  We develop a frequency-domain method for calculating the self-force acting on
a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime.
Existing frequency-domain methods, which are tailored for bound orbits, are
inadequate here for several reasons. One must account for the continuous
spectrum in the scattering problem, deal with slowly-convergent radial
integrals that are hard to evaluate numerically, and confront the
inapplicability of the standard self-force method of "extended homogeneous
solutions", which only works for compactly supported sources. We tackle each of
these issues in turn, and then present a full numerical implementation, in
which we calculate the self-force correction to the scatter angle due to
scalar-field back-reaction. We perform a range of internal validation tests, as
well as ones based on comparison with existing time-domain results. We discuss
the merits and remaining limitations of our method, and outline directions for
future work.
