Does Repeated Particle Interactions Lead to Underestimating Energy Loss?

[Ado]

Hi !
I'm not sure to post my question in the right place so I'm sorry if I'm wrong...!
I have a particle associated with a certain spectrum in energy S (differential cross section).
When the particle interacts I use this distribution to have the energy lost.
Now, if my particle interacts 2 times, to have the distribution associated, I convolve 2 times my first distribution.
Am I wrong ?

Thanks in advance !

 

[mathman]

There are two random variables involved, energy loss first interaction, energy loss second interaction. Each of these has a distribution function. To get the distribution of the total energy loss, you can use the convolution of these distribution functions. Your assumption is that they are the same - are they?

 

[Ado]

I wanted to confirm that I could apply this method in this situation.
Thanks for your reply !

 

[mathman]

I would be careful about using the same distribution. After the first interaction, the particle has less energy, so I would expect the energy loss distribution for the second interaction to be different..

 

[Ado]

Yes, I expect these calculations to overestimate the reality !

Thx!

 

[mfb]

Overestimate in which way? Energy loss for lower-energetic particles can be larger, then you underestimate the energy loss.

For each final energy, you can integrate over the intermediate energy to get the probability of this final energy. That is the mathematically sound approach - simplifications might work depending on the situation.

 

[Ado]

Yes, in this sense, we underestimate the energy loss.
Thanks for all your answers!