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Rayleigh and Raman cross sections for the hydrogen molecule
ATOMIC DATA 5, 305-313 (1973)
RAYLEIGH AND RAMAN CROSS SECTIONS FOR THE H Y D R O G E N MOLECULE
A. LEWIS FORD Harvard College Observatory, Cambridge, Mass. 02138 and J. C. BROWNE Departments of Computer Sciences and Physics The University of Texas, Austin, Tex. 78712
The TABLES list calculated values of Rayleigh and Raman light scattering cross sections for molecular hydrogen for wavelengths exceeding 1200 A.
This research was supported by the Robert A. Welch Foundation of Houston, Tex., by the Office of Naval Research under Contract No. N00014-67-A-0126-0017, and by the National Science Foundation
305
Copyright O 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
Atomic Data, Vot. 5, No. 3, 1973
A. L. F O R D A N D J. C. B R O W N E
CONTENTS
INTRODUCTION Outline of the Calculation Method TABLES. Rayleigh and Raman Cross Sections for Initial Rotational Level: I.J=0 II. J = 1 III. J = 2 IV. J = 3 TABLES. Cross Sections for a Thermal Distribution of Initial Rotational Levels V. T = 1 0 0 ° K VI. T = 300 ° K
INTRODUCTION
Cross sections are given for the cases in which the molecule is initially in the rotational states J = 0, 1, 2, and 3 and for thermal distributions with T = 100°K and 300°K and a 3 : 1 ortho to para ratio.
The cross sections for Rayleigh and Raman light scattering by molecular hydrogen are of considerable astrophysical interest in the interpretation of the solar opacity and of the spectra of the Jovian planets (Belton et al., 1 WallacO2). Estimates are available from the work of Dalgarno and Williams 5 and of Victor, Browne, and Dalgarno. 1° Recent developments (Dalgarno, Ford, and Browne, 4 Ford and Browne 6) have yielded data from which reliable cross sections can be calculated. We report here an extensive, accurate tabulation of the cross sections for wavelengths exceeding 1200 ~ . The TABLES list Rayleigh and Raman light scattering cross sections for molecular hydrogen for unpolarized incident radiation, integrated over all angles of the scattered photon. The cross sections can be expressed (Dalgarno and Williams 5) in terms of the components of the dynamic polarizability tensor of the molecule, the accurate calculation of which is described in detail elsewhere. 6 In addition to the tabulated cross sections, coefficients q are given for the expansion of each of the cross sections as a series in inverse powers of the wavelength. The cross sections are given for large 2t by 8
Q = (10s/x _ AE)4 ~
(q/Xi)
Outline of the Calculation Method The dynamic polarizability components upon which these TABLES are based were computed by a direct sum-over-states procedure. This procedure consists of an approximate evaluation of the equation for the dynamic polarizability a(~o) = ~ fob b (Eb-E07-~2 where o~ is the circular frequency of the photon, fob is the oscillator strength for the transition between the state [ 0 ~ of energy E 0 and the state I b ~ of energy Eb, and the s u m is over all states of the molecule for which fob does not vanish. The sum over the infinite number of exact eigenstates of the molecular Hamiltonian was approximated by a sum over a finite number of matrix eigenvectors of the molecular Hamiltonian. The basis sets from which these matrix eigenvectors were constructed were such that the oscillator strength sums S(0) and S ( - 1 ) were closely satisfied (Dalgarno and Epstein3). The sum over b formally is a sum over all vibrational and rotational, as well as electronic, states. For the lowest excited states which are involved, B 1Z +u and C lII~, the sum over vibrational levels and integration over the nuclear translational continuum were evaluated explicitly. For the other excited electronic states in the sum, the sum over vibrational and rotational levels was carried out using closure.
cm z,
i=0
where AE is the transition energy in cm -1 and X is the wavelength of the incident light in A. The cross section is zero if ( 1 0 s / x - hE) is negative. The expansions converge to the number of significant figures given in the TABLE for X/> 5000 A and to three significant figures for X/> 3000 A.
Atomic Data, Vol. 5, No.
3, 1973
306
R A Y L E I G H A N D RAMAN CROSS SECTIONS F O R H 2
The accuracy of the calculations is indicated by the very close agreement (to within 1%) with the very elaborate calculations of Kolos and Wolniewicz9 for the static polarizability, with refractive index measurements (tabulated in Victor and Dalgarno 11) in the wavelength range 1850 A to 6328 A, and with the polarizability anisotropy for the v = 0 vibrational level measured at 6328 A by Bridge and Buckingham.2 Furthermore, the polarizability (v--= 0) at 1215 A is within 3% of the value measured by Gill and Heddle 7 and is within 0.2% of the semiempirical values of Vie-
tor and Dalgarno. 11 The computed v = 0 to v = 1 vibrational Raman matrix elements of the polarizability and polarizability anisotropy at 4047 A agree to within experimental error with the measurements of Golden and Crawford.s
Acknowledgments We gratefully acknowledge the assistance of Professor A. Dalgarno and his encouragement that these tables be prepared.
References
1. M. J. S. Belton, M. B. McElroy, and M. J. Price, Astrophys. J. 164, 191 (1971)
7. P. Gill and D. W. O. Heddle, J. Opt. Soc. Am. 53, 847 (1963)
2. N. F. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966)
8. D. M. Golden and B. Crawford, Jr., J. Chem. Phys. 36, 1654 (1962)
3. A. Dalgarno and S. T. Epstein, J. Chem. Phys. 50, 2837 (1969)
9.
4. A. Dalgarno, A. L. Ford, and J. C. Browne, Phys. Rev. Letters 27, 1033 (1971)
10.
5. A. Dalgarno and D. A. Williams, Month. Notices Roy. Astron. Soc. 124, 313 (1962)
W. Kolos and L. Wolniewicz, J. Chem. Phys. 51, 5002 (1969) G. A. Victor, J. C. Browne, and A. Dalgarno, Proc. Phys. Soc. (London) 92, 42 (1967)
11. G. A. Victor and A. Dalgarno, J. Chem. Phys. 50, 2535 (1969)
6. A. L. Ford and J. C. Browne, Phys. Rev. A, Vol. 7 (1973)
12. L. Wallace, Astrophys. J. 176, 249 (1972)
307
Atomic Data, VoL 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
TABLE I. Rayleigh and R a m a n Cross Sections for Initial Rotational Level o f J = 0 LIGHT SCATTERING CROSS-SECTIONS IN UNITS OF CM**2 INITIAL ROTATIONAL LEVEL IS J=0
WAVELENGTH (ANGSTROMS) 1150.00 1175°00 1200.00 1215°70
1250°00 1300°00 [350°00 l*O0.OC 1450°00 1500°00 1550.00 1600°00 1650.00 1700,00 1750.00 1800.00 1850.00 L900,00 1950°00 2000,00 2050°00 2100.00 2150.00 2200.00 2250°00 2300°00 2350.00 2*00,00 2450.00 2500.00 2550.00 2600°00 2650.00 2700°00 2750.00 2800.00 2850.00 2900.00 2950.00 3000°00 3100,00 3200.00 3300.00 3400.00 3500,00 3600°00 3700°00 3800.00 3900.00 4000.00 4100°00 4200,00 &300.00 *~00.00 4500°00 4b00°00 WT00.00 4800°00 4900.00 5000,00 5500°00 6000.00 7000°00 8000,00 9000,00 INFINITY
PURE RAYLSIGH 4.072E-24 3°023£-24 2.351E-24 2°0~IE-24 1.547E-2, 1°09,E-2, 8°100El25 6°205E-25 4°877E-25 3°912E-25 3.19CE-25 2°638E-25 2,207E-25 I.866E-25 1°592E-25 1,~68E-25 1.184E-25 1,032E-25 9,0.1E-26 7,962E-26 7.046E-~6 6.262E-26 5.588E-26 5,005E-26 ~°499E-26 *.056E-26 3.669E-26 3,327E-26 3.026E-26 2°758E-26 2°521E-26 2°309E-26 2.119E-2b I.949E-26 1.795E-26 1.657E-26 I°532E-26 1.419E-26 1.317E-26 1,223E-26 1,060E-26 9.240E-27 8°092E-27 7.I19E-27 6.290£-27 5.579E-27 4°967E-27 4.~37E-27 3.977E-27 3.575E-27 3,224E-27 2.914E-27 2.042E-27 2.400E-27 2°186E-27 1°996E-27 I°825£-27 1.673E-27 I°536E-27 1,~14El27 9,551E-28 6.689E-28 3°570E-28 2.078E-28 I.291E-28 0.
ROT. RAMAN S-B~NCH 5.956E-25 3°669E-25 2°480E-25 2.002E-25 1°331E-25 8°135E-26 5.392E-26 9.782El26 2°Tb5E-26 2.088E-26 1.618E-26 1.280E-26 1,031E-26 8.429E-27 64978E-27 5°842E-27 4.938E-27 4,211E-27 3.618E-27 3.131E-27 2.726E-27 2,387E-27 2.102E-27 1,859E-27 I°651£-27 I.473E-27 I.319E-27 1°185E-27 1°06~E-27 9.658E-28 8.758E-28 7,963E-28 7o258E-28 6.632E-28 6.073£-28 5.573E-28 5.125E-28 4,122E-28 4°358E-28 4,030E-28 3.462E-28 2.993E-28 2.601E-28 2°273E-28 I°995E-28 1.759E-28 I.557£-28 1.384E-28 1.234E-28 I.I05£-28 9,915E-29 8o926E-29 8.059E-29 7°294E-29 6.619E-29 b.021£-29 5.489£-29 5°014E-29 4.590£-29 4,210E-29 2,80bE-29 1,941E-29
I°014E-29 5.789E-30 3,533E-30 0.
RAYI.EIGH PLUS ROT. RAMAN 4.668E-24 3°390E-24 2.599E-24 2.2,I£-2, ~,680E-24 I°175E-24 8.639E-25 6.583E-25 5.~53E-25 4.120E-25 3°352£-25 2°766E-25 2,311E-25 1.950E-25 1.661E-25 1,*27E-25 1°23~E-25 1.07.E-25 9°403E-26 8°275E-26 7.319E-26 6.501E-26 5°798E-26 5,191E-26 4.664E-26 4°204E-26 3.800E-26 3.446E-26 3°133E-26 2.855E-26 2.608E-26 2,388E-26 2.191E-26 2°015E-26 1.856E-26 1,713E-26 1.584E-26 1,466E-26 1.360E-26 I,263E-26 1°095E-26 9.539E-27 8.352E-27 7.346E-27 6°489E-27 5.755E-27 5.122E-27 4°575E-27 4.100E-27 3.686E-27 3,323E-27 3.004E-27 2.722E-27 2.473E-27 2.252E-27 2.056E-27 I°880£-27 I.723E-27 1.582£-27 1,456E-27 9,832E-28 b.883E-28 3.671£-28 2°135E-28 1,326E-28 0.
VIBRATIONAL RAMAN Q-BRANCH S-BRANCH 5.306E-25 3°I00E-25 3°033E-25 1°519E-25 I°9'IE-25 8.690E°26 I.523E-25 6.440E-26 9°606E-26 3.677E-26 5.525E-26 I.902E-26 3.489E-26 [.II2E-2b 2.351E-26 7°062E-27 I°661E-26 4.762E-27 1°217E-26 3°359E-27 9.177E-27 2°456E-27 7°088E-27 1°848E-27 5.5~2E-27 1,423E-27 4°~70E-27 l,ll8E-Z7 3.631E-27 8°928E-28 2°986E-27 7,234E-28 2,.82E-27 5,936E-28 2.083E-27 *,923E-28 1,762E-27 *°123E-28 1,503E-27 3,483E-28 1.290E-27 2.965E-28 1,115E-27 2,542E-28 9.6~3E-28 2°193E-28 8°456E-28 1,902E-28 7.419E-28 1.659E-28 6°537E-28 I.654E-28 5.784E-28 I.280E-28 5,136E-28 1.131E-28 4.577E-28 1°003E-28 4.092E-28 6.931E-29 3.670E-28 7.977E-29 3,300E-28 7,147E-29 2.976E-28 6°422E-29 2.690E-28 5.785E-29 2°437E-28 5,225E-29 2.21,E-28 4.731E-29 2.014E-28 4.293E-29 1°837E-28 3,903E-29 1.678E-28 3.557E-29 1,536E-28 3,2~7E-29 1,293E-28 2.721E-29 1.096E-28 2.295E-29 9o337E-29 I.947E-29 7.999E-29 1.661E-29 6.885E-29 1.424E-29 5.953E-29 I.227E-29 5.168E-29 I.062E-29 4.504E-29 9.220E-30 3.939E-29 8.038E-30 3°457E-29 7.032E-30 3,043E-29 6°171E-30 2.687E-29 5,432E-30 2.379E-29 ~.795E-30 2.IIIE-29 *.244E-30 I.879E-29 3.765E-30 I.675E-29 3°349E-30 i°498E-29 2.985E-30 1.341E-29 2.666E-30 I°204E-29 2.386E-30 1,082E-29 2,139E-30 6,519E-30 1,272E-30 4.067E-30 7.826E-31 I.713£-30 3°206£-31 7°786E-31 1,413£-31 3.725E-31 6.531E-32 0. 0.
VOTOI
COEFFICIENTS IN 1/WAVELENGTH EXPANSION (WAVELENGTH IN ANGSTROMS. CROSS-SECTION IN CM**2) 0 l
3 5
8.311E-,5 0o 1.2~4E-38 0° 1o512E-32 0.
