Where does the 2π factor come from in the scattering cross section?

[david_clint]

Homework Statement

Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step.

Homework Equations

see attachment

The Attempt at a Solution

I got sigma (without the 2PI) by changing variable to t =cos theta, thus integrating between minus and plus 1and using m=n in the legendre polynomial,

so I am wondering if the 2PI came from integrating over the phi dependence as we are dealing with scattering from a radial potential?

I also need prodding in the right direction for the next step!

 

[Avodyne]

Yes, the 2pi comes from integrating over phi, and so there should be a 2pi in front of the integral sign in the last equation.

 

[sxc656]

Yes, the 2pi comes from integrating over phi, and so there should be a 2pi in front of the integral sign in the last equation.

Thanks:)