The proton has a charge radius

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Particles, interactions and experiment

Particle Physics, Ch Decay rates, cross sections and phase space

Problem

r_p = 0.84\,\mathrm{fm}

, giving a geometric area

\pi r_p^2 \approx 22\,\mathrm{mb}

. At a certain low beam momentum the measured cross section for antiproton-proton annihilation is

\sigma = 600\,\mathrm{mb}

. Someone argues: 'Since

\sigma = \pi r^2

defines the size of the target, the true radius involved here must be

r = r_p\sqrt{\sigma/(\pi r_p^2)} \approx 4.4\,\mathrm{fm}

, more than five times the accepted proton radius.' Identify the error in this argument and state what the cross section actually measures.