# Thompson scattering, simple integral?

1. May 11, 2010

In theory this is a simpel integral problem which i can't solve

So i'm doing some plasma physics, and it comes with the derivation of the Thompson scattering (please bear with the first time i've tried using latex, im sorry some of the greek lowercase laters look like superscripts, there not supposed to)

So i'm at the point where i have the total cross-section $$\sigma$$T = the integral of (d$$\sigma$$/d$$\Omega$$) d$$\Omega$$.
ok so i've been given (d$$\sigma$$/d$$\Omega$$) = re2sin2$$\theta$$

so the integral d$$\Omega$$ = d$$\theta$$d$$\phi$$, with $$\theta$$ between 0 and pi, and $$\phi$$ between 0 and 2pi.

but so the $$\phi$$ integral just gives 2pi, and in my attempt the integral of sin2$$\theta$$ with respect to $$\theta$$ over 0 and pi, is just pi/2?

yet looking at my notes, and the actual thompson scattering they have $$\sigma$$T = 8pi*re2/3

now in my notes it says that the ingtegral over sin2$$\theta$$ d$$\theta$$ can become the integral over -sin2$$\theta$$ dcos$$\theta$$ still with $$\theta$$ between 0 and pi, and this yes, gives the required answer of 8pire2/3.

but hows do they change the intergral to that?

that is my only qualm, how they change the integral, and how my method of just ingetraing sin2$$\theta$$ d$$\theta$$ is not just pi/2???

i appreciate any help! :D (sorry for the long explanation)

2. May 11, 2010