H. Uberall
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.