Transition frequencies and absolute strengths of H2 170 and H2 180 ...
21
462 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Transition frequencies and absolute strengths of H 2 170 and H 2 180 in the 6.2-gim region Robert A. Toth Jet PropulsionLaboratory,California Institute of Technology,Pasadena, California 91109 Received June 21, 1991; revised manuscript received October 11, 1991 High-resolution spectra of oxygen-enriched samples of water vapor were recorded with a Fourier-transform spectrometer covering transitions in the (010)-(000) bands. The measured line frequencies were used along with measurements taken from studies at microwave and far-infrared frequencies to obtain rotational energy levels in the (000) and (010) states of H2 170 and H2 180. Measurements of the line strengths were fitted to a model in which as many as 18 transition moment parameters were determined. The results produced com- puted line-strength values that are in excellent agreement with the 623 H2 'O experimental transition strengths and 696 H2 180 values. These results provide a more accurate representation of the line positions and strengths for the (010)-(000) bands of H2 170 and H2 180 than those previously available. INTRODUCTION This study involves high-resolution measurements of line positions and absolute strengths in the (010)-(000) bands of H21'O and H2 180 covering the 1000-2225-cm'1 region. This task complements my recent study' of the (010)-(000) band of H2 160 Previous laboratory frequency measurements of H21'0 and H2' 8 O in the 6.2-,m spectral region include the studies by Guelachvili,' Williamson et al., 3 and Camy- Peyret et al. 4 Guelachvili2 recorded high-spectral- resolution data for natural water-vapor samples with a Fourier-transform spectrometer (FTS) and reported mea- surements of transition frequencies in the (010)-(000) bands of H2 6 0, H21 7 0, and H2 8 0. Williamson et al. 3 ob- tained 0.04-cm'l-resolution spectra of H2, 8 -enriched samples and determined the rotational energy levels in the (000) and (010) vibrational states from the line- frequency measurements. Spectra of natural water-vapor samples for the region between 1800 and 2200 cm-' were observed with a FTS by Camy-Peyret et al., 4 and the data were analyzed to determine the vibration-rotation parameters of a Watson-type Hamiltonian' for the (010)- (000) bands of H2' 7 0 and H2 8 0. There have not been any reports in the literature of H2' 7 O and H2' 8 O line-strength measurements in the (010)-(000) bands, although values for these parameters are given in the 1986 edition of the HITRAN database 6 ; these values, in turn, were taken from a tabulation by Flaud et al., 7 which presents an atlas of H2 6 0, H21 7 0, and H2' 8 O line positions and strengths between 0 and 4350 cm-'. The line-strength calculations for the (010)- (000) bands were based on H21 6 o measurements, and the H21 7 0 and the H2' 8 0 values were inferred from the H21 6 0 results. In the present investigation values of the line-center po- sitions measured in this study were used in conjunction with far-IR measurements between 33 and 280 cm-' (H2 8 O) by Johns 8 and between 50 and 730 cm-' (21 7 0 and H2 8 0) by Kauppinen and Kyro' and with microwave measurements obtained by DeLucia et al.' (2170), Steenbeckeliers and Bellet" (H2, 7 O and H21 8 0), and DeLucia et al.' 2 (H21 8 0) to obtain values of the ground- state energy levels for these two species. Energy levels in the (010)state were determined from the (010)-(000) band measurements and the ground-state levels. The experi- mental line strengths were analyzed by the method I used in the analysis of H2' 6 O data.' Briefly, the method is based on the theory developed by Flaud and Camy- Peyret," in which the original 8 elements 3 of the dipole moment expansion are used along with 11 additional terms in a least-squares analysis of the measured line strengths. The initial eight elements were found to be adequate when only the stronger transitions were consid- ered; however, inclusion of the weaker line strengths re- quired additional terms in the theory. EXPERIMENTAL DETAILS The spectra were obtained with a FTS located at the McMath solar telescope facility at the Kitt Peak National Observatory. The experimental conditions and extent of the measurements are given in Table 1. All data were obtained with an absorption path of 2.39 m, and the sample temperatures were 297 K. The H2 7 0 and H2 8 O samples were purchased from Merck and Company, Inc.; the stated isotopic purities were 98.1% H2 8 0 for one sample and 60.4% H21 7 0 for the other. The first set of spectra was for the 0 8 -enriched sample, as is noted in the table. The experiments using the H2 7 0 sample followed the H21 8 O runs, and it was determined from an analysis of the spectra that the gas sample of the initial H2 7 0 run (0.31 Torr of total pressure) contained less H2 7 0 (percent relative abundance of 42.9% H2L7O) than the manufac- turer's stated purity of 60.4%. The spectra of the follow- ing two runs showed increases in the H21 7 0 relative abundances of the samples (52.1%and 59.9%o), whereas the H2 8 O relative content in these samples showed decreases. The decreases indicated that a small residue of H 2 1 8 0 molecules remained in the absorption cell even after the absorption cell was pumped, purged with N 2 , and evacu- ated again, which was the procedure followed before the 0740-3224/92/040462-21$05.00 © 1992 Optical Society of America Robert A. Toth
Transcript of Transition frequencies and absolute strengths of H2 170 and H2 180 ...
462 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992
Transition frequencies and absolute strengths of H2 170 andH2 180 in the 6.2-gim region
Robert A. Toth
Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109
Received June 21, 1991; revised manuscript received October 11, 1991
High-resolution spectra of oxygen-enriched samples of water vapor were recorded with a Fourier-transformspectrometer covering transitions in the (010)-(000) bands. The measured line frequencies were used alongwith measurements taken from studies at microwave and far-infrared frequencies to obtain rotational energylevels in the (000) and (010) states of H2 170 and H2 180. Measurements of the line strengths were fitted to amodel in which as many as 18 transition moment parameters were determined. The results produced com-puted line-strength values that are in excellent agreement with the 623 H2 'O experimental transitionstrengths and 696 H2 180 values. These results provide a more accurate representation of the line positionsand strengths for the (010)-(000) bands of H2 170 and H2 180 than those previously available.
INTRODUCTION
This study involves high-resolution measurements of linepositions and absolute strengths in the (010)-(000) bandsof H21'O and H2 180 covering the 1000-2225-cm'1 region.This task complements my recent study' of the (010)-(000)band of H2 160
Previous laboratory frequency measurements of H21'0and H2'8O in the 6.2-,m spectral region include thestudies by Guelachvili,' Williamson et al.,3 and Camy-Peyret et al.4 Guelachvili2 recorded high-spectral-resolution data for natural water-vapor samples with aFourier-transform spectrometer (FTS) and reported mea-surements of transition frequencies in the (010)-(000)bands of H2 60, H2170, and H2 8
0. Williamson et al. 3 ob-tained 0.04-cm'l-resolution spectra of H2,8 -enrichedsamples and determined the rotational energy levelsin the (000) and (010) vibrational states from the line-frequency measurements. Spectra of natural water-vaporsamples for the region between 1800 and 2200 cm-' wereobserved with a FTS by Camy-Peyret et al.,4 and thedata were analyzed to determine the vibration-rotationparameters of a Watson-type Hamiltonian' for the (010)-(000) bands of H2'70 and H2 80.
There have not been any reports in the literature ofH2'7 O and H2'8 O line-strength measurements in the(010)-(000) bands, although values for these parametersare given in the 1986 edition of the HITRAN database 6
;
these values, in turn, were taken from a tabulation byFlaud et al., 7 which presents an atlas of H2 6
0, H2170,and H2'8 O line positions and strengths between 0 and4350 cm-'. The line-strength calculations for the (010)-(000) bands were based on H216o measurements, and theH2170 and the H2'8 0 values were inferred from the H216 0
results.In the present investigation values of the line-center po-
sitions measured in this study were used in conjunctionwith far-IR measurements between 33 and 280 cm-'(H2 8 O) by Johns 8 and between 50 and 730 cm-' (21 7 0
and H280) by Kauppinen and Kyro' and with microwavemeasurements obtained by DeLucia et al.' (2170),
Steenbeckeliers and Bellet" (H2,7O and H2180), andDeLucia et al.'2 (H218 0) to obtain values of the ground-state energy levels for these two species. Energy levels inthe (010) state were determined from the (010)-(000) bandmeasurements and the ground-state levels. The experi-mental line strengths were analyzed by the method I usedin the analysis of H2'6 O data.' Briefly, the method isbased on the theory developed by Flaud and Camy-Peyret," in which the original 8 elements 3 of the dipolemoment expansion are used along with 11 additionalterms in a least-squares analysis of the measured linestrengths. The initial eight elements were found to beadequate when only the stronger transitions were consid-ered; however, inclusion of the weaker line strengths re-quired additional terms in the theory.
EXPERIMENTAL DETAILS
The spectra were obtained with a FTS located at theMcMath solar telescope facility at the Kitt Peak NationalObservatory. The experimental conditions and extent ofthe measurements are given in Table 1. All data wereobtained with an absorption path of 2.39 m, and thesample temperatures were 297 K. The H270 and H28Osamples were purchased from Merck and Company, Inc.;the stated isotopic purities were 98.1% H2 8 0 for onesample and 60.4% H2170 for the other. The first set ofspectra was for the 0 8-enriched sample, as is noted in thetable. The experiments using the H27 0 sample followedthe H218O runs, and it was determined from an analysis ofthe spectra that the gas sample of the initial H2 70 run(0.31 Torr of total pressure) contained less H2 70 (percentrelative abundance of 42.9% H2L7O) than the manufac-turer's stated purity of 60.4%. The spectra of the follow-ing two runs showed increases in the H2170 relativeabundances of the samples (52.1% and 59.9%o), whereas theH28 O relative content in these samples showed decreases.The decreases indicated that a small residue of H2180
molecules remained in the absorption cell even after theabsorption cell was pumped, purged with N2, and evacu-ated again, which was the procedure followed before the
0740-3224/92/040462-21$05.00 © 1992 Optical Society of America
Robert A. Toth
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 463
Table 1. Experimental Conditions of Spectra Used in the H2 170 and H2 180 Measurementsa
Unapodized Total % Abundance of IsotopicRange of Spectral Sample Abd ces
Measurements Resolution Pressure Species(cm-') (cm-') (Torr) H2 160 H2 7o H2 18o HD 180 HD 170
1170-2149 0.0056 0.25 ND 0.62 98.1 1.2 ND1061-2192 0.0056 0.65 ND 0.62 98.1 1.2 ND1009-2192 0.0056 1.41 ND 0.62 98.1 1.2 ND1009-2299 0.0056 4.99 ND 0.62 98.1 1.2 ND1170-2129 0.0056 0.31 ND 42.9 35.8 ND 0.21102-2198 0.0056 1.33 ND 52.1 30.7 ND 0.21061-2224 0.0056 5.21 ND 59.9 27.3 ND 0.2
aAbsorption path length for all spectral runs was 2.39 m, and sample temperatures were 297 K. ND, not determined.
H2170 study began. Further checks of the H2 `50 and the
H2170 relative abundances in the samples were deter-
mined from the spectra and from the H2170 and the H2
180spectral absorptions observed in the H2
16 0 spectra usedin the earlier report.' The H2
6̀0 samples used in thatstudy' contained normal isotopic amounts of H2
170(0.036%) and H2
180 (0.204%). By these procedures the un-certainties in the H2
180 amounts in the H2'80 samples(first four entries in Table 1) were estimated to be slightlyless than 1%, whereas the H2
170 and the H28̀ 0 relative
amounts in the H2170 samples (last three entries in
Table 1) were estimated to be uncertain by approximately2% and 1%, respectively.
As is noted in Table 1, the impurities in the H2180
sample were found to be H2170 (0.62%) and HD 180 (1.2%),
whereas impurities observed in the spectra of the H2170
samples were H2180 and HD 170 (0.2%). The HDO impu-
rities were not noted by the manufacturer, and their pres-ence was determined from an analysis of additionalspectra; one gas sample contained enriched HD 8̀ 0 (cre-ated from a mixture of D2 0 and H2
150), and anothersample contained HD "0. The H2
160 contents in theH2
170 and H2180 samples were not determined, mainly be-
cause of the difficulty in separating, for a given observedH2
160 line, the contribution resulting from the low-pressure H2
6̀ 0 content in the vacuum tank that enclosedthe FTS from that in the 02-enriched samples. A com-parison of the H2
160 absorptions observed in the runsnoted in the table with that taken of the evacuated cellindicated that the H2
160 amount in any of the runs listedin Table 1 was less than 0.5% in relative abundance.
The H2170 and the H2
18 0 liquid samples obtained fromthe distributor were contained in sealed and evacuatedglass tubes. Contamination of the samples by the atmo-sphere was minimized in the transfer of the evaporatedisotopic species from the container to the 2.39-m-long cellby employing a special glass envelope. The apparatusconsisted of a sleeve that contained the sealed liquidsample and a glass arm in which a movable metal piecewas situated. The sealed apparatus was pumped for anhour or more, and, when the monitored pressure was ex-tremely low, the metal piece was moved toward the sealedtube; if necessary, the procedure was repeated until thesealed tube containing the sample broke. Soon after thecontents were allowed to evaporate into the apparatus,the pumping action was cut off, and the 02 -enriched watervapor was allowed to flow into the absorption cell. Twoidentical apparatuses were constructed; one was used
for the H2 O experiment and the other for the H2170-
enriched sample.The IR source was a Globar, and the radiation traveled
through short open spaces and the absorption cell beforeentering the vacuum tank. Atmospheric contributionswere minimized by purging the open spaces with cooledN2 gas. A He-cooled, As-doped Si detector collected theIR radiation, and each spectral run consisted of at leasteight superimposed interferograms. The compositeinterferograms were transformed into spectral data at theKitt Peak facility. During the 50-min or longer observa-tion period for each FTS run, the gas sample pressure andtemperature were monitored continuously. Total samplepressures were measured with a Baratron gauge, andthe sample temperatures were inferred from readings oftwo thermistor probes in thermal contact with the absorp-tion cell walls. The estimated uncertainties in the mea-sured pressures and temperatures were 0.5% and 1.0 K,respectively.
Two computer programs were used to measure thespectra. These were used in the analysis of H2
160 spec-tral and were described in an earlier report.'4 Briefly,one program, labeled LINEFINDER, determines line-centerpositions and relative absorption peaks; the other pro-gram uses the technique of nonlinear least-squares, inwhich absorption line positions, strengths, linewidths, andcontinuum parameters are fitted simultaneously in an in-teractive mode on the computer. The measured line posi-tions obtained by either technique were calibrated andcorrected by reference to known H2
160 calibration fre-quencies' as calibration standards. The observed H2
160lines resulted mainly from the low-pressure (200-,um totalpressure) H2
6̀0 content in the vacuum tank and theslight, if any, H2
160 impurity in the 02-enriched samplesin the absorption cell.
