Abstract:In this study, the result of calculations using rotational, translational and Galilean invariant quasiparticle random-phase approximation is presented for the low-lying dipole excitations in the even-even 160 Gd nucleus. Calculations are carried out for both ∆K =1 and ∆K =0 branches. The analysis shows that the main part of spin-1 states, observed at energy 2.4-4 MeV in 160 Gd, have M1 character and are interpreted as main fragments of the scissors mode. The calculations indicate the presence of a few prominent negativeparity dipole ∆K =1 states in the investigated energy region, in agreement with experiment.

In this paper, gK -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g eff s ) of the 167−179 Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of gK and g eff s were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the gK factors exhibit good agreement with the experimental gK factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of gK is obtained for κ = (45/A) MeV and q = −1.

The beta decay properties of collective I^K = 1*1 states in doubly even deformed Er nuclei are investigated in the framework of the rotational invariant random-phase approximation. It is shown that an essential decrease of the rate of the allowed P-decay to the excited l*-states as compared with that to the ground state may be due to the orbital nature of the states. The model Hamiltonian includes restoring rotational invariance of the deformed single particle Hamiltonian forces and the spin-spin interactions. The analytical expressions for the Gamov-Teller (G-T) and Fermi (F) decay matrix elements are derived. The single-particle energies were obtained from the Warsaw deformed Woods-Saxon potential with deformation parameter S2 =0.24.The numerical residts for P* transition from Tm to Er indicate the importance of using rotational invariant Hamiltonian to explain experimental data.

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