An inverse problem related to channel scattering operators

In this paper, we study the inverse scattering related to a channel scattering operator $S_{\alpha\beta}$ in $N$ ‐body problems. Given the incoming and outgoing channels $\alpha$ , $\beta$ associated with a same, but arbitary cluster decomposition, $a$ , of the $N$ ‐body system, we prove that all effective interactions between the mass‐centers of the clusters in $a$ can be reconstructed from the high energy asymptotics of scattering matrices $S_{\alpha\beta}(\lambda)$ .