COHERENT STATE ANALYSIS OF ELLIOTT'S MODEL

Abstract

Anatysis of the time evolution of the coherent states for a two-dimensional version of Elliott's rotational model reveals a uniform rotation of the nuclear quacfrupole. The explanation of nuclear collective motion in terms of a miaoscopic description of the many- particle system is a longstanding problem. A remarkable step forward towards its solution has been taken by J. P. Elliott (I) with the introduction of the SU(3) model for nuclear rotations. Elliott has shown that the SU(3) symmetry of the oscillator mean field defines a natural subspace of the shell model in which a semi-realistic nuclear Hamiltonian has a rotational spectrum. However, the model is a static one and the conclusion about rotational properties is based merely on considerations about stationary states. Questions about the nature of rotational motion, such as what is rotating ? and how is it rotating ? are not answered. Therefore it appears that part of the physical insight is still missing. In this paper we present a timedependent counterpart of Elliott's model. We investigate the propagation of wavepackets associated with Elliott's subspace. These wavepackets are the Perelomov coherent states for the unitary goup, the time evolution of which is evaluated through the Time Dependent Variational h-inciple (TDVP) (2,3). The preliminary study we report on in this paper, concerns the two-dimensional version of the model (41.