Abstract

The collision-induced absorption fundamental band of N2 has been investigated in the 2100–2600 cm−1 spectral region. Laboratory measurements have been undertaken over the temperature range 193–297 K. Binary-absorption coefficients for N2 absorption induced by collisions with N2 and O2 are reported and compared with N2 temperature-dependent continua from atmospheric measurements.

© 1993 Optical Society of America

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References

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  1. L. S. Bernstein, D. C. Robertson, J. A. Conant, B. P. Sandford, “Measured and predicted atmospheric transmission in the 4.0–5.3-mm region, and the contribution of continuum absorption by CO2 and N2,” Appl. Opt. 18, 2454–2464 (1979).
    [CrossRef] [PubMed]
  2. C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
    [CrossRef]
  3. S. P. Reddy, C. W. Cho, “Induced infrared absorption of nitrogen and nitrogen–foreign gas mixtures,” Can. J. Phys. 43, 2331–2342 (1965).
    [CrossRef]
  4. M. M. Shapiro, H. P. Gush, “The collision induced fundamental and first overtone bands of O2 and N2,” Can. J. Phys. 44, 949–963 (1966).
    [CrossRef]
  5. D. T. Sheng, G. E. Ewing, “Collision induced infrared absorption of gaseous N2 at low temperatures,” J. Chem. Phys. 55, 5425–5430 (1971).
    [CrossRef]
  6. D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Investigation of the absorption of IR radiation by atmospheric gases: water, nitrogen, nitrous oxide,” Rep. AFCRL-71-0124 (U.S. Air Force Cambridge Research Laboratory, Hanscom Air Force Base, Mass., 1971).
  7. V. I. Dianov-Klokov, I. P. Malkov, “Absorption near 4.3 μm in the Earth’s atmosphere by the N2–N2 and N2–O2 complexes,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 411–414 (1973).
  8. N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).
  9. M. E. Thomas, M. J. Linevsky, “Integrated intensities of N2, CO2, and SF6 vibrational bands from 1800 to 5000 cm−1 as a function of density and temperature,” J. Quant. Spectrosc. Radiat. Transfer 42, 465–470 (1989).
    [CrossRef]
  10. P. L. Roney, F. Reid, J. M. Theriault, “Transmission window near 2400 cm−1: an experimental and modeling study,” Appl. Opt. 30, 1995–2004 (1991).
    [CrossRef] [PubMed]
  11. F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.
  12. S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.
  13. R. Le Doucen, C. Cousin, V. Menoux, “Carbon furnace infrared source,” J. Phys. E 17, 1107 (1984).
    [CrossRef]
  14. R. Le Doucen, V. Menoux, M. Larvor, C. Haeusler, “Réalisation d’un spectromètre infrarouge de résolution moyenne, corrié de la coma,” Appl. Opt. 19, 3110–3112 (1980).
    [CrossRef]
  15. R. Le Doucen, J. P. Houdeau, C. Cousin, V. Menoux, “Variable path-length, low temperature cells for absorption spectroscopy,” J. Phys. E 18, 199–200 (1985).
    [CrossRef]
  16. R. Le Doucen, C. Cousin, C. Boulet, A. Henry, “Temperature dependence of the absorption in the region beyond the 4.3-μm band head of CO2–1: pure CO2 case,” Appl. Opt. 24, 897–906 (1985).
    [CrossRef] [PubMed]
  17. R. Le Doucen, C. Cousin, C. Boulet, A. Henry, “Temperature dependence of the absorption in the region beyond the 4.3-μm band head of CO2–2: N2 and O2 broadening,” Appl. Opt. 24, 3899–3907 (1985).
    [CrossRef] [PubMed]
  18. J. Susskind, J. E. Searl, “Synthetic atmospheric transmittance spectra near 15 and 4.3 μm,” J. Quant. Spectrosc. Radiat. Transfer 19, 195–215 (1978).
    [CrossRef]
  19. J. M. Theriault, P. L. Roney, F. Reid, “Atmospheric transmission in the 2.8–5.5 μm region: description of the Fourier interferometric transmissionmeter and typical results at low temperature,” Appl. Opt. 29, 3654–3666 (1990).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

1989 (2)

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

M. E. Thomas, M. J. Linevsky, “Integrated intensities of N2, CO2, and SF6 vibrational bands from 1800 to 5000 cm−1 as a function of density and temperature,” J. Quant. Spectrosc. Radiat. Transfer 42, 465–470 (1989).
[CrossRef]

