Two-Body Collision: Lab and CM Frames

Elastic two-body scattering reduced to one body of mass mu in a central potential. The centre-of-mass collision is the primary scene (particles meet and recoil back-to-back through the deflection angle chi); a compact lab-frame inset, a V(r) profile and a fixed-scale differential cross-section polar with the analytic Rutherford overlay are secondary panels. Hard sphere and Coulomb are closed-form; Yukawa is integrated.