# Mass attenuation coefficient

## Definition

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

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

or equivalently

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

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

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 $[\mu/\rho] = \sigma/(uA)$, where $\sigma$ is the cross-section in barns/atom (1 barn = $10^{-24}$ cm2), $u$ is the atomic mass unit, and $A$ 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

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

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