|Message: Re: Implement channel cross sections||Not Logged In (login)|
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The interaction length you refer to is the mean interaction length, given by
1/(number density)/(cross section) . This is different from the actual interaction length which is the sampled distance to a particular interaction. The actual interaction length will be distributed about the mean and so could be shorter or longer than the mean.
So, when an interaction due to a larger cross section occurs, it will usually, but not always, happen in a shorter distance than one due to a smaller cross section.
More importantly, in the case of competing processes, when one process occurs at the end of a given step, its actual interaction length is re-sampled, while the actual interaction lengths of the other processes are not. For these the preceding step length is subtracted to get new, shorter interaction lengths, which may now be shorter than the re-sampled length of the first process. So, after a sufficient number of steps, a rare process will occur instead of a more likely one.