Diabatic and Adiabatic Collective Motion in a Model Pairing System

Abstract

Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schr\"odinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.Comment: 23 pages, 7 ps figures. Latex, uses revtex and graphic