Past exam of the theoretical physics II course of the University of Cambridge / 2014 / Paper 1 / 3 / c / Solution

At large $r$, $|\mathbf{r}-{\mathbf{r}}_j|=r-\hat{\mathbf{r}}\cdot {\mathbf{r}}_j+O(r^{-1})$. Retain the displacement in the phase, but replace the denominator by $r$. ThereforeThe differential scattering cross-section is $|f{|}^2$ for elastic scattering with this unit incident plane-wave normalization. interference depends on outgoing direction and centre separation as well as the incoming phases already contained in $c_j$.