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The Casimir energies for plate-sphere system and sphere-sphere system underPFA in the presence of one extra compactified universal dimension are analyzed.We find that the Casimir energy between a plate and a sphere in the case ofsphere-based PFA is divergent. The Casimir energy of plate-sphere system in thecase of plate-based PFA is finite and keeps negative. The extra-dimensioncorrections to the Casimir energy will be more manifest if the sphere is largeror farther away from the plate. It is shown that the negative Casimir energyfor two spheres is also associated with the sizes of spheres and extra space.The larger spheres and the longer distance between them make the influence fromthe additional dimension stronger.

international journal of theoretical physics

The proximity force approximation for the Casimir energy of plate-sphere  and sphere-sphere systems in the presence of one extra compactified universal  dimension