Abstract
In the frame of a method originally proposed by Jean, an exact expression is found for the eigenvalues of some residual interaction Hamiltonians in the degenerate model of spherical nuclei. The limits of validity of the isopairing force and other similar schematic forces are examined and extended. For the nondegenerate model, in a particular case (small energy gap between the various shells) a simple approximate formula for the eigenvalues of the pairing Hamiltonian is derived.
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