  We study quantum effects of recently discovered kink solitons which are
constructed self-consistently by coupling to a single, excited fermion bound
state. Our studies are based on the observation that in a semi-classical
expansion the energies of this single level and of the Dirac sea should be
treated equally. For these kink solutions we compute the energy of the Dirac
sea as the fermion vacuum polarization energy. We find it to be substantial and
to typically outweigh the energy gain from binding the single level.
