  The problem of recovering the asymptotics of a short range perturbation of
the Euclidean metric on R^n from fixed energy scattering data is studied. It is
shown that if two such metrics, g1, g2, have scattering data at some fixed
energy which are equal up to smoothing, then there exists a diffeomorphism \psi
`fixing infinity' such that \psi^*(g1) - g2 is rapidly decreasing. Given the
scattering matrix at two energies, it is shown that the asymptotics of a metric
and a short range potential can be determined simultaneously. These results
also hold for a wide class of scattering manifolds.