e
I°724E-26
7 b
0. l°gl8E-20
TRANSITION ENERGY (CM-l)
Atomic Data, VoL 5, No. 3, 1973
0°00
2.563E-,6 -2.119E-45 b.257E-40 -7°232E-39 1o079E-33 -h619E-32
l.558E-*b -1.563El'4 ~°588El*0 -6.48bE-38 9.161E-34 -lo698E-31
I°612E-27
I=551E-27
-2.995E-26 2°228E-21 354°39
308
3°335E-47 -5.359E-45 1°135E-~0 -2,372E-38 2.592E-3~ -b°b76E-32 *o967E-26
-3°585E-25 2.403E-21
-1.519E-25
4162.06
4~98°75
8.bLOE-22
SUM 8.407E-25 4.552E-25 2.810E-25 2.167E-25 1o328E-25 7.427E-26 ~°b02E-26 3°057E-26 2o137E-26 1.553E-26 I°I63E-Z6 8°935E-27 7.005E-27 5.588E-27 *°524E-27 3.709E-27 3.075E-27 2.575E-27 2.175E-27 1°851E-27 1°587E-27 1.369E-27 [.188E-27 1.036E-27 9.078E-28 7.991E-28 7°063E-28 6°267E-28 5.581E-28 *°985E-28 4.467E-28 4°015E-28 3o618E-28 3.269E-28 2°960E-28 2.687E-28 2.~4qE-28 2°227E-28 2.03.E-28 1.861E-28 1.565E-28 1.325E-28 1.128E-28 9°660E-29 8°309E-29 7.180E-29 b . Z2gE-29 5°426E-29 ~.743E-29 ~.160E-29 3.660E-29 3.230E-29 2.858E-29 2°536E-29 2,255E-29 2.010E-29 1.796E-29 1.608E-29 1.442E-29 1.296E-29 7°790E-30 ~°850El30 2°034E-30 9°199El31
*.378E-31 O°
RAYLEIGH AND RAMAN CROSS SECTIONS FOR Hz
T A B L E II. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 1 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) liS0,00 I175°00 I200°0C 1215.70 ~250.0C 1300,00 135U,00 I~00°00 1450°00 1500°00 1550,00 Ib00,00 1650,00 1700,0C 1750.00 l~00°00 185~,00 190U.00 1950°00 2000.00 2050.00 2100.00 2150.00 2200°00 2250.00 2300°00 235U°00 2400°00 2450°00 2500,00 ~550o00 2800,00 2650.00 2700.00 2750.00 2800.00 2850.00 2900°00 2950.00 3000,00 3100,00 3200.00 3300.00 3400,00 3500,00 ~800,00 5700°00 5800,00 3900,00 4000,00 4100°0~ 4200,00 ~300,00 ~00,00 4500,00 4600°00 ~700°00 4800°0~ 4900.00 5000,00 5500°00 6000°00 7000.00 8000,00 9000,00 INFINITY
PURE RAYLEIGH 4,349E-24 3.196E-24 2°~69E-24 2,137E-24 |,o12£-2~ I°133E-2~ 8.365£-25 6e392£-25 5°uI5E-25 4,016E-25 3,272E-25 2,703£-25 2,Z60£-25 I,909E-25 1,627E-25 1,398E-25 Io210E-25 I°053E-25 9,227E-26 8,124E-26 7,187£-26 6,386E-26 5,897E-26 5,102E-26 4.58~E-26 4°133£-26 3°737E-26 3.389E-26 3,o82E-26 2,809E-26 2,567E-26 2,350E-26 2,157£-26 1°983E-26 I,827E-26 I°687E-26 I°559E-26 I°444E-26 1.3~0E-26 I°24~E-26 I°07gE-26 g,39gE-27 8°230E-27 7°240E-27 6°396£-27 5°873E-27 5°050E-27 4°511E-27 4.063E-27 3,635E-27 3,277E-27 2,gb3E-27 2,685£-27 2°440E-27 2,222E-27 2,028E-27 i°855E-27 I°700E-27 1,561E-27 1,436E-27 9°705E-28 6°797E-28 3.627E-28 2°IIIE-28 I.311E-28 0,
CO]~mFICIENTS 0 I 2 3 4 5 b 7 TRANSITION ENERGY (CM-I)
1
ROT. RAMAN S-BRANCH 3,509E-25 2.163E-25 1,464£-25 1.182E-25 7,885E-26 4.8iI£-26 3,191E-26 2,239£-26 1,837£-26 1.237E-26 g,582£-27 7,582£-27 6,t05£-27 4,990E-27 4,130E-27 3.457£-27 2,921£-27 2,491E-27 2,140E-27 1.851E-27 1,611E-27 I,410E-27 1,241E-27 1,097E-27 g,745E-28 8.889E-28 7,777£-28 6,985£-28 6,294E-28 5,689E-28 5,158£-28 4°686£-28 4°270£-28 3,900E-28 3.570E-28 3.275E-28 3.010E-28 2°772£-28 2,558E-28 2°384£-28 2°029E-28 1,752E-28 I,522E-28 I,328£128 1°165E-28 1,028E-28 9°078E-29 8,080£-29 7,182E-29 6,421E-29 5,758£-29 5,179E-29 4,672E-29 4°225E-29 3.830E-29 3,481E-29 3,170E-29 2°893£-29 2.848£-29 2°425£-29 I°608E-29 i,I07E-29 5°728£-30 3,238E-30 I,957E-30 0,
IN I/WAVELENGTH EXPANSION 8.w42E-w5 0, 1,275E-38 0. 1o564E-~2 0, 1,801E-28 0, 2,022E-20 0,0U
IN UNITS OF CM**2
RAYLEIGH PLUS ROT. RAMAN ~,700E-24 3,~12E-2~ 2°616E-24 2,255E-24 I,690E-24 I,181E-24 8,684E-25 b,616E-25 5,178£-25 4,140E-25 3,367E-25 2,779E-25 2,B21£-25 ~,959E-25 1,668E-25 1,433E-25 I°239E-25 1,078E-25 9,441E-26 8,309E-26 7,348E-26 6,527E-26 5,821E-26 5,211E-26 4°682E-26 4,220E-26 3.815E-26 3°459E-26 3,144E-26 2,886E-26 2,818E-26 2.397E-26 2°200E-26 2,022E-26 i°863E-26 I°719El26 1,589E-26 1,472E-26 1,365E-26 1,288E-26 I.099£-26 9,574E-27 8,382E-27 7,373E-27 6°512E-27 5°775£-27 5°141£-27 4,592E-27 4,115£-27 3,699E-27 3°334E-27 3°014E-27 2°732E-27 2°482E-27 2,260E-27 2,063E-27 1.887E-27 I°729E-27 I,588£-27 I°461E-27 9°866E-28 6,g07E-28 3,684E-28 2,143E-28 I,331E-28 0,
VOTO VIBRATIONAL RAMAN Q-BRANCH S-BRANCH 6.536E-25 1,847E-25 3,628E-25 9,046E-28 2,276E-25 5,177E-28 1.769E-25 3.837E-26 1.099E-25 2.192£-26 6°231E-26 I.~34E-26 3,896E-28 b,633£-27 2e606E-26 ~e213£-27 1,831E-26 2,840£-27 i,336E-26 2,00~E-27 1,00~E-2b 1,465E-27 7,732E-27 1,102£-27 b,078E-27 8.485E-28 4,855E-27 0,664E-28 3,937E-27 5,321E-28 3,233£-27 4,311£-28 2,684E-27 3,536E-28 2,249E-27 2,g32E-28 I,902E-27 2,455E-28 1.620E-27 2,073E-28 1,390£-27 1,764£-28 I°200E-27 i,512E-Z8 I,0~2E-27 1,303E-28 9°091£-28 1,130E-28 7,972E-28 9,854E-29 7.021E-28 8,632E-29 b,20gE-28 7,594E-29 5,512E-28 6,709E-29 4,9LOE-28 5,949E-29 4,38gE-28 5,294E-29 3,93WE-28 4°726£-29 3,537E-28 4,232£-29 3°I~8E-2~ 3°801E-29 2.882E-25 3,423E-29 2.610E-28 3°090E-29 2°370E-28 2,796E-29 2,156£-28 2°536E-29 I°966E-28 2°305E-29 I°796~-28 2,099E-29 1,643E-28 1.915£-29 I°383E-28 I,603E-29 I°172E-28 1,351E-29 9°983E-29 I°145E-29 8°550E-29 9,756£-30 7,358E-29 8°356E-30 8°360E-29 7,190E-30 5,521E-29 b°213E-30 4°811E-29 5°390E-30 4,208E-29 ~°894£-30 3°692E-29 ~°I01£-30 3°250E-29 3°594E-30 2°869E-29 3°160E-30 2°5WOE-29 2,786£-30 2°254E-29 2°482E-30 2°006E-29 2o182E-30 I°789E-29 I°938E-30 I°599E-29 I°725E-30 1,432E-29 ~,539E-30 I°285E-29 I°375E-30 I°155E-29 I°231E-30 6°958E-30 7,265E-31 4°3~IE-30 4°437E-31 I°829E-30 I,786E-31 8,318E-31 7,716E-32 3,981E-31 3°485E-32 0° 0,
1 SUM 8.383E-25 4.531E-25 2.794E-25 Z.153E-25 1.319E-25 7,306E-26 4=560E-26 3o027E-20 2.115E-26 I. 536E-26 1°151E-26 8.834E-27 6,924E-27 5,522E-27 4,z~.69E-27 3~66WE-27 3.037E-27 2.543E-27 2. 147E-27 le827E-27 1,566E-27 1,351E-27 1o172E-27 1o022E-27 8,957E-28 7o885E-28 6,96gE-28 b.183E-28 5.505E-28 ~o918E-28 4.407E-28 3°960E-28 3.569E-28 3o224E-28 2,919E-28 2.650E-28 2.410E-28 2,197E-28 2o006E-28 1,835E-28 i. 544E.-28 1.307E-28 I,I13E-28 9.525£-29 8o193E-29 7.079E-29 6.14.3E-29 5.350E-29 ~.677E-29 4° I02E-29 3,609E-29 3o185E-29 2,818E-29 2.501E-29 2.224E-29 1.983E-29 1,771E-2g 1.586E-29 1.422E-29 1.278E-29 7.685E-30 4.785E-30 2.UO8E-30 g.087E-31 4.329E-31 O.
(WAVELENGTH IN ANGSTROMS, CROSS-SECTION IN CM**2)
I,550E-46 -2,15~E-45 3,782E-~0 -7.337E-39 6o523E-34 -I,640E-32 9,745£-28 -3.032E-26 1o348E-21 587,87
309
1,659E-46 -I,722E-44 4,957E-40 -7,217E-38 1,00WE-33 -legi0E-31 1,724E-27 -4,076E-25 2,708E-21
2,033E-47 -3o427E-45 6o915£-41 -loSl8E-3U le582E-34 -~o280E-32 3eO39E-28 -9e753E-26 5o282E-22
4156.15
~713,83
Atomic Data, Vol. 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
T A B L E III. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 2 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) I15~,00 I175,00 120G,O0 1215,70 1250,00 1300.00 1350,00 l~O0,O0 1450,00 1500.00 1550.00 160O.O0 1650,00 1700,00 1750,00 1800.00 ~850.00 1900,00 1950.00 2000.00 2050,00 2100.Oh 2150,00 2200,00 2250,00 2300.00 2350,00 2400.00 245G.00 2500,00 2550,00 260U.00 2650,00 2700,00 2750,00 2800,00 2850.00 2900.00 2950.00 3000,00 3100o00 3200,00 3300.00 3~00,00 3500.00 3600.00 3700.06 3800.00 3900.00 4000,00 4100,00 4200,00 4300.00 4400.00 4500,00 4600.00 4700.0C 4~00,00 49U0.00 5000,00 5500.0C 6000.00 7~00,00 8000,00 9000,00 INFINITY
PURE RAYLEIGH 4.35&E-2~ 3,199E-2~ 2,473E-24 2.140E-~4 1,615E-2~ 1,136E-24 8,385E-25 6,~08E-25 5.027E-25 4,026E-25 3.280E-25 2,710E-25 2,266E-Z5 1.914E-25 l,o31E-25 1,402E-25 I.zI3E-25 1,056E-25 9,251E-26 8.145E-26 7.206E-26 6.402E-26 5,712E-26 5.115E-26 4.596E-26 4.144E-26 3.747E-26 3.398E-26 3,090E-z6 2,816E-26 2,673E-26 2,356E-26 2.~62E-26 1.988E-20 hB32E-26 1,691E-26 hfi63E-26 1,~48E-26 1.343E-26 I.248E-26 1,081E-26 9,423E-27 8,251E-27 7,259E-27 6.412E-27 5.687E-27 5,063E-27 4,523E-27 4,053E-27 3.B44E-27 3.285E-27 2,970E-27 2.692E-27 2.~46E-27 2.228E-27 2.033E-27 1.~60E-27 1,705E-27 1,565E-27 1,440E-27 9.730E-28 6.814E-28 3,636E-2~ 2,116E-28 1.314E-28 0.
COEFFICIENTS
8,463E-45 O, 1,279E-38 O+ 1.569E-32 O, 1.805E-26
3 5 6 7
0,
2,025E-20 TRANSITION ENERGY (C~-I)
Atomic Data, Vol. 5, No.
2
ROTATIONAL RAMAN RAYLEIGH PLUS OzBRANCH S-BRANCH ROT. RAMAN 1.287E-~5 3,312E-25 4,811E-24 7.848E-26 2 , 0 1 2 E - 2 5 3.479E-24 5.278E-26 1.349E-25 2,660E-24 4.251E-26 I.oB5E-25 2.291E-2N 2.817E-~6 7 . 1 6 ~ E - 2 6 1,714E-24 1.717E-26 4,348E-2b 1,196E-24 1.137E-26 2.868E-26 8.785E-25 7,967E-27 2,G04E-26 6.688E-25 5,825E-27 1.461El26 5,231E-25 4.400E-27 1.100E-26 4,180E-25 3.411E-27 b.504E-27 3,399E-25 2,701E-~7 6,715E-27 2,804E-25 2,177E-27 5.396E-27 2.341E-25 1,781E-27 4,404E-27 hg76E-25 1.476E-27 3.6~0E-27 h683E-25 1 . 2 3 6 E - 2 7 3.043E-27 1.444E-25 1,0~6E-27 2.568E-27 1,249~-25 8.931E-28 2.187E-27 hOe7E-25 7.683E-28 1 . 8 7 7 E - 2 7 9.516E-26 6,656E-28 1,622E-27 8,374E-26 5.802E-28 1.411E-27 7.405E-26 5,087E-28 1.234E-27 6,577E-26 4.~83E-28 1.085E-27 5.865E-26 3.970E-28 9.583E-28 5,250E-2o 3,531E-28 8.503E-28 4,717E-2b 3,154E-28 7.576E-28 4,251E-2o 2°827E-28 6,776E-28 3,843E-26 2.543E-28 6,082E-28 3.~84E-26 2.296E-28 5 . 4 7 6 E - 2 8 3.167E-26 2.078E-28 4 , 9 ~ 6 E - 2 8 2.886E-26 1.887E-28 4.480E-28 2,637E-26 h718E-28 4,069E-28 2.~14E-26 1,568E-28 3.705E-28 2.215E-26 1.43~E-28 3.382E-28 2,037E-26 1.315E-28 3.094E-28 hB76E-26 1,209E~28 Z.836E-28 1.731E-26 hl13E-28 2,606E-28 1,601E-26 hOZ7E-28 2.398E-28 1,~82~-26 9,489El29 2,211E-28 1.375E-26 8,786E-29 2.043E-28 h277E-26 7,568E-29 1,751E-28 1,106E-26 6,560E-29 1,511E-28 9,640E-27 5.717E-29 1.311E-28 8,440E-27 5.008E-29 1,143E-28 7.~23E-27 4°408E-29 1.ooIE-28 6,557E-27 3,897E-29 8,811E-29 5.814E-27 3 , 4 6 0 E - 2 9 7 , 7 8 5 E - 2 9 5,175E-27 3,083E-29 6.905E-29 4.623E-27 2,757E-29 6,146E-29 4.142E-27 2,474E-29 5.489E-29 3.724E-27 2.227E-29 4 , 9 1 8 E - 2 9 3,357E-27 2,010E-29 4,419E-29 3.034E-27 h820E-29 3,982E-29 2.750E-27 1.652E-29 3.597E-29 2.499E-27 hSO3E-29 3.258E-29 2.275E-27 1.371E-29 2.957E-29 2.077E-27 1,253E-29 2,691E-29 1.899E-27 1.148E-29 2.454E-29 1,741E-27 1.054E-29 2,242E-29 h59~E.27 9~695E-30 2 . 0 5 2 E - 2 9 1.470E-27 6~551E-30 1,354E-29 9,931E-28 4.596E-30 9.276E-30 6.953E-28 2.469E-30 4,751E-30 3.709E-28 1,450E-30 2.659E-30 2,157E-28 9,101E-31 1.590E-30 1,339E-28 8.052E-37 0. 8.052E-37
IN 1/WAVELENGTH EXPANSION
1
0,00
3, 1973
IN UNITS OF CM**2
5,105E-47 ~.206E-46 1,242E-40 1,431E-39 2,136E-34 3,191E-33 3,180E-28 5.884E-27 4.3SOE-22 -354.39
(WAVELENGTH IN ANGSTROMS,
1,375E-46 -2,690E-45 3,399E-40 -9,274E-39 5,931E-34 -2,097E-32 8,961E-28 -3,917E-26 1,252E-21
VIBRATIONAL RAMAN V 0 TO 1 Q-BRANCH O-BRANCH S-BRANCH 6,419E-25 5.742E-26 1.318E-25 3.566E-25 2.673E-26 5°972E-26 2.242E-25 1 , 4 7 3 E - 2 6 3,216E-26 1,744E-25 1,070E-26 2.307E-26 1,086E-25 5.882E-27 1.238E-26 6,165E-26 2.912E-27 5.943E-27 3,860E-26 1,642E-27 3,267E-27 2,584E-26 1,012E-27 1.970E-27 1.817E-26 6 . 6 5 3 E - 2 8 1.269E-27 ~.326E-26 4.592E-28 8.611E-28 9,974E-27 3.293E-28 6,080E-28 7.685E-27 2,438E-28 4.435E-28 6°040El27 1,849E-28 3,322E-28 4.829E-27 1,433E-28 2,545E-28 3,917E-27 1,131E-28 I,988E-28 3.217E-27 9.072E-29 1.578E-28 2,671E-27 7.374E-29 1.270E-28 2.239E-27 6 . 0 6 5 E - 2 9 1.036E-28 1.893E-27 5,041E-29 8.537E-29 1,613E-27 4.230El29 7.I07E-29 1.384E-27 3.579E-29 5.968E-29 1,195E-27 3 , 0 5 1 E - 2 9 5,052E-29 1.038E-27 2.618E-29 4,307E-29 9.058E-28 2,261E-29 3,695E-29 7.944E-28 1.96~E-29 3.190E-29 6.997E-28 1,715E-29 2.768E-29 6,189E-28 1.504E-29 2.415E-29 5.~94E-28 1.326E-29 2.116El29 4.895E-28 1,173E-29 1,862E-29 ~.375E-28 hO42E-29 1,645E-29 3.922E-28 9,283E-30 1,459E-29 3.527E-28 8.301E-30 1,298E-29 3,179E-28 7 , 4 4 6 E - 3 0 I,159E-29 2.874E-28 6*699E-30 1,037E-29 2.603E-28 6,042E-30 9,315E-30 2.364E-28 5,465E-30 8,386E-30 2.151E-28 4.954E-30 7.569E-30 1.901E-28 4e501E-30 6,647E-30 1.792E-28 4,099E-30 6,208E-30 1,640E-28 3,740E-30 5,6~0E-30 1,380E-28 3,131E-30 4.684E-30 1,169E-28 2,641E-30 3,918E-30 9.962E-29 2.241E-30 3,298E-30 8.533E-29 1,913E-30 2,793E-30 7,344E-29 1,642E-30 2,379E-30 6.349E-29 1,416E-30 2.036E-30 5°512E-29 1.226E-30 1.750E-30 *.804E-29 [.067E-30 1.511E-30 4.201E-29 9.319E-31 1,310E-30 3,687E-29 8,168E-31 1.1~OE-30 3,2~6E-29 7.184E-31 9,950E-31 2,865E-29 6,339E-31 8.71~E-31 2.537E-29 5.610E-31 7.654E-31 2,252~-29 4,978E-31 6,7~1E-31 2,004E-29 4 . 4 2 9 E - 3 1 5,954E-31 1,787E-29 3.951E-31 5,271E-31 1,597E-29 3,532El31 4,677E-31 1,431E-29 3,165E-31 4.159E-31 1.284E-29 2,842E-31 3~706E~31 h155E-29 2~557E-3l ~ 3,309E-3.1 6.958E-30 1 . 5 4 8 E - 3 1 1.926El31 4.343E-30 9,729E-32 1,162Eo31 1.831E-30 4.179E-32 4.569E-32 8.334E-31 1,947E-32 1.928E-32 3.994E-31 9,600E-33 8.484E-33 O. 6,875E-34 O.
