Ok, I need to do some integrals. I'm trying to find the number of electrons scattering per unit time into a given longitudinal velocity.
I need to do the integral:
![](http://www.forkosh.dreamhost.com/mimetex.cgi?%5Cint_0%5E%5C1%20du%5Cint_0%5E%5Cinfty%20dq%20%7B1%5Cover%20%28qu%29%5E3%7D%282-u%5E2%29%5Cdelta%28p_z%20-%20qu%29f%28q%29)
where
![](http://www.forkosh.dreamhost.com/mimetex.cgi?f%28q%29)
is typically a Gaussian.
I can do the
![](http://www.forkosh.dreamhost.com/mimetex.cgi?u)
integral first which seems like the right thing to do. But then to check it, I can integrate over
![](http://www.forkosh.dreamhost.com/mimetex.cgi?p_z)
from the momentum acceptance to infinity and get the Touschek lifetime. But I can't see how it gives the right answer. Anyway, its fun to get back to this stuff.
1 comment:
maths...fun ???
I may have a very different notion of what "fun" can be.
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