Cranked Relativistic Mean Field Description of Superdeformed Rotational Bands

The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertia J (2) of the observed bands but also the alignment properties of the singleparticle orbitals. In the relativistic mean field (RMF) theory the nucleus is described as a system of point-like nucleons, Dirac spinors, coupled to the meson and Coulomb fields. The nucleons interact via the exchange of several mesons, namely a scalar σ -meson, which provides a strong intermediate range attraction, the isoscalar-vector ω-meson responsible for a very strong repulsion at short distances and the isovector-vector ρ-meson which takes care of the symmetry energy. This theory with only seven parameters fitted to the properties of several spherical nuclei provides an economic and accurate way to describe many properties of finite nuclei throughout the periodic table [1]. The RMF theory formulated in the rotating frame cranked RMF theory [2, 3] (further CRMF) has been recently applied for a systematic investigation of superdeformed (SD) rotational bands observed in the A ∼ 140− 150 mass region [4]. It was shown that this theory provides a rather good agreement with the available experimental data on the dynamic moments of inertia J . It reproduces the trend of the changes of the charge quadrupole moments Q0. Moreover, the classification of the SD bands in terms of the number of filled high-N intruder orbitals, originally suggested within the cranked Nilsson (further CN) model [5], is supported by the CRMF theory. As the linking transitions from superdeformed states have not been identified in this mass region, the relative properties of different SD bands play an important role in our understanding of their structure. One way to identify the single-particle orbital by which two SD bands differ is to compare the difference in their dynamic moments of inertia J (2) observed in experiment with the ones obtained in calculations. However, the deficiency of this approach is that different (especially, non-intruder) orbitals have rather similar contributions to the total J . This prevents a unique definition of the underlying configuration in terms of non-intruder orbitals due to the uncertainty related to the single-particle energies in the SD minimum. An alternative way to analyse the contributions coming from specific orbitals and thus to identify the configuration is the effective alignment approach suggested by I. Ragnarsson [6]. The effective alignment of two bands is defined as the difference between their spins at constant rotational frequency Ωx: i B,A eff (Ωx) = IB(Ωx) − IA(Ωx). The notation