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Within the Random-Phase Approximation the method of self-consistent determination of the isoscalar and isovector effective separable interactions restoring a broken symmetry of the deformed mean-field is given. The method allows to treat more rigorously without free parameters the properties of the scissors mode and is used to develop the rotational invariant microscopic model of the states with K π = 1 + . The spurious state separates out and has zero energy. An important consequence of this separation is the fragmentation of the scissors mode and the collectivization of the low-lying 1 + states. In addition to the isoscalar restoring interactions the consideration of the isovector restoring forces in calculations causes the splitting of the states with large B(M1) strength at low energy. The model contains a single parameter of isovector spin-spin interactions and it allows one to describe satisfactorily the fragmentation of the scissors mode and the dependence of the summed B(M1) strength on δ 2 and A in deformed nuclei.

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Using the quasiparticle phonon nuclear model (QPNM) and taking into account the spin–spin interaction, the effects of the spin polarization on spin gyromagnetic factors (gs) as well as the intrinsic magnetic moments (gK) of the deformed odd neutron 155-165 Dy isotopes were studied. The calculated values of gs and gK are in fair agreement with the experiment as well as with other microscopic calculations. Our calculations indicated that because of the core polarization, the gs factors of the nucleons in the nucleus reduce noticeably from its free nucleon value and the spin–spin interactions play an important role in the explanation of the quenching of the gs factors. A very good reproduction of the phenomenological quenching of gs factor from its free values [Formula: see text] is obtained for 155-165 Dy .