New Geiger-Nuttall law of odd-Z nuclei and long-lived island beyond the stable line

Recently,we analyze the α-decay data of even-Z nuclei and propose the new Geiger-Nuttall law where the effects of the quantum numbers of α-core relative motion are naturally embedded in the law [Physical Review C 85,044608(2012)].In this paper,we firstly test whether the new law without any change of parameters can be applied to the α-decays of odd-Z nuclei which are more complicated than those of even-even nuclei. Then the nuclear shell effect around N=126 is analyzed for very proton-rich nuclei with Z=85–92 based on the data of α-decay energies and half-lives. A long-lived island beyond the stable line is proposed where the half-lives of nuclei on this island are abnormally long. The mechanism of the appearance of the island and its significance to other mass ranges are discussed.