CROSS-SECTION
IN CM**2)
1.653E-46 -1=700E-44 4.927E-~0 -7.I12E-38 9.955E134 -I,880E'31 h706E-27 -4+005E-25 2,674E-21
U14.48
4144,36
3]0
3,27[El48 -5.267E-46 1,302E-41 -2~543E-39 3.258E-35 -7~578E-33 6,619E-29 -I,796E-26 1o194E-22 3807=67
5.604E-48 -1,317E-45 2*496E-41 -6.843E-39 6,761E-35 -2.157E-32 l,461E-28 -5.349E-26 2.775E-22 4917,94
SUH 8.311E-25 4o430E-25 2o7HE-25 2oOU2E-25 [o268E-25 7.050E-26 ~o351E-26 2o882E-26 2oGIOE-26 1.458£-26 Io091E-26 8o372E-27 6.557E-27 5,227E-27 4.229E-27 3,465E-27 2.872E-27 2.403E-27 2.02~E-27 1.727E-27 1.48CE-27 1o276E-27 1.107E-27 9o653E-28 8.45~E-28 7°446E-28 6.581E-28 5,838E-28 5.198E-28 4.644E-28 4,161E-28 3,740E-28 3,370E-28 3°044E-28 2,757E-28 2°502E-28 2o276E-28 2.075E-28 1.895E-28 1.?33E-28 1.458E-28 1.235F-28 1,052E-28 9,UO3E-29 7o746E-29 6.694E-29 5.810E-29 5.061E-29 4.425E-29 3,882E-29 3.417E-29 3.016E-29 2o670E-29 2.~69E-29 2.108E-29 1.879E-29 1o680E-29 1o504E-29 1.350E-29 1,213E-29 7°JOSE-30 4.556El30 1°919E-30 8,722E-31 4,L75E-31 6.875E-34
RAYLEIGH AND RAMAN CROSS SECTIONS FOR H~
TABLE IV. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 3 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) 1150.00 1175.0C 1200.00 1215.70 1~50.00 1300.00 1350.00 1600.00 1450,00 1500,00 1550,00 1600.00 1650,00 1700.00 1750,00 1800.00 1850=00 1900,00 1950,00 2000,00 2050.00 2100,00 2150,00 2200.00 2250.00 2300,00 2350.00 2400,00 2450.00 2500.00 2550.00 2600,00 2050,00 2700,00 2750,00 2800.00 2850e00 2900,00 2950,00 3000,00 3100,00 3200.00 3300,00 3600.00 3500.00 3600.00 3700,00 3800°00 3900,00 4000.00 4100°00 4200.00 4300.00 6400.00 4500.00 4600,00 4700.00 4800.00 4900,00 5000°00 5500.00 6000,00 7000,00 8000,00 9000.00 INFINITY
PURE RAYLEIGH 4°471E-2~ 3.274E-24 2.525E-24 2.183E-24 1.644E-24 1.155E-zQ 8,514E-25 6,501E-25 5.097E-25 4.080E-25 3.322E-25 2.744E-2fi 2°Z93E-2fi 1.937E-25 1.651E-25 1.418E-25 1.227E-25 1.068E-25 9.354E-26 8.235E-20 7,284E-26 6.472E-26 5.773E-26 5.170E-26 4.045E-26 4,187E-26 3.786E-26 3,433E-26 3.122E-26 2,845E-20 2.600E-26 2.381E-26 2.185E-26 2.009E-20 1.851E-26 1.708E-20 1.579E-26 1.462E-26 1,356E-26 1.260E-2h 1.092E-26 9,516E-27 8.333E-27 7.330E-27 6,475E-27 5,743E-27 5,112E-27 4.567E-27 4,093E-27 3.079E-27 3.317E-27 2.999E-27 2.718E-27 2*470E-27 2.249E-27 2.053E-27 1°~78E-27 1,721E-27 1.580E-27 1.4fi4E-27 9.823E-28 6.878E-28 3.671E-28 2.136E-28 1.327E-28 O.
COEFFICI~WTS
IN 1/WAVELENGTH EXPANSION
0 1 2 3 4 5 6 7 8 TRANSITION ENERGY (CM-I)
8.542E-45 O= 1,295E-38 O* 1,594E-32 O. 1.840E-26 O, 2,071E-20 0.00
ROTATIONAL RAMAN O-BRANCH S-BRANCH 1.745£-25 3o100E-25 1.055E-25 1.870E-25 7.062E-26 1.255E-2fl 5.676E-26 1.009E-25 3.750E-26 6.6fi6E-26 2,280E-26 4.038E-26 1,507E-26 2.662E-26 1.056E-26 1.860E-26 7,715E-27 1.355E-26 5=826E-27 1,020E-26 4.516E-27 7.886E-27 3.576E-27 6.225E-27 2.882E-27 5.002E-27 2.358E-27 4.080E-27 1.954E-27 3.371E-27 1,038E-27 2.817E-27 1.386E-27 2°377E-27 1.184E-27 2.023E-27 1,019E-27 1,736E-27 8.826E-28 1.499E-27 7.696E-28 1,304E-27 6,750E-28 1,140E-27 5.9filE-28 1.002Eo27 5,272E-28 8.846E-28 4.690E-28 7,846E-28 4.191E-28 0,988E-28 3.758E-28 6.247E-28 3.382E-28 5*605E-28 3,054E-28 5.045E-28 2.766E-28 4,554E-28 2.512E-28 4.124E-28 2.288E-28 3*744E-28 2,089E-28 3,408E-28 1.912E-28 ~.109E-28 h754E-28 2.843E-28 1.612E-28 2.605E-28 1.485E-28 2,392E-28 1.371E-28 2.201E-28 1,267E-28 2.028E-28 1.174E-28 1,873E-28 1.012E-28 1°605E-28 8.779E-29 1.383E-28 7°658E-29 1.199E-28 bo714E-29 1.044E-28 5.915E-29 9,141E-29 5,23~E-29 8.036E-29 4.650E-29 7,094E-29 4.147E-29 6,286E-29 3,712E-29 5,590E-29 3.333E-29 4.988E-29 3.003E-29 4.465E-29 2.713E-29 4,008E-29 2,459E-29 3,608E-29 2.233E-29 3,257E-29 2.034E-29 2=947E-29 1.857E-29 2.673E-29 1,699E-29 2,429E-29 1,558E-29 2.213E-29 1,431E-29 2.020E-29 1.318E-29 1.847E-29 8,9~2E-30 1.213E-29 6.300E-30 8,271E-30 3.41~E-30 4.194E-30 2.022E-30 2,324E-30 1.280E-30 1.375E-30 7.866E-30 O.
b*622E-47 9*175E-40 1,611E-40 3.114E-39 2.770E-34 6.937E-33 4.123E-28 1.277E-26 5.080E-22 -587.07
IN UNITS OF CM**2
3 RAYLEIGH PLUS ROT. ~ 4.956E-24 3,568E-24 2,721E-24 2.341E-24 1.748E-24 1,218E-24 8,931E-25 6,793E-25 5.310E-25 4=241E-25 3.446E-25 2e842E-25 2.372E-25 2.001E-25 1,704E-25 1.463E-25 1.264E-25 1.100E-25 9.630E-26 8,473E-26 7,492El26 6,653E-20 5,933E-26 5,311E-26 4.770E-26 4.299E-26 3.886E-26 3.fi23~-26 3.203E-26 2,919E-26 2,666E-26 2,~41E-26 2,239E-26 2,059E-26 1,897E-26 1,750E-26 1,618E-26 1,498E-26 1.389E-26 1.291E-26 1.118E-26 9.742E-27 8.529E-27 7.501E-27 6.626E-27 5.875E-27 5.230E-27 4.671E-27 4.186E-27 3,762E-27 3.392E-27 3.066E-27 2.779E-27 2.524E-27 2.299E-27 2.098E-27 1,919E-27 1,759E-27 1,615E-27 1,486E-27 1,003E-27 7.024E-28 3.747E-28 2.179E-28 1.353E-28 7.866E-36
(WAVELENGTH IN ANGSTROMS,
1.297E-46 -3.235E-45 3,211E-40 -1.116E-38 5.610E-34 -2.525E-32 8,488E-2~ -4.723E-26 1.188E-21 1034,74
3 1]
Q-BRANCH 6.753E-25 3.710E-25 2.319E-25 1.800E-25 1,116E-25 b,312E-20 3.943E-26 2,635E-26 1.850E-26 1=349E-26 1,014E-26 7o808E-27 6o134E-27 ~.902E-27 3.974E-27 3.263E-27 2o708E-27 2.270E-27 1,919E-27 1.635E-27 1,403E-27 1.211E-27 1.051E-27 9.175E-28 8,0~6E-28 7,087E-28 6.267E-28 5.564E-28 4.956E-28 4.430E-28 3.971E-28 3.571E-28 3.219E-28 2.909E-28 2.636E-28 2.393E-28 2.177E-28 1.985E-28 1.814E-28 1.660E-28 1.397E-28 1.184E-28 1.009E-28 8.639E-29 7.436E-29 b°429E-29 5,581E-29 4.864E-29 4°255E-29 3.734E-29 3,287E-29 2.~02E-29 2.570E-29 2.281E-29 2,030E-29 1.811E-29 1.619E-29 1.450E-29 1.301E-29 1o170E-29 7°056E-30 4,406E-30 1,861E-30 8.479E-31 4.070E-31 O.
VIBRATIONAL RAMAN V 0 TO 1 O-BRANCH S-BRANCH S~H 8.u18E-25 8.050E-26 1o260E-25 4.631E-25 3.080E-26 5.527E-26 2.~I2E-25 2,014E-26 2,912E-26 2.152E-25 1.458E-26 2.066E-26 1o304E-25 7,975E-27 1o086E-26 7.215E-26 3.931E-27 5.098E-27 4.439E-26 2,211E-27 2.750E-27 2°934E-26 1,361E-27 1°632E-27 2.043E-26 8,934E-28 1.037E-27 1.~81E-26 6*162E-28 6°950E-28 1°107E-26 4,417E-28 4.855E-28 8o485E-27 3.266E-28 3.507E-28 6.642E-27 2°478E-28 2.604E-28 1.921E-28 1.979E-28 5°292E-27 4=279E-27 1,516E-28 1.534E-28 3.505E-27 1,216E-28 1.209E-28 2.g04E-27 9.884E-29 9.677E-29 8.131E-29 7.8~4E-29 2o430E-27 6,759E-29 6.~32E-29 2°051E-27 5.672E-29 5.327E-29 1o745E-27 4,800E-29 4,453E-29 1o495E-27 4.093E-29 3.753E-29 1o289E-27 3.514E-29 3°187E-29 1.118E-27 3,036E-29 2,724E-29 9.751E-28 Z,638E-29 2.343E-29 8.544E-28 2.304E-29 2,026E-29 7o520E-28 2,022E-29 1.762E-29 6.646E-28 1,782E-29 1.539E-29 5.896E-28 1,577E-29 1.351E-29 5°249E-28 1*401E-29 1.190E-29 4.689E-28 1,250E-29 1.~52E-29 4o202E-28 1,118E-29 9.341E-30 3.776E-28 1,003E-29 8.319E-30 3°402E-28 9,028E-30 7.431E-30 3.G74E-28 8.147E-30 6,658E-30 2°784E-28 7,371E-30 5.981E-30 2,527E-28 b,686E-30 5,388E-30 2,298E-28 6.078E-30 4,864E-30 2°095E-28 5.537E-30 4.402E-30 1°913E-28 1.750E-28 5,055E-30 3,992E-30 1.473E-28 4.237E-30 3,304E-30 1.247E-28 3,576E-30 2°755E-30 1.062E-28 3.038E-30 2°312E-30 2.596E-30 1.953E-30 9°094E-29 7=U24E-29 Z.230E-30 1.658E-30 1,926E-30 1.415E-30 6°763E-29 1,670E-30 1,214E-30 5°870E-29 1,455E-30 1,046E-30 5°114E-29 1.272E-30 9.043E-31 4°472E-29 1,116E-30 7,850E-31 3°924E-29 9.831E-31 6,838E-31 3.~54E-29 8.685E-31 5,976E-31 3.049E-29 7.695E-31 5.239E-31 2.699E-29 6*838E-31 4.605E-31 2°396E-29 6,092E-31 4°059E-31 2.132E-29 5.441h-31 3~586E-31 1.901E-29 4,871E-31 3°176E-31 I°b99E-29 4,370E-31 2°819E-31 1=522E-29 3.930E-31 2.507E-31 I.366E-29 3,540E-31 " 2°234E-31 1°228E-29 2,159E-31 1°289E-31 7o400E-30 1.367E-31 7.70~E.32 4.620E-30 5.967E-32 2°973E-32 1.950E-30 2.831E-32 1.228E-32 8.885E-31 1.424E-32 5.276E-33 4.265E-31 6.913E-34 0. 6.g13E-34
CROSS-SECTION IN CM**2)
1.667E-40 -1°714E-44 4,986E-40 -7*192E-38 1,011E-33 -1,906E-31 1.737E-27 -4.072E-25 2.730E-21
4.261E-48 -6,444E-46 1,099E-41 -3°111E-39 4,253E-35 -9o269E-33 8=634E-29 -2,195E-26 1.550E-22
3,947E-48 -1.057E-45 1.915E-41 -5,781E-39 5.475E-35 -1°887E-32 1,228E-28 -4.805E-26 2.~01E-22
4126,76
3569°08
5109.35
Atomic Data, VoL 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
T A B L E V. Cross S e c t i o n s for a T h e r m a l Distribution o f Initial R o t a t i o n a l Levels with T = 100 ° K LIGHT SCATTERING CROSS SECTIONS IN UNITS OF CM**2 THERMAL AVERAGE (WITH 3 TO i ORTHO TO PARA RATIO) WAVELENGTH (ANGSTROMS) ltSO.O0 1175,0C I~00.00 1~15.70 1250,00 1300.00 1350.00 1400.00 I~50,00 1500.00 1550,00 1600,00 1650.00 1700.00 1750,0Q 1800,00 1850.00 1900,00 195G.00 2000,00 2050.00 Zt00,O0 2150.00 2200°00 2250,00 2300°00 2350,00 2~00,00 2~50.00 2500,00 2550,00 2600,0C 2650,00 2700,00 2750,00 2800,00 2850.00 2900.00 2950,0~ 3000,00 3100,00 3200.00 3300,00 3~00.00 3500,00 3600.00 3700,00 3800,00 3900,00 4000.00 ~IO0,O0 4200.00 ~300.00 ~00.00 ~500,00 ~600,00 4700,0~ ~800.00 4900,00 5000,00 5500,00 bO00.O0 7000,00 8000.00 9000,00 INFINITY
AtO~
PURE RAYLEIGH 4.245E-z~ 3.131E-2~ 2,~25E-2~ 2,101E-24 I.588E-2~ I,I18E-24 8.266E-25 6,322E-25 4.963E-25 3,977E-25 3,241E-25 2*079£-25 2,240E-25 1,893E-25 1,614E°25 I*387E-25 1,200£-25 I*045E°25 9.157E-26 8,064E-26 7,134E-26 6.340E-26 5,656E-26 5.066E-26 4,552£-26 4.104E-26 3.712E-26 3,366E°26 3,061E-26 2.790E-~6 2*549E-26 2.335E-26 2.143E-2~ 1,970E-26 I*815E-26 1,676E-26 1,5~9E*Zb 1,435E-26 1.331E-2~ 1,237E-2~ 1,072E-26 g*339E-27 8,179E-27 7.~95E-27 6,356E-27 5.638£-27 5,019E-27 4,484E-27 ~*0~8E-27 3.012E-27 3.257E-27 2,945E-27 2,66gE-27 2,425E-27 2.20gE-27 2*0~6E-27 I,844E-27 ~,690E-27 ~.552E-27 I*428E-27 9,648£-28 6.757E-28 3.606E-28 2.098E-28 1.303E-28 O,
DO~O, ~Olm 5, NOI 3, 1973
ROTATIONAL O-BRANCH 1.525E-27 9.302E-28 6.255E-28 5,037E-28 3,338£-28 2.034E-28 I,340E-28 9,438E-29 6,901E-29 5,213E-29 ~*041E-29 3,200E-29 2*579E-29 2,109E-29 1,748E-29 1.465E-29 1.240E-29 I*058E-29 g,lO2E-30 7,885E-30 6*874E-30 6,027E-30 5,311£-30 %*704E-30 4,184E-30 3,736E-30 3,350E-30 3.013E-30 2,720E-30 2*4~2E-30 2,23~E-30 2,035E-30 I*858E-30 1,700E-30 ~,55~E-30 1,432E-30 1.319E-30 1.217E-30 1.12~E-30 1,041E-30 8,969E-31 7,774E-31 6,775E-31 5*936E-3~ 5,225E-3[ 4,6|9E-3! 4,I0~E-31 3,054E-31 3,268E-31 2,933E-31 2.640E-31 2.383E-31 2.157E-31 ~.958E-3~ ~.782E-31 L,625E-31 I,486E-31 1,361E-31 1,250E-~I 1,149E-31 7*768E-32 5,45~E-32 2.929E-32 1,721E-32 1.080E-32 1,163E-38
FOR T = I00.0
