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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 thecombined 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 shownto play an important role in explanation of shape and strength of the breakupcross section. In addition, we predict the invariant mass spectra for binarysubsystems 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 $^{11}$Lilargely contribute to make low-lying peaks in the invariant mass spectra. Onthe other hand, in the present analysis, it is suggested that the contributionsof the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.

Coulomb breakup reactions of $^{11}$Li in the coupled-channel $^9$Li~+~$n$~+~$n$ three-body model