The resistive coated sphere in the presence of a point generated wave field

We consider the low-frequency scattering problem of a point source generate d incident field by a small penetrable sphere. The sphere, which is also lo ssy, contains in its interior a co-ecentric spherical core on the boundary of which an impedance boundary condition is satisfied. An appropriate modif ication of the incident wave field allows for the reduction of the solution to the corresponding scattering problem of plane wave incidence, by moving the point source to infinity. For the near field, we obtain the low-freque ncy coefficients of the zeroth and the first order. This was done with the help of the corresponding solution for the hard core problem and an appropr iate use of linearity with respect to the Robin parameter. In the far held, we derive the leading non-vanishing terms for the normalized scattering am plitude and the scattering cross-section, which are both of the second orde r, as well as for the absorption cross-section, which is of the zeroth orde r. The special cases of a lossy or a lossless penetrable sphere, of a resis tive sphere, and of a hard sphere are recovered by an appropriate choice of the physical or the geometrical parameters. Copyright (C) 1999 John Wiley & Sons, Ltd.