Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton ($2p$) radioactivity, the $2p$ decay energies (\textit{Q}$_{2p}$) are extracted by the Weizs\"{a}cker-Skyrme-4 (WS4) model, the finite-range droplet model (FRDM), the Kourra-Tachibaba-Uno-Yamada (KTUY) model and the Hartree-Fock-Bogoliubov mean-field model with the BSk29 Skyrme interaction (HFB29). Then, the $2p$ radioactivity half-lives are calculated within the generalized liquid drop model (GLDM) by inputting the four types of \textit{Q}$_{2p}$ values. By the energy and half-life constraints, it is found that the probable $2p$ decay candidates are the nuclei beyond the proton-drip line in the region of \textit{Z} $<$50 or \textit{Z}$\leq 50$ based on each nuclear mass model. In the region beyond \textit{Z}=50, the $2p$-decaying candidates are predicted only using the HFB29 mass model. Finally, the competition between the true $2p$ radioactivity and $\alpha$-decay for the nuclei above the \textit{N}=\textit{Z}=50 shell closures is discussed. It is shown that $^{101}$Te, $^{111}$Ba and $^{114}$Ce prefer to $2p$ radioactivity and the dominant decay mode of $^{107}$Xe and $^{116}$Ce is $\alpha$-decay.