β decays of isotones with neutron magic number of N=126 and r-process nucleosynthesis

beta decays of the isotones with N = 126 are studied by shell-model calculations taking into account both the Gamow-Teller (GT) and first-forbidden (FF) transitions. The FF transitions are found to be important to reduce the half-lives, by nearly twice to several times, from those by the GT contributions only. Possible implications of the short half-lives of the waiting point nuclei on the r-process nucleosynthesis during the supernova explosions are discussed. A slight shift of the third peak of the element abundances in the r process toward a higher mass region is found.