Confinement of Atoms under General Boundary Conditions

The energy spectrum of a nonrelativistic quantum particle and hydrogen-like atom is considered under the most general conditions of confinement in a spatial box (vacuum cavity). It is shown that the rear-rangement of the lowest energy levels occurring in this case turns out to be considerably more significant when compared with the case of confinement achieved by the impenetrable potential barrier. The role in the rear-rangement of this level, played by the von Neumann-Wigner level repulsion effect, is emphasized. For an atom confined in a spherical cavity of radius R, it is also shown that, when the role of the cavity boundary is played by the surface layer of nonzero depth d, the atomic ground state possesses a deep and pronounced minimum for the physically reasonable width and depth of that surface layer, in which the binding energy turns out to be an order of magnitude larger than that of the lowest 1s-level of a free atom E-1s. Also, it becomes possible to achieve a mode when the binding energy of an atom is noticeably higher than E-1s at R on the order of 10-100 nm.