Decomposition of scattering phase shifts of coupled-channels systems in the complex scaling method

The decomposition of scattering phase shifts in single-channel systems is extended to coupled-channels systems in the complex scaling method. The present method describes the contribution of the resonant states to the phase shift separately from the background in each channel phase shift of the coupled-channels system. We apply this method to the ($^{3}\mathrm{H}+p)+(^{3}\mathrm{He}+n)$ model for $^{4}\mathrm{He}$, and show that the decomposition of phase shifts in coupled-channels systems provides useful information about the structure of scattering states.