  The problem of spontaneous pair creation in static external fields is
reconsidered. A weak version of the conjecture proposed by G Nenciu (1980) is
seated and proved. The method reduces the proof of the general conjecture to
the study of the evolution, associated with a time dependent Hamiltonian, of a
vector which is eigenvector of this Hamiltonian at some given time. Possible
ways of proving the general conjecture are discussed.