1985 (3)

1984 (1)

R. Le Doucen, C. Cousin, V. Menoux, “Carbon furnace infrared source,” J. Phys. E 17, 1107 (1984).
[CrossRef]

1980 (1)

1979 (2)

L. S. Bernstein, D. C. Robertson, J. A. Conant, B. P. Sandford, “Measured and predicted atmospheric transmission in the 4.0–5.3-mm region, and the contribution of continuum absorption by CO2 and N2,” Appl. Opt. 18, 2454–2464 (1979).
[CrossRef] [PubMed]

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

1978 (1)

J. Susskind, J. E. Searl, “Synthetic atmospheric transmittance spectra near 15 and 4.3 μm,” J. Quant. Spectrosc. Radiat. Transfer 19, 195–215 (1978).
[CrossRef]

1973 (1)

V. I. Dianov-Klokov, I. P. Malkov, “Absorption near 4.3 μm in the Earth’s atmosphere by the N2–N2 and N2–O2 complexes,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 411–414 (1973).

1971 (1)

D. T. Sheng, G. E. Ewing, “Collision induced infrared absorption of gaseous N2 at low temperatures,” J. Chem. Phys. 55, 5425–5430 (1971).
[CrossRef]

1966 (1)

M. M. Shapiro, H. P. Gush, “The collision induced fundamental and first overtone bands of O2 and N2,” Can. J. Phys. 44, 949–963 (1966).
[CrossRef]

1965 (1)

S. P. Reddy, C. W. Cho, “Induced infrared absorption of nitrogen and nitrogen–foreign gas mixtures,” Can. J. Phys. 43, 2331–2342 (1965).
[CrossRef]

Abren, L. W.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

Anderson, G. P.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.

Bernstein, L. S.

Boulet, C.

Burch, D. E.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Investigation of the absorption of IR radiation by atmospheric gases: water, nitrogen, nitrous oxide,” Rep. AFCRL-71-0124 (U.S. Air Force Cambridge Research Laboratory, Hanscom Air Force Base, Mass., 1971).

Chetwynd, J. H.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

Cho, C. W.

S. P. Reddy, C. W. Cho, “Induced infrared absorption of nitrogen and nitrogen–foreign gas mixtures,” Can. J. Phys. 43, 2331–2342 (1965).
[CrossRef]

Clough, S. A.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.

Conant, J. A.

Cousin, C.

Dianov-Klokov, V. I.

V. I. Dianov-Klokov, I. P. Malkov, “Absorption near 4.3 μm in the Earth’s atmosphere by the N2–N2 and N2–O2 complexes,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 411–414 (1973).

Ewing, G. E.

D. T. Sheng, G. E. Ewing, “Collision induced infrared absorption of gaseous N2 at low temperatures,” J. Chem. Phys. 55, 5425–5430 (1971).
[CrossRef]

Farmer, C. B.

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

Gallery, W. O.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

Gryvnak, D. A.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Investigation of the absorption of IR radiation by atmospheric gases: water, nitrogen, nitrous oxide,” Rep. AFCRL-71-0124 (U.S. Air Force Cambridge Research Laboratory, Hanscom Air Force Base, Mass., 1971).

Gush, H. P.

M. M. Shapiro, H. P. Gush, “The collision induced fundamental and first overtone bands of O2 and N2,” Can. J. Phys. 44, 949–963 (1966).
[CrossRef]

Haeusler, C.

Henry, A.

Houdeau, J. P.

R. Le Doucen, J. P. Houdeau, C. Cousin, V. Menoux, “Variable path-length, low temperature cells for absorption spectroscopy,” J. Phys. E 18, 199–200 (1985).
[CrossRef]

Ilin, Y. A.

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

Kncizys, H. X.

S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.

Kneizys, F. X.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

Larvor, M.

Le Doucen, R.

Linevsky, M. J.

M. E. Thomas, M. J. Linevsky, “Integrated intensities of N2, CO2, and SF6 vibrational bands from 1800 to 5000 cm−1 as a function of density and temperature,” J. Quant. Spectrosc. Radiat. Transfer 42, 465–470 (1989).
[CrossRef]

Malkov, I. P.

