Decay mode of the $2_1^+$ resonant state of $^6$He populated by the $^6$He breakup reaction by $^{12}$C at 240 MeV/nucleon is investigated. The continuum-discretized coupled-channels method is adopted to describe the formation of the $2_1^+$ state, w
hereas its decay is described by the complex-scaled solutions of the Lippmann-Schwinger equation. From analysis of invariant mass spectra with respect to the $alpha$-$n$ and $n$-$n$ subsystems, coexistence of two decay modes is found. One is the simultaneous decay of two neutrons correlating with each other and the other is the emission of two neutrons to the opposite directions. The latter is found to be free from the final state interaction and suggests existence of a di-neutron in the $2_1^+$ state of $^6$He.
We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in
$^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.
We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to trea
t boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.
