Electromagnetic wave scattering by a small impedance body of an arbitrary shape

It is proved that electromagnetic wave scattering problem for a small impedance body D of an arbitrary shape is uniquely solvable and the scattered field can be found in the form e = ∇× ∫_s g(x, t)J(t)dt, where S is the smooth surface of the small body D, J is a tangential field on S, and g(x, t):= e^ik|x-t|/4π|x-t|. The full field is E = E₀ + e, where E₀ is the incident field. The scattering amplitude is A(α, β, k) = -ζ|S|/4π √ϵ/μ [β, τ∇×E₀(O)], where the origin O is assumed to be inside D, β := x/|x|,|x| →∞, τ := τ_pq := δ_pq - 1/|S| ∫_s N_p(t)N_q(t)dt, α is the unit vector in the direction of the incident plane wave, ϵ and μ are dielectric and magnetic constants of the medium, and δ_pq is the unit tensor.