What is the linear attenuation coefficient and how does it relate to interaction probability?
Answers
Answered by
0
For a LAC μμ, the probability of interaction after a path length l<<1/μl<<1/μ, is approximately: P≈l⋅μP≈l⋅μ, e.g. if l=0.001cml=0.001cm and μ=100cm−1μ=100cm−1, then the probability of interactions is approximately: P≈10%P≈10%. This no longer applies when l≳1/μl≳1/μ.
More precisely, the probability of interaction (or the fraction of incident radiation which will interact) is:
P=1−e−l⋅μP=1−e−l⋅μ
Or equivalently the Transmittance is,
T=e−l⋅μT=e−l⋅μ
This is often expressed using the mean-free-path λ=1/μλ=1/μ, such that typically a photon will interact after a distance λλ
More precisely, the probability of interaction (or the fraction of incident radiation which will interact) is:
P=1−e−l⋅μP=1−e−l⋅μ
Or equivalently the Transmittance is,
T=e−l⋅μT=e−l⋅μ
This is often expressed using the mean-free-path λ=1/μλ=1/μ, such that typically a photon will interact after a distance λλ
Answered by
16
The linear attenuation coefficient is defined using fractional beam absorption, i.e.
where is the intensity of the beam. Rearranging a bit leaves you with:
The right hand side can be interpreted as the probability of interaction per unit length. It is properly constrained between 0 and 1 because no change in intensity can be greater than the total intensity . Integrating both sides will give the probability of absorption over some distance which DilithiumMatrix covers nicely in their answer.
where is the intensity of the beam. Rearranging a bit leaves you with:
The right hand side can be interpreted as the probability of interaction per unit length. It is properly constrained between 0 and 1 because no change in intensity can be greater than the total intensity . Integrating both sides will give the probability of absorption over some distance which DilithiumMatrix covers nicely in their answer.
Attachments:
Similar questions