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_sq6T-Z04Q9R4chm8MJcSJD-_NnYlPPJFx8orsBEJ1PoFGrrI4r60zwTomdx770hiXXwKw4mEXMD1cX9BnOo6528GzBU2FQt9FJkLqnP2RcDgXJtJb1pp5TTrGWVPAfenoDRd1ngrhtesjZyaj4ML-EblhsZavXP8_JAF2zQGNGtmdqJTD9H_bFELujJmRhcl2dLxr6fVWSGwXMILlfxyD3VA_xv-AvOR5wdlN-1tkGCA=s0-d)
where
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tlC_I1URdUU_ScPT3zRPVtDZ-pxrvxr-7yo31PSjp3zHdDrUfpFPJFDaSrra7YvMdCCQ6jVq9ouMHY88QNK43moVmiUoU8CoGEoKfZpioymOfD8w=s0-d)
is typically a Gaussian.
I can do the
![](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tMbG6YYyB-T4MME6NT3OL4jC0A3OQBqHbdM1UWZODuVAEIL2gprJe4dBWMXAxRoDAVoXRAHJDGBNaPFogy00_TpMvg3hJ8V_Ulrl5eP6ZR9xk=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_uLZwYV5WhOP4wvS_Gk5_pxLGN1oChvV62MN-wJ7bCFxV8Cz7yUikcUoNOUHREQlrBpV_q8l98qwOOkkty2juVUJyDS0KiHsgcPhnLBKouBMxBV-Q=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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