${}^{164}\mathrm{P}\mathrm{b}$: A possible heaviest $N=Z$ doubly magic nucleus

We confirm by using the Skyrme Hartree-Fock-Bogoliubov calculation that ${}^{164}\mathrm{P}\mathrm{b}$ is a possible heaviest $N=Z$ doubly magic nucleus whose lifetime is long enough to be measured on accelerator experiments. We estimate the proton-emission and alpha-decay half-lives of ${}^{164}\mathrm{P}\mathrm{b}$. The estimated proton-emission half-life ranges from $0.1\mathrm{p}\mathrm{s}$ to $10\mathrm{n}\mathrm{s}$, while the alpha decay can be safely neglected.