.3)6.0 (0.2)5.8 (0.1)6.1 (0.2)6.0 (0.1)6.8 (0.2)8.1 (0.1)7.2 (0.0)5.1 (0.0)5.2 (0.0)4.8 (0.4)5.5 (0.1)2.6 (0.1)5.0 (0.1)5.2 (0.1)6.1 (0.0)7.0 (0.1)4.6 (0.3)5.7 (0.1)4.9 (0.0)7.8 (0.1).8.5 (2.5)6.2 (0.1)6.1 (0.0)6.3 (0.0)4.6 (0.1)5.7 (0.4)6.2 (0.2)6.1 (0.1)6.0 (0.1)6.2 (0.0)6.1 (0.0)6.3 (0.0)6.3 (0.1)3.3 (0.0)5.4 (0.1)6.9 (0.0)5.7 (0.1)4.7 (0.2)5.7 (0.0)7.2 (0.0)6.2 (0.0)5.1 (0.1)7.4 (0.1)
11.8 (0.1)5.7 (0.2)8.5 (0.1)
Freq. (cm-l)
5867.855315868.144705868.248495868.290675869.185195869.652245870.155675870.267475871.108385871.271565872.222685872.551895872.619015872.827905873.144685873.504345874.100725874.134665875.224645876.022075876.994525878.470885878.931145878.988195879.109415879.424705879.534725879.684245879.803695881.949575882.318115882.649135882.948805889.016675891.742965891.757735891.796565894.442935899.326675899.971745900.316905900.458285900.898965901.240805902.793345904.640645905.855215907.919395908.914565909.008575909.098115910.'25015910.315995917.62064
2300 APPLIED OPTICS I Vol. 29, No. 15 / 20 May 1990
S' JgFreq. (cn 1)
5854. 165125854. 193125854.272785854.415385854.442035854.943285854.982075855.204045855.441705855.575335855.917645856.060355856.753375856.817285856.986955857.050345857.482415857.739015858.573115858.711725858.724495858.808925858.931845858.977085858.988065859.068885859.225015859.942475860.148775860.449755860.487405860.515095860.726535861.094725861.113525861.389975862.809555862.903335863.000885863.043655863.160865863.551785863.690535863.991535864.018785864.068455864.080565864.283585864.546335864.745225864.918185866.729885866.777955866.88766
S
1.8371.4361.6821.0303.9341.3180.9081.7851.9670.9250.7681.2680.7501.1050.8471.7951.1952.1840.7830. 9910.7812.4742.2591.0861.3871.6942.4621.5250.9180.8861.6570.9402.3180.7781.2500.8371.9720.9960.8892. 1541.0612.8231.3611.1791.3831.0155.5052.0640.9111.3701.5011.3141.0330.805
1.6781.2530.8390.8841.7890.8471.7251.6651.4511.4041.0281.1562.7036.1142.9391.7440.8391.0332.2531.3891.0291.4081.5101.3462.3591.2400.9011.2223.2730.8994.8562.7651.1531.9371.3761.1573.9520.9490.9960.8312.4042.1831.3311.0091.7570.8651.5161.3663.1111.6921.1483.2150.9561.144
292817221772236386230389301308482375
72116115114311305302383498402726699654694686710691405136166478
73129214236154149
82310312228248236217225114394388387306307486
( 8)( 1)( 3)( 9)( 1)( 3)( 4)( 1)( 1)( 1)( 2)(10)( 0)( 0)( 0)( 2)( 3)( 6)( 5)( 1)( 0)( 5)( 6)( 3)( 9)(22)(13)( 3)( 1)( 1)( 7)( 2)( 0)( 1)( 2)( 4)( 0)( 2)( 5)( 2)( 3)( 2)( 3)( 3)( 1)( 3)( 2)( 2)( 0)
( 0)( 0)( 2)( 1)( 0)
7.0 (0.1)12.0 (0.0)6.0 (0.1)
11.7 (0.1)6.2 (0.0)8.1 (0.0)6.2 (0.1)8.1 (0.0)7.1 (0.0)7.2 (0.0)9.1 (0. 0)8.0 (0.1)3.3 (0.0)4.2 (0. 0)4.2 (0.0)4.2 (0.0)7.2 (0.0)7.2 (0.1)7.1 (0.1)8.1 (0.0)9.3 (0.0)8.3 (0.1)
11.3 (0.1)11.1 (0. 0)10.7 (0.1)11.0 (0.2)11.0 (0.1)11.2 (0.0)11.0 (0.0)
