Abstract

Broadening of the spectral lines by resonance and Van der Waals forces in the Schumann–Runge system of O2, the first and second positive systems of N2, the beta and gamma systems of NO and the first negative system of N2+ is treated by means of the impact approximation. At temperatures of 1000°K and higher, the broadening effect of the resonance forces is negligible; there is hence no J dependence in the widths. Van der Waals constants are calculated for the electronic–vibrational levels of interest using available discrete and continuous oscillator strengths. Half-widths in the various systems have been computed for 0<¯v,v<¯12, 1000°K T 18,000°K and ρ/ρ0 = 10,10−1. In general, there is not much width variation with vibrational band in a system.

© 1967 Optical Society of America

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References

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  1. A. A. Michelson, Astrophys. J. 2, 251 (1895).
    [CrossRef]
  2. W. Lenz, Z. Physik 25, 299 (1924).
    [CrossRef]
  3. V. F. Weisskopf, Z. Physik 75, 287 (1932).
    [CrossRef]
  4. R. G. Breene, The Shift and Shape of Spectral Lines (Pergamon Press, Oxford, 1961), Chaps. 1 and 2.
  5. E. Lindholm, Z. Physik 109, 223 (1938).
    [CrossRef]
  6. H. Margenau, Rev. Mod. Phys. 11, 1 (1939).
    [CrossRef]
  7. G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950).
  8. F. R. Gilmore, J. Quant. Spectry. Radiative Transfer 5, 369 (1965).
    [CrossRef]
  9. G. R. Cook, B. K. Ching, Aerospace Corporation, Rept. No. TDR-469(9260-01)-4 (1965).
  10. F. R. Gilmore, Rand Memorandum RM-1543 (1955).
  11. W. R. Thorson, R. M. Badger, J. Chem. Phys. 37, 609 (1957).
    [CrossRef]
  12. D. Weber, S. S. Penner, J. Chem. Phys. 26, 860 (1957).
    [CrossRef]

1965

F. R. Gilmore, J. Quant. Spectry. Radiative Transfer 5, 369 (1965).
[CrossRef]

1957

W. R. Thorson, R. M. Badger, J. Chem. Phys. 37, 609 (1957).
[CrossRef]

D. Weber, S. S. Penner, J. Chem. Phys. 26, 860 (1957).
[CrossRef]

1939

H. Margenau, Rev. Mod. Phys. 11, 1 (1939).
[CrossRef]

1938

E. Lindholm, Z. Physik 109, 223 (1938).
[CrossRef]

1932

V. F. Weisskopf, Z. Physik 75, 287 (1932).
[CrossRef]

1924

W. Lenz, Z. Physik 25, 299 (1924).
[CrossRef]

1895

A. A. Michelson, Astrophys. J. 2, 251 (1895).
[CrossRef]

Badger, R. M.

W. R. Thorson, R. M. Badger, J. Chem. Phys. 37, 609 (1957).
[CrossRef]

Breene, R. G.

R. G. Breene, The Shift and Shape of Spectral Lines (Pergamon Press, Oxford, 1961), Chaps. 1 and 2.

Ching, B. K.

G. R. Cook, B. K. Ching, Aerospace Corporation, Rept. No. TDR-469(9260-01)-4 (1965).

Cook, G. R.

G. R. Cook, B. K. Ching, Aerospace Corporation, Rept. No. TDR-469(9260-01)-4 (1965).

Gilmore, F. R.

F. R. Gilmore, J. Quant. Spectry. Radiative Transfer 5, 369 (1965).
[CrossRef]

F. R. Gilmore, Rand Memorandum RM-1543 (1955).

Herzberg, G.

G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950).

Lenz, W.

W. Lenz, Z. Physik 25, 299 (1924).
[CrossRef]

Lindholm, E.

E. Lindholm, Z. Physik 109, 223 (1938).
[CrossRef]

Margenau, H.

H. Margenau, Rev. Mod. Phys. 11, 1 (1939).
[CrossRef]

Michelson, A. A.