ENERGY LEVELS
The same technique' used to determine values of the rota-tional energy levels in the (000) and (010) vibrationalstates of H2 "
6O was used here to obtain term values for thestates of H2"0 and H28'0. The concept employs combina-tion difference frequencies (CDF's) in the ground state de-termined from measurements in the (010)-(000) band plusadditional measurements obtained in the (020)-(000),(100)-(000), and (001)-(000) bands, used in conjunctionwith microwave measurements10 "12 and H2"0 far-IR mea-surements8 to determine values of the ground-state rota-
Robert A. Toth
464 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992
Table 2. Rotational Energy Levels of the (000) and (010) Vibrational States of H2 170 and H2180a(000) (010)
J Ka Kc H2 170 H2180 H2170 H2
180 J K. Kc
0 0 0 0.000001 0 1 23.773511 1 1 36.931111 1 0 42.186942 0 2 70.004672 1 2 79.227342 1 1 94.970542 2 1 134.145272 2 0 135.431183 0 3 136.537623 1 3 141.902413 1 2 173.110093 2 2 205.481823 2 1 211.435783 3 1 283.561663 3 0 283.767764 0 4 221.620814 1 4 224.304234 1 3 275.130554 2 3 299.438924 2 2 315.078494 3 2 380.805934 3 1 382.175994 4 1 485.209034 4 0 485.236845 0 5 324.660995 1 5 325.880235 1 4 398.879405 2 4 415.128025 2 3 445.793445 3 3 502.179685 3 2 507.174395 4 2 607.159295 4 1 607.397405 5 1 737.620615 5 0 737.624156 0 6 445.719226 1 6 446.244966 1 5 541.996836 2 5 551.609386 2 4 601.960806 3 4 647.072206 3 3 659.986796 4 3 753.705106 4 2 754.811816 5 2 884.077796 5 1 884.113906 6 1 1038.765396 6 0 1038.765957 0 7 584.940897 1 7 585.161947 1 6 702.885977 2 6 708.016367 2 5 781.37727
222222322222
33
2122144222322222229952327232896153032332
0 .0000023.754902 0.536.748647 0.542.023428 0.569.927440 0.578.988654 0.594.788645 0.5
133.475798 0.7134.783115 0.7136.336669 0.7141.568060 0.7172.882910 0.7204.755913 0.7210.799282 0.7282.09458 3282.30709 3221.23401 1
223.828555 0.7274.80321 2298.62018 1314.45946 1379.29162 4380.70252 3482.64357 2482.67262 2324.04675 3325.21574 1398.36052 3414.16819 2445.15858 4500.59627 1505.72884 2604.54422 3604.79294 3733.67939 2733.68310 7444.84623 2445.34623 1541.18017 3550.45085 2601.23786 1645.38263 3658.61010 3751.03301 2752.18752 3880.07636 4880.11463 3
1033.19414 61033.19456 8583.77780 2583.98653 2701.69433 3706.59783 2780.45286 2
1591.325651615.115121631.315011636.872741661.459491673.347341689.992761738.027541739.228481728.260261735.665751768.704191809.444071815.079051902.159351902.328951813.611951817.626391871.654961903.569071918.657761999.463292000.598782122.932372122.952731916.673581918.654881996.853772019.551692049.712122120.972402125.178832244.959652245.134522397.778812397.781152037.397762038.325092141.944542156.471422206.855002266.157872277.323992391.567392392.386802544.409962544.433882723.622322723.622802175.937412176.360282304.999142313.445762388.07275
5232422232222322444332256435347366534543326375
101040
54324
1588.275671612.046011628.060061633.634711658.333901670.037111686.733371734.218521735.437741725.016891732.262771765.398011805.576711811.290621897.452821897.627241810.187321814.087161868.253851899.608941914.880911994.703311995.870132117.008492117.029711913.022641914.933521993.276892015.453962045.922672116.138582120.454652238.974952239.157052390.353582390.356082033.488702034.376912138.088592152.182122202.992752261.217532272.646142385.513572386.365872536.909672536.934892714.444362714.444462171.740742172.143242300.774272308.906062384.04199
10 02 13 13 13 23 23 23 23 24 32 33 32 34 32 32 32 44 43 42 42 45 42 44 42 43 52 55 53 52 52 52 52 54 54 53 53 66 62 62 63 62 62 63 63 62 64 69 6
10 63 71 74 74 73 7
0o 00 11 11 00 21 21 12 12 00 31 31 22 22 13 13 00 41 41 32 32 23 23 14 14 0
1 51 42 4
3 33 2
4 15 15 00 61 61 52 52 4
4 34 25 25 16 16 00 71 71 62 62 5
Robert A. Toth
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 465
Table 2. Continued
(000) (010)
J Ka Kc H2170 H2
180 H2 170 H2180 J Ka Kc
7 3 5 814.61075 37 3 4 840.86487 57 4 4 924.64153 67 4 3 928.29587 37 5 3 1055.05411 77 5 2 1055.25530 67 6 2 1209.81339 47 6 1 1209.81842 97 7 1 1386.41873 207 7 0 1386.41898 98 0 8 742.39857 48 1 8 742.49085 58 1 7 881.09903 48 2 7 883.65191 28 2 6 981.49596 48 3 6 1003.78133 38 3 5 1048.65714 48 4 5 1119.48803 48 4 4 1128.93814 38 5 4 1250.49869 68 5 3 1251.29115 48 6 3 1405.14811 168 6 2 1405.18093 48 7 2 1582.19624 168 7 1 1582.19672 168 8 1 1778.30779 258 8 0 1778.30779 259 0 9 918.10200 29 1 9 918.14050 89 1 8 1076.80099 39 2 8 1078.02032 89 2 7 1199.96295 39 3 7 1213.56231 49 3 6 1281.26845 69 4 6 1337.48949 39, 4 5 1357.55585 89 5 5 1470.22554 59 5 4 1472.68499 99 6 4 1624.69354 69 6 3 1624.84233 129 7 3 1801.98494 169 7 2 1801.99017 99 8 2 1998.95625 199 8 1 1998.95635 199 9 1 2212.16617 3009 9 0 2212.16617 300
10 0 10 1112.02499 1010 1 10 1112.04116 510 1 9 1290.22818 610 2 9 1290.79853 310 2 8 1435.36731 810 3 8 1443.04107 410 3 7 1536.15667 610 4 7 1577.68835 510 4 6 1613.90094 710 5 6 1713.84955 1010 5 5 1720.18418 1210 6 5 1868.33073 1210 6 4 1868.85882 910 7 4 2045.63885 1210 7 3 2045.66456 7
812.76176839.54954921.89590925.69983
1050.990301051.203261204.169511204.174961378.986431378.98643740.91235740.99874879.49487881.91415980.22238
1001.705861047.328651116.636231126.439161246.368651247.206161399.428061399.463361574.678261574.678451768.801551768.80155916.25779916.29360
1074.763081075.909521198.199661211.185761279.797671334.479351355.199271466.018371468.612211618.896341619.055941794.374751794.380451989.352021989.352022200.405352200.405351109.787081109.802111287.734851288.267351433.028991440.288061534.368371574.449571611.653571709.540261716.199911862.454881863.020212037.934052037.96225
32233342
14143336325224544
25353030354423344
14877
128
80802525
433225548
11105
155
18
2434.229072457.676102562.599552565.345412715.502552715.635882894.986452894.989663097.342253097.342252332.400262332.591522485.151292489.726332590.964022624.229282665.609122757.665972764.944322910.996372911.525163090.568123090.587883293.602853293.603563515.934813515.934812506.825842506.912462682.375332684.746922813.056572835.152512899.398552976.122092992.136333130.731493132.392683310.257163310.346993513.800243513.803123737.253253737.253253976.586493976.586492699.207812699.247452896.917832898.118993052.430923066.051643156.736323217.110973247.243223374.393383378.758813553.910923554.231633757.746183757.76049
232538
106
45451034373433977
10151020204
1534749384649
18103030252544
154436
111684
10118
15
2429.135042453.057632556.462172559.313992707.921732708.062232885.717212885.720633086.188263086.188262327.885082328.066022480.505702484.877282586.633592618.921342661.004042751.418542758.960162903.329662903.886433081.201013081.222073282.341963282.342643502.607813502.607812501.959362502.040832677.283412679.533592808.280282829.561082894.705662969.722022986.259133122.969523124.716493300.787083300.883043502.422713502.425983723.804043723.804043960.908953960.908952693.956142693.993382891.359772892.492163047.092383060.103983151.809733210.499313241.486233366.517863371.098973544.334423544.676203746.245373746.26098
3242325
101313546333417434
10202420204333623412678310101212353554324386521055315
7 3 57 3 47 4 47 4 37 5 37 5 27 6 27 6 17 7 17 7 08 0 88 1 88 1 78 2 78 2 68 3 68 3 58 4 58 4 48 5 48 5 38 6 38 6 28 7 28 7 18 8 18 8 09 0 99 1 99 1 89 2 89 2 79 3 79 3 69 4 69 4 59 5 59 5 49 6 49 6 39 7 39 7 29 8 29 8 19 9 19 9 0
10 0 1010 1 1010 1 910 2 910 2 810 3 810 3 710 4 710 4 610 5 610 5 510 6 510 6 410 7 410 7 3
(continued overleaf)
Robert A. Toth
466 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992
Table 2. Continued(000) (010)
J Ka K. H2 170 H2180 11 170 H2180 J Ka KV
2243.31375 452243.31440 802457.83590 502457.83590 502685.84239 902685.84239 901324.12157 81324.12830 201521.51755 91521.78224 61687.38292 51691.48503 121810.66703 81839.03757 101896.45521 81980.75352 181994.66386 72135.85851 102137.41991 102312.99648 902313.09838 542511.16195 502511.16608 252726.85000 3002726.85010 3001554.33465 51554.33768 51770.71182 111770.83503 71956.23550 81958.35833 132102.55395 252120.51612 172202.89734 902270.10752 142296.59750 1002426.94740 3002430.92450 3001802.59895 61802.60001 62037.79639 52037.85408 102242.21211 62243.29282 502410.54103 3002421.16090 902530.58221 300
2068.84310 802068.84365 802322.71550 2002322.74833 72545.51450 3002545.88172 10
2352.98827 502352.98860 1002625.41069 3002625.41889 500
2654.94766 3002654.94779 300
2233.60323 302233.60362 302445.95550 252445.95550 252671.62985 1002671.62985 1001321.45434 81321.46052 51518.54258 51518.78799 41684.43944 41688.28644 51808.36235 71835.48680 201894.19587 61976.29723 111990.85690 52129.89782 102131.56620 152305.19585 452305.30636 102501.45280 802501.45732 20
1551.20212 41551.20496 81767.22511 121767.33865 61952.67815 301954.65356 102099.56255 102116.56486 42200.43699 3002265.43837 102293.01000 852420.88520 252425.12391 3001798.96549 71798.96637 72033.76570 42033.81822 52238.03206 102239.02987 352406.76989 132416.78403 402527.68887 902575.97123 3002622.01033 402064.67225 802064.67291 202318.11367 202318.13820 352540.65963 402541.17262 402729.76880 300
2348.24648 252348.24651 40
2649.60481 902649.60481 90
3982.193973982.193974223.110654223.11065
40404040
2909.51494 22909.53331 63128.98788 63129.59052 133308.19035 103316.11966 73435.06637 103479.64817 203529.44342 103641.47384 403651.36020 83821.33008 403822.28735 404025.23810 504025.29633 404250.85300 3004250.85555 60
3137.70051 43137.70941 43378.69726 63378.99964 33580.27923 353584.72620 83731.75210 403762.72165 63836.95240 503931.26571 253950.91300 3004112.22326 50
3383.70953 83383.71324 193646.08238 53646.23492 53868.96959 53871.41260 204045.34602 40
3647.480503647.481003931.133483931.21109
3928.943803928.943804233.811734233.84680
4228.028474228.028474544.652994544.65299
40404040
50504050
40405050
3968.60945 40 10 8 33968.61025 40 10 8 24208.52029 20 10 9 24208.52029 20 10 9 1
10 10 110 10 0
2903.84380 5 11 0 112903.86091 3 11 1 113122.94139 5 11 1 103123.50601 9 11 2 103302.22939 4 11 2 93309.74527 12 11 3 93429.72577 3 11 3 83472.75155 8 11 4 83523.74050 5 11 4 73633.45155 8 11 5 73643.79532 8 11 5 63811.64162 10 11 6 63812.68000 300 11 6 54013.61061 40 11 7 54013.67143 15 11 7 44236.76675 40 11 8 44236.76895 40 11 8 3
11 9 311 9 2
3131.57518 6 12 0 123131.58339 3 12 1 123372.13552 5 12 1 113372.41739 3 12 2 113573.67560 15 12 2 103577.86090 3 12 3 103725.96590 40 12 3 93755.45790 12 12 4 93831.07000 300 12 4 83923.04649 15 12 5 83943.49850 40 12 5 7
12 6 712 6 6
3377.09551 5 13 0 133377.09926 4 13 1 133638.97577 11 13 1 123639.11705 8 13 2 123861.71641 7 13 2 113864.00033 10 13 3 114038.65473 8 13 3 104057.66655 40 13 4 10
13 4 913 5 913 5 8
3640.34227 40 14 0 143640.34344 12 14 1 143923.44902 40 14 1 133923.52195 15 14 2 134166.66191 300 14 2 124167.85026 15 14 3 124366.48340 300 14 3 114378.55929 40 14 4 113921.24790 25 15 0 153921.24810 25 15 1 154225.51964 15 15 1 144225.55707 40 15 2 144488.52332 40 15 2 134219.74131 20 16 0 164219.74131 20 16 1 164535.74571 40 17 0 174535.74571 40 17 1 17
0 Values are in inverse centimotors, and stimated uncertainties are in inverse centimeters timies 105.
101010101010111111111111111111111111111111111111111212121212121212121212121213131313131313131313131414141414141414151515151516161717
8 38 29 29 1
10 110 00 111 111 102 102 93 93 84 84 75 75 66 66 57 57 48 48 39 39 20 121 121 112 112 103 103 94 94 85 85 76 76 60 131 131 122 122 113 113 104 104 95 95 80 141 141 132 132 123 123 114 110 151 151 142 142 130 161 160 171 17
Robert A. Toth
Vol. 9, No. 4/April 1992/J Opt. Soc. Am. B 467
tional energies. The additional measurements obtained inthe 2.7-,um region (2850-4300 cm-') are not reported here.
Initially, CDF's and pure rotational frequencies withquantum numbers involving J 6 were fitted by usingthe Hamiltonian of Watson,5 including terms of K' withn < 10. The accurate term values for the lowest (J < 4)energy levels obtained in this way were then used as astarting point to determine values of the higher J, Ka, andK, levels by adding the determined value of the lower rota-tional level to the CDF's and pure rotational frequencies.These results were weighted and averaged, with thehighest weight given to the values obtained from themicrowave measurements.
After the ground-state values and associated estimateduncertainties were obtained, the rotational energy levelsin the (010) state were derived by adding the appropriatelower-state energy level to each measured transition fre-quency of the (010)-(000) band. These results wereweighted and then averaged for each level.
Table 2 lists values of the rotational energy levels andassociated uncertainties obtained in this study for the(000) and (010) states of H2,70 and H2,80. The uncertain-ties given for the ground-state levels are estimates of ab-solute uncertainties, whereas, for the excited-state levels,the uncertainties relate to the precision of the measure-ments, as is noted in Ref. 1.
It was also pointed out in the H2,60 report' that a least-squares fit of all of the CDF and pure rotational measure-ments to the Hamiltonian did not fit with residuals thatwere within the overall accuracy of the measurements, es-pecially for values with J > 12. The same result is seenin the present study for both isotopic species. However,as is further noted in Ref. 1, the parameters obtainedfrom the fits were of high enough accuracy to permit ade-
quate computation of the matrix elements of the directioncosines that are involved in the analysis of the linestrengths. The vibration-rotation parameters obtainedfrom these fits for the (000) states of H2170 and H2,8 0 aregiven in Table 3, along with values of these parameters forthe (010) states derived by Camy-Peyret et al.4 The appli-cation of these values to the line-strength analysis is dis-cussed below.
LINE STRENGTHSThe strength S of a H20 transition at frequency v may beexpressed to good approximation by
S = C(V/Q)(gT)[1 - exp(-v/kT)]
x exp[-E(L)/kT] IR(L, U)j2, (la)
where
C = 8r'1/3hc,
Q = QV X QR,
E(L) = Ev(L) + ER(L), (lb)
where Q is the partition function, which can be expressedas the product of the vibrational, Qv, and the rotational,QR, partition functions; g is the degeneracy caused by thenuclear spin of the lower state level; k is the Boltzmannconstant; T is the temperature; E(L) is the lower-stateenergy, which is equal to the sum of the lower-state vibra-tional energy Ev(L) and the rotational energy ER(L); andR(L, U) is the vibration-rotation dipole moment matrixelement connecting the lower state L with the upperstate U. When T = 296 K, QR = 175.5 and QR = 176.1for H2,70 and H2 8O, respectively, and Qv = 1.0004 for
Table 3. Vibration-Rotation Energy Level Parameters of the (000) and (010) States of H2 170 and H2 180
H2 NO H2 180
Parameter (000) (010)- (000) (010)
A 27.6954551 30.9195 27.531288 30.7311B 14.5213409 14.68579 14.5218844 14.68445C 9.2570365 9.10918 9.2380179 9.09099AK 3.2104569 x 10 5.727 x 102 3.1698583 x 102 5.650 x 102
ASK -5.693317 x 10-3 -7.543 x 103 -5.704319 x 103 -7.476 x 103
AS 1.232580 x 10-3 1.3894 x 10-3 1.2507967 x 10-3 1.3882 x 10-3
HK 1.224641 x 10-4 3.70 x 10-4 1.27559 x 10-4 3.67 x 10-4
HKJ., -8.0301625 x 10-6 -4.310 x 10-5 -2.23195 x 10-5 -4.65 x 10-5
HJK 3.410 x 10-6 4.80 x 10-6Hi -1.12328 x 10-6 5.45 x 10-7 3.84932 x 10-7 5.62 x 10-7
LK -9.71486 x 10-s -2.44 x 10-6 -6.45387 x 10-7 -2.445 x 10-6
LKKJ -7.5812 x 107 1.5086 x 10-
Li 3.50756 x 10-8 3.3233 x 10-9
PK 6.4657 x 109 1.0594 x 10- 3.22513 x 109 1.0594 x 10-
AK 1.088133 x 10 3 3.639 x 103 1.28393 x 103 3.634 x 10-3Si 4.93109 x 10-4 5.780 x 10-4 5.09357 x 10-4 5.784 x 10-4
hK 1.67287 x 10-5 7.94 x 10-5 3.05251 x 10-5 7.76 x 10-5hJK -2.05715 x 10-5 -2.68263 x 10-7 1.02 x 10-6hi 3.5230 x 10-7 2.83 x 10-7 2.89792 x 10-7 2.82 x 10-7
1K -7.56917 x 107 -2.88 x 107 -1.93 x 10 7
1KJ 1.735 x 106
a Parameters taken from Ref. 4.
RobertA. Toth
468 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992
Table 4. Matrix Elements Used in the Expansion of the Dipole Moment for B-TypeTransitions of Water Vapora
j n (JKIA'(j)IJ'K')/(JKIF(X)IJ'K + AK), AK = +1
2 1 J'(J' + 1) + J(J + 1)3 1 K 2 + K2
4 1 K 2 K25 1 K' 2 -K 2 - 2m6 1 (K' 2
_ K2)(K' 2- K 2
- 2m)7 1 J(J + 1) - 2m(m - 1) + (2m - 1)KAK - K2 - 18 3 [(J' - KAK - 1)(J' - KAK - 2)(J' + KAK + 2)(J' + KAK + 3)]1/29 1 K' 2J'(J + 1) - K2 J(J + 1)
10 1 K' 4 -K 4
11 1 (K'2 -K 2)[J'(J' + 1) + J(J + 1)]12 1 K' 2 (J' 2
+ j)213 1 K 6
14 1 K'4
15 1 K' 2 J'(J' + 1)16 1 K'6 - K 6
17 1 J'(J' + 1) if m = 0 and J = K or J' = K,'; otherwise 018 1 J'(J' + 1) if m = 0 and J = K or J' = K,' - 1; otherwise 019 1 J'(J' + 1) if m 0 and J = K, or J' = Kr'; otherwise 0
'Matrix elements forj = 2 toj = 8 are taken from Ref. 13. J' - J = 0, ±1; m = [J'(J' + 1) - J(J + 1)]/2; K' - K = nK.
Table 5. Dipole Moment Expansion Coefficients Derived from Least-Squares Fits of H2 170 and H2 150Measured Lines Strengths in the (010)-(000) Bands (values in debeyes)a
H2_17 H2 18o
Spectral Coverage (cm-') Spectral Coverage (cm-')
1087-1699 1701-2198 1009-1699 1700-2219
1 0.1311(5) 0.1286(10) 0.1299(5) 0.1287(7)2 1.29(27) x 10-5 1.45(47) x 10-5 3.83(27) x 10-5 9.24(483) x 10-63 2.77(651) x 10-5 -1.94(87) x 10-4 -6.32(556) x 10-5 -1.96(106) x 10-44 -6.43(12) x 10-' -5.99(29) x 10-3 -6.32(9) x 10-3 -6.04(32) x 10-35 -3.09(20) x 10- 4 -3.44(87) x 10-4 -4.59(17) x 10-4 -2.98(62) x 10-46 -2.61(70) x 10-5 -8.5(122) x 10-6 -3.38(75) x 10-5 3.0(153) x 10-7
7 6.67(22) x 10-5 3.22(124) x 10-5 7.21(24) x 10-5 1.55(137) x 10-5
8 -5.06(15) x 10-5 -1.55(20) x 10-5 -5.91(14) x 10-5 -2.14(13) x 10-59 -1.23(23) x 10-5 -1.16(351) x 10-6 -1.54(21) x 10-5 8.7(464) x 10-7
10 1.42(22) x 10-5 1.25(12) x 10-5 1.82(15) x 10-5 1.16(80) x 10-5
11 2.81(115) x 10-6 5.1(134) x 10-7 5.17(80) x 10-6 1.80(129) x 10-612 5.39(101) x 10-8 3.74(678) x 10-9 1.74(67) x 10-8 1.65(393) x 10-913 1.39(38) x 10-7 -2.77(277) x 10-8 2.93(173) x 10-" -265(781) x 10-814 -2.17(275) x 10-6 4.34(312) x 10-6 5.25(159) x 10-6 4.24(515) x 10-615 -7.93(168) x 10-6 -1.14(128) x 10-6 -4.35(108) x 10-6 -1.87(84) x 10-616 1.25(30) x 10-7 6.86(193) x 10-8 1.10(116) x 10-817 2.63(62) x 10-5 -6.45(98) x 10-5 -286(180) x 10-518 -3.84(59) x 10-5 -1.63(92) x 10-5
Nb 359 264 415 2810r%c 4.5 4.4 4.6 4.1
'Values given within parentheses are uncertainties in the last digit(s).6N represent the number of line strengths used in the least-squares fit.
cr,% is the standard deviation resulting from the least-squares fit in percent:
both species, and for temperatures within 30 K of 300 KQ(T) = Q(296 K)(296/T)3/ 2.
Without consideration of near-resonance effects, thevibration-rotation dipole moment element R(L, U), givenin Eq. (1), can be expressed as
R(L,U)= zu(j)x(j)
x(j) = (V", J", K", KIA(j)IV', J', Ka' K'), (2)
0% = 00{[(S&b. - Sca)/Sobj] /N} 12.
where u(j) are the dipole moment coefficients, A(j) arethe transformed transition moment operators, and primesand double primes denote upper and lower states, respec-tively. x(1) is the matrix element of the direction cosinesin which A(1) = oa with a = z for A-type transitions anda = x for B-type transitions. The asymmetric top wavefunctions, AS(V, J, Ka, K), are expressed as an expansionof the symmetry-adapted wave functions, s(J,'K,y), as
RobertA. Toth
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 469
AS(V, J, Ka, Kc) = T, C(J, Ka, K1J, Ky)s(J, Ky), (3)
where the C's are coefficients of the wave functions; thusthe lower- and the upper-state wave functions are ex-
pressed in terms of symmetry-adapted rotational wavefunctions.
