How Does Photon Energy Influence Exponential Attenuation in Matter?

[Orlando]

I am researching how photon intensity attenuates within matter and am a bit confused by what I have come across.

Several sources state that the attenuation of photon intensity within matter is exponential (as a function of depth). The explanation is that photon interactions with electrons in matter are probabilistic and the chances of such interactions must therefore be equal for each photon in order for an exponential relationship to eventuate, otherwise the attenuation coefficient would not be constant.

However, all sources state that with Compton interactions a photon is scattered with decreased energy and that the energy of an incident photon influences the probability of the photon being scattered at a particular angle (this is based on the Klein-Nishina differential cross section). My issue is that this does not agree with the exponential attenuation theory as it appears to me that as the incident photons lose energy as they are scattered, the rate at which they lose energy will decrease as it will become less likely that they will be scattered at large angles. An exponential relationship would require a constant rate of energy loss, would it not?

Can someone help me understand this? Much appreciated.

 

[xts]

If you speak about attenuation, you usually consider collimated beam (usually of defined frequency). Thus single Compton interaction (or any other scattering) removes this photon from the original beam - so it is considered lost - the same as absorbed photon.

Further history of scattered (in any mechanism) photon does not count - the original beam is already weakened, and probability that after many scatterings photon eventually returns to the beam is usually neglected.

 

[Orlando]

Thanks for the response, that makes sense.