Difference between revisions of "Absorption length"
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The absorption length arises from the imaginary part of the [[atomic scattering factor]], ''f''<sub>2</sub>. It is closely related to the absorption cross-section, and the mass absorption coefficient. Specifically, the '''atomic photoabsorption cross-section''' can be computed via: | The absorption length arises from the imaginary part of the [[atomic scattering factor]], ''f''<sub>2</sub>. It is closely related to the absorption cross-section, and the mass absorption coefficient. Specifically, the '''atomic photoabsorption cross-section''' can be computed via: | ||
:<math> | :<math> | ||
| − | \sigma = 2 r_e \lambda | + | \sigma = 2 r_e \lambda f_2 |
</math> | </math> | ||
| + | Where ''λ'' is the x-ray wavelength, and ''r<sub>e</sub>'' is the classical electron radius. | ||
==See Also== | ==See Also== | ||
Revision as of 14:37, 6 June 2014
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.
Absorption
The absorption follows a simple Beer-Lambert law:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{I(x)}{I_0} = e^{ - x / \epsilon } }
The attenuation coefficient (or absorption coefficient) is simply the inverse of the absorption length; Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu = 1/\epsilon}
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{I(x)}{I_0} = e^{ - \mu x } }
Calculating
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:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma = 2 r_e \lambda f_2 }
Where λ is the x-ray wavelength, and re is the classical electron radius.
