Phys. Dept., Catholic Univ. of America, Washington, DC 20064
M. F. Werby
NRL, Code 7181, Stennis Space Center, MS 39529
The basic principle of the resonance scattering theory, or RST [Flax et al., J. Acoust. Soc. Am. 63, 723 (1978)] consists in separating the scattering amplitude for elastic objects into two parts: a nonresonant background (assumed that of rigid-body scattering for solid-metal and thick-shell objects, as shown above and earlier by Junger), and a series of resonance amplitudes that can be represented as in the Breit--Wigner nuclear scattering theory (cf. reference above). It is shown that this way of subdividing the scattering amplitude into two parts follows naturally from Hilbert--Schmidt theory. For not-so-thick shells, the correct background was given by Werby [original derivation published in Acoustic Resonance Scattering, edited by H. Uberall (Gordon and Breach, New York, 1992)]. Subtraction of the appropriate background in partial wave space can be facilitated by representing the modal amplitudes (and resonances) as a function of frequency, or as done in a more recently introduced approach [Talmant et al., J. Acoust. Soc. Am. 86, 278 (1989)], by representing the total amplitude as a function of mode number. This furnishes an unambiguous classification scheme for all orders of resonances, and allows one to isolate fluid-borne waves as recently identified by Talmant et al.