  We explore the role of an intermediate state (phase) in homogeneous
nucleation phenomenon by examining the decay process through a doubly-humped
potential barrier. As a generic model we use the fourth- and sixth-order Landau
potentials and analyze the Fokker-Planck equation for the one-dimensional
thermal diffusion in the system characterized by a triple-well potential. In
the low temperature case we apply the WKB method to the decay process and
obtain the decay rate which is accurate for a wide range of depth and curvature
of the middle well. In the case of a deep middle well, it reduces to a
doubly-humped-barrier counterpart of the Kramers escape rate: the barrier
height and the curvature of an initial well in the Kramers rate are replaced by
the arithmetic mean of higher(or outer) and lower(or inner) partial barriers
and the geometric mean of curvatures of the initial and intermediate wells,
respectively. It seems to be a universal formula. In the case of a
shallow-enough middle well, Kramers escape rate is alternatively evaluated
within the standard framework of the mean-first-passage time problem, which
certainly supports the WKB result. The criteria whether or not the existence of
an intermediate state can enhance the decay rate are revealed.
