Low-lying Dipole Modes in $^{26,28}$Ne in the Quasiparticle Relativistic Random Phase Approximation

The low-lying isovector dipole strengths in neutron rich nuclei $^{26}$Ne and $^{28}$Ne are investigated in the quasiparticle relativistic random phase approximation. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method where the contribution of the resonant continuum to pairing correlations is properly treated. Numerical calculations are tested in the case of isovector dipole and isoscalar quadrupole modes in the neutron rich nucleus $^{22}$O. It is found that in present calculation low-lying isovector dipole strengths at $E_x < 10$ MeV in nuclei $^{26}$Ne and $^{28}$Ne exhaust about 4.9% and 5.8% of the Thomas-Reiche-Kuhn dipole sum rule, respectively. The centroid energy of the low-lying dipole excitation is located at 8.3 MeV in $^{26}$Ne and 7.9 MeV in $^{28}$Ne