Mass attenuation coefficient

The mass attenuation coefficient is the quotient of the absorption coefficient and the density of the respective material. Like the linear absorption coefficient, it expresses how strongly electromagnetic radiation is attenuated when passing through a material, depending on its photon energy . Its dimension is area / mass, the usual unit cm ² / g.

The exponential decrease in the initial intensity is described by the Lambert-Beer law : ${\ displaystyle I_ {0}}$

{\ displaystyle I = I_ {0} \, \ exp (- \ mu \, d)}

Here µ is the linear attenuation coefficient and d is the penetration depth into the material.

Attenuation coefficient of iron (black curve). The colored curves show the proportions of the individual effects. A clear absorption edge is visible at around 7 keV.

The mass attenuation coefficient µ / ( : density) is often preferred to µ in practice because it is almost constant in a large energy range, which is important for gamma radiation, and is also similar for many materials (see figure opposite for iron). It also allows a density different from the usual one to be taken into account. Above 2 MeV it is in the order of magnitude of 0.05 cm² / g. Expressed with the mass attenuation coefficient, the mass occupancy ρ · d must be used in the Lambert-Beer law instead of the penetration depth . It then reads ${\ displaystyle \ rho}$ ${\ displaystyle \ rho}$

{\ displaystyle I = I_ {0} \, \ exp \ left (- {\ frac {\ mu} {\ rho}} \, \ rho d \ right)}

μ / ρ: mass attenuation coefficient; ρ: density.

Tabulated values of the mass attenuation coefficient can be found in Ref.

Physical effects involved

Above 1 MeV, the attenuation is mainly due to Compton scattering and pair formation . At lower energies, on the other hand, absorption by the photo effect dominates , slightly overlaid by Rayleigh scattering .

The mass attenuation coefficient for the photoelectric effect depends not only on the material but also on the energy or the wavelength of the X-rays.

{\ displaystyle {\ frac {\ mu} {\ rho}} = C \ lambda ^ {3} Z ^ {3}}

Z is the number of protons in the atomic nucleus, λ is the wavelength of the X-rays and C is a parameter that depends on the material and the wavelength. It changes at the absorption edges .

Individual evidence

↑ JH Hubbell, Seltzer, SM: Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients . National Institute of Standards and Technology (NIST). Retrieved October 21, 2009.

[1] JH Hubbell, Seltzer, SM: Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients . National Institute of Standards and Technology (NIST). Retrieved October 21, 2009.