Abstract

Measurements of Rayleigh scattering from atoms and molecules in the gaseous state at 1-atm pressure are described. The use of a Q-switched ruby laser of 8-MW average power and care in minimizing spurious light permitted the determination of very small depolarizations. No depolarization could be detected in the scattering from argon and helium. However, finite depolarization ratios ρν (for vertically polarized incident light) were measured for xenon and methane: 1.55(±0.25) × 10−4 and 1.27 (±0.23) × 10−4, respectively. Departures from ideal-gas behavior provide the most plausible explanation for these findings.

Depolarization ratios were also measured in hydrogen, deuterium, nitrogen, and nitrous oxide, and were found to be lower than generally accepted values. Measured differential-scattering cross sections at 60° for He, Ar, Xe, CH4, H2, D2, N2, and N2O were within experimental error of values calculated from known indices of refraction. The angular dependence of Rayleigh scattering in N2 as a function of the polarization states of both incident and scattered radiation was studied from 30° to 150°, and was found to be in agreement with theory.

© 1968 Optical Society of America

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References

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  1. R. Ananthakrishnan, Proc. Indian Acad. Sci. 2, 153 (1935).
  2. S. Parthasarathy, Indian J. Phys. 25, 22 (1951).
  3. F. R. Dintzis and R. S. Stein, J. Chem. Phys. 40, 1459 (1964).
    [Crossref]
  4. N. Bridge and A. Buckingham, J. Chem. Phys. 40, 2733 (1964).
    [Crossref]
  5. Andre Massoulier, J. Phys. Radium 24, 342 (1963).
  6. Alfons Weber, Sergio P. S. Porto, Leonard E. Cheesman, and Joseph J. Barrett, J. Opt. Soc. Am. 57, 19 (1967).
    [Crossref]
  7. J. Cabannes, Ann. Physik 15, 5 (1921).
  8. P. Daure, Compt. Rend. 180, 2032 (1925).
  9. G. Vaucouleurs, Ann. Physik 6, 211 (1951.)
  10. T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
    [Crossref]
  11. Robert D. Watson and Maynard D. Clark, Phys. Rev. Letters 14, 1057 (1965).
    [Crossref]
  12. See, for example, M. Born, Optik, (Julius Springer-Verlag, Berlin, 1933).
    [Crossref]
  13. Fig. 1 shows the experimental arrangement for horizontally polarized incident light. All depolarization measurements were performed with vertical polarization, for which the laser, Glan–Thompson prism, and entrance-port window were rotated 90°. Relatively poor results were obtained with the entrance window normal to the incident beam.
  14. Alan DeSilva, University of Maryland, private communication.
  15. For example, the commercially measured purities of the helium, argon, xenon, methane used were 99.999%, 99.999%, 99.995%, and 99.95%.
  16. Ralph R. Rudder, Thesis, The University of Michigan, 1967.
  17. A. Buckingham and M. Stephen, Trans. Faraday Soc. 53, 884 (1967).
    [Crossref]
  18. S. Kielich, Acta Phys. Polon. 19, 149 (1960).
  19. O. Theimer and R. Paul, J. Chem. Phys. 42, 2508 (1965).
    [Crossref]
  20. The seemingly significant wavelength dependence of this equation, due to the λ4 term, is removed when we recall that σ0 varies as 1/λ4. Thus, the true wavelength dependence is only that due to the slight dispersion of the refractive index μ.
  21. A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51, 1173, 1179 (1955).
    [Crossref]
  22. Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, Molecular Theory of Gases and Liquids, (John Wiley & Sons, Inc., New York, 1954).
  23. P. G. Wilkinson, J. Quant. Spectry. Radiative Transfer 6, 823 (1966).
    [Crossref]
  24. Shardanand, Phys. Rev. 160, 67 (1967).
    [Crossref]
  25. Actually ρu was generally measured. For sake of comparison, Eq. (4) has been used, when appropriate, to compute ρv from the experimental values.
  26. I. R. Rao, Indian J. Phys. 2, 61, (1927).
  27. H. Volkmann, Ann. Physik 24, 457 (1935).
    [Crossref]
  28. Landolt–Börnstein, Ed., Zahlenwerte and Funktionen aus Physik, Chemie, Astronomie, Geophysik, und Technik, II Band, 8 Teil, Optische Konstanten, (Springer-Verlag, Berlin, 1962).

1967 (3)

A. Buckingham and M. Stephen, Trans. Faraday Soc. 53, 884 (1967).
[Crossref]

Shardanand, Phys. Rev. 160, 67 (1967).
[Crossref]

Alfons Weber, Sergio P. S. Porto, Leonard E. Cheesman, and Joseph J. Barrett, J. Opt. Soc. Am. 57, 19 (1967).
[Crossref]

1966 (1)

P. G. Wilkinson, J. Quant. Spectry. Radiative Transfer 6, 823 (1966).
[Crossref]

1965 (3)

O. Theimer and R. Paul, J. Chem. Phys. 42, 2508 (1965).
[Crossref]

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Robert D. Watson and Maynard D. Clark, Phys. Rev. Letters 14, 1057 (1965).
[Crossref]

1964 (2)

F. R. Dintzis and R. S. Stein, J. Chem. Phys. 40, 1459 (1964).
[Crossref]

N. Bridge and A. Buckingham, J. Chem. Phys. 40, 2733 (1964).
[Crossref]

1963 (1)

Andre Massoulier, J. Phys. Radium 24, 342 (1963).

