(a) Show from (10.125) that the integral of the shadow scattering differential cross section, summed over outgoing polarizations, can be written in the short-wavelength limit as

and therefore is equal to the projected area of the scatterer, independent of its detailed shape. (b) Apply the optical theorem to the "shadow" amplitude A0.125) to obtain the total cross section under the assumption that in the forward direction the contribution from the illuminated side of the scatterer is negligible incomparison.

Transcribed Image Text:

elle, -), ei(x-*;)-k d²k d'x. d'x Osh