The matrix elements involved in R(L,U) and used inthis study are given in Table 4. The elements j = 2 to
Table 6. Line Positions (cm-') and Strengths (cm-2/atm at 296 K) Observedin the (010)-(000) Band of H2 170a
Observed Upper Lower Observed Observed Upper Lower ObservedPosition o - c J Ka K, J K K, Strength %s (o - c)% R Position o - c J Ka K, J K, KC Strength %s (o - c)% R
1011.8642 -331063.78473 -41071 .5454 251087.45195 -11099.2071 81101.21611104.686961110.02881118.837661120.7391132.628611137.57371147.661751148.590301151.80011163 .84271165.63411169.596431172.156051185.511101194.864281208.457881210.22881217.302961221.251581222.44711222.78691225.5591236.97351240.81261241.23521242.90031243.148721246.58011246.59871250.42821255.937841256.94741259.33591261.87261264.061911264.49541264.59261264.70811264.788611266.48971266.67331269.60133*1270.48901272.39351278.28674*1279.41761283.49501283.74361284.61971284.980981286.154131286.83161288.577981288.6029
*1290.7441*1294.4926*1294.64651294.71881305.290911310.321621310.487851311.308421311.432311311.49551312.7899
-2-2-42-29524
-36-55
-79-29-23
0-3-1-4
0-19
.51
-1-11161
365050
16-71-7
-420
-7-4
-270.4-10
-13-5
-37-13-425
-1648
-2909
-23.40
-1302
-20824
-117
10 1 10 11 2 99 0 9 10 3 89 1 9 10 2 8
10 2 9 11 3 89 2 7 10 5 66 2 5 7 5 29 1 8 10 4 76 1 6 7 4 38 0 8 9 3 78 2 6 9 5 58 1 8 9 2 77 2 5 8 5 48 1 7 9 4 69 2 8 10 3 76 2 4 7 5 35 1 5 6 4 25 2 3 6 5 2
10 3 8 11 4 77 0 7 8 3 67 1 6 8 4 57 1 7 8 2 68 2 7 9 3 64 1 4 5 4 16 1 5 7 4 49 3 7 10 4 6
10 4 7 11 5 66 0 6 7 3 59 0 9 9 3 6
10 5 6 11 6 510 6 5 11 7 410 6 4 11 7 510 5 5 11 6 65 1 4 6 4 3
10 7 4 11 8 310 7 3 11 8 43 1 3 4 4 09 4 6 10 5 56 1 6 7 2 5
11 4 7 12 5 89 5 5 10 6 49 5 4 10 6 54 1 3 5 4 29 6 4 10 7 39 6 3 10 7 47 2 6 8 3 5
10 4 6 11 5 78 3 6 9 4 55 0 5 6 3 49 7 2 10 8 36 2 5 6 5 29 4 5 10 5 69 8 1 10 9 23 1 2 4 4 18 0 8 8 3 56 1 6 6 4 38 4 5 9 5 48 5 4 9 6 38 5 3 9 6 48 6 3 9 7 28 6 2 9 7 39 9 0 10 10 1
14 1 14 15 0 158 7 2 9 8 18 4 4 9 5 57 3 5 8 4 47 5 3 8 6 27 5 2 8 6 37 4 4 8 5 34 0 4 5 3 3
*1 2744853
5 15 54 2 7 62 87 1
(4.50E-04)1 .57E-034.20E-046.55E-046.OOE-046.01E-041 .58E-038.80E-041 .47E-033.64E-044.71E-031 .26E-031 .35E-038.45E-043.71E-045.56E-048.98E-041. 18E-031 .08E-028.57E-035 . 09E -031 .09E-021 .95E-034. 13E-031 .94E-031 .77E-038.28E-031 .20E-041.45E-038. lOE-042.92E-044.73E-041 .26E-024.35E-041 .20E-043.94E-042.50E-034.08E-024.50E-041 .92E-035.38E-032.85E-031 .02E-033.12E-031 .36E-027.79E-042.50E-024.49E-022.06E-033.09E-048. 13E-038.28E-042.97E-033.93E-049.46E-042.60E-021 .72E-026. 1OE-039.55E-033.38E-032.60E-049.51E-045 .88E-039.25E-032.83E-021.75E-024.75E-022.67E-022.19E-023.60E-048.95E-03
15 11.115 -18.35 -7.2
10 2.510 7.03 -2.5
10 8.43 8.1
15 9.32 1.62 0.03 -4.66 -9.3
10 -10.1'10 4.86 0.43 -0.45 0.84 -1.84 9.32 1.04 1.75 -4.83 4.83 -3.33 1.2
15 -41.74 -4.84 -6.9
10 0.910 -8.13 -3.5
10 5.610 -13.35 2.45 -1.02 -0.1
15 -19.03 3.43 -3.85 2.73 -0.13 1.84 0.5
10 7.33 6.82 -2.54 7.85 -4.13 0.13 3.43 4.0
15 22.95 0.33 -2.62 -5.33 0.83 -2.34 3.6
15 -24.615 16.74 -2.92 1.33 1.13 -0.48 -10.43 -1.13 3.2
10 -8.05 -4.9
1312.7937 281.40 1314.5502 -5
1314.84670 -2*1314.8671 1221315.60660 51316.69398 -2
1.31 1317.6987 -51.20 *1319.03447 11.32 1321.71018 -2
1322.7408 -301.31 1323.0879 31.15 1323.3340 -51.24 1324.8194 -81.28 1328.11969 6
1332.4171 -261332.81743 -2
1.09 1334.59150 -41.24 1334.62057 81.25 1335.07246 -81.19 1335.1005 01.24 1335.11047 11.20 1336.31207 -21.14 *1337.20330 -41.15 1337.33270 11.16 1337.86198 -21.14 1338.18809 21.19 1340.3716 2
1340.8431 -81.07 1341.20325 01.00 1342.5141 1
1345.8593 141345.9131 -4
1.12 1347.45433 01349.8318 -221352.68247 11355.17728 2
1.08 1355.1986 -61.18 1356.21315 0
1358.15287 21.02 1358.8788 101.01 *1359.0154 -361.11 1359.56488 -20.94 1359.88415 -10.94 1360.84579 41.15 1360.9458 -91.08 1361.0569 171.11 1366.16064 51.16 1366.8744 20.86. 1366.9887 1
1370.01554 41.06 1371.47365 -80.77 1371.83295 01.09 1375.1261 22
1375.13552 -70.96 1376.60142 -21.05 1376.7033 30.98 1377.0940 -220.98 1377.40175 40.90 1377.4113 330.90 1377.89778 -5
1378.66873 11384.29146 4
0.81 1385.30822 01.03 1385.33218 61.08 1386.4180 -120.95 1387.13262 -110.95 1387.75111 41.02 1387.99739 01.12 1389.45639 2
1391.57678 -20.87 1392.06588 -1
(continued overleaf)
7 6 111 3 87 4 3
13 0 136 2 55 1 5
10 3 77 7 09 3 66 2 4
13 2 1113 1 129 1 88 3 54 1 47 2 56 5 26 5 17 0 7
12 0 1212 1 126 4 36 6 16 4 26 3 47 3 49 2 7
12 1 1112 2 1112 3 1013 1 1313 0 133 0 3
11 2 96 3 3
11 0 1111 1 118 1 7
11 1 1011 2 105 5 05 2 4
11 3 95 4 2
10 2 85 4 15 3 3
12 1 1212 0 129 2 75 3 24 1 4
10 1 1010 1 910 2 9
7 1 611 4 88 2 66 0 62 0 2
10 3 87 2 54 4 14 4 04 1 36 1 5
11 1 1111 0 11
5 1 49 1 84 3 2
8 7 212 4 98 5 4
14 1 147 3 46 2 4
11 4 88 8 1
10 4 76 5 1
14 3 1214 2 139 4 59 4 64 4 17 5 27 6 17 6 27 3 4
13 1 1313 0 13
7 5 27 7 07 5 37 4 38 4 59 5 4
13 2 1213 1 1213 2 1113 2 1213 1 124 3 2
12 3 107 4 4
12 1 1212 0 128 4 4
12 2 1112 1 116 6 16 3 3
12 2 106 5 1
11 3 96 5 26 4 2
12 2 1112 1 1110 3 86 4 35 2 3
11 0 1111 2 1011 1 10
7 4 312 3 99 3 76 3 33 3 1
11 2 98 3 65 5 05 5 14 4 06 4 2
11 2 1011 1 10
5 4 110 2 9
5 4 1
2.69E-02 59.65E-04 107.70E-02 62.58E-03 101.45E-01 64.09E-02 41.15E-03 31.61E-02 41.11E-02 42.42E-04 102.OOE-04 10
(6.1OE-04)1.30E-03 101. 17E-02 37.26E-04 101.17E-03 101.40E-01 44. OE-02 54.OOE-03 32.50E-03 37.55E-03 32.25E-01 89.20E-02 57.36E-02 42.50E-01 51.05E-01 6(7. 71E-04}7.22E-04 32.30E-03 37.15E-04 106.1OE-04 101.80E-03 55.30E-02 22.52E-03 38.30E-02 72.20E-02 38.12E-03 41.33E-03 107.20E-03 32.40E-03 44.23E-01 51.51E-01 37.90E-04 51.65E-01 3
(2.56E-03)(5.02E-01)
1.99E-01 55.52E-03 31.90E-03 42.21E-02 36.35E-01 43.48E-01 55.92E-02 106.32E-03 152.11E-02 39.70E-03 53.OOE-04 152.08E-02 54.82E-03 57.20E-03 57.26E-03 31.48E-01 41. 04E -00 33.52E-01 31.02E-03 104.25E-03 35.71E-03 31.57E-02 39.49E-03 25.73E-02 31.35E-00 3
-4.72.2
-5.9-11.8
1.53.24.3
-8.61.1
-0.73.9
8.11.91.06.12.2
-10.7-5.42.02.64.7
-6.12.6
-0.34.2
0.16.11.37.96.3
-2.33.4
-7.5-3.36.9
-6.71.61.7
-0.42.1-0.6-1.3
-4.7-0.72.40.4
-0.52.5
-8.0-12.3-0.40.5
19.37.4
-6.03.7
-0.44.6-0.21.3
-2.5-0.22.4
-6.52.1
-1.11.3
0.871.041.021.141.111.141.040.781.04
1.001.050.990.890.930.931.051.121.121.000.851.001.051.050.911.091.081.05
1.401.101.031.041.101.100.991.051.050.921.081.010.991.010.981.041.351.341.011.031.101.091.031.030.99
1.021.051.080.991.030.970.971.000.991.301.300.991.031.03
Robert A. Toth
470 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Robert A. Toth
Table 6. ContinuedObserved Upper Lower Observed Observed Upper Lower ObservedPosition o - c J Ka K J Ka K, Strength %s (o - c)% R Position o - c J Ka K, J Ka K, Strength %s (o - c)% R
-5 6 2 4 7 3 50 4 3 1 5 4 2
-4 9 2 8 10 1 96 9 0 9 10 1 10
33 9 1 9 10 0 10-4 4 2 3 5 3 2-5 9 3 7 10 2 84 5 2 3 6 3 40 13 2 12 13 3 110 13 1 12 13 2 11
-4 10 4 7 11 3 8-2 8 1 7 9 2 82 10 1 101 10 0 101 5 0 5
-1 8 2 708 081 8 1 8
-3 4 2 21 3 3 123 30
-1 3 1 3-1 12 2 110 7 16
14 12 1 11-2 8 3 6-1 3 2 226 9 1 9-1 9 0 9-6 4 0 427 2657 073 6 15
-3 7 1 73 3 2 1
12 11 2 10-2 9 4 611 11 1 1003 03-2 5 1 4-3 8 1 80 13 3 1108 0826 062 7 350 6 16
-1 6 2 53 2 2 13 10 2 97 2 20
-4 4 1 321 10 1 91 2 1 2
-18 12 3 101 7 1 71 3 1 24 5 050 9 284 5 1 53 7 07
17 8 4 55 11 3 9
-1 5 2 462 12 2 1013 10 5 65 9 181 2 1 12 6 342 8 27
-2 6 1 60 4 043 10 3 8
-13 12 4 9
10 2 910 1 95 3 29 1 89 1 99 0 95 3 34 4 04 4 14 2 2
12 3 108 2 7
12 2 109 2 74 3 19 2 89 1 84 3 18 1 78 1 87 2 68 0 84 3 2
11 3 910 3 711 2 93 3 06 2 58 2 7
13 4 108 1 77 1 78 2 67 0 77 1 63 3 0
10 3 83 3 15 2 4
10 2 83 2 1
12 4 97 2 64 2 36 1 69 3 76 0 67 1 69 3 6
11 4 86 1 5
12 3 911 4 79 2 73 2 27 2 58 3 66 2 55 1 5
10 4 712 5 8
1.O1E-01 104.50E-01 5
(1 .92E-02}1.64E-01 35.55E-02 31.21E-00 37.04E-03 36.95E-01 33.77E-04 101.05E-03 42. 06E -03 34.74E-02 34.40E-02 41.53E-02 33.60E-02 51.34E-01 51.20E-01 83.77E-01 44.67E-01 48.27E-01 32.48E-00 23.22E-01 33.79E-03 103.20E-01 41.32E-03 104.38E-02 57.95E-01 33.55E-02 41.08E-01 61.55E-02 31.02E-01 47.92E-01 32.07E-01 32.75E-01 32.56E-00 34.20E-03 41.75E-03 51.21E-02 32.55E-02 61.10E-00 32.58E-01 3(1 .93E-04)8.70E-02 54.90E-01 53.02E-02 21.47E-00 45.70E-01 34.12E-00 43.42E-02 41.38E-00 3
(5.80E-01)1.26E-02 42.09E-00 32.25E-03 41.85E-01 72.63E-00 32.55E-00 33.29E-02 38.41E-01 35.57E-01 5(1 .O1E-02)2.54E-03 42.91E-01 38.15E-04 104.16E-04 101.10E-01 41.18E-00 31.40E-01 32.42E-01 51.04E-00 41.23E-00 22.33E-02 31. 17E-03 6
-6.20.8
-0.31.25.77.30.87.2-0.82.4
-0.2-4.5-0.6-1.9-4.7-6.1-1.42.0
-0.2-0.36.00.72.03.9
-3.40.2
-8.3-7.7-2.31.1
-1.21.03.01.92.28.6
-4.32.61.6
-2.9
-3.4-2.44.0
-2.21.60.2
-7.5-0.3
-2.4-1.21.80.01.51.3
-1.31.0
-3.2
-0.71.6-0.8-6.4-0.1-1.21.5
-1.0-0.8-0.2-2.7-0.9
1.04 1492.96538 -21.02 1495.40097 41.01 1495.88382 -11.08 1497.52335 31.08 1497.66307 51.06 1498.83510 90.98 1499.2850 501.05 1502.72747 0
1503.0445 -11.24 1503.26145 30.91 1503.52675 -31.03 1503.65536 31.25 1503.95602 -11.25 1504.68970 31.05 1504.74125 01.02 1505.6445 -71.07 1505.6674 -531.08 1505.68915 -11.05 1505.8175 41.01 1505.84837 111.02 1505.89656 11.08 1506.03797 21.19 1506.06260 -51.04 1506.34424 11.19 1507.16725 -30.96 1507.33904 01.05 1507.51045 81.21 1508.27299 91.21 1508.3566 -221.05 1508.37176 -121.03 1508.39105 -111.08 1509.39922 01.04 1509.58755 11.07 1509.9006 611.05 1510.09010 -11.16 1511.6447 -40.88 1512.45278 11.16 1513.65316 -11.04 1513.81311 01.05 1514.04494 01.18 1514.25426 0
1514.4329 471.18 1514.447 911.07 *1515.2951 40.96 1515.36195 11.07 1516.27428 31.03 1517.37201 01.04 1517.79420 21.13 1518.18742 -51.04 1519.01160 01.05 1519.45142 81.13 1519.55708 01.07 1522.51227 91.10 1522.76315 11.14 1523.62186 -11.06 1525.88245 41.07 1527.0593 261.10 1528.86525 41.07 1529.38025 21.14 1530.0502 -90.86 1530.18393 01.07 1531.31127 -21.03 1531.78812 01.09 1534.31352 0
1534.7799 341.10 1534.7855 251.05 1535.21804 -40.96 1535.88778 01.08 1536.48181 41.11 1536.67101 31.07 1536.80971 -11.05 1538.48143 31.02 1538.61105 -11
4 1 46 0 6
5 0 5 3.68E-00 36 1 5 3.72E-01 3
1 1 1 2 2 011 2 9 11 3 89 3 7 9 4 67 2 6 7 3 5
10 1 10 9 2 71 1 0 2 2 19 0 9 8 3 6
10 4 7 10 5 65 1 5 5 2 48 1 7 8 2 63 0 3 4 1 44 2 3 5 1 48 3 6 8 4 56 5 2 6 6 16 5 1 6 6 07 5 3 7 6 27 5 2 7 6 18 5 4 8 6 39 4 6 9 5 59 5 5 9 6 4
10 5 6 10 6 58 5 3 8 6 28 4 5 8 5 45 4 2 5 5 15 4 1 5 5 06 4 2 6 5 19 6 3 9 7 28 6 3 8 7 28 6 2 8 7 16 2 5 6 3 47 3 5 7 4 4
10 5 5 10 6 47 4 3 7 5 25 1 4 4 4 16 3 4 6 4 38 4 4 8 5 35 3 3 5 4 23 1 3 4 0 44 3 2 4 4 1
10 7 4 10 8 310 7 3 10 8 28 7 2 8 8 14 3 1 4 4 0
10 2 8 10 3 75 2 4 5 3 35 0 5 5 1 44 1 4 4 2 35 3 3 6 2 49 4 5 9 5 42 0 2 3 1 36 3 3 6 4 24 2 3 4 3 27 1 6 7 2 53 2 2 3 3 1
10 4 6 10 5 57 0 7 6 3 47 3 4 7 4 34 0 4 3 3 13 1 3 3 2 23 2 1 3 3 09 2 7 9 3 63 2 2 4 1 3
11 4 7 11 5 66 1 5 5 4 26 0 6 5 3 31 0 1 2 1 24 2 2 4 3 18 3 5 8 4 42 1 2 3 0 34 0 4 4 1 3
11 3 8 11 4 7
1.29E-00 39.20E-03 42.18E-02 2(1 .77E-01)3.56E-04 104.74E-00 37.OOE-04 151.27E-02 55.88E-01 49.29E-02 44.90E-00 41.06E-00 21.56E-01 3
(6.22E-02)(2.07E-02)(1 .74E-02)(5.21E-02)(2.98E-02)(1.13E-02}4. 77E - 03 35.47E-03 31.05E-02 4(7. 84E-02)7.25E-02 15
(2.52E-01)6.70E-02 155.OOE-03 59.10E-03 23.10E-03 51.04E-00 59.85E-02 61.80E-03 101.50E-01 68.30E-04 105.55E-01 52.65E-02 32.80E-01 31.48E-00 27.80E-01 35.82E-04 101.94E-04 10
(2.44E-03)2.83E-01 4(1. 1OE-02}(5.36E-01)2.25E-00 52.63E-00 26.40E-02 53.33E-02 31.90E-00 32.05E-01 5
(2.05E-00)6.98E-01 35.96E-01 54.55E-03 54.95E-03 53.55E-01 32.15E-03 31.05E-00 21.85E-00 39.35E-02 63.08E-01 44.38E-03 10
(8.51E-04)3.05E-03 45.07E-00 37.55E-01 46.00E-02 53.95E-00 21.24E-00 37.40E-03 5
1.9 1.07-1.6 1.12
1392.244201393.439491394.518701394.784741394.88781396.394641399.785151402.639961402.94211403.870271406.443901407.130951408.448941408.979641409.499201412.925331414.259761414.489531416.478051416.922521417.119941420.587251420.64131421.347231422.46191424.266311427.268071428.89241430.024841431.43591432.346751433.446611433.928211433.961681434.273151438.105611439.96541441.605071444.492501445.244371448.939581450.25171451.301231452.235841452.733131453.384201453.585441454.259811455.077951455.666891456.52691461.550731461.911571464.20991468.343931469.265281470.428661471.184611472.935621473.051471476.397691477.082141477.554851477.72591477.93831482.412431484.510951484.780621485.945021486.715691487.731721488.363321492.6140
-1.6-1.4-1.3
-0.22.0
-23.60.4-0.3-4.93.72.2
-2.9
4.32.25.6
-15.6
-18.19.82.34.53.5
-12.50.6
-1.6-8.7-5.30.82.71.60.24.84.8
8.4
7.11.16.8
-3.88.31.8
-4.0-0.23.8
-2.2-1.17.6
-0.1-0.4
-13.0-1.21.2
3.3-1.1-0.6-0.3-3.22.0
-3.4
1.051.081.031.05
1.050.780.961.091.091.071.041.010.830.830.830.830.830.940.850.870.840.930.910.910.910.750.740.741.041.000.870.920.870.990.930.981.070.980.67
0.660.981.051.031.101.070.970.941.070.981.021.071.020.960.860.990.961.061.021.041.040.970.840.901.071.021.001.071.091.02
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 471
Table 6. Continued
Observed Upper Lower Observed Observed Upper Lower Observed
Position o - c J Ka K, J Ka K, Strength %s (o - c)% R Position o - c J Ka Kc J Ka K, Strength %s (o - c)% R
1539.20209 21539.98378 41541.8427 01542.30694 61542.53779 61542.83513 -251546.86822 11547.20788 01549.0952 -61550.70253 11551.0604 71551.2143 51551.2941 61551.3821 91553.4407 181553.66987 21554.3945 -41554.5616 21555.15017 01556.57647 01557.26842 11560.5096 -161561.31037 31561.56404 -41562.8874 101564.91745 01566.48900 51569.30765 21572.92819 11573.56947 21574.02422 31574.0356 -71574.3994 -81577.77598 -71584.97285 -11585.47077 11586.56447 61587.08088 21587.5885 -301590.77482 01592.53170 51592.77750 -31596.14785 01596.4970 -441597.32608 11598.06232 01600.23459 21602.8901 71603.46713 -31603.5764 91606.19062 11608.5991 -921613.09923 01615.75800 21616.1141 11617.8825 -631619.80127 -41619.98808 -11620.3637 1361620.7732 151621 .69306 01624.52838 01631.31498 -31632.16655 -21634.55892 01635.09607 -31635.73544 -121636.0899 121637.37570 01639.96981 11641.96895 -11642.9671 101643.52724 3
2 1 26 1593682652310 3 76247259456435 1 48 187 168448544320002 1 13034 133 1 28171 1 17439 182 2 12026331 0 15327348537176425424 3 17533 3 18353 2 16 164227529632205 4 13 133305235 1 54 149361 1 04 4 16528634232 1 18624406242021 1 13 123 1 24225339285245323 2 15 5 1422
2 2 162494583553210 4 663373410 3 87345237256439379455231 1 12203 1 24223 2 17442028368453 1 22 1 17261 1 06258279466247356335248444229284 145235 1 5845
10 5 63 136342204236 164223 21
10 2 91 0 15327439543302029555337 171 1 10003032 2 13 3 14408354 3 14 4 13 126424 13
(2.70E-00)5.21E-01 46.87E-02 159.10E-02 101.98E-00 48.93E-03 34.47E-01 37.25E-01 31.26E-03 53.04E-02 43.17E-00 103.94E-03 53.16E-03 101.50E-03 102.52E-03 51.76E-01 4
