Unified Description of Phenomenological Models of Ground-State Bands in Even-Even Nuclei

A generalized stretching model for the description of the ground band levels in even-even nuclei is developed under the provision that the higher-order cranking corrections and Coriolis-antipairing effects, as well as the corrections due to quadrupole centrifugal stretching, are all effectively included in the stretching term expressible in terms of a "generalized stretching variable" $t$. A basic set of equations is derived by writing the nuclear moment of inertia $\mathcal{I}$ as a function of $t$ as ${\mathcal{I}}_{0}f\left(t\right)\mathrm{}$. It is shown that practically all the successful two- and three-parameter models advanced during the past few years can be obtained from this basic set of equations through appropriate choices for $f\left(t\right)\mathrm{}$. For example, a linear cutoff in the Taylor's expansion for $f\left(t\right)\mathrm{}$ gives the equations of the variable moment-of-inertia model. The interrelationships, and the correspondence of respective parameters, in various models are established. Further, it is shown that, for models in which $f\left(t\right)\mathrm{}$ is also an explicit function of the nuclear spin $I$, the effective moment of inertia for excited states is renormalized from the value ${\mathcal{I}}_{0}f\left(t\right)\mathrm{}$ by an additional spin-dependent term.