Mass attenuation coefficient

Definition

The mass attenuation coefficient in cm²/g can be written as a sum of separated photoelectric mass absorption coefficients [math][\mu/\rho]_{PE}[/math] and coherent [math][\sigma/\rho]_{coh}[/math] and incoherent [math][\sigma/\rho]_{incoh}[/math] scattering contributions:

[math][\mu/\rho]_{TOT}=[\mu/\rho]_{PE} +[\sigma/\rho]_{coh} +[\sigma/\rho]_{incoh}[/math]

or equivalently

[math][\mu/\rho]_{TOT}=[\mu/\rho]_{PE} +[\mu/\rho]_{coh} +[\mu/\rho]_{incoh}.[/math]

It is recommended that [math][\mu/\rho]_{TOT}[/math] be used to distinguish this from the mass absorption coefficient [math][\mu/\rho]_{PE}[/math] (q.v.) as they are both commonly presented as [math][\mu/\rho][/math].

The last two contributions are angle-dependent. Note that while absorptive processes are linear (see absorption coefficient), coherent scattering (and incoherent scattering) are not linear and hence the attenuation coefficient does not obey the Beer-Lambert Law.

The mass attenuation coefficient is conventionally given by the symbol [math][\mu/\rho] = \sigma/(uA)[/math], where [math]\sigma[/math] is the cross-section in barns/atom (1 barn = [math]10^{-24}[/math] cm²), [math]u[/math] is the atomic mass unit, and [math]A[/math] is the relative atomic mass of the target element (i.e. in amu; the mass relative to 12 for carbon 12).

Where a material is composed of separate layers, the total absorption is given by the sum

[math]\ln\Big({I\over{I_0}}\Big)\Big|_{pe} = -\sum_i \Big[{\mu\over\rho}\Big]_{pe,i}[\rho t]_i.[/math]

Sometimes mass fractions are used as an approximation for a mixture, assuming that each atomic scatterer is independent.

See also

• Absorption coefficient
• Cross-section
• Linear attenuation coefficient