Mean free path

In physics, the mean free path is the average distance traveled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions), which modify its direction or energy or other particle properties.

The following table lists some typical values for air at different pressures at room temperature.

In gamma-ray radiography the mean free path of a pencil beam of mono-energetic photons is the average distance a photon travels between collisions with atoms of the target material. It depends on the material and the energy of the photons:

where μ is the linear attenuation coefficient, μ/ρ is the mass attenuation coefficient and ρ is the density of the material. The Mass attenuation coefficient can be looked up or calculated for any material and energy combination using the NIST databases

In X-ray radiography the calculation of the mean free path is more complicated, because photons are not mono-energetic, but have some distribution of energies called a spectrum. As photons move through the target material, they are attenuated with probabilities depending on their energy, as a result their distribution changes in process called spectrum hardening. Because of spectrum hardening, the mean free path of the X-ray spectrum changes with distance.

Sometimes one measures the thickness of a material in the number of mean free paths. Material with the thickness of one mean free path will attenuate 37% (1/e) of photons. This concept is closely related to half-value layer (HVL): a material with a thickness of one HVL will attenuate 50% of photons. A standard x-ray image is a transmission image, an image with negative logarithm of its intensities is sometimes called a number of mean free paths image.

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