Shift operator techniques for the classification of multipole-phonon states. III. The quadrupole-phonon eigenstates of O0l

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Abstract
It is shown that the non‐l‐degenerated normalized eigenstates of O0l can be identified with previously constructed quadrupole‐phonon states which have been labeled by the intermediate angular momentum values. The l‐degenerated O0l eigenstates are proven to be identical to the corresponding eigenstates of the fifth label generating operator S. From the analysis of the relationship between O0l and S, a rigorous expression for S in terms of canonical operators is withdrawn, while it also becomes possible to obtain the S eigenvalues in exact irrational form.