Intrinsic states of deformed odd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi></mml:math>nuclei in the mass regions (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>151</mml:mn><mml:mi>≤</mml:mi><mml:mi>A</mml:mi><mml:mi>≤</mml:mi><mml:mn>193</mml:mn></mml:math>) and (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>≥</mml:mo><mml:mn>221</mml:mn></mml:math>)

A review of the empirical data on intrinsic states of odd-$A$ nuclei in the mass range $151\ensuremath{\le}A\ensuremath{\le}193$ and $A\ensuremath{\ge}221$ is presented. Global summaries of the data are presented in tables for each isotopic and isotonic chain, wherein the excitation energy, the $log\mathrm{ft}$ values, the moment-of-inertia parameter, and the decoupling parameter (for $K=\frac{1}{2}$ bands) are listed for single-particle, vibrational admixed, and pure vibrational states. Similar data are separately presented for three-quasiparticle excitations in the rare-earth region. Taking guidance from the systematics on nuclear deformation, the single-particle deformed potential for axially symmetric and reflection-symmetric shapes (the Nilsson model) modified by the hexadecapole deformation is used to interpret the data. Other variations of the Nilsson model, which include axially asymmetric shapes ($\ensuremath{\gamma}$ deformation) and especially reflection-asymmetric shapes (octupole deformation), have also been used to interpret the data in certain limited regions. Systematics for the intrinsic excitations are presented and discussed in terms of these models. The newly emerging regions of the octupole-quadrupole deformation and superdeformation are also discussed.

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