For a massive scalar field in 3+1 dimensions, Casimir energy decays as e^{-2mL} for independent plate boundary conditions and as e^{-mL} when the boundaries are interconnected.
Dalvit, P Milonni, D Roberts, and F
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New vacuum boundary effects of massive field theories
For a massive scalar field in 3+1 dimensions, Casimir energy decays as e^{-2mL} for independent plate boundary conditions and as e^{-mL} when the boundaries are interconnected.