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:
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uuUzD_8rvcA20HIFgE6-c8Z75mf8x9oFgR1SG3uCJumbdjsiXpLINr6NrGLYPeyAm2trQNettvM8oSIrC27DV2swhOq3vxYLIUtiPy5IA_T5Cxu6MWjplyAg6PY0r55AMCxqg1NqyuSw632N5mRdtYXoHgqJXrgpqVniwNLJxWiPNlo1izdC6FRYME4RaHHW4pbbKUQkoeTtRWR-EE8PIYp3u4egWQci02FyZbceC9MA=s0-d)
where
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sp-aD4jn4JZZZYF9_OFdmDylopVbktjf2D_Rhid-4ekOnOUCNIpwIa_ZwmDM-94x2KDD6cPUxU3rPE29Er0gXuZzRbdBoQZ3_YmE9mCQYdwl0wlg=s0-d)
is typically a Gaussian.
I can do the
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sCRm_9uYCYWGtSXSGXsSgRruhghMALG3_1ZDGzQQD_JtIxKheYj4gA4EIPjHweSBsWPSnAaMvyO5EWwKdPLQeEhz0Y_d6Mchy-qHX6OJ2qmZU=s0-d)
integral first which seems like the right thing to do. But then to check it, I can integrate over
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_thFUKlIJ0H-8XlWh3LtGVp1Mlr65gCWOK2YO4o3SYhaG9-l5hPAEq8fb_KOpJQRbkavpJ_S9NF_glBuryknB9LMTz8FLY3nELbe-3may86x9Jmpg=s0-d)
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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