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A model Hamiltonian describing a two-level system with a crossing plus apairing force is investigated using technique of large-amplitude collectivemotion. The collective path, which is determined by the decoupling conditions,is found to be almost identical to the one in the Born-Oppenheimerapproximation for the case of a strong pairing force. For the weak pairingcase, the obtained path describes a diabatic dynamics of the system.Comment: 3 pages, Latex using epsf.sty, 2 postscript figures included. Talk  presented at Conference on ``Atomic Nuclei and Metallic Clusters: Finite  Many-Fermion Systems'' (September 1 -- 5, 1997, Prague, Czech Republic), to  be published in Czechoslovak J. Phy

Large Amplitude Collective Motion in Nuclei and Metallic Clusters: Applicability of adiabatic theory for a pairing model