  We study the level crossing of the fermion system described by the euclidean
Dirac Hamiltonian in the valley background.
  One chiral fermion level is shown to cross twice the zero value in the case
of well-separated instanton-anti-instanton background.
  Below a critical separation, however, level crossings are absent. The
phenomenon can be interpreted as the transition to a gauge field configuration
of purely perturbative nature, below a critical instanton-anti-instanton
separation. In the context of high-energy electroweak interactions, our
findings seem to definitely invalidate some optimistic argument concerning the
observability of baryon number violation based on the use of the optical
theorem in conjunction with the valley fields.
