Abstract
The Casimir energy of a solid ball (or cavity in an infinite medium) is calculated by a direct frequency summation using contour integration. The dispersion is taken into account, and the divergences are removed by making use of the zeta function technique. The Casimir energy of a dielectric ball (or cavity) turns out to be positive and increasing as the radius of the ball decreases. The latter eliminates completely the possibility of explaining, via the Casimir effect, the sonoluminescence for bubbles in a liquid. Besides, the Casimir energy of the air bubbles in water proves to be immensely smaller than the amount of the energy emitted in a sonoluminescent flash. The dispersive effect is shown to be unimportant for the final result.
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