  We consider the relativistic scattering of unequal-mass scalar particles
through graviton exchange in the small-angle high-energy regime. We show the
self-consistency of expansion around the eikonal limit and compute the
scattering amplitude up to the next-to-leading power correction of the light
particle energy, including gravitational effects of the same order. The first
power correction is suppressed by a single power of the ratio of momentum
transfer to the energy of the light particle in the rest frame of the heavy
particle, independent of the heavy particle mass. We find that only
gravitational corrections contribute to the exponentiated phase in impact
parameter space in four dimensions. For large enough heavy-particle mass, the
saddle point for the impact parameter is modified compared to the leading order
by a multiple of the Schwarzschild radius determined by the mass of the heavy
particle, independent of the energy of the light particle.
