Reliable nuclear weak rates are key inputs for understanding the origin of heavy elements and constraining the environments of the corresponding stellar nucleosynthesis. We present the effective stellar β^--decay rates of the N=50, 82, 126 r-process waiting-point nuclei in realistic stellar environments with high temperature, high density and strong magnetic field. Both allowed and first-forbidden transitions are considered, and transitions from the low-lying states of parent nuclei due to the thermal population are taken into account properly. The stellar β^--decay rates of the N=50, 82 waiting points are not sensitive to stellar temperature, while those of the N=126 waiting points increase rapidly with stellar temperature. With the increase of stellar density, the electron chemical potential increases accordingly, which leads to reduction of the stellar β-decay rates. Besides, the stellar β-decay rates are found to increase rapidly with the magnetic field B when B 10^14 G. Depending on the stellar temperature, density and magnetic field, the rates may vary by several orders of magnitude, which indicates that dynamic β-decay rates for corresponding stellar conditions may be indispensable inputs for understanding the r-process nucleosynthesis.
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