A plane wave E 0 exp[i(k 0 r t)] scatters from a dielectric cube with volume V = a 3 and electric susceptibility

A plane wave E₀ exp[i(k₀ · r − ωt)] scatters from a dielectric cube with volume V = a³ and electric susceptibility χ << 1. Two cube edges align with k₀ and E₀.
(a) Calculate the differential scattering cross section in the Born approximation.

(b) Show that σ_Born ≈ 1/4 k²a⁴χ² when ka >> 1. The near-forward direction dominates the scattering when ka >> 1.
(c) The weak scattering assumed by the Born approximation implies that|E_rad|/|E₀|<<1 for all q, even when r ≈ a. Deduce from this that the ka. >> 1 result of part (b) is valid only when σ_Born << χa².