I'm reading the section on scattering in Goldstein's Classical Mechanics, and I have a rather basic question about this.
It says that scattering in the laboratory is a two-body problem because of the recoil of the scatterer. Therefore, we convert the obtained data into center of mass coordinates in order to find the true scattering angle, the angle that we would get if the scatterer didn't recoil. However, I'm having a hard time understanding what exactly this center of mass system is. The figure (3.25) below shows the path of two particles moving towards each other, but it looks like it is simply the laboratory problem shown in the frame of reference where the center of mass is not moving.
My question: It still looks like a two-body problem to me, especially since the scatterer is deviating from its path. How does this simply the situation? Figure 3.25 still doesn't show a situation where the scatterer's position is fixed. Neither does figure 3.24.