Abstract

We measured at 296 K the rotational line strengths and pressure-broadening coefficients for the 1.27-μm, a 1ΔgX 3Σg -, v = 0–0 band of O2 with a Fourier transform infrared spectrometer using an optical path length of 84 m, a spectral resolution of 0.01 cm-1, and sample pressures between 13 and 104 kPa. The integrated band strength is 7.79(17) × 10-6 m-2 Pa-1 [7.89(17) × 10-5 cm-2 atm-1], and the Einstein A coefficient for spontaneous emission is 2.237(51) × 10-4 s-1, which corresponds to an upper-state 1/e lifetime of 1.24(3) h. The pressure-broadening coefficients decrease with increasing N and range from 19 to 38 MHz/kPa (FWHM). The mean value for the transitions studied is 30.3(21) MHz/kPa [0.1024(71) cm-1/atm] (FWHM). The Einstein A coefficient determined here is in good agreement with the widely accepted value of 2.58 × 10-4 s-1 initially obtained by Badger et al. [J. Chem. Phys. 43, 4345 (1965)] more than 30 years ago. The standard uncertainties given above are one standard deviation.

© 1998 Optical Society of America

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  1. L. Herzberg, G. Herzberg, “Fine structure of the infrared atmospheric oxygen bands,” Astrophys. J. 105, 353–359 (1947).
    [CrossRef]
  2. R. P. Lowe, “Interferometric spectra of the Earth’s airglow (1.2 to 1.6-μm),” Philos. Trans. R. Soc. London Ser. A 264, 163–169 (1969).
    [CrossRef]
  3. R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
    [CrossRef]
  4. J. M. Russell, M. G. Mlynczak, L. L. Gordley, “Overview of the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) experiment for the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) mission,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, pp. 406–414 (1994).
    [CrossRef]
  5. W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
    [CrossRef]
  6. M. G. Mlynczak, B. T. Marshall, “A reexamination of the role of the solar heating in the O2 atmospheric and infrared atmospheric bands,” Geophys. Res. Lett. 23, 657–660 (1996).
    [CrossRef]
  7. M. G. Mlynczak, D. S. Olander, “On the utility of the molecular oxygen dayglow emissions as proxies for middle atmospheric ozone,” Geophys. Res. Lett. 22, 1377–1380 (1995).
    [CrossRef]
  8. M. G. Mlynczak, D. J. Nesbitt, “The Einstein coefficient for spontaneous emission of the O2 (a1Δg) state,” Geophys. Res. Lett. 22, 1381–1384 (1995).
    [CrossRef]
  9. R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
    [CrossRef]
  10. Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).
  11. L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
    [CrossRef]
  12. W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
    [CrossRef]
  13. R. R. Gamache, A. Goldman, L. S. Rothman, “Improved spectral parameters for the three most abundant isotopomers of the oxygen molecule,” J. Quant. Spectrosc. Radiat. Transfer (to be published).
  14. C. Amiot, J. Verges, “The magnetic dipole a1Δg(v′ = 0)–X3Σg- transition in the oxygen afterglow,” Can. J. Phys. 59, 1391–1398 (1981).
    [CrossRef]
  15. Y. Endo, M. Mizushima, “Microwave resonance lines of 16O2 in its electronic ground state (X3Σg-),” Jpn. J. Appl. Phys. 21, L379–L380 (1982).
    [CrossRef]
  16. K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
    [CrossRef]
  17. G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
    [CrossRef]
  18. 1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.
  19. L. Wallace, W. Livingston, “Spectroscopic observations of atmospheric trace gases over Kitt Peak: 1. Carbon dioxide and methane from 1979 to 1985,” J. Geophys. Res. 95, 9823–9827 (1990).
    [CrossRef]
  20. D. C. Tobin, L. L. Strow, W. J. Lafferty, W. B. Olson, “Experimental investigation of the self- and N2-broadened continuum within the ν2 band of water vapor,” Appl. Opt. 35, 4724–4734 (1996).
    [CrossRef] [PubMed]
  21. E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
    [CrossRef]
  22. E. E. Whiting, R. W. Nicholls, “Reinvestigation of rotational-line intensity factors in diatomic spectra,” Astrophys. J. Suppl. No. 235 27, 1–19 (1974).
    [CrossRef]
  23. T. K. Balasubramanian, V. P. Bellary, “Intensity distribution in the rotational structure of 1Δ–3Σ and 1Π–3Σ transitions in diatomic molecules,” J. Mol. Spectrosc. 63, 249–255 (1988).
  24. V. P. Bellary, T. K. Balasubramanian, “On the rotational intensity distribution in the a1Δg → X3Σg- magnetic dipole transition of oxygen molecule,” J. Mol. Spectrosc. 126, 436–442 (1987).
    [CrossRef]
  25. G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950), p. 21.
  26. R. L. Gattinger, A. Vallance Jones, “Observation and interpretation of O2 1.27-μ emission enhancements in aurora,” J. Geophy. Res. 78, 8305–8313 (1973).
    [CrossRef]
  27. W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
    [CrossRef]

