New treatment of breakup continuum in the method of continuum discretized coupled channels

A new method of pseudostate discretization is proposed for the method of continuum discretized coupled channels to deal with three-body breakup processes. In the method, discrete $S$-matrix elements to the pseudo (discretized) continuum states are transformed into smooth ones to the exact continuum states of the projectile. As for the basis functions for describing pseudostate wave functions, we take real- and complex-range Gaussian functions, which form in good approximation a complete set in a finite configuration space being important for breakup processes. This ``approximate-completeness'' property is essential to make transformed $S$-matrix elements accurate. Moreover, the use of these Gaussian bases is expected to be very useful to describe four-body breakup processes. Accuracy of the method is tested quantitatively for two realistic examples: elastic and projectile-breakup processes in $d+^{58}\mathrm{Ni}$ scattering at $80\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and those in $^{6}\mathrm{Li}+^{40}\mathrm{Ca}$ at $156\phantom{\rule{0.3em}{0ex}}\text{MeV}$.