Direct mode summation for the Casimir energy of a solid ball

The Casimir energy of a solid ball placed in an infinite medium is calculated by a direct frequency summation using the contour integration. It is assumed that the permittivity and permeability of the ball and medium satisfy the condition epsilon(1)mu(1) = epsilon(2)mu(2). After deriving the general expression for the Casimir energy, a compact ball is considered when xi(2) = (epsilon(1) - epsilon(2))(2)/(epsilon(1) + epsilon(2))(2) << 1. Calculations are carried out which are of the first order in xi(2) and take account of the fifth-order terms in the uniform asymptotic expansion of the Bessel functions involved. The implication of the results to attempt to explain sonoluminescence via the Casimir effect is briefly discussed.