1996 (3)

M. G. Mlynczak, B. T. Marshall, “A reexamination of the role of the solar heating in the O2 atmospheric and infrared atmospheric bands,” Geophys. Res. Lett. 23, 657–660 (1996).
[CrossRef]

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

D. C. Tobin, L. L. Strow, W. J. Lafferty, W. B. Olson, “Experimental investigation of the self- and N2-broadened continuum within the ν2 band of water vapor,” Appl. Opt. 35, 4724–4734 (1996).
[CrossRef] [PubMed]

1995 (2)

M. G. Mlynczak, D. S. Olander, “On the utility of the molecular oxygen dayglow emissions as proxies for middle atmospheric ozone,” Geophys. Res. Lett. 22, 1377–1380 (1995).
[CrossRef]

M. G. Mlynczak, D. J. Nesbitt, “The Einstein coefficient for spontaneous emission of the O2 (a1Δg) state,” Geophys. Res. Lett. 22, 1381–1384 (1995).
[CrossRef]

1992 (2)

Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

1990 (1)

L. Wallace, W. Livingston, “Spectroscopic observations of atmospheric trace gases over Kitt Peak: 1. Carbon dioxide and methane from 1979 to 1985,” J. Geophys. Res. 95, 9823–9827 (1990).
[CrossRef]

1988 (2)

L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
[CrossRef]

T. K. Balasubramanian, V. P. Bellary, “Intensity distribution in the rotational structure of 1Δ–3Σ and 1Π–3Σ transitions in diatomic molecules,” J. Mol. Spectrosc. 63, 249–255 (1988).

1987 (1)

V. P. Bellary, T. K. Balasubramanian, “On the rotational intensity distribution in the a1Δg → X3Σg- magnetic dipole transition of oxygen molecule,” J. Mol. Spectrosc. 126, 436–442 (1987).
[CrossRef]

1985 (1)

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

1984 (1)

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

1982 (1)

Y. Endo, M. Mizushima, “Microwave resonance lines of 16O2 in its electronic ground state (X3Σg-),” Jpn. J. Appl. Phys. 21, L379–L380 (1982).
[CrossRef]

1981 (1)

C. Amiot, J. Verges, “The magnetic dipole a1Δg(v′ = 0)–X3Σg- transition in the oxygen afterglow,” Can. J. Phys. 59, 1391–1398 (1981).
[CrossRef]

1980 (1)

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

1979 (1)

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

1974 (1)

E. E. Whiting, R. W. Nicholls, “Reinvestigation of rotational-line intensity factors in diatomic spectra,” Astrophys. J. Suppl. No. 235 27, 1–19 (1974).
[CrossRef]

1973 (1)

R. L. Gattinger, A. Vallance Jones, “Observation and interpretation of O2 1.27-μ emission enhancements in aurora,” J. Geophy. Res. 78, 8305–8313 (1973).
[CrossRef]

1970 (1)

W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
[CrossRef]

1969 (1)

R. P. Lowe, “Interferometric spectra of the Earth’s airglow (1.2 to 1.6-μm),” Philos. Trans. R. Soc. London Ser. A 264, 163–169 (1969).
[CrossRef]

1965 (1)

R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
[CrossRef]

1947 (1)

L. Herzberg, G. Herzberg, “Fine structure of the infrared atmospheric oxygen bands,” Astrophys. J. 105, 353–359 (1947).
[CrossRef]

Amiot, C.

