Compactification of the Energy Surfaces for $n$ Bodies

For $n$ bodies moving in Euclidean $d$-space under the influence of a homogeneous pair interaction we compactify every center of mass energy surface, obtaining a $\big(2d(n -1)-1\big)$-dimensional manifold with corners in the sense of Melrose. After a time change, the flow on this manifold is globally defined and nontrivial on the boundary.