  At leading order, there are three inelastic scattering processes beginning
with a quantum kink and a fundamental meson. Meson multiplication, in which the
final state is a kink and two mesons, was treated recently. In this note we
treat the other two, (anti)-Stokes scattering, in which the kink's shape mode
is (de-)excited and the final state contains one meson. In the case of a
general scalar kink, we find analytic formulas for the forward and backward
scattering amplitudes and probabilities as functions of the momentum of the
incident meson. The general results are then specialized to the kink of the
$\phi^4$ double-well model.
