Validity of Many-Body Approximation Methods for a Solvable Model II: Linearization Procedures

摘要

The validity of methods used in the study of many particle systems was investigated by using the same approximations in treating a simple model for which exact solutions are avail able. The model consisted of N fermions distributed in two Nfold degenerate levels and interacting via a monopole-monopole force. The excitation of the first collective state above the ground state was calculated using the folowing methods: (1) The method of linearized equations of motion, (2) linearization with the inclusion of renormalized single particle energies, (3) a new self-consistent linearization method. The results of these approximation methods were then compared with exact results and with the results of ordinary perturbation theory found in a previous paper. It was found that renormalization of the single particle energies leads to a considerable improvement of the results over that obtained with ordinary linearization method, especially for small numbers of particles. Further improvement was obtained with the self-consistent linearization method. The possibility of applying this latter method to more realistic problems was briefly discussed. (Author)