Two-proton (2p) radioactivity is an exotic nuclear decay mode resulting in the simultaneous emission of two protons. The ground-state 2p radioactivity was discovered in the decay of 45Fe in 2002. Later, this novel decay mode was also found in the decays of 48Ni, 54Zn, and 19Mg.In order to study a promising 2p radioactivity candidate 30Ar, an experiment was performed at the Fragment Separator of GSI in Darmstadt (Germany). The in-flight decay technique, which is based on the tracking of the in-flight decay products by using the silicon strip detectors, was employed. Several calibration and alignment procedures were performed to achieve the best-possible accuracy of position and angle measurements. In order to determine the angular and half-life resolutions as well as the detection efficiency, the decays of the previously-known 2p emitter 19Mg were remeasured. The 2p radioactivity of 19Mg ground state and sequential emission of protons from several known excited states in 19Mg were confirmed. The deduced 2p decay energies are consistent with previous data. The evidence on a new excited state in 19Mg at 8.9^(+0.8)_(-0.7) MeV above the 2p threshold was found. It was tentatively suggested that this new 19Mg state decays by sequential emission of protons via two unknown 18Na resonances at 2.5^(+0.7)_(-0.3) MeV and 4.0^(+1.5)_(-0.6) MeV above the 1p threshold, respectively.Two previously-unknown proton-unbound nuclei 30Ar and 29Cl were identified by measuring the trajectories of their in-flight decay products 28S+p+p and 28S+p, respectively. The analysis of 28S-proton angular correlations provided information on the decay energies and structure of the observed states in 30Ar and 29Cl. The assigned ground state and first excited state of 29Cl were found at 1.8^(+0.1)_(-0.1) MeV and 2.3^(+0.1)_(-0.1) MeV above the one-proton threshold, respectively. The ground state of 30Ar was found to be 2.45^(+0.05)_(-0.10) MeV above the 2p emission threshold. Due to a strong Thomas-Ehrman shift, the lowest states in 30Ar and 29Cl point to a violation of isobaric mirror symmetry in the structure of these unbound nuclei. Detailed theoretical calculations of the correlations between 2p decay products followed by the Monte Carlo simulations of the detector response to the 2p decay were performed in order to investigate the decay mechanism of the 30Ar ground state. Its decay is located in a transition region between simultaneous 2p decay and sequential emission of protons. Such an interplay between the true three-body and the sequential two-body decay mechanisms is the first-time observation in a nuclear ground state. The theoretical investigations of the transition dynamics demonstrated a surprisingly strong sensitivity of the decay correlation patterns to the 2p decay energy of the 30Ar ground state and the one-proton decay energy as well as the one-proton decay width of the 29Cl ground state. The first hint on so-called fine structure in the decay of 30Ar*(2+) was obtained by detecting two decay branches into both ground state and first excited state of 28S. The comparison of the experimental 28S-proton angular correlations with those resulting from the Monte Carlo simulations of the detector response illustrates that other observed 30Ar excited states decay by sequential emission of protons via intermediate resonances in 29Cl. The decay schemes of the observed states in 30Ar and 29Cl were constructed.
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