[QUE/QFT-15013] QFT-PROBLEM

Show that the Rutherford scattering cross section for a second quantized Dirac particle in an external Coulomb field \((Ze^2/r)\) is given by \begin{equation} \frac{d\sigma}{d\Omega} = \frac{Z^2\alpha^2(1-v^2\sin^2(\theta/2))}{4|\vec{k}|^2 v^2 \sin^4(\theta/2)}. \end{equation} where \(\vec{k}\) is the momentum of the incident particle and \(\theta \) is the angle of scattering.