C. Amiot, J. Verges, “The magnetic dipole a1Δg(v′ = 0)–X3Σg- transition in the oxygen afterglow,” Can. J. Phys. 59, 1391–1398 (1981).
[CrossRef]

Badger, R. M.

R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
[CrossRef]

Baker, D. J.

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

Balasubramanian, T. K.

T. K. Balasubramanian, V. P. Bellary, “Intensity distribution in the rotational structure of 1Δ–3Σ and 1Π–3Σ transitions in diatomic molecules,” J. Mol. Spectrosc. 63, 249–255 (1988).

V. P. Bellary, T. K. Balasubramanian, “On the rotational intensity distribution in the a1Δg → X3Σg- magnetic dipole transition of oxygen molecule,” J. Mol. Spectrosc. 126, 436–442 (1987).
[CrossRef]

Barth, C. A.

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

Bellary, V. P.

T. K. Balasubramanian, V. P. Bellary, “Intensity distribution in the rotational structure of 1Δ–3Σ and 1Π–3Σ transitions in diatomic molecules,” J. Mol. Spectrosc. 63, 249–255 (1988).

V. P. Bellary, T. K. Balasubramanian, “On the rotational intensity distribution in the a1Δg → X3Σg- magnetic dipole transition of oxygen molecule,” J. Mol. Spectrosc. 126, 436–442 (1987).
[CrossRef]

Benner, D. C.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Berger, H.

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

Brown, L. R.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Camy-Peyret, C.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Carleton, N. P.

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

Chiu, C. C. W.

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

Cohen, E. A.

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

Connes, P.

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

Endo, Y.

Y. Endo, M. Mizushima, “Microwave resonance lines of 16O2 in its electronic ground state (X3Σg-),” Jpn. J. Appl. Phys. 21, L379–L380 (1982).
[CrossRef]

Evans, W. F. J.

W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
[CrossRef]

Flaud, J.-M.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Gamache, R. R.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

R. R. Gamache, A. Goldman, L. S. Rothman, “Improved spectral parameters for the three most abundant isotopomers of the oxygen molecule,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Gattinger, R. L.

R. L. Gattinger, A. Vallance Jones, “Observation and interpretation of O2 1.27-μ emission enhancements in aurora,” J. Geophy. Res. 78, 8305–8313 (1973).
[CrossRef]

Goldman, A.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

R. R. Gamache, A. Goldman, L. S. Rothman, “Improved spectral parameters for the three most abundant isotopomers of the oxygen molecule,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Gordley, L. L.

J. M. Russell, M. G. Mlynczak, L. L. Gordley, “Overview of the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) experiment for the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) mission,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, pp. 406–414 (1994).
[CrossRef]

Herzberg, G.

L. Herzberg, G. Herzberg, “Fine structure of the infrared atmospheric oxygen bands,” Astrophys. J. 105, 353–359 (1947).
[CrossRef]

G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950), p. 21.

Herzberg, L.

L. Herzberg, G. Herzberg, “Fine structure of the infrared atmospheric oxygen bands,” Astrophys. J. 105, 353–359 (1947).
[CrossRef]

Hillig, K. W.

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

Hougen, J. T.

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

Hsu, Y. T.

Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).

Lafferty, W. J.

Lee, Y. P.

Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).

Lee, Y.-P.

L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
[CrossRef]

Lin, L.-B.

L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
[CrossRef]

Livingston, W.

L. Wallace, W. Livingston, “Spectroscopic observations of atmospheric trace gases over Kitt Peak: 1. Carbon dioxide and methane from 1979 to 1985,” J. Geophys. Res. 95, 9823–9827 (1990).
[CrossRef]

Llewellyn, E. J.

W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
[CrossRef]

Lowe, R. P.

R. P. Lowe, “Interferometric spectra of the Earth’s airglow (1.2 to 1.6-μm),” Philos. Trans. R. Soc. London Ser. A 264, 163–169 (1969).
[CrossRef]

Malathy Devi, V.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Marshall, B. T.

M. G. Mlynczak, B. T. Marshall, “A reexamination of the role of the solar heating in the O2 atmospheric and infrared atmospheric bands,” Geophys. Res. Lett. 23, 657–660 (1996).
[CrossRef]

Massie, S. T.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Millot, G.