1960 (1)

S. Kielich, Acta Phys. Polon. 19, 149 (1960).

1955 (1)

A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51, 1173, 1179 (1955).
[Crossref]

1951 (2)

G. Vaucouleurs, Ann. Physik 6, 211 (1951.)

S. Parthasarathy, Indian J. Phys. 25, 22 (1951).

1935 (2)

H. Volkmann, Ann. Physik 24, 457 (1935).
[Crossref]

R. Ananthakrishnan, Proc. Indian Acad. Sci. 2, 153 (1935).

1927 (1)

I. R. Rao, Indian J. Phys. 2, 61, (1927).

1925 (1)

P. Daure, Compt. Rend. 180, 2032 (1925).

1921 (1)

J. Cabannes, Ann. Physik 15, 5 (1921).

Ananthakrishnan, R.

R. Ananthakrishnan, Proc. Indian Acad. Sci. 2, 153 (1935).

Barrett, Joseph J.

Born, M.

See, for example, M. Born, Optik, (Julius Springer-Verlag, Berlin, 1933).
[Crossref]

Bridge, N.

N. Bridge and A. Buckingham, J. Chem. Phys. 40, 2733 (1964).
[Crossref]

Buckingham, A.

A. Buckingham and M. Stephen, Trans. Faraday Soc. 53, 884 (1967).
[Crossref]

N. Bridge and A. Buckingham, J. Chem. Phys. 40, 2733 (1964).
[Crossref]

Buckingham, A. D.

A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51, 1173, 1179 (1955).
[Crossref]

Byron Bird, R.

Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, Molecular Theory of Gases and Liquids, (John Wiley & Sons, Inc., New York, 1954).

Cabannes, J.

J. Cabannes, Ann. Physik 15, 5 (1921).

Cheesman, Leonard E.

Clark, Maynard D.

Robert D. Watson and Maynard D. Clark, Phys. Rev. Letters 14, 1057 (1965).
[Crossref]

Curtiss, Charles F.

Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, Molecular Theory of Gases and Liquids, (John Wiley & Sons, Inc., New York, 1954).

Daure, P.

P. Daure, Compt. Rend. 180, 2032 (1925).

DeSilva, Alan

Alan DeSilva, University of Maryland, private communication.

Dintzis, F. R.

F. R. Dintzis and R. S. Stein, J. Chem. Phys. 40, 1459 (1964).
[Crossref]

George, T. V.

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Goldstein, L.

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Hirschfelder, Joseph O.

Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, Molecular Theory of Gases and Liquids, (John Wiley & Sons, Inc., New York, 1954).

Kielich, S.

S. Kielich, Acta Phys. Polon. 19, 149 (1960).

Massoulier, Andre

Andre Massoulier, J. Phys. Radium 24, 342 (1963).

Parthasarathy, S.

S. Parthasarathy, Indian J. Phys. 25, 22 (1951).

Paul, R.

O. Theimer and R. Paul, J. Chem. Phys. 42, 2508 (1965).
[Crossref]

Pople, J. A.

A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51, 1173, 1179 (1955).
[Crossref]

Porto, Sergio P. S.

Rao, I. R.

I. R. Rao, Indian J. Phys. 2, 61, (1927).

Rudder, Ralph R.

Ralph R. Rudder, Thesis, The University of Michigan, 1967.

Shardanand,

Shardanand, Phys. Rev. 160, 67 (1967).
[Crossref]

Slama, L.

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Stein, R. S.

F. R. Dintzis and R. S. Stein, J. Chem. Phys. 40, 1459 (1964).
[Crossref]

Stephen, M.

A. Buckingham and M. Stephen, Trans. Faraday Soc. 53, 884 (1967).
[Crossref]

Theimer, O.

O. Theimer and R. Paul, J. Chem. Phys. 42, 2508 (1965).
[Crossref]

Vaucouleurs, G.

G. Vaucouleurs, Ann. Physik 6, 211 (1951.)

Volkmann, H.

H. Volkmann, Ann. Physik 24, 457 (1935).
[Crossref]

Watson, Robert D.

Robert D. Watson and Maynard D. Clark, Phys. Rev. Letters 14, 1057 (1965).
[Crossref]

Weber, Alfons

Wilkinson, P. G.

P. G. Wilkinson, J. Quant. Spectry. Radiative Transfer 6, 823 (1966).
[Crossref]

Yokoyama, M.

