Matrix theory of elastic resonance scattering and its application to fluid-filled cavities

A fundamental matrix theory is developed for the exact isolation of resonan ce amplitudes in the elastic held scattered by a penetrable target. This th eory is based on the fact that, in order to remain unitary, the S-matrix mu st be expanded in the product of the background and resonance matrices that are also unitary. The unitarity makes the isolation of the resonance matri x always possible. In the T-matrix formalism, the global scattering matrix is given as the sum of the background matrix, the resonance matrix and thei r mutual interaction. Therefore, when the mutual interaction is not taken i nto account, the matrix theory returns to the classical resonance scatterin g theory. The matrix theory is applied to cylindrical and spherical fluid-f illed cavities, and exact expressions for the resonance coefficients are fo und, allowing us to obtain correct information on the cavities' resonances. The validity of the matrix theory is also demonstrated by numerical calcul ations performed for a cylindrical water-filled cavity in aluminum medium a nd for a cylindrical mercury-filled cavity in epoxy medium. For individual partial waves, the resonance coefficients are equal in magnitude to the res idual coefficients used in the classical theory. But there are seat differe nces in phase: thus, for the total wave, two theories present different res onance spectra even in magnitude.