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

Mizushima, M.

Y. Endo, M. Mizushima, “Microwave resonance lines of 16O2 in its electronic ground state (X3Σg-),” Jpn. J. Appl. Phys. 21, L379–L380 (1982).
[CrossRef]

Mlynczak, M. G.

M. G. Mlynczak, B. T. Marshall, “A reexamination of the role of the solar heating in the O2 atmospheric and infrared atmospheric bands,” Geophys. Res. Lett. 23, 657–660 (1996).
[CrossRef]

M. G. Mlynczak, D. S. Olander, “On the utility of the molecular oxygen dayglow emissions as proxies for middle atmospheric ozone,” Geophys. Res. Lett. 22, 1377–1380 (1995).
[CrossRef]

M. G. Mlynczak, D. J. Nesbitt, “The Einstein coefficient for spontaneous emission of the O2 (a1Δg) state,” Geophys. Res. Lett. 22, 1381–1384 (1995).
[CrossRef]

J. M. Russell, M. G. Mlynczak, L. L. Gordley, “Overview of the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) experiment for the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) mission,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, pp. 406–414 (1994).
[CrossRef]

Nesbitt, D. J.

M. G. Mlynczak, D. J. Nesbitt, “The Einstein coefficient for spontaneous emission of the O2 (a1Δg) state,” Geophys. Res. Lett. 22, 1381–1384 (1995).
[CrossRef]

Nicholls, R. W.

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

E. E. Whiting, R. W. Nicholls, “Reinvestigation of rotational-line intensity factors in diatomic spectra,” Astrophys. J. Suppl. No. 235 27, 1–19 (1974).
[CrossRef]

Noxon, J. F.

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

O’Neil, R. R.

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

Ogilvie, J. F.

Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).

L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
[CrossRef]

Olander, D. S.

M. G. Mlynczak, D. S. Olander, “On the utility of the molecular oxygen dayglow emissions as proxies for middle atmospheric ozone,” Geophys. Res. Lett. 22, 1377–1380 (1995).
[CrossRef]

Olson, W. B.

Pendleton, W. R.

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

Perrin, A.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Read, W. G.

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

Reese, R. J.

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

Rinsland, C. P.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Rothman, L. S.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

R. R. Gamache, A. Goldman, L. S. Rothman, “Improved spectral parameters for the three most abundant isotopomers of the oxygen molecule,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

Rouillé, G.

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

Rusch, D. W.

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

Russell, J. M.

J. M. Russell, M. G. Mlynczak, L. L. Gordley, “Overview of the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) experiment for the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) mission,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, pp. 406–414 (1994).
[CrossRef]

Saint-Loup, R.

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

Sanders, R. W.

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

Schadee, A.

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

Smith, M. A. H.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Strow, L. L.

Tatum, J. B.

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

Thomas, R. J.

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

Tipping, R. H.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Tobin, D. C.

Toth, R. A.

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

Traub, W. A.

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

Vallance Jones, A.

R. L. Gattinger, A. Vallance Jones, “Observation and interpretation of O2 1.27-μ emission enhancements in aurora,” J. Geophy. Res. 78, 8305–8313 (1973).
[CrossRef]

Verges, J.

C. Amiot, J. Verges, “The magnetic dipole a1Δg(v′ = 0)–X3Σg- transition in the oxygen afterglow,” Can. J. Phys. 59, 1391–1398 (1981).
[CrossRef]

Wallace, L.

L. Wallace, W. Livingston, “Spectroscopic observations of atmospheric trace gases over Kitt Peak: 1. Carbon dioxide and methane from 1979 to 1985,” J. Geophys. Res. 95, 9823–9827 (1990).
[CrossRef]

Whiting, E. E.

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

E. E. Whiting, R. W. Nicholls, “Reinvestigation of rotational-line intensity factors in diatomic spectra,” Astrophys. J. Suppl. No. 235 27, 1–19 (1974).
[CrossRef]

Whitlock, R. F.

R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
[CrossRef]

Wood, H. C.

W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
[CrossRef]

Wright, A. C.

