The Nucleus Resolved, Ch Reactions: four-vectors, amplitudes and partial waves
Problem
A beam of 20Ne ions (mass number 20) scatters elastically from a stationary hydrogen target. The scattering is known to be isotropic in the centre-of-mass frame. A researcher measures the laboratory angular distribution of the scattered 20Ne ions and finds every scattered ion within about 3∘ of the beam, with a count per steradian several hundred times what the same events would give spread evenly over the whole sphere, and climbing towards the edge of that cone. They write: "The reaction amplitude itself must be strongly forward-peaked; this is direct evidence of a grazing, surface-dominated reaction mechanism, since an isotropic process would give a flat laboratory distribution." Find the error in this reasoning, and state what the laboratory distribution actually shows about the reaction.