Gamow shell model predictions for six-proton unbound nucleus $^{20}$Si

Proton-rich nuclei beyond the proton drip line are of great interest in nuclear structure physics, due to exotic phenomena such as proton emissions and the Thomas-Ehrman shift (TES). In this work, we employ the Gamow shell model (GSM) to investigate the structure and decay of $^{20}$Si, a candidate for six-proton (6$p$) emission, which can be produced via two-neutron knockout from the drip line nucleus $^{22}$Si. We predict that its ground state decays via $6p$ emission to the ground state of $^{14}$O, with a decay energy $E_{6p} = 10.125$ MeV and a width of 371~keV. A $2^+$ state is predicted at 1.7 MeV, comparable with that in $^{18}$Mg, indicating the disappearance of the $Z=14$ magic number in $^{20}$Si. Instead, analyses of the many-body configurations and the average occupancies of the mirror states suggest the presence of $dynamic$ TES in low-lying states of $^{19}$Al/$^{19}$C and $^{20}$Si/$^{20}$C. Further evidence is provided by analyzing the contributions of different components of the GSM Hamiltonian. Moreover, this study offers the first theoretical description of $^{20}$Si and guidance for future experiments.