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The present calculations involved full diagonalization of many matrices of dimension 1000 and partial (iterative) diagonalization of matrices of dimension 150 × (J + 1). Each set of levels thus takes a few hours on a powerful workstation. In contrast, perturbative calculations are generally limited to matrices of dimension less than a 100 and can be performed on a personal computer.
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We thank S. Miller for helpful comments on this manuscript, and the U.K. Engineering and Physical Science Research Council, the U.K. Particle Physics and Astronomy Research Council, the North Atlantic Treaty Organization, the Royal Society, the Natural Sciences and Engineering Research Council of Canada, the Petroleum Research Fund, NASA, NSF, and the Russian Fund for Fundamental Studies, all of whom supported aspects of this project.
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