8.3 (0.0)4.6 (0.1)5.2 (0.0)9.1 (0.0)3.3 (0.0)4.5 (0. 0)5. 9 (0.1)6.2 (0.0)5.0 (0.0)4.9 (0.1)3. 5 (0.1)7.2 (0.0)7.2 (0.0)6.1 (0.1)6.4 (0.0)6.2 (0.0)6.0 (0.1)6.1 (0.0)4.2 (0.0)8.2 (0.0)8.1 (0.0)8.1 (0.0)7.2 (0.0)7.2 (0.0)9.2 (0.0)
Freq. (cm-f1)
6112. 018826114.482646114.495856114. 550676114. 561996114. 610226114. 663036114. 676416114.748716116. 592526116. 722956118. 256786120.587226 12 1. 130786121. 683066123. 003296123. 106696123.417496123.482646123.529326123.586366123.652236123. 739446123. 910406124.059686124.081016124. 158916124. 260556124. 906726125.742936127. 104196127. 182216129.029546129.364376129. 890106132. 361996132. 789966132. 851196132. 894636132. 958376133.066376133. 103296133. 120166133. 132956133. 355106133. 512466139.822046139. 879266140.100746140.303226140 .528556141.431116141. 699236141. 919776141. 977486142.076986142. 151336142. 174746142.252056145.040506145.273876145.473056145.639476147. 989196149.533746150. 141446150. 399846156 .58527
S
1. 1678. 3799.4313. 2461. 6533. 880
11. 93011. 1400. 8781. 0120. 9431.0231. 2800. 8731. 1992.4081. 3861.4711. 3871. 0413. 6280. 8632. 3581. 1794.4111. 3182 . 7431. 2311. 1460. 7810. 7891. 2500. 8020. 7691. 3657. 5472. 1192. 0160. 7964.2701.5221.4513. 2933. 5690. 8621. 1101. 1041.0741. 1170.8040. 7671.0020. 9131. 2781. 8530. 9241 .1290. 8992. 9991. 0950. 7950. 9191. 6290. 8621. 1700. 9610. 9220. 881
253 (0)559 (2)624 (2)543 (9)695 (25)619 (21)556 (0)641 (7)572 (25)175 ( 2)161 (12)177 ( 4)119 (10)116 (15)123 C3)667 (3)690 (4)673 (69)711 ( 4)664 (31)686 ( 2)710 (106)690 (16)689 (0)691 (3)743 (0)728 (16)717 (10)704 (33)533 (13)237 (1)237 (2)223 (7 )244 (2)238 (2)809 (7)851 (12)813 (7)181 (4)753 (17)825 ( 3)760 (16)764 (15)865 (10)187 (2)179 (0)307 (15)482 (8)389 (9)406 (15)489 ( 9)1104 (186)1059 (202)905 (10)905 (39)952 (26)881 (27 )899 (89)957 (13)230 (19)239 (14)236 (9)239 (5)361 (17)
1021 (44)1012 (22)941 (101)325 ( 7)
6. 59. 9
10.49. 7
11.010.49. 8
10. 610.05. 35. 15. 34. 34.24.4
10. 811. 010. 911. 210. 811.011. 211.011. 011.011.411. 311. 211. 19. 66. 36. 36. 16.46. 3
12. 012. 312.05.411. 512. 111. 611. 612.45. 55.47. 29. 18. 18. 39. 2
14. 013. 712. 712. 713. 012. 512. 613. 06. 26. 36 .26. 37. 8
13 .513.412. 97.4
(0. 0)(0. 0)(0. 0)(0. 1)(0. 2)(0. 2)(0. 0)(0. 1)(0. 2)(0. 0)(0. 2)(0. 1)(0. 2)(0. 3)(0. 1)(0. 0)(0. 0)(0. 7)(0. 0)(0. 3)(0. 0)(0. 9)(0. 1)(0. 0)(0. 0)(0. 0)(0. 1)(0. 1)(0. 3)(0. 1)(0. 0)(0. 0)(0. 1)(0. 0)(0. 0)(0. 1)(0. 1)(0. 1)(0. 1)(0. 1)(0. 0)(0. 1)(0. 1)(0. 1)(0. 0)(0. 0)(0. 2)(0. 1)(0. 1)(0. 2)(0. 1)(1. 2)(1.4)(0. 1)(0. 3)(0. 2)(0. 2)(0. 6)(0. 1)(0. 3)(0. 2)(0. 1)(0. 1)(0. 2)(0. 3)(0. 2)(0. 7)(0. 1)
20 May 1990 / Vol. 29, No. 15 / APPLIED OPTICS 2301
Table , continuedFreq.- (m- 1)
