Scattering cross-section

The scattering cross-section, "σ"_scat, relates the scattering of light or other radiation to the number of particles present. In terms of area, the "total cross-section" (σ) is the sum of the cross-sections due to absorption, scattering and luminescence: $sigma\; =\; sigma\_A\; +\; sigma\_S\; +\; sigma\_L$

The total cross-section is related to the absorbance of the light intensity through Beer-Lambert's law, which says absorbance is proportional to concentration: $A\_lambda\; =\; C\; l\; sigma$, where "C" is the concentration as a number density, A_λ is the absorbance at a given wavelength, "λ", and "l" is the path length. The extinction or absorbance of the radiation is the logarithm (decadic or, more usually, natural) of the reciprocal of the transmittance: [cite book|chapter=2. Spectrophotometry|isbn=8121926335|first=P.K.|last=Bajpai|title=Biological Instrumentation and Biology|url=http://books.google.com/books?id=THq-cOPO8RQC&pg=PA14&dq=%22extinction+coefficient%22+transmittance+length+concentration&ei=wn2qR6O-MojcygSe4YSSCg&sig=7y0ZqfPG98k-j7EMPS9ivanHyd4#PPA14,M1] $A\_lambda\; =\; -\; log\; mathcal\{T\}$

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:

$L\_V\; =\; frac\{3.9\}\{C\; sigma\_\{scat$

The quantity "Cσ"_scat is sometimes denoted "b"_scat, the scattering coefficient per unit length.GoldBookRef|title=Scattering cross-section, σ_scat|file=S05490]

Units

Its SI unit is the square meter, m², although smaller units are usually used in practice. The name "cross-section" arises because it has the dimensions of area.

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. [SIbrochure|pages=127–28]

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 Ų = 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

*Cross section (physics)
*Nuclear cross section
*Neutron cross section
*Scattering amplitude

References