V. I. Dianov-Klokov, I. P. Malkov, “Absorption near 4.3 μm in the Earth’s atmosphere by the N2–N2 and N2–O2 complexes,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 411–414 (1973).

Menoux, V.

R. Le Doucen, J. P. Houdeau, C. Cousin, V. Menoux, “Variable path-length, low temperature cells for absorption spectroscopy,” J. Phys. E 18, 199–200 (1985).
[CrossRef]

R. Le Doucen, C. Cousin, V. Menoux, “Carbon furnace infrared source,” J. Phys. E 17, 1107 (1984).
[CrossRef]

R. Le Doucen, V. Menoux, M. Larvor, C. Haeusler, “Réalisation d’un spectromètre infrarouge de résolution moyenne, corrié de la coma,” Appl. Opt. 19, 3110–3112 (1980).
[CrossRef]

Moskalenko, N. I.

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

Namkung, J. S.

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

Norton, R. H.

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

Parzhin, S. N.

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

Pembrook, J. D.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Investigation of the absorption of IR radiation by atmospheric gases: water, nitrogen, nitrous oxide,” Rep. AFCRL-71-0124 (U.S. Air Force Cambridge Research Laboratory, Hanscom Air Force Base, Mass., 1971).

Reddy, S. P.

S. P. Reddy, C. W. Cho, “Induced infrared absorption of nitrogen and nitrogen–foreign gas mixtures,” Can. J. Phys. 43, 2331–2342 (1965).
[CrossRef]

Reid, F.

Rinsland, C. P.

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

Robertson, D. C.

Rodionov, L. V.

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

Roney, P. L.

Sandford, B. P.

Searl, J. E.

J. Susskind, J. E. Searl, “Synthetic atmospheric transmittance spectra near 15 and 4.3 μm,” J. Quant. Spectrosc. Radiat. Transfer 19, 195–215 (1978).
[CrossRef]

Selby, J. E. A.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

Shapiro, M. M.

M. M. Shapiro, H. P. Gush, “The collision induced fundamental and first overtone bands of O2 and N2,” Can. J. Phys. 44, 949–963 (1966).
[CrossRef]

Sheng, D. T.

D. T. Sheng, G. E. Ewing, “Collision induced infrared absorption of gaseous N2 at low temperatures,” J. Chem. Phys. 55, 5425–5430 (1971).
[CrossRef]

Shettle, E. P.

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.

Susskind, J.

J. Susskind, J. E. Searl, “Synthetic atmospheric transmittance spectra near 15 and 4.3 μm,” J. Quant. Spectrosc. Radiat. Transfer 19, 195–215 (1978).
[CrossRef]

Theriault, J. M.

Thomas, M. E.

M. E. Thomas, M. J. Linevsky, “Integrated intensities of N2, CO2, and SF6 vibrational bands from 1800 to 5000 cm−1 as a function of density and temperature,” J. Quant. Spectrosc. Radiat. Transfer 42, 465–470 (1989).
[CrossRef]

Zander, R.

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

Appl. Opt. (6)

Can. J. Phys. (2)

S. P. Reddy, C. W. Cho, “Induced infrared absorption of nitrogen and nitrogen–foreign gas mixtures,” Can. J. Phys. 43, 2331–2342 (1965).
[CrossRef]

M. M. Shapiro, H. P. Gush, “The collision induced fundamental and first overtone bands of O2 and N2,” Can. J. Phys. 44, 949–963 (1966).
[CrossRef]

Izv. Acad. Sci. USSR Atmos. Oceanic Phys. (2)

V. I. Dianov-Klokov, I. P. Malkov, “Absorption near 4.3 μm in the Earth’s atmosphere by the N2–N2 and N2–O2 complexes,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 9, 411–414 (1973).

N. I. Moskalenko, Y. A. Ilin, S. N. Parzhin, L. V. Rodionov, “Pressure induced IR absorption in atmospheres,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 15, 632–637 (1979).

