  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 treat 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.
