Direct mode summation for the Casimir energy of a solid ball

Abstract

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 ${\epsilon }_1{\mu }_1={\epsilon }_2{\mu }_2$. Upon deriving the general expression for the Casimir energy, a dilute compact ball is considered $({\epsilon }_1-{\epsilon }_2{)}^2/({\epsilon }_1+{\epsilon }_2{)}^2\ll 1$. In this case the calculations are carried out which are of the first order in ${\xi }^2$ and take account of the five terms in the Debye expansion of the Bessel functions involved. The implication of the obtained results to the attempts of explaining the sonoluminescence via the Casimir effect is shortly discussed.

REVTeX, 7 pages, no figures and tables, treatment of a dilute dielectric ball is revised, new references are added

References in corpus (5)

• Casimir energy in the MIT bag model
• Observability of the Bulk Casimir Effect: Can the Dynamical Casimir Effect be Relevant to Sonoluminescence?
• Simple method for calculating the Casimir energy for sphere
• Justification of the zeta function renormalization in rigid string model
• Casimir effect in dielectrics: Bulk Energy Contribution

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• Casimir energy calculation for massive scalar field on spherical surfaces: an alternative approach
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