[UPSC CSE 1991] Central Force Motion and Gravitation (Q127, 20M)

Define differential scattering cross-section for a scattering process, the differential scattering cross-section for neutrons scattered elastically from a solid is of the form \alpha(\theta) = A c^{-B(\vec{K}_i \cdot \vec{K}_f)^2} where A and B are constants and \vec{K}_i and \vec{K}_f are respectively the wave vectors of the incident and scattered neutron. Determine the total scattering cross-section. [\vec{K}_i] = [\vec{K}_f]