The influence of level crossings on the collective dynamics

Abstract

Level crossings, arising in a deformed shell model have a strong influence on the collective masses. As a schematic picture we set up the multi-level model (MLM), consisting of a series of equidistant level crossing, and apply this to different approximations for a collective Hamiltonian. The results are compared to a complete generator coordinate method description. If the residual interaction between the crossing states is strong, all the model Hamiltonians work well. But for small or vanishing residual interaction they all fail to reproduce the proper dynamical behaviour. A simple generalization is proposed in which the collective Hamiltonian is allowed to contain projectors. In this form it is able to reproduce the static and the dynamic structure of the MLM for an arbitrary residual interaction.