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The low-lying isovector dipole strengths in neutron rich nuclei $^{26}$Ne and$^{28}$Ne are investigated in the quasiparticle relativistic random phaseapproximation. Nuclear ground state properties are calculated in an extendedrelativistic mean-field theory plus BCS method where the contribution of theresonant continuum to pairing correlations is properly treated. Numericalcalculations are tested in the case of isovector dipole and isoscalarquadrupole modes in the neutron rich nucleus $^{22}$O. It is found that inpresent calculation low-lying isovector dipole strengths at $E_x < 10$ MeV innuclei $^{26}$Ne and $^{28}$Ne exhaust about 4.9% and 5.8% of theThomas-Reiche-Kuhn dipole sum rule, respectively. The centroid energy of thelow-lying dipole excitation is located at 8.3 MeV in $^{26}$Ne and 7.9 MeV in$^{28}$Ne.Comment: 20pages 5 figures. Accepted for publication in Physical Review

physical review. c. nuclear physics/physical review. c, nuclear physics

Low-lying dipole modes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ne</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>26</mml:mn><mml:mo>,</mml:mo><mml:mn>28</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>in the quasiparticle relativistic random phase approximation

Low-lying dipole modes inNe26,28in the quasiparticle relativistic random phase approximation