C1.43E-00)C1 .27E-00)5.63E-00 31.71E-00 35.35E-00 46.14E-04 157.40E-01 41.30E-02 31.12E-03 3
(5.32E-01}2.56E-00 41.14E-02 56.35E-00 37.55E-02 31.01E-02 49.36E-04 154.05E-03 108.88E-03 51.30E-02 44.12E-02 31.55E-03 44.22E-02 37.77E-04 101.72E-01 34.37E-02 32.60E-02 34.60E-03 103.09E-04 156.80E-02 53.55E-02 31.08E-01 61.12E-01 62.53E-02 44.21E-02 32.70E-01 44.40E-04 155.67E-00 32.92E-02 57.15E-03 4
(6. 09E-04}2.02E-01 82.17E-00 31.56E-04 159.90E-03 42.22E-03 51.10E-00 51.54E-00 44.60E-00 38.40E-01 47.35E-02 5
(2.39E-02)1.82E-03 48.16E-02 67.34E-02 54.05E-00 32.05E-03 41.18E-00 3
-4.7-10.2-9.80.91.41.33.0
-0.83.90.7
-0.4-0.8-0.74.9
-4.6
-1.66.80.0
-28.9-9.05.6
-8.7
5.75.0
-0.9-3.74.2
20.5-8.77.44.90.22.12.71.20.62.01.03.05.80.10.74.35.7
-1.12.51.4
-11.6-3.2-1.96.3
-0.83.7
-30.10.9
-9.56.03.51.53.3
-7.7
1.3-1.40.5
-0.61.6
-0.3
1.041.060.991.041.021.011.031.040.750.871.060.850.810.780.730.981.051.041.071.051.050.791.070.820.771.041.070.911.060.950.860.710.900.850.900.980.751.010.791.050.941.020.74
1.060.901.011.010.990.981.000.731.070.930.780.650.971.08
0.930.931.061.071.091.020.970.890.830.940.891.070.841.06
1643.69541644.076051644.257931644.49101645.581771648.861451649.032951649.297021649.573821650.034191650.832781653.458861653.943271654.766131658.760451658.800201664.858171665.661081666.173151667.541651668.36681668.906181670.164661671.709531672.192781674.802321675.25321675.363011676.298781676.73761676.87081678.485651679.264871679.385381679.41741681.088831681.267801684.113141685.186771685.520271688.68161690.893171692.369331693.671381695.840581696.225321696.677531697.034001697.414771699.43561700.024281701.17771701.71191702.297341702.41101702.96351703.97101704.14921704.16921704.675351705.844341706.2141708.49601709.864981709.89031710.22641710.86771711.08641711.517501713.664091714.473521714.548511716.28720
10 7 6 20 5 5 0
-1 2 2 03 7 6 1
-13 7 2 5-1 8 2 73 3 0 3-1 6 2 5-1 2 1 24 4 1 36 5 2 3
-11 7 2 63 6 4 3
-6 6 4 2-2 6 3 40 2 2 10 6 2 40 3 1 31 4 1 3
-1 3 2 2-22 6 6 1-1 5 2 3-4 6 3 3-1 4 0 40 5 1 42 4 3 22 5 3 3
-18 6 3 3.5 7 3 4
100 7 5 331 7 5 20 7 4 43 4 2 3
-1 5 3 214 7 3 56 4 1 4
18 7 4 3-2 8 3 5-1 7 2 5-2 4 3 118 6 4 30 3 3 0
-2 5 0 5-8 5 2 4-2 2 2 10 6 1 50 3 3 11 5 1 5
-8 5 1 40 9 3 6
-9 4 3 2-25 8 5 413 8 5 3-3 2 2 033 8 4 568 5 4 20 7 3 46 8 6 35 8 6 23 6 2 4.4 5 3 33 9 3 7
21 10 3 8-1 8 2 69 8 4 4
-6 6 2 5-18 9 4 5-15 10 4 6-3 6 0 6-1 6 1 6-1 3 2 22 6 3 42 8 4 4
8 536 432 118 548 187 342 125 321 014 045 146 335 505 515 412 126 152 023 223 137 524 325 423 135 055 056 066 247 256 606 616 514 145 236 423 036 528 267 164 227 163 214 145 151 106 063 224 044 239 274 237 617 621 117 526 156 437 707 715 335 248 449 458 177 536 169 36
10 3 75 155 052 116 258 35
(3.31E-04}6.40E-03 4 5.6 0.839.95E-01 4 1.1 1.079.75E-04 7 -1.9 0.691.79E-03 5 -9.7 0.862.22E-02 6 5.6 0.865.84E-00 3 1.0 1.051.60E-01 4 -1.0 0.926.1OE-00 3 0.3 1.078.55E-01 5 -1.0 1.112.18E-00 3 -0.6 1.07
(2.27E-02) 0.881.94E-02 3 2.6 0.816.40E-03 5 1.4 0.819.26E-02 4 1.2 0.872.OOE-00 3 -2.4 1.093.55E-01 6 3.1 1.072.41E-00 3 0.5 1.065.14E-01 3 2.6 1.017.27E-01 5 -3.7 1.109.40E-04 10 -6.5 0.753.68E-01 3 -0.7 0.953.39E-02 3 4.8 0.872.26E-00 3 -2.9 1.051.29E-00 3 -3.1 1.136.33E-03 3 -7.6 1.03
(1.74E-03} 0.972.60E-01 10 -2.5 1.044.15E-01 3 0.2 1.041.50E-03 10 10.7 0.754.40E-03 5 8.5 0.757.90E-03 4 4.3 0.791.69E-00 3 -3.0 1.111.18E-00 3 -1.9 1.042.40E-02 10 6.4 0.857.44E-00 4 -0.5 1.052.25E-02 5 -1.5 0.795.40E-02 5 -2.3 1.044.18E-01 10 3.1 1.094.64E-01 3 -2.5 1.051.55E-03 10 -9.8 0.831.17E-00 3 -2.6 1.066.30E-00 4 -4.0 1.043.30E-01 10 -10.3 1.14
(4.56E-00) 1.071.95E-01 7 -10.2 1.163.60E-01 7 -7.2 1.072.24E-00 3 0.2 1.051.75E-00 3 -1.2 1.005.25E-02 3 -1.3 1.051.23E-00) 1.025.13E-03 15 15.5 0.721.46E-03 5 0.5 0.721.30E-00 4 4.8 1.051.44E-02 10 -13.0 0.784.52E-04 10 -0.38.28E-02 5 2.7 0.877.35E-04 10 11.2 0.652.01E-04 10 -8.61.25E-01 5 1.0 0.943.OOE-01 3 -2.4 1.044.23E-03 10 -3.0 0.803.86E-03 4 6.4 0.774.79E-02 3 0.5 1.105.85E-03 4 3.8 0.785.30E-01 10 -5.3 1.103.52E-02 4 -5.3 1.034.25E-03 3 0.1 1.041.70E-00 3 0.6 1.025.20E-00 3 1.7 1.021.33E-00 4 2.6 1.045.60E-01 5 2.9 1.053.04E-02 4 3.6 1.02
(continued overleaf)
Robert A. Toth
472 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Robert A. Toth
Table 6. ContinuedUpee _
UpeoeObserved Upper Lower Observed Observed Upper Lower ObservedPosition o - c J K K, J K K, Strength %s (o - c)% R Position o - c J K K, J K K, Strength %s (o - c)% R
1.13 1790.86107 5 7 5 31.09 1791.50832 -2 8 5 40.81 1793.24203 3 9 5 51.02 1794.3374 -2 11 3 90.77 1795.11698 2 4 3 10.71 1796.70507 4 10 5 61.07 1797.47377 -1 11 0 110.98 1797.50833 1 11 1 110.71 1798.72343 1 9 1 80.64 1800.51783 -1 5 3 21.13 1803.64788 -1 9 2 81.02 1804.3633 -2 12 4 91.03 1804.86632 1 11 1 101.02 1805.46211 -11 11 2 101.01 1805.89400 9 5 3 31.05 1809.27525 1 9 2 71.12 1809.5671 -31 12 2 101.00 1810.7496 1 12 5 81.09 1813.5722 -1 12 0 121.00 1813.58783 -1 12 1 120.87 1813.8911 -7 12 3 100.94 1815.5939 3 11 4 70.79 1818.89748 -3 10 1 91.00 1819.24678 -5 10 3 71.15 1820.36442 -1 6 3 41.01 1821.31803 3 10 2 91.02 1824.3627 9 12 1 111.01 1824.6620 4 12 2 111.02 1825.40788 -1 5 2 31.12 1825.73994 3 5 3 21.03 1829.3719 5 13 0 130.71 1829.3784 -19 13 1 13
1831.1733 10 13 2 110.99 1831.60473 -4 6 3 31.04 1832.1547 2 3 3 11.03 1832.26828 1 7 3 51.12 1834.0475 5 10 6 41.02 1837.66210 10 9 6 3
1838.18931 -4 11 1 101.16 1838.86858 -3 10 2 81.07 1839.16453 -8 4 4 11.19 1839.2965 -23 8 6 21.02 1839.3621 -24 11 2 101.02 1839.39102 -5 4 4 01.03 1839.5086 -30 6 6 01.04 1839.54453 0 6 6 11.18 1839.73431 -5 7 6 11.04 1839.9322 -14 7 6 21.03 1840.0316 -2 9 6 41.00 1840.0620 63 10 6 51.09 1840.0695 7 8 6 31.02 1842.85198 -3 8 3 61.16 1843.4834 -3 13 1 120.94 *184.88188 -17 14 1 141.07 1846.25507 -5 5 4 10.79 1847.8217 -48 4 4 00.98 1850.39005 8 6 4 21.05 1853.65656 1 9 3 70.87 1856.91502 0 12 1 111.02 1857.37810 8 11 3 81.02 1857.4821 1 12 2 111.00 *1860.10015 0 15 0 150.70 1862.19591 -6 6 3 31.23 1862.4594 -4 7 4 31.20 1862.78358 -8 5 4 21.00 1862.92565 -2 4 3 20.99 1864.32853 -6 5 4 11.04 1865.1493 2 11 2 91.14 1866.08865 -4 10 3 80.98 1872.73519 -2 7 3 40.97 *1875.0402 0 16 1 160.97 1875.24738 3 13 1 120.98 1875.52310 0 13 2 12
7 4i8 4!94 11 2 1(3 2 i
10 410 1 1C10 0 1C8275058 1 7
12 3 1CI11 0 1111 1 1142283 6
12 1 1112 4 911 1 1111 0 1112 2 1110 5 692894652391812 0 1212 1 1241442312 1 1212 0 1213 1 1260620262410 5 595410 2 993733085310 1 933165 1652752753955
10 5 685472513 0 1313 0 135 144136 15826
11 2 1010 4 711 1 1014 1 1452471643130343210 3 892770715 0 1512 2 1112 1 11
2.08E-02 65 3.15E-02 36 4.62E-03 50 1.55E-03 42 8.25E-01 87 4.70E-03 60 2.40E-01 6
7.65E-02 37 3.84E-01 553.18E-02 37 1.35E-01 50 8.37E-04 1515.50E-03 5
1.85E-03 65.25E-01 41.13E-01 44.33E-04 103.20E-04 153.18E-02 39.70E-02 41.22E-03 71.68E-03 35.96E-02 44.97E-03 49.20E-01 41.88E-01 55.64E-04 101.55E-03 33.98E-01 51.24E-00 33.60E-02 51.18E-02 52.80E-04 104.98E-03 58.10E-03 41.72E-01 35.48E-04 104.99E-03 37.00E-02 61.84E-02 31.89E-00 33.14E-03 102.40E-02 106.39E-01 37.48E-03 52.26E-02 31.90E-02 46.68E-03 101.64E-03 41.75E-03 101.12E-02 52.70E-01 44.88E-04 101.67E-02 68.23E-03 4
(8.98E-04)3.65E-03 54.46E-02 39.67E-03 46.30E-03 32.67E-02 35.20E-03 41.77E-01 37.92E-03 53.89E-01 36.32E-02 41.13E-00 32.31E-02 55.90E-02 34.00E-03 51.50E-03 69.65E-03 43.30E-03 4
1720.058281721.369011724.05331724.480491724.83101725.55061726.212701726.816521727.24461728.15081728.283811729.692431730.458981730.641101732.400051735.851731736.255641737.960151740.577361740.776721740.96771741.000621741.63771742. 126451742.75261742.779941744.421221744.495231747.650631747.68381747.98881749.55101751.92031753.389761753.884701754.90471757.132171757.591981759.46461762.202721762.559731764.273311764.335041764.513811764.857881765.791331766.60641766.728151768. 183681771.448941774.070051774.83691775.253111776.353261776.755341777.01771777.134931778.97801779.910591781.067291781.145411782.587071783.02951786.077781786.67271786.840391787.339951788.027501788.16311789.622081790.383761790.619531790.70491
3 7 1 60 10 3 7
33 4 4 1-5 7 4 36 9 4 64 9 5 5-1 7 3 50 6 1 53 9 5 45 9 6 3
-1 7 2 6-2 7 0 70 4 2 34 7 1 74 6 4 22 3 2 16 9 2 72 5 4 1
-1 8 3 6-2 4 4 011 8 3 57 7 2 56 9 4 51 4 4 1
-12 8 1 7-3 5 4 28 5 2 44 6 4 30 8 1 8
35 11 3 80 7 4 4
-5 10 5 6-45 10 6 5
0 7 1 66 8 4 5
-29 11 5 6-2 9 3 7-4 6 2 561 11 4 8-2 10 2 8-5 9 4 6-2 9 1 85 9 0 9
-8 9 1 91 10 5 50 3 3 0
-2 9 2 8-2 3 3 10 3 3 01 7 2 6
15 10 4 77 9 5 40 10 3 8
-1 8 2 6-1 4 2 22 10 4 60 8 1 73 4 3 17 9 3 6
-2 10 0 10-4 10 1 105 8 5 33 11 5 6
-5 10 2 9-10 11 2 9
3 8 2 7-6 7 5 2-1 4 3 2-4 11 4 81 6 5 11 5 5 01 5 5 15 6 5 2
7 0 710 2 85 1 47 3 48 5 38 6 27 2 65 2 48 6 38 7 27 1 76 1 63 1 26 0 66 3 32 1 29 1 85 3 28 2 74 3 17 4 46 3 48 5 44 3 28 0 85 3 34 1 36 3 47 0 7
11 2 97 3 59 6 39 7 26 2 58 3 6
11 4 79 2 85 1 4
10 5 510 1 99 3 79 0 98 1 88 0 8
10 4 63 0 39 1 92 2 02 2 16 1 5
10 3 89 4 5
10 2 97 3 53 1 39 5 57 2 64 0 48 4 59 1 99 0 98 4 4
10 6 510 1 1011 1 107 1 67 4 33 2 1
11 3 96 4 25 4 15 4 26 4 3
2.60E-014.93E-034.80E-041 .77E-013.20E-031.OOE-038.80E-024.70E-012.62E-037.44E-049.1 OE-023.54E-003.33E-001.18E-001.02E-012.24E-004.58E-024.40E-011.07E-011.35E-011 .65E-022.75E-019.80E-033.90E-013.82E-021.42E-018.30E-012.95E-012.13E-004.07E-035.37E-021.39E-033.65E-041.18E-006.84E-021 .70E-031.44E-021 .90E-003.91E-045.15E-039.57E-034. lOE-021. 18E-003.98E-011.74E-032.33E-021 .55E-021 .24E-00
{3.60E-00)4.27E-019.50E-031 .43E-021.40E-026.55E-023.60E-011.47E-032.36E-011.42E-022.97E-021.98E-016.02E-011.13E-024.78E-041.56E-024.40E-037.50E-016.30E-022.55E-00
(9.58E-04)3.50E-021.12E-013.65E-021 .03E-01
7 -7.02 -0.5
10 -13.13 0.88 9.55 2.78 -1.3
15 -13.610 -11.310 10.86 2.13 1.53 1.85 1.26 2.05 0.14 -4.74 4.68 -5.7
10 -0.36 -6.95 -8.45 3.55 -3.83 -2.83 2.36 -3.95 1.93 0.1
10 8.73 1.04 -4.6
10 -10.64 0.15 -6.43 -1.25 2.07 -0.3
10 2.13 1.85 1.35 -11.35 1.85 2.96 0.35 5.16 2.34 2.5
5 1.03 -0.34 3.13 -1.34 -2.14 2.26 1.36 -2.45 4.43 0.75 4.35 5.62 4.8
15 -25.35 -4.74 -1.64 0.34 -1.55 3.4
3 3.25 2.04 -0.23 1.4
-2.2-1.53.27.65.9
-2.4-5.0-9.5-0.11.53.97.91.52.72.1
-0.76.2
-28.1-6.2-4.62.0
-2.8-0.34.21.34.12.8
-5.9-4.3-2.2-3.0-4.7-9.79.93.91.7
-11.43.2
-6.50.7
-4.6-12.7-4.0-3.1-2.0-1.20.05.42.0
-4.84.60.75.61.53.9
3.81.53.43.4
-5.04.1
-4.02.6
-1.72.1
-4.51.60.14.68.31.43.9
0.991.001.021.201.041.041.021.020.981.060.98
1.281.281.040.94
1.031.031.260.790.980.871.030.97
1.341.081.061.031.03
1.071.091.01
0.980.970.931.030.970.971.030.940.940.950.950.981.010.970.99
1.031.031.021.040.970.970.870.971.041.061.061.041.091.040.930.951.081.040.970.97
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 473
Table 6. Continued
Observed Upper Lower Observed Observed Upper Lower Observed
Position o - c J K. K, J Ka K, Strength %s (o - c)% R Position o - c J Ka K J Ka K, Strength %s (o - c)% R
4 0.65 2.46 -0.43 -0.85 6.25 6.06 -0.54 -1.9
10 1.86 4.8
15 13.915 -42.915 21.93 3.9
10 0.110 -4.64 -1.2
10 -12.05 -2.06 -6.45 -2.56 3.5
10 -4.615 -29.24 -3.54 -1.2
10 6.910 -4.65 -1.24 -5.0
10 -0.84 -1.4
10 0.910 -9.910 4.16 7.4
15 -9.94 -1.53 -1.15 0.24 2.13 0.07 2.5
10 -2.610 10.14 0.73 -4.94 0.44 1.33 -2.55 -1.5
15 28.36 -4.73 -2.63 -2.85 4.12 0.15 0.1
0.941.101.071.040.930.920.940.940.920.95
1.040.970.960.93
1.111.031.070.920.97
1.041.040.921.101.021.040.870.99
1.04
0.961.041.041.131.120.94
1.131.040.921.081.041.041.14
1.031.051.061.041.041.14
1992.68788 -11 6 4 3 5 1 42001.79333 -2 9 5 5 8 4 42005.80201 -7 8 2 6 7 1 72010.87255 0 7 6 2 6 5 12010.91188 1 7 6 1 6 5 22012.90463 -2 9 5 4 8 4 52015.74648 -16 9 3 6 8 2 72020.60271 -1 7 4 4 6 1 52020.8305 21 5 4 1 4 1 42027.5729 0 11 5 7 10 4 62033.6808 -11 10 4 6 9 3 72034.8105 0 12 5 8 11 4 72035.31283 1 8 6 3 7 5 22035.53382 5 8 6 2 7 5 32039.28842 3 8 3 6 7 0 72041.2693 -2 10 5 5 9 4 62054.77997 -3 8 4 5 7 1 6
*2058.57634 -52 7 7 0 6 6 12058.96602 1 9 6 4 8 5 32059.84824 -6 9 6 3 8 5 42066.5063 -27 6 4 2 5 1 52070.56560 -12 9 2 7 8 1 82073.67185 0 11 5 6 10 4 72078.71605 5 10 3 7 9 2 82081.22593 0 10 6 5 9 5 42083.78420 -23 8 7 2 7 6 12083.7902 3 8 7 1 7 6 22084.0060 -9 10 6 4 9 5 52086.4023 -5 11 4 7 10 3 82092.7539 -4 9 3 7 8 0 82095.02308 2 9 4 6 8 1 72098.6171 58 6 5 2 5 2 32101.1459 0 11 6 6 10 5 52108.4378 0 11 6 5 10 5 62108.6191 -21 9 7 3 8 6 22108.65504 3 9 7 2 8 6 32113.5416 -15 7 5 3 6 2 42117.5594 0 12 6 7 11 5 62119.1006 15 7 4 3 6 1 6
*2129.51583 0 8 8 1 7 7 02129.6193 20 8 5 4 7 2 52132.90385 0 10 7 4 9 6 32133.0668 -15 10 7 3 9 6 42134.2901 -32 10 2 8 9 1 92140.3099 -8 10 4 7 9 1 82144.2676 -24 11 3 8 10 2 92147.9495 -14 10 3 8 9 0 92149.2352 -33 9 5 5 8 2 6
*2155.05680 -21 9 8 1 8 7 22156.9656 0 11 7 4 10 6 52164.0268 30 7 5 2 6 2 52174.4298 -63 10 5 6 9 2 7
*2180.2038 0 10 8 3 9 7 22196.1488 -39 11 2 9 10 1 10
*2198.2787 0 9 9 0 8 8 12205.2167 0 11 8 3 10 7 4
*2224.1543 0 10 9 2 9 8 1
1.55E-02 31.04E-02 45.35E-03 33.11E-02 39.35E-02 72.92E-02 21.52E-02 25.27E-03 51.95E-03 101.05E-03 103.05E-03 38.94E-04 104.05E-02 31.36E-02 31.15E-02 33.20E-03 41.O1E-02 55.35E-02 35.20E-03 21.58E-02 35.08E-04 104.85E-03 32.65E-03 61.18E-03 35.35E-03 41.77E-02 35.93E-03 31.83E-03 31.83E-03 51.41E-03 51.63E-03 7
{7.64E-04}5.25E-04 101.57E-03 62.28E-03 36.58E-03 2
{3.93E-04)3.28E-04 157.28E-04 109.OOE-03 71.23E-03 42.18E-03 46.83E-04 104.62E-04 101.68E-03 68.01E-04 101.40E-03 43.82E-04 103.36E-03 106.95E-04 103.89E-04 106.77E-04 101.13E-03 103.73E-04 101.05E-03 72.83E-04 153.24E-04 15
0.12.4
-0.1-3.6-3.3-1.31.82.04.5
-1.58.0
-3.5-1.2-0.42.11.90.0
-4.90.41.8
-3.0-3.24.4
-2.01.70.51.04.81.03.64.4
-0.90.33.5
-0.3
-32.6-9.90.5
-6.6-1.9-8.0-6.20.0
-2.86.96.12.03.6
-2.76.83.6
-8.3-5.4
-15.9-9.7
1.151.021.141.061.061.031.091.151.210.981.050.941.061.061.171.021.161.131.051.06
1.161.021.111.041.131.131.041.061.181.17
1.031.131.13
1.281.341.12
1.191.151.21
1.29
aAn asterisk denotes a doubled absorption, with the quantum assignment given for the stronger transition. The strength given represents the sum of the
strengths of the two comparable transitions. o - c is the observed minus the computed line position in inverse centimeters times 105. The computed values
are derived from energy levels given in Table 2. %s is the estimated uncertainty in the measured line strength given in percent. Line strengths given
within braces are the computed values derived in this study; (o - c)% is the observed minus the computed line strength in percent. R is the ratio of the
computed line strength derived in this study to that given in Ref. 7.
