Excitation during collective deformation: How simple it is

In the frame of the time dependent Hartree-Fock-Bogolyubov method a simple model for the excitation of a nucleus during a collective deformation is presented. The Hilbert space consists of all single and multiple pair excitations the nucleons of each pair being in time reversed states. The non-adiabatic transitions within this space are treated correctly. Treating the selfconsistency ofλ andΔ only in an average way reduces the multichannel calculation to a set of Landau-Zener problems. These give the excitation probability of each pair. Introducing average quantities yields an analytic solution for the excitation energy in the fission process, the collective kinetic energy at the scission point and the mean number of pair excitations for any deformation.