  In quantum field theory it is believed that the spontaneous decay of excited
atomic or molecular level is due to the interaction with continuum of field
modes. Besides, the atom makes a transition from upper level to lower one so
that the probability to find the atom in the excited state tends to zero. In
this paper it will be shown that the mathematical model in single-photon
approximation may predict another behavior of this probability generally.
Namely, the probability to find the atom in the excited state may tend to a
nonzero constant so that the atom is not in the pure state finally. This effect
is due to that the spectrum of the complete hamiltonian is not purely
absolutely continuous and has a discrete level outside the continuous part.
Namely, we state that in the corresponding invariant subspace, determining the
time evolution, the spectrum of the complete hamiltonian when the field is
considered in three dimensions may be not purely absolutely continuous and may
have an eigenvalue. The appearance of eigenvalue has a threshold character. If
the field is considered in two dimensions the spectrum always has an eigenvalue
and the decay is absent.
