# Breit-Wigner Cross section

1. Feb 21, 2005

### secret2

Is anyone familiar with Breit-Wigner Cross section? Say, for a reaction with 2 particles in the initial state, 1 intermediate and 2 final:

$$\sigma = \frac{g \pi \lambda^2 \Gamma_i \Gamma_f}{(E-E_0)^2 + \frac{\Gamma^2}{4}}$$

I can't see why for the wavelength we should use the momentum of EITHER one particle in the initial state. Sure, I can choose either one because in the COM frame it doesn't matter which momentua of the initial particles I choose. But in the derivation of the above equation it is not obvious why the momentum cannot be, say, the TOTAL momentum in the lab frame. Afterall, isn't it true that working in the COM frame is simply a convention?

2. Feb 23, 2005

### dextercioby

Okay.Here's my advice:do the computation if the lab frame.From the very beginning till the end.No reference to COM,whatsoever.And then compare the results...

Yes,it is true.Most (if not all) scattering processes are analyzed using the COM reference frame for ease of calculations and for the fact that the COM is ALWAYS an IRS (elementary,relativistic level)...

Daniel.