Abstract
The physical and mathematical properties of bound-state matter configurations which are made of massive scalar fields with a non-trivial (non-minimal) coupling to the electromagnetic field of a central charged reflecting shell of radius Rs are studied analytically. In particular, we explicitly prove that the Klein-Gordon wave equation for the composed charged-reflecting-shell-nonminimally-coupled-linearized-massive-scalar-field system is amenable to an analytical treatment in the dimensionless weak coupling regime (or equivalently, in the dimensionless small-mass regime) μαQ≪1 (here μ,Q, and α are respectively the proper mass of the non-minimally coupled scalar field, the electric charge of the spherically symmetric supporting shell, and the non-minimal coupling parameter of the composed Maxwell-scalar theory). We derive a remarkably compact resonance formula {μ(α,Q,Rs;n)}n=1n=∞ for the allowed masses of the supported spatially regular scalar fields in the composed charged-shell-nonminimally-coupled-massive-scalar-field bound-state configurations.
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