QFT: differential cross section from center of mass to lab frame

[bnado]

I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|² and the differential cross section in the center of mass frame dσ/dΩ_CM; I now have to go into the lab frame, where the nucleus is initially at rest, and consider the limit of a infinite massive nucleus MN→∞, and compute dσ/dΩ_lab.

Is there a general procedure to go from the first to the second? I first wrote dσ/dt and then multiplied it for a rather complicated expression that I found on a book to obtain dσ/dΩ_lab. However, taking the infinite massive nucleus limit, the result I get is not what I'm supposed to.

 

[andrien]

you should involve the fact
(dσ/dΩ')_lab dΩ'=(dσ/dΩ)_CM dΩ,which exploits the fact that the number of scattered particles passing through a cross section is same in both frames.