Mass attenuation coefficient

Mass attenuation coefficient is defined as

${\displaystyle {\frac {\mu }{\rho _{m}}},}$

where

• μ is the attenuation coefficient (linear attenuation coefficient);
• ρ_m is the mass density.

When using the mass attenuation coefficient, the Beer–Lambert law is written in alternative form as

${\displaystyle I=I_{0}\,e^{-(\mu /\rho _{m})\lambda }}$

where

${\displaystyle \lambda =\rho _{m}\ell }$ is the area density known also as mass thickness, and ${\displaystyle \ell }$ is the length, over which the attenuation takes place.

Mass attenuation coefficient of iron with contributing sources of attenuation: coherent scattering, incoherent scattering, photoelectric absorption, and two types of pair production. The discontinuity of photoelectric absorption values are due to K-edge. Graph data came from NIST's XCOM database.

Mass attenuation coefficient values shown for all elements with atomic number Z smaller than 100 collected for photons with energies from 1 keV to 20 MeV. The discontinuities in the values are due to absorption edges which were also shown.

Tables of photon mass attenuation coefficients are essential in radiological physics, radiography (for medical and security purposes), dosimetry, diffraction, interferometry, crystallography, and other branches of physics. The photons can be in form of X-rays, gamma rays, and bremsstrahlung.

The values of mass attenuation coefficients, based on proper values of photon cross section, are dependent upon the absorption and scattering of the incident radiation caused by several different mechanisms such as

• Rayleigh scattering (coherent scattering);
• Compton scattering (incoherent scattering);
• photoelectric absorption;
• pair production, electron-positron production in the fields of the nucleus and atomic electrons.

The actual values have been thoroughly examined and are available to the general public through three databases run by National Institute of Standards and Technology (NIST):

1. XAAMDI database;[2]
2. XCOM database;[3]
3. FFAST database.[4]

If several known chemicals are dissolved in a single solution, the concentrations of each can be calculated using a light absorption analysis. First, the mass attenuation coefficients of each individual solute or solvent, ideally across a broad spectrum of wavelengths, must be measured or looked up. Second, the attenuation coefficient of the actual solution must be measured. Finally, using the formula

${\displaystyle \mu =(\mu /\rho )_{1}\rho _{1}+(\mu /\rho )_{2}\rho _{2}+\ldots ,}$

the spectrum can be fitted using ρ₁, ρ₂, … as adjustable parameters, since μ and each μ/ρ_i are functions of wavelength. If there are N solutes or solvents, this procedure requires at least N measured wavelengths to create a solvable system of simultaneous equations, although using more wavelengths gives more reliable data.

• Absorption coefficient
• Absorption cross section
• Attenuation length
• Attenuation
• Beer–Lambert law
• Cargo scanning
• Compton edge
• Compton scattering
• Cross section
• High-energy X-rays
• Mean free path
• Molar attenuation coefficient
• Propagation constant
• Radiation length
• Scattering theory
• Transmittance