We develop a complete stationary scattering theory for Schr & ouml;dinger operators on Rd, d >= 2, with C2 long-range potentials. This extends former results in the literature, in particular require a higher degree of smoothness. In this sense, the spirit of our paper is similar to H & ouml;r(1997), Section 4.7], which also develop a scattering theory under the C2 condition, however being very different from ours. While the Agmon-H & ouml;rmander theory is based on the Fourier transform and a momentum-space representation, our theory is entirely position-space based and may be seen as more related to our previous approach to scattering theory on manifolds, Ito and Skibsted (2013), (2019), and (2021). The C2 regularity is natural in the Agmon-H & ouml;rmander theory as well as in our theory, in fact probably being "optimal" in the Euclidean setting. We prove equivalence of the stationary scattering theory and a developed position-space based timedependent scattering theory. 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 Cruz-Sampedro and Skibsted (2013). Another key ingredient is strong radiation condition bounds for the limiting resolvents originating in Herbst and Skibsted (1991). They improve formerly known ones by Isozaki (1980) and Saito<overline> (1979) and considerably simplify the stationary approach. We obtain the bounds by a new commutator scheme whose elementary form allows a small degree of smoothness.
