The beta-decay rates of neutron-rich nuclei relevant to the r-process nucleosynthesis are mostly beyond experimental reach. Their predictions demand a self-consistent extrapolation of various nuclear properties away from the experimentally known regions. The allowed transitions approximation commonly used in large-scale microscopic calculations also needs to be revised in different mass regions. The density functional+continuum QRPA approximation to self-consistent calculations of the ground state properties, Gamow-Teller and first-forbidden beta-decay transitions of nuclei far from stability is developed. Systematic calculations are performed of the allowed and first-forbidden beta-decay rates for the r-process relevant nuclides near the closed neutron shells at N=50,82,126. The importance of first-forbidden decays near Zgreater than or equal to50, Napproximate to82 and near N=126 is shown. The total beta-decay half-lives in the region east of the Pb-208 are estimated. A comparison with recent experimental data, global calculations, and self-consistent microscopic predictions is presented.
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