Scattering 1 Classical scattering of a charged particle (Rutherford ...

QRecoilqVirtualGammaRealGammaFigure 12: A schematic of the scatteing of a photon from the field of a charge Qx2(−vt,b,0)QVx2’S2x1x3x1’Px3’S1Figure 13: The geometry uses for calculating the EM impulse due to the EM fielda Fourier transform to the wave equations for the vector and scalar potentials;[k 2 − ω 2 /c]V (k, ω) = (−1/ǫ)ρ(k, ω)[k 2 − ω 2 /c] ⃗ A(k, ω) = (−µ) ⃗ J(k, ω)Then let ρ = Qδ(⃗x − ⃗ V t) and ⃗ J = ⃗ V ρ. Apply a Fourier transform to obtainρ = Q 2π δ(ω − ⃗ k · ⃗v)The potentials then have the form;V = −2πǫQ δ(ω − ⃗ k · ⃗v)k 2 − ω 2 /c 2⃗A = ⃗v/c 2 VThe fields are then obtained from ⃗ E = ⃗ ∇V − ∂ ⃗ A∂tand ⃗ B = ⃗ ∇ × ⃗ AThis results in;⃗E( ⃗ k, ω) = i(ω⃗v/c 2 − ⃗ k)V22