# Mass Attenuation Coefficient and Probability of Interaction

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?

## 1 Answer

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.

• 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. – cadillac Apr 7 '20 at 6:17
• @cadillac What are you actually trying to calculate, then? Because the probability of interaction requires more information. – probably_someone Apr 7 '20 at 15:14