R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (2)

L. Herzberg, G. Herzberg, “Fine structure of the infrared atmospheric oxygen bands,” Astrophys. J. 105, 353–359 (1947).
[CrossRef]

W. A. Traub, N. P. Carleton, P. Connes, J. F. Noxon, “The latitude variation of O2 dayglow and O2 abundance on Mars,” Astrophys. J. 229, 846–850 (1979).
[CrossRef]

Astrophys. J. Suppl. No. 235 (1)

E. E. Whiting, R. W. Nicholls, “Reinvestigation of rotational-line intensity factors in diatomic spectra,” Astrophys. J. Suppl. No. 235 27, 1–19 (1974).
[CrossRef]

Can. J. Phys. (1)

C. Amiot, J. Verges, “The magnetic dipole a1Δg(v′ = 0)–X3Σg- transition in the oxygen afterglow,” Can. J. Phys. 59, 1391–1398 (1981).
[CrossRef]

Geophys. Res. Lett. (4)

W. R. Pendleton, D. J. Baker, R. J. Reese, R. R. O’Neil, “Decay of O2(a1Δg) in the evening twilight airglow: implications for the radiative lifetime,” Geophys. Res. Lett. 23, 1013–1016 (1996).
[CrossRef]

M. G. Mlynczak, B. T. Marshall, “A reexamination of the role of the solar heating in the O2 atmospheric and infrared atmospheric bands,” Geophys. Res. Lett. 23, 657–660 (1996).
[CrossRef]

M. G. Mlynczak, D. S. Olander, “On the utility of the molecular oxygen dayglow emissions as proxies for middle atmospheric ozone,” Geophys. Res. Lett. 22, 1377–1380 (1995).
[CrossRef]

M. G. Mlynczak, D. J. Nesbitt, “The Einstein coefficient for spontaneous emission of the O2 (a1Δg) state,” Geophys. Res. Lett. 22, 1381–1384 (1995).
[CrossRef]

J. Chem. Phys. (1)

R. M. Badger, A. C. Wright, R. F. Whitlock, “Absolute intensities of the discrete and continuous absorption bands of oxygen gas at 1.26 and 1.065 μ and the radiative lifetime of the 1Δg state of oxygen,” J. Chem. Phys. 43, 4345–4350 (1965).
[CrossRef]

J. Geophy. Res. (1)

R. L. Gattinger, A. Vallance Jones, “Observation and interpretation of O2 1.27-μ emission enhancements in aurora,” J. Geophy. Res. 78, 8305–8313 (1973).
[CrossRef]

J. Geophys. Res. (2)

R. J. Thomas, C. A. Barth, D. W. Rusch, R. W. Sanders, “Solar mesosphere explorer near-infrared spectrometer: measurements of the 1.27-μm radiances and the inference of mesospheric ozone,” J. Geophys. Res. 89, 9569–9580 (1984).
[CrossRef]

L. Wallace, W. Livingston, “Spectroscopic observations of atmospheric trace gases over Kitt Peak: 1. Carbon dioxide and methane from 1979 to 1985,” J. Geophys. Res. 95, 9823–9827 (1990).
[CrossRef]

J. Mol. Spectrosc. (5)

E. E. Whiting, A. Schadee, J. B. Tatum, J. T. Hougen, R. W. Nicholls, “Recommended conventions for defining transition moments and intensity factors in diatomic molecular spectra,” J. Mol. Spectrosc. 80, 249–256 (1980).
[CrossRef]

K. W. Hillig, C. C. W. Chiu, W. G. Read, E. A. Cohen, “The pure rotation spectrum of a1Δg O2,” J. Mol. Spectrosc. 109, 205–206 (1985).
[CrossRef]

G. Rouillé, G. Millot, R. Saint-Loup, H. Berger, “High-resolution stimulated Raman spectroscopy of O2,” J. Mol. Spectrosc. 154, 372–382 (1992).
[CrossRef]

T. K. Balasubramanian, V. P. Bellary, “Intensity distribution in the rotational structure of 1Δ–3Σ and 1Π–3Σ transitions in diatomic molecules,” J. Mol. Spectrosc. 63, 249–255 (1988).

