Three-body correlations for the ground-state decay of the lightest two-proton emitter 6 Be are studied both theoretically and experimentally. Theoretical studies are performed in a three-body hyperspherical-harmonics cluster model. In the experimental studies, the ground state of 6 Be was formed following the α decay of a 10 C beam inelastically excited through interactions with Be and C targets. Excellent agreement between theory and experiment is obtained demonstrating the existence of complicated correlation patterns which can elucidate the structure of 6 Be and, possibly, of the A=6 isobar.

The interaction of an E/A=70-MeV (7)Be beam with a Be target was used to populate levels in (6)Be following neutron knockout reactions. The three-body decay of the ground and first excited states into the α+p+p exit channel were detected in the High Resolution Array. Precise three-body correlations extracted from the experimental data allowed us to obtain insight into the mechanism of the three-body democratic decay. The correlation data are in good agreement with a three-cluster-model calculation and thus validate this theoretical approach over a broad energy range.

The interaction of an E/A=57.6-MeV 17 Ne beam with a Be target was used to populate levels in 16 Ne following neutron knockout reactions. The decay of 16 Ne states into the three-body 14 O+p+p continuum was observed in the High Resolution Array (HiRA). For the first time for a 2p emitter, correlations between the momenta of the three decay products were measured with sufficient resolution and statistics to allow for an unambiguous demonstration of their dependence on the long-range nature of the Coulomb interaction. Contrary to previous measurements, our measured limit Γ < 80 keV for the intrinsic decay width of the ground state is not in contradiction with the small values (of the order of keV) predicted theoretically.PACS numbers: 25.10.+s, 23.50.+z, 21.60.Gx, 27.20.+n Introduction -Two-proton (2p) radioactivity [1] is the most recently discovered type of radioactive decay. It is a facet of a broader three-body decay phenomenon actively investigated within the last decade [2]. In binary decay, the correlations between the momenta of the two decay products are entirely constrained by energy and momentum conservation. In contrast for three-body decay, the corresponding correlations are also sensitive to the internal nuclear structure of the decaying system and the decay dynamics providing, in principle, another way to constrain this information from experiment. In 2p decay, as the separation between the decay products becomes greater than the range of the nuclear interaction, the subsequent modification of the initial correlations is determined solely by the Coulomb interaction between the decay products. As the range of the Coulomb force is infinite, its long-range contribution to the correlations can be substantial, especially, in heavy 2p emitters.

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The complete three-body correlation pictures are experimentally reconstructed for the two-proton decays of the 6 Be and 45 Fe ground states. We are able to see qualitative similarities and differences between these decays. They demonstrate very good agreement with the predictions of a theoretical three-body cluster model. Validity of the theoretical methods for treatment of the three-body Coulombic decays of this class is thus established by the broad range of lifetimes and nuclear masses spanned by these cases. Implementations for decay dynamics and nuclear structure of 2p emitters are discussed.

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Following neutron knockout from a 13 O beam, 12 O fragments were created and the three decay products following two-proton decay were detected. A new ground-state mass was determined by the invariant mass method implying a decay kinetic energy of 1.638(24) MeV, and the width was found to be less than 72 keV. The latter is inconsistent with previous measurements with lower experimental resolutions, but consistent with theoretical estimates. The isobaric analog of 12 O in 12 N was produced from proton knockout reactions with the same beam and decayed by twoproton emission to the isobaric analog state in 10 B with a decay kinetic energy of 1.165(29) MeV. It represents only the second case of an analog state where two-proton decay is the only isospin and energy conserving particle decay mode. With our measurements of the mass excesses of 12 O and it analog, the quadratic form of the isobaric multiplet mass equation was found to fit the A=12 quintet and any deviations are less than the magnitude found for the A=8 quintet and A=7 and 9 quartets.

8 C is found to decay to four protons and an α particle in two 2p emission steps. The correlations between the protons in the first step ( 8 C to 6 Be) exhibit a significant enhancement in the region of the decay phase space where the two protons have small relative energy, a region sometimes called the diproton region. The decay of the isobaric analog of 8 C in 8 B is also found to decay by 2p emission. This is the first case of isospin-allowed 2p decay between isobaric analog states.