Scalar wave diffraction from zero-range scatterers

The zero-range approximation for wave scattering is popularized. The general idea of the approximation is outlined and the theory is applied to solve an illustrative example: diffraction on a system of four identical scatterers forming a T-d-symmetry structure. The group theoretical methods are used to decompose a scattered wave into four partial waves adequate to the symmetry group of the target. Concepts of partial scattering amplitudes, associated phase shifts and partial cross sections for the nonspherical target considered are introduced and utilized. It is shown that under some conditions a phenomenon of resonant scattering may occur.