where r ≡ ≡ ( x , y , z ) is the position vector; r ≡ ≡ | r | ; e i k z is the incoming plane wave with the wavenumber k along the z axis; e i k r / r is the outgoing spherical wave; θ is the scattering angle (angle between the incident and scattered direction); and f ( θ θ ) is the scattering amplitude. The dimension of the scattering amplitude is length. The scattering amplitude is a probability amplitude ; the differential cross-section as a function of scattering angle is given as its modulus squared,