5917.696035919 .628735920.674375921. 107215924. 243875929.962335933.717115946.737195992. 501265992. 566605993.638295993.813155994.140775994. 526085994. 566845994. 583075994. 735065995.216455995.492875995. 568595997.269385997. 338665997.362385997.424395997.440875997.491875997.506115997.552705997. 618226014.613336024. 791516034. 776896038.234886039.024586039.658356039.739726039.751486040.384496040.405506040.947976040.990546041.496466041.557876042.091346042.439176055. 086376055.527886055.899236057.525166057. 531886063. 391006064. 325206064. 375816066.708136068. 15 2796074. 736426076. 108986085.166116085.252146087.183466095. 640016095.831576098.449256098.464426100.846736100.956846107.167366109. 721846109.882436110.03641
S
1. 2120. 8760. 7710. 9071.0621.0641.0151.0791. 2191. 6960.7801.0596. 7682.0701. 8581. 2121. 1780. 9071. 2900. 8990. 9531.0351. 7100. 8081. 3521. 3970. 9042.4910. 7990. 7940. 8510. 9041. 2360. 9490. 8561.0401. 1620. 7790. 7701.4090. 8820. 7990. 7581. 2050. 7581. 2300. 7530. 7891. 1801.0641.0620. 7781.0171. 3380. 9500. 9050. 8970. 7621. 1190. 8381. 1841. 2280.7720. 9341.4460. 7931. 2090. 9261.0452.066
495 C7)400 C2)226 (7)351 (0)596 (4)492 (0)479 C0)272 (5)970 (6)930 (53)778 (33)787 C3)9 C2)
815 (5)788 (19)844 C0)832 (9)698 (13)832 (24)682 (1)448 C6)647 (18)725 (13)654 (12)712 (15)691 (48)637 (25)700 ( 0)716 (16)108 (0)59 (2)71 (3)
801 (3)648 (3)304 (4)567 (16)555 (19)443 (20)509 (10)389 2)362 (11)307 C5)315 (5)206 (7)115 (9)109 (16)68 (0)87 (4)19 (19)
513 (108)226 (8)259 (4)25 (6)94 (9)81 (0)26 (3)16 (6)53 (7)46 (3)19 (6)76 (3)92 (0)84 (5)20 (0)
451 (4)485 (19)120 (3)73 (0)76 (4)78 (1)
9. 2 (0. 1)8. 3 (0. 0)6. 1 (0. 1)7. 7 (0. 0)
10. 2 (0. 0)9. 2 (0. 0)9.1 (0. 0)6. 7 (0. 1)
13. 1 (0. 0)12. 8 (0. 3)11. 7 (0. 3)11. 8 (0. 0)0 .9 (0. 2)
12. 0 (0. 0)11. 8 (0. 2)12. 2 (0. 0)12. 1 (0. 1)11. 1 (0. 1)12. 1 (0. 2)10. 9 (0. 0)8. 8 (0. 1)
10. 6 (0. 2)11. 3 (0. 1)10. 7 (0. 1)11. 2 (0. 1)11.0 (0.4)10. 5 (0. 2)11.1I (0. 0)11. 2 (0. 1)4. 1 (0. 0)2. 9 (0. 1)3.2 (0. 1)
11. 9 (0. 0)10. 6 (0. 0)7. 1 (0. 1)9.9 (0. 1)9. 8 (0. 2)8. 7 (0. 2)9.4 (0. 1)8. 1 (0. 0)7. 8 (0. 1)7. 2 (0. 1)7. 3 (0. 1)5. 8 (0. 1)4.2 (0. 2)4. 1 (0. 3)3. 2 (0. 0)3. 6 (0. 1)1. 5 (1. 5)9.4 (1. 1)6. 1 (0. 1)6. 6 (0. 1)1. 8 (0. 3)3. 8 (0. 2)3.5 (0. 0)1. 8 (0. 1)1.3 (0. 3)2. 7 (0. 2)2.5 (0. 1)1. 5 (0. 3)3.4 (0. 1)3. 7 (0. 1)3. 5 (0. 1)1. 5 (0. 0)8. 8 (0. 1)9. 1 (0. 2)4.3 (0. 1)3. 3 (0. 0)3.4 (0. 1)3.4 (0. 0)
strengths of this band were available from the earlierstudy' and ground state energies for the transitionswere taken from the work of Tarrago, et al.5 In mostcases, because of severe blending, the entire manifoldstrength was used instead of trying to use individuallines in the manifolds. As noted in the earlier paper,'the precision of measuring the strengths of individualcomponents of strongly blended manifolds is not near-ly as good as for the entire manifold. The 2v3 mani-folds between P10 and R9 were used to determine thetemperature of the cold gas; in all cases the rotationaltemperature turned out to be higher than and within 5K of the Ge thermometer temperature and with anRMS standard error of -2 K or less.
