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Frank-Condon factors for H2O+ molecular bands
Oil324633/83
Planer. Spuce SC;., Vol. 31, No. I I, pp. 1371 137% 1983 Prmted inGreat Britain.
FRANK-CONDON
$3.M) +O.oO
PergamonPress Ltd.
FACTORS FOR H,O+ BANDS
MOLECULAR
N. N. SHEFOV Institute of Physics of the Atmosphere, U.S.S.R. Academy of Sciences, Moscow, U.S.S.R. (Receiued 25 January 1983) Abstract-Frank-Condon factors for H,O+ bands have been calculated. They are used to estimate the photon scattering coefficient g8,0 for the (8,O) band at 6158 A.
There are some features of water vapour ions H,O+ in cometary spectra (Herzberg, 1976) and in upper atmospheric spectra (Herzberg, 1980b; Krassovsky et al., 1981). To interpret these it is necessary to know transition probabilities for various bands of the a2AI8’S, system of H,O+. Some data of structure of vibrational levels for upper and lower states were given by Lew (1976) and potential function data have been given by Herzberg (1980). These data lead one to the conclusion that the potential of upper state ‘A, may be satisfactorily approximated by a harmonic oscillator potential. There is a potential barrier for the lower state TABLE
“y,, 5 6 7 8 9 10 11 12 13 14 15 16 17
1. FRANK-C• 0
7458 0.115 6987 0.140 6542 0.146 6158 0.134 5793 0.109 5489 0.0808 5189 0.0544 4924 0.0337 4689 0.0194 4471 0.0104 4272 0.00518 - ___ 4106 0.00244 3921 0.00107
‘B, and the potential function may be presented by a perturbed harmonic oscillator with a Gaussian barrier (Flygare, 1978). Calculations of the Frank-Condon factors r~“,~,,have been made according to the methods described by Chan and Stelman (1963); Somorjai and Hornig (1962); and Volkenstein et al. (1972). The quevfpvalues and the corresponding wavelengths (A) are given in Table 1 below. The sums xqvrvrp equal 1 with an accuracy better than l-2%. An additional check of the calculations is provided by a comparison with results of the laboratory
NDONFACTORS~,.,.,OFTHE HzO+ MOLECULE
1
2
3
4
8333 0.0928 7739 0.0456 7224 0.00803 6714 0.00171 6324 0.0246 5973 0.0588
9400 0.00522 8652 0.00826 8013 0.0456
10730 0.0322 9767 0.0645 8953 0.0470 8292 0.00860 7616 0.00356 7112 0.0320 6609 0.0542 6166 0.0482 5804 0.0229 5474 0.00242 5176 0.00357 4934 0.0239 4660 0.0450
12430 0.0598 11150 0.0193 10100 0.000675 9218 0.0300 8433 0.0544 7820 0.0325 7216 0.00290 6691 0.00610 6266 6D3lO 5884 0.0451 5541 0.0340 5262 0.0120 4962 0.000120
4357 0.0282 4150 0.0138
( 0.0571 6502 0.0246 6079 0.00200 5702
4623 0.0645 4399 0.0550 1371
1372
N. N. SHEFOV
measurements of the intensities of the (11,0),(11, l), (13,0), (13, l), (15,0), (l&l) bands published by Erman and Brzozowski (1973). From their work the transition probabilities ratios are A,,,o/A,,,, = 0.82; A,,,,/A,,., = 0.30; Ai5,JAi5 i = 0.18. Since A,.,., is proportional to v&.. *qu,“,,, with v,,,.. being a wave number, the data of Table 1 predict that A,,.,/Ai,,, = 0.92, Ai3JAi3,i = 0.31 and A,,,o/A,,,l = 0.14. These values are in good agreement with measured data. Bands observed both in comets (Herzberg, 1976) and in the laboratory are indicated in Table 1 by boxes. They correspond to large q,.,..-values which lie on the Condon parabola. The q,,,,, values allow us to estimate the photon scattering coefficient gv,“,, (Chamberlain, 1978) for the (8,O) 6158 A band. This transition is observed in the red region of comet spectra and of the upper atmosphere spectra. It is predominant in v’ = 8 sequence and reaches about 76%. The absolute value of the transition probability A,,, is about 7.8 x lo5 s-l based on laboratory measurements of life times of various vibrational levels by Erman and Brzozowski (1973). Hence gs.e is 0.060 for the Earth. The brightness of 10 R is due to 2 x lo8 H,O+ molecule number per 1 cm’ column. It can be noted that the (8,O) n subband lines corresponding to the transitions from lower rotational levels of the ground state are not blended by Fraunhofer lines of the solar spectrum which might have distorted intensities of exciting radiation. This g8,0 value is close to a preliminary estimation (Shefov, 1982) and it is several times greater than the value estimated by Krassovsky (1981) on the basis of the emission intensity and H,O+ ion concentrations in the F2 region according to mass spectrometric measurements.