J. Chem. Phys. (1)

D. T. Sheng, G. E. Ewing, “Collision induced infrared absorption of gaseous N2 at low temperatures,” J. Chem. Phys. 55, 5425–5430 (1971).
[CrossRef]

J. Geophys. Res. (1)

C. P. Rinsland, R. Zander, J. S. Namkung, C. B. Farmer, R. H. Norton, “Stratospheric infrared continuum absorptions observed by the ATMOS instrument,” J. Geophys. Res. 94, 303–322 (1989).
[CrossRef]

J. Phys. E (2)

R. Le Doucen, C. Cousin, V. Menoux, “Carbon furnace infrared source,” J. Phys. E 17, 1107 (1984).
[CrossRef]

R. Le Doucen, J. P. Houdeau, C. Cousin, V. Menoux, “Variable path-length, low temperature cells for absorption spectroscopy,” J. Phys. E 18, 199–200 (1985).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

J. Susskind, J. E. Searl, “Synthetic atmospheric transmittance spectra near 15 and 4.3 μm,” J. Quant. Spectrosc. Radiat. Transfer 19, 195–215 (1978).
[CrossRef]

M. E. Thomas, M. J. Linevsky, “Integrated intensities of N2, CO2, and SF6 vibrational bands from 1800 to 5000 cm−1 as a function of density and temperature,” J. Quant. Spectrosc. Radiat. Transfer 42, 465–470 (1989).
[CrossRef]

Other (3)

F. X. Kneizys, G. P. Anderson, E. P. Shettle, L. W. Abren, J. H. Chetwynd, J. E. A. Selby, W. O. Gallery, S. A. Clough, “lowtran 7: status, review and impact for short to long-wavelength infrared applications,” presented at the Conference of the Advisory Group for Aerospace Research and Development, Copenhagen, 9–10 October, 1989.

S. A. Clough, H. X. Kncizys, E. P. Shettle, G. P. Anderson, “Atmospheric radiance and transmittance: FASCOD2,” presented at the Sixth Annual Conference on Atmospheric Radiation, Williamsburg, Va., 6–10 May, 1986.

D. E. Burch, D. A. Gryvnak, J. D. Pembrook, “Investigation of the absorption of IR radiation by atmospheric gases: water, nitrogen, nitrous oxide,” Rep. AFCRL-71-0124 (U.S. Air Force Cambridge Research Laboratory, Hanscom Air Force Base, Mass., 1971).

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Figures (6)

Fig. 1
Fig. 1

Collision-induced absorption of pure nitrogen at T = 297 K and σ = 2349 cm−1. Plot of the absorption coefficient versus dN22.

Fig. 2
Fig. 2

Collision-induced absorption by N2–O2 in the 0–1 band of N2; T = 297 K and σ = 2400 cm−1. Plot k(σ)/dN2 versus dO2 for two different initial N2 fillings: dN2, dN2 = 5.2 amagat and dN2 = 9.5 amagat.

Fig. 3
Fig. 3

Normalized absorption coefficient kN–N(σ); temperature dependence of the line shape.

Fig. 4
Fig. 4

Normalized absorption coefficient kN–N(σ); temperature dependence at various wave numbers.

Fig. 5
Fig. 5

Wave-number dependence of the collision efficiency of oxygen compared with that of nitrogen [cf. Eq. (5)]. T = 297 K; ●, experimental results × 100.

Fig. 6
Fig. 6

Temperature dependence of the collision efficiency of oxygen compared with that of nitrogen [cf. Eq. (5)]. ○, experimentals results averaged over the spectral region 2100–2500 cm−1.

Tables (4)

Tables Icon

Table 1 Binary-Induced Collision Absorption Coefficient kN–N(σ) (10−6 cm−1 amagat−2) as a Function of Wave Number and Temperature

Tables Icon

Table 2 Binary-Induced Collision Absorption Coefficient kN–N(σ) (10−6 cm−1 amagat−2) at Room Temperature: Comparison with Previous Results

Tables Icon

Table 3 Integrated Intensities for the 1–0 Collision-Induced Absorption Vibrational Band of N2: Comparison with Previous Results

Tables Icon

Table 4 Temperature Dependence of the Collision Efficiency of Oxygen Compared with That of Nitrogena

Equations (6)

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

k ( σ ) = k N - N ( σ , T ) d N 2 2 ,
k ( σ ) = k N - N ( σ , T ) d N 2 2 + k N - O ( σ , T ) d N 2 d O 2 ,
k ( σ ) / d N 2 = k N - N ( σ , T ) d N 2 + k N - O ( σ , T ) d O 2 .
α 2 = band k N - N ( σ ) d σ .
e ( σ , T ) = k N - O ( σ , T ) / k N - N ( σ , T ) .
e ( σ , 297 ) e ( 297 ) = 0.83 ± 0.02.

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