On the solution to the large amplitude collective motion of finite interacting Fermi systems

Abstract

Hartree-Fock-Bogoliubov (HFB) states shaped by auxiliary external fields form an appropriate basis for executing the concept of generator coordinates to large amplitude collective motion. We present a nonperturbational expansion of the Hamilton kernel which is adapted to structural changes of a local HFB vacuum state. Neglecting four quasiparticle terms in this treatment this kernal depends only on the static potential energy, the overlap between the generator states, and a cranking-like coupling term originated by the external field. The physical role of the overlap function is reconsidered. The diagonalization of the overlap matrix and subsequent removal of small-norm eigenstates is suggested to be the consistent way for constructing the proper subspace that saves the conditions of smooth and slow collective motion. Practical examples for realistic nuclear systems demonstrate that this collective subspace turns out to have in fact a surprisingly small and therefore feasible dimension compared to the huge space spanned by the multi-quasiparticle excitations referred to a fixed vacuum. The application of the “horizontal” expansion opens a new field for the exploration of the dynamics of shape transitions, pair-field fluctuations, quantal rotational motion and tunneling phenomena. The proposed method is considered as the logical extension of the potential energy calculations to obtain a quantized collective motion.