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Core-particle coupling models are made viable by assuming that coreproperties such as matrix elements of multipole and pairing operators andexcitation spectra are known independently. From the completeness relation, itis seen, however, that these quantities are themselves algebraic functions ofthe calculated core-particle amplitudes. For the deformed rare-earth nucleus158Gd, we find that these sum rules are well-satisfied for the ground stateband, implying that we have found a self-consistent solution of the non-linearKerman-Klein equations.Comment: revtex and postscript, including 1 figure(postscript), submitted to  Phys.Rev.Let

Application of the Kerman-Klein Method to the Solution of a Spherical Shell Model for a Deformed Rare-Earth Nucleus