Systematic Behaviour at Large Degeneracies in a Soluble Model

Abstract

The use of the Time Dependent Hartree-Fock (TDHF) approximation to describe the time-evolution of one body densities in nuclear systems is by now well understood. It has been tested both in realistic situations involving the collision of heavy nuclear fragments and in model systems where a detailed comparison of exact and TDHF results can be done. It has been stressed¹ that in general TDHF as a zero order approximation lacks an expansion parameter on which to base a systematic analysis of higher order corrections. However in some simple models, namely the Lipkin, Meshkov and Glick² (LMG) model and a one dimensional system with attractive delta-interactions such a parameter exists¹. In this contribution we study the effects that the existence of this large N limit in the LMG model has on the calculation of eigenvalues, its 1/N corrections, and on the evolution of correlations in the exact wave function.