that are hardly accessible to direct measuring, whereas the actual asymptotic energy/momentum are unaffected, so the discussion is physically rather meaningless so far. The situation improves in the case of non-central collisions of two particles with impact parameter $b$. In first order perturbation theory this is described in the following way: A particle moves straight ahead to the point of minimal distance $r_0$ from the scattering centre, its interaction vertex. There its radial momentum reverses by the exchange of a virtual particle and it flies away along a straight line at a scattering angle $\vartheta_0$ from its ingoing direction.

(100,65)(10,-15) (10,10)[(1,0)[80]{}]{} (30,10)[(-1,0)[20]{}]{} (30,10) (30,10)[(-3,5)[20]{}]{} (30,10)[(-3,-5)[10]{}]{} (10,10)[(5,-3)[15]{}]{} (20,-6) (10,-6)[(1,0)[80]{}]{} (30,10)[(0,-1)[16]{}]{} (31,11)[V]{} (10,11)[A]{} (20,-1)[B]{}(19,-10)[C]{}(30,-10)[D]{}(15,40)[outgoing particle]{}(64,12)[incoming particle]{} (70,0)[(0,1)[10]{}]{} (70,0)[(0,-1)[6]{}]{}(72,0)[$b$]{}(24,11)[$\vartheta_0$]{}

In the figure the particle comes from the right, the scattering centre is denoted by C and the vertex by V. A, B, and D are auxiliary points. We may read off the following relations. The triangles VCD and AVB are similar with the angles at $\angle$CVD and $\angle$BAV being equal to $\vartheta_0/2$. The radial component $\overrightarrow{\rm VB}$ of the momentum $\vec
p=\overrightarrow{\rm VA}$ at V is $$p_r=p\sin\frac{\vartheta_0}{2},$$ the relation between the particle’s minimal distance $r_0=\overline{\rm VC}$ from C and the impact parameter is 