RAMAN RAYLEIGH PLUS S-BRANCH ROT. RAMAN 4.424E-25 4.089E-24 2,726E-25 3.405E-24 1.843E-25 2,610E-24 1.488E-25 2,250E-24 9*899£-26 I,687E-24 6.051E-26 1,179E-24 4,012E-26 8,569E-25 2.814E-26 6,b05£o25 2.058E-26 5,170E-25 1,554E-26 4,133E-25 I*204E-26 3,362E-25 9*530E-27 2,77~E-25 7.674E-27 2.317E-25 b , 2 7 2 E ° 2 7 I*956Eo25 5,I92E-27 1.666~-25 4*346E-27 I*430E-25 3.673£-27 I.237E-25 3.132E-27 1,077E-25 2.691E-27 9.427£-26 2.328E-27 8,297E-20 2*027E-27 7*338E-20 1,774E-27 6.518E-26 1,562E-27 5,813E-26 1,381E-27 5,20~E-26 |,227E-27 4,075E-26 1.094E-27 4.214L-26 g*Tg3E-28 3,810E-26 8,798E-28 3.454£-26 7.929E-28 3.140E-26 7,168E-28 2,862E-26 6*498E-28 2*615E-26 5,907E-28 2.394E-26 5.383E-28 2*IgTE-26 4,918E-28 2,020E-26 ~.502E-28 I,861E-26 ~*131E-28 1,717E-26 3.798E-28 1.587E-26 3,~98E-28 1.470E-26 3.228E-28 1.363E-26 2*g85E-28 1,266E-26 2*5~3E-28 1,097E-26 2.215E-28 9,562E-27 1 , 9 2 4 E - 8 8 8,372E-27 ~*680E-28 7.363E-27 1,474E-28 6,504E-27 1.299E-28 5,768E-27 I*150E-28 5,~34E-27 1.021E-28 6,586E-27 g,lO5E-29 4,1~0E-27 8.143E-29 3.694E-27 7,306E-29 3.330E-27 6.575E-29 3*01~E-27 5,933E-29 2,729E-27 5.368E-29 2,479E-27 ~.86gE-29 2.258E-27 4.~27E-29 2.060E-27 ~,034E-Zg 1,885E-27 3.683E-29 ~*727E-27 3.370E-29 [,586E-27 3*090E-29 1,459E-27 2.054E-29 9*854E-28 1*4~8E-29 6,899E-28 7.370E-30 3,680~-28 ~,188E-30 2,1~0E-28 2.543E-30 1.329E-28 O* 1,163E-38
312
(DEGREES EBLVIN)
Q-BRANCH 6.074£-25 3.~03E-25 2.150E-25 1,677E-25 I*047E-25 5,966£-26 3,743E-26 2*510E-26 1.767E-26 1,291E-26 9,716E-27 7.490E-27 5.890E-27 4.711E-27 3.822E-27 3.140E-27 2.608£-27 2,~87E-27 1.849£-27 I.576E-27 I.352£-27 1.168£-27 I*01~E°27 8,852E-28 7,764£-28 6,840E-28 6,050E-28 5,371E-28 4.785E'28 4,277E-28 3,835E-28 3,448E-28 3,~0gE-28 2,8~0E-28 2*545E-28 2,311E-28 2.[03E'28 1.?18E-28 1.752E-28 I,603E-28 I*350E-28 1.143E-28 9,741E-29 8*3~3E-29 7.180E-29 6.207E-29 5,389E-29 4,696E-29 4,~07E'29 3,604E-29 3,~72E-29 2*801E-29 2*~79E-2g 2.201E-29 1.958E-29 1,746E-29 1,561E-29 1,398E-29 1.254E-29 ~*~28E-29 6,794E-30 4.238£-30 ~.786E-30 8.117E-31 3.885E-31 O*
VIBRATIONAL RAMAN V 0 TO 1 O-BRANCH S-BRANCH 8.816£-28 2,310£-25 3,171E-28 1,131E-25 I.747£-28 6.471E-26 I.268E-28 4.795E-20 5,974£-29 2,737E-20 3.452£-29 1,416E-26 1,947E-29 8,276E-27 1,200E-29 5.255E-27 7,886£-30 3.542£-27 5.442£-30 2.499E-27 3,903E-30 1,826£-27 2.887E-30 1,374E-27 2.1glh-30 1.058E-27 1.699E-30 8.307E-28 1,341£-30 6.634E-28 1,075£-30 5,374£-28 8,739£-31 ~,~09E-28 7,188E-31 3.656E-28 5,975E-31 3.061£-28 5,013E-3[ 2.586E-28 4.241E-31 2.201E-28 3,616£-31 1.886~-28 3,103E-31 I.627£-28 2,680£-31 1.WII£-28 2,328E-31 I°230E-28 2,032E-31 I°078E-28 I,783£-31 g,483E-29 1,571E-31 8,379£-29 1.390£-31 7.432E-29 ~,235E-31 6.614E-29 1,100E-31 5.g06£-29 9,840E-32 5o290E-2g 8,826£-32 4,752E-2g 7.940£-32 ~,280£-2g 7,163E-32 3.865E-29 6,478£-32 3.498E-2g 5,872£-32 3.]74E-29 5.336E-32 2.885E-29 4,859E-32 2*628E-29 4,433E-32 2.399£-29 3,712Eo32 2.009E-2g 3,130£-32 1,693E-29 2*657£-32 1,436£-29 2.268E-32 1,224E-29 l,g46E-32 I*~9E*29 1.679E-32 9,034E-30 I,45~E-32 7,811E-30 1,265E-32 6.780E-30 I*I05E-32 5,908E-30 ~,687E-33 5,165E-30 8,520E-33 4,530E-30 7,518E-33 3,g85E-30 6.653E-33 3,515E-30 5,905E-33 3,109E-30 5,254E-33 2.757E-30 4,687E-33 2.450E-30 ~*!90£-33 2,182E-30 3,755£-33 1,948E-30 3,372£-33 1.742E-30 3.034E-33 1,561E*30 1,837E-33 9.245E-31 ~*155E-33 5.869E-31 4.g64E-34 2.303E-31 2.3~5E-34 1.005E°31 1,142E-34 4.596E-32 8,077E-36 0,
SUM 8.3glE*25 4.538E-25 2.799E-25 2.157E-25 1.322£-25 7.385E-26 4.57~E-20 3.U37E-26 2.122E-26 1.541E-26 I.L55E-20 8.867£-27 6.950E-27 5.543E-27 4.487E-27 3.678£-27 3.050E-27 2o553E-27 2.156E-27 I.835E-27 1.573£-27 I°357E-27 I.177E-27 I°027E-27 8.997E-28 7.91g£-28 7.00GE-28 6.211E-28 5.530E-28 4.g4OE-28 ~.~27£-28 3.g78E-28 3.585E-28 3.238E-28 2.933£-28 2.062E-28 2.421E-28 2.207E-28 2.015E-28 1.843E-28 1.551E-28 1.313E-28 |°I18E-28 9.509E*2g 8.232E-29 7.Z12E-29 6.171E-29 5.375E-29 4.69gE-29 4.121E-Zg 3.626E-29 3.200E-29 2=832E-29 2.512E-29 2.234E-29 I.992E-29 I.77gE-29 1.593£-29 1.42gE-29 1.284E-29 7.720E-30 4.807E-30 2.016E-30 9°125E-31 4°346E°31 8,077E-36
R A Y L E I G H A N D RAMAN CROSS SECTIONS FOR H 2
T A B L E VI. Cross S e c t i o n s for a Thermal Distribution of Initial Rotational Levels with T = 300 ° K LIGHT SCATTERING CROSSSECTIONS THERMAL AVERAGE (WITH 3 TO 1 ORTHO TO PARA RATIO) FOR T = WAVELENGTH (ANGSTROMS) I150,00 I175.00 li00.00 IZ15o70 125U.00 1300.00 [350,00 1400,00 1450.00 1500,00 1550,0U 1600,00 1650,00 1700.00 1750o00 1800,00 185U,00 1900,00 1950°00 2000.00
2050.00 2100.00 2150,00 2200,00 2250,00 2300.00 2350,00 2400,00 2450,00 2500,00 2550,00 2600,00 2650.00 2700.00 ~750,00 2800.00 2850,00 2900,00 2950.00 300~°00 31UUo0G 3Z00°0C 3300,00 3400o00 350b,00 3600o00 3700,00 3800,0G 3900,0U ~00G.00 ~100o0C 4200,00 ~300.00 ~400,00 ~500,00 4600°00 4700.00 4800.00 4900,00 5000,00 5500,00 b000°00 7000.00 8000.00 9000.00 INFIhITY
PURE RAYLEIGH 4.325£-2~ 3.181E-2~ 2,460E-2~ 2,129E-24 1.607E-24 1.130£-2~ 8.3W7E-25 6.380£-25 5.006E-25 4.010£-25 3.867E-25 2,b99E-25 2,257£-25 1.906E-25 Iob25E-25 1.396E-25 1.208E-25 1.052E-25 9,217E-26 8,116£-2b 7,180E-26 6.380E-26 5,692£-26 5,097E-26 4.580E-26 4°129E-26 3,734E-26 3,386E-26 3,079£-26 2,807E-26 2.564£-26 2,348E-26 2,155E-26 h982E-26 h826E-26 I,685E-26 1,558E-26 1,443E-26 1,339£-26 1.244E-ae 1,078E-26 9,392E-27 S.224£-27 7°Z35E-27 6.391E-27 5°669E-27 5.046E-27 4,508£-27 4.040£-27 3.b32E-27 3.175£°27 2.961£-27 2.083E-27 2.438E-27 2°221E-27 2,u27E-27 I°854£-27 I,b99£-27 I,560E-27 I°436E-27 9°099E-28 6,792E-28 3.625E-aU 2,I09E-28 1.310£-28 0°
ROTATIONAL O-BRANCH 3,131£-2b 1.901E-Zb 1,275E-26 [.026£-26 b,Tg0E-27 4.133£-27 2,734E-27 I*916£-27 I*400E-27 1,058£-27 8,|99£-28 6.4926-28 5,232E-28 4,280£-28 3o547E-28 2,973£-28 2,516E-28 2,148E-28 I,848£-28 1,601E-28 1,396£-28 1,224E-28 1.079£-28 9o557£-29 8,502E-29 7,595£-29 6,809E-29 b,127£-29 5°531E-29 5.009E-29 4,548£-29 4,142E-29 3,781E-29 3o460E-29 3.173E-29 2,916E-29 2°68bE-29 2,478E-29 2°291E-29 2o122E-2g 1.828E-29 1°585E-29 I*382E-29 1.212E-29 1°067E-29 9,436E-30 8,38dE-30 7,47XE-30 6*684E-30 6°000E-30 5°403£-30 4°S80E-30 4,420E-30 4,013E-30 3,654E-30 3°334E-30 3,049E-30 2,795E-30 2,567E-30 2,362E-30 1,599E-30 1,125E-30 6.068E°31 3°579E-31 2°257E-31 8,206E-37
RAMAN S-BRANCH 3,765E-25 2,314E-25 1.562E-25 1.261E-25 8*376E-26 5.115E-26 3,389E-26 2,376E-26 1.736E-26 h311E-26 1,015E-26 8,031E-27 6,464E-27 5.282E-27 4o371E-27 3,658E-27 3o091E-27 2,634£-27 2°263E-27 1,957£-27 1.703E-27 1,491£-27 1,312E-27 Io160£-27 1,030E-27 go183E-28 8,218E-28 7,3S0£-28 6°650E-28 6,¢IOE-28 5,447E-28 4.950£-28 4,510E-28 4,119£-28 3,770E-28 3,459E-28 3.179E-28 2,928E-28 2.701£-28 2*496E-28 2,143£-28 I,850E-28 I*607E-28 I°403E-28 1.230E-28 I°084E-28 9°583£-29 8.508E-29 7*581E-29 6,777E-29 6,078E-29 5,466E-29 4,930E-29 4°459E-29 4°042£-29 3°673E-29 3.345E-29 3°053E-29 2,792E-29 2,559E-29 1,697E-29 h168E-29 6°042E-30 3,416E-30 2°064E-30 0°
IN UNITS OF CM**2
300.0
RAYLEIGH PLUS ROT. RAMAN 4,733E-24 3,432£-24 2,b29£-2% 2,265E-24 1,697£-24 1,186£-24 8,713E-25 6,637E-25 5,19WE-25 4.152E-25 3,376E-25 2,786£-25 2,327£-25 1,964E-25 1,672E-25 I,436E-25 1,2425-25 1.081E-25 9,462£-2b 8,327E-2b 7,364E-26 6,541£-2o 5,834£-26 5,223E-2b 4,692E-26 4,22g£-26 3,8235-26 3,466£-26 3°151E-26 2,872E-26 2o623E-26 2°402£-26 2,204E-26 2,026£-26 h867£-26 I°723£-26 Io593E-26 1°475E-26 1°368El26 I,271E-26 1,101E-2b 9,593E-27 8,399£-27 7°387E-27 6°525£-27 5°786£-27 5.151£-27 4,601E-27 4*123E-27 3°706E-27 3°341£-27 3°020£-27 2°737E-27 2°487E-27 2°265E-27 2°067E-27 I°890E-27 I°733E-27 I,59~E-27 h464E-27 9°885E-28 6,920E-28 3,691E-28
2,147E-28 I,333E-28 8,206E-37
313
(DEGREES KELVIN)
Q-BRANCH 6o383E-25 3,550£-25 2.233E-25 Io737E-25 1.081E-25 b.139£-2b 3.844E-26 2*573£-26 1,809E-26 1,320£-26 9.930E-27 7°650E-27 6.013E-27 4.807E-27 3.898E-27 3,202£-27 2,658E-27 2o228E-27 1,884£-27 |.606E-27 1.377E-27 1.189E-27 1,033£-27 9.013E-28 7.904£-28 6.962£-28 6.157E-28 5,46b£-28 4,870E-28 4o352£-28 3,902£-28 3,508E-28 3,163E-28 2o858£-28 2.589£-28 2.35[£-28 2o139E-28 h951£-28 1,782E-28 Io631E-28 I,373E-28 1.163E-28 9*906E-29 8°484E-29 7o302E-29 6°313E-29 5°480E-29 4,775E-29 4*176£-29 3,665E-29 3,226Eo29 2.848E-29 2,521E-29 2°238£-29 I°991E-29 Io776E-29 1.587E-29 Io~22E-29 1°276E-29 [°147E-29 6,910E-30 4*312E-30 I°817E-30 8o264£-31 3,957£-31 0°
VIBRATIONAL RAMAN V 0 TO i O-BRANCH S-BRANCH 1,421£-26 1.892E-25 6.561£-27 9.153£-26 3,599£-27 5,191E-26 2.609E-27 3.830E-26 1,431E-27 2.169E-26 7.069£-28 1.I12£-2b 3.982E-28 6.458E-27 2*452£-28 4,078£-27 1.611E-28 2.737E-27 I,IIIE-28 |.924E-27 7,g68E-29 |,601E-27 5.894E-29 [.051£-27 4,472E-29 S.076E-28 3.467E-29 6.329E-28 2,737E-29 5.045£-28 2,194£-29 ~,080E-28 1.7845-29 3,342E-28 1.467E-29 2.767E-28 1,220£-29 2o31~E-28 1,023E-29 I,952£-28 8.659E-30 I,660E-28 7.383E-30 1.421£-28 6,337£-30 1.225£-28 5,474£-30 1.061E-28 4.755E-30 g.245£-29 4°153E-30 8.094£-29 3,644E-30 7.117E-29 3,211£-30 6.284£-29 2.842£-30 5,570E-29 2,524£-30 4,955E-29 2°250£-30 4°422E-29 2.013£-30 3°958E-29 h806£-30 3,554E-29 1,625£-30 3,199E-29 h466£-30 2°887£-29 1.326E-30 2,612E-29 1,202E-30 2°369E-29 I,093E-30 2,152E-29 9,954E-31 I°960£-29 9,08~E-31 1.788E-29 7o611E-31 1.496E-29 6.421E-31 1.260E-29 5.452£-31 I°068E-29 4,657E-31 9°I00E-30 3,998[-31 7.794E-30 3°450£-31 6°706£-30 2.991£-31 5.794£-30 2.603£-31 5°027E-30 2.275£-31 ~.377E-30 1,996£-31 3°824E-30 I,756E-31 3.352E-30 I,551£-31 2,9~7£-30 1°373£-31 2°598E-30 1,219E-31 2°297E-30 Io086£-31 2,036£-30 9°690£-32 Io808E-30 8°670E-32 1.610E-30 7°774E-32 [,436E-30 6°985E-32 1,284E-30 6,289[-32 I°149E-30 3,822£-32 6o788E-31 2.411E-32 4.150E-31 I,045£-32 I°675E-31 4°914E-33 7.263E-32 2°449£-33 3°295E-32 1,451£-34 0.
SUM 8.417E-25 4.531E-25 2.788£-25 2.|46E-25 1.313£-25 7.322£-26 4.529E-26 3.005£-26 2.099E-26 1.524E-26 1.141E-26 8.760£-27 6.865E-27 5.474E-27 4.430£-27 3.632£-27 3.018E-27 2.520£-27 2.128£-27 1.811£-27 1.552E-27 1.33g£-27 1.161£-27 1.013E-27 8.876E-28 7.813E-28 6.905E-28 6.127£-28 5.455E-28 4.873E-28 4.307E-28 3.924E-28 3.536k-28 3°195E-28 2.893E-28 2.626E-28 2.388£-28 2.177E-28 1.988E-28 I.b18£-28 Io530E-28 I°295E-28 I.I03E-28 9.441E-29 8.121E-29 7.018E-29 6.08gE-29 5.304£-29 4.637E-29 4.067E-29 3.579E-29 3.158£-29 2.795£-29 2°480E-29 2.206E-29 1.966£-29 1.757E-29 1.573£-29 1.411E-29 [.268E-29 7.627E-30 4.751E-30 |o995E-30 9°040E-31 ~.311E-31 1°451E-34
Atomic Data, Vol. 5, No. 3, 1973
RAYLEIGH AND RAMAN CROSS SECTIONS FOR THE H Y D R O G E N MOLECULE
A. LEWIS FORD Harvard College Observatory, Cambridge, Mass. 02138 and J. C. BROWNE Departments of Computer Sciences and Physics The University of Texas, Austin, Tex. 78712
The TABLES list calculated values of Rayleigh and Raman light scattering cross sections for molecular hydrogen for wavelengths exceeding 1200 A.