A. A. Michelson, Astrophys. J. 2, 251 (1895).
[CrossRef]

Penner, S. S.

D. Weber, S. S. Penner, J. Chem. Phys. 26, 860 (1957).
[CrossRef]

Thorson, W. R.

W. R. Thorson, R. M. Badger, J. Chem. Phys. 37, 609 (1957).
[CrossRef]

Weber, D.

D. Weber, S. S. Penner, J. Chem. Phys. 26, 860 (1957).
[CrossRef]

Weisskopf, V. F.

V. F. Weisskopf, Z. Physik 75, 287 (1932).
[CrossRef]

Astrophys. J.

A. A. Michelson, Astrophys. J. 2, 251 (1895).
[CrossRef]

J. Chem. Phys.

W. R. Thorson, R. M. Badger, J. Chem. Phys. 37, 609 (1957).
[CrossRef]

D. Weber, S. S. Penner, J. Chem. Phys. 26, 860 (1957).
[CrossRef]

J. Quant. Spectry. Radiative Transfer

F. R. Gilmore, J. Quant. Spectry. Radiative Transfer 5, 369 (1965).
[CrossRef]

Rev. Mod. Phys.

H. Margenau, Rev. Mod. Phys. 11, 1 (1939).
[CrossRef]

Z. Physik

W. Lenz, Z. Physik 25, 299 (1924).
[CrossRef]

V. F. Weisskopf, Z. Physik 75, 287 (1932).
[CrossRef]

E. Lindholm, Z. Physik 109, 223 (1938).
[CrossRef]

Other

R. G. Breene, The Shift and Shape of Spectral Lines (Pergamon Press, Oxford, 1961), Chaps. 1 and 2.

G. Herzberg, Spectra of Diatomic Molecules (D. Van Nostrand Company, Inc., New York, 1950).

G. R. Cook, B. K. Ching, Aerospace Corporation, Rept. No. TDR-469(9260-01)-4 (1965).

F. R. Gilmore, Rand Memorandum RM-1543 (1955).

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Tables (19)

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Table I Vibrational Oscillator Strength Sources

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Table II Electronic Oscillator Strengths

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Table III Van der Waals Constants for the O2 B Statea

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Table IV Van der Waals Constants for the NO A Statea

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Table V Van der Waals Constants for the NO B Statea

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Table VI Van der Waals Constants for the N2 A Statea

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Table VII Van der Waals Constants for the N2 B Statea

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Table VIII Van der Waals Constants for the N2 C Statea

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Table IX Van der Waals Constants for the N2+ B Statea

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Table X Van der Waals Constants for the NO X Statea

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Table XI Van der Waals Constants for the O2 X Statea

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Table XII Van der Waals Constants for the N2 X Statea

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Table XIII Half-Widths in the N2 First Positive System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XIV Half-Widths in the O2 Schumann–Runge System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XV Half-Widths in the N2 Second Positive System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XVI Half-Widths in the NO Gamma System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XVII Half-Widths in the NO Beta System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XVIII Half-Widths in the N2 First Negative System. Temperature 8000°K. Relative Density 10. Units are sec−1. Numbers Should be Multiplied by 1010

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Table XIX Half-Widths in the N2 First Positive System. Temperature 8000°K. Relative Density 10−1. Units are sec−1. Numbers Should be Multiplied by 108

Equations (6)

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I ( ν ) = ( δ / π ) / [ ( ν - ν 0 ) 2 + δ 2 ] ,
δ = v i N i ρ i 2 .
[ π 2 b / h v ρ 5 ] ± [ 2 π B / h v ρ 2 ] = 1.
δ v J v J = π / v ³ / k b k ² / N k + v j N j [ ( ρ + 2 + ρ 2 ) / 2 ] .
b = ( 3 / 2 ) ( e h / 2 π ) 4 ( I / m 2 )             a b f A a f b B / ( E A - E a ) ( E B - E b ) ( E A - E a + E B - E b )
ρ = ( π 2 b / h v ) ¹ / .

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