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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 $alpha$ 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.
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The $^{6}$Be continuum states were populated in the charge-exchange reaction $^1$H($^{6}$Li,$^{6}$Be)$n$ collecting very high statistics data ($sim 5 times 10^6$ events) on the three-body $alpha$+$p$+$p$ correlations. The $^{6}$Be excitation energy region below $sim 3$ MeV is considered, where the data are dominated by contributions from the $0^+$ and $2^+$ states. It is demonstrated how the high-statistics few-body correlation data can be used to extract detailed information on the reaction mechanism. Such a derivation is based on the fact that highly spin-aligned states are typically populated in the direct reactions.
Background: Theoretical calculations have shown that the energy and angular correlations in the three-body decay of the two-neutron unbound O26 can provide information on the ground-state wave function, which has been predicted to have a dineutron configuration and 2n halo structure. Purpose: To use the experimentally measured three-body correlations to gain insight into the properties of O26, including the decay mechanism and ground-state resonance energy. Method: O26 was produced in a one-proton knockout reaction from F27 and the O24+n+n decay products were measured using the MoNA-Sweeper setup. The three-body correlations from the O26 ground-state resonance decay were extracted. The experimental results were compared to Monte Carlo simulations in which the resonance energy and decay mechanism were varied. Results: The measured three-body correlations were well reproduced by the Monte Carlo simulations but were not sensitive to the decay mechanism due to the experimental resolutions. However, the three-body correlations were found to be sensitive to the resonance energy of O26. A 1{sigma} upper limit of 53 keV was extracted for the ground-state resonance energy of O26. Conclusions: Future attempts to measure the three-body correlations from the ground-state decay of O26 will be very challenging due to the need for a precise measurement of the O24 momentum at the reaction point in the target.
The $beta$-decay process of the $^6$He halo nucleus into the $alpha+d$ continuum is studied in an updated three-body model. The $^6$He nucleus is described as an $alpha+n+n$ system in hyperspherical coordinates on a Lagrange-mesh. The shape and absolute values of the transition probability per time and energy units of new experiments are reproduced with a modified $alpha+d$ potential. The obtained total transition probabilities are $2.48 times 10^{-6}$ s$^{-1}$ for the full energy region and $2.40 times 10^{-6}$ s$^{-1}$ for the cut-off $E>150$ keV. The strong cancellation between the internal and halo parts of the $beta$ decay matrix element is a challenge for future {it ab initio} calculations.
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 experiments, the intrinsic decay width of the $^{16}$Ne ground state was found to be narrow ($Gamma<60$~keV), consistent with theoretical estimates.
The reaction mechanisms of the two-neutron transfer reaction $^{12}$C($^6$He,$^4$He) have been studied at 30 MeV at the TRIUMF ISAC-II facility using the SHARC charged-particle detector array. Optical potential parameters have been extracted from the analysis of the elastic scattering angular distribution. The new potential has been applied to the study of the transfer angular distribution to the 2$^+_2$ 8.32 MeV state in $^{14}$C, using a realistic 3-body $^6$He model and advanced shell model calculations for the carbon structure, allowing to calculate the relative contributions of the simultaneous and sequential two-neutron transfer. The reaction model provides a good description of the 30 MeV data set and shows that the simultaneous process is the dominant transfer mechanism. Sensitivity tests of optical potential parameters show that the final results can be considerably affected by the choice of optical potentials. A reanalysis of data measured previously at 18 MeV however, is not as well described by the same reaction model, suggesting that one needs to include higher order effects in the reaction mechanism.
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