In the case of comets account must be taken of the variation with heliocentric distance r of the solar radiation dilution factor. For instance, for Halley’s comet in the perihelion on 9 February 1986 r is 0.59 a.u. and gs,e is 0.17. Acknowledgement-I
thank Professor V. 1. Krassovsky for his advice and interest in this work. REFERENCES
Chamberlain, J. W. (1978j Theory of Planetary Atmosphere. Academic Press, New York. Chan, S. I. and Stelman, D. (1963) Oscillators perturbed by Gaussian barriers. J. them. Phys. 39, 545. Erman, P. and Brzozowski, J. (1973) Direct measurements of lifetimes of excited levels in H20+. Phys. Lett. 46A, 79. Flygare, W. H. (1978) Molecular Structure and Dynamics. Prentice-Hall, Englewood Cliffs, New Jersey. Herzberg, G. (1976) Cometary spectra and related topics. Me!m.Soc. r. Sci: Liige, 6 ser., 9; 115. Herzberz. G. (1980a) Suectroscouic studies based on the pioneering work ofR. S. Mullikdn. J. phys. Chem. 84,209X Herzberg, G. (1980b) H,O+ ions in the upper atmosphere. Ann. Gt!ophys. 36,605. Krassovsky, V. I. (1981) A cause of appearance of the H,O+ twilight emission in the upper atmosphere. Cosm. Invest., U.S.S.R. 19, 305. Krassovsky, V. I., Semenov, A. I., Sobolev, V. G. and Shefov, N. N. (1981) On the water vapour in the upper atmosphere. Geomagn. Aeron. 21, 373. Lew,H.(1976) ElectronicspectrumofH,O+. Can. 1. Phys. 54, 2028. Shefov, N. N. (1982) On the efficacy of fluorescence of H,O+ ions in the upper atmosphere. Geomagn. Aeron. 22,688. Somorjai, R. L. and Hornig, D. F. (1962) Double-minimum potentials in hydrogen-bonded solids. J. them. Phys. 36, 1980. Volkenstein, M. A., Gribov, L. A., Elyashevich, M. A. and Stepanov, B. 1. (1972) Molecular Vibrations. Nauka, Moscow.
Planer. Spuce SC;., Vol. 31, No. I I, pp. 1371 137% 1983 Prmted inGreat Britain.
FRANK-CONDON
$3.M) +O.oO
PergamonPress Ltd.
FACTORS FOR H,O+ BANDS
MOLECULAR
N. N. SHEFOV Institute of Physics of the Atmosphere, U.S.S.R. Academy of Sciences, Moscow, U.S.S.R. (Receiued 25 January 1983) Abstract-Frank-Condon factors for H,O+ bands have been calculated. They are used to estimate the photon scattering coefficient g8,0 for the (8,O) band at 6158 A.
There are some features of water vapour ions H,O+ in cometary spectra (Herzberg, 1976) and in upper atmospheric spectra (Herzberg, 1980b; Krassovsky et al., 1981). To interpret these it is necessary to know transition probabilities for various bands of the a2AI8’S, system of H,O+. Some data of structure of vibrational levels for upper and lower states were given by Lew (1976) and potential function data have been given by Herzberg (1980). These data lead one to the conclusion that the potential of upper state ‘A, may be satisfactorily approximated by a harmonic oscillator potential. There is a potential barrier for the lower state TABLE
“y,, 5 6 7 8 9 10 11 12 13 14 15 16 17
1. FRANK-C• 0
7458 0.115 6987 0.140 6542 0.146 6158 0.134 5793 0.109 5489 0.0808 5189 0.0544 4924 0.0337 4689 0.0194 4471 0.0104 4272 0.00518 - ___ 4106 0.00244 3921 0.00107
‘B, and the potential function may be presented by a perturbed harmonic oscillator with a Gaussian barrier (Flygare, 1978). Calculations of the Frank-Condon factors r~“,~,,have been made according to the methods described by Chan and Stelman (1963); Somorjai and Hornig (1962); and Volkenstein et al. (1972). The quevfpvalues and the corresponding wavelengths (A) are given in Table 1 below. The sums xqvrvrp equal 1 with an accuracy better than l-2%. An additional check of the calculations is provided by a comparison with results of the laboratory
NDONFACTORS~,.,.,OFTHE HzO+ MOLECULE
1
2
3
4
8333 0.0928 7739 0.0456 7224 0.00803 6714 0.00171 6324 0.0246 5973 0.0588
9400 0.00522 8652 0.00826 8013 0.0456
10730 0.0322 9767 0.0645 8953 0.0470 8292 0.00860 7616 0.00356 7112 0.0320 6609 0.0542 6166 0.0482 5804 0.0229 5474 0.00242 5176 0.00357 4934 0.0239 4660 0.0450
