On a paradox" in the scattering theory

Abstract

The solution of the "paradox" in scattering theory is considered, according to which the extinction cross section is expressed in terms of the forward scattering amplitude (the so-called "optical theorem"), whereas for a point source, and as a consequence, for any emitter located at a finite distance from the scatterer, a similar ratio is often written through a scattered field near the emitter, i.e. determined by "backscattering". A clear picture of the formation of radiation losses during the transition of energy from the source to the scatterer is presented. It is shown that although the field backscattered to the source determines the change in its radiation characteristics (the Purcell effect), the optical theorem includes an extinction factor which is generally related to the work of the incident wave on the currents induced in the scatterer. This factor passes into the forward scattering amplitude in the limiting case of a plane incident wave. Keywords: optical theorem, energy conservation, radiation losses, Purcell effect, point source of radiation.