j = 8 are those given by Flaud and Camy-Peyret," andthe next 11 terms (i = 9 to j = 19) were empiricallyderived and found to be necessary in the H2 6o analysis.'In the present analysis as many as 18 matrix elements(j = 1 to and includingj = 18) were used. Several fitting
schemes were tried in the H2160 study, and the general
one found to be most productive was to break the data intospectral intervals and to fit each set of data separately.This procedure was also found to be best in performingthe analysis on the present data sets; the method that
1880.75251880.974761883.84541884.392961887.52391887.52931888.42261888.454881888.79421888.96071889.10691889.4153
*1889. 70521890.207041893.27941893.41471897.343281898.62871899.35161902 .61301906.066721910.611261911.06341911.13131912.541961912.572111915.17101915.33501916.801051918.273211924.82991927.464951930.02931932.4298
*1933.73801934.2589
*1935.26431935 .842451937.012551937.274461941.496901941.827761943.49151945.32281949.82251950.333551952.054631957.592751960.690751961.930711969.829201981.05081982.700421985.99861986.00271986.883581988.354971988.5099
15 11 3 9-1 6 2 411 8 4 4-4 6 4 37 7 7 0
44 7 7 1-3 8 7 114 8 7 20 12 2 10-9 9 7 220 9 7 3
-15 10 7 40 17 0 17
-8 6 4 20 14 1 130 14 2 130 12 3 10
56 4 4 11 5 3 3
24 7 4 40 7 3 40 13 2 110 15 1 140 15 2 14
-1 5 5 1-1 5 5 00 13 3 11
-34 9 4 5-5 8 4 50 7 4 30 13 3 100 9 4 6
10 8 5 37 9 5 4
-57 8 8 129 7 5 2
122 9 8 1-7 10 4 7-1 6 5 2
-13 6 5 12 6 3 4-3 7 2 50 11 4 8
37 6 4 322 4 4 1-2 8 4 41 12 4 9
-1 8 3 51 7 5 3-7 7 5 210 5 4 248 4 4 0-8 8 5 443 6 6 151 6 6 0-5 8 5 3.3 9 4 55 7 3 5
10 2 851581753276176286286311 3 996396410 6 516 1 1653313 2 1213 1 1211 2 941440463362512 3 1014 2 1314 1 1344044112 2 1091873463412 4 983582692787272597293654154250561610 3 761631273511 3 8726642643413313743550551744836606
7.90E-035.03E-021.13E-036.30E-014.OOE-031.33E-039.30E-042.75E-032.80E-031.49E-035.40E-043.96E-044.47E-042.16E-019.78E-042.80E-038.30E-034.74E-042.35E-029.50E-021.89E-012.76E-037.86E-042.12E-042.40E-017.37E-019.60E-049.29E-041.31E-012.69E-017.36E-041.78E-022.88E-045.22E-046.89E-048.95E-043.92E-042.06E-023.94E-011.33E-015.22E-024.95E-022.60E-036.29E-043.33E-033.60E-022.45E-031.91E-026.42E-021.85E-013.1OE-035.09E-047.70E-021.99E-016.62E-022.78E-023.33E-028.88E-03
.
Robert A. Toth
474 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Robert A. Toth
Table 7. Line Positions (cm-') and Strengths (cm-2/atm at 296 K) Observedin the (O10)-(000) Band of H2 0a
Observed Upper Lower Observed Observed Upper Lower ObservedPosition o - J K K J Ka K, Strength %s (o - c)% R Position o - c J K K J K K, Strength %s (o - c)% R
1009.5539 -41016.2653 231053.6295 -71055.874 1031061.67089 -411069.01183 -11084.12971 -101098.7398 -221100.9788 -61102.8337 -141108.6768 -281116.69930 -21120.6148 -421129.86635 -11135.3393 -31137.67335 11145.16522 01146.02626 -91152.0025 51162.7459 -101165.84597 -341165.90815 41165.9257 -141170.03485 -31184.13804 01191.92087 11205.07959 -21209.29393 -291211.430 211216.19269 01217.9074 -111219.64240 -11220.72679 -151222.1611 -591222.9103 181234.9516 -61238.5082 -431239.0281 41239.4807 351241.2012 51242.24388 01244.78805 01249.5898 -351253.52209 -21253.92388 -171258.3019 -231259.9493 -11261.57712 -291262.2615 -111262.8249 71262.94896 -31263.70927 -361263.72188 -191265.18893 -71267.63985 -16
*1268.8225 -25*1271.6429 -191272.1053 -461276.71900 13
*1277.84852 -21280.5560 -431282.75416 -281282.80632 -11283.3436 -301284.27381 91284.99010 11286.82051 -51286.84734 2
*1289.2779 -120*1292.0969 -6
10 1 1082 773 4
10 1 990 991 9
10 2 992 762 591 861 680 882 681 852 472 592 881 762 45 1 552 3
10 3 842 370 771 671 782 74 1 481 86 1 593 7
10 4 760 690 9
11 5 610 5 682 7
10 6 510 6 410 5 55 1 4
10 7 43 1 394 661 6
11 4 795 572 695 496 496 34 1 383 6
10 4 650 597 2
15 0 1562 594 598 180 83 1 284 561 685 485 386 386 299 0
14 1 14
11 2 995486311 4 810 3 810 2 811 3 810 5 675210 4 774393795592765185410 3 794675364265211 4 75508368458269365 4 1845744
10 4 611 5 673593612 6 711 6 585411 7 411 7 511 6 664311 8 344010 5 572512 5 810 6 483510 6 510 7 310 7 454294511 5 763410 8 316 1 1665210 5 610 9 283544 1954643963964972973
10 10 115 0 15
5.10E-041.46E-041.37E-041 .73E-041.45E-035.50E-047.32E-045.40E-046.44E-041 .73E-039.22E-041.43E-033.09E-044.69E-031.43E-041.39E-039.25E-041.39E-033.65E-045.OOE-049.19E-041.14E-033.47E-041.08E-028.88E-035.03E-031.07E-021.85E-031.81E-044.34E-031.85E-031.74E-038.39E-031.42E-043.40E-041.48E-031.80E-048.90E-043.37E-045.OOE-041.34E-02
(4.15E-04)3.90E-042.48E-033.93E-024.72E-042.OOE-031.32E-025.68E-031.09E-033.14E-032.66E-032.32E-027.1OE-044.65E-022.06E-031.87E-043.18E-048.26E-037.93E-043.53E-042.93E-032.56E-029.62E-041.78E-026.20E-039.55E-033.52E-034.OOE-048.30E-04
10 11.515 -15.115 9.510 -2.35 2.33 8.83 3.23 -13.78 7.93 3.9
15 11.73 3.4
10 -13.13 -0.3
15 -44.13 2.75 -0.74 -4.6
15 -19.66 -6.73 -3.04 -2.65 0.22 -0.52 -1.33 7.82 -0.34 -4.1
10 4.03 -2.96 1.33 -3.82 1.9
10 -2.410 -8.48 -2.6
10 -1.15 1.8
15 13.85 -2.42 -0.1
4 1.33 -1.53 -2.85 -10.03 6.34 -0.92 0.52 3.83 -0.23 -6.42 0.75 -1.23 0.83 3.5
15 -11.810 -3.62 1.55 -5.5
15 22.82 1.33 -4.24 4.64 -3.54 0.83 -6.03 4.1
15 19.33 -0.9
1.52 1292.941871.25 *1292.98988
*1302.202361.40 1302.695821.42 1308.458351.41 1308.634171.38 1309.255971.25 1309.591051.15 1310.38931.31 1311.03841.21 1311.04191.33 1312.23921.20 1312.42281.32 1312.4271.10 1312.632571.16 1312.945341.28 1313.16091.25 1313.695631.12 1316.322811.16 *1317.386651.09 1320.256101.23 1320.54381.06 1320.83711.26 1321.00341.19 1322.084181.24 1322.205351.20 1322.22861.11 1322.87800.86 1323.34071.15 1326.524711.16 1331.44291.12 1332.191161.19 1332.608800.91 1332.617901.07 1332.734701.04 1332.765430.80 1332.838700.97 1334.310340.96 1334.64541.03 1335.375561.11 *1335.457930.88 1335.517701.07 1336.42141.07 1338.31731.17 1338.651681.06 1339.66771.00 1339.82891.14 1343.28100.99 1343.329820.93 1345.725260.93 1347.575821.09 1348.68811.10 1350.750231.05 1352.638851.14 1352.658800.85 1354.066581.26 1355.602740.85 1356.280871.03 1356.843860.76 1357.06700.97 1357.15921.06 1357.16151.03 1358.80590.93 1358.860290.96 1359.080730.97 1363.951060.89 1364.244750.89 1364.35012
1367.992211.22 1368.92863
8 8 4 4 9 5 5 9.32E-03 2-6 8 7 2 9 8 1 6.21E-03 3
-10 8 8 1 9 9 0 2.71E-03 2-6 7 3 5 8 4 4 2.83E-02 3-2 7 5 3 8 6 2 1.72E-02 30 7 5 2 8 6 3 4.98E-02 3
-4 7 4 4 8 5 3 2.66E-02 30 4 0 4 5 3 3 2.19E-02 40 5 1 5 5 4 2 3.90E-04 10
-36 7 6 2 8 7 1 9.85E-03 4-47 7 6 1 8 7 2 2.96E-02 4-37 5 2 3 5 5 0 2.65E-04 1020 13 0 13 14 1 14 2.47E-03 6-1 13 1 13 14 0 14 8.35E-04 6-1 6 2 5 7 3 4 1.41E-01 50 7 4 3 8 5 4 7.95E-02 6
-1 11 3 8 12 4 9 9.60E-04 10-3 5 1 5 6 2 4 3.98E-02 4
-12 10 3 7 11 4 8 1.11E-03 3-6 7 7 0 8 8 1 1.74E-02 31 9 3 6 10 4 7 1.10E-02 21 13 2 11 14 3 12 1.70E-04 10
-47 13 1 12 14 2 13 7.08E-04 152 13 2 12 14 1 13 1.91E-04 104 9 1 8 9 4 5 1.15E-03 3
11 14 1 14 14 2 13 4.20E-04 50 14 0 14 14 1 13 1.39E-04 10
-12 6 2 4 6 5 1 2.71E-04 100 13 3 11 14 2 12 (6.04E-05)2 8 3 5 9 4 6 1.19E-02 3
-69 4 1 4 4 4 1 7.OOE-04 10-4 7 0 7 7 3 4 4.17E-03 3-1 12 0 12 13 1 13 2.40E-03 4012 112 13 013 7.75E-03 3
-1 6 5 2 7 6 1 1.30E-01 55 6 5 1 7 6 2 4.32E-02 4
-3 7 2 5 7 5 2 1.17E-03 103 6 4 3 7 5 2 2.05E-01 4
-33 12 2 10 13 3 11 2.17E-04 10-1 6 4 2 7 5 3 6.95E-02 30 6 6 1 7 7 0 9.20E-02 100 6 3 4 7 4 3 2.34E-01 50 7 3 4 8 4 5 1.01E-01 40 12 1 11 13 2 12 8.45E-04 15
-1 12 2 11 13 1 12 2.31E-03 7-37 9 2 7 9 5 4 7.61E-04 7
612 310 13 211 6.87E-04 5-4 13 1 13 13 2 12 5.90E-04 6
1 13 0 13 13 1 12 1.66E-03 3-1 3 0 3 4 3 2 5.50E-02 4-1 11 2 9 12 3 10 2.55E-03 49 12 4 9 13 3 10 2.18E-04 10
-1 6 3 3 7 4 4 8.45E-02 3111 011 12 112 2.27E-02 31 11 1 11 12 0 12 7.87E-03 34 8 1 7 8 4 4 1.36E-03 30 11 1 10 12 2 11 7.40E-03 4
-3 11 2 10 12 1 11 2.51E-03 30 5 2 4 6 3 3 1.36E-01 3
-12 11 3 9 12 2 10 8.17E-04 518 5 5 1 6 6 0 1.11E-01 6
-44 5 5 0 6 6 1 3.33E-01 6-4 10 2 8 11 3 9 2.57E-03 3-3 5 4 2 6 5 1 1.59E-01 44 5 4 1 6 5 2 4.79E-01 60 5 3 3 6 4 2 1.98E-01 3112 112 12 211 5.33E-03 35 12 0 12 12 1 11 1.88E-03 4
-1 9 2 7 10 3 8, 2.32E-02 45 b 1 4 5 2 3 3.03E-01 5
1.9-3.2-0.52.5
-3.7-7.2-1.43.22.01.01.2
-6.07.18.51.1
-2.62.62.70.9
-6.70.3
-6.715.0-5.32.9
-7.0-7.86.9
4.1-0.95.2
-6.90.4
-6.2-6.52.2
-4.0-6.7-2.6-9.3-5.31.4
14.45.9
-1.9-0.29.12.61.44.70.9
-4.2-4.0-0.1-1.33.14.9
-5.53.24.24.20.1
-3.9-3.5-3.20.46.04.8
-8.3
1.020.820.741.060.940.941.001.100.950.870.870.881.181.181.091.001.011.121.010.791.021.041.091.090.951.36
0.87
1.020.951.011.151.150.920.920.880.971.010.970.851.031.021.061.060.881.001.311.321.070.990.941.011.121.120.971.041.041.060.980.890.900.990.960.961.001.271.270.991.08
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 475
Table 7. Continued
Observed Upper Lower Observed Observed Upper Lower Observed
Position o - c J Ka K, J Ka K, Strength %s (o - c)% R Position o - c J Ka K, J Ka K Strength %s (o - c)% R
1369.42164 0 5 3 21372.49561 -1 10 0 101372.53907 3 10 1 101372.57177 -1 10 1 91373.1890 0 11 4 81373.94959 1 10 2 91374.87860 0 6 0 61375.0745 6 7 1 61375.44784 1 8 2 61375.66455 1 10 3 81376.23932 0 2 0 21382.33616 3 7 2 51383.32545 6 4 4 11383.35030 -2 4 4 01385.07293 1 11 1 111385.30126 4 11 0 111385.5814 17 4 1 31385.90105 -2 6 1 51388.48389 -6 5 1 41389.01607 1 9 1 81389.91036 -1 4 3 21390.23100 1 6 2 41391.32592 1 4 3 11391.79875 1 9 2 81392.15728 3 9 0 91392.25375 0 9 1 91393.88008 -2 4 2 31396.53209 0 9 3 71400.0873 12 13 2 121400.54005 1 5 2 31400.9436 -11 13 1 121402.13700 4 10 4 71404.59618 0 8 1 71405.72605 2 10 1 101406.22128 -1 10 0 101407.29376 -4 5 0 51410.11421 1 8 2 71411.59153 5 8 0 81411.80823 0 8 1 81414.28465 1 4 2 21414.78019 -1 3 3 11414.98365 -2 3 3 01417.76384 1 12 2 111417.80330 -1 3 1 31418.86017 5 7 1 61419.4577 33 12 1 111420.72168 0 8 3 61424.87420 1 3 2 21426.13134 3 9 1 91427.19627 -1 9 0 91429.41122 3 7 2 61429.48476 -4 4 0 41430.74204 4 7 0 71431.23090 1 7 1 71431.49075 -1 6 1 51431.99890 -10 3 2 11435.21968 11 11 2 101435.35365 0 9 4 61438.50196 1 11 1 101442.70975 -5 3 0 31442.82606 2 5 1 41446.15185 -2 8 1 81447.2163 0 13 3 111448.39026 5 8 0 81448.91265 -1 7 3 51449.50218 1 6 0 61450.48781 2 6 2 51450.59909 -2 6 1 61451.91149 6 2 2 11452.20410 0 10 2 9
6 4311 1 1111 0 1111 2 1012 3 911 1 106 337 439 37
11 2 93 3 18 3 6 ,5 505 5 1
11 2 1011 1 104 406 425 4 1
10 2 95 4 17 355 42
10 1 910 1 1010 0 105 32
10 2 813 3 116 34
13 2 1111 3 89 28
10 2 910 1 95 329 189 199 095 334 404 4 1
12 3 104 228 27
12 2 109 274 3 19 289 188 174 3 18 188 087 264 32
11 3 910 3 711 2 93 306 258 27
13 4 108 178 267 177 167 073 30
10 3 8
6.35E-01 62.18E-02 36.35E-02 37.35E-03 42.12E-04 152.11E-02 34.95E-03 39.90E-03 101.99E-02' 37.44E-03 37.44E-03 31.42E-01 41.OOE-00 53.44E-01 35.46E-03 31.66E-02 31.09E-03 54.44E-03 39.80E-03 105.67E-02 51.36E-00 31.05E-01 44.20E-01 51.98E-02 31.55E-01 55.40E-02 41.09E-00 56.84E-03 33.46E-04 106.91E-01 31.19E-03 52.21E-03 34.92E-02 54.31E-02 41.48E-02 33.56E-02 31.41E-01 41.20E-01 53.78E-01 34.52E-01 38.14E-01 52.43E-00 43.69E-03 43.OOE-01 33.23E-01 5(1 .26E-03}4.65E-02 67.65E-01 33.67E-02 41.13E-01 31.02E-01 31.58E-02 38.1 1E-01 32.69E-01 32.07E-01 42.40E-00 104.20E-03 101.71E-03 41.24E-02 52.45E-02 31.09E-00 22.51E-01 21.71E-04 158.37E-02 42.97E-02 34.93E-01 35.65E-01 41.49E-00 34.OOE-00 4
_ 3.30E-02_ 7
1.5 1.00-0.8 1.10-3.8 1.102.5 1.03
-11.8 0.90-1.6 1.021.1 1.033.3 0.973.1 1.001.6 0.967.0 1.051.4 1.01
-2.3 0.940.8 0.942.6 1.223.7 1.223.6 0.963.5 0.974.3 0.96
-2.8 1.024.4 0.99
-0.6 1.02-3.7 0.992.5 1.01
-7.6 1.08-3.2 1.09-1.8 1.033.7 0.95
-1.6 1.222.5 1.02
11.4 1.218.9 0.883.5 1.01
-2.0 1.180.7 1.19
-0.2 1.020.4 1.00
-6.5 1.07-1.6 1.071.4 1.021.0 0.970.4 0.98
-1.9 1.172.4 1.053.7 1.01
1.052.2 0.94
-0.6 1.01-0.5 1.151.3 1.151.9 1.001.2 1.021.7 1.061.3 1.062.5 1.01
-1.6 1.012.6 1.145.0 0.86
-1.6 1.14-0.7 1.012.8 1.02
-1.4 1.12-17.3 1.16-3.0 1.122.5 0.94
-0.4 1.052.2 1.000.6 1.050.3 1.00
-10.3 1.11
1453.343151454.085671454.94661458.33081459.237831461.29602.1465.545401466.777831467.676441468.347791470.046401470.087311471.620861472.32201474.25871474.273791479.083731480.764681481.977451483.171471483.926061484.971581485.654391490.040361492.308531493.276941493.867321495.081721495.79391496.144241496.454381500.158931500.283361500.765351500.959071501.188361501.248411502.16101502.285121503.55361503.70361503.715501503.740331503.752171503.887281503.901611504.062981504.073131504.423071505.049981505.295591505.437231505.66031506.251281506.400371506.41231506.44521506.502601506.52331506.5438
*1506.73311506.799471507.239141508.07911508.110761509.133521510.184541511.028761511.31651511.59438
