  We develop a complete stationary scattering theory for Schr\"odinger
operators on $\mathbb R^d$, $d\ge 2$, with $C^2$ long-range potentials. This
extends former results in the literature, in particular [Is1, Is2, II, GY],
which all require a higher degree of smoothness. In this sense the spirit of
our paper is similar to [H\"o2, Chapter XXX], which also develops a scattering
theory under the $C^2$ condition, however being very different from ours. While
the Agmon-H\"ormander theory is based on the Fourier transform, our theory is
not and may be seen as more related to our previous approach to scattering
theory on manifolds [IS1,IS2,IS3]. The $C^2$ regularity is natural in the
Agmon-H\"ormander theory as well as in our theory, in fact probably being
`optimal' in the Euclidean setting. We prove equivalence of the stationary and
time-dependent theories by giving stationary representations of associated
time-dependent wave operators. Furthermore we develop a related stationary
scattering theory at fixed energy in terms of asymptotics of generalized
eigenfunctions of minimal growth. A basic ingredient of our approach is a
solution to the eikonal equation constructed from the geometric variational
scheme of [CS]. Another key ingredient is strong radiation condition bounds for
the limiting resolvents originating in [HS]. They improve formerly known ones
[Is1, Sa] and considerably simplify the stationary approach. We obtain the
bounds by a new commutator scheme whose elementary form allows a small degree
of smoothness.
