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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.

Abstract:In this paper the Quasiparticle-Phonon Nuclear Model (QPNM), based on QRPA (Quasiparticle Random Phase Approximation) phonons, has been utilized to investigate spin polarization effects on the groundstate magnetic properties such as intrinsic magnetic moment ( K ) and effective spin gyromagnetic factor ( ) of odd-mass deformed 165−179 Hf isotopes with K > 1/2. Investigations of the spin polarization effects of the even core on the magnetic moments show that the spin gyromagnetic factors ( ) of the nucleons in the nucleus differ noticeably from the corresponding values for free nucleons and that the spin-spin interactions play an important role in the re-normalization of factors of the odd-mass 165−179 Hf isotopes. In addition, some theoretical predictions are presented for the magnetic moments of 165 Hf, 167 Hf, and 169 Hf, whose ground state magnetic moments haven't been experimentally determined yet. PACS

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