  The Landau--Zener effect is generalized for many-body systems with pairing
residual interactions. The microscopic equations of motion are obtained and the
$^{14}$C decay of $^{223}$Ra spectroscopic factors are deduced. An asymmetric
nuclear shape parametrization given by two intersected spheres is used. The
single particle level scheme is determined in the frame of the superasymmetric
two-center shell. The deformation energy is computed in the
microscopic-macroscopic approximation. The penetrabilities are obtained within
the WKB approximation. The fine structure of the cluster decay analyzed in the
frame of this formalism gives a very good agreement with the experimental ratio
of partial half-lives obtained in special conditions
