Perturbative estimates on the transport cross section in quantum   scattering by hard obstacles
  The quantum scattering by smooth bodies is considered for small and large values of $kd$, with $k$ the wavenumber and $d$ the scale of the body. In both regimes, we prove that the forward scattering exceeds the backscattering. For high $k$, we need to assume that the body is strictly convex. 
W. De Roeck, E.L. Lakshtanov