Conclusions

The additivity principle in highly and SD rotational bands of the $A\sim130$ mass region has been studied within the cranked Hartree+Fock theory based on the SLy4 energy density functional and the cranked relativistic mean-field theory with the NL1 Lagrangian. The main results can be summarized as follows:

• The two sets of effective s.p. charge quadrupole moments $q_{20}^{\mbox{\rm\scriptsize {eff}}}$ and $q_{22}^{\mbox{\rm\scriptsize {eff}}}$, transition quadrupole moments $q_t^{\mbox{\rm\scriptsize {eff}}}$, and effective angular momenta $j^{\mbox{\rm\scriptsize {eff}}}$ have been produced. This rich output allows for an easy and simple determination of transition quadrupole moments $Q_t$ in highly deformed and SD bands in the $A\sim130$ mass region. In some cases, configuration assignments based on the relative (effective) alignment method can be done based on the calculated values of effective angular momenta $j^{\mbox{\rm\scriptsize {eff}}}$ (see, however, Sec. 3.3).
• Our statistical analysis of distributions of residuals confirms that the additivity principle is well fulfilled in the self-consistent approaches that properly take into account polarization effects.
• The contribution from the triaxial degree of freedom to the transition quadrupole moment is usually small, but it cannot be ignored when aiming at a quantitative reproduction of experimental data. The average magnitude of $q_{22}^{\mbox{\rm\scriptsize {eff}}}$ values is greater in the CHF+SLy4 model than in CRHF+NL1, thus suggesting that the potential energy surfaces produced in the former model are more $\gamma$-soft.
• For the majority of s.p. orbitals, there is a considerable difference between the effective and bare expectation values of one-body operators. This indicates the importance of polarization effects (shape polarization for quadrupole moments and the shape and time-odd-mean-field polarization for angular momentum alignment).
• With very few exceptions, there is a great deal of consistency between CHF and CRMF results for the effective s.p. moments and alignments.

So far, the additivity principle has been investigated only for highly deformed or SD bands in the $A$$\sim$130-150 mass region. It would be interesting to extend such studies to other high spin structures. The most promising candidates are: (i) terminating bands in the $A\sim 110$ mass region characterized by very weak pairing and appreciable $\gamma$-softness [14], and (ii) SD rotational bands in the $A\sim 60$ and $A\sim 80$ mass regions of superdeformation [46]. Work along these lines is in progress.