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

We confirm by using the Skyrme Hartree-Fock-Bogoliubov calculation that ${}^{164} \mathrm{Pb}$ 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 ${}^{164} \mathrm{Pb}$. The estimated proton-emission half-life ranges from $0.1 \, \mathrm{ps}$ to $10 \, \mathrm{ns}$, while the alpha decay can be safely neglected.