V. P. Bellary, T. K. Balasubramanian, “On the rotational intensity distribution in the a1Δg → X3Σg- magnetic dipole transition of oxygen molecule,” J. Mol. Spectrosc. 126, 436–442 (1987).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

L.-B. Lin, Y.-P. Lee, J. F. Ogilvie, “Linestrengths of the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2,” J. Quant. Spectrosc. Radiat. Transfer 5, 375–380 (1988).
[CrossRef]

Jpn. J. Appl. Phys. (1)

Y. Endo, M. Mizushima, “Microwave resonance lines of 16O2 in its electronic ground state (X3Σg-),” Jpn. J. Appl. Phys. 21, L379–L380 (1982).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A (1)

R. P. Lowe, “Interferometric spectra of the Earth’s airglow (1.2 to 1.6-μm),” Philos. Trans. R. Soc. London Ser. A 264, 163–169 (1969).
[CrossRef]

Planet. Space Sci. (1)

W. F. J. Evans, H. C. Wood, E. J. Llewellyn, “Ground-based photometric observations of the 1.27 μ band of O2 in the twilight airglow,” Planet. Space Sci. 18, 1065–1073 (1970).
[CrossRef]

Spectrochim. Acta (1)

Y. T. Hsu, Y. P. Lee, J. F. Ogilvie, “Intensities of lines in the band a1Δg(v′ = 0)–X3Σg-(v″ = 0) of 16O2 in absorption,” Spectrochim. Acta 9, 1227–1230 (1992).

Other (4)

J. M. Russell, M. G. Mlynczak, L. L. Gordley, “Overview of the Sounding of the Atmosphere Using Broadband Emission Radiometry (SABER) experiment for the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) mission,” in Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research, J. Wang, P. B. Hays, eds., Proc. SPIE2266, pp. 406–414 (1994).
[CrossRef]

R. R. Gamache, A. Goldman, L. S. Rothman, “Improved spectral parameters for the three most abundant isotopomers of the oxygen molecule,” J. Quant. Spectrosc. Radiat. Transfer (to be published).

1996 version of the HITRAN database described in L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth , “The HITRAN molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transfer48, 469–507 (1992).A CDROM version of the 1996 database is available from L. S. Rothman, Harvard Observatory, P-248, Harvard University, Cambridge, Mass. 02138.

G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950), p. 21.

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Figures (3)

Fig. 1
Fig. 1

Fourier transform infrared spectrum of the 1.27-μm (7882-cm-1) a 1Δ g X 3Σ g -, v = 0–0 band of O2. A logarithm base-e absorbance scale is used. We recorded the spectrum at 0.01-cm-1 resolution using a path length of 84.05 m, a sample pressure of 13.34 kPa, and a sample temperature of 296 K. The region near the q Q branch is expanded in the insert.

Fig. 2
Fig. 2

Fourier transform infrared spectrum of the 1.27-μm (7882-cm-1) a 1Δ g X 3Σ g -, v = 0–0 band of O2. The conditions are the same as those in Fig. 1 except for the sample pressure, which is 104.3 kPa. The small offset in the baseline is attributed to the collision-induced absorption continuum.

Fig. 3
Fig. 3

(a) Observed and (b) calculated spectra in the Q-branch region of the a 1Δ g X 3Σ g -, v = 0–0 band of O2. A logarithm base-e absorbance scale is used. The experimental spectrum is the same as that in Fig. 2. The simulation uses a Voigt line-shape profile with an N-dependent Lorentzian linewidth, as described in the text; a Gaussian Doppler FWHM of 0.01718 (ν/ν 0) cm-1 for ν 0 = 7883.8 cm-1, and an integrated band strength of 7.75 × 10-6 m-2 Pa-1 for a path length of 84.05 cm and a pressure of 104.3 kPa.

Tables (1)

Tables Icon

Table 1 Rotational Line Strengths, Integrated Band Intensities, and Self-Pressure-Broadening Widths for the a1Δ g X3Σ g - Band of O2 at 296 K a,b

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

  α ν d ν = 2 π 2 3 0 hc 1 2 J j + 1   f j n ν ij S ij ,
f j = C isotopic Q v Q rot 2 J j + 1 exp - E j / kT ,
S ij = μ 2 q ν ν L ij ,
A = 1 4 π 0 64 π 4 ν 0 3 h μ 2 q vv ,
Γ = Γ 0 + Δ Γ N N + 1 + J J + 1 - 4 / 2 ,

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