Landau-Zener effect in superfluid nuclear systems
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