Investigation of quadrupole moments and dipole vibrations in deformed nuclei

Key Words: 126-136Ba, 164-170Er, 176-180Hf, Quadrupole moments, Deformation parameters, QRPA, Nuclear collective excitations, Electric dipole transitions, Magnetic dipole transitions, Scissors mode 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 electric dipole vibration mode and is used to develop the translational and Galilean invariant microscopic model of the states with spin and parity I ? = 1? . The Goldstone mode separates out and has zero energy. The predicted new branch of 1- coherent pairing fluctuations, associated with forces restoring Galilean invariance, appears below the two-quasipartical boundary. The model contains a single parameter of isovector dipole-dipole interactions and it allows one to describe satisfactorily both the energy and fragmentation of the Giant dipole resonance. Developed method where translational, Galileo and rotational invariance are restored self-consistently by using separable effective forces, are presented for the ground state dipole response in the even mass isotopes 128-136Ba, 164-170Er and 176-180Hf. Average resonance energy of the electric and magnetic dipole mode excitations, the energy-weighted and non-energy weighted sum rules have been investigated. Results of the calculations show that the model which use the Hamiltonian with broken symmetry strongly overestimates the summed B(E1) and B(M1) value of dipole excitations. In the rotational invariant case agreement between the calculated and the experimental average excitation energies of the scissors mode is rather good for all investigated nuclei. Introduction of the restoring forces essentially reduces B(Ml) strength and decreases substantially the discrepancy with the experiments for the low lying excitations. A destructive interference between the orbit and spin part of the M1 strength has been found for barium isotopes near the shell closer. For all the nuclei under investigation, the low-lying M1 transitions have ?K=1 character as it is the case for the well-deformed nuclei. The relative contribution of ?K=0 transitions to the total dipole decay width at spectroscopic energy region is small. Quadrupole moments of 166?180 Hf isotopic chain nuclei have been calculated by using superfluid model with Woods-Saxon potential. Our results showed that quadrupole moments and ß 2 deformation parameters of nuclei which have been calculated theoretically are in good agreement with the appropriate experimental data.