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I have lists of partial mass attenuation coefficients (photo-e, scattering, pp) from a mixture of substance (elements). How can I calculate for the probability of the interactions?

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You need two things:

  • The density $\rho$ of the material, and
  • The length $\ell$ of the material.

Then, for mass attenuation coefficient $k$ (which has units of area over mass), the probability of interaction is

$$P=1-e^{-k\rho\ell}$$

As you can see, the interaction probability approaches zero as the length goes to zero, and it approaches 1 as the length goes to infinity.

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  • $\begingroup$ Thank you for that. But all I really have are MAC of the substance. I have the mass attenuation for photoelectric, compton, pair production and the total MAC. $\endgroup$ – cadillac Apr 7 '20 at 6:17
  • $\begingroup$ @cadillac What are you actually trying to calculate, then? Because the probability of interaction requires more information. $\endgroup$ – probably_someone Apr 7 '20 at 15:14

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