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Let H be the Schrodinger operator obtained by separating the kinetic energy of the center of mass from H. H acts in M :~L(R), and its explicit form depends on the coordinates of R. We adopt the Jacobi coordinates. A partition of the set {1, 2, 3} into nonempty disjoint subsets is called a cluster decomposition. We call {(1), (2), (3)} (resp. {(i, /), k} , i<j) a 3-cluster decomposition (resp. a 2-cluster decomposition). We denote by Az the set of all 2-cluster decompositions. For a^A2 with a={(i, j), k] , we define the Jacobi coordinates (*a, yJ by

High-energy behavior of total scattering cross sections for {3}-body quantum systems