  For a class of negative slowly decaying potentials including the attractive
Coulombic one we study the classical scattering theory in the low-energy
regime. We construct a (continuous) family of classical orbits parametrized by
initial position $x\in \R^d$, final direction $\omega\in S^{d-1}$ of escape (to
infinity) and the energy $\lambda\geq 0$, yielding a complete classification of
the set of outgoing scattering orbits. The construction is given in the
outgoing part of phase-space (a similar construction may be done in the
incoming part of phase-space). For fixed $\omega\in S^{d-1}$ and $\lambda\geq
0$ the collection of constructed orbits constitutes a smooth manifold that we
show is Lagrangian. The family of those Lagrangians can be used to study the
quantum mechanical scattering theory in the low-energy regime for the class of
potentials considered here. We devote this study to a subsequent paper.
