The acoustic scattering by thin-walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex-k plane is directly analyzed using Cauchy's residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid-loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, fiat-plate Lamb wave for the fluid-loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free-field scattering process are also analyzed in terms of the resonance excitation of these modes. , PACS numbers: 43.30. Gv, 43.20.Fn, 43.40.Ey INTRODUCTIONThe study of the acoustic scattering from submerged, elastic targets has become increasingly fashionable in the last decade. Much of the more recent work has been concerned with resonance scattering theory and its implications for the inverse scattering problem. However, advances in this area will also have an impact on the more general question of fluid-elastic structure interactions, which have much more diverse applications. In this context, we note that the fluidloaded, elastic spherical shell is the simplest, nontrivial, three-dimensional example of such a dynamical system amenable to a numerical/analytical treatment over an extended frequency range. A solid physical understanding of the scattering from this target will surely yield dividends when the subtleties associated with more complicated structures are encountered. This acoustic scattering problem, which is the subject of the present article, thus takes on special significance.The earliest investigation of the acoustic scattering from an elastic spherical shell was apparently by Junger. • This article was quite modern in perspective in that it touched on a number of issues of current interest. For example, it was in this article that the concept of the separation of the scattering solution for shells into two terms, a "rigid body scattering" (background) contribution and a "radiation scattering" (resonant) contribution, was first introduced. While Junger's analysis also underscored the profound effects of fluid loading on the dynamical characteristics of the shell in vacuum, 2 this analysis must be regarded as incomplete; the thin shell theory employed by this author was later found to be inadequate for the bending modes of a spherical shell. 3 A scattering formalism utilizing the full linearized, elastic equations of motion for the spherical shell was later given by Goodman and Stern 4 and subsequently employed by Hickling • in a theoretical study of steady state and transient solutions. Hickling's analysis of the scattering of short transient pulses led him to propose that the component of the sc...

The scattering of sound by objects buried in underwater sediments is studied in the context of an exactly soluble model. The model consists of two fluid half-spaces separated by a planar, fluid, transition layer of arbitrary thickness. Attenuation is included in any of these regions by using complex wave numbers. A directional source field, generated in the upper half-space by a continuous line array, insonifies an object placed in the lower half-space. The scattered field detected by another line array placed anywhere in the system may be calculated. The solution is determined from the T matrix for the bounded scattering system and is exact (in linear acoustics) to all orders of multiple scattering among the interfaces and object. Numerical results are presented to investigate the effect of the local acoustic environment on the free-field, in-water scattering resonances of thin spherical shells. The field scattered by a shallowly buried object is discussed with emphasis on the importance of evanescent wave scattering in detection from above the sediment over an extended range. An initial set of experiments meant to verify the model are described. Results are presented and discussed for the measured scattering response of buried, spherical, evacuated, steel shells, that are 2.25% and 11% of the outer radius in thickness.

We investigate, in the MIT bag model, the M1 transitions of low-lying hadrons. We perform the following calculations: (I) We recompute 32 hadron masses with a choice of bag parameters designed to give the correct values for the proton magnetic moment, pp, and several masses, M,, M,, MA, M,, and M D ;(2) we compute q, q', q, mixing in an untrustworthy approximation; and (3) we compute the widths for 38 M 1 transitions.

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