CASIMIR ENERGY FOR A SPHERICAL CAVITY IN A DIELECTRIC - APPLICATIONS TO SONOLUMINESCENCE

In a series of papers, Schwinger [Proc. Natl. Acad. Sci. U.S.A. 90, 95 8 (1993); 90, 2105 (1993); 90, 4505 (1993); 90, 7285 (1993); 91, 6473 (1994)] proposed that the ''dynamical Casimir effect'' might provide t he driving force behind the puzzling phenomenon of sonoluminescence. M otivated by that exciting suggestion, we have computed the static Casi mir energy of a spherical cavity in an otherwise uniform material. As expected, the result is divergent; yet a plausible finite answer is ex tracted, in the leading uniform asymptotic approximation. This result agrees with that found using zeta-function regularization. Numerically , we find far too small an energy to account for the large burst of ph otons seen in sonoluminescence. If the divergent result is retained, i t is of the wrong sign to drive the effect. Dispersion does not resolv e this contradiction. In the static approximation, the Fresnel drag te rm is zero; on the other hand, the electrostriction could be comparabl e to the Casimir term. It is argued that this adiabatic approximation to the dynamical Casimir effect should be quite accurate.