Transition energy correlations in the three-body continuum of Borromean Halo Nuclei

Energy correlations in transitions from the bound state to the three-body continuum of Borromean halo nuclei are considered. A core+n+n three-body cluster model which reproduces experimentally known properties of $^6$He and $^{11}$Li has been used to study low-lying resonances and soft modes. The analysis of the correlated responses in $^6$He shows that in the case of the narrow three-body $2^+_1$ resonance the transition energy correlations are the same as in the intrinsic correlated structure in $3\rightarrow 3$ scattering. They differ significantly for wide $2^+_2$, $1^+_1$ resonances, and also for the soft dipole and monopole modes, where, due to the transition operators, the intertwining of the ground state and the three-body continuum plays a significant role.