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

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 $\frac{d \sigma}{d \Omega_{CM}}$; 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 $M_N \to \infty$, and compute $\frac{d \sigma}{d \Omega_{lab}}$.

Is there a general procedure to go from the first to the second? I first wrote $\frac{d \sigma}{dt}$ and then multiplied it for a rather complicated expression that I found on a book to obtain $\frac{d \sigma}{d \Omega_{lab}}$. However, taking the infinite massive nucleus limit, the result I get is not what I'm supposed to.

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Hmmm...as the target mass grows the CoM frame gets slower and slower with respect to the lab frame (and should come to a halt in the limit as $M_n \to \infty$), no? – dmckee Apr 3 '13 at 16:09
@dmckee so you are saying that just by taking the limit $M_n \to \infty$ in $\frac{d \sigma}{d \Omega_{cm}}$ I would get the right answer for $\frac{d \sigma}{d \Omega_{lab}}$? I didn't think about it. I don't know if it works but I'll try to do it tomorrow – user22710 Apr 3 '13 at 16:29
Well, I haven't sat down and figured it for myself. You might also look to see if you can find a ratio like $M_N^\alpha v_{CM}^\beta$ that stays finite in the limit and write the whole thing in terms of that ratio. But try the simplest possible option first. – dmckee Apr 3 '13 at 17:02