Abstract

The effect of velocity-dependent collision broadening on the shape of spectral lines is investigated. Computations show that the modified line shape has a narrower half-width than the conventional Voigt profile.

© 1975 Optical Society of America

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References

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  1. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959).
  2. V. Ye. Zuev, Propagation of Visible and Infrared Waves in the Atmosphere (‘Sovetskoe Radio’, Moscow, USSR, 1970; Wiley, New York, 1974).
  3. D. W. Posener, Aust. J. Phys. 12, 184 (1959).
    [Crossref]
  4. E. E. Whiting, J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
    [Crossref]
  5. We assume in this paper that γL is collision dominated.
  6. J. Y. Wang, Appl. Opt. 13, 56 (1974).
    [Crossref] [PubMed]
  7. That σ may not be a constant can have a serious effect on the behavior of k(ω) for large ω.
  8. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Std. (U.S.) Appl. Math. Ser. (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).
  9. R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
    [Crossref]

1974 (1)

1973 (1)

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

1968 (1)

E. E. Whiting, J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[Crossref]

1959 (1)

D. W. Posener, Aust. J. Phys. 12, 184 (1959).
[Crossref]

Calawa, A. R.

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

Eng, R. S.

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

Harman, T. C.

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

Kelley, P. L.

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

Mooradian, A.

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

Penner, S. S.

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959).

Posener, D. W.

D. W. Posener, Aust. J. Phys. 12, 184 (1959).
[Crossref]

Wang, J. Y.

Whiting, E. E.

E. E. Whiting, J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[Crossref]

Zuev, V. Ye.

V. Ye. Zuev, Propagation of Visible and Infrared Waves in the Atmosphere (‘Sovetskoe Radio’, Moscow, USSR, 1970; Wiley, New York, 1974).

Appl. Opt. (1)

Aust. J. Phys. (1)

D. W. Posener, Aust. J. Phys. 12, 184 (1959).
[Crossref]

Chem. Phys. Lett. (1)

R. S. Eng, P. L. Kelley, A. Mooradian, A. R. Calawa, and T. C. Harman, Chem. Phys. Lett. 19, 524 (1973).
[Crossref]

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

E. E. Whiting, J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).
[Crossref]

Other (5)

We assume in this paper that γL is collision dominated.

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959).

V. Ye. Zuev, Propagation of Visible and Infrared Waves in the Atmosphere (‘Sovetskoe Radio’, Moscow, USSR, 1970; Wiley, New York, 1974).

That σ may not be a constant can have a serious effect on the behavior of k(ω) for large ω.

Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, Natl. Bur. Std. (U.S.) Appl. Math. Ser. (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).

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Figures (1)

FIG. 1
FIG. 1

Normalized line shapes for y(0) = 10, mass ratios of 0 (—) and 2(---).

Tables (2)

Tables Icon

TABLE I Values of k (x = 0) for various mass ratios and values of y(0).

Tables Icon

TABLE II Values of half-widths for various mass ratios and values of y(0).

Equations (12)

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k ( ω ) = k 0 π - y e - t 2 d t y 2 + ( x - t ) 2 ,
γ C ( u ) = n σ u - v P m ( v ) d 3 v ,
k ( ω ) = S x 2 π 3 / 2 - γ C ( u ) P M ( u ) d 3 u = 2 S n σ ( γ D x π ) 2 ( 2 k T μ ) 1 / 2 S γ D 2 x 2 π 3 / 2 γ 0 ,
γ C ( u ) = 4 π n σ 0 v 2 g ( u , v ) P m ( v ) d v ,
g ( u , v ) = u + v 2 / 3 u , u > v = v + u 2 / 3 v , u < v .
γ C ( u ) = γ C ( 0 ) [ 1 + f ( u / v m ) ] = γ 0 ( 1 1 + m / M ) 1 / 2 [ 1 + f ( u / v m ) ] ,
f ( x ) = { x E ( x ) + 1 2 [ E ( x ) / x - 1 ] + 1 2 ( e - x 2 - 1 ) } ,
E ( x ) = 0 x e - u 2 d u .
k ( ω ) = k 0 π 2 y ( t ) t 2 d t d cos θ d ϕ e - t 2 y ( t ) 2 + ( x - t cos θ ) 2 ,
y ( t ) = γ C ( t ) / γ D , γ C ( t ) = γ 0 ( 1 + m / M ) - 1 / 2 { 1 + f [ t ( m / M ) 1 / 2 ] } .
k ( ω ) = k 0 π [ 0 y ( t ) e - t 2 d t { [ y ( t ) 2 + ( x - t ) 2 ] - 1 + [ y ( t ) 2 + ( x + t ) 2 ] - 1 } + 0 y ( t ) e - t 2 d t { ( x - t ) y ( t ) 2 + ( x - t ) 2 - ( x + t ) y ( t ) 2 + ( x + t ) 2 } ] .
a b f ( x ) d x = i = 0 N - 1 a + i δ a + ( i + 1 ) δ f ( x ) d x ,