  A three-body semiclassical model is proposed to describe the nucleon transfer
and emission reactions in a heavy-ion collision. In this model the two heavy
particles, i.e. nuclear cores A$_1(Z_{A_1}, M_{A_1})$ and A$_2(Z_{A_2},
M_{A_2})$, move along classical trajectories $\vec R_1(t)$ and $\vec R_2(t)$
respectively, while the dynamics of the lighter neutron, n, is considered from
a quantum mechanical point of view. Here, $M_i$ are the nucleon masses and
$Z_i$ are the Coulomb charges of the heavy nuclei ($i=1,2$). A Faddeev-type
semiclassical formulation using realistic paired nuclear-nuclear potentials is
applied so that all three channels (elastic, rearrangement and break-up) are
described in an unified manner. In order to solve these time-dependent
equations the Faddeev components of the total three-body wave-function are
expanded in terms of the input and output channel target eigenfunctions. In the
special case when the nuclear cores are identical (A$_1 \equiv$ A$_2$) and the
two-level approximation in the expansion over target functions the
time-dependent semiclassical Faddeev equations are resolved in an explicit way.
To determine the realistic $\vec R_1(t)$ and $\vec R_2(t)$ trajectories of the
nuclear cores a self-consistent approach based on the Feynman path integral
theory is applied.