-11820
-2-103-4-12-1
1230
-21
-1500
-2-500
28-118-6624223-1-29
1-13-5-30-5110-50932
-2540
-3-57
15518
110-20
343020
552
2 204 13
13 2 1110 1 92 1 2
12 3 107 173 125 059 287 075 1 58 45
10 5 611 3 95 249 186 342 1 18 276 164 04
10 3 84 146 061 1 1
11 2 99 37
10 1 107 26
11 4 81 1 08 175 1 5
10 4 73 034 23
12 5 88 36
11 5 79 466 526 5 17 537 528 54
10 5 69 558 538 455 426 439 546 42
10 6 59 64
11 6 69 638 638 627 6 16 257 35
10 5 57 437 446 343 139 555 33
3 3 1 1.39E-00 2 3.5 1.005 2 4 5.83E-01 3 3.1 1.02
13 3 10 6.15E-04 3 -4.8 1.1710 2 8 (1.28E-02) 1.113 2 1 (2.04E-00) 1.03
12 4 9 2.35E-03 5 2.3 1.137 2 6 1.72E-01 3 -3.3 1.094 2 3 2.58E-00 3 2.4 1.026 1 6 2.49E-00 3 1.0 1.059 3 7 3.37E-02 5 2.1 1.087 1 6 5.43E-01 4 -1.7 1.096 0 6 8.25E-01 4 1.2 1.049 3 6 1.07E-02 2 5.0 0.84
11 4 7 4.30E-04 10 -2.5 0.7511 4 8 2.50E-03 8 -5.6 1.09
6 1 5 2.85E-01 3 1.5 0.999 2 7 1.01E-01 6 -7.6 1.097 2 5 1.40E-01 4 2.6 0.923 2 2 1.21E-00 4 4.2 1.028 3 6 2.41E-01 2 -0.1 1.056 2 5 1.01E-00 2 0.0 1.075 1 5 1.22E-00 4 1.5 1.04
10 4 7 2.45E-02 5 -0.4 1.065 0 5 3.60E-00 10 2.2 1.036 1 5 3.69E-01 3 1.5 1.072 2 0 1.32E-00 3 3.7 1.02
11 3 8 9.15E-03 3 -6.2 1.119 4 6 2.25E-02 4 -0.3 1.039 2 7 2.81E-04 5 -3.7 0.677 3 5 C1.73E-01} 1.02
11 5 7 (1.40E-03} 0.982 2 1 4.49E-00 6 -0.5 1.028 2 6 9.50E-02 5 -1.2 1.075 2 4 5.61E-01 6 -1.6 1.05
10 5 6 1.32E-02 3 2.1 0.964 1 4 4.64E-00 3 1.1 1.045 1 4 1.04E-00 3 2.7 0.99
12 6 7 5.44E-04 5 1.4 0.918 4 5 1.58E-01 4 -3.1 1.01
11 6 6 6.09E-04 10 -0.1 0.889 5 5 1.17E-02 3 1.7 0.946 6 1 6.27E-02 3 -0.1 0.826 6 0 2.09E-02 4 -0.1 0.817 6 2 1.74E-02 3 -1.5 0.827 6 1 5.36E-02 3 1.2 0.828 6 3 2.96E-02 4 -2.6 0.83
10 6 5 5.51E-03 4 1.2 0.869 6 4 5.02E-03 3 7.3 0.848 6 2 1.06E-02 3 4.5 0.838 5 4 7.85E-02 4 -1.0 0.925 5 1 8.32E-02 5 -0.2 0.896 5 2 (2.36E-01} 0.899 6 3 (1.40E-02} 0.846 5 1 7.70E-02 5 -2.8 0.90
10 7 4 2.05E-03 4 7.1 0.769 7 3 1.50E-03 5 -3.7 0.75
11 7 5 1.73E-04 15 -27.2 0.779 7 2 4.80E-03 10 2.7 0.748 7 2 9.05E-03 10 -1.5 0.748 7 1 3.OOE-03 10 -2.1 0.747 7 0 1.61E-02 10 -1.6 0.746 3 4 9.26E-01 10 -6.4 1.027 4 4 1.01E-01 10 -10.7 0.98
10 6 4 (1.81E-03) 0.867 5 2 1.47E-01 4 -4.5 0.918 3 5 6.73E-03 4 8.7 0.846 4 3 5.78E-01 4 -1.2 0.974 0 4 1.44E-00 3 1.7 1.03
10 4 6 4.04E-04 10 9.1 0.735 4 2 2.73E-01 8 1.0 0.96
(continued overleaf)
Robert A. Toth
476 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Robert A. Toth
Table 7. ContinuedObserved Upper Lower Observed Observed Upper Lower ObservedPosition o - c J K K J Ka Kc Strength %s (o - c)% R Position o - c J K K, J K K, Strength %s (o - c)% R
0.920.950.880.650.651.090.650.950.651.061.000.930.771.040.961.030.940.970.750.570.990.960.830.981.030.931.071.000.990.980.871.030.811.030.901.001.001.041.051.021.041.061.021.011.021.040.840.730.820.771.030.930.780.701.041.011.041.021.021.030.711.000.661.040.880.720.911.030.88
1573.604121580.364821581.482601581.701931582.993361585.094631587.462081589.218391589.665151591.34261591.426011593.774441593.869681597.479661599.007081600.474061600.576441603.287891606.438301609.879781611.279641612.58901612.694501615.039001615.203561616.433451616.805901617.301851619.006201621.585251628.060041629.061331631.922221632.204981632.786351633.465951634.751451637.811051638.16631638.407651638.51031639.323041639.352091640.077711640.649131643.043211645.327751646.02821646.282171646.453271647.019821647.562151650.295951651.830451652.686441655.229861656.424591661.812621662.335331663.24081663.28581663.497931664.008621666.631051668.101911668.619261669.230131670.656641671.2926
0.83 1671.40825
1 6 4 2-3 5 4 23 7 5 3
-1 4 3 10 3 3 1
11 8 3 51 3 2 16 6 1 6
-2 4 2 2-18 9 6 3
1 7 5 22 5 4 10 2 2 01 3 1 32 3 3 00 5 1 50 5 2 31 4 1 4
-1 9 3 6-3 1 1 0-1 4 4 120 8 6 31 10 2 91 6 5 1
-14 8 6 21 4 4 0
-3 2 1 10 4 2 3
-2 6 2 40 2 0 2
-2 1 1 1-1 3 1 21 3 1 24 9 2 82 4 2 2
-1 5 3 31 5 2 4
-3 5 3 224 5 5 1-6 3 2 1
-75 7 6 2-3 5 5 011 7 6 11 4 2 24 2 2 0
-4 7 2 51 8 2 7
-4 3 0 3-4 2 1 2-1 6 2 5-2 4 1 30 5 2 3
-1 7 2 6-2 6 4 3-4 6 4 2-1 2 2 10 6 3 44 6 2 40 3 1 3
-30 6 6 1-22 8 7 2-1 4 1 3-3 3 2 20 5 2 3
-1 6 3 30 4 0 4
-1 5 1 48 4 3 2
25 5 3 3-3 6 3 3
735633844524422928414523515
105 6845634313220423422616321
10 2 9101532954936744955533202330717111000303221835331440431441642312853643854413211818734212101532404514633550551212541615202752963322313432542313505505
606
6 2 4 2.71E-01)
8.87E-03 21.34E-02 21.66E-03 64.05E-02 34.03E-02 47.80E-04 51.63E-01 54.18E-02 22.56E-02 33.31E-04 104.50E-03 63.60E-02 46.80E-02 51.01E-01 41.03E-01 84.02E-02 32.52E-02 62.41E-01 44.50E-04 55.80E-00 63.04E-02 36.43E-04 51.09E-03 32.42E-03 42.43E-04 101.00E-02 3
(2.01E-00)1.85E-01 42.37E-03 41.00E-00 41.45E-00 34.35E-00 38.40E-01 51.69E-03 48.15E-02 32.53E-02 38.21E-02 57.40E-02 42.03E-03 33.97E-00 3
(3.59E-04)6.45E-03 61.10E-03 51.17E-00 39.81E-01 51.77E-03 52.06E-02 2
(5.74E-00)5.84E-00 31.61E-01 38.10E-01 32.16E-00 32.30E-02 22.03E-02 26.67E-03 51.95E-00 39.16E-02 43.30E-01 42.42E-00 41.01E-03 51.01E-04 154.98E-01 47.35E-01 43.79E-01 53.30E-02 32.31E-00 31.25E-00 56.27E-03 31.49E-03 4
1511.754001512.059771512.22921512.64251512.65751512.72401
*1513.07321513.19752
*1513.54051514.662121514.857701514.900731515.123291515.466981515.661731516.765811517.647021520.458621521.8187
*1523.39881523.482151525.286381526.358131527.357801527.506881528.092731528.482661528.983571530.773491532.88371532.89231533.057351533.54441533.700451533.73071534.178421534.564851535.384141535.529911536.561341536.850761539.304931539.506361540.193881544.382631544.492451545.964051545.97091547.613221547.77441548.118301549.544721549.741251550.26641551.527021551.950281552.134001553.794421554.598741558.132651560.647171561.335581561.91201563.545281566.048321569.407121570.003801570.022581570.905381571.14345
0 8 4 43 4 3 28 11 5 6
36 10 7 414 10 7 30 10 2 8
-76 9 7 21 4 3 19 8 7 20 5 0 51 5 2 41 5 3 3
-3 8 0 80 4 1 42 5 3 2
-3 2 0 210 9 4 50 6 3 3
25 9 1 911 9 8 12 3 2 26 10 4 62 7 0 70 7 3 42 3 1 3
-1 4 0 45 9 2 74 3 2 1
-1' 3 2 210 11 4 7
-13 6 0 6-1 1 0 13 6 1 51 2 1 2
-32 5 0 53 4 2 2
-3 18 3 53 4 0 41 11 3 83 2 1 23 6 1 5
-1 8 2 6-3 9 3 65 5 2 3
-2 6 2 40 7 2 52 6 4 3
-17 9 4 56 8 1 80 8 4 4
-1 5 1 4-1 4 3 2-1 7 1 6
-52 9 5 40 0 0 03 2 1 12 3 0 33 4 1 31 3 1 23 1 1 1
-1 9 1 8-3 2 2 137 9 2 73 2 0 21 6 3 34 8 5 30 5 3 20 1 0 10 7 1 7
.3 7 3 4
8 5 34 4 1
11 6 510 8 310 8 210 3 79 8 14 4 08 8 15 1 45 3 36 2 47 3 54 2 35 4 13 1 39 5 46 4 28 2 69 9 03 3 1
10 5 56 3 47 4 33 2 23 3 19 3 63 3 04 1 3
11 5 65 3 32 1 25 4 23 0 34 3 24 3 18 4 44 1 3
11 4 72 2 16 2 48 3 59 4 55 3 26 3 37 3 47 3 4
10 3 87 2 59 3 75 2 35 2 36 4 3
10 4 71 1 12 2 03 1 24 2 23 2 12 0 28 4 53 1 28 5 42 1 17 2 69 4 66 2 51 1 06 2 48 2 7
2.68E-027.53E-01
(1.84E-03)6.48E-041.96E-041.07E-021.80E-032.55E-012.70E-032.04E-005.30E-015.95E-026.20E-042.50E-008.15E-01
(1.69E-00)3.55E-021.95E-013.25E-04
(3.13E-04)5.84E-014.51E-035. 1OE-03
(3.62E-01)1.04E-001.98E-039.85E-021.86E-003.10E-014.54E-032.95E-034.95E-007.34E-043.75E-009.11E-037.52E-016.15E-021.16E-007.85E-032.73E-005.41E-019.45E-027.43E-02
(1.95E-00)4.44E-017.07E-013.13E-021.56E-033.75E-031.63E-033.09E-001.73E-012.90E-03
(9.16E-04)1.33E-001.23E-005.50E-001.55E-00
(5.23E-00)7.60E-011.13E-035.23E-013.00E-042.38E-001.13E-028.05E-046.72E-026.35E-004.38E-039.70E-03
3 0.43 -1.7
10 13.810 4.25 -6.14 7.34 -0.4
10 6.53 1.08 1.05 1.7
10 -12.95 -0.83 -0.7
7 0.44 -3.4
10 -7.9
3 0.23 0.04 5.2
3 1.95 1.15 -10.33 1.85 2.44 1.1
10 3.14 -0.6
15 -14.810 -5.515 -11.43 -0.13 0.05 -1.25 -1.94 3.73 1.14 -7.55 -5.2
5 0.03 -0.74 7.8
15 -21.65 1.44 8.03 0.16 -2.9
10 -8.3
6 -4.45 -1.16 -0.73 -1.1
4 -3.45 -0.34 1.7
10 -1.04 1.23 8.53 3.8
10 -10.74 1.54 4.15 3.9
8.610.35.73.32.54.61.61.66.67.8
-2.94.55.5
-0.12.41.35.7
-7.2-5.22.05.8
-2.8-4.55.99.75.6
-8.23.1
-2.5-0.30.03.90.33.46.40.32.10.3
-0.3
6.01.71.02.3
-7.11.6
-2.60.9
-1.90.53.37.66.0
-1.30.2
-2.51.3
-5.8-43.3-1.01.31.71.7
-1.5-1.5-3.9
-11.8
0.830.860.750.930.950.780.990.930.970.660.750.861.001.000.960.970.940.990.721.040.880.680.740.780.680.881.040.950.901.051.051.061.010.800.950.870.930.880.821.040.720.820.731.041.040.840.851.041.050.911.071.050.890.790.791.040.861.071.060.780.731.011.050.940.861.051.090.970.931.05
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 477
Table 7. Continued
Observed Upper Lower Observed Observed Upper Lower Observed
Position o - c J Ka Kc J K Kc Strength %s (o - c)% R Position o - c J K. K, J Ka K, Strength %s (o - c)% R
1672.60478 1 7 3 41674.72708 -9 7 5 31674.86810 1 7 5 21675.29604 -3 5 3 21675.78040 1 4 2 31676.2190 19 3 3 11676.34746 -8 7 4 41676.6554 -6 8 4 51676.94755 3 7 3 51676.9671 -20 7 4 41677.43977 4 6 3 41677.75049 0 4 1 41679.23765 2 7 4 31680.781661681.410661682.347661683.81931686.827981688.22261689.194111690.238181692.195061692.696911693.221521693.242341693.699511694.656791696.08311696.506021697.79481698.09181698.689051699.15481699.71701700.215261701.970361702.024641702.21411702.23571702.396491703.121931704.90481705.1311706.461421706.835881707.117871707.138701707.969791708.272961710.330151710.766651710.788081711.631411715.378151716.996451718.64761718.780771719.764421722.51591722.537241723.50651723.920431724.919551725.288461726.10861726.20451726.394501726.726031727.297011727.75578
0 8 3 5-1 4 3 10 7 2 56 6 4 32 3 3 0
-9 7 3 53 5 0 5
-4 5 2 4-3 2 2 10 3 3 11 8 3 6
-2 6 1 50 5 1 58 5 1 4-3 4 3 22 9 3 62 5 4 2
10 11 3 9-4 2 2 010 8 5 48 8 5 3
-2 8 4 5-3 5 3 32 7 3 4
-48 8 6 36 8 6 21 6 2 41 9 3 79 10 3 8
100 8 5 4-4 9 4 5-1 6 2 51 10 4 6
-2 8 2 6-7 8 4 40 6 0 6
-1 6 1 6-3 6 3 42 3 2 2
-10 8 4 40 11 4 7
-2 7 1 6-37 4 4 1
3 10 3 7.3 7 4 34 9 4 63 7 3 5
34 9 5 53 6 1 52 7 2 63' 9 5 4-3 9 6 4
-28 9 6 3-1 7 0 70 4 2 30 7 1 71 6 4 2
7 2 56 6 06 6 15 2 34 1 44 0 46 5 19 1 86 4 28 1 77 0 73 0 36 5 28 2 64 2 27 1 67 1 63 2 18 0 84 1 45 1 51 1 03 2 27 4 36 0 64 0 44 2 34 2 39 2 76 1 5
10 4 61 1 17 6 17 6 27 5 25 2 46 4 37 7 07 7 15 3 38 4 49 4 59 2 79 3 66 1 6
10 3 78 1 77 5 35 1 55 0 56 2 52 1 18 3 5
11 3 87 0 75 1 4
10 2 87 3 48 5 37 2 68 6 25 2 47 1 78 6 38 7 18 7 26 1 63 1 26 0 66 3 3
4.20E-011.37E-034.10E-031.14E-001.62E-001.42E-037.80E-034.31E-042.36E-023.45E-042.25E-037.38E-002.35E-025.55E-024.69E-013.93E-011.48E-031.16E-002.81E-046.50E-003.21E-014.29E-003.70E-013.19E-022.01E-012. 20E -001.80E-001.19E-005.35E-025.OOE-042.76E-041.24E-004.63E-031.56E-031.63E-023.04E-018.01E-027.30E-04
{2.29E-04)1.32E-014 .41E-033.62E -031.34E-043 .50E-025 .42E-013 .99E-034.68E-026.05E-031. 70E -005.14E-005.27E-011.30E-002 .97E-023. 22E-032.60E-01
{6.41E-04)(4 .82E-03)
1.77E-012.85E-038.67E-02
{9.89E-04)5 .45E-019.10E-023.20E-032.72E-047.OOE-043 .40E-003.44E-001 .20E-009.80E-02
6 -2.34 3.34 3.04 -6.45 -3.06 1.85 3.0
10 -17.53 4.5
10 -10.65 -16.54 -2.03 2.76 -4.75 -1.03 -2.4
10 -20.04 -1.6
15 -29.83 -2.84 -8.33 -4.26 -1.53 -8.43 -2.44 -3.54 -0.24 -4.94 -6.76 -12.2
10 8.26 -1.23 5.44 6.45 -2.33 0.13 -1.8
10 5.6
4 5.64 2.83 3.6
10 0.86 -4.43 -0.25 -3.95 2.24 5.53 0.93 0.83 -1.45 1.23 2.04 -5.95 -3.5
4 0.94 -2.66 -0.5
5 1.95 5.36 6.7
15 16.015 1.710 -2.410 6.010 3.03 -2.3
1.07 1732.301960.72 1733.42830.72 1733.51721.05 1736.327221.07 1737.007240.99 1737.716840.78 1738.378680.74 1738.659420.84 1739.108190.80 1739.59340.89 1739.890301.06 1740.130950.78 1740.650791.10 1741.887031.04 1743.700471.09 1743.878560.86 1743.898631.03 1744.288180.84 1745.286351.06 1747.461921.09 1749.599331.05 1749.712701.03 1749.95400.82 1750.323541.11 1752.20271.07 1753.651551.01 1753.821611.04 1756.55121.14 1758.536400.91 1759.357510.73 1759.445401.06 1760.960640.70 1761.025620.70 1761.128450.78 1761.290551.02 1762.669690.86 1763.239960.65 1764.151440.65 1764.60070.93 1767.725890.80 1769.517240.76 1770.211250.61 1770.43131.00 1771.836621.07 1773.312821.01 1773.871861.06 1773.907830.78 1774.636151.01 1775.467671.02 1777.447231.03 1777.662591.02 1777.735551.00 1778.069461.03 1781.340451.10 1781.572680.90 1782.362401.07 1782.690011.00 1783.182900.76 1783.686801.05 1783.904030.70 1784.46490.98 1784.747341.09 1785.563160.70 1785.809380.64 1785.876660.64 1786.025871.01 1786.693421.02 1788.490241.01 1791.114181.00 1791.4805
-1 3 2 19 5 4 10 9 2 73 4 4 05 8 3 6
-3 4 4 10 5 4 26 7 2 55 8 3 55 8 1 7
-18 9 4 51 6 4 34 5 2 4
-7 10 4 76 7 4 42 8 2 78 8 0 8
-4 8 1 82 11 3 80 10 5 6
-12 11 5 62 8 4 53 10 6 5
12 7 1 67 10 5 5
-1 9 3 71 6 2 5
-44 11 4 814 9 4 6-2 10 2 80 10 5 52 9 0 90 9 1 8
-3 9 1 9-2 3 3 0-1 3 3 1-3 9 2 80 3 3 0
-30 12 4 90 7 2 62 9 5 40 10 4 7
-4 11 5 7-1 10 3 8-3 4 2 23 8 2 6
-4 8 1 73 4 3 1
-19 10 4 6-4 8 5 35 10 0 10
-4 10 1 103 9 3 61 11 5 6
-1 10 1 90 7 5 2
-4 10 2 9-5 8 2 7-1 11 2 90 4 3 2
-21 11 4 8-3 6 5 12 5 5 02 5 5 10 6 5 24 7 5 3