This research was supported by the Robert A. Welch Foundation of Houston, Tex., by the Office of Naval Research under Contract No. N00014-67-A-0126-0017, and by the National Science Foundation
305
Copyright O 1973 by Academic Press, Inc. All rights of reproduction in any form reserved.
Atomic Data, Vot. 5, No. 3, 1973
A. L. F O R D A N D J. C. B R O W N E
CONTENTS
INTRODUCTION Outline of the Calculation Method TABLES. Rayleigh and Raman Cross Sections for Initial Rotational Level: I.J=0 II. J = 1 III. J = 2 IV. J = 3 TABLES. Cross Sections for a Thermal Distribution of Initial Rotational Levels V. T = 1 0 0 ° K VI. T = 300 ° K
INTRODUCTION
Cross sections are given for the cases in which the molecule is initially in the rotational states J = 0, 1, 2, and 3 and for thermal distributions with T = 100°K and 300°K and a 3 : 1 ortho to para ratio.
The cross sections for Rayleigh and Raman light scattering by molecular hydrogen are of considerable astrophysical interest in the interpretation of the solar opacity and of the spectra of the Jovian planets (Belton et al., 1 WallacO2). Estimates are available from the work of Dalgarno and Williams 5 and of Victor, Browne, and Dalgarno. 1° Recent developments (Dalgarno, Ford, and Browne, 4 Ford and Browne 6) have yielded data from which reliable cross sections can be calculated. We report here an extensive, accurate tabulation of the cross sections for wavelengths exceeding 1200 ~ . The TABLES list Rayleigh and Raman light scattering cross sections for molecular hydrogen for unpolarized incident radiation, integrated over all angles of the scattered photon. The cross sections can be expressed (Dalgarno and Williams 5) in terms of the components of the dynamic polarizability tensor of the molecule, the accurate calculation of which is described in detail elsewhere. 6 In addition to the tabulated cross sections, coefficients q are given for the expansion of each of the cross sections as a series in inverse powers of the wavelength. The cross sections are given for large 2t by 8
Q = (10s/x _ AE)4 ~
(q/Xi)
Outline of the Calculation Method The dynamic polarizability components upon which these TABLES are based were computed by a direct sum-over-states procedure. This procedure consists of an approximate evaluation of the equation for the dynamic polarizability a(~o) = ~ fob b (Eb-E07-~2 where o~ is the circular frequency of the photon, fob is the oscillator strength for the transition between the state [ 0 ~ of energy E 0 and the state I b ~ of energy Eb, and the s u m is over all states of the molecule for which fob does not vanish. The sum over the infinite number of exact eigenstates of the molecular Hamiltonian was approximated by a sum over a finite number of matrix eigenvectors of the molecular Hamiltonian. The basis sets from which these matrix eigenvectors were constructed were such that the oscillator strength sums S(0) and S ( - 1 ) were closely satisfied (Dalgarno and Epstein3). The sum over b formally is a sum over all vibrational and rotational, as well as electronic, states. For the lowest excited states which are involved, B 1Z +u and C lII~, the sum over vibrational levels and integration over the nuclear translational continuum were evaluated explicitly. For the other excited electronic states in the sum, the sum over vibrational and rotational levels was carried out using closure.
cm z,
i=0
where AE is the transition energy in cm -1 and X is the wavelength of the incident light in A. The cross section is zero if ( 1 0 s / x - hE) is negative. The expansions converge to the number of significant figures given in the TABLE for X/> 5000 A and to three significant figures for X/> 3000 A.
Atomic Data, Vol. 5, No.
3, 1973
306
R A Y L E I G H A N D RAMAN CROSS SECTIONS F O R H 2
The accuracy of the calculations is indicated by the very close agreement (to within 1%) with the very elaborate calculations of Kolos and Wolniewicz9 for the static polarizability, with refractive index measurements (tabulated in Victor and Dalgarno 11) in the wavelength range 1850 A to 6328 A, and with the polarizability anisotropy for the v = 0 vibrational level measured at 6328 A by Bridge and Buckingham.2 Furthermore, the polarizability (v--= 0) at 1215 A is within 3% of the value measured by Gill and Heddle 7 and is within 0.2% of the semiempirical values of Vie-
tor and Dalgarno. 11 The computed v = 0 to v = 1 vibrational Raman matrix elements of the polarizability and polarizability anisotropy at 4047 A agree to within experimental error with the measurements of Golden and Crawford.s
Acknowledgments We gratefully acknowledge the assistance of Professor A. Dalgarno and his encouragement that these tables be prepared.
References
1. M. J. S. Belton, M. B. McElroy, and M. J. Price, Astrophys. J. 164, 191 (1971)
7. P. Gill and D. W. O. Heddle, J. Opt. Soc. Am. 53, 847 (1963)
2. N. F. Bridge and A. D. Buckingham, Proc. Roy. Soc. (London) A295, 334 (1966)
8. D. M. Golden and B. Crawford, Jr., J. Chem. Phys. 36, 1654 (1962)
3. A. Dalgarno and S. T. Epstein, J. Chem. Phys. 50, 2837 (1969)
9.
4. A. Dalgarno, A. L. Ford, and J. C. Browne, Phys. Rev. Letters 27, 1033 (1971)
10.
5. A. Dalgarno and D. A. Williams, Month. Notices Roy. Astron. Soc. 124, 313 (1962)
W. Kolos and L. Wolniewicz, J. Chem. Phys. 51, 5002 (1969) G. A. Victor, J. C. Browne, and A. Dalgarno, Proc. Phys. Soc. (London) 92, 42 (1967)
11. G. A. Victor and A. Dalgarno, J. Chem. Phys. 50, 2535 (1969)
6. A. L. Ford and J. C. Browne, Phys. Rev. A, Vol. 7 (1973)
12. L. Wallace, Astrophys. J. 176, 249 (1972)
307
Atomic Data, VoL 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
TABLE I. Rayleigh and R a m a n Cross Sections for Initial Rotational Level o f J = 0 LIGHT SCATTERING CROSS-SECTIONS IN UNITS OF CM**2 INITIAL ROTATIONAL LEVEL IS J=0
WAVELENGTH (ANGSTROMS) 1150.00 1175°00 1200.00 1215°70
1250°00 1300°00 [350°00 l*O0.OC 1450°00 1500°00 1550.00 1600°00 1650.00 1700,00 1750.00 1800.00 1850.00 L900,00 1950°00 2000,00 2050°00 2100.00 2150.00 2200.00 2250°00 2300°00 2350.00 2*00,00 2450.00 2500.00 2550.00 2600°00 2650.00 2700°00 2750.00 2800.00 2850.00 2900.00 2950.00 3000°00 3100,00 3200.00 3300.00 3400.00 3500,00 3600°00 3700°00 3800.00 3900.00 4000.00 4100°00 4200,00 &300.00 *~00.00 4500°00 4b00°00 WT00.00 4800°00 4900.00 5000,00 5500°00 6000.00 7000°00 8000,00 9000,00 INFINITY
PURE RAYLSIGH 4.072E-24 3°023£-24 2.351E-24 2°0~IE-24 1.547E-2, 1°09,E-2, 8°100El25 6°205E-25 4°877E-25 3°912E-25 3.19CE-25 2°638E-25 2,207E-25 I.866E-25 1°592E-25 1,~68E-25 1.184E-25 1,032E-25 9,0.1E-26 7,962E-26 7.046E-~6 6.262E-26 5.588E-26 5,005E-26 ~°499E-26 *.056E-26 3.669E-26 3,327E-26 3.026E-26 2°758E-26 2°521E-26 2°309E-26 2.119E-2b I.949E-26 1.795E-26 1.657E-26 I°532E-26 1.419E-26 1.317E-26 1,223E-26 1,060E-26 9.240E-27 8°092E-27 7.I19E-27 6.290£-27 5.579E-27 4°967E-27 4.~37E-27 3.977E-27 3.575E-27 3,224E-27 2.914E-27 2.042E-27 2.400E-27 2°186E-27 1°996E-27 I°825£-27 1.673E-27 I°536E-27 1,~14El27 9,551E-28 6.689E-28 3°570E-28 2.078E-28 I.291E-28 0.
ROT. RAMAN S-B~NCH 5.956E-25 3°669E-25 2°480E-25 2.002E-25 1°331E-25 8°135E-26 5.392E-26 9.782El26 2°Tb5E-26 2.088E-26 1.618E-26 1.280E-26 1,031E-26 8.429E-27 64978E-27 5°842E-27 4.938E-27 4,211E-27 3.618E-27 3.131E-27 2.726E-27 2,387E-27 2.102E-27 1,859E-27 I°651£-27 I.473E-27 I.319E-27 1°185E-27 1°06~E-27 9.658E-28 8.758E-28 7,963E-28 7o258E-28 6.632E-28 6.073£-28 5.573E-28 5.125E-28 4,122E-28 4°358E-28 4,030E-28 3.462E-28 2.993E-28 2.601E-28 2°273E-28 I°995E-28 1.759E-28 I.557£-28 1.384E-28 1.234E-28 I.I05£-28 9,915E-29 8o926E-29 8.059E-29 7°294E-29 6.619E-29 b.021£-29 5.489£-29 5°014E-29 4.590£-29 4,210E-29 2,80bE-29 1,941E-29
I°014E-29 5.789E-30 3,533E-30 0.
RAYI.EIGH PLUS ROT. RAMAN 4.668E-24 3°390E-24 2.599E-24 2.2,I£-2, ~,680E-24 I°175E-24 8.639E-25 6.583E-25 5.~53E-25 4.120E-25 3°352£-25 2°766E-25 2,311E-25 1.950E-25 1.661E-25 1,*27E-25 1°23~E-25 1.07.E-25 9°403E-26 8°275E-26 7.319E-26 6.501E-26 5°798E-26 5,191E-26 4.664E-26 4°204E-26 3.800E-26 3.446E-26 3°133E-26 2.855E-26 2.608E-26 2,388E-26 2.191E-26 2°015E-26 1.856E-26 1,713E-26 1.584E-26 1,466E-26 1.360E-26 I,263E-26 1°095E-26 9.539E-27 8.352E-27 7.346E-27 6°489E-27 5.755E-27 5.122E-27 4°575E-27 4.100E-27 3.686E-27 3,323E-27 3.004E-27 2.722E-27 2.473E-27 2.252E-27 2.056E-27 I°880£-27 I.723E-27 1.582£-27 1,456E-27 9,832E-28 b.883E-28 3.671£-28 2°135E-28 1,326E-28 0.
VIBRATIONAL RAMAN Q-BRANCH S-BRANCH 5.306E-25 3°I00E-25 3°033E-25 1°519E-25 I°9'IE-25 8.690E°26 I.523E-25 6.440E-26 9°606E-26 3.677E-26 5.525E-26 I.902E-26 3.489E-26 [.II2E-2b 2.351E-26 7°062E-27 I°661E-26 4.762E-27 1°217E-26 3°359E-27 9.177E-27 2°456E-27 7°088E-27 1°848E-27 5.5~2E-27 1,423E-27 4°~70E-27 l,ll8E-Z7 3.631E-27 8°928E-28 2°986E-27 7,234E-28 2,.82E-27 5,936E-28 2.083E-27 *,923E-28 1,762E-27 *°123E-28 1,503E-27 3,483E-28 1.290E-27 2.965E-28 1,115E-27 2,542E-28 9.6~3E-28 2°193E-28 8°456E-28 1,902E-28 7.419E-28 1.659E-28 6°537E-28 I.654E-28 5.784E-28 I.280E-28 5,136E-28 1.131E-28 4.577E-28 1°003E-28 4.092E-28 6.931E-29 3.670E-28 7.977E-29 3,300E-28 7,147E-29 2.976E-28 6°422E-29 2.690E-28 5.785E-29 2°437E-28 5,225E-29 2.21,E-28 4.731E-29 2.014E-28 4.293E-29 1°837E-28 3,903E-29 1.678E-28 3.557E-29 1,536E-28 3,2~7E-29 1,293E-28 2.721E-29 1.096E-28 2.295E-29 9o337E-29 I.947E-29 7.999E-29 1.661E-29 6.885E-29 1.424E-29 5.953E-29 I.227E-29 5.168E-29 I.062E-29 4.504E-29 9.220E-30 3.939E-29 8.038E-30 3°457E-29 7.032E-30 3,043E-29 6°171E-30 2.687E-29 5,432E-30 2.379E-29 ~.795E-30 2.IIIE-29 *.244E-30 I.879E-29 3.765E-30 I.675E-29 3°349E-30 i°498E-29 2.985E-30 1.341E-29 2.666E-30 I°204E-29 2.386E-30 1,082E-29 2,139E-30 6,519E-30 1,272E-30 4.067E-30 7.826E-31 I.713£-30 3°206£-31 7°786E-31 1,413£-31 3.725E-31 6.531E-32 0. 0.
VOTOI
COEFFICIENTS IN 1/WAVELENGTH EXPANSION (WAVELENGTH IN ANGSTROMS. CROSS-SECTION IN CM**2) 0 l
3 5
8.311E-,5 0o 1.2~4E-38 0° 1o512E-32 0.
