Abstract
A two-level numerically soluble shell model previously utilized by Lipkin, Meshkov, and Glick to investigate the accuracy of the random phase and related approximations is applied to the study of boson expansion methods for the description of a vibrational spectrum. Since the model is expressed completely in terms of quasi-spin operators, the required correspondence to boson operators is given by well-known results from the theory of ferromagnetism. The expansions required are also obtained independently by the methods current in nuclear physics. The spectra computed from several harmonic and anharmonic oscillator approximations to the exact Hamiltonian are compared with the results of an exact diagonalization, and possible analogies with the case of vibrational nuclei are drawn.
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