Can the spin-orbit interaction break the channel degeneracy (conservation) of the two-channel orbital Kondo problem?

Abstract.Two-level systems (TLS) interacting with conduction electrons are possibly described by the two-channel Kondo Hamiltonian. In this case the channel degeneracy is due to the real spin of the electrons. The possibility of breaking that degeneracy (conservation) has interest on his own. In fact, we show that the interaction of the conduction electrons with a spin-orbit scatterer nearby the TLS leads to the breaking of the channel degeneracy (conservation) only in the case of electron-hole symmetry breaking. The generated channel symmetry breaking TLS-electron couplings are, however, too weak to result in any observable effects.