Absorption length

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The absorption length or attenuation length in x-ray scattering is the distance over which the x-ray beam is absorbed. By convention, the absorption length ϵ is defined as the distance into a material where the beam flux has dropped to 1/e of its incident flux.


The absorption follows a simple Beer-Lambert law:

The attenuation coefficient (or absorption coefficient) is simply the inverse of the absorption length;


The absorption length arises from the imaginary part of the atomic scattering factor, f2. It is closely related to the absorption cross-section, and the mass absorption coefficient. Specifically, the atomic photoabsorption cross-section can be computed via:

Where λ is the x-ray wavelength, and re is the classical electron radius. The attenuation coefficient is given by:

where ρ is density, Na is the Avogadro constant, and ma is the atomic molar mass. Note that the mass attenuation coefficient is simply .

Elemental dependence


Energy dependence

Notice that the absorption undergoes sharp increases when passing through an absorption edge.






Elemental/Energy dependence


Related forms

As can be seen, there are many related quantities which express the material's absorption:

  • Absorption length , the distance over which the intensity falls to 1/e.
  • Attenuation coefficient , the characteristic inverse-distance for attenuation.
  • Mass attenuation coefficient , the density-scaled attenuation.
  • Absorptive atomic scattering factor , the intrinsic dissipative interaction of the material.
  • Atomic photoabsorption cross-section , the cross-section ('effective size') of the atom's x-ray absorption (capture) efficiency.
  • Imaginary refractive index , the resonant component of the refractive index.
  • Imaginary Scattering Length Density , the absorptive component of the scattering contrast.

See also scattering factors for a comparison of the quantities related to f1.

See Also