-1 8 5 47 9 5 5
-4 4 3 121 12 5 8
2 1 2 2.21E-00 105 3 2 (4.22E-01)9 1 8 4.29E-02 104 3 1 1.37E-01 48 2 7 1.12E-01 64 3 2 3.99E-01 55 3 3 1.38E-01 56 3 4 2.80E-01 67 4 4 1.87E-02 38 0 8 3.86E-02 38 5 4 (9.50E-03)6 3 4 2.76E-01 54 1 3 8.65E-01 59 5 4 3.57E-03 47 3 5 5.20E-02 78 1 8 1.04E-01 107 1 7 7.00E-01 107 0 7 2.10E-00 4
11 2 9 3.65E-03 49 6 3 1.45E-03 5
11 4 7 1.70E-03 58 3 6 7.40E-02 59 7 2 4.00E-04 106 2 5 1.22E-00 59 6 4 4.70E-04 59 2 8 1.44E-02 35 1 4 1.98E-00 5
10 5 5 3.47E-04 109 3 7 9.43E-03 5
10 1 9 5.20E-03 510 4 6 1.88E-03 48 1 8 1.20E-00 59 0 9 4.39E-02 48 0 8 3.66E-01 43 0 3 2.41E-02 32 2 0 1.19E-00 49 1 9 1.50E-02 32 2 1 3.49E-00 6
11 5 6 2.82E-04 106 1 5 3.95E-01 49 4 5 1.46E-02 3
10 3 8 9.80E-03 510 6 4 1.65E-04 1510 2 9 1.43E-02 53 1 3 3.28E-01 67 3 5 6.45E-02 47 2 6 2.32E-01 64 0 4 1.48E-02 59 5 5 1.39E-03 78 4 4 1.12E-02 59 1 9 1.93E-01 69 0 9 6.OOE-01 88 4 5 2.93E-02 3
10 6 5 5.83E-04 410 0 10 5.65E-03 47 4 3 6.42E-02 3
10 1 10 1.62E-02 37 1 6 7.60E-01 5
11 1 10 4.58E-03 33 2 1 2.37E-00 4
11 3 9 9.57E-04 46 4 2 3.50E-02 45 4 1! 1.11E-01 45 4 2 3.68E-02 46 4 3 1.01E-01 37 4 4 2.24E-02 38 4 5 3.34E-02 39 4 6 4.55E-03 43 2 2 8.00E-01 10
11 6 5 1.69E-04 10
0.4
-7.70.01.4
-2.8-1.4-7.44.81.7
-5.30.90.5
-2.5-7.2-1.3-1.4-1.4-0.8-0.41.3
-3.03.3
-5.14.44.3
-6.6-0.45.48.33.1
-1.2-5.84.2
-0.92.2
-2.25.3
-6.64.92.0
-15.02.7
-4.7-4.3-4.25.0
-4.13.11.14.6
-1.2-1.55.7
-1.01.61.63.8
-2.8-0.21.3
-1.2-1.8-2.63.73.20.74.0
-6.3
1.041.001.091.001.061.001.000.930.861.120.771.011.010.741.021.121.011.011.130.691.001.040.620.980.691.101.000.721.061.141.001.011.161.021.061.031.161.030.680.990.991.100.671.141.060.930.981.070.770.991.021.020.850.681.210.981.210.981.191.031.150.980.970.980.990.991.001.021.030.65
(continued overleaf)
Robert A. Toth
478 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992 Rbr .Tt
Table 7. Continued
Observed Upper Lower- Observed Observed Upper Lower ObservedPosition 0 - J Ka, K, J K K, Strength %s (o - c)% R Position o - J K, J K K, Strength %s (o - c)% R
1.04 1877.776981.02 1879.465341.02 1879.784730.97 1882.01341.09 1882.01871.07 1882.87910.97 1882.91391.29 1883.24111.22 1883.37011.27 1883.52671.02 1883.790471.27 1885.389160.92 1885.769631.03 *18614091.03 1889.63081.28 1889.756250.76 1890.47910.97 1893.17981.01 1893.421460.85 1894.904600.97 1897.852091.35 1902.606781.35 1907.062831.03 1907.381441.07 1907.44341.03 1907.680951.03 1907.712521.08 1911.322181.13 1911.49600.99 1911.868970.99 1913.75910.97 1913.931340.97 1920.09160.96 1922.089900.95 1922.393350.96 1923.66410.96 1926.51691.03 1927.60940.96 *1927.92990.98 *1929.42371.00 1929.818200.97 1930.701571.02 1932.116751.02 1932.390620.96 1935.69680.92 1937.170750.98 1938.383121.45 1938.69576
1940.16751.08 1944.12571.04 1946.198441.08 1947.095671.09 1947.35070.96 1954.406170.96 1955.734210.96 1957.029200.85 1958.10401.04 1964.171741.12 1971.78941.02 1975.46221.09 1977.629821.04 1980.761331.02 1980.76600.94 1981.990520.91 1984.28881.18 1984.553281.05 1987.153010.95 1996.530350.95 2002.647030.92 2005.60255
-3 6 2 458 4406 4310 7 7 0-5 7 7 1-18 8 7 108 7233 10 7 369 7233 9 7 3-2 10 7 40 12 2 1036 420 17 0 170 14 1 130 14 2 130 12 3 9
-14 4 4 10 12 3 1035 3327 4407 34-2 13 2 10 15 1 140 15 2 14-1 5 5 115 500 13 3 1-5 9 4 5-3 8 4 5-11 5 4 2-2 7 4 3-9 8 3 53 13 3 10-2 9 4 658 5379 5437 5235 8 8 111 9 8 10 14 3 12-7 10 4 726 52-5 6 5 1-23 6 5 1-3 6 3 4-6 11 4 807 2516 6 4 312 4 4 148 4412 12 4 90 15 2 13-4 8 3 507 53-2 7 5 20 13 4 1005 420 14 4 155 4 4 0-1 8 5 476 6193 6 6 0-1 8 5 3-1 7 3 519 45-4 6 4 3-1 9 5 5-3 8 2 6-3 7 6 2
5 1 54.92E-02 38 1 7 1.27E-03 35 3 26.28E-01 27 6 14.10E-03 67 6 2 1.36E-03 68 6 2 1.03E-03 48 6 33.06E-03 4
10 6 42.09E-04 109 6 3 1.45E-03 69 6 45.21E-04 10
10 6 55.90E-04 511 3 92.83E-03 55 3 32.07E-01 416 1 16 3.70E-04 1013 2 12 (9.78E-04)13 1 12 3.10E-03 411 4 87.38E-04 44 1 46.55E-04 1511 2 98.29E-03 44 0 42.63E-02 46 3 39.80E-02 36 2 51.80E-01 S12 3 10 2.73E-03 414 2 13 7.70E-04 514 1 13 2.50E-04 104 4 02.40E-01 54 4 17.30E-01 312 2 10 9.25E-04 39 1 8 1.03E-03 77 3 4 126E-01 45 1 5(3.26E-04)6 3 42.77E-01 38 0 83.16E-04 1012 4 97.66E-04 48 3 5 1.85E-02 38 2 63.33E-04 109 2 77.08E-04 107 2 58.70E-04 158 7 27.10E-04 59 7 24.70E-04 1013 2 11 8.10E-04 49 3 62.07E-02 35 4 13.92E-01 35 4 21.30E-01 36 2 4 2.13E-04)5 0 55.27E-02 410 3 72.55E-03 46 1 65.08E-02 36 1 66.90E-04 103 1 23.30E-03 57 3 53.35E-02 311 3 82.42E-03 314 3 12 1.64E-04 157 2 6 1.91E-02 36 4 26.37E-02 36 4 3 1.85E-01 312 3 92.54E-04 104 1 33.45E-03 313 3 10 2.15E-04 103 1 33.62E-04 157 4 37.90E-02 35 5 0 1.99E-01 35 5 16.62E-02 37 4 42.52E-02 36 0 69.25E-03 48 3 63.52E-02 35 1 4 1.68E-02 48 4 4 1.03E-02 67 1 75.55E-03 56 5 13.10E-02 4
1792.068281794.041641794.073821795.369231796.407891797.96461800. 038741800.62261800 .80431801.486991801.679111802. 045371806.574461810.11461810. 129041810. 522251814. 200251815 .450261816. 058961817.330401817. 729081820 .933351821.212451821.834491822. 094111825.890551825 .897151827. 525401827.799941827.897201828.476331832. 270811834.016011834.329831834 .367901834.517351834.674091834.701371834.726961834.76861834 .79441834 .832401834 .935111835.34441835.771191835.906651838.468451840.01031840.15081840.79649*1841.377901842.226501845.185651849.338691853.347531853.874771855.27617*1856.575171857.619671858. 272431858.366561858.477951859.865421861.904281861.941351869. 2799
*1871.494831871.63721871.891921876. 71628
-1 10 5 6-5 1 1 0 1-1 1 1 1 1-3 9 1 8-1 5 3 2
-15 1 1 5 72 928-7 13 3 10-4 12 4 9-6 1 1 1 10-1 5 3 3-12 1 1 2 104 927-6 12 0 12-1 12 1 120 12 3 101 1 1 4 71 10 1 91 6 342 10 3 70 10 2 9-5 12 1 112 12 2 12 5 320 5 230 13 0 131 13 1 132 3313 6332 7 354 10 6 4
-2 9 6 310 8 6 20 660
-10 6 6 1-2 7 6 15 1 1 1 10
-3 4 4 15 7 62
-11 9 6 424 10 6 54 863-2 4 4 01 1 1 6 63 11 2 103 10 2 8
-3 8 3 62 13 1 1212 13 2 12-4 5 4 1-5 14 1 140 440-5 6 4 2-1 9 3 70 12 1 11
-4 12 2 1-3 1 1 3 818 15 0 151 7 430 542-8 4 3 20 633
-1 5 4 1-4 10 3 82 1 1 2 97 7340 16 1 168 13 1 12-2 13 2 120 1 1 3 9
10 4 710 1 1010 0 108 275 05
1 1 4 88 1713 2 112 3 1011 0 14 22111 118 3611 0 112 2 110 5 69 285 239 469 1812 0 1212 1 124 234 1412 1i1212 0 122 026 066 2410 5 59 548 536 516 527 52
10 2 93 307 539 55
10 5 68 543 31
11 5 710 1 99 377 2513 0 1313 1 135 1413 0 134 136 158 26
1 1 2 101 1 1 1010 4 714 1 147 164 313 035 244 329 27
10 3 87 07
15 0 1512 2 1112 1 110 2 8
4.99E-032.40E-018.OOE-023.50E-013.28E-025.02E-041.30E-011 .93E-047.69E-045.27E-035.30E-011 .92E-031.10E-013.43E-029.66E-021.10E-031.71E-036. 11E-028.80E-014.80E-031.80E-015.41E-041.57E-031 .24E-004.07E-013.886-021.25E-028.56E-034.88E-031.66E-015.97E-04(4.91E-03)3.68E-038. OOE -032.35E-022.04E-027.OOE-021.96E-006.60E-031.64E-031.72E-031.06E-026.45E-012. 15E-042.40E-021 .83E-022.60E-014.50E-041.40E-048.80E-031 .70E-021 .03E-033.90E-034.45E-029.63E-032.87E-026.25E-035.20E-038.45E-033.70E-016.30E-021.88E-011 .15E-005.82E-022. 28E-02
(4.04E-03)1.48E-031 .04E-023.36E-038.OOE-03
443
10335
104554454
10533335432464346
4663
1035
101033
10454
101546
105334543553455
3325
2.7-6.1-6.1-9.51.4
-0.20.0
-6.5-0.6-1.14.28.0-3.90.0
-6.4-9.20.21.9-2.00.6
-0.5-1.2-4.4-0.40.72.7-0.76.54.2
-1.0-4.3
0.40.8-1.33.8-6.9-0.50.8-0.3-8.4-3.6-1.85.3
-4-4-0.1-2.7-4.4-12.01.31.13.92.01.32.51.72.91.71.3-5.9-0.24.3
-2.0-1.30.3
4.18.45.22.0
2.83.2
-0.12.82.34.83.85.0
-1.95.6
-1.13.20.72.6
5.1-1.66.8-1.08.0-2.1-4.73.2-6.9-9.5-3.7-2.33.9-4.1-4.0
-0.76.75.13.3
-0.85.9
-14.1-1.1-1.45.5
-0.5-1.4-1.8
2.10.94.1
-12.12.5
-4.8-5.5-20.92.81.0
-2.1-2.73.3
-0.1-8.8-1.5-3.7-3.9-5.12.77.63.02.23.2-4.5
1.091.171.020.950.950.950.950.970.960.960.970.901.031.050.950.950.841.140.911.111.011.060.890.950.951.021.030.891.241.001.181.031.270.830.971.191.211.170.950.950.880.941.031.021.191.130.921.121.241.161.030.890.871.081.031.030.861.160.841.231.021.051.051.021.171.041.171.001.171.05
Robert A. Toth
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 479
Table 7. Continued
Upper Lower Upper LowerObserved Observed Observed Observed
Position o - c J K K, J Ka K, Strength %s (o - c)% R Position o- c J Ka K, J Ka K, Strength %s (o - c)% R
2005.64419 -8 7 6 1 6 5 2 9.30E-02 4 -4.5 1.05 2095.44171 0 11 6 6 10 5 5 5.10E-04 6 -2.7 1.00
2008.08019 -7 9 5 4 8 4 5 2.95E-02 3 0.5 1.02 2102.95935 0 9 7 3 8 6 2 2.30E-03 4 3.4 1.12
2011.31860 1 10 5 6 9 4 5 1.07E-02 4 4.6 0.98 2102.99792 0 9 7 2 8 6 3 6.61E-03 3 -0.9 1.12
2012.79147 -4 9 3 6 8 2 7 1.48E-02 4 0.4 1.11 2106.68387 0 7 5 3 6 2 4 4.44E-04 10 0.0 1.50
2015.28200 0 7 4 4 6 1 5 5.55E-03 4 2.7 1.18 2108.0117 0 12 5 7 11 4 8 1.83E-04 10 -0.8 1.022015.3286 10 5 4 1 4 1 4 2.01E-03 10 -0.3 1.30 2113.9680 24 7 4 3 6 1 6 8.23E-04 6 -8.2 1.56
2021.79805 7 11 5 7 10 4 6 1.05E-03 5 -0.4 0.94 2122.8768 0 8 5 4 7 2 5 1.36E-03 6 -7.8 1.44
2028.85062 0 12 5 8 11 4 7 9.05E-04 7 -0.8 0.91 *2123.62142 4 8 8 1 7 7 0 9.13E-03 5 -3.1 1.31
2029.99777 2 8 6 3 7 5 2 4.02E-02 3 -2.2 1.05 2127.18945 2 10 7 4 9 6 3 2.26E-03 5 1.7 1.10
2030.23180 3 8 6 2 7 5 3 1.33E-02 4 -3.0 1.05 2127.36459 -5 10 7 3 9 6 4 7.50E-04 5 1.3 1.10
2030.30047 0 10 4 6 9 3 7 2.75E-03 5 -0.4 1.05 2130.7986 -18 10 2 8 9 1 9 4.50E-04 5 -16.0 1.322035.14352 -2 8 3 6 7 0 7 1.18E-02 4 1.9 1.22 2135.73632 9 10 4 7 9 1 8 1.65E-03 10 -7.7 1.28
2036.61951 -11 10 5 5 9 4 6 3.12E-03 4 0.4 1.01 2141.4585 8 11 3 8 10 2 9 8.60E-04 10 0.7 1.23
2049.72415 -6 8 4 5 7 1 6 1.05E-02 4 -0.3 1.19 2142.7468 -34 9 5 5 8 2 6 4.OOE-04 10 0.7 1.40
2053.5810 8 9 6 4 8 5 3 5.10E-03 4 -1.5 1.04 2143.84620 1 10 3 8 9 0 9 1.44E-03 10 1.2 1.352054.51442 3 9 6 3 8 5 4 1.55E-02 4 0.0 1.04 *2149.1255 -28 9 8 1 8 7 2 3.35E-03 5 -1.8 1.30
2061.1502 7 6 4 2 5 1 5 5.48E-04 10 -3.9 1.39 2150.5904 0 11 7 5 10 6 4 2.29E-04 10 3.6 1.082067.28145 -9 9 2 7 8 1 8 4.96E-03 3 -4.3 1.23 2151.21655 0 11 7 4 10 6 5 7.OOE-04 10 5.6 1.08
2069.34572 -3 11 5 6 10 4 7 2.54E-03 4 1.8 1.01 2157.61134 -4 7 5 2 6 2 5 4.30E-04 15 -11.7 2.12
2075.72220 -1 10 6 5 9 5 4 5.26E-03 10 0.5 1.02 2168.3182 0 10 5 6 9 2 7 7.OOE-04 10 1.4 1.39
2075.8999 -31 10 3 7 9 2 8 1.20E-03 6 -1.0 1.16 2174.2290 0 10 8 3 9 7 2 8.55E-04 8 3.0 1.28
2078.1677 70 8 7 2 7 6 1 1.83E-02 5 2.0 1.12 2174.2355 0 10 8 2 9 7 3 2.85E-04 8 3.0 1.28
2078.1733 17 8 7 1 7 6 2 6.10E-03 5 2.0 1.13 *2192.1074 0 9 9 0 8 8 1 1.08E-03 7 -11.6 1.67
2078.65779 -4 10 6 4 9 5 5 1.84E-03 6 5.8 1.03 2192.4270 -28 11 2 9 10 1 10 3.38E-04 15 -34.2 1.42
2083.4524 -4 11 4 7 10 3 8 1.75E-03 4 -2.0 1.08 2198.8045 0 11 8 4 10 7 3 (7.99E-05)2088.6488 7 9 3 7 8 0 8 1.57E-03 4 9.1 1.27 2198.8349 0 11 8 3 10 7 4 2.38E-04 10 -1.2 1.25
2090.22715 0 9 4 6 8 1 7 1.74E-03 5 6.3 1.23 *2219.16827 0 10 9 2 9 8 1 4.14E-04 10 8.5 1.672091.7513 21 6 5 2 5 2 3 8.50E-04 10 -3.6 1.56
aAn asterisk denotes a doubled absorption, with the quantum assignment given for the stronger transition. The strength given represents the sum of the
strengths of the two comparable transitions. o - c is the observed minus the computed line position in inverse centimeters times 105. The computed values
are derived from energy levels given in Table 2. %s is the estimated uncertainty in the measured line strength given in percent. Line strengths given
within braces are the computed values derived in this study; (o - c)% is the observed minus the computed line strength in percent. R is the ratio of the
computed line strength derived in this study to that given in Ref. 7.
resulted in the most accurate representation of the experi-mental values was to separate the line strengths into tworegions for each isotopic species and to fit each set. Thefirst set contained line strengths whose line frequen-cies were lower than 1700 cm-', and the second set in-volved measurements for frequencies equal to and above1700 cm-'. Values and associated estimated uncertain-ties of the matrix elements derived from these fits aregiven in Table 5. The measured line strengths wereleast-squares fitted by using the expressions given inEqs. (1)-(3) and outlined in Ref. 1. It should be noted thatthe measured line strengths were normalized to 100% ofthe isotopic sample, and these normalized values were usedin the analyses. The lower portion of Table 5 lists thenumber of lines fitted in each set and the values ofthe standard deviation in percent, o-%, resulting fromthe least-squares fit of the strengths. o-% is defined by
1/2
-% = 100 { [(Sobs - Scal)/Sobs] 2/N , (4)
where N is the number of lines included in the fit. Theinitial analysis included all the useful measured strengthsin one fit per species: for H21'0, 623 lines with o-% =7.0% and, for H2
18 0, 696 lines with u% = 6.1%.
