Dynamics and non-adiabaticity in the fission process

The fission process takes a time which is not appreciably longer than single-particle times. Therefore, it is not clear that the fragmentation process can be described in an adiabatic limit. In the paper the excitation of the nucleus during the deformation process is calculated both analytically and numerically within the framework of the cranking model. The model nucleus is defined by a Hamiltonian containing a deforming Nilsson-type single-particle Hamiltonian, pairing interaction, and a schematic residual interaction. For this time-dependent Hamiltonian, the time-dependent Schroedinger equation is solved by (i) perturbation expansion for the analytic discussion and (ii) direct numerical procedure. For the numerical solution, the Hilbert space is confined to the BCS ground state and a limited number of two quasi-particle excitations corresponding to lowest excitation energy. Calculations have been performed for a vibrating calcium and a fissioning uranium nucleus. (Auth.)