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Skyrme-QRPA calculations for low-lying excitation modes in deformed neutron-rich nuclei

Low-frequency modes of excitation in deformed neutron-rich nuclei are studied by means of the quasiparticle random-phase approximation on the Skyrme-Hartree-Fock-Bogoliubov mean field. We investigate the microscopic structure of the soft $K^π=0^{+}$ modes systematically in neutron-rich Magnesium isotopes with $N=22, 24, 26$ and 28 close to the drip line, and it is found that the strong collectivity in $^{34}$Mg and $^{40}$Mg is acquired due to the coherent coupling between the $β$ vibration and the pairing vibration of neutrons. Microscopic structure of the $K^π=2^{+}$ modes changes gradually associated with the location of the Fermi level of neutrons, and it is found that the proton particle-hole excitation generating the $γ-$vibrational mode in $^{24}$Mg continues to play a key role in the near-drip-line nucleus $^{40}$Mg. The low-frequency octupole excitations are also investigated and the microscopic mechanism for the enhancement of transition strengths is discussed.