Matrix Theory of Elastic Resonance Scattering and its Application to Fluid-Filled Cavities

A fundamental matrix theory is developed for the exact isolation of resonance amplitudes in the elastic field scattered by a penetrable target. This theory is based on the fact that, in order to remain unitary, the S-matrix must be expanded in the product of the background and resonance matrices that are also unitary. The unitarity makes the isolation of the resonance matrix always possible. In the T-matrix formalism, the global scattering matrix is given as the sum of the background matrix, the resonance matrix and their mutual interaction. Therefore, when the mutual interaction is not taken into account, the matrix theory returns to the classical resonance scattering theory. The matrix theory is applied to cylindrical and spherical fluid-filled cavities, and exact expressions for the resonance coefficients are found, allowing us to obtain correct information on the cavities' resonances. The validity of the matrix theory is also demonstrated by numerical calculations performed for a cylindrical water-filled cavity in aluminum medium and for a cylindrical mercury-filled cavity in epoxy medium. For individual partial waves, the resonance coefficients are equal in magnitude to the residual coefficients used in the classical theory. But there are great differences in phase; thus, for the total wave, two theories present different resonance spectra even in magnitude.