e
I°724E-26
7 b
0. l°gl8E-20
TRANSITION ENERGY (CM-l)
Atomic Data, VoL 5, No. 3, 1973
0°00
2.563E-,6 -2.119E-45 b.257E-40 -7°232E-39 1o079E-33 -h619E-32
l.558E-*b -1.563El'4 ~°588El*0 -6.48bE-38 9.161E-34 -lo698E-31
I°612E-27
I=551E-27
-2.995E-26 2°228E-21 354°39
308
3°335E-47 -5.359E-45 1°135E-~0 -2,372E-38 2.592E-3~ -b°b76E-32 *o967E-26
-3°585E-25 2.403E-21
-1.519E-25
4162.06
4~98°75
8.bLOE-22
SUM 8.407E-25 4.552E-25 2.810E-25 2.167E-25 1o328E-25 7.427E-26 ~°b02E-26 3°057E-26 2o137E-26 1.553E-26 I°I63E-Z6 8°935E-27 7.005E-27 5.588E-27 *°524E-27 3.709E-27 3.075E-27 2.575E-27 2.175E-27 1°851E-27 1°587E-27 1.369E-27 [.188E-27 1.036E-27 9.078E-28 7.991E-28 7°063E-28 6°267E-28 5.581E-28 *°985E-28 4.467E-28 4°015E-28 3o618E-28 3.269E-28 2°960E-28 2.687E-28 2.~4qE-28 2°227E-28 2.03.E-28 1.861E-28 1.565E-28 1.325E-28 1.128E-28 9°660E-29 8°309E-29 7.180E-29 b . Z2gE-29 5°426E-29 ~.743E-29 ~.160E-29 3.660E-29 3.230E-29 2.858E-29 2°536E-29 2,255E-29 2.010E-29 1.796E-29 1.608E-29 1.442E-29 1.296E-29 7°790E-30 ~°850El30 2°034E-30 9°199El31
*.378E-31 O°
RAYLEIGH AND RAMAN CROSS SECTIONS FOR Hz
T A B L E II. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 1 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) liS0,00 I175°00 I200°0C 1215.70 ~250.0C 1300,00 135U,00 I~00°00 1450°00 1500°00 1550,00 Ib00,00 1650,00 1700,0C 1750.00 l~00°00 185~,00 190U.00 1950°00 2000.00 2050.00 2100.00 2150.00 2200°00 2250.00 2300°00 235U°00 2400°00 2450°00 2500,00 ~550o00 2800,00 2650.00 2700.00 2750.00 2800.00 2850.00 2900°00 2950.00 3000,00 3100,00 3200.00 3300.00 3400,00 3500,00 ~800,00 5700°00 5800,00 3900,00 4000,00 4100°0~ 4200,00 ~300,00 ~00,00 4500,00 4600°00 ~700°00 4800°0~ 4900.00 5000,00 5500°00 6000°00 7000.00 8000,00 9000,00 INFINITY
PURE RAYLEIGH 4,349E-24 3.196E-24 2°~69E-24 2,137E-24 |,o12£-2~ I°133E-2~ 8.365£-25 6e392£-25 5°uI5E-25 4,016E-25 3,272E-25 2,703£-25 2,Z60£-25 I,909E-25 1,627E-25 1,398E-25 Io210E-25 I°053E-25 9,227E-26 8,124E-26 7,187£-26 6,386E-26 5,897E-26 5,102E-26 4.58~E-26 4°133£-26 3°737E-26 3.389E-26 3,o82E-26 2,809E-26 2,567E-26 2,350E-26 2,157£-26 1°983E-26 I,827E-26 I°687E-26 I°559E-26 I°444E-26 1.3~0E-26 I°24~E-26 I°07gE-26 g,39gE-27 8°230E-27 7°240E-27 6°396£-27 5°873E-27 5°050E-27 4°511E-27 4.063E-27 3,635E-27 3,277E-27 2,gb3E-27 2,685£-27 2°440E-27 2,222E-27 2,028E-27 i°855E-27 I°700E-27 1,561E-27 1,436E-27 9°705E-28 6°797E-28 3.627E-28 2°IIIE-28 I.311E-28 0,
CO]~mFICIENTS 0 I 2 3 4 5 b 7 TRANSITION ENERGY (CM-I)
1
ROT. RAMAN S-BRANCH 3,509E-25 2.163E-25 1,464£-25 1.182E-25 7,885E-26 4.8iI£-26 3,191E-26 2,239£-26 1,837£-26 1.237E-26 g,582£-27 7,582£-27 6,t05£-27 4,990E-27 4,130E-27 3.457£-27 2,921£-27 2,491E-27 2,140E-27 1.851E-27 1,611E-27 I,410E-27 1,241E-27 1,097E-27 g,745E-28 8.889E-28 7,777£-28 6,985£-28 6,294E-28 5,689E-28 5,158£-28 4°686£-28 4°270£-28 3,900E-28 3.570E-28 3.275E-28 3.010E-28 2°772£-28 2,558E-28 2°384£-28 2°029E-28 1,752E-28 I,522E-28 I,328£128 1°165E-28 1,028E-28 9°078E-29 8,080£-29 7,182E-29 6,421E-29 5,758£-29 5,179E-29 4,672E-29 4°225E-29 3.830E-29 3,481E-29 3,170E-29 2°893£-29 2.848£-29 2°425£-29 I°608E-29 i,I07E-29 5°728£-30 3,238E-30 I,957E-30 0,
IN I/WAVELENGTH EXPANSION 8.w42E-w5 0, 1,275E-38 0. 1o564E-~2 0, 1,801E-28 0, 2,022E-20 0,0U
IN UNITS OF CM**2
RAYLEIGH PLUS ROT. RAMAN ~,700E-24 3,~12E-2~ 2°616E-24 2,255E-24 I,690E-24 I,181E-24 8,684E-25 b,616E-25 5,178£-25 4,140E-25 3,367E-25 2,779E-25 2,B21£-25 ~,959E-25 1,668E-25 1,433E-25 I°239E-25 1,078E-25 9,441E-26 8,309E-26 7,348E-26 6,527E-26 5,821E-26 5,211E-26 4°682E-26 4,220E-26 3.815E-26 3°459E-26 3,144E-26 2,886E-26 2,818E-26 2.397E-26 2°200E-26 2,022E-26 i°863E-26 I°719El26 1,589E-26 1,472E-26 1,365E-26 1,288E-26 I.099£-26 9,574E-27 8,382E-27 7,373E-27 6°512E-27 5°775£-27 5°141£-27 4,592E-27 4,115£-27 3,699E-27 3°334E-27 3°014E-27 2°732E-27 2°482E-27 2,260E-27 2,063E-27 1.887E-27 I°729E-27 I,588£-27 I°461E-27 9°866E-28 6,g07E-28 3,684E-28 2,143E-28 I,331E-28 0,
VOTO VIBRATIONAL RAMAN Q-BRANCH S-BRANCH 6.536E-25 1,847E-25 3,628E-25 9,046E-28 2,276E-25 5,177E-28 1.769E-25 3.837E-26 1.099E-25 2.192£-26 6°231E-26 I.~34E-26 3,896E-28 b,633£-27 2e606E-26 ~e213£-27 1,831E-26 2,840£-27 i,336E-26 2,00~E-27 1,00~E-2b 1,465E-27 7,732E-27 1,102£-27 b,078E-27 8.485E-28 4,855E-27 0,664E-28 3,937E-27 5,321E-28 3,233£-27 4,311£-28 2,684E-27 3,536E-28 2,249E-27 2,g32E-28 I,902E-27 2,455E-28 1.620E-27 2,073E-28 1,390£-27 1,764£-28 I°200E-27 i,512E-Z8 I,0~2E-27 1,303E-28 9°091£-28 1,130E-28 7,972E-28 9,854E-29 7.021E-28 8,632E-29 b,20gE-28 7,594E-29 5,512E-28 6,709E-29 4,9LOE-28 5,949E-29 4,38gE-28 5,294E-29 3,93WE-28 4°726£-29 3,537E-28 4,232£-29 3°I~8E-2~ 3°801E-29 2.882E-25 3,423E-29 2.610E-28 3°090E-29 2°370E-28 2,796E-29 2,156£-28 2°536E-29 I°966E-28 2°305E-29 I°796~-28 2,099E-29 1,643E-28 1.915£-29 I°383E-28 I,603E-29 I°172E-28 1,351E-29 9°983E-29 I°145E-29 8°550E-29 9,756£-30 7,358E-29 8°356E-30 8°360E-29 7,190E-30 5,521E-29 b°213E-30 4°811E-29 5°390E-30 4,208E-29 ~°894£-30 3°692E-29 ~°I01£-30 3°250E-29 3°594E-30 2°869E-29 3°160E-30 2°5WOE-29 2,786£-30 2°254E-29 2°482E-30 2°006E-29 2o182E-30 I°789E-29 I°938E-30 I°599E-29 I°725E-30 1,432E-29 ~,539E-30 I°285E-29 I°375E-30 I°155E-29 I°231E-30 6°958E-30 7,265E-31 4°3~IE-30 4°437E-31 I°829E-30 I,786E-31 8,318E-31 7,716E-32 3,981E-31 3°485E-32 0° 0,
1 SUM 8.383E-25 4.531E-25 2.794E-25 Z.153E-25 1.319E-25 7,306E-26 4=560E-26 3o027E-20 2.115E-26 I. 536E-26 1°151E-26 8.834E-27 6,924E-27 5,522E-27 4,z~.69E-27 3~66WE-27 3.037E-27 2.543E-27 2. 147E-27 le827E-27 1,566E-27 1,351E-27 1o172E-27 1o022E-27 8,957E-28 7o885E-28 6,96gE-28 b.183E-28 5.505E-28 ~o918E-28 4.407E-28 3°960E-28 3.569E-28 3o224E-28 2,919E-28 2.650E-28 2.410E-28 2,197E-28 2o006E-28 1,835E-28 i. 544E.-28 1.307E-28 I,I13E-28 9.525£-29 8o193E-29 7.079E-29 6.14.3E-29 5.350E-29 ~.677E-29 4° I02E-29 3,609E-29 3o185E-29 2,818E-29 2.501E-29 2.224E-29 1.983E-29 1,771E-2g 1.586E-29 1.422E-29 1.278E-29 7.685E-30 4.785E-30 2.UO8E-30 g.087E-31 4.329E-31 O.
(WAVELENGTH IN ANGSTROMS, CROSS-SECTION IN CM**2)
I,550E-46 -2,15~E-45 3,782E-~0 -7.337E-39 6o523E-34 -I,640E-32 9,745£-28 -3.032E-26 1o348E-21 587,87
309
1,659E-46 -I,722E-44 4,957E-40 -7,217E-38 1,00WE-33 -legi0E-31 1,724E-27 -4,076E-25 2,708E-21
2,033E-47 -3o427E-45 6o915£-41 -loSl8E-3U le582E-34 -~o280E-32 3eO39E-28 -9e753E-26 5o282E-22
4156.15
~713,83
Atomic Data, Vol. 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
T A B L E III. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 2 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) I15~,00 I175,00 120G,O0 1215,70 1250,00 1300.00 1350,00 l~O0,O0 1450,00 1500.00 1550.00 160O.O0 1650,00 1700,00 1750,00 1800.00 ~850.00 1900,00 1950.00 2000.00 2050,00 2100.Oh 2150,00 2200,00 2250,00 2300.00 2350,00 2400.00 245G.00 2500,00 2550,00 260U.00 2650,00 2700,00 2750,00 2800,00 2850.00 2900.00 2950.00 3000,00 3100o00 3200,00 3300.00 3~00,00 3500.00 3600.00 3700.06 3800.00 3900.00 4000,00 4100,00 4200,00 4300.00 4400.00 4500,00 4600.00 4700.0C 4~00,00 49U0.00 5000,00 5500.0C 6000.00 7~00,00 8000,00 9000,00 INFINITY
PURE RAYLEIGH 4.35&E-2~ 3,199E-2~ 2,473E-24 2.140E-~4 1,615E-2~ 1,136E-24 8,385E-25 6,~08E-25 5.027E-25 4,026E-25 3.280E-25 2,710E-25 2,266E-Z5 1.914E-25 l,o31E-25 1,402E-25 I.zI3E-25 1,056E-25 9,251E-26 8.145E-26 7.206E-26 6.402E-26 5,712E-26 5.115E-26 4.596E-26 4.144E-26 3.747E-26 3.398E-26 3,090E-z6 2,816E-26 2,673E-26 2,356E-26 2.~62E-26 1.988E-20 hB32E-26 1,691E-26 hfi63E-26 1,~48E-26 1.343E-26 I.248E-26 1,081E-26 9,423E-27 8,251E-27 7,259E-27 6.412E-27 5.687E-27 5,063E-27 4,523E-27 4,053E-27 3.B44E-27 3.285E-27 2,970E-27 2.692E-27 2.~46E-27 2.228E-27 2.033E-27 1.~60E-27 1,705E-27 1,565E-27 1,440E-27 9.730E-28 6.814E-28 3,636E-2~ 2,116E-28 1.314E-28 0.
COEFFICIENTS
8,463E-45 O, 1,279E-38 O+ 1.569E-32 O, 1.805E-26
3 5 6 7
0,
2,025E-20 TRANSITION ENERGY (C~-I)
Atomic Data, Vol. 5, No.
2
ROTATIONAL RAMAN RAYLEIGH PLUS OzBRANCH S-BRANCH ROT. RAMAN 1.287E-~5 3,312E-25 4,811E-24 7.848E-26 2 , 0 1 2 E - 2 5 3.479E-24 5.278E-26 1.349E-25 2,660E-24 4.251E-26 I.oB5E-25 2.291E-2N 2.817E-~6 7 . 1 6 ~ E - 2 6 1,714E-24 1.717E-26 4,348E-2b 1,196E-24 1.137E-26 2.868E-26 8.785E-25 7,967E-27 2,G04E-26 6.688E-25 5,825E-27 1.461El26 5,231E-25 4.400E-27 1.100E-26 4,180E-25 3.411E-27 b.504E-27 3,399E-25 2,701E-~7 6,715E-27 2,804E-25 2,177E-27 5.396E-27 2.341E-25 1,781E-27 4,404E-27 hg76E-25 1.476E-27 3.6~0E-27 h683E-25 1 . 2 3 6 E - 2 7 3.043E-27 1.444E-25 1,0~6E-27 2.568E-27 1,249~-25 8.931E-28 2.187E-27 hOe7E-25 7.683E-28 1 . 8 7 7 E - 2 7 9.516E-26 6,656E-28 1,622E-27 8,374E-26 5.802E-28 1.411E-27 7.405E-26 5,087E-28 1.234E-27 6,577E-26 4.~83E-28 1.085E-27 5.865E-26 3.970E-28 9.583E-28 5,250E-2o 3,531E-28 8.503E-28 4,717E-2b 3,154E-28 7.576E-28 4,251E-2o 2°827E-28 6,776E-28 3,843E-26 2.543E-28 6,082E-28 3.~84E-26 2.296E-28 5 . 4 7 6 E - 2 8 3.167E-26 2.078E-28 4 , 9 ~ 6 E - 2 8 2.886E-26 1.887E-28 4.480E-28 2,637E-26 h718E-28 4,069E-28 2.~14E-26 1,568E-28 3.705E-28 2.215E-26 1.43~E-28 3.382E-28 2,037E-26 1.315E-28 3.094E-28 hB76E-26 1,209E~28 Z.836E-28 1.731E-26 hl13E-28 2,606E-28 1,601E-26 hOZ7E-28 2.398E-28 1,~82~-26 9,489El29 2,211E-28 1.375E-26 8,786E-29 2.043E-28 h277E-26 7,568E-29 1,751E-28 1,106E-26 6,560E-29 1,511E-28 9,640E-27 5.717E-29 1.311E-28 8,440E-27 5.008E-29 1,143E-28 7.~23E-27 4°408E-29 1.ooIE-28 6,557E-27 3,897E-29 8,811E-29 5.814E-27 3 , 4 6 0 E - 2 9 7 , 7 8 5 E - 2 9 5,175E-27 3,083E-29 6.905E-29 4.623E-27 2,757E-29 6,146E-29 4.142E-27 2,474E-29 5.489E-29 3.724E-27 2.227E-29 4 , 9 1 8 E - 2 9 3,357E-27 2,010E-29 4,419E-29 3.034E-27 h820E-29 3,982E-29 2.750E-27 1.652E-29 3.597E-29 2.499E-27 hSO3E-29 3.258E-29 2.275E-27 1.371E-29 2.957E-29 2.077E-27 1,253E-29 2,691E-29 1.899E-27 1.148E-29 2.454E-29 1,741E-27 1.054E-29 2,242E-29 h59~E.27 9~695E-30 2 . 0 5 2 E - 2 9 1.470E-27 6~551E-30 1,354E-29 9,931E-28 4.596E-30 9.276E-30 6.953E-28 2.469E-30 4,751E-30 3.709E-28 1,450E-30 2.659E-30 2,157E-28 9,101E-31 1.590E-30 1,339E-28 8.052E-37 0. 8.052E-37
IN 1/WAVELENGTH EXPANSION
1
0,00
3, 1973
IN UNITS OF CM**2
5,105E-47 ~.206E-46 1,242E-40 1,431E-39 2,136E-34 3,191E-33 3,180E-28 5.884E-27 4.3SOE-22 -354.39
(WAVELENGTH IN ANGSTROMS,
1,375E-46 -2,690E-45 3,399E-40 -9,274E-39 5,931E-34 -2,097E-32 8,961E-28 -3,917E-26 1,252E-21
VIBRATIONAL RAMAN V 0 TO 1 Q-BRANCH O-BRANCH S-BRANCH 6,419E-25 5.742E-26 1.318E-25 3.566E-25 2.673E-26 5°972E-26 2.242E-25 1 , 4 7 3 E - 2 6 3,216E-26 1,744E-25 1,070E-26 2.307E-26 1,086E-25 5.882E-27 1.238E-26 6,165E-26 2.912E-27 5.943E-27 3,860E-26 1,642E-27 3,267E-27 2,584E-26 1,012E-27 1.970E-27 1.817E-26 6 . 6 5 3 E - 2 8 1.269E-27 ~.326E-26 4.592E-28 8.611E-28 9,974E-27 3.293E-28 6,080E-28 7.685E-27 2,438E-28 4.435E-28 6°040El27 1,849E-28 3,322E-28 4.829E-27 1,433E-28 2,545E-28 3,917E-27 1,131E-28 I,988E-28 3.217E-27 9.072E-29 1.578E-28 2,671E-27 7.374E-29 1.270E-28 2.239E-27 6 . 0 6 5 E - 2 9 1.036E-28 1.893E-27 5,041E-29 8.537E-29 1,613E-27 4.230El29 7.I07E-29 1.384E-27 3.579E-29 5.968E-29 1,195E-27 3 , 0 5 1 E - 2 9 5,052E-29 1.038E-27 2.618E-29 4,307E-29 9.058E-28 2,261E-29 3,695E-29 7.944E-28 1.96~E-29 3.190E-29 6.997E-28 1,715E-29 2.768E-29 6,189E-28 1.504E-29 2.415E-29 5.~94E-28 1.326E-29 2.116El29 4.895E-28 1,173E-29 1,862E-29 ~.375E-28 hO42E-29 1,645E-29 3.922E-28 9,283E-30 1,459E-29 3.527E-28 8.301E-30 1,298E-29 3,179E-28 7 , 4 4 6 E - 3 0 I,159E-29 2.874E-28 6*699E-30 1,037E-29 2.603E-28 6,042E-30 9,315E-30 2.364E-28 5,465E-30 8,386E-30 2.151E-28 4.954E-30 7.569E-30 1.901E-28 4e501E-30 6,647E-30 1.792E-28 4,099E-30 6,208E-30 1,640E-28 3,740E-30 5,6~0E-30 1,380E-28 3,131E-30 4.684E-30 1,169E-28 2,641E-30 3,918E-30 9.962E-29 2.241E-30 3,298E-30 8.533E-29 1,913E-30 2,793E-30 7,344E-29 1,642E-30 2,379E-30 6.349E-29 1,416E-30 2.036E-30 5°512E-29 1.226E-30 1.750E-30 *.804E-29 [.067E-30 1.511E-30 4.201E-29 9.319E-31 1,310E-30 3,687E-29 8,168E-31 1.1~OE-30 3,2~6E-29 7.184E-31 9,950E-31 2,865E-29 6,339E-31 8.71~E-31 2.537E-29 5.610E-31 7.654E-31 2,252~-29 4,978E-31 6,7~1E-31 2,004E-29 4 . 4 2 9 E - 3 1 5,954E-31 1,787E-29 3.951E-31 5,271E-31 1,597E-29 3,532El31 4,677E-31 1,431E-29 3,165E-31 4.159E-31 1.284E-29 2,842E-31 3~706E~31 h155E-29 2~557E-3l ~ 3,309E-3.1 6.958E-30 1 . 5 4 8 E - 3 1 1.926El31 4.343E-30 9,729E-32 1,162Eo31 1.831E-30 4.179E-32 4.569E-32 8.334E-31 1,947E-32 1.928E-32 3.994E-31 9,600E-33 8.484E-33 O. 6,875E-34 O.
