File:Shape deformations 4.jpg

Summary

(a) Observed rotational bands in \(_{68}^{166}\)Er\(_{98}\). Excitation energies (in MeV) of levels are written on the r.h.s., while the spin-parity \(I\pi\) on the l.h.s. The levels belonging to a band are connected by strongly enhanced E2 transitions. The bands are labeled by the component \(K^{\pi}\) of the total angular momentum with respect to the symmetry axis ; \(K^{\pi}=0^{+}\) and 2\(^{+}\) for the ground and the first excited bands, respectively. For \(K\)=0 \(R\)-symmetry implies a restriction on the I-values fulfilling the condition, (\(-\)1)\(^{I}\) = \(r\). Consequently, only even- or odd-\(I\) values appear in a given rotational band. The ground state band of deformed even-even nuclei consists of even integer values of \(I\) with positive parity, since the configuration, in which a doubly degenerate time-reversed pair of one-particle levels in a deformed potential are pairwise filled, has \(r\)=+1. (b) Three lowest-lying rotational bands are observed in \(_{92}^{238}\)U\(_{146}\). Due to \(R\)-symmetry of the deformation the rotational band with \(K^{\pi}\)=\(0^{-}\) and \(r=-1\) has members with \(I^{\pi}=1^{-},3^{-},5^{-}\), ..., while the one with \(K^{\pi}\)=\(0^{-}\) and \(r=+1\) has those with \(I^{\pi}=0^{-},2^{-},4^{-},\) ...

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