Abstract

An accurate measurement has been made of the Raman scattering cross section of the 992 cm−1 line of benzene. Previous cross-section measurements were either made indirectly by comparison with the Rayleigh scattering cross section or by using a pulsed light source. In the present measurement the cross section was measured directly using a cw argon laser as the light source. The results give a peak differential cross section of 1.05(±0.08)×10−29 cm2 per molecule, per steradian, per wavenumber of linewidth, per plane of polarization for an incident light beam with a wavelength of 4880 Å, and a linewidth of 2.3 (±0.05) cm−1. Allowing for the wavelength dependence and the optical dispersion, our total cross section agrees to within 20% with two other results. The Raman scattering cross sections of other liquids have been measured by use of the 992 cm−1 line of benzene as a reference. These values, together with details of the absolute cross-section measurement, are presented.

© 1968 Optical Society of America

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References

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  1. H. W. Schrotter and H. J. Bernstein, J. Mol. Spectry. 12, 1 (1964).
    [Crossref]
  2. G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
    [Crossref]
  3. F. J. McClung and D. Weiner, J. Opt. Soc. Am. 54, 641 (1964); D. Weiner, S. E. Schwarz, and F. J. McClung, J. Appl. Phys. 36, 2395 (1965).
    [Crossref]
  4. T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
    [Crossref]
  5. G. Bret, Compt. Rend,  260, 6323 (1965).
  6. F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
    [Crossref]
  7. P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, New York, 1958) 4th ed.
  8. Since the spectrometer and the standard lamp are calibrated in terms of wavelength, the appropriate parameters are measured in terms of per unit wavelength, and the final result is then converted in terms of per unit wavenumber.
  9. Value of the refractive index for benzene extrapolated from data given in American Institute of Physics Handbook, (McGraw-Hill Book Company, New York, 1963), 2nd ed.
  10. International Critical Tables (McGraw-Hill Book Company, New York, 1930).

1965 (3)

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

G. Bret, Compt. Rend,  260, 6323 (1965).

F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
[Crossref]

1964 (2)

1962 (1)

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Bernstein, H. J.

H. W. Schrotter and H. J. Bernstein, J. Mol. Spectry. 12, 1 (1964).
[Crossref]

Bret, G.

G. Bret, Compt. Rend,  260, 6323 (1965).

Damen, T. C.

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, New York, 1958) 4th ed.

Eckhardt, G. E.

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Hellwarth, R. W.

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Leite, R. C. C.

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

McClung, F. J.

F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
[Crossref]

F. J. McClung and D. Weiner, J. Opt. Soc. Am. 54, 641 (1964); D. Weiner, S. E. Schwarz, and F. J. McClung, J. Appl. Phys. 36, 2395 (1965).
[Crossref]

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Porto, S. P. S.

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

Schrotter, H. W.

H. W. Schrotter and H. J. Bernstein, J. Mol. Spectry. 12, 1 (1964).
[Crossref]

Schwarz, S. E.

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Wagner, W. G.

F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
[Crossref]

Weiner, D.

F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
[Crossref]

F. J. McClung and D. Weiner, J. Opt. Soc. Am. 54, 641 (1964); D. Weiner, S. E. Schwarz, and F. J. McClung, J. Appl. Phys. 36, 2395 (1965).
[Crossref]

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Woodbury, E. J.

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

Compt. Rend (1)

G. Bret, Compt. Rend,  260, 6323 (1965).

J. Mol. Spectry. (1)

H. W. Schrotter and H. J. Bernstein, J. Mol. Spectry. 12, 1 (1964).
[Crossref]

J. Opt. Soc. Am. (1)

Phys. Rev. Letters (3)

T. C. Damen, R. C. C. Leite, and S. P. S. Porto, Phys. Rev. Letters 14, 9 (1965).
[Crossref]

G. E. Eckhardt, R. W. Hellwarth, F. J. McClung, S. E. Schwarz, D. Weiner, and E. J. Woodbury, Phys. Rev. Letters 9, 455 (1962).
[Crossref]

F. J. McClung, W. G. Wagner, and D. Weiner, Phys. Rev. Letters 15, 96 (1965).
[Crossref]

Other (4)

P. A. M. Dirac, Principles of Quantum Mechanics (Oxford University Press, New York, 1958) 4th ed.

Since the spectrometer and the standard lamp are calibrated in terms of wavelength, the appropriate parameters are measured in terms of per unit wavelength, and the final result is then converted in terms of per unit wavenumber.

Value of the refractive index for benzene extrapolated from data given in American Institute of Physics Handbook, (McGraw-Hill Book Company, New York, 1963), 2nd ed.

International Critical Tables (McGraw-Hill Book Company, New York, 1930).

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Figures (2)

Fig. 1
Fig. 1

Geometric arrangement of the sample, laser beam, and the detectors.

Fig. 2
Fig. 2

Angular distribution of the 992-cm−1 line of benzene.

Tables (3)

Tables Icon

Table I Differential cross section of the 992 cm−1 line of benzene.

Tables Icon

Table II Linewidth, depolarization ratio (ρ), and the relative peak value of the Raman differential cross section of a number of liquids.

Tables Icon

Table III Comparison of cross-section measurements.

Equations (20)

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d σ α β ( θ , φ ) = power scattered into the β mode incident power density per α mode .
N β = n 3 η 2 cm - 2 ,
d σ α β N β / N = d σ ( θ , φ ) = power scattered to an angular position ( θ , φ ) steradian , molecule , unit wavenumber , plane of polarization × 1 I 0
d σ / d Ω = ( 2 π e ) 4 η β 4 0 2 h 2 c 2 | γ { β x β γ γ x α α ( η γ - η α ) + β x β γ γ x α α η γ + η α } | 2 ,
P R = [ P L / area of beam ] · d σ × number of molecules intercepted in volume of interest = [ P L / area of beam ] · d σ × N × volume of sample intercepted by the laser beam and the detector D S = P L · d σ · N · l 0 ,
d σ = P R / P L · N · l 0 · Ω .
K L = S A S ( λ ) F ( λ ) d λ amps watts ,
S L = K L η L P L F ( λ ) d λ amps ,
P L = A · S L · η L S T L S ( λ ) F ( λ ) d λ watts .
K R = 2 R η R k w S ( λ ) T ( λ ) d λ amps watts ,
K R = 2 R η R h w S ( λ 1 ) T ( λ ) d λ .
S R = K R P R ( λ 1 ) f ( λ ) T ( λ ) d λ .
P R ( λ 1 ) = S R · S ( λ 1 ) · h w 2 R η R T ( λ ) d λ f ( λ ) T ( λ ) d λ .
Ω = h w / D 2 n 2 ,
l 0 = l [ D / ( D - D ) ] ,
d σ P = P R ( λ 1 ) / P L · N · l 0 · Ω .
d σ P = S R R 1 S L [ T ( λ ) d λ T ( λ ) f ( λ ) d λ ] ψ ,
ψ = S [ n 2 D ( D - D ) 2 A l N ] T L S ( λ 1 ) ( η R η L ) [ 1 S ( λ ) F ( λ ) d λ ] .
d σ / d Ω = k η β 4 = d σ P Δ η β π / 2 ,
κ = d σ / d Ω η β 4 = d σ P · Δ η β · π / 2 η β 4 .