Scattering cross-section

The scattering cross-section, σ_scat, relates the scattering of light or other radiation to the number of particles present. Its SI unit is the square metre, m², although smaller units are usually used in practice. The name cross-section arises because it has the dimensions of area.

The definition of the scattering cross-section is derived from the Beer-Lambert law expressed in terms of the number concentration of particles, C,

E(λ) = Clσ

where E(λ) is the extinction at a given wavelength, λ, and l is the path length. The extinction of the radiation is the logarithm (decadic or, more usually, natural) of the ratio of the incident spectral intensity, I₀ to the transmitted spectral intensity, I,

E = log(I₀/I)

and, in general, has three independant componants, due to absorption, scattering and luminescence:

σ = σ_abs + σ_scat + σ_lum

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Relation to physical size

There is no simple relationship between the scattering cross-section and the physical size of the particles, as the scattering cross-section depends on the wavelength of radiation used. This can be seen when driving in foggy weather: the droplets of water (which form the fog) scatter red light less than they scatter the shorter wavelengths present in white light, and the red rear fog light can be distinguished more clearly than the white headlights of an approaching vehicle. That is to say that the scattering cross-section of the water droplets is smaller for red light than for light of shorter wavelengths, even though the physical size of the particles is the same.

Meteorological range

The scattering cross-section is related to the meteorological range, L_V, by the theoretical expression

L_V = 3.9/Cσ_scat

The quantity Cσ_scat is sometimes denoted b_scat.

Units

When the scattered radiation is visible light, it is conventional to measure the path length in centimetres. To avoid the need for conversion factors, the scattering cross-section is expressed in cm² (1 cm² = 10⁻⁴ m²) and the number concentration in cm⁻³ (1 cm⁻³ = 10⁶ m⁻³). The measurement of the scattering of visible light is known as nephelometry, and is effective for particles of 2–50 µm in diameter: as such, it is widely used in meterology and in the measurement of atmospheric pollution.

Scattering cross-sections are also widely used in the description of the scattering of neutrons by atomic nuclei. In this case, the conventional unit is the barn, b, where 1 b = 10⁻²⁸ m² = 100 fm².^[1]

The scattering of X-rays can also be described in terms of scattering cross-sections, in which case the square ångström, Ų, is a convenient unit: 1 Å² = 10⁻²⁰ m² = 10⁴ pm². However, in crystallography, it is more usual to express X-ray scattering in terms of structure factors, f.

See also

• Absorption cross-section, σ_abs
• Cross section (physics)
• Nuclear cross section
• Neutron cross section
• Scattering amplitude, also known as scattering length

References

• International Union of Pure and Applied Chemistry. "scattering cross-section, σ_scat". Compendium of Chemical Terminology Internet edition.

1. ^ Bureau International des Poids et Mesures (2006). The International System of Units (SI) (8th Edn). ISBN 92-822-2213-6. pp. 127–28.