Studies of continuum states in${16}$ Ne using three-body correlation techniques

Two-proton decay of the unbound $ T_{z} =-2$ nucleus$^{16}$Ne , produced in one-neutron knockout from a 500 MeV/u$^{17}$Ne beam, has been studied at GSI. The ground state, at a resonance energy 1.388(15) MeV, ( $ \Gamma =0.082(15)$ MeV) above the$^{14}$O +p+p threshold, and two narrow resonances at $ E_{r} =3.220(46)$ MeV and 7.57(6) MeV have been investigated. A comparison of the energy difference between the first excited 2$^{+}$ state and the 0$^{+}$ ground state in$^{16}$Ne with its mirror nucleus$^{16}$C reveals a small Thomas-Ehrman shift (TES) of $ +70(46)$ keV. A trend of the TES for the T = 2 quintet is obtained by completing the known data with a prediction for$^{16}$F obtained from an IMME analysis. The decay mechanisms of the observed three resonances were revealed from an analysis of the energy and angular correlations of the$^{14}$O +p+p decay products. The ground state decay can be considered as a genuine three-body (democratic) mode and the excited states decay sequentially via states in the intermediate nucleus$^{15}$F , the 3.22 MeV state predominantly via the$^{15}$F ground-state resonance, while the 7.57 MeV state decays via the 5/2$^{+}$ resonance in$^{15}$F at 2.8 MeV above the$^{14}$O +p+p threshold. Further, from an analysis of angular correlations, the spin-parity of the 7.57 MeV state has been determined as $ I^{\pi} =2^{+}$ and assigned as the third 2$^{+}$ state in$^{16}$Ne based on a comparison with$^{16}$C.