12430 0.0598 11150 0.0193 10100 0.000675 9218 0.0300 8433 0.0544 7820 0.0325 7216 0.00290 6691 0.00610 6266 6D3lO 5884 0.0451 5541 0.0340 5262 0.0120 4962 0.000120
4357 0.0282 4150 0.0138
( 0.0571 6502 0.0246 6079 0.00200 5702
4623 0.0645 4399 0.0550 1371
1372
N. N. SHEFOV
measurements of the intensities of the (11,0),(11, l), (13,0), (13, l), (15,0), (l&l) bands published by Erman and Brzozowski (1973). From their work the transition probabilities ratios are A,,,o/A,,,, = 0.82; A,,,,/A,,., = 0.30; Ai5,JAi5 i = 0.18. Since A,.,., is proportional to v&.. *qu,“,,, with v,,,.. being a wave number, the data of Table 1 predict that A,,.,/Ai,,, = 0.92, Ai3JAi3,i = 0.31 and A,,,o/A,,,l = 0.14. These values are in good agreement with measured data. Bands observed both in comets (Herzberg, 1976) and in the laboratory are indicated in Table 1 by boxes. They correspond to large q,.,..-values which lie on the Condon parabola. The q,,,,, values allow us to estimate the photon scattering coefficient gv,“,, (Chamberlain, 1978) for the (8,O) 6158 A band. This transition is observed in the red region of comet spectra and of the upper atmosphere spectra. It is predominant in v’ = 8 sequence and reaches about 76%. The absolute value of the transition probability A,,, is about 7.8 x lo5 s-l based on laboratory measurements of life times of various vibrational levels by Erman and Brzozowski (1973). Hence gs.e is 0.060 for the Earth. The brightness of 10 R is due to 2 x lo8 H,O+ molecule number per 1 cm’ column. It can be noted that the (8,O) n subband lines corresponding to the transitions from lower rotational levels of the ground state are not blended by Fraunhofer lines of the solar spectrum which might have distorted intensities of exciting radiation. This g8,0 value is close to a preliminary estimation (Shefov, 1982) and it is several times greater than the value estimated by Krassovsky (1981) on the basis of the emission intensity and H,O+ ion concentrations in the F2 region according to mass spectrometric measurements.
In the case of comets account must be taken of the variation with heliocentric distance r of the solar radiation dilution factor. For instance, for Halley’s comet in the perihelion on 9 February 1986 r is 0.59 a.u. and gs,e is 0.17. Acknowledgement-I
thank Professor V. 1. Krassovsky for his advice and interest in this work. REFERENCES
Chamberlain, J. W. (1978j Theory of Planetary Atmosphere. Academic Press, New York. Chan, S. I. and Stelman, D. (1963) Oscillators perturbed by Gaussian barriers. J. them. Phys. 39, 545. Erman, P. and Brzozowski, J. (1973) Direct measurements of lifetimes of excited levels in H20+. Phys. Lett. 46A, 79. Flygare, W. H. (1978) Molecular Structure and Dynamics. Prentice-Hall, Englewood Cliffs, New Jersey. Herzberg, G. (1976) Cometary spectra and related topics. Me!m.Soc. r. Sci: Liige, 6 ser., 9; 115. Herzberz. G. (1980a) Suectroscouic studies based on the pioneering work ofR. S. Mullikdn. J. phys. Chem. 84,209X Herzberg, G. (1980b) H,O+ ions in the upper atmosphere. Ann. Gt!ophys. 36,605. Krassovsky, V. I. (1981) A cause of appearance of the H,O+ twilight emission in the upper atmosphere. Cosm. Invest., U.S.S.R. 19, 305. Krassovsky, V. I., Semenov, A. I., Sobolev, V. G. and Shefov, N. N. (1981) On the water vapour in the upper atmosphere. Geomagn. Aeron. 21, 373. Lew,H.(1976) ElectronicspectrumofH,O+. Can. 1. Phys. 54, 2028. Shefov, N. N. (1982) On the efficacy of fluorescence of H,O+ ions in the upper atmosphere. Geomagn. Aeron. 22,688. Somorjai, R. L. and Hornig, D. F. (1962) Double-minimum potentials in hydrogen-bonded solids. J. them. Phys. 36, 1980. Volkenstein, M. A., Gribov, L. A., Elyashevich, M. A. and Stepanov, B. 1. (1972) Molecular Vibrations. Nauka, Moscow.