Coulomb symmetry breaking in one- and two-electron atoms

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Abstract
The existence of additional (more general than geometrical) symmetry is established for two important physical systems. The first of them is the excited hydrogen atom in perpendicular electric and magnetic fields when only the terms linear in the field strength are taken into account (corresponding to first-order perturbation theory). In particular, one of the fields can be absent, some additional discrete symmetry transformations appear. The second system is the doubly excited two-electron atom with the dipole approximation for the electron-electron interaction. The additional symmetry of these systems can be considered as a residual one related to the high symmetry of the unperturbed hydrogen-type system (the hydrogen atom and the two-electron atom with non-interacting electrons). The lowering of this initial symmetry, depending on the form of the symmetry-breaking interaction, is analysed.