  The effect of spontaneous breaking of initial SO(3) symmetry is shown to be
possible for an H-like atom in the ground state, when it is confined in a
spherical box under general boundary conditions of "not going out" through the
box surface (i.e. third kind or Robin's ones), for a wide range of physically
reasonable values of system parameters. The reason is that such boundary
conditions could yield a large magnitude of electronic wavefunction in some
sector of the box boundary, what in turn promotes atomic displacement from the
box center towards this part of the boundary, and so the underlying SO(3)
symmetry spontaneously breaks. The emerging Goldstone modes, coinciding with
rotations around the box center, restore the symmetry by spreading the atom
over a spherical shell localized at some distances from the box center. Atomic
confinement inside the cavity proceeds dynamically -- due to the boundary
condition the deformation of electronic wavefunction near the boundary works as
a spring, that returns the atomic nuclei back into the box volume.
