Advanced Quantum Mechanics Schwabl · Problem 15.2

Interacting Fields, Quantum Electrodynamics

Physics — Quantum Mechanics · mott-scattering-klein-gordon

Problem

For the scattering of Klein–Gordon particles in an external Coulomb potential, show that the differential scattering cross-section is

\frac{d\sigma}{d\Omega} = \frac{(\alpha Z)^2}{4E^2 v^4 \sin^4 \frac{\vartheta}{2}} ,

in contrast to the Mott scattering formula for spin-

\frac{1}{2}

particles, Eq. (15.5.23):

\frac{d\sigma}{d\Omega} = \frac{(\alpha Z)^2 (1 - v^2 \sin^2 \frac{\vartheta}{2})}{4E^2 v^4 \sin^4 \frac{\vartheta}{2}} .