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We present a method for smoothing discrete breakup $S$-matrix elementscalculated by the method of continuum-discretized coupled-channels (CDCC). Thissmoothing method makes it possible to apply CDCC to four-body breakupreactions. The reliability of the smoothing method is confirmed for two cases,$^{58}$Ni($d$, $p n$) at 80 MeV and the $E1$ transition of $^6$He. We applyCDCC with the smoothing method to $^6$He breakup reaction at 22.5 MeV.Multi-step breakup processes are found to be important.

Description of Four-Body Breakup Reaction with the Method of Continuum-Discretized Coupled-Channels