CROSS-SECTION
IN CM**2)
1.653E-46 -1=700E-44 4.927E-~0 -7.I12E-38 9.955E134 -I,880E'31 h706E-27 -4+005E-25 2,674E-21
U14.48
4144,36
3]0
3,27[El48 -5.267E-46 1,302E-41 -2~543E-39 3.258E-35 -7~578E-33 6,619E-29 -I,796E-26 1o194E-22 3807=67
5.604E-48 -1,317E-45 2*496E-41 -6.843E-39 6,761E-35 -2.157E-32 l,461E-28 -5.349E-26 2.775E-22 4917,94
SUH 8.311E-25 4o430E-25 2o7HE-25 2oOU2E-25 [o268E-25 7.050E-26 ~o351E-26 2o882E-26 2oGIOE-26 1.458£-26 Io091E-26 8o372E-27 6.557E-27 5,227E-27 4.229E-27 3,465E-27 2.872E-27 2.403E-27 2.02~E-27 1.727E-27 1.48CE-27 1o276E-27 1.107E-27 9o653E-28 8.45~E-28 7°446E-28 6.581E-28 5,838E-28 5.198E-28 4.644E-28 4,161E-28 3,740E-28 3,370E-28 3°044E-28 2,757E-28 2°502E-28 2o276E-28 2.075E-28 1.895E-28 1.?33E-28 1.458E-28 1.235F-28 1,052E-28 9,UO3E-29 7o746E-29 6.694E-29 5.810E-29 5.061E-29 4.425E-29 3,882E-29 3.417E-29 3.016E-29 2o670E-29 2.~69E-29 2.108E-29 1.879E-29 1o680E-29 1o504E-29 1.350E-29 1,213E-29 7°JOSE-30 4.556El30 1°919E-30 8,722E-31 4,L75E-31 6.875E-34
RAYLEIGH AND RAMAN CROSS SECTIONS FOR H~
TABLE IV. Rayleigh and Raman Cross Sections for Initial Rotational Level of J = 3 LIGHT SCATTERING CROSS-SECTIONS INITIAL ROTATIONAL LEVEL IS J= WAVELENGTH (ANGSTROMS) 1150.00 1175.0C 1200.00 1215.70 1~50.00 1300.00 1350.00 1600.00 1450,00 1500,00 1550,00 1600.00 1650,00 1700.00 1750,00 1800.00 1850=00 1900,00 1950,00 2000,00 2050.00 2100,00 2150,00 2200.00 2250.00 2300,00 2350.00 2400,00 2450.00 2500.00 2550.00 2600,00 2050,00 2700,00 2750,00 2800.00 2850e00 2900,00 2950,00 3000,00 3100,00 3200.00 3300,00 3600.00 3500.00 3600.00 3700,00 3800°00 3900,00 4000.00 4100°00 4200.00 4300.00 6400.00 4500.00 4600,00 4700.00 4800.00 4900,00 5000°00 5500.00 6000,00 7000,00 8000,00 9000.00 INFINITY
PURE RAYLEIGH 4°471E-2~ 3.274E-24 2.525E-24 2.183E-24 1.644E-24 1.155E-zQ 8,514E-25 6,501E-25 5.097E-25 4.080E-25 3.322E-25 2.744E-2fi 2°Z93E-2fi 1.937E-25 1.651E-25 1.418E-25 1.227E-25 1.068E-25 9.354E-26 8.235E-20 7,284E-26 6.472E-26 5.773E-26 5.170E-26 4.045E-26 4,187E-26 3.786E-26 3,433E-26 3.122E-26 2,845E-20 2.600E-26 2.381E-26 2.185E-26 2.009E-20 1.851E-26 1.708E-20 1.579E-26 1.462E-26 1,356E-26 1.260E-2h 1.092E-26 9,516E-27 8.333E-27 7.330E-27 6,475E-27 5,743E-27 5,112E-27 4.567E-27 4,093E-27 3.079E-27 3.317E-27 2.999E-27 2.718E-27 2*470E-27 2.249E-27 2.053E-27 1°~78E-27 1,721E-27 1.580E-27 1.4fi4E-27 9.823E-28 6.878E-28 3.671E-28 2.136E-28 1.327E-28 O.
COEFFICI~WTS
IN 1/WAVELENGTH EXPANSION
0 1 2 3 4 5 6 7 8 TRANSITION ENERGY (CM-I)
8.542E-45 O= 1,295E-38 O* 1,594E-32 O. 1.840E-26 O, 2,071E-20 0.00
ROTATIONAL RAMAN O-BRANCH S-BRANCH 1.745£-25 3o100E-25 1.055E-25 1.870E-25 7.062E-26 1.255E-2fl 5.676E-26 1.009E-25 3.750E-26 6.6fi6E-26 2,280E-26 4.038E-26 1,507E-26 2.662E-26 1.056E-26 1.860E-26 7,715E-27 1.355E-26 5=826E-27 1,020E-26 4.516E-27 7.886E-27 3.576E-27 6.225E-27 2.882E-27 5.002E-27 2.358E-27 4.080E-27 1.954E-27 3.371E-27 1,038E-27 2.817E-27 1.386E-27 2°377E-27 1.184E-27 2.023E-27 1,019E-27 1,736E-27 8.826E-28 1.499E-27 7.696E-28 1,304E-27 6,750E-28 1,140E-27 5.9filE-28 1.002Eo27 5,272E-28 8.846E-28 4.690E-28 7,846E-28 4.191E-28 0,988E-28 3.758E-28 6.247E-28 3.382E-28 5*605E-28 3,054E-28 5.045E-28 2.766E-28 4,554E-28 2.512E-28 4.124E-28 2.288E-28 3*744E-28 2,089E-28 3,408E-28 1.912E-28 ~.109E-28 h754E-28 2.843E-28 1.612E-28 2.605E-28 1.485E-28 2,392E-28 1.371E-28 2.201E-28 1,267E-28 2.028E-28 1.174E-28 1,873E-28 1.012E-28 1°605E-28 8.779E-29 1.383E-28 7°658E-29 1.199E-28 bo714E-29 1.044E-28 5.915E-29 9,141E-29 5,23~E-29 8.036E-29 4.650E-29 7,094E-29 4.147E-29 6,286E-29 3,712E-29 5,590E-29 3.333E-29 4.988E-29 3.003E-29 4.465E-29 2.713E-29 4,008E-29 2,459E-29 3,608E-29 2.233E-29 3,257E-29 2.034E-29 2=947E-29 1.857E-29 2.673E-29 1,699E-29 2,429E-29 1,558E-29 2.213E-29 1,431E-29 2.020E-29 1.318E-29 1.847E-29 8,9~2E-30 1.213E-29 6.300E-30 8,271E-30 3.41~E-30 4.194E-30 2.022E-30 2,324E-30 1.280E-30 1.375E-30 7.866E-30 O.
b*622E-47 9*175E-40 1,611E-40 3.114E-39 2.770E-34 6.937E-33 4.123E-28 1.277E-26 5.080E-22 -587.07
IN UNITS OF CM**2
3 RAYLEIGH PLUS ROT. ~ 4.956E-24 3,568E-24 2,721E-24 2.341E-24 1.748E-24 1,218E-24 8,931E-25 6,793E-25 5.310E-25 4=241E-25 3.446E-25 2e842E-25 2.372E-25 2.001E-25 1,704E-25 1.463E-25 1.264E-25 1.100E-25 9.630E-26 8,473E-26 7,492El26 6,653E-20 5,933E-26 5,311E-26 4.770E-26 4.299E-26 3.886E-26 3.fi23~-26 3.203E-26 2,919E-26 2,666E-26 2,~41E-26 2,239E-26 2,059E-26 1,897E-26 1,750E-26 1,618E-26 1,498E-26 1.389E-26 1.291E-26 1.118E-26 9.742E-27 8.529E-27 7.501E-27 6.626E-27 5.875E-27 5.230E-27 4.671E-27 4.186E-27 3,762E-27 3.392E-27 3.066E-27 2.779E-27 2.524E-27 2.299E-27 2.098E-27 1,919E-27 1,759E-27 1,615E-27 1,486E-27 1,003E-27 7.024E-28 3.747E-28 2.179E-28 1.353E-28 7.866E-36
(WAVELENGTH IN ANGSTROMS,
1.297E-46 -3.235E-45 3,211E-40 -1.116E-38 5.610E-34 -2.525E-32 8,488E-2~ -4.723E-26 1.188E-21 1034,74
3 1]
Q-BRANCH 6.753E-25 3.710E-25 2.319E-25 1.800E-25 1,116E-25 b,312E-20 3.943E-26 2,635E-26 1.850E-26 1=349E-26 1,014E-26 7o808E-27 6o134E-27 ~.902E-27 3.974E-27 3.263E-27 2o708E-27 2.270E-27 1,919E-27 1.635E-27 1,403E-27 1.211E-27 1.051E-27 9.175E-28 8,0~6E-28 7,087E-28 6.267E-28 5.564E-28 4.956E-28 4.430E-28 3.971E-28 3.571E-28 3.219E-28 2.909E-28 2.636E-28 2.393E-28 2.177E-28 1.985E-28 1.814E-28 1.660E-28 1.397E-28 1.184E-28 1.009E-28 8.639E-29 7.436E-29 b°429E-29 5,581E-29 4.864E-29 4°255E-29 3.734E-29 3,287E-29 2.~02E-29 2.570E-29 2.281E-29 2,030E-29 1.811E-29 1.619E-29 1.450E-29 1.301E-29 1o170E-29 7°056E-30 4,406E-30 1,861E-30 8.479E-31 4.070E-31 O.
VIBRATIONAL RAMAN V 0 TO 1 O-BRANCH S-BRANCH S~H 8.u18E-25 8.050E-26 1o260E-25 4.631E-25 3.080E-26 5.527E-26 2.~I2E-25 2,014E-26 2,912E-26 2.152E-25 1.458E-26 2.066E-26 1o304E-25 7,975E-27 1o086E-26 7.215E-26 3.931E-27 5.098E-27 4.439E-26 2,211E-27 2.750E-27 2°934E-26 1,361E-27 1°632E-27 2.043E-26 8,934E-28 1.037E-27 1.~81E-26 6*162E-28 6°950E-28 1°107E-26 4,417E-28 4.855E-28 8o485E-27 3.266E-28 3.507E-28 6.642E-27 2°478E-28 2.604E-28 1.921E-28 1.979E-28 5°292E-27 4=279E-27 1,516E-28 1.534E-28 3.505E-27 1,216E-28 1.209E-28 2.g04E-27 9.884E-29 9.677E-29 8.131E-29 7.8~4E-29 2o430E-27 6,759E-29 6.~32E-29 2°051E-27 5.672E-29 5.327E-29 1o745E-27 4,800E-29 4,453E-29 1o495E-27 4.093E-29 3.753E-29 1o289E-27 3.514E-29 3°187E-29 1.118E-27 3,036E-29 2,724E-29 9.751E-28 Z,638E-29 2.343E-29 8.544E-28 2.304E-29 2,026E-29 7o520E-28 2,022E-29 1.762E-29 6.646E-28 1,782E-29 1.539E-29 5.896E-28 1,577E-29 1.351E-29 5°249E-28 1*401E-29 1.190E-29 4.689E-28 1,250E-29 1.~52E-29 4o202E-28 1,118E-29 9.341E-30 3.776E-28 1,003E-29 8.319E-30 3°402E-28 9,028E-30 7.431E-30 3.G74E-28 8.147E-30 6,658E-30 2°784E-28 7,371E-30 5.981E-30 2,527E-28 b,686E-30 5,388E-30 2,298E-28 6.078E-30 4,864E-30 2°095E-28 5.537E-30 4.402E-30 1°913E-28 1.750E-28 5,055E-30 3,992E-30 1.473E-28 4.237E-30 3,304E-30 1.247E-28 3,576E-30 2°755E-30 1.062E-28 3.038E-30 2°312E-30 2.596E-30 1.953E-30 9°094E-29 7=U24E-29 Z.230E-30 1.658E-30 1,926E-30 1.415E-30 6°763E-29 1,670E-30 1,214E-30 5°870E-29 1,455E-30 1,046E-30 5°114E-29 1.272E-30 9.043E-31 4°472E-29 1,116E-30 7,850E-31 3°924E-29 9.831E-31 6,838E-31 3.~54E-29 8.685E-31 5,976E-31 3.049E-29 7.695E-31 5.239E-31 2.699E-29 6*838E-31 4.605E-31 2°396E-29 6,092E-31 4°059E-31 2.132E-29 5.441h-31 3~586E-31 1.901E-29 4,871E-31 3°176E-31 I°b99E-29 4,370E-31 2°819E-31 1=522E-29 3.930E-31 2.507E-31 I.366E-29 3,540E-31 " 2°234E-31 1°228E-29 2,159E-31 1°289E-31 7o400E-30 1.367E-31 7.70~E.32 4.620E-30 5.967E-32 2°973E-32 1.950E-30 2.831E-32 1.228E-32 8.885E-31 1.424E-32 5.276E-33 4.265E-31 6.913E-34 0. 6.g13E-34
CROSS-SECTION IN CM**2)
1.667E-40 -1°714E-44 4,986E-40 -7*192E-38 1,011E-33 -1,906E-31 1.737E-27 -4.072E-25 2.730E-21
4.261E-48 -6,444E-46 1,099E-41 -3°111E-39 4,253E-35 -9o269E-33 8=634E-29 -2,195E-26 1.550E-22
3,947E-48 -1.057E-45 1.915E-41 -5,781E-39 5.475E-35 -1°887E-32 1,228E-28 -4.805E-26 2.~01E-22
4126,76
3569°08
5109.35
Atomic Data, VoL 5, No. 3, 1973
A. L. FORD AND J. C. BROWNE
T A B L E V. Cross S e c t i o n s for a T h e r m a l Distribution o f Initial R o t a t i o n a l Levels with T = 100 ° K LIGHT SCATTERING CROSS SECTIONS IN UNITS OF CM**2 THERMAL AVERAGE (WITH 3 TO i ORTHO TO PARA RATIO) WAVELENGTH (ANGSTROMS) ltSO.O0 1175,0C I~00.00 1~15.70 1250,00 1300.00 1350.00 1400.00 I~50,00 1500.00 1550,00 1600,00 1650.00 1700.00 1750,0Q 1800,00 1850.00 1900,00 195G.00 2000,00 2050.00 Zt00,O0 2150.00 2200°00 2250,00 2300°00 2350,00 2~00,00 2~50.00 2500,00 2550,00 2600,0C 2650,00 2700,00 2750,00 2800,00 2850.00 2900.00 2950,0~ 3000,00 3100,00 3200.00 3300,00 3~00.00 3500,00 3600.00 3700,00 3800,00 3900,00 4000.00 ~IO0,O0 4200.00 ~300.00 ~00.00 ~500,00 ~600,00 4700,0~ ~800.00 4900,00 5000,00 5500,00 bO00.O0 7000,00 8000.00 9000,00 INFINITY
AtO~
PURE RAYLEIGH 4.245E-z~ 3.131E-2~ 2,~25E-2~ 2,101E-24 I.588E-2~ I,I18E-24 8.266E-25 6,322E-25 4.963E-25 3,977E-25 3,241E-25 2*079£-25 2,240E-25 1,893E-25 1,614E°25 I*387E-25 1,200£-25 I*045E°25 9.157E-26 8,064E-26 7,134E-26 6.340E-26 5,656E-26 5.066E-26 4,552£-26 4.104E-26 3.712E-26 3,366E°26 3,061E-26 2.790E-~6 2*549E-26 2.335E-26 2.143E-2~ 1,970E-26 I*815E-26 1,676E-26 1,5~9E*Zb 1,435E-26 1.331E-2~ 1,237E-2~ 1,072E-26 g*339E-27 8,179E-27 7.~95E-27 6,356E-27 5.638£-27 5,019E-27 4,484E-27 ~*0~8E-27 3.012E-27 3.257E-27 2,945E-27 2,66gE-27 2,425E-27 2.20gE-27 2*0~6E-27 I,844E-27 ~,690E-27 ~.552E-27 I*428E-27 9,648£-28 6.757E-28 3.606E-28 2.098E-28 1.303E-28 O,
DO~O, ~Olm 5, NOI 3, 1973
ROTATIONAL O-BRANCH 1.525E-27 9.302E-28 6.255E-28 5,037E-28 3,338£-28 2.034E-28 I,340E-28 9,438E-29 6,901E-29 5,213E-29 ~*041E-29 3,200E-29 2*579E-29 2,109E-29 1,748E-29 1.465E-29 1.240E-29 I*058E-29 g,lO2E-30 7,885E-30 6*874E-30 6,027E-30 5,311£-30 %*704E-30 4,184E-30 3,736E-30 3,350E-30 3.013E-30 2,720E-30 2*4~2E-30 2,23~E-30 2,035E-30 I*858E-30 1,700E-30 ~,55~E-30 1,432E-30 1.319E-30 1.217E-30 1.12~E-30 1,041E-30 8,969E-31 7,774E-31 6,775E-31 5*936E-3~ 5,225E-3[ 4,6|9E-3! 4,I0~E-31 3,054E-31 3,268E-31 2,933E-31 2.640E-31 2.383E-31 2.157E-31 ~.958E-3~ ~.782E-31 L,625E-31 I,486E-31 1,361E-31 1,250E-~I 1,149E-31 7*768E-32 5,45~E-32 2.929E-32 1,721E-32 1.080E-32 1,163E-38
FOR T = I00.0