To determine the effective lower state energy for theunassigned lines the rotational temperature was used.The uncertainty in the values of E" so determined, dueto the uncertainty in the rotational temperature, is afunction of E". The uncertainty of E", as determinedby Eq. (3), was computed for a room temperatureuncertainty of 1 K and a low temperature uncertaintyof 2 K. Over the range of E" measured the uncertain-ties of E" are <5% from this source; they are much lessthan this for middle values of E". However, anotherand more important source of error is due to the uncer-tainty of the measured values of absorption strengths.As before, the uncertainty in E" due to this effect is afunction of E". This is illustrated in Fig. 1 where weplot the uncertainty in E" due to an uncertainty of 5%in the measured strengths of both the room tempera-ture strengths and the reduced temperature strengthmeasurements.
Equation (3) was used to determine an empiricalvalue for E" for the CH4 lines in the 5500-6200 cm-'interval. The results of this determination, for morethan 1600 lines, are reported in Table I. The E"determination is given in cm-1 as well as in terms of theequivalent value of J and its corresponding error. Thetable also shows the line position and room tempera-ture strength, as reported in the earlier work. Thereare fewer lines reported here than appeared in theearlier compilation. This is because many of the linesin the earlier work apparently have high energy groundstates and disappear or become too weak to measure atlow temperature. Also, some lines are blended andcould not be measured accurately enough at any tem-perature to allow accurate determination of the lowerstate energy. This may explain the majority of caseswhere the RMS deviations are significantly greaterthan predicted by computations leading to Fig. 2. Tokeep the table to a reasonable length only lines withroom temperature strengths >0.75 X 10-3 cm-2 atm'1are listed. Finally, to gain some estimate of how wellthis method works, we note that at -5600 cm-' there isa group of manifolds which can be tentatively assigned
Table II. Empirical JX Determinations for some Lines Tentatively
Freq. (cm1)
Assigned to 2V4 I V3
Strength Assign. Empir. J"
5597.14097 3.15 RO 0.4 (0.4)5606.53602 3.03 RI 1.5 (0.1)5615.42948 3.80 R2 2.2 (0.1)5615.66336 2.48 R2 2.4 (0.1)5624.39095 2.86 R3 3.2 (0.0)5624.69497 3.22 R3 3.1 (0.1)5625.64853 2.39 R3 3.2 (0.1)5632.51153 2.34 R4 4.2 (0.0)5633.11988 2.28 R4 4.2 (0.0)5633.63995 2.77 R4 4.3 (0.0)5634.14105 3.27 R4 4.3 (0.0)
Note: Strengths are in units of 10 3 cm - atm 1
at room temperature.
to the 2V4 + V3 band of12CH 4. The measured positions,strengths and empirical J" are shown in Table II formanifolds with J" <5. An unambiguous assignmentabove this value was not possible. Considering thatthe greatest uncertainty in the J" determination oc-curs for the low J" the results tabulated here shouldencourage confidence in the method. A complete listof the measured lines can be obtained on request to theauthor.
References1. J. S. Margolis, "Measured Line Positions and Strengths of Meth-
ane Between 5500 and 6180 cm-1," Appl. Opt. 27, 4038-4050(1988).
2. J. Ballard and W. B. Johnston, "Self-Broadened Widths andAbsolute Strengths of 12CH 4 Lines in the 1310-1370 cm-' Re-gion," J. Quant. Spectrosc. Radiat. Transfer. 36, 365-371 (1986).
3. V. Malathy Devi, B. Fridovich, G. D. Jones, and D. G. S. Snyder,"Strengths and Lorentz Broadening Coefficients for SpectralLines in the P3 and V2 + P4 bands of 12CH 4 and 13CH4," J. Mol.Spectrosc. 97, 333-342 (1983).
4. K. Fox, "On the Rotational Partition Function for TetrahedralMolecules," J. Quant. Spectrosc. Radiat. Transfer. 10,1335-1342(1970).
5. G. Tarrago, M. Dang-Nhu, G. Poussigue, G. Guelachvili, and C.Amiot, "The Ground State of Methane 12CH 4 Through the For-bidden Lines of the P3 Band," J. Mol. Spectrosc. 57, 246-263(1975).
2302 APPLIED OPTICS / Vol. 29, No. 15 / 20 May 1990
