Several states of proton-unbound isotopes $^{30}$Ar and $^{29}$Cl were investigated by measuring their in-flight decay products, $^{28}$S+proton+proton and $^{28}$S+proton, respectively. A refined analysis of $^{28}$S-proton angular correlations indicates that the ground state of $^{30}$Ar is located at $2.45^{+0.05}_{-0.10}$ MeV above the two-proton emission threshold. The theoretical investigation of the $^{30}$Ar ground state decay demonstrates that its mechanism has the transition dynamics with a surprisingly strong sensitivity of the correlation patterns of the decay products to the two-proton decay energy of the $^{30}$Ar ground state and the one-proton decay energy as well as the one-proton decay width of the $^{29}$Cl ground state. The comparison of the experimental $^{28}$S-proton angular correlations with those resulting from Monte Carlo simulations of the detector response illustrates that other observed $^{30}$Ar excited states decay by sequential emission of protons via intermediate resonances in $^{29}$Cl. Based on the findings, the decay schemes of the observed states in $^{30}$Ar and $^{29}$Cl were constructed. For calibration purposes and for checking the performance of the experimental setup, decays of the previously-known states of a two-proton emitter $^{19}$Mg were remeasured. Evidences for one new excited state in $^{19}$Mg and two unknown states in $^{18}$Na were found.
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