  The low-energy scattering of two charged particles is analyzed using a
renormalization group approach based on dimensional regularization with
power-divergence subtraction. A nontrivial solution with a marginally unstable
direction is found, corresponding to a system with a bound state at zero
energy. For purely energy-dependent perturbations around this solution, the
power counting agrees with that from Wilsonian methods. These terms in the
effective potential are in direct correspondence with the the terms in the
Coulomb-distorted effective-range expansion. We also study perturbations that
depend on off-shell momenta as well as energy, and we show that these affect
only the off-shell form of the scattering matrix. These terms are of higher
order that the corresponding energy-dependent ones and so terms in the
potential that depend only on the off-shell momenta do not have definite orders
in power counting.
