Solving the problem of multiple scattering on an arbitrary number of scatterers in the homogeneous three-dimensional space

The article offers an approach to the solution of the problem of multiple scattering on a set of bodies in the homogeneous boundless space. For this purpose we consider the problem of multiple scattering of two bodies located in a primary field of a plane wave. The initial nonperturbed scattering amplitudes of each scatterer are assumed known. The solution is constructed by the calculation of repeated rescattering of plane waves between scatterers. The integral equations permitting one to calculate resultant scattering amplitudes for each of them and a cumulative scattering amplitude of a system consisting of two scatterers are obtained. It is shown that the solution of this problem allows one to solve the problem of the scattering field for an arbitrary number of scatterers. The expressions for the scattering amplitude in the case of an arbitrary primary field are given. The relation between integral equations for multiple scattering in the homogeneous space and those for multiple scattering of a single body near the plane boundary is demonstrated. The approximate expressions for calculation of the scattering amplitude in the case of multiple scattering are presented.