VALIDITY OF MANY-BODY APPROXIMATION METHODS FOR A SOLVABLE MODEL II: LINEARIZATION PROCEDURES.
MARYLAND UNIV COLLEGE PARK
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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