Shift operator techniques for the classification of multipole-phonon states. VII. Self-consistent single step algorithm for R(5) O l eigenstate and eigenvalue determination

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Abstract
A previously derived set of quadratic relations in the R(5) shift operators Okl (‖k‖?3), is shown to be in such a way complete, that any O0l eigenvector and corresponding eigenvalue can be unambiguously obtained in a step by step calculation which starts at the highest angular momentum state. Such a calculation strictly follows the pattern of an algorithm, which unlike the tree generating mechanism, has unlimited applicability. Previous knowledge of the existence and of the degeneracy of a state not being required the algorithm itself accounts for the l multiplicity of states and is therefore called self‐consistent.