title: Acoustic scattering by inhomogeneous spheres.
abstract: Acoustic scattering problems are considered when the material parameters (density rho and speed of sound c) are spherically symmetric functions of position. Explicit separated solutions are derived (i) when rho(r) = exp(beta r) and c(-2) is a linear function of r(-1), and (ii) when rho(r) = exp(-beta r2) and c(-2) is a linear function of r2. In both cases, the radial parts of the solutions are given in terms of Coulomb wave functions or Whittaker functions; these are well-studied special functions, closely related to confluent hypergeometric functions. Two problems are discussed in detail: scattering by an inhomogeneous sphere embedded in a homogeneous fluid, and scattering by a homogeneous sphere with a concentric inhomogeneous coating.
authors.affiliation: Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden 80401-1887, USA. pamartin@mines.edu
authors.forename: P A
authors.initials: PA
authors.lastname: Martin