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In physics, the attenuation length or absorption length is the distance \( \lambda \) into a material when the probability has dropped to 1/e that a particle has not been absorbed. Alternatively, if there is a beam of particles incident on the material, the attenuation length is the distance where the intensity of the beam has dropped to 1/e, or about 63% of the particles have been stopped.

Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer-Lambert law:

\( P(x)=e^{{-x/\lambda }}\!\,. \)

In general \( \lambda \) is material and energy dependent.
See also

Beer's Law
Mean free path
Attenuation coefficient
Attenuation (electromagnetic radiation)
Radiation length

References

S. Eidelman; et al. (2004). Particle Data Group (ed.). "Review of particle physics". Physics Letters B. 592 (1–4): 1–5. arXiv:astro-ph/0406663. doi:10.1016/j.physletb.2004.06.001. PMID 10020536.
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