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Acta Phys. Polon. (1)

S. Kielich, Acta Phys. Polon. 19, 149 (1960).

Ann. Physik (3)

H. Volkmann, Ann. Physik 24, 457 (1935).
[Crossref]

J. Cabannes, Ann. Physik 15, 5 (1921).

G. Vaucouleurs, Ann. Physik 6, 211 (1951.)

Compt. Rend. (1)

P. Daure, Compt. Rend. 180, 2032 (1925).

Indian J. Phys. (2)

S. Parthasarathy, Indian J. Phys. 25, 22 (1951).

I. R. Rao, Indian J. Phys. 2, 61, (1927).

J. Chem. Phys. (3)

O. Theimer and R. Paul, J. Chem. Phys. 42, 2508 (1965).
[Crossref]

F. R. Dintzis and R. S. Stein, J. Chem. Phys. 40, 1459 (1964).
[Crossref]

N. Bridge and A. Buckingham, J. Chem. Phys. 40, 2733 (1964).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Radium (1)

Andre Massoulier, J. Phys. Radium 24, 342 (1963).

J. Quant. Spectry. Radiative Transfer (1)

P. G. Wilkinson, J. Quant. Spectry. Radiative Transfer 6, 823 (1966).
[Crossref]

Phys. Rev. (2)

Shardanand, Phys. Rev. 160, 67 (1967).
[Crossref]

T. V. George, L. Goldstein, L. Slama, and M. Yokoyama, Phys. Rev. 137, A369 (1965).
[Crossref]

Phys. Rev. Letters (1)

Robert D. Watson and Maynard D. Clark, Phys. Rev. Letters 14, 1057 (1965).
[Crossref]

Proc. Indian Acad. Sci. (1)

R. Ananthakrishnan, Proc. Indian Acad. Sci. 2, 153 (1935).

Trans. Faraday Soc. (2)

A. Buckingham and M. Stephen, Trans. Faraday Soc. 53, 884 (1967).
[Crossref]

A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51, 1173, 1179 (1955).
[Crossref]

Other (9)

Joseph O. Hirschfelder, Charles F. Curtiss, and R. Byron Bird, Molecular Theory of Gases and Liquids, (John Wiley & Sons, Inc., New York, 1954).

The seemingly significant wavelength dependence of this equation, due to the λ4 term, is removed when we recall that σ0 varies as 1/λ4. Thus, the true wavelength dependence is only that due to the slight dispersion of the refractive index μ.

Actually ρu was generally measured. For sake of comparison, Eq. (4) has been used, when appropriate, to compute ρv from the experimental values.

Landolt–Börnstein, Ed., Zahlenwerte and Funktionen aus Physik, Chemie, Astronomie, Geophysik, und Technik, II Band, 8 Teil, Optische Konstanten, (Springer-Verlag, Berlin, 1962).

See, for example, M. Born, Optik, (Julius Springer-Verlag, Berlin, 1933).
[Crossref]

Fig. 1 shows the experimental arrangement for horizontally polarized incident light. All depolarization measurements were performed with vertical polarization, for which the laser, Glan–Thompson prism, and entrance-port window were rotated 90°. Relatively poor results were obtained with the entrance window normal to the incident beam.

Alan DeSilva, University of Maryland, private communication.

For example, the commercially measured purities of the helium, argon, xenon, methane used were 99.999%, 99.999%, 99.995%, and 99.95%.

Ralph R. Rudder, Thesis, The University of Michigan, 1967.

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Figures (2)

Fig. 1
Fig. 1

Experimental arrangement for Rayleigh-scattering experiments. L—laser; P—Glan–Thompson prism; B—razor–blade baffle; D—scattering detector; M—intensity monitor; N—neon reference source; A—polarization analyzer; F—filter; PM—photomultiplier tube.

Fig. 2
Fig. 2

Angular dependence of Rayleigh scattering in nitrogen as a function of the polarization states of incident and scattered light.

Tables (3)

Tables Icon

Table I Theoretical and measured scattering anisotropies for spherically symmetric particles.

Tables Icon

Table II Measured depolarization ratios of asymmetric scatterers.

Tables Icon

Table III Measured and calculated Rayleigh-scattering cross sections.

Equations (9)

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

σ 12 d Ω 2 σ ( Ω 1 , ɛ 1 ; Ω 2 , ɛ 2 ) d Ω 2 = σ 0 [ ( 1 - ρ v ) cos 2 ψ + ρ v ] ,
σ 0 4 π 2 ( μ - 1 ) 2 N 0 2 λ 1 4 ( 3 3 - 4 ρ v )
ρ v = σ V H / σ V V .
ρ u = 2 ρ v / ( 1 + ρ v ) .
σ a σ 0 ρ v .
σ V V = σ 0 σ V H = σ H V = σ 0 ρ v σ H H = σ 0 [ ( 1 - ρ v ) cos 2 θ + ρ v ] .
ρ v 2 π 5 ( λ 2 π ) 4 N 0 H 6 ( y ) r 0 3 y 4 σ 0 ,
y = 2 ( * / k T ) 1 2 .
σ 0 = T f T B T m T w ( R 0 2 s 1 s 2 ) ( L sin θ s 2 R 0 ) ( 1 N 0 ) I s I c ,