RAMAN RAYLEIGH PLUS S-BRANCH ROT. RAMAN 4.424E-25 4.089E-24 2,726E-25 3.405E-24 1.843E-25 2,610E-24 1.488E-25 2,250E-24 9*899£-26 I,687E-24 6.051E-26 1,179E-24 4,012E-26 8,569E-25 2.814E-26 6,b05£o25 2.058E-26 5,170E-25 1,554E-26 4,133E-25 I*204E-26 3,362E-25 9*530E-27 2,77~E-25 7.674E-27 2.317E-25 b , 2 7 2 E ° 2 7 I*956Eo25 5,I92E-27 1.666~-25 4*346E-27 I*430E-25 3.673£-27 I.237E-25 3.132E-27 1,077E-25 2.691E-27 9.427£-26 2.328E-27 8,297E-20 2*027E-27 7*338E-20 1,774E-27 6.518E-26 1,562E-27 5,813E-26 1,381E-27 5,20~E-26 |,227E-27 4,075E-26 1.094E-27 4.214L-26 g*Tg3E-28 3,810E-26 8,798E-28 3.454£-26 7.929E-28 3.140E-26 7,168E-28 2,862E-26 6*498E-28 2*615E-26 5,907E-28 2.394E-26 5.383E-28 2*IgTE-26 4,918E-28 2,020E-26 ~.502E-28 I,861E-26 ~*131E-28 1,717E-26 3.798E-28 1.587E-26 3,~98E-28 1.470E-26 3.228E-28 1.363E-26 2*g85E-28 1,266E-26 2*5~3E-28 1,097E-26 2.215E-28 9,562E-27 1 , 9 2 4 E - 8 8 8,372E-27 ~*680E-28 7.363E-27 1,474E-28 6,504E-27 1.299E-28 5,768E-27 I*150E-28 5,~34E-27 1.021E-28 6,586E-27 g,lO5E-29 4,1~0E-27 8.143E-29 3.694E-27 7,306E-29 3.330E-27 6.575E-29 3*01~E-27 5,933E-29 2,729E-27 5.368E-29 2,479E-27 ~.86gE-29 2.258E-27 4.~27E-29 2.060E-27 ~,034E-Zg 1,885E-27 3.683E-29 ~*727E-27 3.370E-29 [,586E-27 3*090E-29 1,459E-27 2.054E-29 9*854E-28 1*4~8E-29 6,899E-28 7.370E-30 3,680~-28 ~,188E-30 2,1~0E-28 2.543E-30 1.329E-28 O* 1,163E-38
312
(DEGREES EBLVIN)
Q-BRANCH 6.074£-25 3.~03E-25 2.150E-25 1,677E-25 I*047E-25 5,966£-26 3,743E-26 2*510E-26 1.767E-26 1,291E-26 9,716E-27 7.490E-27 5.890E-27 4.711E-27 3.822E-27 3.140E-27 2.608£-27 2,~87E-27 1.849£-27 I.576E-27 I.352£-27 1.168£-27 I*01~E°27 8,852E-28 7,764£-28 6,840E-28 6,050E-28 5,371E-28 4.785E'28 4,277E-28 3,835E-28 3,448E-28 3,~0gE-28 2,8~0E-28 2*545E-28 2,311E-28 2.[03E'28 1.?18E-28 1.752E-28 I,603E-28 I*350E-28 1.143E-28 9,741E-29 8*3~3E-29 7.180E-29 6.207E-29 5,389E-29 4,696E-29 4,~07E'29 3,604E-29 3,~72E-29 2*801E-29 2*~79E-2g 2.201E-29 1.958E-29 1,746E-29 1,561E-29 1,398E-29 1.254E-29 ~*~28E-29 6,794E-30 4.238£-30 ~.786E-30 8.117E-31 3.885E-31 O*
VIBRATIONAL RAMAN V 0 TO 1 O-BRANCH S-BRANCH 8.816£-28 2,310£-25 3,171E-28 1,131E-25 I.747£-28 6.471E-26 I.268E-28 4.795E-20 5,974£-29 2,737E-20 3.452£-29 1,416E-26 1,947E-29 8,276E-27 1,200E-29 5.255E-27 7,886£-30 3.542£-27 5.442£-30 2.499E-27 3,903E-30 1,826£-27 2.887E-30 1,374E-27 2.1glh-30 1.058E-27 1.699E-30 8.307E-28 1,341£-30 6.634E-28 1,075£-30 5,374£-28 8,739£-31 ~,~09E-28 7,188E-31 3.656E-28 5,975E-31 3.061£-28 5,013E-3[ 2.586E-28 4.241E-31 2.201E-28 3,616£-31 1.886~-28 3,103E-31 I.627£-28 2,680£-31 1.WII£-28 2,328E-31 I°230E-28 2,032E-31 I°078E-28 I,783£-31 g,483E-29 1,571E-31 8,379£-29 1.390£-31 7.432E-29 ~,235E-31 6.614E-29 1,100E-31 5.g06£-29 9,840E-32 5o290E-2g 8,826£-32 4,752E-2g 7.940£-32 ~,280£-2g 7,163E-32 3.865E-29 6,478£-32 3.498E-2g 5,872£-32 3.]74E-29 5.336E-32 2.885E-29 4,859E-32 2*628E-29 4,433E-32 2.399£-29 3,712Eo32 2.009E-2g 3,130£-32 1,693E-29 2*657£-32 1,436£-29 2.268E-32 1,224E-29 l,g46E-32 I*~9E*29 1.679E-32 9,034E-30 I,45~E-32 7,811E-30 1,265E-32 6.780E-30 I*I05E-32 5,908E-30 ~,687E-33 5,165E-30 8,520E-33 4,530E-30 7,518E-33 3,g85E-30 6.653E-33 3,515E-30 5,905E-33 3,109E-30 5,254E-33 2.757E-30 4,687E-33 2.450E-30 ~*!90£-33 2,182E-30 3,755£-33 1,948E-30 3,372£-33 1.742E-30 3.034E-33 1,561E*30 1,837E-33 9.245E-31 ~*155E-33 5.869E-31 4.g64E-34 2.303E-31 2.3~5E-34 1.005E°31 1,142E-34 4.596E-32 8,077E-36 0,
SUM 8.3glE*25 4.538E-25 2.799E-25 2.157E-25 1.322£-25 7.385E-26 4.57~E-20 3.U37E-26 2.122E-26 1.541E-26 I.L55E-20 8.867£-27 6.950E-27 5.543E-27 4.487E-27 3.678£-27 3.050E-27 2o553E-27 2.156E-27 I.835E-27 1.573£-27 I°357E-27 I.177E-27 I°027E-27 8.997E-28 7.91g£-28 7.00GE-28 6.211E-28 5.530E-28 4.g4OE-28 ~.~27£-28 3.g78E-28 3.585E-28 3.238E-28 2.933£-28 2.062E-28 2.421E-28 2.207E-28 2.015E-28 1.843E-28 1.551E-28 1.313E-28 |°I18E-28 9.509E*2g 8.232E-29 7.Z12E-29 6.171E-29 5.375E-29 4.69gE-29 4.121E-Zg 3.626E-29 3.200E-29 2=832E-29 2.512E-29 2.234E-29 I.992E-29 I.77gE-29 1.593£-29 1.42gE-29 1.284E-29 7.720E-30 4.807E-30 2.016E-30 9°125E-31 4°346E°31 8,077E-36
R A Y L E I G H A N D RAMAN CROSS SECTIONS FOR H 2
T A B L E VI. Cross S e c t i o n s for a Thermal Distribution of Initial Rotational Levels with T = 300 ° K LIGHT SCATTERING CROSSSECTIONS THERMAL AVERAGE (WITH 3 TO 1 ORTHO TO PARA RATIO) FOR T = WAVELENGTH (ANGSTROMS) I150,00 I175.00 li00.00 IZ15o70 125U.00 1300.00 [350,00 1400,00 1450.00 1500,00 1550,0U 1600,00 1650,00 1700.00 1750o00 1800,00 185U,00 1900,00 1950°00 2000.00
2050.00 2100.00 2150,00 2200,00 2250,00 2300.00 2350,00 2400,00 2450,00 2500,00 2550,00 2600,00 2650.00 2700.00 ~750,00 2800.00 2850,00 2900,00 2950.00 300~°00 31UUo0G 3Z00°0C 3300,00 3400o00 350b,00 3600o00 3700,00 3800,0G 3900,0U ~00G.00 ~100o0C 4200,00 ~300.00 ~400,00 ~500,00 4600°00 4700.00 4800.00 4900,00 5000,00 5500,00 b000°00 7000.00 8000.00 9000.00 INFIhITY
PURE RAYLEIGH 4.325£-2~ 3.181E-2~ 2,460E-2~ 2,129E-24 1.607E-24 1.130£-2~ 8.3W7E-25 6.380£-25 5.006E-25 4.010£-25 3.867E-25 2,b99E-25 2,257£-25 1.906E-25 Iob25E-25 1.396E-25 1.208E-25 1.052E-25 9,217E-26 8,116£-2b 7,180E-26 6.380E-26 5,692£-26 5,097E-26 4.580E-26 4°129E-26 3,734E-26 3,386E-26 3,079£-26 2,807E-26 2.564£-26 2,348E-26 2,155E-26 h982E-26 h826E-26 I,685E-26 1,558E-26 1,443E-26 1,339£-26 1.244E-ae 1,078E-26 9,392E-27 S.224£-27 7°Z35E-27 6.391E-27 5°669E-27 5.046E-27 4,508£-27 4.040£-27 3.b32E-27 3.175£°27 2.961£-27 2.083E-27 2.438E-27 2°221E-27 2,u27E-27 I°854£-27 I,b99£-27 I,560E-27 I°436E-27 9°099E-28 6,792E-28 3.625E-aU 2,I09E-28 1.310£-28 0°
ROTATIONAL O-BRANCH 3,131£-2b 1.901E-Zb 1,275E-26 [.026£-26 b,Tg0E-27 4.133£-27 2,734E-27 I*916£-27 I*400E-27 1,058£-27 8,|99£-28 6.4926-28 5,232E-28 4,280£-28 3o547E-28 2,973£-28 2,516E-28 2,148E-28 I,848£-28 1,601E-28 1,396£-28 1,224E-28 1.079£-28 9o557£-29 8,502E-29 7,595£-29 6,809E-29 b,127£-29 5°531E-29 5.009E-29 4,548£-29 4,142E-29 3,781E-29 3o460E-29 3.173E-29 2,916E-29 2°68bE-29 2,478E-29 2°291E-29 2o122E-2g 1.828E-29 1°585E-29 I*382E-29 1.212E-29 1°067E-29 9,436E-30 8,38dE-30 7,47XE-30 6*684E-30 6°000E-30 5°403£-30 4°S80E-30 4,420E-30 4,013E-30 3,654E-30 3°334E-30 3,049E-30 2,795E-30 2,567E-30 2,362E-30 1,599E-30 1,125E-30 6.068E°31 3°579E-31 2°257E-31 8,206E-37
RAMAN S-BRANCH 3,765E-25 2,314E-25 1.562E-25 1.261E-25 8*376E-26 5.115E-26 3,389E-26 2,376E-26 1.736E-26 h311E-26 1,015E-26 8,031E-27 6,464E-27 5.282E-27 4o371E-27 3,658E-27 3o091E-27 2,634£-27 2°263E-27 1,957£-27 1.703E-27 1,491£-27 1,312E-27 Io160£-27 1,030E-27 go183E-28 8,218E-28 7,3S0£-28 6°650E-28 6,¢IOE-28 5,447E-28 4.950£-28 4,510E-28 4,119£-28 3,770E-28 3,459E-28 3.179E-28 2,928E-28 2.701£-28 2*496E-28 2,143£-28 I,850E-28 I*607E-28 I°403E-28 1.230E-28 I°084E-28 9°583£-29 8.508E-29 7*581E-29 6,777E-29 6,078E-29 5,466E-29 4,930E-29 4°459E-29 4°042£-29 3°673E-29 3.345E-29 3°053E-29 2,792E-29 2,559E-29 1,697E-29 h168E-29 6°042E-30 3,416E-30 2°064E-30 0°
IN UNITS OF CM**2
300.0
RAYLEIGH PLUS ROT. RAMAN 4,733E-24 3,432£-24 2,b29£-2% 2,265E-24 1,697£-24 1,186£-24 8,713E-25 6,637E-25 5,19WE-25 4.152E-25 3,376E-25 2,786£-25 2,327£-25 1,964E-25 1,672E-25 I,436E-25 1,2425-25 1.081E-25 9,462£-2b 8,327E-2b 7,364E-26 6,541£-2o 5,834£-26 5,223E-2b 4,692E-26 4,22g£-26 3,8235-26 3,466£-26 3°151E-26 2,872E-26 2o623E-26 2°402£-26 2,204E-26 2,026£-26 h867£-26 I°723£-26 Io593E-26 1°475E-26 1°368El26 I,271E-26 1,101E-2b 9,593E-27 8,399£-27 7°387E-27 6°525£-27 5°786£-27 5.151£-27 4,601E-27 4*123E-27 3°706E-27 3°341£-27 3°020£-27 2°737E-27 2°487E-27 2°265E-27 2°067E-27 I°890E-27 I°733E-27 I,59~E-27 h464E-27 9°885E-28 6,920E-28 3,691E-28
2,147E-28 I,333E-28 8,206E-37
313
(DEGREES KELVIN)
Q-BRANCH 6o383E-25 3,550£-25 2.233E-25 Io737E-25 1.081E-25 b.139£-2b 3.844E-26 2*573£-26 1,809E-26 1,320£-26 9.930E-27 7°650E-27 6.013E-27 4.807E-27 3.898E-27 3,202£-27 2,658E-27 2o228E-27 1,884£-27 |.606E-27 1.377E-27 1.189E-27 1,033£-27 9.013E-28 7.904£-28 6.962£-28 6.157E-28 5,46b£-28 4,870E-28 4o352£-28 3,902£-28 3,508E-28 3,163E-28 2o858£-28 2.589£-28 2.35[£-28 2o139E-28 h951£-28 1,782E-28 Io631E-28 I,373E-28 1.163E-28 9*906E-29 8°484E-29 7o302E-29 6°313E-29 5°480E-29 4,775E-29 4*176£-29 3,665E-29 3,226Eo29 2.848E-29 2,521E-29 2°238£-29 I°991E-29 Io776E-29 1.587E-29 Io~22E-29 1°276E-29 [°147E-29 6,910E-30 4*312E-30 I°817E-30 8o264£-31 3,957£-31 0°
VIBRATIONAL RAMAN V 0 TO i O-BRANCH S-BRANCH 1,421£-26 1.892E-25 6.561£-27 9.153£-26 3,599£-27 5,191E-26 2.609E-27 3.830E-26 1,431E-27 2.169E-26 7.069£-28 1.I12£-2b 3.982E-28 6.458E-27 2*452£-28 4,078£-27 1.611E-28 2.737E-27 I,IIIE-28 |.924E-27 7,g68E-29 |,601E-27 5.894E-29 [.051£-27 4,472E-29 S.076E-28 3.467E-29 6.329E-28 2,737E-29 5.045£-28 2,194£-29 ~,080E-28 1.7845-29 3,342E-28 1.467E-29 2.767E-28 1,220£-29 2o31~E-28 1,023E-29 I,952£-28 8.659E-30 I,660E-28 7.383E-30 1.421£-28 6,337£-30 1.225£-28 5,474£-30 1.061E-28 4.755E-30 g.245£-29 4°153E-30 8.094£-29 3,644E-30 7.117E-29 3,211£-30 6.284£-29 2.842£-30 5,570E-29 2,524£-30 4,955E-29 2°250£-30 4°422E-29 2.013£-30 3°958E-29 h806£-30 3,554E-29 1,625£-30 3,199E-29 h466£-30 2°887£-29 1.326E-30 2,612E-29 1,202E-30 2°369E-29 I,093E-30 2,152E-29 9,954E-31 I°960£-29 9,08~E-31 1.788E-29 7o611E-31 1.496E-29 6.421E-31 1.260E-29 5.452£-31 I°068E-29 4,657E-31 9°I00E-30 3,998[-31 7.794E-30 3°450£-31 6°706£-30 2.991£-31 5.794£-30 2.603£-31 5°027E-30 2.275£-31 ~.377E-30 1,996£-31 3°824E-30 I,756E-31 3.352E-30 I,551£-31 2,9~7£-30 1°373£-31 2°598E-30 1,219E-31 2°297E-30 Io086£-31 2,036£-30 9°690£-32 Io808E-30 8°670E-32 1.610E-30 7°774E-32 [,436E-30 6°985E-32 1,284E-30 6,289[-32 I°149E-30 3,822£-32 6o788E-31 2.411E-32 4.150E-31 I,045£-32 I°675E-31 4°914E-33 7.263E-32 2°449£-33 3°295E-32 1,451£-34 0.
SUM 8.417E-25 4.531E-25 2.788£-25 2.|46E-25 1.313£-25 7.322£-26 4.529E-26 3.005£-26 2.099E-26 1.524E-26 1.141E-26 8.760£-27 6.865E-27 5.474E-27 4.430£-27 3.632£-27 3.018E-27 2.520£-27 2.128£-27 1.811£-27 1.552E-27 1.33g£-27 1.161£-27 1.013E-27 8.876E-28 7.813E-28 6.905E-28 6.127£-28 5.455E-28 4.873E-28 4.307E-28 3.924E-28 3.536k-28 3°195E-28 2.893E-28 2.626E-28 2.388£-28 2.177E-28 1.988E-28 I.b18£-28 Io530E-28 I°295E-28 I.I03E-28 9.441E-29 8.121E-29 7.018E-29 6.08gE-29 5.304£-29 4.637E-29 4.067E-29 3.579E-29 3.158£-29 2.795£-29 2°480E-29 2.206E-29 1.966£-29 1.757E-29 1.573£-29 1.411E-29 [.268E-29 7.627E-30 4.751E-30 |o995E-30 9°040E-31 ~.311E-31 1°451E-34
Atomic Data, Vol. 5, No. 3, 1973