Phenomenological description of new features of rotational spectra

Abstract

It is shown that the energy expression as a cubic polynomial (CP) in spin $I$, in addition to giving an excellent fit to the excitation energies of the ground-band levels in all even-even nuclei, also reproduces a critical spin ${I}_{c}$ beyond which the squared rotational frequency ${\ensuremath{\omega}}^{2}$ decreases although the moment of inertia $\mathcal{g}$ keeps on increasing, thus resulting in back bending in $\mathcal{g}\ensuremath{-}{\ensuremath{\omega}}^{2}$ plots. This feature is predicted to appear not only in well-deformed nuclei but at quite low spins in nearly spherical nuclei as well. Further, the CP formula predicts the nuclear moment of inertia for the first ${2}^{+}$ state to be smaller than that for the ground state for most of the hard rotors; correspondence of this characteristic with the shrinkage deduced from muonic atom studies and M\ossbauer experiments is discussed.