RESULTS
Tables 6 and 7 list 695 lines of H2170 and 755 lines of
H2150 used in the H2
170 and H2180 analyses, respectively.
Entries for the tables include the observed line position,the observed minus the computed line position (o - c), ro-tational quantum assignments, the observed strength, theestimated uncertainty in the measured strength (%s), theobserved minus the computed line strength in percent[(o - c)%], and the ratio R of the computed line strengthto that given in the tabulation by Flaud et al.7 (and in the1986 edition of the HITRAN database'). The values for theline strength are normalized to 100% of the isotopic spe-cies in units of inverse square centimeters per atmosphere(1 atm = 760 Torr), whereas the values in Ref. 7 weregiven in cm'1/(mol cm-2) and reduced by the normal iso-topic abundance (3.7 x 10-4 for H2
170 and 2.04 x 10-3 forH2
150, as defined in an early U.S. Air Force GeophysicsLaboratory report). Therefore values from Ref. 7 wereconverted to inverse centimeters per atmosphere by apply-ing the factor 2.48 x 1019 and dividing the result by theproper isotopic abundance in natural water to determinethe values of R given in Tables 6 and 7.
The observed positions are given to three, four, or fivedecimal places in Tables 6 and 7, which indicates the accu-
Robert A. Toth
480 J. Opt. Soc. Am. B/Vo. 9, No. 4/April 1992Robert A. Toth
Table 8. Comparison of Computed Line Strengths of H2 16 0, H2 170, and H 2 180 Transitionsin the (1O)-(OOO) Bands with Strengths ;! 1 CM-2 /atm at 296 Ka
Upper Lower Line Position (cm-') Line StrengthJ Ka IC~ J Ka, K~ 12 160 1720 H 2
180 H2
160 H2
170 H 2180
4 3 24 2 33 3 03 2 15 1 46 1 62 2 12 1 23 1 25 0 52 1 16 1 64 1 41 1 11 1 03 0 34 1 45 0 52 0 23 1 33 2 12 1 24 0 42 1 25 2 35 1 40 0 03 0 34 1 33 1 22 0 21 0 11 1 02 1 12 0 21 1 13 1 23 2 14 2 23 0 32 1 25 2 32 2 13 1 34 0 45 1 44 2 35 3 24 1 43 3 05 0 52 2 15 1 44 3 22 2 06 1 63 2 27 0 74 2 33 2 18 1 87 1 66 2 59 0 93 3 04 3 25 3 24 4 15 4 1
5 45 34 44 36 27 03 33 24 26 13 26 25 02 22 24 14 25 13 13 23 33 04 12 25 35 21 13 14 23 22 11 11 02 01 10 03 03 14 12 11 05 12 12 03 15 04 15 23 03 24 11 14 24 21 15 02 16 13 12 17 06 25 18 12 23 24 23 34 3
1 1394.474442 1399.204241 1419.508002 1436.818245 1447.951637 1456.509790 1456.887071 1464.905103 1472.051236 1473.514202 1487.348545 1489.841975 1496.248910 1498.803211 1505.604284 1507.058333 1521 .234534 1521 .309053 1522.686122 1533.182310 1533.916563 1540.299803 1541.954181 1542.159832 1545.156643 1554.352391 1557.609232 1558.530922 1559.690161 1560.257201 1569.788670 1576.185441 1616.711552 1623.559181 1627.827480 1634.967113 1635.651902 1645.969353 1647.404102 1652.400361 1653.267104 1654.511242 1662.809302 1669.392943 1675.172765 1675.515154 1683.177993 1683.983663 1684.835201 1695.459464 1695.928200 1699.933923 1700.500773 1704.453431 1706.349265 1717.405491 1718.611686 1733.390612 1734.650582 1739.838797 1751 .423295 1756.818874 1761 .828588 1768.120191 1772.714191 1792.659403 1830.132040 1844.180672 1869.34567
1.301.112.442.441.061.483.992.042.522.471.161.013.521.274.514.592.522.021.691 .021.833.961.172.631.953.091.395.541.575.232.356.255.682.011 .031.454.353.981.165.745.992.151.982.392.341.271.671.217.531.186.684.471.801.251.255.101.283.483.232.202.131.181.891.163.572.441 .251.971.17
'Lnpositions are also computed. 'he computed transition frequencies are derived from energy-level values obtained in this study for HI "Oand H2 lBand derived from values given in Ref.l1for H2 60 The computed line strengths for H2 O6are taken from Ref. 1
1392.065891396.394681417.119921434. 273121445.244391453 .384201454.259781461.911561469.265271470 .428621484.5 10941486.715711492.965401495.883831502. 727471503.956031518. 187471517. 794181519. 557081530.183931531 .311291536.809721538.481401539. 202071542.537731551.060331554 .394541555. 150171556. 576471557.268411566.488951572.928181613. 099231619. 988091624.528381631.315011632.166571641 .968961643.527211649.032921649.573831650 .832721658.800201665 .661 081671 .709541672.192781679.264841679 .385391681.088771690.893171692 .369351695 .840601697.414851700.024371702.297371713.664101714 .473531729.692451730 .458981735 .851711747.650631753.389761757. 592021764 .334991768.183681788.027511825.739911839.164611864.32859
1389.910371393.880101414.983671431.999001442 .826041450.59911145 1.911431459.237831466.777831467.676411481.977461483 .926061490.040411493.276941500.158911501.188331515.466981514 .662121516. 765811527.506861528.983531533 .700441535.384111536. 561311540.193831548.118311551.527021552. 133981553 .794391554 .598731563.545251570.022581609.879811616.805931621 .585251628.060061629.061341638.407711640.077701646.028241646.282211647.562151655 .229871662 .335331668.619261669. 230141675.780391675.296071677. 750491686.827961689.194081692.195091694 .656711696.083131698. 689091710 .330161710.788061726.394511726.726031732 .301971744.288221750.323421753.821601760.960621764.151441783.904031821.834471834.701401859.86543
1.351.152.512.521.061.484.132.122.562.481.181 .043.551.314.624.632.602.091.721.051.863.991.222.701.943.151.415.721.605.322.416.365.712.041.011.444.403.941.165.615.882.161.942.322.261 .261.641.177.231.136.364.321.741.211.215.061.263.453.182.182.111.161.861.153.462.371.281.981 .19
1.331.142.492.511.081.504.112.122.592.521.191.053.611.314.654.722.602.091.741.051.864.081.222.701.963.151.435.721.595.352.416.415.852.091.031.494.534.071.185.786.122.192.052.402.331.331 .741.207.481.206.554.561.771.231 .245.111.303.493.272.242.131.181.911.163.602.461.271.981.18
Vol. 9, No. 4/April 1992/J. Opt. Soc. Am. B 481
Table 9. Comparison of Computed Line Strengths between H2160, H2170, and H2 1O Transitionsin the (010)-(000) Bands with Strengths 2 10- and < 10-3 cm-2/atm at 296 K'
Upper Lower Line Position (cm-') Line Strength
J Ka K, J K. K, H2 160 H 217 0 H2 180 H 2
16 0 H 217
o H2 180
8 2 6 9 5 5 1120.83199 1120.73848 1120.61522 3.10 3.30 3.496 2 4 7 5 3 1151.54389 1151.80089 1152.00245 3.97 4.08 4.379 2 8 10 3 7 1152.44405 1148.59025 1145.16522 9.20 9.23 9.315 1 5 6 4 2 1165.04880 1163.84299 1162.74600 5.41 5.29 5.349 0 9 9 3 6 1229.36368 1225.55739 1222.16169 1.77 1.70 1.45
10 6 5 11 7 4 1242.79913 1240.81254 1239.02806 8.32 8.66 8.746 1 6 6 4 3 1286.02852 1284.61999 1283.34390 9.61 9.43 9.189 9 0 10 10 1 1292.37138 1290.74410 1289.27910 2.48 2.43 2.42
14 1 14 15 0 15 1297.18346 1294.49273 1292.09696 6.05 5.94 6.285 1 5 5 4 2 1312.71458 1311.49551 1310.38930 3.95 3.89 3.826 2 4 6 5 1 1322.55790 1322.74120 1322.87812 2.32 2.44 2.52
13 1 12 14 2 13 1326.13480 1323.33405 1320.83757 5.53 6.10 6.024 1 4 4 4 1 1333.48904 1332.41736 1331.44359 7.22 7.19 7.069 2 7 9 5 4 1341.10070 1340.37158 1339.66804 7.20 7.71 7.75
12 1 11 13 2 12 1343.67838 1340.84318 1338.31730 6.68 7.21 7.2313 1 13 13 2 12 1348.75662 1345.85916 1343.28104 5.22 5.62 5.3611 3 9 12 2 10 1363.06264 1359.88416 1357.06712 7.52 7.95 7.9111 4 8 12 3 9 1381.53127 1377.09422 1373.18900 2.26 2.42 2.3713 2 12 13 3 11 1406.15052 1402.94210 1400.08718 3.27 3.50 3.4713 3 11 13 4 10 1453.52441 1450.25170 1447.21630 1.76 1.93 2.0110 5 6 11 4 7 1484.25730 1477.93817 1472.32199 4.13 4.43 4.4110 7 4 10 8 3 1516.42749 1514.43243 1512.64214 5.20 5.54 5.596 1 5 5 4 2 1536.14923 1534.78525 1533.54437 8.05 8.51 8.438 5 3 9 4 6 1579.24711 1574.03567 1569.40708 8.16 7.44 7.748 3 5 9 2 8 1590.40421 1587.58880 1585.09452 8.21 7.68 7.447 6 2 8 5 3 1649.51909 1643.69530 1638.51105 3.25 3.31 3.59
11 4 8 11 3 9 1792.33058 1788.16314 1784.46511 9.15 9.58 9.5912 4 9 12 3 10 1808.37193 1804.36332 1800.80434 7.16 7.71 7.7412 1 11 12 0 12 1828.20791 1824.36261 1820.93330 5.19 5.48 5.4710 6 4 10 5 5 1840.29811 1834.04745 1828.47629 5.72 6.10 6.234 4 0 4 1 3 1854.12165 1847.82218 1842.22650 8.41 8.98 9.908 7 1 8 6 2 1894.65358 1888.42263 1882.87928 8.49 9.35 9.819 7 3 9 6 4 1895.37937 1889.10670 1883.52637 4.23 4.65 4.92
10 7 4 10 6 5 1895.73830 1889.41515 1883.79049 5.06 5.66 5.9614 1 13 13 2 12 1897.37239 1893.27940 1889.63080 8.86 9.77 9.784 4 1 4 1 4 1904.76087 1898.62814 1893.17994 5.06 5.31 6.10
15 1 14 14 2 13 1915.19557 1911.06340 1907.38144 7.25 8.22 8.2313 3 11 12 2 10 1919.51347 1915.17100 1911.32218 8.26 8.94 8.8913 3 10 12 4 9 1927.85947 1924.82990 1922.08987 6.73 7.42 7.278 5 3 8 2 6 1937.22038 1930.02920 1923.66405 2.61 2.85 3.309 5 4 9 2 7 1939.12451 1932.42973 1926.51683 5.32 5.74 6.668 8 1 8 7 2 1940.26738 1933.73857 1927.92955 4.31 4.96 5.387 5 2 7 2 5 1941.75733 1934.25861 1927.60937 7.53 8.29 9.939 8 1 9 7 2 1941.82823 1935.26308 1929.42359 2.80 3.23 3.576 4 3 6 1 6 1951.12921 1945.32243 1940.16734 6.22 6.45 7.734 4 0 3 1 3 1987.34023 1981.05032 1975.46165 3.44 3.65 3.94
12 5 8 11 4 7 2041.51131 2034.81050 2028.85062 8.64 9.25 9.126 4 2 5 1 5 2072.53993 2066.50657 2061.15013 4.92 5.23 5.696 5 2 5 2 3 2106.34669 2098.61652 2091.75109 6.73 7.64 8.81
11 6 6 10 5 5 2107.54635 2101.14590 2095.44171 4.94 5.30 5.247 5 3 6 2 4 2121.26806 2113.54175 2106.68387 3.47 3.93 4.447 4 3 6 1 6 2124.88690 2119.10045 2113.96776 7.52 8.00 8.90
10 2 8 9 1 9 2138.18845 2134.29042 2130.79878 4.65 4.91 5.2210 7 3 9 6 4 2139.47892 2133.06695 2127.36464 6.75 7.38 7.4011 3 8 10 2 9 2147.40554 2144.26784 2141.45842 7.76 8.23 8.549 5 5 8 2 6 2156.56416 2149.23487 2142.74714 3.18 3.59 3.97
11 7 4 10 6 5 2163.43045 2156.96560 2151.21655 5.96 6.70 6.617 5 2 6 2 5 2171.25580 2164.02650 2157.61138 3.45 4.00 4.80
10 5 6 9 2 7 2181.34399 2174.43043 2168.31820 5.54 6.31 6.9011 2 9 10 1 10 2200.30574 2196.14919 2192.42798 3.64 4.04 4.5410 9 2 9 8 1 2231.13708 2224.15430 2219.16827 2.18 2.67 2.84
a Strengths are in inverse square centimeters per atmosphere times 104. Line positions are also computed. The computed transition frequencies derivedfrom the energy level values obtained in this study for H2 17Q and H2 180 and derived from values given in Ref. 1 for H2160. The computed line strengths forH2 160 are taken from Ref. 1.
Robert A. Toth
482 J. Opt. Soc. Am. B/Vol. 9, No. 4/April 1992
racy of these measurements. Obviously, the most accu-rate estimates are given with five significant figures pastthe decimal, and, as was reported in Ref. 1, the absoluteuncertainty for these measurements is ±6 x 10-5 cm-'.The computed line positions were derived from the rota-tional energies given in Table 2. An asterisk next to theline-position value denotes a doubled absorption for whichthe two transitions were not adequately resolved in thespectra. The quantum assignments given for one ofthese features is for the stronger transition, and the valueof the observed strength represents the sum of thestrengths of the two comparable transitions.
Because of the close proximity of a few lines to otherfeatures of comparable or greater strength, only the linepositions of these lines were determined with the aid ofthe LINEFINDER program, and therefore the observedstrengths were not obtained. These lines are noted inTables 6 and 7, with the line strengths (computed) givenwithin braces. The computed line strengths were derivedfrom the dipole moment expansion coefficients givenin Table 5 and Eqs. (1)-(3). Not all the line-strengthmeasurements given in the tables were included in theleast-squares analyses. Entries with %s = 15% were notincluded because these transitions resulted in averagedvalues with uncertainties of as much as 60% to possiblyless than 10%. This range of uncertainty for each ofthese transitions arises for one or more of the followingreasons: (a) blending, (b) weakness of the transitionintensity, and (c) poor agreement between the valuesderived from the various spectra.
Several entries for the ratio R in Table 6 and six entriesfor R in Table 7 are missing because of the absence ofthese transitions in Ref. 7. The computations involved increating the tabulation of Ref. 7 included lower limits forthe line strengths for each isotopic species; transitionsmissing from Ref. 7 but included here have strengths thatare lower than those lower limits.
DISCUSSION
In Ref. 7 the line strengths of the three isotopic speciesfor the (010)-(000) bands were computed by using thetransition moment constants quoted by Camy-Peyret andFlaud'6 for H2
160. Therefore in Ref. 7 it was assumedthat, for a given transition, the strength (normalized to100% of the species) is the same for all three isotopes, ex-cept for slight differences that are due to the lower-stateenergies. This is a reasonable assumption with regard toa first approximation for computing the H2"7O and H2'80line strengths. The contents of Table 8 compare the com-puted strengths between H2
160, H2`7O, and H2"8O for tran-sitions with values greater than 1 cm-2/atm; the resultswere derived from this study for H2`70 and H2`80 andfrom Ref. 1 for H2
160. Inspection of the contents of Table8 shows that, on the average, the above assumption holdstrue for the strongest intensities of the (010)-(000) bands.
Two transitions indicate a 4% difference between theH2
16 0 and H21 8O values, whereas the majority of the
entries agree, within 2%, with one other.A similar comparison is shown in Table 9 for the weaker
transitions measured in this study and in the H216 0
study.' Inspection of the computed strengths listed inTable 9 shows a somewhat different picture for this com-parison; a few transitions in the lower-frequency regionhave some agreement with one another, whereas for theAKa = 3 transitions in the high-frequency range there islittle agreement between the values. For example, the752-62 5 transition (2171.2558 cm-' for H2`6O) has acomputed H2
16 0 strength that is 39% lower than that forH2
5O and 16% lower than the value shown for H21 70.
ACKNOWLEDGMENTS
I thank the Kitt Peak National Observatory for the use ofthe FTS and J. Wagner for assistance in obtaining theH2 0 spectra. The Atmospheric Trace Molecule Spec-troscopy dedicated computer facility was used in the analy-sis of the experimental data. The research described inthis paper was performed at the Jet Propulsion Labora-tory, California Institute of Technology, under contractwith the National Aeronautics and Space Administration.
REFERENCES
1. R. A. Toth, J. Opt. Soc. Am. B 8, 2236-2255 (1991).2. G. Guelachvili, J. Opt. Soc. Am. 73, 137-150 (1983).3. J. G. Williamson, K. Narahari Rao, and L. H. Jones, J. Mol.
Spectrosc. 40, 372-387 (1971).4. C. Camy-Peyret, J.-M. Flaud, and N. Papineau, C. R. Acad.
Sci. Paris B 290, 537-540 (1980).5. J. K. G. Watson, J. Chem. Phys. 46, 1935-1949 (1967).6. L. S. Rothman, R. R. Gamache, A. Goldman, L. R. Brown,
R. A. Toth, H. M. Pickett, R. L. Poynter, J.-M. Flaud,C. Camy-Peyret, A. Barbe, N. Husson, C. P. Rinsland, andM. A. H. Smith, Appl. Opt. 26, 4058-4097 (1987).
7. J.-M. Flaud, C. Camy-Peyret and R. A. Toth, Water VapourLine Parameters from Microwave to Medium Infrared(Pergamon, London, 1981).
8. J. W C. Johns, J. Opt. Soc. Am. B 2, 1340-1354 (1985).9. J. Kauppinen and E. Kyro, J. Mol. Spectrosc. 84, 405-423
(1980).10. F. C. DeLucia and P. Helminger, J. Mol. Spectrosc. 56, 138-
145 (1975).11. G. Steenbeckeliers and J. Bellet, C. R. Acad. Sci. Paris B 273,
471-474 (1971).12. F. C. DeLucia, P. Helminger, R. L. Cook, and W Gordy, Phys.
Rev. A 6, 1324-1326 (1972).13. J.-M. Flaud and C. Camy-Peyret, J. Mol. Spectrosc. 55, 278-
310 (1975).14. L. R. Brown, J. S. Margolis, R. H. Norton, and B. D. Stedry,
Appl. Spectrosc. 37, 287-292 (1983).15. R. A. McClatchey, W S. Benedict, S. A. Clough, D. E. Burch,
R. F. Calfee, K. Fox, L. S. Rothman, and J. S. Garing,'AFCRL atmospheric absorption line parameters compila-tion," Environmental Research Papers No. 434 AFGRL-TR-0096 (U.S. Air Force Geophysics Laboratory, Bedford, Mass.,1973).
16. C. Camy-Peyret and J.-M. Flaud, Mol. Phys. 32, 523-537(1976).
Robert A. Toth
